Eigen_analysisstageMatrixFile00 0.0000 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 13:50:09.593 UTC The 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 UTC speciesName00 Gentiana pneumonanthe 2012-10-10 08:45:54.921 UTC Species 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 UTC stages11 [S,J,V,G,D] 2014-07-22 09:16:58.632 UTC Stage 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 UTC barPlot A 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 UTC 2012-10-10 11:25:12.531 UTC projectionMatrix Projection 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 0.0232 2012-10-12 11:31:11.508 UTC elasticityMatrix 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 UTC The 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 sensitivityMatrix1 The 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 0.0284 2012-10-10 11:50:32.796 UTC sensitivityMatrix2 The 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 0.028 2012-10-10 11:55:22.796 UTC eigenanalysis Eigen 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 UTC displayinput1output00net.sf.taverna.t2.activitiesrshell-activity1.4net.sf.taverna.t2.activities.rshell.RshellActivity input 1 false output 0 0 false localhost 6311 false false input R_EXP output TEXT_FILE net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize 1 net.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.Retry 1.0 1000 5000 0 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net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokedisplayinputEigen_analysiseigenanalysisEigen_analysisstage_matrixStageMatrix_ReadFromFilestage_matrixEigen_analysisspeciesNamespeciesNameStageMatrix_ReadFromFilestagesstagesStageMatrix_ReadFromFilestage_matrix_filestageMatrixFilebarPlotEigen_analysisbarPlotprojectionMatrixEigen_analysisprojectionMatrixelasticityMatrixEigen_analysiselasticityMatrixsensitivityMatrix1Eigen_analysissensitivityMatrix1sensitivityMatrix2Eigen_analysissensitivityMatrix2eigenanalysisdisplayoutput ff5bc61b-0d13-4622-adc8-2aedd7b7038c 2012-07-13 09:20:52.134 UTC 57db3fed-16a3-43ca-a4f9-d41c254d9b77 2012-09-26 11:51:20.375 UTC 6ad79f50-2ace-4bb4-b896-fc34810868c6 2012-09-26 13:51:56.437 UTC 34d1cf2c-a02a-4b6e-b39d-b6f55da1a025 2012-07-11 20:58:04.370 UTC d200135a-b430-4ff3-aec3-cb4139f821ca 2012-10-10 11:55:23.78 UTC f9d69679-5e04-46e4-b77b-c70d19cb4c0d 2012-07-13 08:51:15.886 UTC a6efda97-4c1a-4ce4-9b65-6a87f8d11e78 2012-07-13 09:14:16.348 UTC 9253e96c-9712-42a9-b19d-c8bf5fdccce1 2012-09-26 13:43:08.906 UTC 9159d5c8-8084-403e-9941-37a0babea12d 2012-07-13 08:10:15.746 UTC ace5fe46-77ef-4a86-b67b-bde22c741ac8 2012-07-13 09:26:09.444 UTC c8693523-8523-47e5-96bc-4648f21b7de9 2012-09-26 11:59:25.0 UTC 4988e019-bf93-40bd-b095-6a33aec7e968 2012-07-13 08:39:49.679 UTC 5ef7089b-9aef-4b96-983f-9c54530ffceb 2012-09-26 13:55:15.687 UTC 35908a90-ddf2-43c5-9910-680a097f4f21 2012-10-02 20:25:51.124 UTC ab5c6e54-c6a6-4ad3-b360-33b41f0efeb1 2012-10-10 11:31:52.500 UTC 6a6df203-47b2-4b26-855f-ff8c48eed2bc 2012-09-19 15:38:42.701 UTC 5a97a8dd-039c-4243-ac5c-b91939948fcb 2012-09-21 05:08:07.641 UTC 18e99b4e-e6d1-4c87-86cb-f4b3f40fec87 2012-07-13 08:43:47.651 UTC e3c6d2f0-266a-430d-84a8-db01d841b6e1 2012-11-26 16:01:45.664 UTC 2335e73d-8ebe-4cff-ba56-f841952e139e 2012-10-12 11:31:11.711 UTC da31b618-4c4c-4a02-a808-22ec64fd999e 2012-10-03 13:50:10.937 UTC 8eb6139c-8930-43f8-bd9a-5603f973b51b 2012-09-26 14:28:53.828 UTC 09aa9ebd-4e1d-4579-83f6-727da90eae35 2012-09-20 13:38:43.850 UTC 17afd103-1e0c-4e98-92eb-dc7f12cf2984 2012-09-21 06:25:47.618 UTC 84a2fa47-f758-4a80-95ba-903147579dca 2012-10-03 14:26:58.218 UTC 16e2a51c-4ee9-4e81-a2a0-515d940f9cc2 2012-10-10 11:22:44.500 UTC e5c21cb7-1882-4efa-81dc-7dd53b920295 2012-09-26 12:05:06.765 UTC e0424e01-ed30-4c94-95b8-143751fca7a2 2012-07-11 16:07:29.317 UTC 6aab6970-a0e8-4ac7-85d8-0906b5cf2907 2012-09-26 12:46:36.531 UTC 6933ad38-f960-4f05-ae40-0352c2a97723 2012-07-11 16:13:31.963 UTC 3e775ac4-0bf5-435e-979e-26753958554c 2012-07-13 06:22:29.620 UTC 200c2914-a49b-469a-ac2d-aa95953266bf 2012-11-26 16:03:04.212 UTC 855397b2-3c8d-4589-9a3a-ededfd630b5c 2012-10-11 09:39:57.0 UTC 051675d9-eeda-46ea-9f3d-ecc62685c7a7 2012-10-17 15:20:43.513 UTC 09eafecd-4f3c-4de3-b883-136d082eefb5 2012-10-02 20:23:53.800 UTC f896aca8-bba2-45e2-8113-e386cbe620ce 2012-09-26 12:25:40.0 UTC 104a6f4f-33c3-4b8c-b4d7-55ac8fa330f7 2012-07-13 07:53:21.635 UTC a70a1e5c-8940-4703-bffa-a89da5537fdb 2012-09-21 05:10:47.15 UTC a5615bef-dcac-45ea-a3ce-cbd4b9875eee 2012-09-26 12:14:28.31 UTC 9fa97e87-bd43-4312-a36f-8ac512988b80 2012-07-13 06:25:39.0 UTC b0e4235a-5fe4-4228-a361-9dd543d8ec95 2012-09-19 15:33:22.278 UTC Eigen analysis 2012-09-26 12:46:27.453 UTC 27fa10ea-ca41-4311-b50c-eb7e2fe66489 2012-07-11 15:49:21.753 UTC 1b962467-4a86-427c-b2bc-6b7e38f5f542 2012-10-03 13:35:23.390 UTC c003690c-273e-46b8-8f1a-629be21b59c3 2014-07-22 09:17:26.532 UTC a2cee785-18ef-4208-8677-b37970b920a7 2012-07-13 07:51:10.754 UTC cf5e0323-5dea-4804-a941-3e537acd204e 2012-10-10 11:26:17.421 UTC 11db6475-ebfc-492f-af7d-3a4185d279ce 2012-09-19 15:49:14.786 UTC 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) . 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 UTC cc5b393c-818f-4016-a1d8-890885b584d3 2012-07-13 09:00:07.232 UTC f8c42ab5-0d43-40e0-94ac-ec6798e927f7 2012-10-11 11:44:45.140 UTC This 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. 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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 UTC 0.0000 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 13:50:09.593 UTC speciesName00 Species 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 UTC Gentiana pneumonanthe 2012-10-10 08:45:54.921 UTC barPlot A 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 UTC 2012-10-10 11:25:12.531 UTC projectionMatrix 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 0.0232 2012-10-12 11:31:11.508 UTC Projection matrix Output port: Creates a grid of colored rectangles to display the stage matrix input. 2012-10-10 11:16:38.125 UTC elasticityMatrix 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 UTC The 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 sensitivityMatrix1 The 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 0.0284 2012-10-10 11:50:32.796 UTC sensitivityMatrix2 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 0.028 2012-10-10 11:55:22.796 UTC The 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 eigenanalysis Eigen 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 UTC 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net.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.Retry 1.0 1000 5000 0 net.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.RshellActivity plot_title 0 false eigenanalysis 1 false plot_size 0 false plot_image 0 0 false localhost 6311 false false plot_title STRING eigenanalysis R_EXP plot_size INTEGER plot_image PNG_FILE net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize 1 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net.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.Retry 1.0 1000 5000 0 net.sf.taverna.t2.coreworkflowmodel-impl1.4net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeProjectionMatrixstage_matrixstage_matrixProjectionMatrixplot_titleProjection_matrixvalueProjectionMatrixplot_sizeCalculatePlotSizeplot_sizeEigenanalysisNonZeroElementsstage_matrixstage_matrixEigenanalysisAllElementsstage_matrixstage_matrixBarPloteigenanalysisEigenanalysisNonZeroElementseigenanalysisBarPlotbar_plot_titlespeciesNameElasticityMatrixeigenanalysisEigenanalysisNonZeroElementseigenanalysisElasticityMatrixplot_titleElasticity_matrixvalueElasticityMatrixplot_sizeCalculatePlotSizeplot_sizeSensitivityMatrixeigenanalysisEigenanalysisNonZeroElementseigenanalysisSensitivityMatrixplot_titleSensitivity_matrix_1valueSensitivityMatrixplot_sizeCalculatePlotSizeplot_sizeSensitivityMatrix_2eigenanalysisEigenanalysisAllElementseigenanalysisSensitivityMatrix_2plot_titleSensitivity_matrix_2valueSensitivityMatrix_2plot_sizeCalculatePlotSizeplot_sizeCalculatePlotSizestage_matrixstage_matrixbarPlotBarPlotbar_plot_imageprojectionMatrixProjectionMatrixplot_imageelasticityMatrixElasticityMatrixplot_imagesensitivityMatrix1SensitivityMatrixplot_imagesensitivityMatrix2SensitivityMatrix_2plot_imageeigenanalysisEigenanalysisNonZeroElementseigenanalysis 11db6475-ebfc-492f-af7d-3a4185d279ce 2012-09-19 15:49:14.786 UTC 8badb0ad-fa34-4fba-b38a-ff0930047c53 2012-11-26 16:01:40.14 UTC 2615d90a-7a5e-464e-89b6-20fec7bc1014 2012-07-13 09:11:19.100 UTC 4753d12c-1f1d-4454-97fe-6a2dcecc38b6 2012-07-13 07:45:12.849 UTC 199c86f0-df6a-425c-b4dd-6aa852bcbff5 2012-07-13 09:03:22.271 UTC e0424e01-ed30-4c94-95b8-143751fca7a2 2012-07-11 16:07:29.317 UTC 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) . 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 UTC bef35e44-1127-458d-b2ee-61048bd64a07 2012-07-13 06:22:03.734 UTC e8d180a6-7a5c-4421-b788-db26f3589ae8 2012-09-20 13:43:51.734 UTC ecef24cd-4e05-4e89-b47d-2627857c98bc 2012-07-13 09:06:31.770 UTC 84a2fa47-f758-4a80-95ba-903147579dca 2012-10-03 14:26:58.218 UTC 274d678f-76a6-4014-9d68-d0189dfe7004 2012-10-03 14:03:09.78 UTC 687a5ff0-61b3-4784-a263-6e7974626f6d 2012-11-26 16:03:00.764 UTC e5c21cb7-1882-4efa-81dc-7dd53b920295 2012-09-26 12:05:06.765 UTC a5615bef-dcac-45ea-a3ce-cbd4b9875eee 2012-09-26 12:14:28.31 UTC 313804e4-faea-485a-bd2f-5a8dded21377 2012-10-17 15:12:36.567 UTC 98e93c16-3991-466d-9ade-6f082f2a3a1c 2012-10-10 11:25:12.781 UTC 17afd103-1e0c-4e98-92eb-dc7f12cf2984 2012-09-21 06:25:47.618 UTC 09eafecd-4f3c-4de3-b883-136d082eefb5 2012-10-02 20:23:53.800 UTC 27e99cfd-69ad-4acb-b09b-46eeb1fffd6f 2012-10-03 14:26:15.218 UTC 418d8b49-71f3-487f-9a5e-55710ede018a 2012-10-10 11:16:38.390 UTC a2cee785-18ef-4208-8677-b37970b920a7 2012-07-13 07:51:10.754 UTC 09aa9ebd-4e1d-4579-83f6-727da90eae35 2012-09-20 13:38:43.850 UTC 3652cbd1-72c4-47e1-9479-ddedb5f81d98 2012-07-13 09:07:01.485 UTC 214b1114-efbc-4d54-bb20-4fa1f9beb89f 2012-09-20 13:37:17.940 UTC 3b844874-3fc8-4b62-9f02-5c86ae0e053d 2012-07-13 09:02:25.256 UTC 6aab6970-a0e8-4ac7-85d8-0906b5cf2907 2012-09-26 12:46:36.531 UTC 431a4612-9885-4ae4-a530-e99099eb9257 2012-09-26 12:51:53.859 UTC 69d11822-5bf3-40d1-a6ce-cc0110a366dd 2012-07-13 08:06:33.163 UTC b14b0461-c322-4ebf-ac0d-e62d7dc57e92 2012-10-10 12:00:57.265 UTC c8693523-8523-47e5-96bc-4648f21b7de9 2012-09-26 11:59:25.0 UTC 4988e019-bf93-40bd-b095-6a33aec7e968 2012-07-13 08:39:49.679 UTC f850930e-3ed8-475e-a717-f9fe5d8af0f0 2012-10-17 15:12:16.758 UTC d876c281-ea57-4da0-a470-f3bfbd4c7ad4 2012-07-11 13:05:24.619 UTC c016cc4f-1001-4237-882d-dceabfdd8d01 2012-10-04 15:00:55.625 UTC 27fa10ea-ca41-4311-b50c-eb7e2fe66489 2012-07-11 15:49:21.753 UTC 5bdb4704-9322-4cbc-8d08-4b87aa1f2318 2012-07-11 22:49:36.115 UTC 8eb6139c-8930-43f8-bd9a-5603f973b51b 2012-09-26 14:28:53.828 UTC This 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. 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