Parametric_BootstrapstageMatrixFile00Here 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): 153-166.2014-06-18 08:53:16.32 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 0.02322014-06-06 13:48:03.530 UTCabundances11In this dialogue appear the fields with the initial abundance per stage observed in the field. As an example Gentiana pneumonanthe has 5 stages with its respective abundance.
The abundance of the stages or categories must be added one by one. First press Add value, fill the abundance of the first stage and press enter; then press Add value and fill once again the next stage abundance; repeat the action until you have fill all the abundance of all stages.
Stage abundance of the year 1987:
1) S (seedlings) 69
2) J (Juveniles) 100
3) V (vegetative) 111
4) G (reproductive individuals) 21
5) D (dormant plants) 43
2014-06-18 08:53:30.104 UTC[69, 100, 111, 21, 43]2014-06-06 13:48:49.284 UTCiterations00Number of iterations for calculation of the resample analysis of the parametric Bootstrap.
Click in Set Value, tip the number in the right window.
2014-06-18 08:53:35.815 UTC100002014-06-06 13:47:15.976 UTCstages11[S, J, V, G, D] 2014-06-06 13:49:16.711 UTCHere 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
2014-06-18 08:53:54.468 UTCplotTitle00Descriptive title for labelling generated output graph. Click in Set Value, tip the text in the right window.
e.g.: Gentiana pneumonanthe, Terschelling (species taxonomic name, place where the research was conducted)
2014-06-18 08:53:42.306 UTCGentiana pneumonanthe, Terschelling2014-06-06 13:47:39.32 UTChistogram0Histogram plotting the frequencies of the lambda values and the 95% confidence intervals resulting from the bootstrap analysis.2014-06-06 14:36:29.892 UTClambda01.23752014-06-06 14:37:00.728 UTCLambda (λ) 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.: Lambda (λ) = 1 (population is stable), Lambda (λ) > 1 (population is growing) and finally Lambda (λ) < 1 (population is decreasing).2014-06-18 08:54:57.109 UTCx0X= List of resampled matrices
it is the list of matrices generated by bootstrap analysis and the number of the matrices at the same time is based on the number of itineration’s.2014-06-06 14:37:55.419 UTCmean0The mean matrix is calculated based on the matrices generated by bootstrap analysis and the number of the matrices at the same time is based on the number of itineration’s.2014-06-18 08:55:16.552 UTCvariance0The variance matrix is calculated based on the matrices generated by bootstrap analysis and the number of the matrices at the same time is based on the number of itineration’s.2014-06-18 08:55:24.883 UTCconfidence_interval095% Confidence interval of Lambda. In statistics, a confidence interval (CI) is a type of interval estimate of a population parameter and is used to indicate the reliability of an estimate. It is an observed interval (i.e. it is calculated from the observations), in principle different from sample to sample, that frequently includes the parameter of interest if the experiment is repeated. How frequently the observed interval contains the parameter is determined by the confidence level or confidence coefficient
2014-06-18 08:54:05.420 UTC2.5% 97.5%
0.9617 1.47652014-06-06 14:36:02.587 UTCdisplayinput1output00net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivityinput1falseoutput00falselocalhost6311falsefalseinputR_EXPoutputTEXT_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Invokeplot_histogramci1plottitle0y1output00net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivityy1falseplottitle0falseci1falseoutput00falselocalhost6311falsefalseyR_EXPplottitleSTRINGciR_EXPoutputPNG_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Invokedisplay_2input1output00net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivityinput1falseoutput00falselocalhost6311falsefalseinputR_EXPoutputTEXT_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Invokedisplay_3input1output00net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivityinput1falseoutput00falselocalhost6311falsefalseinputR_EXPoutputTEXT_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Invokedisplay_4input1output00net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivityinput1falseoutput00falselocalhost6311falsefalseinputR_EXPoutputTEXT_FILEnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeWorkflow32iterations0abundances1stage_matrix1frows1fcols1confidence_interval11x11mean11y11variance11lambda00net.sf.taverna.t2.activitiesdataflow-activity1.5net.sf.taverna.t2.activities.dataflow.DataflowActivitynet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeStageMatrix_ReadFromFilestages1stageMatrixFile0stageMatrix11net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivitystageMatrixFile0falsestages1falsestageMatrix11falselocalhost6311falsefalsestageMatrixFileTEXT_FILEstagesSTRING_LISTstageMatrixR_EXPnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflow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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 UTCnet.sf.taverna.t2.activitiesinteraction-activity1.5net.sf.taverna.t2.activities.interaction.InteractionActivityunsortedStages1text/plainjava.lang.StringfalsesortedStages11recruitedStages11reproductiveStages11http://biovel.googlecode.com/svn/trunk/popmod/mpm/select_stages.htmlLocallyPresentedHtmlfalsenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeFecundityCols_FromReproductiveStagesall_values1some_values1indices11net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivitysome_values1falseall_values1falseindices11falselocalhost6311falsefalsesome_valuesSTRING_LISTall_valuesSTRING_LISTindicesINTEGER_LISTnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.InvokeFecundityRows_FromRecruitedStagesall_values1some_values1indices11net.sf.taverna.t2.activitiesrshell-activity1.5net.sf.taverna.t2.activities.rshell.RshellActivitysome_values1falseall_values1falseindices11falselocalhost6311falsefalsesome_valuesSTRING_LISTall_valuesSTRING_LISTindicesINTEGER_LISTnet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Parallelize1net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.ErrorBouncenet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Failovernet.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Retry1.0100050000net.sf.taverna.t2.coreworkflowmodel-impl1.5net.sf.taverna.t2.workflowmodel.processor.dispatch.layers.Invokedisplayinputplot_histogramciplot_histogramplottitleplot_histogramydisplay_2inputdisplay_3inputdisplay_4inputWorkflow32iterationsWorkflow32abundancesWorkflow32stage_matrixWorkflow32frowsWorkflow32fcolsStageMatrix_ReadFromFilestagesStageMatrix_ReadFromFilestageMatrixFileCategoriseStages_InteractionunsortedStagesFecundityCols_FromReproductiveStagesall_valuesFecundityCols_FromReproductiveStagessome_valuesFecundityRows_FromRecruitedStagesall_valuesFecundityRows_FromRecruitedStagessome_valueshistogramlambdaxmeanvarianceconfidence_interval5ddec6d6-2ef8-4a1b-8905-4ebc313e8a5f2012-03-30 15:53:45.576 UTCc666682d-b97f-4ae5-a33a-2c2dbd8cc73a2012-06-27 09:44:02.36 UTC50e537db-c0d0-478d-b55b-5b53de52ec3d2012-12-10 15:51:50.369 UTCMaria Paula Balcázar-Vargas, Jonathan Giddy and Gerard Oostermeijer2014-06-06 13:46:10.288 UTC0c1873c5-fc98-40c8-960c-bd11f90600722012-06-27 09:34:26.127 UTCd3856b08-20d7-4f7d-8d0f-7cefebd654f02012-06-08 05:56:58.172 UTC1bc8b332-e0fa-4c1b-9693-2e7b0297d6352012-06-08 07:34:34.886 UTCf364089f-de01-4c6d-b4e8-3e0f55f8952f2012-06-08 06:30:14.837 UTCe4416b66-0517-4982-9ffc-07d9225b4cb42012-04-27 10:20:27.369 UTC26a58a12-7058-4ecc-8626-8f4208df050d2012-04-27 06:37:14.879 UTC87080ba6-c0da-4929-875b-a334cd6c80dc2012-07-04 15:48:37.846 UTC23b013c9-2e87-45bc-890e-3d5def9f9a832014-06-06 13:47:40.696 UTC60c89fa1-3c42-4a86-98d4-d6aaf4dc5b362012-06-08 06:21:13.990 UTC9980e502-edf8-45be-b834-da4a69c1aa6f2012-06-27 09:38:41.13 UTC3da39227-d90d-44b6-93e6-a5c6c6635c282012-03-30 15:42:09.674 UTC4ea704d2-63f2-441a-8b1f-db2f572016032012-06-08 07:06:43.835 UTCcfb364a7-5ddb-4e0a-b21e-1cb457ad502b2014-06-18 08:57:09.231 UTC553eb85d-393a-488a-84ae-6190b23e80cc2012-03-30 15:56:49.708 UTCcc5e2437-fb37-4ea4-afa4-7045fc85a4a02014-06-06 13:48:49.476 UTCParametric Bootstrap or Resample a projection matrix Workflow2014-06-06 13:46:18.805 UTC85e5205a-e20f-42a5-85b6-857a1bcf67512012-04-27 10:04:31.201 UTC29186c39-3022-4d52-90d0-8f7fd7bcef272012-03-30 15:47:32.455 UTC66a88eef-1fea-4ca5-9ae4-939bd0edae282014-06-06 13:46:52.704 UTC11e7d70b-f717-4c5c-8a85-34f089e83e462012-06-27 11:46:08.466 UTC1e66a160-d9a3-485d-b31e-cac2c674a2962012-03-30 15:59:19.350 UTC622978b8-0ac3-4cdc-af2f-99cda8a601182012-07-05 06:58:48.484 UTC5ad8da23-95d6-4f62-b1fc-82689c17ffd72012-03-30 15:52:40.327 UTC8c458bf5-19ef-437d-a53b-a5bfa71620712012-06-08 07:11:39.27 UTC513eb95e-60b6-4fda-925b-db4b1892790f2012-06-08 05:40:34.264 UTCbbd91183-5416-4e35-9f8b-ff03ef6a41802012-06-08 05:51:09.38 UTC068f4c47-ac93-41d1-928b-e5313ddf7dc92012-03-30 15:27:01.885 UTCa8d38c46-62d4-4961-b455-4806d44d3fdb2012-12-10 16:03:03.918 UTCf4c20700-97e2-48ee-b22a-c3455eabd7192014-06-06 13:46:28.636 UTCb4a948a5-2b99-4d2c-9a59-abe7fa51e5ef2012-06-08 06:12:12.618 UTCd4579895-8820-446d-b9c1-159f21cc25c12014-06-06 14:38:09.552 UTC5ab6188e-351e-422a-8cc1-509c82eb2b082012-12-10 15:52:33.878 UTCbed37407-0362-4432-81ed-8ced9db83ac62012-06-08 05:40:45.808 UTCbfd39e81-094d-4674-be1c-1e5fca6b53ec2012-06-07 14:06:09.942 UTC99a5ecac-18df-45ae-bbfa-d180b0469b442012-06-08 07:14:48.566 UTCa879538b-4910-4e8a-a540-c9aff93865f02014-06-06 14:36:14.30 UTCc3000dba-a0f1-40f4-a168-de916bebc7902012-06-08 05:43:58.397 UTCe62695c3-51aa-4a6d-8618-f111c476b87b2012-06-08 07:13:44.794 UTC25c69bcd-ad78-444f-bfe1-db3b3ad627e02012-06-08 07:17:05.238 UTC14392d07-d8b9-4f50-bc62-0b34587632522012-06-08 06:07:15.536 UTC348192ff-7a44-4a75-a3b4-af3adf25ea2b2012-04-27 06:08:00.914 UTC80cf8449-de9e-4745-8f59-ce71d97be12a2014-07-07 12:00:35.881 UTCa133ef6e-8380-48ae-bf11-d723416c8d312014-06-18 08:51:59.339 UTC883b826f-2fec-4ad9-bfcd-0768310191942012-12-10 15:45:31.213 UTC8237763e-e3d3-4a89-8154-c0e7ebe6ac992012-03-30 15:58:10.751 UTCb4a946c8-ae89-4e65-961d-5dcd474c82e82012-06-08 05:49:37.212 UTC899640f6-c19b-4a69-bd65-aebd8ff84a432012-06-27 09:42:10.621 UTCc2e78088-fb3a-46f2-a1d2-fa7b6006145a2012-06-08 05:42:53.3 UTCc4f7056b-5e74-4606-a058-96a8bea622002012-04-27 10:33:54.68 UTC7681491c-5178-4844-b9b1-e1c1ba4e29852012-04-27 10:36:47.808 UTC988ac270-9072-4975-bca6-93d37a0c0adf2014-07-07 12:03:36.203 UTCbe4e3ff1-a001-453f-9159-dc9657d4fcdb2012-06-08 05:58:16.24 UTCa882140e-69ee-4bd3-a75c-63fb903629452012-06-08 06:23:08.447 UTC74b62ae0-b939-4a30-b321-6be0a8abd35e2012-06-27 11:45:40.418 UTC6a5c611c-cfcf-4964-9c89-f254b5521e152012-04-26 16:16:27.814 UTC2a67baca-21bc-4bc2-8e77-0754a7070ef32012-06-08 06:05:07.24 UTC09f91d33-9f50-4983-96c9-1335ed1f92b42012-04-27 06:19:38.161 UTCdcabfdeb-51a1-4ac8-91d0-f50ef43f28bb2012-06-08 07:04:17.60 UTC940fe2e3-58d4-475d-8bcf-3ede6bf0dabb2012-06-08 07:47:49.992 UTCc1c17ab3-ff6e-4202-90f2-8269713273402012-06-27 08:45:51.822 UTCcfe0f676-d994-4cf6-9af7-e7b8b4ce60832012-04-27 10:33:07.555 UTCf8a070c5-cf92-4946-85c2-d7d88d5517c12014-06-06 14:36:31.112 UTC6ad4d84d-6c33-4a35-9142-512f206419d22012-07-04 15:55:59.146 UTC482df01a-aece-421a-87e6-87c6fed3098c2012-04-27 06:16:05.128 UTCThe Parametric Bootstrap or Resample a projection matrix Workflow provides an environment to resample a projection matrix using a multinomial distribution for transitions and a log normal distribution for fertilities (Stubben, Milligan, and Nantel. 2011). The resample is based on number of plants surveyed. The projection matrix A is first split into separate transition and fertility matrices. Dead fates are added to the transition matrix and the columns are then sampled from a Multinomial distribution based on the size in each corresponding stage class in n. The fertility rates are sample from a Log Normal distribution using the lnorms function. The same variance is applied to all rates by default. (Stubben, Milligan and Nantel 2013, Caswell 2001 see section 12.1.5.2).
The goal of a demographic analysis is very often to estimate lambda, because lambda is estimated from imperfect data, such estimation are uncertain. Therefore, when the results have policy implications it is important to quantify that uncertainty. Confidence interval is one of the traditional tools to doing so (see outputs: Confidence interval of Lambda).
Analyses:
• Lambda (λ)
• Mean matrix
• Variance matrix
• Histogram
• Confidence interval of Lambda
• X= List of resampled matrices
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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
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For further details see:
Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.
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
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