Matrix_Population_Molabel00Descriptive title for labelling generated outputs.2012-11-01 12:14:05.640 UTCGentiana pneumonanthe, Terschelling2012-10-23 15:39:06.31 UTCshortTermYears00102012-10-29 13:44:13.835 UTCThis value will be use to plot a graph that shows a simulation of the number of individuals per stage a few years after the study. This value represents the years of axis X of the output graph: StageVectorPlotShortTerm.
2012-11-01 11:51:21.500 UTClongTermYears00This value contains the maximum number of iterations in the transient dynamic analysis, and hence the total number of years for the long term graphs.
The number of years will be used in two output graphs:
1) StageVectorPlotLongTermProportional: the proportion of individuals per stage in the long term.
2) StageVectorPlotLongTermLogarithmic: the number of individuals per stage in the long term.
2012-11-01 11:51:48.46 UTC502012-10-29 13:44:37.435 UTCstageMatrixFile000.0000 0.0000 0.0000 7.6660 0.0000
0.0579 0.0100 0.0000 8.5238 0.0000
0.4637 0.8300 0.9009 0.2857 0.8604
0.0000 0.0400 0.0090 0.6190 0.1162
0.0000 0.0300 0.0180 0.0000 0.02322012-11-21 15:47:44.807 UTCThe stage matrix input file2013-06-13 10:53:46.598 UTCstages11Stage input port:
The names of the stages or categories of the input matrix. It is very important that the stages names are not longer than 8 characters. The name of the stages must be added one by one.
The respective name stages must be filled one by one. First press add value, fill a stage name (not longer than 8 characters) and press enter, then press add value and fill once again the next stage name, repeat the action until you have fill all the stages names.
In the following example, the matrix has 5 stages or categories:
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
The stages of this matrix are called:
1) Seedlings S
2) Juveniles J
3) Vegetative V
4) Reproductive individuals G
5) Dormant plants D
2013-06-13 10:54:06.95 UTC[S, J, V, G, D]2013-08-07 11:13:18.774 UTCiterations00100002012-12-10 16:16:31.915 UTCNumber of iterations for calculation of confidence interval2012-12-10 16:16:40.761 UTCstable_stage_distribution0A bar plot which shows the stable stage distribution (w) of the analysed matrix. In other words, the proportion of individuals per stage.2012-11-01 12:16:09.906 UTCprojection_matrix0The stage matrix, displayed with coloured squares to highlight the magnitude of the values.2012-11-01 10:39:02.187 UTCeigenanalysis_elasticity_matrix0The elasticity matrix, displayed with coloured squares to highlight the magnitude of the values.2012-11-01 12:16:26.656 UTCeigenanalysis_sensitivity_matrix_10A sensitivity matrix showing the sensitivities of the actual transitions (i.e. the sensitivity values of non-zero elements), displayed with coloured squares to highlight the magnitude of the values.2012-11-01 10:40:25.78 UTCeigenanalysis_sensitivity_matrix_20A sensitivity matrix showing the sensitivities of all possible transitions (i.e. the sensitivity values of zero and non-zero elements), displayed with coloured squares to highlight the magnitude of the values.2012-11-01 10:41:08.312 UTCstage_matrix0A stage matrix contains transitions probabilities from each stage to the next. In the example, the selected species, Gentiana pneumonanthe, has a matrix of 5 x 5 stages (Oostermeijer et al., 1996).2012-11-01 10:14:42.968 UTC S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.02322012-11-01 10:16:15.78 UTCeigenanalysis0$lambda1
[1] 1,232338
$stable.stage
S J V G D
0,14218794 0,16166957 0,65944861 0,02285525 0,01383863
$sensitivities
S J V G D
S 0 0 0 0,006042076 0
J 0,14255579 0,1620878 0 0,02291438 0
V 0,08206359 0,0933074 0,3806 0,01319088 0,00798695
G 0 2,7675986 11,28901 0,391255815 0,2369016
D 0 0,3325676 1,35654 0 0,02846721
$elasticities
S J V G D
S 0 0 0 0,037589187 0
J 0,006706037 0,001315287 0 0,15406651 0
V 0,03088315 0,062844075 0,27823767 0,003058271 0,005576792
G 0 0,089832455 0,08252831 0,196541848 0,022353201
D 0 0,008096016 0,01983398 0 0,000537213
$repro.value
S J V G D
1 3,792468 2,18317 64,755197 7,781288
$damping.ratio
[1] 2,0902
2012-10-31 12:11:52.131 UTCEigen analysis
The Eigen analysis results are a set of demographic statistics:
Lambda or dominant eigenvalue: This value describes the population growth rate of a stage matrix. The population will be stable, grow or decrease at a rate given by lambda: e.g.: λ = 1 (population is stable), λ > 1 (population is growing) and finally λ < 1 (population is decreasing).
The stable stage distribution (w): It is the proportion of the number of individuals per stage. It is given analytically by the right eigenvector (another property of the transition matrix) that corresponds to the dominant eigenvalue
Elasticity and Sensitivity: Sensitivity and elasticity analyses are prospective analyses.
The sensitivity matrix: The sensitivity gives the effect on λ of changes in any entry of the matrix, including those that may, at a given context, be regarded as fixed at zero or some other value. The derivative tells what would happened to λ if aij was to change, not whether, or in what direction, or how much, aij actually change. The hypothetical results of such impossible perturbations may or may not be of interest, but they are not zero. It is up to you to decide whether they are useful (Caswell 2001).
When comparing the λ-sensitivity values for all matrix elements one can find out in what element a certain increase has the biggest impact on λ. However, a 0.01 increase in a survival matrix element is hard to compare to a 0.01 increase in a reproduction matrix element, because the latter is not bound between 0 and 1 and can sometimes take high values. Increasing matrix element a14 (number of S (seedlings) the next year produced by a G (Reproductive individuals)) with 0.01 from 7.666 to 7.676 does not have a noticeable effect on λ. For comparison between matrix elements it can therefore be more insightful to look at the impact of proportional changes in elements: by what percentage does λ change if a matrix element is changed by a certain percentage? This proportional sensitivity is termed elasticity (Description based on Oostermeijer data, based on Jongejans & de Kroon 2012).
The Elasticity matrix: The elasticities of λ with respect to the stage are often interpreted as the “contributions” of each of the stages to λ. This interpretation relies on the demonstration, by de Kroon et al (1986) that the elasticitis of the λ with respect to the stage, always sum to 1. For further information see: de Kroon, et al., 1986. and Caswell 2001.
Reproductive value (v): scaled so v[1]=1. To what extent will a plant or animal of a determinate category or stage , contribute to the ancestry of future generation.
The damping ratio: it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, the larger the p, the quicker the population converges.2012-11-01 12:16:19.0 UTCshort_term_stage_vector_plot0A plot that charts the number of individuals per stage vs. years in the short-term (e.g. 5 or 10 years). The number of years is related to the short-term years input value.2012-11-01 11:47:06.281 UTClong_term_logarithmic_stage_vector_plot0The number of individuals per stage in the long term2012-11-01 11:46:16.968 UTCpopulation_projection0Population projection:
Lambda or dominant eigenvalue: The population will be stable, grow or decrease at a rate given by lambda: e.g.: λ = 1 (population is stable), λ > 1 (population is growing) and finally λ < 1 (population is decreasing). e.g. The projected population growth rate (λ) is 1.237, meaning that the population is projected to increase with 23% per year if these model parameters remain unchanged.
The stable stage distribution (stable.stage): It is the proportion of the number of individuals per stage and it is given by (w).
Stage vector (stage.vectors): it is the projection of the number of individuals per category per year in the long term, the long term was stipulated in the input port (long term years) (e.g. 50 years).
Population sizes (pop.sizes): it is the total population size per year in the long-term (e.g. 50 years).
Population change (pop.changes): are the lambda values per year in the long-term (e.g. 50 years).
2012-11-01 12:14:44.46 UTC$lambda
[1] 1.232338
$stable.stage
S J V G D
0.14218794 0.16166957 0.65944861 0.02285525 0.01383863
$stage.vectors
0 1 2 3 4 5 6 7
S 69 161 176.33333 187.22072 219.09046 261.92397 318.22637 389.44517
J 100 179 201.69476 214.57709 249.78014 298.27181 362.08839 442.95984
V 111 258 467.40332 685.98643 903.75302 1149.34660 1437.18683 1783.39662
G 21 23 24.42009 28.57702 34.16400 41.50779 50.79720 62.39105
D 43 6 10.15818 14.70876 19.13949 24.22235 30.22041 37.46071
8 9 10 11 12 13 14
S 478.33138 588.52367 724.70467 892.75361 1099.9811 1355.4346 1670.2865
J 543.96054 669.21317 824.03064 1015.09148 1250.7042 1541.1537 1899.1418
V 2204.99218 2721.56781 3356.41003 4137.71650 5099.9406 6285.3667 7746.0003
G 76.76396 94.52670 116.44612 143.47580 176.7958 217.8635 268.4762
D 46.29325 57.12499 70.44214 86.83496 107.0256 131.9009 162.5519
15 16 17 18 19 20 21
S 2058.3178 2536.5199 3125.836 3852.0783 4747.0575 5849.9764 7209.1464
J 2340.3370 2884.0582 3554.118 4379.8647 5397.4679 6651.5012 8196.8954
V 9545.8697 11763.8434 14497.093 17865.3551 22016.1771 27131.3836 33435.0416
G 330.8504 407.7177 502.445 619.1814 763.0404 940.3234 1158.7961
D 200.3221 246.8664 304.224 374.9074 462.0130 569.3564 701.6396
22 23 24 25 26 27 28
S 8884.1038 10948.218 13491.904 16626.585 20489.572 25250.078 31116.629
J 10101.3442 12448.269 15340.474 18904.649 23296.916 28709.674 35380.022
V 41203.2756 50776.363 62573.642 77111.875 95027.892 117106.479 144314.761
G 1428.0284 1759.814 2168.685 2672.553 3293.488 4058.691 5001.679
D 864.6572 1065.550 1313.118 1618.205 1994.175 2457.498 3028.468
29 30 31 32 33 34 35
S 38346.204 47255.483 58234.725 71764.863 88438.565 108986.20 134307.83
J 43600.144 53730.113 66213.658 81597.604 100555.825 123918.76 152709.79
V 177844.559 219164.602 270084.859 332835.826 410166.224 505463.41 622901.75
G 6163.759 7595.834 9360.634 11535.465 14215.591 17518.41 21588.61
D 3732.096 4599.204 5667.773 6984.612 8607.403 10607.23 13071.69
36 37 38 39 40 41 42
S 165512.64 203967.51 251356.91 309756.66 381724.90 470414.08 579709.13
J 188190.08 231913.78 285796.15 352197.45 434026.28 534867.07 659136.99
V 767625.48 945974.02 1165759.69 1436609.93 1770388.96 2181717.52 2688613.33
G 26604.46 32785.68 40403.04 49790.20 61358.36 75614.23 93182.29
D 16108.74 19851.41 24463.65 30147.49 37151.89 45783.69 56420.97
43 44 45 46 47 48 49
S 714397.57 880379.2 1084924.8 1336994.0 1647628.4 2030435.1 2502182.2
J 812279.54 1001002.9 1233573.9 1520179.9 1873375.5 2308631.7 2845014.5
V 3313280.28 4083081.1 5031735.8 6200799.1 7641480.1 9416886.1 11604786.2
G 114832.08 141511.9 174390.5 214908.1 264839.4 326371.6 402200.1
D 69529.71 85684.1 105591.8 130124.7 160357.7 197614.8 243528.3
$pop.sizes
[1] 3.440000e+02 6.270000e+02 8.800097e+02 1.131070e+03 1.425927e+03
[6] 1.775273e+03 2.198519e+03 2.715653e+03 3.350341e+03 4.130956e+03
[11] 5.092034e+03 6.275872e+03 7.734447e+03 9.531719e+03 1.174646e+04
[16] 1.447570e+04 1.783901e+04 2.198372e+04 2.709139e+04 3.338576e+04
[21] 4.114254e+04 5.070152e+04 6.248141e+04 7.699821e+04 9.488782e+04
[26] 1.169339e+05 1.441020e+05 1.775824e+05 2.188416e+05 2.696868e+05
[31] 3.323452e+05 4.095616e+05 5.047184e+05 6.219836e+05 7.664940e+05
[36] 9.445797e+05 1.164041e+06 1.434492e+06 1.767779e+06 2.178502e+06
[41] 2.684650e+06 3.308397e+06 4.077063e+06 5.024319e+06 6.191659e+06
[46] 7.630217e+06 9.403006e+06 1.158768e+07 1.427994e+07 1.759771e+07
$pop.changes
[1] 1.822674 1.403524 1.285293 1.260689 1.244995 1.238412 1.235219 1.233715
[9] 1.232996 1.232652 1.232488 1.232410 1.232372 1.232354 1.232346 1.232342
[17] 1.232340 1.232339 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[25] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[33] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[41] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[49] 1.232338
2012-11-01 11:42:50.109 UTClong_term_proportional_stage_vector_plot0Stage vector plot long term proportional:
Is the proportion of individuals per stage in the long term (e.g.: 50 years) 2012-11-01 11:45:40.640 UTCdamping_ratio02.0901.2012-11-01 11:44:15.62 UTCDamping ratio:
The ratio between the dominant eigenvalue and the second highest eigenvalue of a transition matrix is called the damping ratio, and it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, (the larger the damping ratio, the quicker the population converges). High damping ratios tell you that the dominant stable stage distribution is reached fairly soon.2012-11-01 12:14:56.312 UTCfundamental_matrix0Age specific survival
The fundamental matrix workflow gives the basic information on age-specific survival, this includes the mean, variance and coefficient of variation (cv) of the time spent in each stage class and the mean and variance of the time to death.
Fundamental matrix (N): is the mean of the time spent in each stage class. e.g.: For our Gentiana example means a J plants will spends, on average, about 1 year as a Juvenile, 11 as vegetative plant, less than a year a reproductive and dormant plant.
Variance (var): is the variance in the amount of time spent in each stage class.
Coefficient of variation (cv): is the coefficient of variation of the time spent in each class (sd/mean- the ratio of the standard deviation to the mean).
Meaneta: is the mean of time to death, of life expectancy of each stage. e.g. The mean age at death is the life expectancy; the life expectancy of a new individual seedling is 8 years.
Vareta: is the variance of time to death.
2012-11-01 10:47:32.328 UTC$N
S J V G D
S 1.00000000 0.0000000 0.0000000 0.0000000 0.0000000
J 0.05855658 1.0101010 0.0000000 0.0000000 0.0000000
V 6.89055876 11.9968091 13.3581662 10.0186246 12.9606017
G 0.20844800 0.4667882 0.3911175 2.9183381 0.6919771
D 0.12890879 0.2523299 0.2464183 0.1848138 1.2628940
$var
S J V G D
S 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000
J 0.05631067 0.01020304 0.0000000 0.0000000 0.0000000
V 129.72009930 164.59050165 165.0824377 157.2694415 165.3219447
G 0.96474493 2.03981226 1.7387357 5.5983592 2.8680368
D 0.18007000 0.32133154 0.3152601 0.2478305 0.3320072
$cv
S J V G D
S 0.000000 NaN NaN NaN NaN
J 4.052468 0.100000 NaN NaN NaN
V 1.652910 1.069391 0.9618417 1.2517398 0.9920649
G 4.712035 3.059674 3.3713944 0.8107646 2.4473757
D 3.291836 2.246508 2.2785654 2.6936618 0.4562542
$meaneta
S J V G D
8.286472 13.726028 13.995702 13.121777 14.915473
$vareta
S J V G D
143.4207 181.1844 181.6537 177.2333 181.2319
2012-11-01 11:37:55.718 UTCgeneration_time08.13022012-10-31 12:12:54.819 UTCGeneration time:
The time T required for the population to increase by a factor of Ro (net reproductive rate).
e.g. for Generation time T and Net reproductive rate Ro:
If T = 8.13 and Ro = 5.46 then the average individual in the study year replaced itself with about five new plants and took approximately 8 years to do so.
2012-11-01 12:15:30.218 UTCnet_reproductive_rate05.46572012-10-31 12:13:22.678 UTCThe net reproductive rate is the mean number of offspring by which a new-born individual will be replaced by the end of its life, and thus the rate by which the population increases from one generation to the next.
2012-11-01 11:40:25.562 UTClambda0histogram_ci_95pc_of_lambda0Histogram generated from the analysis of the confidence interval of lambda.2013-08-07 11:16:00.614 UTCconfidence_interval_95pc_of_lambda0Calculate bootstrap distributions of population growth rates (lambda) by randomly sampling with replacement from a stage-fate data frame of observed transitions. Resampling transitions with equal probability.2013-08-07 11:14:21.803 UTCsurvival_curve_plot0A plot of survival curves is produced, one point for each stage.2013-08-07 11:18:14.490 UTCsensitivity_matrix0See Eigen analysis2013-08-07 11:17:25.838 UTCsensitivity_plot0A sensitivity matrix plot showing the sensitivities values of the actual transitions (i.e. the sensitivity values of non-zero elements) per stage.2013-08-07 11:17:44.69 UTCelasticity_matrix0See Eigen analysis2013-08-07 11:15:05.271 UTCelasticity_plot0An Elasticity matrix plot showing the elasticities values per stage.2013-08-07 11:15:28.261 UTCcohen_cumulative_distance0Cohen’s cumulative distance measures the difference between observed and expected vectors along the matrix path that the population would take to reach the expected population vector. It is a function of both the observed stage distribution (n0) and the structure of the matrix (A) (Williams et al 2011). Cohen’s cumulative distance will not work for reducible matrices and returns a warning for imprimitive matrices (although will not function for imprimitive matrices with nonzero imaginary components in the dominant eigenpair) (Caswell 2001).2013-08-07 11:14:00.633 UTCkeyfitz_delta0A distance measure between probability vectors of n (Observed Stage Distribution, abundances per stage) and w (Stable Stage Distribution). Its maximum value is 1 and its minimum is 0 when the vectors are identical.2013-08-07 11:16:19.882 UTCAbundance_Interactionstages1abundances11Abundance iteraction:
Initial abundance: In this dialogue authomatically appears the fields to fill out the initial abundance per stage observed in the field (see data below). After fill out the abundances, the user confirms the numbers.
As a example Gentiana pneumonanthe has 5 stages with its respective abundance:
stage abundance
1) S (seedlings) 69
2) J (Juveniles) 100
3) V (vegetative) 111
4) G (reproductive individuals) 21
5) D (dormant plants) 43
2012-11-01 11:56:16.812 UTCnet.sf.taverna.t2.activitiesinteraction-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.interaction.InteractionActivitystages1text/plainjava.lang.Stringfalseabundances11http://biovel.googlecode.com/svn/tags/mpm-20130805/set_abundance.htmlLocallyPresentedHtmlfalsenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeStageMatrix_ReadFromFilestage_matrix_file0stages1stage_matrix11net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix_file0falsestages1falsestage_matrix11falselocalhost6311falsefalsestage_matrix_fileTEXT_FILEstagesSTRING_LISTstage_matrixR_EXPnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeCategoriseStages_InteractionunsortedStages1sortedStages11recruitedStages11reproductiveStages11With this dialogue automatically appears the names of the stages or categories of the census data file. When the dialogue appears, the stages are in disorder, so the user drags and organizes the stages according to the order in the life cycle. Then, the author chooses if the stage belongs to the recruited, reproductive category or it should be excluded. Recruited means that new individuals can be recruited to this (these) stage(s). Reproductive stages are those that reproduce (produce offspring) (in this example the stage G). In the census data file Dt1.txt, x is use to denote when a plant has died in the second year, so the user must selected in the excluded column. Then the user clicks in confirm and you will read stages submitted.
In the following example, the life cycle of Gentiana pneumonanthe has 5 stages or categories:
1) Seedlings S
2) Juveniles J
3) Vegetative V
4) Reproductive individuals G
5) Dormant plants D2012-11-01 14:53:35.21 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.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeAbundance_InteractionstagesStageMatrix_ReadFromFilestage_matrix_fileStageMatrix_ReadFromFilestagesCategoriseStages_InteractionunsortedStagesStageMatrixAnalysisabundancesStageMatrixAnalysislabelStageMatrixAnalysislongTermYearsStageMatrixAnalysisshortTermYearsStageMatrixAnalysisstage_matrixStageMatrixAnalysisstagesStageMatrixAnalysisfrowsStageMatrixAnalysisfcolsConfidence_intervalstage_matrixConfidence_intervalabundancesConfidence_intervaliterationsConfidence_intervalfcolsConfidence_intervalfrowsplot_histogramciplot_histogramyplot_histogramplottitleOutputEigenanalysisinputOutputElasticityMatrixinputOutputSensitivityMatrixinputOutputFundamentalMatrixinputOutputConfidenceIntervalinputOutputStageMatrixinputFecundityCols_FromReproductiveStagesall_valuesFecundityCols_FromReproductiveStagessome_valuesFecundityRows_FromRecruitedStagesall_valuesFecundityRows_FromRecruitedStagessome_valuesstable_stage_distributionprojection_matrixeigenanalysis_elasticity_matrixeigenanalysis_sensitivity_matrix_1eigenanalysis_sensitivity_matrix_2stage_matrixeigenanalysisshort_term_stage_vector_plotlong_term_logarithmic_stage_vector_plotpopulation_projectionlong_term_proportional_stage_vector_plotdamping_ratiofundamental_matrixgeneration_timenet_reproductive_ratelambdahistogram_ci_95pc_of_lambdaconfidence_interval_95pc_of_lambdasurvival_curve_plotsensitivity_matrixsensitivity_plotelasticity_matrixelasticity_plotcohen_cumulative_distancekeyfitz_delta3e559db0-7ac1-47cf-b89a-aa9cbf3dd1352012-10-30 09:34:50.603 UTC6addddd1-bdf4-4f01-a226-aed869898b462012-10-23 15:39:43.253 UTCf8683e08-b7e0-4a1b-a119-e977d6ba23e52012-12-09 23:15:12.16 UTC61e17b4e-2110-470a-8aa8-db97ea3341e02012-07-11 15:46:57.885 UTC5bdb4704-9322-4cbc-8d08-4b87aa1f23182012-07-11 22:49:36.115 UTC31de0f25-8b52-4b7c-a868-4eb26381b7682012-07-11 16:08:08.989 UTCThe Matrix Population Models Workflow provides an environment to perform several analyses on a stage-matrix with no density dependence:
- Eigen analysis;
- Age specific survival;
- Generation time (T);
- Net reproductive rate (Ro);
- Transient Dynamics;
- Bootstrap of observed census transitions (Confidence intervals of lambda);
- Survival curve;
- Keyfitz delta;
- Cohen's cumulative distance.
This workflow requires an instance of Rserve on localhost
This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.
This workflow uses R packages ‘popbio’ (Stubben & Milligan 2007; Stubben, Milligan & Nantel 2011) and 'popdemo' (Stott, Hodgson and Townley 2013).
References:
Caswell, H. 1986. Life cycle models for plants. Lectures on Mathematics in the Life Sciences 18: 171-233.
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
de Kroon, H. J., A. Plaiser, J. van Groenendael, and H. Caswell. 1986. Elasticity: The relative contribution of demographic parameters to population growth rate. Ecology 67: 1427-1431.
Horvitz, C., D.W. Schemske, and Hal Caswell. 1997. The relative "importance" of life-history stages to population growth: Prospective and retrospective analyses. In S. Tuljapurkar and H. Caswell. Structured population models in terrestrial and freshwater systems. Chapman and Hall, New York.
Jongejans E. & H. de Kroon. 2012. Matrix models. Chapter in Encyclopaedia of Theoretical Ecology (eds. Hastings A & Gross L) University of California, p415-423
Mesterton-Gibbons, M. 1993. Why demographic elasticities sum to one: A postscript to de Kroon et al. Ecology 74: 2467-2468.
Oostermeijer J.G.B., M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.
Stott, I., S. Townley and D.J. Hodgson 2011. A framework for studying transient dynamics of population projection matrix models. Ecology Letters 14: 959–970
Stubben, C & B. Milligan. 2007. Estimating and Analysing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22 (11): 1-23
Stubben, C., B. Milligan, P. Nantel. 2011. Package ‘popbio’. Construction and analysis of matrix population models. Version 2.3.1
van Groenendael, J., H. de Kroon, S. Kalisz, and S. Tuljapurkar. 1994. Loop analysis: Evaluating life history pathways in population projection matrices. 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12:02:36.167 UTC3618d570-4189-464f-8921-ae27391d65122012-10-18 11:17:27.472 UTCe8da845b-093d-4f3c-9e1c-8dbcfdb703fb2012-10-17 15:44:05.374 UTCdad66a92-b095-4e96-9df2-ab862f7175022014-07-07 12:14:51.201 UTC42e22b26-02a1-413f-99ef-dfa978e86c1f2012-10-23 14:48:02.159 UTCe491d0ce-ea60-47c4-94f0-cb8f923433da2012-10-23 15:41:09.199 UTC2d852a79-7b62-40cc-a176-aadadbfc2c032012-10-17 14:40:53.717 UTC44a252e2-ecff-46af-9f58-6565b239d7402013-06-21 16:32:51.692 UTC199c86f0-df6a-425c-b4dd-6aa852bcbff52012-07-13 09:03:22.271 UTC9e143465-5ee4-45f6-9c66-8d740fe4cd4c2012-10-30 09:57:13.720 UTC27fa10ea-ca41-4311-b50c-eb7e2fe664892012-07-11 15:49:21.753 UTC9cc9920c-7d50-4c5b-9800-20cc1cfd72cf2012-09-20 14:54:19.489 UTC9159d5c8-8084-403e-9941-37a0babea12d2012-07-13 08:10:15.746 UTCaab9fd22-7f16-41d7-a280-1f426ec850972012-10-23 15:42:20.102 UTCa6efda97-4c1a-4ce4-9b65-6a87f8d11e782012-07-13 09:14:16.348 UTC67a81702-50a5-4851-b279-8f7d093f1a772013-08-07 11:18:16.183 UTCa6f209c5-1062-4064-b41a-91caff11da782013-06-10 15:21:06.432 UTCMaria Paula Balcázar-Vargas, Jonathan Giddy and Gerard Oostermeijer2012-10-30 15:58:04.755 UTC809f0035-d1b9-448d-bae6-6481cc68b7c72012-10-29 13:11:22.192 UTC12eeeead-ffb3-4fcd-944c-efcb7de6a5fd2012-10-18 10:18:38.541 UTCa9aad80c-7c18-49db-9df4-43cd4491e5d62013-08-06 20:01:44.615 UTC53b6584e-7b75-48ac-976b-11154cef701f2012-07-13 09:04:05.440 UTC6a6df203-47b2-4b26-855f-ff8c48eed2bc2012-09-19 15:38:42.701 UTC9f3c6f78-3407-4093-9c43-7b3f2bbdf1ff2013-06-21 11:04:07.52 UTC476bc827-2680-4ba5-b6b6-878b59202d8f2012-10-30 09:50:32.390 UTC6317b32f-0f55-4e22-9c4b-72bbe80796ca2012-10-17 11:48:27.846 UTC0b9f50d2-2082-445a-9321-26618c1783b12013-06-21 10:54:15.434 UTC9fa97e87-bd43-4312-a36f-8ac512988b802012-07-13 06:25:39.0 UTC44f38a9d-ca0e-4648-becd-807d0b736f042012-10-17 15:28:51.127 UTCa8004bfd-bcb7-4f8f-986c-a4c03dc24ca72013-02-12 09:16:55.687 UTC6cd6cb7d-5cb3-49b8-927d-76374ba1a0f62013-06-21 16:26:03.812 UTCac715f0e-f99c-46df-bfe6-0c70a550bb612012-11-01 11:48:54.375 UTCba0a12e6-e2cc-428f-b901-978b4d2e83202012-10-18 11:26:48.0 UTCe8d180a6-7a5c-4421-b788-db26f3589ae82012-09-20 13:43:51.734 UTC6e4e9dd0-334b-403a-9632-8423f9636fe72012-07-11 13:00:55.837 UTCd64b5ae1-a5ad-4260-89b2-9822403cfc282012-10-17 14:53:12.993 UTC290bff82-b044-4475-9f8a-65e5a8ee3c3b2012-11-01 11:51:22.265 UTC2de604ef-97f6-4f76-9392-556104352c062012-11-26 15:47:00.314 UTCff5bc61b-0d13-4622-adc8-2aedd7b7038c2012-07-13 09:20:52.134 UTCe9f0545f-d40e-4670-a3cb-7535676647582013-08-07 11:15:31.980 UTC1378f96b-c536-4968-a27f-2c7956207e6f2012-10-12 09:24:28.167 UTCe9b5e5d2-9871-4eba-b7a1-0635c8fc1bf52012-07-13 09:10:07.45 UTC1426c3c1-f38e-452e-8b2a-d045c56296e12012-10-16 15:15:35.841 UTCe0424e01-ed30-4c94-95b8-143751fca7a22012-07-11 16:07:29.317 UTC6bf5fc1d-7f9a-48a3-8b77-b4cf27f2b52a2012-10-17 14:47:18.255 UTC11db6475-ebfc-492f-af7d-3a4185d279ce2012-09-19 15:49:14.786 UTC6315c9ba-381a-44ce-82cd-ea6f5aae35d52012-07-13 09:27:13.462 UTC9c9a25e0-f9f5-4a03-b681-b41060114a602012-11-26 15:43:26.632 UTCbef35e44-1127-458d-b2ee-61048bd64a072012-07-13 06:22:03.734 UTC36fe5bbb-4c71-45c0-b68d-472ccadbcaba2012-11-01 10:14:45.687 UTC5639ee4e-2035-4cc9-911f-fb435d58a9302012-10-07 22:14:42.810 UTCcc5b393c-818f-4016-a1d8-890885b584d32012-07-13 09:00:07.232 UTCb0e4235a-5fe4-4228-a361-9dd543d8ec952012-09-19 15:33:22.278 UTC92219602-e4d9-4381-a61c-1956a05664d42013-06-21 09:23:14.7 UTC366c8de1-e00d-447a-b851-7d7dc5deef4e2012-10-17 16:05:49.72 UTC2c8f7b54-a34c-4da8-9719-403157b44c3e2013-06-21 16:28:07.95 UTC2e59c48d-737b-4181-94aa-7d2643b8387a2013-06-21 11:09:17.93 UTCf7125a55-d200-4c9f-9806-6b05549b428a2012-10-29 13:42:50.131 UTCEigen_analysisstage_matrix110.0000 0.0000 0.0000 7.6660 0.0000
0.0579 0.0100 0.0000 8.5238 0.0000
0.4637 0.8300 0.9009 0.2857 0.8604
0.0000 0.0400 0.0090 0.6190 0.1162
0.0000 0.0300 0.0180 0.0000 0.02322012-10-03 13:50:09.593 UTCThe stage matrix file input port:
Here comes the stage matrix without the stage names (as you see in the example). It should be provied as a txt-file.
Example from:
J. Gerard B. Oostermeijer; M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.2012-10-10 09:01:24.171 UTCspeciesName00Species name input port:
In this input port comes the title of the bar plot that will be generated with the analysis. As an example, it can be the name of the species or the name of the place where the research has been conducted, between others.
2012-10-10 08:46:17.484 UTCGentiana pneumonanthe2012-10-10 08:45:54.921 UTCbarPlot02012-10-10 11:25:12.531 UTCA bar plot which shows the stable stage distribution (w) of the analyzed matrix. It plots the proportion of individuals per stage. 2012-10-10 11:25:10.921 UTCprojectionMatrix0 Projection matrix
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.02322012-10-12 11:31:11.508 UTCProjection matrix Output port:
Creates a grid of colored rectangles to display the stage matrix input.2012-10-10 11:16:38.125 UTCelasticityMatrix0The output port: Elasticity matrix
Creates a grid of colored rectangles to display the elasticities.
The elasticities of λ with respect to the stage are often interpreted as the “contributions” of each of the stages to λ. This interpretation relies on the demonstration, by de Kroon et al (1986), that the elasticites of the λ with respect to the stage, always sum to 1. For further information see:
Literature:
de Kroon, Hans, Anton Plaisier, Jan van Groenendael, and Hal Caswell. 1986. Elasticity: The Relative Contribution of Demographic Parameters to Population Growth Rate. Ecology 67:1427–1431
Caswell, H. 2001. Matrix population models, construction, analysis and interpretation. Second edition. Sinauer Associates, Inc Publishers.
2012-10-10 11:26:17.171 UTC Elasticity matrix
S J V G D
S 0.0000 0.0000 0.0000 0.0368 0.0000
J 0.0066 0.0013 0.0000 0.1571 0.0000
V 0.0302 0.0633 0.2732 0.0030 0.0054
G 0.0000 0.0922 0.0824 0.1971 0.0223
D 0.0000 0.0082 0.0196 0.0000 0.0005
2012-10-10 11:31:52.234 UTCsensitivityMatrix10 Sensitivity matrix
S J V G D
S 0.0000 0.0000 0.0000 0.0059 0.0000
J 0.1413 0.1650 0.0000 0.0228 0.0000
V 0.0808 0.0944 0.3753 0.0130 0.0078
G 0.0000 2.8526 11.339 0.3942 0.2385
D 0.0000 0.3398 1.3509 0.0000 0.02842012-10-10 11:50:32.796 UTCThe sensitivity matrix output:
Creates a grid of colored rectangles to display the sensitivities. In this graph are only shown the sensitivities of the actual transitions. 2012-10-10 11:44:24.250 UTCsensitivityMatrix20The sensitivity matrix output 2
Creates a grid of colored rectangles to display the sensitivities. In this graph are shown the sensitivities of the all posible transitions. 2012-10-10 11:47:16.562 UTC Sensitivity matrix
S J V G D
S 0.037 0.043 0.171 0.006 0.004
J 0.141 0.165 0.656 0.023 0.014
V 0.080 0.094 0.375 0.013 0.008
G 2.442 2.853 11.34 0.394 0.239
D 0.291 0.340 1.351 0.047 0.0282012-10-10 11:55:22.796 UTCeigenanalysis1Eigen analysis output
The Eigen analysis results are a set of demographic statistics:
1) Lambda or dominant eigenvalue: The population will be stable, grow or decrease at a rate given by lambda: eg: λ = 1 (population is stable), λ > 1 (population is growing) and finally λ < 1 (populatiopn is decreasing) . E.g. The projected population growth rate (λ) is 1.237, meaning that the population is projected to increase with 23% per year if these model parameters remain unchanged.
2) The stable stage distribution: It is the proportion of the number of individuals per stage and it is given by (w).
Elasticity and Sensitivity: Sensitivity and elasticity analyses are prospective analyses.
3) The sensitivity matrix: The sensitivity gives the effect on λ of changes in any entry of the matrix, including those that may, an a given context, be regarded as fixed at zero or some other value. The derivative tells what would happened to λ if aij was to change, not whether, or in what direction, or how much, aij actually change. The hypothetical results of such impossible perturbations may or may not be of interest, but they are not zero. It is up to you to decide whether they are useful (Caswell 2001).
When comparing the λ-sensitivity values for all matrix elements one can find out in what element a certain increase has the biggest impact on λ. However, a 0.01 increase in a survival matrix element is hard to compare to a 0.01 increase in a reproduction matrix element, because the latter is not bound between 0 and 1 and can sometimes take high values. Increasing matrix element a14 (number of S (seedlings) the next year produced by an G (Reproductive individuals)) with 0.01 from 7.666 to 7.676 does not have a noticeable effect on λ. For comparison between matrix elements it can therefore be more insightful to look at the impact of proportional changes in elements: by what percentage does λ change if a matrix element is changed by a certain percentage? This proportional sensitivity is termed elasticity (Description based on Oostermeijer data, based on Jongejans & de Kroon 2012).
4) The Elasticity matrix: The elasticities sum to 1 across the whole matrix (Caswell 1986; de Kroon et al. 1986; Mesterton-Gibbons 1993) and can be interpreted as proportional contributions of the corresponding vital rates to the matrix (see van Groenendael et al. 1994).
5) Reproductive value (v): scaled so v[1]=1. To what extent will a plant or animal of a determinate category or stage , contribute to the ancestry of future generation.
6) The damping ratio: it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, the larger the p, the quicker the population converges.
Those statistics are function of the vital rates, and througt them of biological and environmental variables.
For further details see:
Caswell, H. 1986. Life cycle models for plants. Lectures on Mathematics in the Life Sciences 18: 171-233.
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
Horvitz, C., D.W. Schemske, and Hal Caswell. 1997. The relative "importance" of life-history stages to population growth: Prospective and retrospective analyses. In S. Tuljapurkar and H. Caswell. Structured population models in terrestrial and freshwater systems. Chapman and Hall, New York.
Jongejans E. & H. de Kroon. 2012. Matrix models. Chapter in Encyclopedia of Theoretical Ecology (eds. Hastings A & Gross L) University of California, p415-423
de Kroon, H. J., A. Plaiser, J. van Groenendael, and H. Caswell. 1986. Elasticity: The relative contribution of demographic parameters to population growth rate. Ecology 67: 1427-1431.
Mesterton-Gibbons, M. 1993. Why demographic elasticities sum to one: A postscript to de Kroon et al. Ecology 74: 2467-2468.
van Groenendael, J., H. de Kroon, S. Kalisz, and S. Tuljapurkar. 1994. Loop analysis: Evaluating life history pathways in population projection matrices. Ecology 75: 2410-2415.
2012-10-11 09:08:40.125 UTC$lambda1
[1] 1.237596
$stable.stage
S J V G D
0.14143023 0.16520742 0.65671474 0.02283244 0.01381517
$sensitivities
S J V G D
S 0.00000000 0.00000000 0.0000000 0.005956842 0.00000000
J 0.14133539 0.16509663 0.0000000 0.022817127 0.00000000
V 0.08083208 0.09442153 0.3753343 0.013049498 0.00789583
G 0.00000000 2.85265996 11.3395869 0.394250955 0.23854854
D 0.00000000 0.33985571 1.3509578 0.000000000 0.02841982
$elasticities
S J V G D
S 0.000000000 0.000000000 0.00000000 0.036898276 0.0000000000
J 0.006612271 0.001334011 0.00000000 0.157150348 0.0000000000
V 0.030286005 0.063324284 0.27322221 0.003012487 0.0054893301
G 0.000000000 0.092200046 0.08246333 0.197189845 0.0223977311
D 0.000000000 0.008238288 0.01964877 0.000000000 0.0005327586
$repro.value
S J V G D
1.000000 3.830406 2.190674 66.184553 7.884991
$damping.ratio
[1] 2.092025
2012-10-10 11:37:42.546 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15:33:22.278 UTC274d678f-76a6-4014-9d68-d0189dfe70042012-10-03 14:03:09.78 UTCe5c21cb7-1882-4efa-81dc-7dd53b9202952012-09-26 12:05:06.765 UTC5ef7089b-9aef-4b96-983f-9c54530ffceb2012-09-26 13:55:15.687 UTC6aab6970-a0e8-4ac7-85d8-0906b5cf29072012-09-26 12:46:36.531 UTC40cc9b1a-f9d9-4f2d-8ef8-1108348f8cc92012-10-10 11:14:12.187 UTCff5bc61b-0d13-4622-adc8-2aedd7b7038c2012-07-13 09:20:52.134 UTCcf5e0323-5dea-4804-a941-3e537acd204e2012-10-10 11:26:17.421 UTC34d1cf2c-a02a-4b6e-b39d-b6f55da1a0252012-07-11 20:58:04.370 UTCc016cc4f-1001-4237-882d-dceabfdd8d012012-10-04 15:00:55.625 UTCa96cc7e4-b508-470e-ba78-4bfd8e1d84992012-10-03 13:57:55.765 UTC3b844874-3fc8-4b62-9f02-5c86ae0e053d2012-07-13 09:02:25.256 UTC18e99b4e-e6d1-4c87-86cb-f4b3f40fec872012-07-13 08:43:47.651 UTC1b962467-4a86-427c-b2bc-6b7e38f5f5422012-10-03 13:35:23.390 UTCThe Eigen analysis results are a set of demographic statistics:
1) Lambda or dominant eigenvalue: The population will be stable, grow or decrease at a rate given by lambda: eg: λ = 1 (population is stable), λ > 1 (population is growing) and finally λ < 1 (populatiopn is decreasing) .
2) The stable stage distribution: It is the proportion of the number of individuals per stage and it is given by (w).
Elasticity and Sensitivity: Sensitivity and elasticity analyses are prospective analyses.
3) The sensitivity matrix: The sensitivity gives the effect on λ of changes in any entry of the matrix, including those that may, an a given context, be regarded as fixed at zero or some other value. The derivative tells what would happened to λ if aij was to change, not whether, or in what direction, or how much, aij actually change. The hypothetical results of such impossible perturbations may or may not be of interest, but they are not zero. It is up to you to decide whether they are useful (Caswell 2001).
When comparing the λ-sensitivity values for all matrix elements one can find out in what element a certain increase has the biggest impact on λ. However, a 0.01 increase in a survival matrix element is hard to compare to a 0.01 increase in a reproduction matrix element, because the latter is not bound between 0 and 1 and can sometimes take high values. Increasing matrix element a14 (number of S (seedlings) the next year produced by an G (Reproductive individuals)) with 0.01 from 7.666 to 7.676 does not have a noticeable effect on λ. For comparison between matrix elements it can therefore be more insightful to look at the impact of proportional changes in elements: by what percentage does λ change if a matrix element is changed by a certain percentage? This proportional sensitivity is termed elasticity (Description based on Oostermeijer data, based on Jongejans & de Kroon 2012).
4) The Elasticity matrix: The elasticities sum to 1 across the whole matrix (Caswell 1986; de Kroon et al. 1986; Mesterton-Gibbons 1993) and can be interpreted as proportional contributions of the corresponding vital rates to the matrix (see van Groenendael et al. 1994).
5) Reproductive value (v): scaled so v[1]=1. To what extent will a plant or animal of a determinate category or stage , contribute to the ancestry of future generation.
6) The damping ratio: it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, the larger the p, the quicker the population converges.
Those statistics are function of the vital rates, and througt them of biological and environmental variables.
For further details see:
Caswell, H. 1986. Life cycle models for plants. Lectures on Mathematics in the Life Sciences 18: 171-233.
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
Horvitz, C., D.W. Schemske, and Hal Caswell. 1997. The relative "importance" of life-history stages to population growth: Prospective and retrospective analyses. In S. Tuljapurkar and H. Caswell. Structured population models in terrestrial and freshwater systems. Chapman and Hall, New York.
Jongejans E. & H. de Kroon. 2012. Matrix models. Chapter in Encyclopedia of Theoretical Ecology (eds. Hastings A & Gross L) University of California, p415-423
de Kroon, H. J., A. Plaiser, J. van Groenendael, and H. Caswell. 1986. Elasticity: The relative contribution of demographic parameters to population growth rate. Ecology 67: 1427-1431.
Mesterton-Gibbons, M. 1993. Why demographic elasticities sum to one: A postscript to de Kroon et al. Ecology 74: 2467-2468.
van Groenendael, J., H. de Kroon, S. Kalisz, and S. Tuljapurkar. 1994. Loop analysis: Evaluating life history pathways in population projection matrices. Ecology 75: 2410-2415.
2012-10-10 11:22:42.62 UTCedb731c0-daa1-4bd7-b8f0-ddbc56a875662012-10-10 11:35:17.156 UTC69d11822-5bf3-40d1-a6ce-cc0110a366dd2012-07-13 08:06:33.163 UTC6ad79f50-2ace-4bb4-b896-fc34810868c62012-09-26 13:51:56.437 UTC8701e660-faa7-4a7c-ae96-282fea7b3c0e2012-10-10 09:01:24.406 UTC98e93c16-3991-466d-9ade-6f082f2a3a1c2012-10-10 11:25:12.781 UTC16e2a51c-4ee9-4e81-a2a0-515d940f9cc22012-10-10 11:22:44.500 UTC418d8b49-71f3-487f-9a5e-55710ede018a2012-10-10 11:16:38.390 UTCcc5b393c-818f-4016-a1d8-890885b584d32012-07-13 09:00:07.232 UTC35908a90-ddf2-43c5-9910-680a097f4f212012-10-02 20:25:51.124 UTCe9b5e5d2-9871-4eba-b7a1-0635c8fc1bf52012-07-13 09:10:07.45 UTC4988e019-bf93-40bd-b095-6a33aec7e9682012-07-13 08:39:49.679 UTC84a2fa47-f758-4a80-95ba-903147579dca2012-10-03 14:26:58.218 UTC53b6584e-7b75-48ac-976b-11154cef701f2012-07-13 09:04:05.440 UTC104a6f4f-33c3-4b8c-b4d7-55ac8fa330f72012-07-13 07:53:21.635 UTC687a5ff0-61b3-4784-a263-6e7974626f6d2012-11-26 16:03:00.764 UTC3a09aae3-3fa4-44e7-a064-e02418cffa922012-10-03 13:54:56.46 UTCc8693523-8523-47e5-96bc-4648f21b7de92012-09-26 11:59:25.0 UTC068ff12d-fddd-45f7-9eec-8222ebfeac1b2012-10-10 11:37:42.796 UTC3e775ac4-0bf5-435e-979e-26753958554c2012-07-13 06:22:29.620 UTC855397b2-3c8d-4589-9a3a-ededfd630b5c2012-10-11 09:39:57.0 UTC6315c9ba-381a-44ce-82cd-ea6f5aae35d52012-07-13 09:27:13.462 UTC87e49604-3a08-48ae-a9be-a45e6e8d0ee62012-10-10 12:01:33.812 UTC57db3fed-16a3-43ca-a4f9-d41c254d9b772012-09-26 11:51:20.375 UTC4753d12c-1f1d-4454-97fe-6a2dcecc38b62012-07-13 07:45:12.849 UTC3652cbd1-72c4-47e1-9479-ddedb5f81d982012-07-13 09:07:01.485 UTC40f5c83b-f16c-4564-a6db-81a91ff724c02012-10-10 12:02:09.375 UTC31de0f25-8b52-4b7c-a868-4eb26381b7682012-07-11 16:08:08.989 UTC199c86f0-df6a-425c-b4dd-6aa852bcbff52012-07-13 09:03:22.271 UTCc38466a8-a606-44d7-8bd3-8f26b8250ef22012-10-10 11:35:50.671 UTCbef35e44-1127-458d-b2ee-61048bd64a072012-07-13 06:22:03.734 UTC09aa9ebd-4e1d-4579-83f6-727da90eae352012-09-20 13:38:43.850 UTCf850930e-3ed8-475e-a717-f9fe5d8af0f02012-10-17 15:12:16.758 UTCf896aca8-bba2-45e2-8113-e386cbe620ce2012-09-26 12:25:40.0 UTC431a4612-9885-4ae4-a530-e99099eb92572012-09-26 12:51:53.859 UTC2615d90a-7a5e-464e-89b6-20fec7bc10142012-07-13 09:11:19.100 UTC313804e4-faea-485a-bd2f-5a8dded213772012-10-17 15:12:36.567 UTC8badb0ad-fa34-4fba-b38a-ff0930047c532012-11-26 16:01:40.14 UTCace5fe46-77ef-4a86-b67b-bde22c741ac82012-07-13 09:26:09.444 UTC27e99cfd-69ad-4acb-b09b-46eeb1fffd6f2012-10-03 14:26:15.218 UTC2335e73d-8ebe-4cff-ba56-f841952e139e2012-10-12 11:31:11.711 UTC27fa10ea-ca41-4311-b50c-eb7e2fe664892012-07-11 15:49:21.753 UTC48960c0c-1f5d-4e1c-a5d0-270927af14402012-10-10 11:59:42.921 UTC8eb6139c-8930-43f8-bd9a-5603f973b51b2012-09-26 14:28:53.828 UTCe0424e01-ed30-4c94-95b8-143751fca7a22012-07-11 16:07:29.317 UTC3f094d6e-7d4f-43ea-a672-8f56b7e9b3272012-09-19 15:54:02.713 UTC9fa97e87-bd43-4312-a36f-8ac512988b802012-07-13 06:25:39.0 UTC5bdb4704-9322-4cbc-8d08-4b87aa1f23182012-07-11 22:49:36.115 UTC7f69fad0-a2a7-42ad-aebe-8b0aa109d5492012-10-10 10:51:54.312 UTCa5615bef-dcac-45ea-a3ce-cbd4b9875eee2012-09-26 12:14:28.31 UTC5a97a8dd-039c-4243-ac5c-b91939948fcb2012-09-21 05:08:07.641 UTC214b1114-efbc-4d54-bb20-4fa1f9beb89f2012-09-20 13:37:17.940 UTC21662d80-f207-4a54-9844-8f24acb91a272012-07-13 09:22:22.131 UTCd876c281-ea57-4da0-a470-f3bfbd4c7ad42012-07-11 13:05:24.619 UTC9253e96c-9712-42a9-b19d-c8bf5fdccce12012-09-26 13:43:08.906 UTC09eafecd-4f3c-4de3-b883-136d082eefb52012-10-02 20:23:53.800 UTC6a6df203-47b2-4b26-855f-ff8c48eed2bc2012-09-19 15:38:42.701 UTCb14b0461-c322-4ebf-ac0d-e62d7dc57e922012-10-10 12:00:57.265 UTCf8c42ab5-0d43-40e0-94ac-ec6798e927f72012-10-11 11:44:45.140 UTC9159d5c8-8084-403e-9941-37a0babea12d2012-07-13 08:10:15.746 UTCe05732a8-9627-4bfa-b871-d8d4a9c53fb62012-07-11 20:55:29.517 UTC61e17b4e-2110-470a-8aa8-db97ea3341e02012-07-11 15:46:57.885 UTC6933ad38-f960-4f05-ae40-0352c2a977232012-07-11 16:13:31.963 UTC11db6475-ebfc-492f-af7d-3a4185d279ce2012-09-19 15:49:14.786 UTCe8d180a6-7a5c-4421-b788-db26f3589ae82012-09-20 13:43:51.734 UTC17afd103-1e0c-4e98-92eb-dc7f12cf29842012-09-21 06:25:47.618 UTCab5c6e54-c6a6-4ad3-b360-33b41f0efeb12012-10-10 11:31:52.500 UTCda31b618-4c4c-4a02-a808-22ec64fd999e2012-10-03 13:50:10.937 UTCa2cee785-18ef-4208-8677-b37970b920a72012-07-13 07:51:10.754 UTCa6efda97-4c1a-4ce4-9b65-6a87f8d11e782012-07-13 09:14:16.348 UTCd200135a-b430-4ff3-aec3-cb4139f821ca2012-10-10 11:55:23.78 UTC9cc9920c-7d50-4c5b-9800-20cc1cfd72cf2012-09-20 14:54:19.489 UTCecef24cd-4e05-4e89-b47d-2627857c98bc2012-07-13 09:06:31.770 UTC6e4e9dd0-334b-403a-9632-8423f9636fe72012-07-11 13:00:55.837 UTC02aaa6ce-772b-4402-a474-2cdfe18e31672012-09-26 12:29:14.359 UTCThis Workflow was created by:
Maria Paula Balcázar-Vargas, Jonathan Giddy and G. Oostermeijer
This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.
This workflow was created using and based on Package ‘popbio’ in R.
Stubben, C & B. Milligan. 2007. Estimating and Analysing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22 (11): 1-23
Stubben, C., B. Milligan, P. Nantel. 2011. Package ‘popbio’. Construction and analysis of matrix population models. Version 2.3.1
2012-09-26 12:44:19.312 UTCa70a1e5c-8940-4703-bffa-a89da5537fdb2012-09-21 05:10:47.15 UTCd2e98a62-d554-4654-a359-39eaa6c9c9d52012-09-20 13:35:32.442 UTCEigen analysis2012-09-26 12:46:27.453 UTCf9d69679-5e04-46e4-b77b-c70d19cb4c0d2012-07-13 08:51:15.886 UTCNet_reproductive_ratstage_matrix110.0000 0.0000 0.0000 7.6660 0.0000
0.0579 0.0100 0.0000 8.5238 0.0000
0.4637 0.8300 0.9009 0.2857 0.8604
0.0000 0.0400 0.0090 0.6190 0.1162
0.0000 0.0300 0.0180 0.0000 0.02322012-10-05 11:35:18.26 UTCThe stage matrix without the stage names (as you see in the example).
Example from:
J. Gerard B. Oostermeijer; M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.2012-10-30 10:56:07.8 UTCrows_fecundity11To perform the Net reproductive rate (Ro), the row(s) in which the recruitment values are found, should be selected.
In the example of the Gentiana species (Oostermeijer et al. 1996. The Journal of Ecology):
Selected lines are S and J (seedlings and juveniles, these stages receive recruits each year from the stage G): therefore, the numbers 1 and 2 are used to identify these rows (S and J).
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
2012-10-11 12:38:55.125 UTC1
22012-10-11 12:07:35.828 UTCcolumns_fecundity1142012-10-11 12:41:11.468 UTCTo perform the net reproductive rate (Ro), the column(s) in which the fecundity values are found, should be selected.
In the example of the Gentiana species (Oostermeijer et al. 1996. The Journal of Ecology):
The selected column is G (reproductive individuals): therefore number 4 will be used to identify the fecundity column (G).
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
2012-10-11 12:41:42.156 UTCnetReproductiveRate0The net reproductive rate (Ro) is mean number of offspring by which a newborn individual will be replaced by the end of its life, and thus the rate by which the population increases from one generation to the next (Caswell, 2001)
2012-10-05 13:15:39.386 UTC5.5685222012-10-11 12:29:27.375 UTCNetReproductiveRateAnalysiscolumns1rows1stage_matrix1result00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falserows1falsecolumns1falseresult00falselocalhost6311falsefalsestage_matrixR_EXProwsDOUBLE_LISTcolumnsDOUBLE_LISTresultDOUBLEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeNetReproductiveRateAnalysiscolumnsNetReproductiveRateAnalysisrowsNetReproductiveRateAnalysisstage_matrixnetReproductiveRatec65932e5-9f7b-4ec2-b218-152de68c32632012-10-05 11:48:11.370 UTCb7b02776-ce57-4b3f-bc6e-b2991aaa4bc72012-10-11 12:41:42.343 UTC18aac4ef-4208-458c-9dbb-9a2e5ee2f3f92012-06-21 14:24:41.784 UTCab28f080-c1c8-43fe-a71e-a83179807fe02012-10-05 13:16:14.823 UTC45f7861f-9c3c-492a-924c-34b896fefa322012-10-05 11:35:49.386 UTC138bd86c-fd0b-4db2-8092-1e9071940e2a2012-09-28 08:45:04.951 UTC74dedf92-5055-45bd-995b-5b9df0a480a82012-10-05 11:40:27.651 UTCaabd83c8-3016-47ec-a1e2-e6d909289dfa2012-06-22 08:38:17.934 UTCThe net reproductive rate (Ro) is mean number of offspring by which a newborn individual will be replaced by the end of its life, and thus the rate by which the population increases from one generation to the next (Caswell, 2001)2012-10-05 13:09:39.573 UTC724a9578-a6b6-44b9-9c02-fcf83e375a672012-09-28 08:40:05.123 UTC3b27b30c-4431-409c-97fd-26b37a8823fb2012-09-28 08:09:20.60 UTCe8363f39-9c04-411e-8d92-7582d6f97c842012-10-05 13:07:24.964 UTCfbc0d966-2c11-49ab-be84-561bb64881ad2012-10-30 10:55:34.10 UTCc6fd9af5-b7a7-460d-83c8-8122aa11253e2012-09-28 08:43:02.498 UTCce28076c-2872-4c26-aa87-5c8a90bde4412012-10-05 13:16:51.604 UTC227252e7-ff41-47fd-af0c-39907febdc422012-09-28 08:07:38.560 UTC1ea1c8b7-0fbe-4b02-8a42-f01ed9ef0f982012-10-11 12:29:40.843 UTC1513fefa-e519-421a-9766-7da5cbcc12ac2012-10-30 10:54:39.215 UTCf589ea15-b89d-415f-b16b-71d6b6abcc592012-09-28 08:41:41.388 UTC5e006443-a6ca-46e2-85ec-b5fe882620552012-10-05 13:09:39.807 UTCb5ec6e6b-d9bd-43b3-86d4-f33bd56402432012-10-05 11:37:41.839 UTCf92df37a-086b-4bbe-b7c2-42bc8660915e2012-06-15 06:42:22.376 UTC7fc87bf9-2dd0-4cc3-8fe6-7ea750b7ef4a2012-10-05 12:54:17.151 UTCe6545437-85f0-42a0-b54f-066b165d7ec62012-10-05 11:51:02.854 UTC3979d4bd-1668-4e90-913b-06b22e1229c62012-06-22 08:39:22.770 UTCa6d860df-36bb-423a-a7e6-586818fccfc82012-09-28 08:06:19.732 UTC24c4057c-5489-458e-a3f7-fbf8799645922012-10-11 12:39:01.78 UTC98ee462f-3718-4938-a959-6a042ad29aff2012-10-05 11:35:18.229 UTCNet reproductive rate (Ro)2012-10-05 13:06:49.104 UTC6cefb97d-5207-40ec-847d-6b62cabd12cb2012-06-15 06:56:38.363 UTCc7b6d5dd-ddc3-4388-9f28-647b74d4f5f42012-06-15 06:54:00.692 UTCe2a9d92c-412f-47fc-a567-39a56abe723e2012-06-15 06:52:47.83 UTC6e3a57e1-23a5-4883-84d6-bf7a14a9b1042012-06-21 14:06:12.125 UTC7aff96c5-929a-4be8-a552-37f0bbfb31372012-10-30 10:56:15.506 UTCc4dc3143-373c-4d4e-adc3-8d8d84dd4a1e2012-10-05 11:50:33.307 UTCMaria Paula Balcázar-Vargas, Jonathan Giddy and Gerard Oostermeijer2012-10-05 11:21:40.276 UTCc55402cf-b409-47b3-b079-4cfb1234f6ce2012-10-05 11:30:55.729 UTCa514d7f6-ae3a-46d8-ac68-684b622d5b542012-10-11 12:06:15.687 UTCc4bce93c-e05f-433c-9f0f-36cb69f249e72012-10-05 11:49:57.167 UTC19bbf243-d943-409c-9004-bb9df6c333492012-06-15 06:40:07.359 UTC81787775-16fe-4c13-90dd-0a48678146ee2012-09-28 08:10:30.76 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06:08:00.914 UTC068f4c47-ac93-41d1-928b-e5313ddf7dc92012-03-30 15:27:01.885 UTC1e66a160-d9a3-485d-b31e-cac2c674a2962012-03-30 15:59:19.350 UTC87080ba6-c0da-4929-875b-a334cd6c80dc2012-07-04 15:48:37.846 UTCf364089f-de01-4c6d-b4e8-3e0f55f8952f2012-06-08 06:30:14.837 UTC8c458bf5-19ef-437d-a53b-a5bfa71620712012-06-08 07:11:39.27 UTC6ad4d84d-6c33-4a35-9142-512f206419d22012-07-04 15:55:59.146 UTCc67364d7-6f73-45a7-9354-8fea75ff1d472012-12-10 15:52:24.824 UTC8237763e-e3d3-4a89-8154-c0e7ebe6ac992012-03-30 15:58:10.751 UTC1866cddd-542f-43a6-b4a7-86d0be66758e2012-06-27 09:47:27.817 UTC2a67baca-21bc-4bc2-8e77-0754a7070ef32012-06-08 06:05:07.24 UTC40a9a875-43ff-4cf2-8eb3-a0b8c624bbec2012-12-10 15:48:03.16 UTC99a5ecac-18df-45ae-bbfa-d180b0469b442012-06-08 07:14:48.566 UTC29186c39-3022-4d52-90d0-8f7fd7bcef272012-03-30 15:47:32.455 UTC7681491c-5178-4844-b9b1-e1c1ba4e29852012-04-27 10:36:47.808 UTC09f91d33-9f50-4983-96c9-1335ed1f92b42012-04-27 06:19:38.161 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UTCWorkflow188input11output0PrettyPrintRinput1output00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivityinput1falseoutput00falselocalhost6311falsefalseinputR_EXPoutputTEXT_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokePrettyPrintRinputoutput1c210d9a-059f-4c52-8df7-0310db5e211f2013-06-21 14:30:38.141 UTCdeb0863c-b567-4755-af9c-b8b74d5e08e52013-06-21 14:31:25.529 UTCStage_Matrix_Analysilabel00Gentiana pneumonanthe, Terschelling2012-10-23 15:39:06.31 UTCDescriptive title for labelling generated outputs.2012-11-01 12:14:05.640 UTCshortTermYears00This value will be use to plot a graph that shows a simulation of the number of individuals per stage a few years after the study. This value represents the years of axis X of the output graph: StageVectorPlotShortTerm.
2012-11-01 11:51:21.500 UTC102012-10-29 13:44:13.835 UTClongTermYears00502012-10-29 13:44:37.435 UTCThis value contains the maximum number of iterations in the transient dynamic analysis, and hence the total number of years for the long term graphs.
The number of years will be used in two output graphs:
1) StageVectorPlotLongTermProportional: the proportion of individuals per stage in the long term.
2) StageVectorPlotLongTermLogarithmic: the number of individuals per stage in the long term.
2012-11-01 11:51:48.46 UTCstages11Stage input port:
The names of the stages or categories of the input matrix. It is very important that the stages names are not longer than 8 characters. The name of the stages must be added one by one.
The respective name stages must be filled one by one. First press add value, fill a stage name (not longer than 8 characters) and press enter, then press add value and fill once again the next stage name, repeat the action until you have fill all the stages names.
In the following example, the matrix has 5 stages or categories:
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
The stages of this matrix are called:
1) Seedlings S
2) Juveniles J
3) Vegetative V
4) Reproductive individuals G
5) Dormant plants D
2013-06-13 10:54:06.95 UTC[S, J, V, G, D]2013-06-13 10:54:21.602 UTCstage_matrix11fcols11frows11abundances11barPlot0A bar plot which shows the stable stage distribution (w) of the analysed matrix. In other words, the proportion of individuals per stage.2012-11-01 12:16:09.906 UTCprojectionMatrix0The stage matrix, displayed with coloured squares to highlight the magnitude of the values.2012-11-01 10:39:02.187 UTCeigenanalysis_elasticity_matrix0The elasticity matrix, displayed with coloured squares to highlight the magnitude of the values.2012-11-01 12:16:26.656 UTCeigenanalysis_sensitivity_matrix_10A sensitivity matrix showing the sensitivities of the actual transitions (i.e. the sensitivity values of non-zero elements), displayed with coloured squares to highlight the magnitude of the values.2012-11-01 10:40:25.78 UTCeigenanalysis_sensitivity_matrix_20A sensitivity matrix showing the sensitivities of all possible transitions (i.e. the sensitivity values of zero and non-zero elements), displayed with coloured squares to highlight the magnitude of the values.2012-11-01 10:41:08.312 UTCeigenanalysis1Eigen analysis
The Eigen analysis results are a set of demographic statistics:
Lambda or dominant eigenvalue: This value describes the population growth rate of a stage matrix. The population will be stable, grow or decrease at a rate given by lambda: e.g.: λ = 1 (population is stable), λ > 1 (population is growing) and finally λ < 1 (population is decreasing).
The stable stage distribution (w): It is the proportion of the number of individuals per stage. It is given analytically by the right eigenvector (another property of the transition matrix) that corresponds to the dominant eigenvalue
Elasticity and Sensitivity: Sensitivity and elasticity analyses are prospective analyses.
The sensitivity matrix: The sensitivity gives the effect on λ of changes in any entry of the matrix, including those that may, at a given context, be regarded as fixed at zero or some other value. The derivative tells what would happened to λ if aij was to change, not whether, or in what direction, or how much, aij actually change. The hypothetical results of such impossible perturbations may or may not be of interest, but they are not zero. It is up to you to decide whether they are useful (Caswell 2001).
When comparing the λ-sensitivity values for all matrix elements one can find out in what element a certain increase has the biggest impact on λ. However, a 0.01 increase in a survival matrix element is hard to compare to a 0.01 increase in a reproduction matrix element, because the latter is not bound between 0 and 1 and can sometimes take high values. Increasing matrix element a14 (number of S (seedlings) the next year produced by a G (Reproductive individuals)) with 0.01 from 7.666 to 7.676 does not have a noticeable effect on λ. For comparison between matrix elements it can therefore be more insightful to look at the impact of proportional changes in elements: by what percentage does λ change if a matrix element is changed by a certain percentage? This proportional sensitivity is termed elasticity (Description based on Oostermeijer data, based on Jongejans & de Kroon 2012).
The Elasticity matrix: The elasticities of λ with respect to the stage are often interpreted as the “contributions” of each of the stages to λ. This interpretation relies on the demonstration, by de Kroon et al (1986) that the elasticitis of the λ with respect to the stage, always sum to 1. For further information see: de Kroon, et al., 1986. and Caswell 2001.
Reproductive value (v): scaled so v[1]=1. To what extent will a plant or animal of a determinate category or stage , contribute to the ancestry of future generation.
The damping ratio: it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, the larger the p, the quicker the population converges.2012-11-01 12:16:19.0 UTC$lambda1
[1] 1,232338
$stable.stage
S J V G D
0,14218794 0,16166957 0,65944861 0,02285525 0,01383863
$sensitivities
S J V G D
S 0 0 0 0,006042076 0
J 0,14255579 0,1620878 0 0,02291438 0
V 0,08206359 0,0933074 0,3806 0,01319088 0,00798695
G 0 2,7675986 11,28901 0,391255815 0,2369016
D 0 0,3325676 1,35654 0 0,02846721
$elasticities
S J V G D
S 0 0 0 0,037589187 0
J 0,006706037 0,001315287 0 0,15406651 0
V 0,03088315 0,062844075 0,27823767 0,003058271 0,005576792
G 0 0,089832455 0,08252831 0,196541848 0,022353201
D 0 0,008096016 0,01983398 0 0,000537213
$repro.value
S J V G D
1 3,792468 2,18317 64,755197 7,781288
$damping.ratio
[1] 2,0902
2012-10-31 12:11:52.131 UTCstageVectorPlotShortTerm0A plot that charts the number of individuals per stage vs. years in the short-term (e.g. 5 or 10 years). The number of years is related to the short-term years input value.2012-11-01 11:47:06.281 UTCstageVectorPlotLongTermLogarithmic0The number of individuals per stage in the long term2012-11-01 11:46:16.968 UTCpopulationProjection0Population projection:
Lambda or dominant eigenvalue: The population will be stable, grow or decrease at a rate given by lambda: e.g.: λ = 1 (population is stable), λ > 1 (population is growing) and finally λ < 1 (population is decreasing). e.g. The projected population growth rate (λ) is 1.237, meaning that the population is projected to increase with 23% per year if these model parameters remain unchanged.
The stable stage distribution (stable.stage): It is the proportion of the number of individuals per stage and it is given by (w).
Stage vector (stage.vectors): it is the projection of the number of individuals per category per year in the long term, the long term was stipulated in the input port (long term years) (e.g. 50 years).
Population sizes (pop.sizes): it is the total population size per year in the long-term (e.g. 50 years).
Population change (pop.changes): are the lambda values per year in the long-term (e.g. 50 years).
2012-11-01 12:14:44.46 UTC$lambda
[1] 1.232338
$stable.stage
S J V G D
0.14218794 0.16166957 0.65944861 0.02285525 0.01383863
$stage.vectors
0 1 2 3 4 5 6 7
S 69 161 176.33333 187.22072 219.09046 261.92397 318.22637 389.44517
J 100 179 201.69476 214.57709 249.78014 298.27181 362.08839 442.95984
V 111 258 467.40332 685.98643 903.75302 1149.34660 1437.18683 1783.39662
G 21 23 24.42009 28.57702 34.16400 41.50779 50.79720 62.39105
D 43 6 10.15818 14.70876 19.13949 24.22235 30.22041 37.46071
8 9 10 11 12 13 14
S 478.33138 588.52367 724.70467 892.75361 1099.9811 1355.4346 1670.2865
J 543.96054 669.21317 824.03064 1015.09148 1250.7042 1541.1537 1899.1418
V 2204.99218 2721.56781 3356.41003 4137.71650 5099.9406 6285.3667 7746.0003
G 76.76396 94.52670 116.44612 143.47580 176.7958 217.8635 268.4762
D 46.29325 57.12499 70.44214 86.83496 107.0256 131.9009 162.5519
15 16 17 18 19 20 21
S 2058.3178 2536.5199 3125.836 3852.0783 4747.0575 5849.9764 7209.1464
J 2340.3370 2884.0582 3554.118 4379.8647 5397.4679 6651.5012 8196.8954
V 9545.8697 11763.8434 14497.093 17865.3551 22016.1771 27131.3836 33435.0416
G 330.8504 407.7177 502.445 619.1814 763.0404 940.3234 1158.7961
D 200.3221 246.8664 304.224 374.9074 462.0130 569.3564 701.6396
22 23 24 25 26 27 28
S 8884.1038 10948.218 13491.904 16626.585 20489.572 25250.078 31116.629
J 10101.3442 12448.269 15340.474 18904.649 23296.916 28709.674 35380.022
V 41203.2756 50776.363 62573.642 77111.875 95027.892 117106.479 144314.761
G 1428.0284 1759.814 2168.685 2672.553 3293.488 4058.691 5001.679
D 864.6572 1065.550 1313.118 1618.205 1994.175 2457.498 3028.468
29 30 31 32 33 34 35
S 38346.204 47255.483 58234.725 71764.863 88438.565 108986.20 134307.83
J 43600.144 53730.113 66213.658 81597.604 100555.825 123918.76 152709.79
V 177844.559 219164.602 270084.859 332835.826 410166.224 505463.41 622901.75
G 6163.759 7595.834 9360.634 11535.465 14215.591 17518.41 21588.61
D 3732.096 4599.204 5667.773 6984.612 8607.403 10607.23 13071.69
36 37 38 39 40 41 42
S 165512.64 203967.51 251356.91 309756.66 381724.90 470414.08 579709.13
J 188190.08 231913.78 285796.15 352197.45 434026.28 534867.07 659136.99
V 767625.48 945974.02 1165759.69 1436609.93 1770388.96 2181717.52 2688613.33
G 26604.46 32785.68 40403.04 49790.20 61358.36 75614.23 93182.29
D 16108.74 19851.41 24463.65 30147.49 37151.89 45783.69 56420.97
43 44 45 46 47 48 49
S 714397.57 880379.2 1084924.8 1336994.0 1647628.4 2030435.1 2502182.2
J 812279.54 1001002.9 1233573.9 1520179.9 1873375.5 2308631.7 2845014.5
V 3313280.28 4083081.1 5031735.8 6200799.1 7641480.1 9416886.1 11604786.2
G 114832.08 141511.9 174390.5 214908.1 264839.4 326371.6 402200.1
D 69529.71 85684.1 105591.8 130124.7 160357.7 197614.8 243528.3
$pop.sizes
[1] 3.440000e+02 6.270000e+02 8.800097e+02 1.131070e+03 1.425927e+03
[6] 1.775273e+03 2.198519e+03 2.715653e+03 3.350341e+03 4.130956e+03
[11] 5.092034e+03 6.275872e+03 7.734447e+03 9.531719e+03 1.174646e+04
[16] 1.447570e+04 1.783901e+04 2.198372e+04 2.709139e+04 3.338576e+04
[21] 4.114254e+04 5.070152e+04 6.248141e+04 7.699821e+04 9.488782e+04
[26] 1.169339e+05 1.441020e+05 1.775824e+05 2.188416e+05 2.696868e+05
[31] 3.323452e+05 4.095616e+05 5.047184e+05 6.219836e+05 7.664940e+05
[36] 9.445797e+05 1.164041e+06 1.434492e+06 1.767779e+06 2.178502e+06
[41] 2.684650e+06 3.308397e+06 4.077063e+06 5.024319e+06 6.191659e+06
[46] 7.630217e+06 9.403006e+06 1.158768e+07 1.427994e+07 1.759771e+07
$pop.changes
[1] 1.822674 1.403524 1.285293 1.260689 1.244995 1.238412 1.235219 1.233715
[9] 1.232996 1.232652 1.232488 1.232410 1.232372 1.232354 1.232346 1.232342
[17] 1.232340 1.232339 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[25] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[33] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[41] 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338 1.232338
[49] 1.232338
2012-11-01 11:42:50.109 UTCstageVectorPlotLongTermProportional0Stage vector plot long term proportional:
Is the proportion of individuals per stage in the long term (e.g.: 50 years) 2012-11-01 11:45:40.640 UTCdampingRatio0Damping ratio:
The ratio between the dominant eigenvalue and the second highest eigenvalue of a transition matrix is called the damping ratio, and it can be considered as a measure of the intrinsic resilience of the population, describing how quickly transient dynamics decay following disturbance or perturbation regardless of population structure, (the larger the damping ratio, the quicker the population converges). High damping ratios tell you that the dominant stable stage distribution is reached fairly soon.2012-11-01 12:14:56.312 UTC2.0901.2012-11-01 11:44:15.62 UTCfundamentalMatrix1Age specific survival
The fundamental matrix workflow gives the basic information on age-specific survival, this includes the mean, variance and coefficient of variation (cv) of the time spent in each stage class and the mean and variance of the time to death.
Fundamental matrix (N): is the mean of the time spent in each stage class. e.g.: For our Gentiana example means a J plants will spends, on average, about 1 year as a Juvenile, 11 as vegetative plant, less than a year a reproductive and dormant plant.
Variance (var): is the variance in the amount of time spent in each stage class.
Coefficient of variation (cv): is the coefficient of variation of the time spent in each class (sd/mean- the ratio of the standard deviation to the mean).
Meaneta: is the mean of time to death, of life expectancy of each stage. e.g. The mean age at death is the life expectancy; the life expectancy of a new individual seedling is 8 years.
Vareta: is the variance of time to death.
2012-11-01 10:47:32.328 UTC$N
S J V G D
S 1.00000000 0.0000000 0.0000000 0.0000000 0.0000000
J 0.05855658 1.0101010 0.0000000 0.0000000 0.0000000
V 6.89055876 11.9968091 13.3581662 10.0186246 12.9606017
G 0.20844800 0.4667882 0.3911175 2.9183381 0.6919771
D 0.12890879 0.2523299 0.2464183 0.1848138 1.2628940
$var
S J V G D
S 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000
J 0.05631067 0.01020304 0.0000000 0.0000000 0.0000000
V 129.72009930 164.59050165 165.0824377 157.2694415 165.3219447
G 0.96474493 2.03981226 1.7387357 5.5983592 2.8680368
D 0.18007000 0.32133154 0.3152601 0.2478305 0.3320072
$cv
S J V G D
S 0.000000 NaN NaN NaN NaN
J 4.052468 0.100000 NaN NaN NaN
V 1.652910 1.069391 0.9618417 1.2517398 0.9920649
G 4.712035 3.059674 3.3713944 0.8107646 2.4473757
D 3.291836 2.246508 2.2785654 2.6936618 0.4562542
$meaneta
S J V G D
8.286472 13.726028 13.995702 13.121777 14.915473
$vareta
S J V G D
143.4207 181.1844 181.6537 177.2333 181.2319
2012-11-01 11:37:55.718 UTCgenerationTime0Generation time:
The time T required for the population to increase by a factor of Ro (net reproductive rate).
e.g. for Generation time T and Net reproductive rate Ro:
If T = 8.13 and Ro = 5.46 then the average individual in the study year replaced itself with about five new plants and took approximately 8 years to do so.
2012-11-01 12:15:30.218 UTC8.13022012-10-31 12:12:54.819 UTCnetReproductiveRate0The net reproductive rate is the mean number of offspring by which a new-born individual will be replaced by the end of its life, and thus the rate by which the population increases from one generation to the next.
2012-11-01 11:40:25.562 UTC5.46572012-10-31 12:13:22.678 UTCsurvivalCurvePlot0sensitivity_matrix1sensitivityPlot0elasticity_matrix1ElasticityPlot0cohenCumulative0keyfitzDelta0Eigen_analysisplotTitle0speciesName0stage_matrix1projectionMatrix00sensitivityMatrix100sensitivityMatrix200elasticityMatrix00barPlot00eigenanalysis11Eigen analysis of a stage matrix model.
This component of the workflow performs the Eigen analysis. This analysis results are a set of demographic statistics: Lambda or dominant eigenvalue (λ), the stable stage distribution, sensitivity and elasticity matrix, reproductive value and damping ratio (see outputs: Eigen_analysis).2012-11-01 10:11:39.406 UTCnet.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeTransientDynamicsplot_title0short_term_years0long_term_years0abundances1stage_matrix1stage_vector_plot_short_term00stage_vector_plot_long_term_logarithmic00pop_projection00stage_vector_plot_long_term_proportional00damping_ratio00Transient Dynamics:
This workflow produces plots of the short-term dynamics and convergence to stable stage distribution using stage vector projections (see outputs: Transient Dynamics).2012-11-01 10:13:40.390 UTCnet.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeFundamental_matrixstage_matrix1rows_fecundity1columns_fecundity1fundamental_matrix11Age specific survival or fundamental analysis.
This workflow gives the basic information on age-specific survival, this includes the fundamental matrix (N): is the mean of the time spent in each stage class, the Variance (var): is the variance in the amount of time spent in each stage class, the Coefficient of variation (cv): is the coefficient of variation of the time spent in each class (sd/mean- the ratio of the standard deviation to the mean), Meaneta: is the mean of time to death, of life expectancy of each stage and Vareta: is the variance of time to death. (see outputs: Age specific survival).2012-11-01 10:11:32.593 UTCnet.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeGeneration_time__T_stage_matrix1rows_fecundity1columns_fecundity1generation_time00Generation time (T):
This component of the workflow calculates the generation time. The time T required for the population to increase by a factor of Ro (net reproductive rate). In other words, T calculates how much time takes to a plant/animal to replace itself by a factor of Ro (see outputs: Generation time). 2012-11-01 10:12:51.109 UTCnet.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeNet_reproductive_ratstage_matrix1columns_fecundity1rows_fecundity1netReproductiveRate00Net reproductive rate (Ro):
This section of the workflow calculates the net reproductive rate (Ro). Ro is the mean number of offspring by which a new-born individual will be replaced by the end of its life, and thus the rate by which the population increases from one generation to the next (see outputs: Net reproductive rate).2012-11-01 10:12:20.156 UTCnet.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSurvival_CurveplotTitle0stageMatrix1fecundityRows1fecundityCols1survivalCurvePlot00net.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSensitivity_and_Elasidentifier0stage_matrix1sensitivityPlot00elasticityPlot00sensitivity_matrix11elasticity_matrix11net.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeCohen_Cumulativeabundances1stage_matrix1cohenCumulative00net.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeKeyfitz_Deltaabundances1stage_matrix1keyfitzDelta00net.sf.taverna.t2.activitiesdataflow-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeEigen_analysisplotTitleEigen_analysisspeciesNameEigen_analysisstage_matrixTransientDynamicsplot_titleTransientDynamicsshort_term_yearsTransientDynamicslong_term_yearsTransientDynamicsabundancesTransientDynamicsstage_matrixFundamental_matrixstage_matrixFundamental_matrixrows_fecundityFundamental_matrixcolumns_fecundityGeneration_time__T_stage_matrixGeneration_time__T_rows_fecundityGeneration_time__T_columns_fecundityNet_reproductive_ratstage_matrixNet_reproductive_ratcolumns_fecundityNet_reproductive_ratrows_fecunditySurvival_CurveplotTitleSurvival_CurvestageMatrixSurvival_CurvefecundityRowsSurvival_CurvefecundityColsSensitivity_and_ElasidentifierSensitivity_and_Elasstage_matrixCohen_CumulativeabundancesCohen_Cumulativestage_matrixKeyfitz_DeltaabundancesKeyfitz_Deltastage_matrixbarPlotprojectionMatrixeigenanalysis_elasticity_matrixeigenanalysis_sensitivity_matrix_1eigenanalysis_sensitivity_matrix_2eigenanalysisstageVectorPlotShortTermstageVectorPlotLongTermLogarithmicpopulationProjectionstageVectorPlotLongTermProportionaldampingRatiofundamentalMatrixgenerationTimenetReproductiveRatesurvivalCurvePlotsensitivity_matrixsensitivityPlotelasticity_matrixElasticityPlotcohenCumulativekeyfitzDelta543f4718-3a39-4813-b1f8-b8173435abc12012-10-10 15:38:22.120 UTC9c9a25e0-f9f5-4a03-b681-b41060114a602012-11-26 15:43:26.632 UTC3618d570-4189-464f-8921-ae27391d65122012-10-18 11:17:27.472 UTCd64b5ae1-a5ad-4260-89b2-9822403cfc282012-10-17 14:53:12.993 UTC3b844874-3fc8-4b62-9f02-5c86ae0e053d2012-07-13 09:02:25.256 UTC51e48dec-1225-494a-a91d-3e17eb05f5c92012-11-26 15:38:34.136 UTC12eeeead-ffb3-4fcd-944c-efcb7de6a5fd2012-10-18 10:18:38.541 UTC0524104c-efee-44ad-a088-f428caefeb8d2012-10-30 10:41:29.116 UTCa0cb373d-9230-4224-8450-1128a876725a2012-10-31 12:11:53.522 UTCf9d69679-5e04-46e4-b77b-c70d19cb4c0d2012-07-13 08:51:15.886 UTC95e5f4d5-c433-4be8-852f-c338eac520492012-10-08 10:37:08.148 UTCa2cee785-18ef-4208-8677-b37970b920a72012-07-13 07:51:10.754 UTC87f752c3-6599-4607-8858-76f668ae65d22012-11-01 10:43:10.78 UTCacb06188-582e-4ece-91ab-034e55a571582012-10-23 15:39:06.238 UTC6e4e9dd0-334b-403a-9632-8423f9636fe72012-07-11 13:00:55.837 UTC85c44158-b0f7-4e74-a6d7-b2d0b0093cc22012-10-31 12:14:30.69 UTC3e775ac4-0bf5-435e-979e-26753958554c2012-07-13 06:22:29.620 UTC42e22b26-02a1-413f-99ef-dfa978e86c1f2012-10-23 14:48:02.159 UTCe8da845b-093d-4f3c-9e1c-8dbcfdb703fb2012-10-17 15:44:05.374 UTCStage Matrix Analysis2013-06-24 09:44:29.102 UTC1378f96b-c536-4968-a27f-2c7956207e6f2012-10-12 09:24:28.167 UTC9c7eab3e-170b-4f26-bb3e-bdc22eecec622012-11-01 11:51:49.687 UTC74f6db81-5630-4171-abfe-07de7363f0592012-10-29 13:43:44.823 UTCaab9fd22-7f16-41d7-a280-1f426ec850972012-10-23 15:42:20.102 UTCd63e1001-8c5e-4619-88e8-829e59b157c42012-09-28 08:44:45.610 UTCa8004bfd-bcb7-4f8f-986c-a4c03dc24ca72013-02-12 09:16:55.687 UTC734e5b89-dbe5-4ffc-8983-e3a2d1b8edc22012-11-01 10:47:38.765 UTC36fe5bbb-4c71-45c0-b68d-472ccadbcaba2012-11-01 10:14:45.687 UTC67747550-2202-4501-9737-d970ee30bbf32012-10-31 12:09:49.944 UTC21662d80-f207-4a54-9844-8f24acb91a272012-07-13 09:22:22.131 UTC2615d90a-7a5e-464e-89b6-20fec7bc10142012-07-13 09:11:19.100 UTCcc5b393c-818f-4016-a1d8-890885b584d32012-07-13 09:00:07.232 UTCba0a12e6-e2cc-428f-b901-978b4d2e83202012-10-18 11:26:48.0 UTCb43beb73-dc0f-46e8-955e-a812ec1eb70f2012-11-21 15:48:35.252 UTCf8683e08-b7e0-4a1b-a119-e977d6ba23e52012-12-09 23:15:12.16 UTC6bf5fc1d-7f9a-48a3-8b77-b4cf27f2b52a2012-10-17 14:47:18.255 UTC2de604ef-97f6-4f76-9392-556104352c062012-11-26 15:47:00.314 UTC214b1114-efbc-4d54-bb20-4fa1f9beb89f2012-09-20 13:37:17.940 UTCace5fe46-77ef-4a86-b67b-bde22c741ac82012-07-13 09:26:09.444 UTC28cbe7df-43ca-4479-a886-649875ad33df2012-10-30 15:59:46.983 UTC31de0f25-8b52-4b7c-a868-4eb26381b7682012-07-11 16:08:08.989 UTCe6fb6b0c-e37d-4469-ac93-c620d440011d2013-06-24 09:44:31.552 UTCd7781dea-d32c-4a00-a1b2-d67f151c32c22012-10-17 15:49:32.177 UTC92f46bea-cd6c-467d-b850-acfaf4f965812012-10-17 15:47:45.898 UTCc6242f65-5053-4fc2-979c-3b45e21ea38b2014-07-07 12:10:16.108 UTCe9b5e5d2-9871-4eba-b7a1-0635c8fc1bf52012-07-13 09:10:07.45 UTC9cc9920c-7d50-4c5b-9800-20cc1cfd72cf2012-09-20 14:54:19.489 UTC745cb63a-e27a-4cbf-8fc0-5a1be24ed0ac2012-11-01 10:17:46.562 UTCd98aaf13-21d0-487f-bb75-eec4eaf390a72012-10-29 13:45:38.787 UTCb0e4235a-5fe4-4228-a361-9dd543d8ec952012-09-19 15:33:22.278 UTCc2d28536-2e5b-45f0-aa16-8a7e15d668de2012-10-23 14:23:17.957 UTCdc590143-bfad-4167-b27c-b57aa45a0d962012-11-01 12:16:36.328 UTC6c9032a6-6f3a-43fc-85f7-4a65f24bdfa02012-10-30 11:05:28.590 UTC2d852a79-7b62-40cc-a176-aadadbfc2c032012-10-17 14:40:53.717 UTC290bff82-b044-4475-9f8a-65e5a8ee3c3b2012-11-01 11:51:22.265 UTC199c86f0-df6a-425c-b4dd-6aa852bcbff52012-07-13 09:03:22.271 UTCbf460b28-85d7-4bbd-bd14-a89dabcc1eb72012-11-01 11:56:17.546 UTCd7a4168c-96b3-4d07-8cd9-20e70968f5e62013-06-21 16:23:59.308 UTC6315c9ba-381a-44ce-82cd-ea6f5aae35d52012-07-13 09:27:13.462 UTC6933ad38-f960-4f05-ae40-0352c2a977232012-07-11 16:13:31.963 UTCcfc0e9b8-dfd4-48f7-8f9f-2c9c121fda8f2012-11-21 15:32:07.803 UTCe05732a8-9627-4bfa-b871-d8d4a9c53fb62012-07-11 20:55:29.517 UTC104a6f4f-33c3-4b8c-b4d7-55ac8fa330f72012-07-13 07:53:21.635 UTC480fcb53-df8f-4656-b52b-a1b8dd3d850d2012-10-23 15:04:23.405 UTC78851c10-ff00-4598-b0e3-e0e96ae2ddb22012-11-01 11:44:23.218 UTCff5bc61b-0d13-4622-adc8-2aedd7b7038c2012-07-13 09:20:52.134 UTC18e99b4e-e6d1-4c87-86cb-f4b3f40fec872012-07-13 08:43:47.651 UTCMaria Paula Balcázar-Vargas, Jonathan Giddy and Gerard Oostermeijer2012-10-30 15:58:04.755 UTC1426c3c1-f38e-452e-8b2a-d045c56296e12012-10-16 15:15:35.841 UTC27fa10ea-ca41-4311-b50c-eb7e2fe664892012-07-11 15:49:21.753 UTCa6efda97-4c1a-4ce4-9b65-6a87f8d11e782012-07-13 09:14:16.348 UTCbd483775-9c66-42a8-bf44-153f086ae7ba2012-10-26 10:38:50.743 UTC3e559db0-7ac1-47cf-b89a-aa9cbf3dd1352012-10-30 09:34:50.603 UTCb740ea7f-7c1a-4ae3-b632-e22a0879bd5c2012-10-12 09:21:33.957 UTCffaaa352-51bf-4d02-83af-18512fb8b0762013-06-10 15:07:19.413 UTCecaea223-12cf-4139-8d0e-03f7ee9539d02012-10-17 15:30:24.563 UTCd0b4659e-61e2-4b62-85f5-726a2f09105c2013-06-21 09:30:22.764 UTCd876c281-ea57-4da0-a470-f3bfbd4c7ad42012-07-11 13:05:24.619 UTCThe Matrix Population Models Workflow provides an environment to perform several analyses on a stage-matrix with no density dependence:
- Eigen analysis;
- Age specific survival;
- Generation time (T);
- Net reproductive rate (Ro);
- Transient Dynamics;
- Bootstrap of observed census transitions (Confidence intervals of λ).
This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.
This workflow was created using and based on Package ‘popbio’ in R. (Stubben & Milligan 2007; Stubben, Milligan & Nantel 2011).
Literature
==========
Caswell, H. 1986. Life cycle models for plants. Lectures on Mathematics in the Life Sciences 18: 171-233.
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
de Kroon, H. J., A. Plaiser, J. van Groenendael, and H. Caswell. 1986. Elasticity: The relative contribution of demographic parameters to population growth rate. Ecology 67: 1427-1431.
Horvitz, C., D.W. Schemske, and Hal Caswell. 1997. The relative "importance" of life-history stages to population growth: Prospective and retrospective analyses. In S. Tuljapurkar and H. Caswell. Structured population models in terrestrial and freshwater systems. Chapman and Hall, New York.
Jongejans E. & H. de Kroon. 2012. Matrix models. Chapter in Encyclopaedia of Theoretical Ecology (eds. Hastings A & Gross L) University of California, p415-423
Mesterton-Gibbons, M. 1993. Why demographic elasticities sum to one: A postscript to de Kroon et al. Ecology 74: 2467-2468.
Oostermeijer J.G.B., M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.
Stott, I., S. Townley and D.J. Hodgson 2011. A framework for studying transient dynamics of population projection matrix models. Ecology Letters 14: 959–970
Stubben, C & B. Milligan. 2007. Estimating and Analysing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22 (11): 1-23
Stubben, C., B. Milligan, P. Nantel. 2011. Package ‘popbio’. Construction and analysis of matrix population models. Version 2.3.1
van Groenendael, J., H. de Kroon, S. Kalisz, and S. Tuljapurkar. 1994. Loop analysis: Evaluating life history pathways in population projection matrices. Ecology 75: 2410-2415.2013-02-12 09:16:55.62 UTCde650b9e-a38c-4765-9e8f-a8b1429037172013-06-21 11:08:53.848 UTC5639ee4e-2035-4cc9-911f-fb435d58a9302012-10-07 22:14:42.810 UTC9159d5c8-8084-403e-9941-37a0babea12d2012-07-13 08:10:15.746 UTCc1878ed1-4b8e-4a7c-ba49-79e0aa4d6b732012-12-10 16:19:50.245 UTCe9fc8f5f-13bf-432d-875e-3c5858b128d02012-12-10 16:26:39.762 UTCf7125a55-d200-4c9f-9806-6b05549b428a2012-10-29 13:42:50.131 UTC4988e019-bf93-40bd-b095-6a33aec7e9682012-07-13 08:39:49.679 UTC11db6475-ebfc-492f-af7d-3a4185d279ce2012-09-19 15:49:14.786 UTCac5a0e53-1ce5-48c4-aa7f-857d0185c16f2012-10-26 10:36:36.257 UTCfbfe4abd-96b0-4223-94c1-eba2a2f968fb2012-10-23 09:36:25.955 UTC69d11822-5bf3-40d1-a6ce-cc0110a366dd2012-07-13 08:06:33.163 UTC9fa97e87-bd43-4312-a36f-8ac512988b802012-07-13 06:25:39.0 UTCe491d0ce-ea60-47c4-94f0-cb8f923433da2012-10-23 15:41:09.199 UTC8b100d25-27a9-4e50-893b-27ca7f42a4e22012-10-23 12:02:36.167 UTC5bdb4704-9322-4cbc-8d08-4b87aa1f23182012-07-11 22:49:36.115 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UTCSensitivity_and_Elasidentifier00stage_matrix11sensitivity_matrix1sensitivityPlot0elasticity_matrix1elasticityPlot0SensitivityPlotidentifier0stage_matrix1sensitivity_plot00sensitivity_matrix11net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falseidentifier0falsesensitivity_matrix11sensitivity_plot00falselocalhost6311falsefalsestage_matrixR_EXPidentifierSTRINGsensitivity_matrixR_EXPsensitivity_plotPNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeElasticityPlotidentifier0stage_matrix1elasticity_plot00elasticity_matrix11net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falseidentifier0falseelasticity_matrix11elasticity_plot00falselocalhost6311falsefalsestage_matrixR_EXPidentifierSTRINGelasticity_matrixR_EXPelasticity_plotPNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSensitivityPlotidentifierSensitivityPlotstage_matrixElasticityPlotidentifierElasticityPlotstage_matrixsensitivity_matrixsensitivityPlotelasticity_matrixelasticityPlotSensitivity and Elasticity2013-01-15 21:10:36.4 UTCb78e8e6c-0769-40b3-b651-d08340980d142013-01-15 21:09:58.530 UTC663c6c33-b50d-4927-ab0e-1ef45940f2242013-01-28 21:51:13.360 UTCba2da66c-56ad-4e93-b3e3-5acc4dbc3ec02013-01-15 21:30:56.337 UTCa97e4075-2be5-4271-8367-aa9258eda6992013-01-15 21:10:40.245 UTCTransientDynamicsstage_matrix110.0000 0.0000 0.0000 7.6660 0.0000
0.0579 0.0100 0.0000 8.5238 0.0000
0.4637 0.8300 0.9009 0.2857 0.8604
0.0000 0.0400 0.0090 0.6190 0.1162
0.0000 0.0300 0.0180 0.0000 0.02322012-10-04 14:37:42.656 UTCA stage matrix, it should be provied as a txt file.
Example from:
J. Gerard B. Oostermeijer; M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.2012-10-04 14:37:32.265 UTCplot_title00Here come the title of the plots. It can be the name of the species or the name of the place where the research has been conducted.2012-10-05 07:45:27.458 UTCGentiana pneumonanthe2012-10-05 09:01:55.697 UTClong_term_years00Number of the maximal iterations. How many iterations in the long-term will be run for the analysis.2012-10-05 07:47:22.811 UTCit can be any number:
e.g.:50, 100, etc.2012-10-04 14:39:24.906 UTCshort_term_years00it can be any number:
e.g.:5, 10, etc.2012-10-04 14:33:31.765 UTCNumber of iterations in the short-term. How many iterations in the short-term will be done for the analysis.2012-10-04 14:33:00.156 UTCabundances1169
100
111
21
432012-10-09 14:11:25.138 UTCThe initial abundance or observed structure per stage:
Example
Gentiana pneumonanthe matrix stage has 5 stages with its respective abundance:
stage abundance
1 S (seedlings) 69
2 J (Juveniles) 100
3 V (vegetative) 111
4 G (reproductive individuals) 21
5 D (dormant plants) 43
2012-10-09 14:11:10.929 UTCpop_projection0$lambda
[1] 1.237596
$stable.stage
S J V G D
0.14143023 0.16520742 0.65671474 0.02283244 0.01381517
$stage.vectors
0 1 2 3 4 5 6 7 8
S 69 160.9860 176.27660 188.67614 222.02436 266.74446 325.59268 400.23427 493.72709
J 100 183.9949 207.16241 222.06641 260.01317 312.04762 380.59040 467.67688 576.82384
V 111 257.9921 471.51823 694.37123 918.49323 1172.95942 1472.86815 1835.40557 2278.93197
G 21 22.9946 24.61207 28.96222 34.79578 42.47230 52.20901 64.40479 79.58338
D 43 5.9956 10.30280 14.94123 19.50731 24.78584 31.04973 38.64969 47.96428
9 10 11 12 13 14 15 16
S 610.08621 754.47932 933.40867 1154.9864 1429.2903 1768.8151 2189.0377 2709.1200
J 712.70787 881.35413 1090.35190 1349.1735 1669.5886 2066.1915 2557.0601 3164.5775
V 2824.80029 3498.56605 4331.35196 5361.3750 6635.7550 8212.7021 10164.1952 12579.2778
G 98.41890 121.75955 150.66351 186.4454 230.7351 285.5515 353.3942 437.3574
D 59.43826 73.60661 91.12249 112.7889 139.5967 172.7699 213.8226 264.6280
17 18 19 20 21 22 23 24
S 3352.7816 4149.3803 5135.2510 6355.3626 7865.3689 9734.1472 12046.940 14909.243
J 3916.4506 4846.9728 5998.5874 7423.8235 9187.6913 11370.6478 14072.266 17415.778
V 15568.1286 19267.0910 23844.8957 29510.3586 36521.9066 45199.3663 55938.553 69229.325
G 541.2706 669.8736 829.0324 1026.0069 1269.7818 1571.4766 1944.853 2406.942
D 327.5037 405.3179 501.6202 620.8033 768.3038 950.8497 1176.768 1456.363
25 26 27 28 29 30 31 32
S 18451.618 22835.646 28261.302 34976.071 43286.241 53570.874 66299.093 82051.486
J 21553.695 26674.765 33012.579 40856.232 50563.505 62577.186 77445.268 95845.945
V 85677.929 106034.653 131228.051 162407.296 200994.603 248750.094 307852.094 380996.486
G 2978.822 3686.577 4562.493 5646.522 6988.113 8648.460 10703.298 13246.358
D 1802.389 2230.629 2760.617 3416.529 4228.282 5232.904 6476.221 8014.944
33 34 35 36 37 38 39 40
S 101546.581 125673.63 155533.17 192487.21 238221.38 294821.80 364870.25 451561.92
J 118618.548 146801.83 181681.34 224848.08 278271.06 344387.11 426212.08 527478.31
V 471519.685 583550.82 722200.10 893791.88 1106153.15 1368970.59 1694232.38 2096775.03
G 16393.638 20288.70 25109.21 31075.06 38458.36 47595.91 58904.50 72899.97
D 9919.262 12276.04 15192.77 18802.51 23269.91 28798.75 35641.22 44109.42
41 42 43 44 45 46 47 48
S 558851.18 691631.92 855960.83 1059333.6 1311026.9 1622521.5 2008026.0 2485124.7
J 652804.99 807908.78 999864.58 1237428.3 1531436.2 1895299.1 2345614.4 2902922.7
V 2594960.16 3211512.02 3974554.08 4918891.8 6087600.3 7533989.1 9324033.9 11539386.0
G 90220.70 111656.77 138185.96 171018.4 211651.6 261939.2 324174.9 401197.5
D 54589.64 67559.91 83611.87 103477.7 128063.6 158491.0 196147.8 242751.7
49
S 3075580.1
J 3592645.2
V 14281096.7
G 496520.4
D 300428.5
$pop.sizes
[1] 3.440000e+02 6.319632e+02 8.898721e+02 1.149017e+03 1.454834e+03 1.819010e+03
[7] 2.262310e+03 2.806371e+03 3.477031e+03 4.305452e+03 5.329766e+03 6.596899e+03
[13] 8.164769e+03 1.010497e+04 1.250603e+04 1.547751e+04 1.915496e+04 2.370613e+04
[19] 2.933864e+04 3.630939e+04 4.493635e+04 5.561305e+04 6.882649e+04 8.517938e+04
[25] 1.054177e+05 1.304645e+05 1.614623e+05 1.998250e+05 2.473027e+05 3.060607e+05
[31] 3.787795e+05 4.687760e+05 5.801552e+05 7.179977e+05 8.885910e+05 1.099717e+06
[37] 1.361005e+06 1.684374e+06 2.084574e+06 2.579860e+06 3.192825e+06 3.951427e+06
[43] 4.890269e+06 6.052177e+06 7.490150e+06 9.269779e+06 1.147224e+07 1.419800e+07
[49] 1.757138e+07 2.174627e+07
$pop.changes
[1] 1.837102 1.408107 1.291216 1.266155 1.250321 1.243704 1.240489 1.238977 1.238255
[10] 1.237911 1.237746 1.237668 1.237630 1.237612 1.237604 1.237600 1.237598 1.237597
[19] 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596
[28] 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596
[37] 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596 1.237596
[46] 1.237596 1.237596 1.237596 1.237596
2012-10-04 14:53:34.718 UTCPopulation projection
The results of a matrix population analysis are a set of demographic statistics:
1) Lambda or dominant eigenvalue: The population will be stable, grow or decrease at a rate given by lambda: e.g.: λ = 1 (population is stable), λ > 1 (population is growing) and finally λ < 1 (population is decreasing).
2) The stable stage distribution: The stable population distribution is given by (w). It is the proportion of the number of individuals per stage.
3) Stage vector (stage.vectors): it is the projection of the number of individuals per stage per year in the long-term (e.g. 50 years).
4) Population sizes (pop.sizes): is the total population size in the long-term (e.g. 50 years).
5) Population change (pop.changes): are the lambda values per year in the long-term (e.g. 50 years).
For further details see Caswell 2001.
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
2012-10-05 08:54:10.519 UTCstage_vector_plot_short_term02012-10-04 14:52:06.984 UTCPlot the number of individuals per stage in the short-term vs years (e.g. 5, 10 years). This value is related to the short-term_years input value. 2012-10-05 07:50:04.913 UTCstage_vector_plot_long_term_proportional0Plot the proportion of individuals per stage in the short-term vs years (e.g. 5, 10 years). This value is related to the short-term_years input value. 2012-10-05 08:56:44.554 UTCstage_vector_plot_long_term_logarithmic0Plot the number of individuals per stage in the long-term vs years (e.g. 50 years). This value is related to the long-term_years input value. 2012-10-05 07:51:23.365 UTCdamping_ratio0StageVectorPlot_ShortTermiterations0plotTitle0populationProjection1stageVectorPlot00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitypopulationProjection1falseplotTitle0falseiterations0falsestageVectorPlot00falselocalhost6311falsefalsepopulationProjectionR_EXPplotTitleSTRINGiterationsINTEGERstageVectorPlotPNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokePopulationProjectionabundances1years0stageMatrix1populationProjection11net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystageMatrix1falseabundances1falseyears0falsepopulationProjection11falselocalhost6311falsefalsestageMatrixR_EXPabundancesINTEGER_LISTyearsINTEGERpopulationProjectionR_EXPnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeDisplayRExpressioninput1output00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivityinput1falseoutput00falselocalhost6311falsefalseinputR_EXPoutputTEXT_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeStageVectorPlot_LongTermProportionaliterations0plotTitle0populationProjection1stageVectorPlot00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitypopulationProjection1falseplotTitle0falseiterations0falsestageVectorPlot00falselocalhost6311falsefalsepopulationProjectionR_EXPplotTitleSTRINGiterationsINTEGERstageVectorPlotPNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeDampingRatiostageMatrix1dampingRatio00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystageMatrix1falsedampingRatio00falselocalhost6311falsefalsestageMatrixR_EXPdampingRatioDOUBLEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeStageVectorPlot_LongTermLogarithmicplotTitle0populationProjection1iterations0stageVectorPlot00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitypopulationProjection1falseplotTitle0falseiterations0falsestageVectorPlot00falselocalhost6311falsefalsepopulationProjectionR_EXPplotTitleSTRINGiterationsINTEGERstageVectorPlotPNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeStageVectorPlot_ShortTermiterationsStageVectorPlot_ShortTermplotTitleStageVectorPlot_ShortTermpopulationProjectionPopulationProjectionabundancesPopulationProjectionyearsPopulationProjectionstageMatrixDisplayRExpressioninputStageVectorPlot_LongTermProportionaliterationsStageVectorPlot_LongTermProportionalplotTitleStageVectorPlot_LongTermProportionalpopulationProjectionDampingRatiostageMatrixStageVectorPlot_LongTermLogarithmicplotTitleStageVectorPlot_LongTermLogarithmicpopulationProjectionStageVectorPlot_LongTermLogarithmiciterationspop_projectionstage_vector_plot_short_termstage_vector_plot_long_term_proportionalstage_vector_plot_long_term_logarithmicdamping_ratio482df01a-aece-421a-87e6-87c6fed3098c2012-04-27 06:16:05.128 UTC26a58a12-7058-4ecc-8626-8f4208df050d2012-04-27 06:37:14.879 UTC9980e502-edf8-45be-b834-da4a69c1aa6f2012-06-27 09:38:41.13 UTC8237763e-e3d3-4a89-8154-c0e7ebe6ac992012-03-30 15:58:10.751 UTCPlots short-term dynamics and convergence to stage stage distribution using stage vector projections.2012-10-04 12:48:21.328 UTC50ed42f5-cfdb-479b-bc87-3a1130c06c8e2012-10-09 13:56:14.799 UTC5ad8da23-95d6-4f62-b1fc-82689c17ffd72012-03-30 15:52:40.327 UTCcfe0f676-d994-4cf6-9af7-e7b8b4ce60832012-04-27 10:33:07.555 UTCc2e78088-fb3a-46f2-a1d2-fa7b6006145a2012-06-08 05:42:53.3 UTC9dc4d45e-3705-4870-8cc3-759ff54fad392012-12-09 22:19:23.950 UTCbed37407-0362-4432-81ed-8ced9db83ac62012-06-08 05:40:45.808 UTC9181aeeb-ce88-4d0f-b3f1-ca04d8cb6cb22012-10-09 13:43:45.648 UTCc7182021-afb1-4b3b-a037-bffc16704a972012-10-09 14:03:43.190 UTC5ddec6d6-2ef8-4a1b-8905-4ebc313e8a5f2012-03-30 15:53:45.576 UTC4bf67caa-4057-482b-8fa2-201dd700c14d2012-10-04 14:09:13.546 UTC1bc8b332-e0fa-4c1b-9693-2e7b0297d6352012-06-08 07:34:34.886 UTC78e91f82-285c-41a9-9cab-b239833395052012-10-10 10:21:45.737 UTCec89a2f1-8fc4-4aa1-b584-32891b8f7e052012-12-09 22:27:30.688 UTCdfd3a284-1086-4b13-be02-2f6e9367c6da2012-10-05 08:18:11.541 UTC3da39227-d90d-44b6-93e6-a5c6c6635c282012-03-30 15:42:09.674 UTCc4f7056b-5e74-4606-a058-96a8bea622002012-04-27 10:33:54.68 UTCThis Workflow was created by:
Maria Paula Balcázar-Vargas, Jonathan Giddy and G. Oostermeijer
This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.
This workflow was created based on Package ‘popbio’ in R.
Stubben, C & B. Milligan. 2007. Estimating and Analysing Demographic Models Using the popbio Package in R. Journal of Statistical Software 22 (11): 1-23
Stubben, C., B. Milligan, P. Nantel. 2011. Package ‘popbio’. Construction and analysis of matrix population models. Version 2.3.1
The example is based on data of the article:
J. Gerard B. Oostermeijer; M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.
2012-10-04 14:16:32.93 UTC60c89fa1-3c42-4a86-98d4-d6aaf4dc5b362012-06-08 06:21:13.990 UTCee381abc-87db-425f-b791-d11417b8b3482012-12-03 14:00:05.316 UTCccb806f8-855c-494f-b2c7-c6ae4d1269d22012-10-09 13:40:13.59 UTCe2df4fe0-58a3-4d72-a606-2324a82cbea72012-10-04 15:01:46.375 UTCbbd91183-5416-4e35-9f8b-ff03ef6a41802012-06-08 05:51:09.38 UTCa13d1602-6348-41b1-889f-0f073bc102be2012-10-09 14:08:03.638 UTC4313b672-b3a3-4bda-923a-01649203aa3d2012-10-09 13:36:17.347 UTC16009d1d-4920-4fb6-8195-a471141396672012-10-04 14:33:41.78 UTC62b72d3b-11fe-48a9-a55a-5ccf2c9215b02012-10-04 14:17:26.78 UTCc3000dba-a0f1-40f4-a168-de916bebc7902012-06-08 05:43:58.397 UTCe7224c60-2256-4a64-b82c-6b4c8712edd12012-12-03 14:08:40.399 UTC899640f6-c19b-4a69-bd65-aebd8ff84a432012-06-27 09:42:10.621 UTCf4dfa9b1-5f6a-46a6-a7ab-5a660a1735eb2012-04-27 06:33:44.26 UTC25c69bcd-ad78-444f-bfe1-db3b3ad627e02012-06-08 07:17:05.238 UTCe4416b66-0517-4982-9ffc-07d9225b4cb42012-04-27 10:20:27.369 UTCb4a948a5-2b99-4d2c-9a59-abe7fa51e5ef2012-06-08 06:12:12.618 UTC3fed235c-fd94-4f38-b0f9-c67673d4cdec2012-10-09 13:58:41.10 UTC1866cddd-542f-43a6-b4a7-86d0be66758e2012-06-27 09:47:27.817 UTCbe4e3ff1-a001-453f-9159-dc9657d4fcdb2012-06-08 05:58:16.24 UTCf9a14997-e7a6-42c3-a068-71946a6c7b152012-10-09 13:42:51.352 UTCbe119d16-31e9-4d74-b9f4-7b640d9fef702012-10-05 09:02:21.629 UTC29186c39-3022-4d52-90d0-8f7fd7bcef272012-03-30 15:47:32.455 UTC64fd8865-03e2-4f14-a3cb-0bf43cf68a952012-12-09 22:46:43.753 UTC0c1873c5-fc98-40c8-960c-bd11f90600722012-06-27 09:34:26.127 UTC14392d07-d8b9-4f50-bc62-0b34587632522012-06-08 06:07:15.536 UTC6dcdcc0c-b4b0-4951-8f57-c053e86d11732012-10-09 14:46:10.18 UTC348192ff-7a44-4a75-a3b4-af3adf25ea2b2012-04-27 06:08:00.914 UTC8c458bf5-19ef-437d-a53b-a5bfa71620712012-06-08 07:11:39.27 UTC7681491c-5178-4844-b9b1-e1c1ba4e29852012-04-27 10:36:47.808 UTCTransientDynamics2012-10-09 13:49:13.614 UTCe62695c3-51aa-4a6d-8618-f111c476b87b2012-06-08 07:13:44.794 UTCfab797b4-caba-41ee-983a-0b82921a56d62012-10-09 13:38:51.290 UTCd84c371a-5a45-44a0-b9fe-b50e31ef11042012-10-09 12:52:29.315 UTCf364089f-de01-4c6d-b4e8-3e0f55f8952f2012-06-08 06:30:14.837 UTCd8579ad9-6856-4e71-8d42-54c9c2fe45de2012-10-05 07:52:04.725 UTCd9a48043-0b5b-4f0e-9e40-42b08aaeba1c2012-10-05 08:56:43.888 UTC78f7c0e0-4894-455e-a7f5-bf542b33cfb52012-10-09 13:04:40.706 UTC37008dc3-b641-4ce5-8171-e51acb9a75102012-10-04 14:21:17.734 UTCa1894ac9-e16b-44c6-b709-02959523bed22012-10-09 14:47:19.421 UTC788d36a7-3aa5-4635-8fda-6cc6d14a7aea2012-10-04 14:50:33.78 UTCeb48f388-bf67-4cc3-b1f1-0ee942b43bfb2012-10-04 12:59:19.203 UTC6a5c611c-cfcf-4964-9c89-f254b5521e152012-04-26 16:16:27.814 UTC1e66a160-d9a3-485d-b31e-cac2c674a2962012-03-30 15:59:19.350 UTC068f4c47-ac93-41d1-928b-e5313ddf7dc92012-03-30 15:27:01.885 UTC2f339d19-c529-4042-b690-13266e3241d72012-06-08 07:10:18.943 UTC513eb95e-60b6-4fda-925b-db4b1892790f2012-06-08 05:40:34.264 UTC7216d451-461d-432f-9858-375bfad4589f2012-10-10 10:26:15.139 UTCb4a946c8-ae89-4e65-961d-5dcd474c82e82012-06-08 05:49:37.212 UTC09f91d33-9f50-4983-96c9-1335ed1f92b42012-04-27 06:19:38.161 UTC9552ea69-d7d6-43aa-a531-26fb89191ac82012-10-09 13:45:12.180 UTCe834859b-80bc-471c-9d69-a382eb1beed02012-10-09 13:49:16.0 UTCd3856b08-20d7-4f7d-8d0f-7cefebd654f02012-06-08 05:56:58.172 UTC0810da52-a748-4a3b-9740-3cf38d6402032012-12-09 22:31:58.714 UTC2a67baca-21bc-4bc2-8e77-0754a7070ef32012-06-08 06:05:07.24 UTC02cee0a9-6b44-4fce-83ef-05c6e79f90e92012-10-09 13:09:14.294 UTC2c5e0d30-c7a5-4522-ae68-29747b6469e02012-10-09 13:54:33.792 UTC60f62b14-9402-4458-987b-424ebf5efc652012-10-04 13:05:46.15 UTCbfd39e81-094d-4674-be1c-1e5fca6b53ec2012-06-07 14:06:09.942 UTC66a08a91-50e5-4bf9-a380-7b43eb4c23b12012-10-05 08:56:55.858 UTC940fe2e3-58d4-475d-8bcf-3ede6bf0dabb2012-06-08 07:47:49.992 UTCc1c17ab3-ff6e-4202-90f2-8269713273402012-06-27 08:45:51.822 UTC5bfc6007-31f4-4868-b2ee-e0a6513d2d7b2012-10-09 14:11:26.845 UTC553eb85d-393a-488a-84ae-6190b23e80cc2012-03-30 15:56:49.708 UTC4ea704d2-63f2-441a-8b1f-db2f572016032012-06-08 07:06:43.835 UTC227fbad4-3ec7-49f6-951e-ff5ffdba467a2012-10-04 14:34:38.515 UTCd019b4fb-2652-4df1-ae4f-11fbb1c392a32012-12-09 22:48:22.305 UTC93fa7d2f-2e7f-44b4-94e2-eb7f16cd96fc2012-10-10 10:17:18.104 UTCf8df75ad-a80d-48c5-ae5b-898c201797bd2012-12-09 22:29:52.759 UTC66e667a6-2f27-489f-bdd5-515c37eb3dd12012-10-09 13:51:04.114 UTC4363668a-7ee4-42d3-8368-ff96c8e665a92012-10-04 14:56:18.125 UTCd61ce379-a6c6-44c3-9527-a85fdb337fd92012-10-09 13:48:46.384 UTCdcabfdeb-51a1-4ac8-91d0-f50ef43f28bb2012-06-08 07:04:17.60 UTCcc338b70-bb81-4797-b81d-fa105fda843d2012-06-27 09:34:01.127 UTC9e035cc1-afd5-4e6e-a6aa-d2a51d92b30d2012-10-09 13:17:10.236 UTCa882140e-69ee-4bd3-a75c-63fb903629452012-06-08 06:23:08.447 UTC99a5ecac-18df-45ae-bbfa-d180b0469b442012-06-08 07:14:48.566 UTC85e5205a-e20f-42a5-85b6-857a1bcf67512012-04-27 10:04:31.201 UTCc666682d-b97f-4ae5-a33a-2c2dbd8cc73a2012-06-27 09:44:02.36 UTCFundamental_matrixstage_matrix110.0000 0.0000 0.0000 7.6660 0.0000
0.0579 0.0100 0.0000 8.5238 0.0000
0.4637 0.8300 0.9009 0.2857 0.8604
0.0000 0.0400 0.0090 0.6190 0.1162
0.0000 0.0300 0.0180 0.0000 0.0232
2012-10-03 14:34:31.812 UTCThe stage matrix file input port:
Here comes the stage matrix without the stage names (as you see in the example). It should be provied as a txt-file.
Example from:
J. Gerard B. Oostermeijer; M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.2012-10-10 12:44:04.359 UTCrows_fecundity11To perform the fundamental matrix analysis N, the row(s) in which the recruitment values are found, should be selected.
In the example of the Gentiana species (Oostermeijer et al. 1996. The Journal of Ecology):
Selected lines are S and J (seedlings and juveniles, these stages receive recruits each year from the stage G): therefore, the numbers 1 and 2 are used to identify these rows.
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
2012-10-11 12:34:12.781 UTC1
22012-10-10 12:36:41.765 UTCcolumns_fecundity1142012-10-10 12:36:25.328 UTCTo perform the fundamental matrix analysis N, the column(s) in which the fecundity values are found, should be selected.
In the example of the Gentiana species (Oostermeijer et al. 1996. The Journal of Ecology):
The selected column is G (reproductive individuals): therefore number 4 will be used to identify the fecundity column (G).
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
2012-10-10 12:38:41.968 UTCfundamental_matrix1$N
S J V G D
S 1.00000000 0.0000000 0.0000000 0.0000000 0.0000000
J 0.05848485 1.0101010 0.0000000 0.0000000 0.0000000
V 6.88603853 11.9918695 13.3528343 10.0128734 12.9527790
G 0.20805087 0.4661775 0.3904662 2.9174703 0.6909984
D 0.12868882 0.2520032 0.2460596 0.1845124 1.2624386
$var
S J V G D
S 0.00000000 0.00000000 0.0000000 0.0000000 0.0000000
J 0.05624588 0.01020304 0.0000000 0.0000000 0.0000000
V 129.59269836 164.45409019 164.9453506 157.1299726 165.1853617
G 0.96262845 2.03661916 1.7354172 5.5941629 2.8634574
D 0.17967383 0.32076827 0.3146653 0.2473139 0.3313126
$cv
S J V G D
S 0.000000 NaN NaN NaN NaN
J 4.055104 0.100000 NaN NaN NaN
V 1.653183 1.069388 0.9618261 1.2519033 0.9922539
G 4.715848 3.061284 3.3737933 0.8107017 2.4488847
D 3.293833 2.247448 2.2797338 2.6952479 0.4559411
$meaneta
S J V G D
8.281263 13.720151 13.989360 13.114856 14.906216
$vareta
S J V G D
143.2630 181.0125 181.4811 177.0582 181.0617
2012-10-10 12:56:28.203 UTCThe fundamental matrix workflow gives the basic information on age-specific survival, this includes the mean, variance and coefficient of variation (cv) of the time spent in each stage class and the mean and variance of the time to death.
Fundamental matrix (N): is the mean of the time spent in each stage class
E.g.:For our Gentiana example means a J plants will spends, on average, about 1 year as a Juvenile, 11 as vegetative plant, less than a year a reproductive and dormant plant.
Variance (var): is the variance in the amount of time spent in each stage class.
Coefficient of variation (cv): is the coefficient of variation of the time spent in each class (sd/mean- the ratio of the standart deviation to the mean).
Meaneta: is the mean of time to death, of life expectancy of each stage.
E.g.:The mean age at death is the life expectancy; the life expectancty of a new individual seedling is 8 years.
Vareta: is the variance of time to death
For further information please see
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
2012-10-10 12:59:24.859 UTCfundamental_matrixcolumns1rows1stage_matrix1a11net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falserows1falsecolumns1falsea11falselocalhost6311falsefalsestage_matrixR_EXProwsDOUBLE_LISTcolumnsDOUBLE_LISTaR_EXPnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Invokefundamental_matrixcolumnsfundamental_matrixrowsfundamental_matrixstage_matrixfundamental_matrix514adf8d-61fa-467f-9395-f5979832478d2012-10-10 12:42:45.593 UTC5af80ab8-1db1-4552-a538-92256862e14e2012-09-26 14:20:30.218 UTC573c3e8c-5192-4dcd-a1b1-4c69d93185d82012-10-03 13:17:26.78 UTC64fd75c1-1560-485f-9e95-f556f284ea0a2012-10-03 14:35:02.156 UTC7bb65b13-5427-4b64-bf88-b97ba2bd87c82012-10-11 11:57:47.796 UTC1d18264c-9c31-446e-b5fe-faf419d8697b2012-10-03 14:35:35.765 UTC5d52fc73-4937-4ab4-a7fb-ff38d0384a112012-10-30 07:01:53.978 UTC02ba332a-4054-4142-88ef-9d17ab76aa382012-10-10 12:43:36.218 UTC26a58a12-7058-4ecc-8626-8f4208df050d2012-04-27 06:37:14.879 UTC044bc39f-c00c-4683-aec3-9b467473c8942012-10-10 12:44:06.562 UTC6a5c611c-cfcf-4964-9c89-f254b5521e152012-04-26 16:16:27.814 UTCdb524ca2-dc25-4036-b866-fb6f2449f18b2012-09-28 15:07:54.812 UTCf4dfa9b1-5f6a-46a6-a7ab-5a660a1735eb2012-04-27 06:33:44.26 UTCMaria Paula Balcázar-Vargas, Jonathan Giddy and Gerard Oostermeijer2012-10-10 12:20:09.765 UTC252c40b1-ea29-47e7-bf0f-3af7aab03d0c2012-10-10 12:47:26.968 UTCae90fa83-15d4-42a1-b5fc-75f5b05405552012-09-26 14:28:58.906 UTC85e5205a-e20f-42a5-85b6-857a1bcf67512012-04-27 10:04:31.201 UTCe1d1c2a5-29c1-4939-b4b2-0980a2dceaea2012-10-10 12:30:26.453 UTC03f85255-cd88-4d89-b6b6-40c5c6eae7f52012-10-10 12:59:26.406 UTC5ad8da23-95d6-4f62-b1fc-82689c17ffd72012-03-30 15:52:40.327 UTC88ba65a7-98b4-4f47-89d6-836e7c1fa9c12012-09-26 14:26:56.765 UTCFundamental matrix2012-09-26 14:05:47.140 UTC482df01a-aece-421a-87e6-87c6fed3098c2012-04-27 06:16:05.128 UTC29186c39-3022-4d52-90d0-8f7fd7bcef272012-03-30 15:47:32.455 UTC553eb85d-393a-488a-84ae-6190b23e80cc2012-03-30 15:56:49.708 UTC554ae0b3-6ab6-4242-9607-94afd162770d2012-10-03 13:28:40.515 UTC73569abf-949f-48f6-92cf-9d91b9b9fc5b2012-10-10 12:59:04.609 UTC028669ad-d798-4123-bf4a-b99951b64e182012-10-11 11:46:36.203 UTC068f4c47-ac93-41d1-928b-e5313ddf7dc92012-03-30 15:27:01.885 UTC1e66a160-d9a3-485d-b31e-cac2c674a2962012-03-30 15:59:19.350 UTC67f6d5fc-c41e-4a15-aa70-06a91d869ca32012-09-26 14:09:13.187 UTCe4172fb8-fbf4-4a13-aad8-b4ea9a55fcaa2012-09-28 15:08:43.718 UTC348192ff-7a44-4a75-a3b4-af3adf25ea2b2012-04-27 06:08:00.914 UTC09f91d33-9f50-4983-96c9-1335ed1f92b42012-04-27 06:19:38.161 UTC4953ee13-f5cd-4472-9bc9-19401eef9af42012-10-11 12:39:20.734 UTC808d955e-b242-463f-9ab0-3e5526d243912012-10-30 07:03:42.367 UTC8237763e-e3d3-4a89-8154-c0e7ebe6ac992012-03-30 15:58:10.751 UTC3da39227-d90d-44b6-93e6-a5c6c6635c282012-03-30 15:42:09.674 UTCThe fundamental matrix workflow gives the basic information on age-specific survival, this includes the mean, variance and coefficient of variation (cv) of the time spent in each stage class and the mean and variance of the time to death.
Fundamental matrix (N): is the mean of the time spent in each stage class
Variance (var): is the variance in the amount of time spent in each stage class.
Coefficient of variation (cv): is the coefficient of variation of the time spent in each class (sd/mean- the ratio of the standart deviation to the mean)
Meaneta: is the mean of time to death, of life expectancy of each stage.
Vareta: is the variance of time to death
For more information see:
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts (pag 118-120)2012-10-10 12:35:37.812 UTC5ddec6d6-2ef8-4a1b-8905-4ebc313e8a5f2012-03-30 15:53:45.576 UTCe4416b66-0517-4982-9ffc-07d9225b4cb42012-04-27 10:20:27.369 UTCfae44800-e1c6-41e0-9784-aa2a44d757512012-09-28 12:28:31.62 UTCCohen_Cumulativeabundances11stage_matrix11cohenCumulative0CalculateCohenCumulativeDistanceabundances1stage_matrix1cohen_cumulative00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falseabundances1falsecohen_cumulative00falselocalhost6311falsefalsestage_matrixR_EXPabundancesINTEGER_LISTcohen_cumulativeDOUBLEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeCalculateCohenCumulativeDistanceabundancesCalculateCohenCumulativeDistancestage_matrixcohenCumulativeCohen Cumulative2013-01-22 06:45:54.433 UTC4403aaae-f67d-4cde-8d3e-6f8f9c817f652013-01-22 06:45:32.736 UTCe420b581-0054-4d82-af0e-79182396dcc62013-01-22 06:45:58.176 UTC350ad4f3-8adb-42a8-bfd6-b9a67cdb739d2013-01-22 07:43:36.673 UTCSurvival_CurvestageMatrix11plotTitle00fecundityRows11fecundityCols11survivalCurvePlot0SurvivalCurvePlotsurvival_curve1plot_title0survival_curve_plot00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitysurvival_curve1falseplot_title0falsesurvival_curve_plot00falselocalhost6311falsefalsesurvival_curveR_EXPplot_titleSTRINGsurvival_curve_plotPNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSurvivalCurveAnalysisstage_matrix1fecundity_rows1fecundity_cols1survival_curve11net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falsefecundity_rows1falsefecundity_cols1falsesurvival_curve11falselocalhost6311falsefalsestage_matrixR_EXPfecundity_rowsINTEGER_LISTfecundity_colsINTEGER_LISTsurvival_curveR_EXPnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSurvivalCurvePlotsurvival_curveSurvivalCurvePlotplot_titleSurvivalCurveAnalysisstage_matrixSurvivalCurveAnalysisfecundity_rowsSurvivalCurveAnalysisfecundity_colssurvivalCurvePlotf0a5f728-ae5b-4bc7-9c1a-c3ae7aaea52e2013-01-11 16:26:13.108 UTC79a3f183-ee97-44d4-a995-2d3ee3ea86e52013-01-11 16:27:47.11 UTCd889120e-eaaa-42aa-be59-547f441203cf2013-01-11 16:47:59.509 UTCe42c0737-b2cc-4e9a-a418-e7e50dc76d482013-01-10 15:39:38.567 UTC7ce04ea6-9907-4d42-b256-746a89ed4a0e2013-01-11 17:25:34.447 UTCe406cf24-e16f-412b-8582-3d93c7f480f82013-01-11 16:57:10.541 UTCa906ae6a-90f1-419a-ba1d-ab69c2e93bc92013-01-10 16:10:54.72 UTC177eccf2-2fce-4c09-94a0-c2c5fa77ecee2013-01-10 15:41:43.396 UTCMaria Paula Balcázar-Vargas, Jonathan Giddy and G. Oostermeijer2013-01-10 15:40:36.927 UTCee31a943-928e-40bb-92ec-c7800db0159a2013-01-11 16:52:44.937 UTC6acb547e-2799-455a-9b3d-6226cdc1e4122013-01-11 16:59:47.395 UTCSurvival Curve2013-01-10 15:39:58.997 UTC4d6db02f-1eb1-424b-843e-f9fd3d691ba52013-01-10 16:40:49.38 UTCf1d94c22-ea2b-4e64-ae0b-0e669c250d452013-01-11 16:58:36.13 UTCa7f508b3-cf63-4714-a790-29aa80fea05e2013-01-11 16:11:35.296 UTC7a05fca2-4829-4703-821a-15c82eeb29b82013-01-11 16:15:08.904 UTC9bb967c3-0f4d-41ec-8df1-4e41927366e82013-01-10 15:40:37.18 UTC5238b5e0-4a59-4eef-9bda-ed668dbacd0e2013-01-11 16:55:31.203 UTCbca1bd86-921e-4a5e-8781-c512073d78f32013-01-11 16:24:51.231 UTCcb903810-0b79-43bb-add5-05a1726756502013-01-11 16:10:12.451 UTCc9aa8a4f-e132-4e41-a439-970908abd5b72013-01-11 16:50:21.663 UTCc3ee08d1-b7e2-4c53-8a53-3c5cdf3937832013-01-09 17:16:37.963 UTCe4074c6e-68d0-4109-aa2f-fb9e2fc9fc162013-01-11 17:23:58.83 UTCe8a0eb32-29ea-4d29-b1c0-109609bbf2382013-01-11 16:20:59.585 UTCKeyfitz_Deltaabundances11stage_matrix11keyfitzDelta0CalculateKeyfitzDeltaabundances1stage_matrix1keyfitz_delta00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falseabundances1falsekeyfitz_delta00falselocalhost6311falsefalsestage_matrixR_EXPabundancesINTEGER_LISTkeyfitz_deltaDOUBLEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeCalculateKeyfitzDeltaabundancesCalculateKeyfitzDeltastage_matrixkeyfitzDeltaKeyfitz Delta2013-01-22 10:43:22.424 UTC2bbadcb3-679a-4798-83a7-1fd99ae7d8982013-01-22 10:45:01.682 UTC350ad4f3-8adb-42a8-bfd6-b9a67cdb739d2013-01-22 07:43:36.673 UTC4403aaae-f67d-4cde-8d3e-6f8f9c817f652013-01-22 06:45:32.736 UTCe420b581-0054-4d82-af0e-79182396dcc62013-01-22 06:45:58.176 UTCGeneration_time__T_stage_matrix110.0000 0.0000 0.0000 7.6660 0.0000
0.0579 0.0100 0.0000 8.5238 0.0000
0.4637 0.8300 0.9009 0.2857 0.8604
0.0000 0.0400 0.0090 0.6190 0.1162
0.0000 0.0300 0.0180 0.0000 0.02322012-10-05 11:35:18.26 UTCA stage matrix
In this import port a stage-matrix should be add. The input data (a .txt-file) has to be a point delimited (see example).
In the pop-up ‘run workflow’ window, click-on ‘set a location’ and seach in your computer the txt-file of your matrix.
Example from:
J. Gerard B. Oostermeijer; M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.2012-10-11 11:35:59.0 UTCrows_fecundity111
22012-10-11 11:53:42.500 UTCTo perform the generation time (T), the row(s) the row(s) in which the recruitment values are found, should be selected.
In the example of the Gentiana species (Oostermeijer et al. 1996. The Journal of Ecology):
Selected lines are S and J (seedlings and juveniles, these stages receive recruits each year from the stage G): therefore, the numbers 1 and 2 are used to identify these rows (S and J).
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
2012-10-11 12:42:20.515 UTCcolumns_fecundity1142012-10-11 11:58:22.562 UTCTo perform the generation time (T), the column(s) in which the fecundity values are found, should be selected.
In the example of the Gentiana species (Oostermeijer et al. 1996. The Journal of Ecology):
The selected column is G (reproductive individuals): therefore number 4 will be used to identify the fecundity column (G).
S J V G D
S 0.0000 0.0000 0.0000 7.6660 0.0000
J 0.0579 0.0100 0.0000 8.5238 0.0000
V 0.4637 0.8300 0.9009 0.2857 0.8604
G 0.0000 0.0400 0.0090 0.6190 0.1162
D 0.0000 0.0300 0.0180 0.0000 0.0232
2012-10-11 12:42:12.468 UTCgeneration_time0Generation time (T):
The time T required for the population to increase by a factor of Ro (net reproductive rate)
e.g.: If Ro (net reproductive rate) = 5.56 and T (generation time) = 8.055
The average plant of the species Gentiana pneumonanthe in Terschelling in the year 1987 replaced itself with almost six new plants and took approximately 8.05 years to do so.
2012-10-11 12:03:38.359 UTC8.0552012-10-17 13:36:56.312 UTCGenerationTimeAnalysiscolumns1rows1stage_matrix1result00net.sf.taverna.t2.activitiesrshell-activity1.5-SNAPSHOTnet.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falserows1falsecolumns1falseresult00falselocalhost6311falsefalsestage_matrixR_EXProwsDOUBLE_LISTcolumnsDOUBLE_LISTresultDOUBLEnet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5-SNAPSHOTnet.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeGenerationTimeAnalysiscolumnsGenerationTimeAnalysisrowsGenerationTimeAnalysisstage_matrixgeneration_timec4bce93c-e05f-433c-9f0f-36cb69f249e72012-10-05 11:49:57.167 UTCe2a9d92c-412f-47fc-a567-39a56abe723e2012-06-15 06:52:47.83 UTC6cefb97d-5207-40ec-847d-6b62cabd12cb2012-06-15 06:56:38.363 UTC18aac4ef-4208-458c-9dbb-9a2e5ee2f3f92012-06-21 14:24:41.784 UTCf589ea15-b89d-415f-b16b-71d6b6abcc592012-09-28 08:41:41.388 UTC91b0ec46-9891-4238-b9e2-57af321626a32012-10-30 10:31:22.988 UTCf29cd8ec-6fe8-4962-9bbc-7c99ef58365d2012-10-11 11:52:57.562 UTCa67ab916-ab83-4d04-acc1-750adbebbea42012-10-11 12:03:39.671 UTCc7b6d5dd-ddc3-4388-9f28-647b74d4f5f42012-06-15 06:54:00.692 UTCd9758ade-7727-44a4-aa75-d0fac485df0d2012-10-17 13:37:14.171 UTCb5ec6e6b-d9bd-43b3-86d4-f33bd56402432012-10-05 11:37:41.839 UTC96405b62-f038-4c52-a831-1787aa510bf02012-10-11 12:40:08.593 UTC04064c96-4b8d-4065-80e5-dfcabcb597de2012-10-11 11:30:15.656 UTC724a9578-a6b6-44b9-9c02-fcf83e375a672012-09-28 08:40:05.123 UTC19bbf243-d943-409c-9004-bb9df6c333492012-06-15 06:40:07.359 UTC3b27b30c-4431-409c-97fd-26b37a8823fb2012-09-28 08:09:20.60 UTCMaria Paula Balcázar-Vargas, Jonathan Giddy and Gerard Oostermeijer2012-10-05 11:21:40.276 UTCThe time T required for the population to increase by a factor of Ro (net reproductive rate)
e.g.:
If Ro (net reproductive rate) = 5.56
and
T (generation time) = 8.055
The average plant of the species Gentiana pneumonanthe in Terschelling in the year 1987 replaced itself with almost six new plants and took approximately 8.05 years to do so.
2012-10-11 12:06:44.656 UTCc4dc3143-373c-4d4e-adc3-8d8d84dd4a1e2012-10-05 11:50:33.307 UTCaabd83c8-3016-47ec-a1e2-e6d909289dfa2012-06-22 08:38:17.934 UTC138bd86c-fd0b-4db2-8092-1e9071940e2a2012-09-28 08:45:04.951 UTC45f7861f-9c3c-492a-924c-34b896fefa322012-10-05 11:35:49.386 UTC88440626-1691-4815-909b-c08836952d2a2012-10-11 11:45:15.453 UTCe6545437-85f0-42a0-b54f-066b165d7ec62012-10-05 11:51:02.854 UTCGeneration time (T)2012-10-05 11:22:20.526 UTCf92df37a-086b-4bbe-b7c2-42bc8660915e2012-06-15 06:42:22.376 UTCc55402cf-b409-47b3-b079-4cfb1234f6ce2012-10-05 11:30:55.729 UTCa6d860df-36bb-423a-a7e6-586818fccfc82012-09-28 08:06:19.732 UTC00e1ecf7-7f9c-4ee5-baea-9403570f30a42012-10-11 12:43:04.531 UTC98ee462f-3718-4938-a959-6a042ad29aff2012-10-05 11:35:18.229 UTCf3629da2-038d-47c2-b494-15ce65b7df822012-10-11 12:02:50.281 UTC227252e7-ff41-47fd-af0c-39907febdc422012-09-28 08:07:38.560 UTCc65932e5-9f7b-4ec2-b218-152de68c32632012-10-05 11:48:11.370 UTC81787775-16fe-4c13-90dd-0a48678146ee2012-09-28 08:10:30.76 UTCe38e9ac0-3bb8-427d-91c6-a40324275e422012-10-11 11:57:10.312 UTCe7b6d547-d809-4376-b8eb-f1208f5c07be2012-10-11 12:06:45.921 UTC3979d4bd-1668-4e90-913b-06b22e1229c62012-06-22 08:39:22.770 UTCc6fd9af5-b7a7-460d-83c8-8122aa11253e2012-09-28 08:43:02.498 UTC74dedf92-5055-45bd-995b-5b9df0a480a82012-10-05 11:40:27.651 UTCd175cac8-5f8c-46ea-bb34-cd41954a2c5e2012-10-11 11:59:17.375 UTC6e3a57e1-23a5-4883-84d6-bf7a14a9b1042012-06-21 14:06:12.125 UTC6ed83074-6a5a-445c-bc2e-d0b4df8783692012-10-11 11:35:56.890 UTC