Simulate stochastic growth from a sequence of matrices

Created: 2014-07-30 12:39:04 Last updated: 2014-08-14 12:13:05

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This workflow is based on the popbio package (script: stoch.projection - Simulate stochastic growth from a sequence of matrices, Stubben, Milligan and Nantel, 2013) based on the The MATLAB code in Box 7.3 (Morris and Doak 2002). For more details of the analysis see: Exploring population growth in a variable environment with computer simulations (Morris and Doak 2002, pag: 229-233 and Caswell 2001, Chapter 14).

Outputs:

• Equal selection data • Stochastic projection • Unequal selection data

We use Gentiana pneumonanthe only as example how to run this workflow.

This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359.

This workflow was created using and based on Package ‘popbio’ in R. (Stubben & Milligan 2007; Stubben, Milligan & Nantel 2011). ==================================================================================

Literature

Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts.

Oostermeijer J.G.B., M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166.

Morris, W. F., and D. F. Doak. 2002. Quantitative conservation biology: Theory and practice of population viability analysis. Sinauer, Sunderland, Massachusetts, USA. 480 pages

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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Descriptions (1)

The Simulate stochastic growth from a sequence of matrices Workflow provides an environment to simulate stochastic growth by projection using whole matrix selection techniques in an independently and identically distributed (iid) environment from a set of 2 or more projection matrices. This workflow is based on the popbio package (script: stoch.projection - Simulate stochastic growth from a sequence of matrices, Stubben, Milligan and Nantel, 2013) based on the The MATLAB code in Box 7.3 (Morris and Doak 2002). For more details of the analysis see: Exploring population growth in a variable environment with computer simulations (Morris and Doak 2002, pag: 229-233 and Caswell 2001, Chapter 14). Outputs: • Equal selection data • Stochastic projection • Unequal selection data We use Gentiana pneumonanthe only as example how to run this workflow. This workflow has been created by the Biodiversity Virtual e-Laboratory (BioVeL http://www.biovel.eu/) project. BioVeL is funded by the EU’s Seventh Framework Program, grant no. 283359. This workflow was created using and based on Package ‘popbio’ in R. (Stubben & Milligan 2007; Stubben, Milligan & Nantel 2011). ================================================================================== Literature Caswell, H. 2001. Matrix population models: Construction, analysis and interpretation, 2nd Edition. Sinauer Associates, Sunderland, Massachusetts. Oostermeijer J.G.B., M.L. Brugman; E.R. de Boer; H.C.M. Den Nijs. 1996. Temporal and Spatial Variation in the Demography of Gentiana pneumonanthe, a Rare Perennial Herb. The Journal of Ecology, Vol. 84(2): 153-166. Morris, W. F., and D. F. Doak. 2002. Quantitative conservation biology: Theory and practice of population viability analysis. Sinauer, Sunderland, Massachusetts, USA. 480 pages 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.

Dependencies (0)

Inputs (8)

Name	Description
stages	The names of the stages or categories of the input matrix. In the following example, the matrix has 5 stages or categories. The respective name stages must be filled one by one. First press add value (see arrow in Fig), 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: The stages of this matrix are called: 1) Seedlings S 2) Juveniles J 3) Vegetative V 4) Reproductive individuals G 5) Dormant plants D
graph_title	Is the main title to be display in the stochastic projection graph. Click in add value and then write the text in the right space. Please do not use a title longer than the suggest it.
intervals	This value is the number of time steps or projection intervals to predict future population size or in other words the time to predict future population size. Click in add value and write the number in the right space.
iterations	It is the number of iterations or the number of realizations of population growth to simulate. Click in add value and write the number in the right space.
probabilities	It is a vector of probability weights used by sample for selecting the projection matrices. In the following example, we use 6 matrices of 6 consecutive years, so if the user selects probabilities weights, the user must fill in 6 probabilities in total that sum up 1. No probability weights: If the user wants to use no probability weights, this is established by: First, click in add value, then in the left window a List is added with a "Some input data goes here" element in the right window. Delete that text. After, deletion the "List" have no elements. When running the workflow, Rshell script will assign NULL to the input. (this is when you are running the wf in Taverna workbench) Probability weights: The respective probabilities must be filled one by one, they must sum up 1. First, press add value (see arrow in Fig.), fill a probability number and press enter; then press add value and fill once again the next probability, repeat the action until you have filled the probabilities for all matrices. The order of the probabilities must follow the order of the years input. Each year represent a matrix. e.g. 0.1, 0.1, 0.1, 0.1, 0.2, 0.4 (all the probabilities must sum up 1)
years	Years in which the data of the matrices were collected. The years must be added one by one as list. First click in add value, fill the first year and press enter, then press add value and fill once again the next year, repeat the action until you have fill all the years. The years can be display as follow: e.g. • 1987 or • 1987-1988
sumweight	A vector of ones and zeroes used to omit stage classes when checking density. threshold. The respective sumweights must be filled one by one, the values must be 1 if the stage is included or 0 if is absent. First, press add value (see arrow in Fig.), fill a sumweights number and press enter; then press add value and fill once again the next sumweight, repeat the action until you have filled the sumweights for all stages. The order of the sumweights must follow the order of the stage input. e.g. 1, 1, 1, 1, 1 (all the stages are included) e.g. 1, 1, 1, 0, 1 (stage G is omit)
nmax	It is a maximum number of individuals beyond which population projections cannot exceed. No density dependence: If the user wants to use no density dependence, this is established by: First, click in add value, then in the left window a List is added with a "Some input data goes here" element in the right window. Delete that text. After deletion the "List" have no elements in the right window. When running the workflow, Rshell script will assign NULL to the input. (this is when you are running the wf in Taverna workbench). Density dependence: If the user wants to introduce a density dependence: Click in add value and write the number in the right space. e.g. 500

Processors (14)

Name	Type	Description
RequestStageMatrices	workflow
ReadStageMatrix	workflow
Flatten_List	localworker	Script flatten(inputs, outputs, depth) { for (i = inputs.iterator(); i.hasNext();) { element = i.next(); if (element instanceof Collection && depth > 0) { flatten(element, outputs, depth - 1); } else { outputs.add(element); } } } outputlist = new ArrayList(); flatten(inputlist, outputlist, 1);
Convert_LRn2_to_RLn2	workflow
graph	rshell	Script library(popbio) if (length(probabilities) == 0) { probabilities <- NULL } if (length(weight) == 0) { weight <- NULL } n_max <- if (length(n_max) == 0) NULL else n_max[1] x.eq <- stoch.projection(matrices, abundances, tmax=intervals, nreps=iterations, nmax=n_max) x.uneq <- stoch.projection(matrices, abundances, tmax=intervals, nreps=iterations, nmax=n_max, prob=probabilities, sumweight=weight) eq<-x.eq uneq<-x.uneq Sum_x.eq<- apply(x.eq, 1, sum) Sum_x.uneq<- apply(x.uneq, 1, sum) max_Sum_x.eq <- max(Sum_x.eq) max_Sum_x.uneq <- max(Sum_x.uneq) maxofall<- max(max_Sum_x.eq, max_Sum_x.uneq) maxrounded<-maxofall+100-(maxofall %% 100) png(stochastic_growth_plot) par(xpd=T, mar=c(5,5,4,6)) hist(Sum_x.eq, xlim=c(0,maxrounded), col="lightblue", breaks=seq(0,maxrounded,100), xlab=paste("Final population size at t=", intervals), main='') par(new=TRUE) hist(Sum_x.uneq, col = rgb(0, 0, 1, 0.2), xaxt='n', yaxt='n', ylab='', xlab='', breaks=seq(0,maxrounded,100), main='') title(graph_title, cex.main=1) legend("topright", c("equal", "unequal"),fill=c("lightblue", rgb(0, 0, 1, 0.2))) abline(v=sum(abundances), lty=3) dev.off() R Server localhost:6311
Abundance_Interaction	interaction	Abundance iteraction: Initial abundance: In this dialogue authomatically appears the fields to fill out the initial abundance per stage observed in the field (see data below). After fill out the abundances, the user confirms the numbers. As a example Gentiana pneumonanthe has 5 stages with its respective abundance: stage abundance 1) S (seedlings) 69 2) J (Juveniles) 100 3) V (vegetative) 111 4) G (reproductive individuals) 21 5) D (dormant plants) 43 Interaction Page http://biovel.googlecode.com/svn/tags/mpm-20140521/set_abundance.html
multiple	stringconstant	Value false
Year	stringconstant	Value Year
AddNames	rshell	Script names(expr) <- labels R Server localhost:6311
OutputFundamentalMatrix_3	workflow
OutputFundamentalMatrix_3_2	workflow
Initial_Population_Vector	stringconstant	Value Select initial population vector
Select_matrix_files	stringconstant	Value Select matrix files
FirstListElement	beanshell	Script elem = list.get(0);

Beanshells (1)

Name	Description	Inputs	Outputs
FirstListElement		list	elem

Outputs (3)

Name	Description
stochastic_projection
equal_selection
unequal_selection

Datalinks (28)

Source	Sink
years	RequestStageMatrices:values_L
multiple:value	RequestStageMatrices:multiple
Year:value	RequestStageMatrices:field
Select_matrix_files:value	RequestStageMatrices:title
Flatten_List:outputlist	ReadStageMatrix:matrix_file
stages	ReadStageMatrix:labels_L
RequestStageMatrices:matrices_LL	Flatten_List:inputlist
ReadStageMatrix:matrix_Rn2	Convert_LRn2_to_RLn2:list_of_r_expressions
probabilities	graph:probabilities
iterations	graph:iterations
intervals	graph:intervals
graph_title	graph:graph_title
stages	graph:stages
AddNames:expr	graph:abundances
Convert_LRn2_to_RLn2:r_list_of_expressions	graph:matrices
sumweight	graph:weight
nmax	graph:n_max
stages	Abundance_Interaction:stages
Initial_Population_Vector:value	Abundance_Interaction:title
FirstListElement:elem	Abundance_Interaction:message
stages	AddNames:labels
Abundance_Interaction:abundances	AddNames:expr
graph:eq	OutputFundamentalMatrix_3:input
graph:uneq	OutputFundamentalMatrix_3_2:input
years	FirstListElement:list
graph:stochastic_growth_plot	stochastic_projection
OutputFundamentalMatrix_3:output	equal_selection
OutputFundamentalMatrix_3_2:output	unequal_selection