Eigen_analysisstageMatrixFile000.0000 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 UTCspeciesName00Gentiana pneumonanthe2012-10-10 08:45:54.921 UTCSpecies 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 UTCstages11[S,J,V,G,D] 2014-07-22 09:16:58.632 UTCStage input port:
Here come 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
2012-10-11 11:44:43.296 UTCbarPlotA 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 UTC2012-10-10 11:25:12.531 UTCprojectionMatrixProjection matrix Output port:
Creates a grid of colored rectangles to display the stage matrix input.2012-10-10 11:16:38.125 UTC 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 UTCelasticityMatrix 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 UTCThe 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 UTCsensitivityMatrix1The 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 UTC 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 UTCsensitivityMatrix2The 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 UTCeigenanalysisEigen 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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16:03:04.212 UTC855397b2-3c8d-4589-9a3a-ededfd630b5c2012-10-11 09:39:57.0 UTC051675d9-eeda-46ea-9f3d-ecc62685c7a72012-10-17 15:20:43.513 UTC09eafecd-4f3c-4de3-b883-136d082eefb52012-10-02 20:23:53.800 UTCf896aca8-bba2-45e2-8113-e386cbe620ce2012-09-26 12:25:40.0 UTC104a6f4f-33c3-4b8c-b4d7-55ac8fa330f72012-07-13 07:53:21.635 UTCa70a1e5c-8940-4703-bffa-a89da5537fdb2012-09-21 05:10:47.15 UTCa5615bef-dcac-45ea-a3ce-cbd4b9875eee2012-09-26 12:14:28.31 UTC9fa97e87-bd43-4312-a36f-8ac512988b802012-07-13 06:25:39.0 UTCb0e4235a-5fe4-4228-a361-9dd543d8ec952012-09-19 15:33:22.278 UTCEigen analysis2012-09-26 12:46:27.453 UTC27fa10ea-ca41-4311-b50c-eb7e2fe664892012-07-11 15:49:21.753 UTC1b962467-4a86-427c-b2bc-6b7e38f5f5422012-10-03 13:35:23.390 UTCc003690c-273e-46b8-8f1a-629be21b59c32014-07-22 09:17:26.532 UTCa2cee785-18ef-4208-8677-b37970b920a72012-07-13 07:51:10.754 UTCcf5e0323-5dea-4804-a941-3e537acd204e2012-10-10 11:26:17.421 UTC11db6475-ebfc-492f-af7d-3a4185d279ce2012-09-19 15:49:14.786 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 UTCcc5b393c-818f-4016-a1d8-890885b584d32012-07-13 09:00:07.232 UTCf8c42ab5-0d43-40e0-94ac-ec6798e927f72012-10-11 11:44:45.140 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 UTCd2e98a62-d554-4654-a359-39eaa6c9c9d52012-09-20 13:35:32.442 UTCc016cc4f-1001-4237-882d-dceabfdd8d012012-10-04 15:00:55.625 UTC418d8b49-71f3-487f-9a5e-55710ede018a2012-10-10 11:16:38.390 UTC02aaa6ce-772b-4402-a474-2cdfe18e31672012-09-26 12:29:14.359 UTC98e93c16-3991-466d-9ade-6f082f2a3a1c2012-10-10 11:25:12.781 UTCedb731c0-daa1-4bd7-b8f0-ddbc56a875662012-10-10 11:35:17.156 UTC6e4e9dd0-334b-403a-9632-8423f9636fe72012-07-11 13:00:55.837 UTC87e49604-3a08-48ae-a9be-a45e6e8d0ee62012-10-10 12:01:33.812 UTCbef35e44-1127-458d-b2ee-61048bd64a072012-07-13 06:22:03.734 UTCee5896b1-4097-4e47-92af-e3e330c7a9ae2012-10-17 15:18:12.929 UTCe9b5e5d2-9871-4eba-b7a1-0635c8fc1bf52012-07-13 09:10:07.45 UTC9cc9920c-7d50-4c5b-9800-20cc1cfd72cf2012-09-20 14:54:19.489 UTC199c86f0-df6a-425c-b4dd-6aa852bcbff52012-07-13 09:03:22.271 UTCecef24cd-4e05-4e89-b47d-2627857c98bc2012-07-13 09:06:31.770 UTC068ff12d-fddd-45f7-9eec-8222ebfeac1b2012-10-10 11:37:42.796 UTC4753d12c-1f1d-4454-97fe-6a2dcecc38b62012-07-13 07:45:12.849 UTC3a09aae3-3fa4-44e7-a064-e02418cffa922012-10-03 13:54:56.46 UTC6315c9ba-381a-44ce-82cd-ea6f5aae35d52012-07-13 09:27:13.462 UTC431a4612-9885-4ae4-a530-e99099eb92572012-09-26 12:51:53.859 UTC40cc9b1a-f9d9-4f2d-8ef8-1108348f8cc92012-10-10 11:14:12.187 UTC274d678f-76a6-4014-9d68-d0189dfe70042012-10-03 14:03:09.78 UTC214b1114-efbc-4d54-bb20-4fa1f9beb89f2012-09-20 13:37:17.940 UTC7f69fad0-a2a7-42ad-aebe-8b0aa109d5492012-10-10 10:51:54.312 UTCe05732a8-9627-4bfa-b871-d8d4a9c53fb62012-07-11 20:55:29.517 UTC48960c0c-1f5d-4e1c-a5d0-270927af14402012-10-10 11:59:42.921 UTCc38466a8-a606-44d7-8bd3-8f26b8250ef22012-10-10 11:35:50.671 UTC3b844874-3fc8-4b62-9f02-5c86ae0e053d2012-07-13 09:02:25.256 UTCe8d180a6-7a5c-4421-b788-db26f3589ae82012-09-20 13:43:51.734 UTCa96cc7e4-b508-470e-ba78-4bfd8e1d84992012-10-03 13:57:55.765 UTC5bdb4704-9322-4cbc-8d08-4b87aa1f23182012-07-11 22:49:36.115 UTC31de0f25-8b52-4b7c-a868-4eb26381b7682012-07-11 16:08:08.989 UTCb14b0461-c322-4ebf-ac0d-e62d7dc57e922012-10-10 12:00:57.265 UTCaf7fe40a-d783-415e-937a-cb50dd0376982012-10-17 15:18:34.963 UTCd876c281-ea57-4da0-a470-f3bfbd4c7ad42012-07-11 13:05:24.619 UTC40f5c83b-f16c-4564-a6db-81a91ff724c02012-10-10 12:02:09.375 UTC3f094d6e-7d4f-43ea-a672-8f56b7e9b3272012-09-19 15:54:02.713 UTC2615d90a-7a5e-464e-89b6-20fec7bc10142012-07-13 09:11:19.100 UTC27e99cfd-69ad-4acb-b09b-46eeb1fffd6f2012-10-03 14:26:15.218 UTC53b6584e-7b75-48ac-976b-11154cef701f2012-07-13 09:04:05.440 UTC69d11822-5bf3-40d1-a6ce-cc0110a366dd2012-07-13 08:06:33.163 UTC61e17b4e-2110-470a-8aa8-db97ea3341e02012-07-11 15:46:57.885 UTC3652cbd1-72c4-47e1-9479-ddedb5f81d982012-07-13 09:07:01.485 UTC21662d80-f207-4a54-9844-8f24acb91a272012-07-13 09:22:22.131 UTC8701e660-faa7-4a7c-ae96-282fea7b3c0e2012-10-10 09:01:24.406 UTCEigen_analysisstage_matrix11The 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 UTC0.0000 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 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 UTCbarPlotA 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 UTC2012-10-10 11:25:12.531 UTCprojectionMatrix 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 UTCelasticityMatrix 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 UTCThe 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 UTCsensitivityMatrix1The 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 UTC 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 UTCsensitivityMatrix2 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 UTCThe 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 UTCeigenanalysisEigen 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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matrixnet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeElasticityMatrixeigenanalysis1plot_title0plot_size0plot_image00net.sf.taverna.t2.activitiesrshell-activity1.4net.sf.taverna.t2.activities.rshell.RshellActivityplot_title0falseeigenanalysis1falseplot_size0falseplot_image00falselocalhost6311falsefalseplot_titleSTRINGeigenanalysisR_EXPplot_sizeINTEGERplot_imagePNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSensitivityMatrixeigenanalysis1plot_title0plot_size0plot_image00net.sf.taverna.t2.activitiesrshell-activity1.4net.sf.taverna.t2.activities.rshell.RshellActivityplot_title0falseeigenanalysis1falseplot_size0falseplot_image00falselocalhost6311falsefalseplot_titleSTRINGeigenanalysisR_EXPplot_sizeINTEGERplot_imagePNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSensitivity_matrix_1value00net.sf.taverna.t2.activitiesstringconstant-activity1.4net.sf.taverna.t2.activities.stringconstant.StringConstantActivitySensitivity matrix 1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSensitivity_matrix_2value00net.sf.taverna.t2.activitiesstringconstant-activity1.4net.sf.taverna.t2.activities.stringconstant.StringConstantActivitySensitivity matrix 2net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeSensitivityMatrix_2eigenanalysis1plot_title0plot_size0plot_image00net.sf.taverna.t2.activitiesrshell-activity1.4net.sf.taverna.t2.activities.rshell.RshellActivityplot_title0falseeigenanalysis1falseplot_size0falseplot_image00falselocalhost6311falsefalseplot_titleSTRINGeigenanalysisR_EXPplot_sizeINTEGERplot_imagePNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeCalculatePlotSizestage_matrix1plot_size00net.sf.taverna.t2.activitiesrshell-activity1.4net.sf.taverna.t2.activities.rshell.RshellActivitystage_matrix1falseplot_size00falselocalhost6311falsefalsestage_matrixR_EXPplot_sizeINTEGERnet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeProjectionMatrixstage_matrixProjectionMatrixplot_titleProjectionMatrixplot_sizeEigenanalysisNonZeroElementsstage_matrixEigenanalysisAllElementsstage_matrixBarPloteigenanalysisBarPlotbar_plot_titleElasticityMatrixeigenanalysisElasticityMatrixplot_titleElasticityMatrixplot_sizeSensitivityMatrixeigenanalysisSensitivityMatrixplot_titleSensitivityMatrixplot_sizeSensitivityMatrix_2eigenanalysisSensitivityMatrix_2plot_titleSensitivityMatrix_2plot_sizeCalculatePlotSizestage_matrixbarPlotprojectionMatrixelasticityMatrixsensitivityMatrix1sensitivityMatrix2eigenanalysis11db6475-ebfc-492f-af7d-3a4185d279ce2012-09-19 15:49:14.786 UTC8badb0ad-fa34-4fba-b38a-ff0930047c532012-11-26 16:01:40.14 UTC2615d90a-7a5e-464e-89b6-20fec7bc10142012-07-13 09:11:19.100 UTC4753d12c-1f1d-4454-97fe-6a2dcecc38b62012-07-13 07:45:12.849 UTC199c86f0-df6a-425c-b4dd-6aa852bcbff52012-07-13 09:03:22.271 UTCe0424e01-ed30-4c94-95b8-143751fca7a22012-07-11 16:07:29.317 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 UTCbef35e44-1127-458d-b2ee-61048bd64a072012-07-13 06:22:03.734 UTCe8d180a6-7a5c-4421-b788-db26f3589ae82012-09-20 13:43:51.734 UTCecef24cd-4e05-4e89-b47d-2627857c98bc2012-07-13 09:06:31.770 UTC84a2fa47-f758-4a80-95ba-903147579dca2012-10-03 14:26:58.218 UTC274d678f-76a6-4014-9d68-d0189dfe70042012-10-03 14:03:09.78 UTC687a5ff0-61b3-4784-a263-6e7974626f6d2012-11-26 16:03:00.764 UTCe5c21cb7-1882-4efa-81dc-7dd53b9202952012-09-26 12:05:06.765 UTCa5615bef-dcac-45ea-a3ce-cbd4b9875eee2012-09-26 12:14:28.31 UTC313804e4-faea-485a-bd2f-5a8dded213772012-10-17 15:12:36.567 UTC98e93c16-3991-466d-9ade-6f082f2a3a1c2012-10-10 11:25:12.781 UTC17afd103-1e0c-4e98-92eb-dc7f12cf29842012-09-21 06:25:47.618 UTC09eafecd-4f3c-4de3-b883-136d082eefb52012-10-02 20:23:53.800 UTC27e99cfd-69ad-4acb-b09b-46eeb1fffd6f2012-10-03 14:26:15.218 UTC418d8b49-71f3-487f-9a5e-55710ede018a2012-10-10 11:16:38.390 UTCa2cee785-18ef-4208-8677-b37970b920a72012-07-13 07:51:10.754 UTC09aa9ebd-4e1d-4579-83f6-727da90eae352012-09-20 13:38:43.850 UTC3652cbd1-72c4-47e1-9479-ddedb5f81d982012-07-13 09:07:01.485 UTC214b1114-efbc-4d54-bb20-4fa1f9beb89f2012-09-20 13:37:17.940 UTC3b844874-3fc8-4b62-9f02-5c86ae0e053d2012-07-13 09:02:25.256 UTC6aab6970-a0e8-4ac7-85d8-0906b5cf29072012-09-26 12:46:36.531 UTC431a4612-9885-4ae4-a530-e99099eb92572012-09-26 12:51:53.859 UTC69d11822-5bf3-40d1-a6ce-cc0110a366dd2012-07-13 08:06:33.163 UTCb14b0461-c322-4ebf-ac0d-e62d7dc57e922012-10-10 12:00:57.265 UTCc8693523-8523-47e5-96bc-4648f21b7de92012-09-26 11:59:25.0 UTC4988e019-bf93-40bd-b095-6a33aec7e9682012-07-13 08:39:49.679 UTCf850930e-3ed8-475e-a717-f9fe5d8af0f02012-10-17 15:12:16.758 UTCd876c281-ea57-4da0-a470-f3bfbd4c7ad42012-07-11 13:05:24.619 UTCc016cc4f-1001-4237-882d-dceabfdd8d012012-10-04 15:00:55.625 UTC27fa10ea-ca41-4311-b50c-eb7e2fe664892012-07-11 15:49:21.753 UTC5bdb4704-9322-4cbc-8d08-4b87aa1f23182012-07-11 22:49:36.115 UTC8eb6139c-8930-43f8-bd9a-5603f973b51b2012-09-26 14:28:53.828 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 UTC9159d5c8-8084-403e-9941-37a0babea12d2012-07-13 08:10:15.746 UTCEigen analysis2012-09-26 12:46:27.453 UTC87e49604-3a08-48ae-a9be-a45e6e8d0ee62012-10-10 12:01:33.812 UTC3f094d6e-7d4f-43ea-a672-8f56b7e9b3272012-09-19 15:54:02.713 UTCf8c42ab5-0d43-40e0-94ac-ec6798e927f72012-10-11 11:44:45.140 UTC6e4e9dd0-334b-403a-9632-8423f9636fe72012-07-11 13:00:55.837 UTC7f69fad0-a2a7-42ad-aebe-8b0aa109d5492012-10-10 10:51:54.312 UTC6315c9ba-381a-44ce-82cd-ea6f5aae35d52012-07-13 09:27:13.462 UTCab5c6e54-c6a6-4ad3-b360-33b41f0efeb12012-10-10 11:31:52.500 UTC104a6f4f-33c3-4b8c-b4d7-55ac8fa330f72012-07-13 07:53:21.635 UTCace5fe46-77ef-4a86-b67b-bde22c741ac82012-07-13 09:26:09.444 UTCa96cc7e4-b508-470e-ba78-4bfd8e1d84992012-10-03 13:57:55.765 UTC53b6584e-7b75-48ac-976b-11154cef701f2012-07-13 09:04:05.440 UTCb0e4235a-5fe4-4228-a361-9dd543d8ec952012-09-19 15:33:22.278 UTC9fa97e87-bd43-4312-a36f-8ac512988b802012-07-13 06:25:39.0 UTC35908a90-ddf2-43c5-9910-680a097f4f212012-10-02 20:25:51.124 UTCda31b618-4c4c-4a02-a808-22ec64fd999e2012-10-03 13:50:10.937 UTCc38466a8-a606-44d7-8bd3-8f26b8250ef22012-10-10 11:35:50.671 UTC068ff12d-fddd-45f7-9eec-8222ebfeac1b2012-10-10 11:37:42.796 UTC21662d80-f207-4a54-9844-8f24acb91a272012-07-13 09:22:22.131 UTC40f5c83b-f16c-4564-a6db-81a91ff724c02012-10-10 12:02:09.375 UTC16e2a51c-4ee9-4e81-a2a0-515d940f9cc22012-10-10 11:22:44.500 UTCcf5e0323-5dea-4804-a941-3e537acd204e2012-10-10 11:26:17.421 UTC31de0f25-8b52-4b7c-a868-4eb26381b7682012-07-11 16:08:08.989 UTCedb731c0-daa1-4bd7-b8f0-ddbc56a875662012-10-10 11:35:17.156 UTC9253e96c-9712-42a9-b19d-c8bf5fdccce12012-09-26 13:43:08.906 UTC5ef7089b-9aef-4b96-983f-9c54530ffceb2012-09-26 13:55:15.687 UTC6933ad38-f960-4f05-ae40-0352c2a977232012-07-11 16:13:31.963 UTCcc5b393c-818f-4016-a1d8-890885b584d32012-07-13 09:00:07.232 UTC48960c0c-1f5d-4e1c-a5d0-270927af14402012-10-10 11:59:42.921 UTCf896aca8-bba2-45e2-8113-e386cbe620ce2012-09-26 12:25:40.0 UTCd2e98a62-d554-4654-a359-39eaa6c9c9d52012-09-20 13:35:32.442 UTCe9b5e5d2-9871-4eba-b7a1-0635c8fc1bf52012-07-13 09:10:07.45 UTC61e17b4e-2110-470a-8aa8-db97ea3341e02012-07-11 15:46:57.885 UTC9cc9920c-7d50-4c5b-9800-20cc1cfd72cf2012-09-20 14:54:19.489 UTC5a97a8dd-039c-4243-ac5c-b91939948fcb2012-09-21 05:08:07.641 UTC3a09aae3-3fa4-44e7-a064-e02418cffa922012-10-03 13:54:56.46 UTCf9d69679-5e04-46e4-b77b-c70d19cb4c0d2012-07-13 08:51:15.886 UTC1b962467-4a86-427c-b2bc-6b7e38f5f5422012-10-03 13:35:23.390 UTC2335e73d-8ebe-4cff-ba56-f841952e139e2012-10-12 11:31:11.711 UTC18e99b4e-e6d1-4c87-86cb-f4b3f40fec872012-07-13 08:43:47.651 UTC40cc9b1a-f9d9-4f2d-8ef8-1108348f8cc92012-10-10 11:14:12.187 UTCff5bc61b-0d13-4622-adc8-2aedd7b7038c2012-07-13 09:20:52.134 UTCa70a1e5c-8940-4703-bffa-a89da5537fdb2012-09-21 05:10:47.15 UTC3e775ac4-0bf5-435e-979e-26753958554c2012-07-13 06:22:29.620 UTC02aaa6ce-772b-4402-a474-2cdfe18e31672012-09-26 12:29:14.359 UTCe05732a8-9627-4bfa-b871-d8d4a9c53fb62012-07-11 20:55:29.517 UTC34d1cf2c-a02a-4b6e-b39d-b6f55da1a0252012-07-11 20:58:04.370 UTC855397b2-3c8d-4589-9a3a-ededfd630b5c2012-10-11 09:39:57.0 UTC57db3fed-16a3-43ca-a4f9-d41c254d9b772012-09-26 11:51:20.375 UTC6ad79f50-2ace-4bb4-b896-fc34810868c62012-09-26 13:51:56.437 UTCd200135a-b430-4ff3-aec3-cb4139f821ca2012-10-10 11:55:23.78 UTC6a6df203-47b2-4b26-855f-ff8c48eed2bc2012-09-19 15:38:42.701 UTCa6efda97-4c1a-4ce4-9b65-6a87f8d11e782012-07-13 09:14:16.348 UTC8701e660-faa7-4a7c-ae96-282fea7b3c0e2012-10-10 09:01:24.406 UTC