Calculate quasi-extinction threshold.

Created: 2014-08-14 11:52:34

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This models do not permit extinction, however we can study quasi-extinction (Caswell 2001). A population is quasi-extinct if it shrinks to a specific fraction of its current size (Ginsbur et al 1982 in Caswell 2001). The quasi-extinction threshold can be chosen in the belief that it would pose a significant threat of the real exaction (Caswell 2001).

METHOD: SIMULATING EXTINCTION PROBABILITIES Keep track of whether the total population density (or the density summed across a subset of the classes with which we are particularly concerned, such as the reproductive classes) has fallen below the quasiextinction threshold each year. The fraction of realizations that first hit the threshold during or before year t gives the cumulative probability of extinction (Morris and Doak 2002). This workflow performs such a calculation.

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)

This workflow estimates by simulation the quasi-extinction probability time cumulative distribution function for a structured population in an independently and identically distributed (iid) stochastic environment. This workflow is based on the popbio package (stoch.quasi.ext - Calculate quasi-extinction threshold, Stubben, Milligan and Nantel, 2013) based on the The MATLAB code in Box 7.5 (Morris and Doak 2002). For more details of the analysis see: Calculating the probability of hitting a quesi-extinction threshold by time t, method: simulating extinction probabilities (Morris and Doak 2002, pag: 241-244 and Caswell 2001, pag: 443-444). This models do not permit extinction, however we can study quasi-extinction (Caswell 2001). A population is quasi-extinct if it shrinks to a specific fraction of its current size (Ginsbur et al 1982 in Caswell 2001). The quasi-extinction threshold can be chosen in the belief that it would pose a significant threat of the real exaction (Caswell 2001). METHOD: SIMULATING EXTINCTION PROBABILITIES Keep track of whether the total population density (or the density summed across a subset of the classes with which we are particularly concerned, such as the reproductive classes) has fallen below the quasiextinction threshold each year. The fraction of realizations that first hit the threshold during or before year t gives the cumulative probability of extinction (Morris and Doak 2002). This workflow performs such a calculation. 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 (9)

Name	Description
stages	the names of the stages or categories of the input matrix. In the following example, the matrix has 5 stages. 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 quasiextinction threshold graph. Click in set value and then write the text in the right space. 100 is the quasiextinction threshold value used in this tutorial run. Please do not use a title longer than the suggest it.
intervals	This value is the farthest future time horizon (e.g. 25) and therefore the years of axis X of the output graph.
iterations	The number of realization of population growth to simulate each run or number of iterations.
probabilities	Probabilities of choosing each submitted matrix. Note that the value of probabilities must equal to 1. This value can be ignore if the user does want use probabilities [ ]. Use probabilities: Each probability corresponding to each year and each year corresponds to a matrix. Probabilities and years should follow the same order. e.g. In this tutorial, 6 matrices are used, therefore 6 probabilities must be used, the probabilities must follow the same order as the submitted matrices (years). [0.1, 0.2, 0.2, 0.2, 0.1, 0.2]. The probabilities must be settled to 1. The first matrix (year = 1987) has a 0.1% probability to be chosen over 1. The second matrix (year = 1988) has a 0.2% probability to be chosen over 1. etc. Ignore probabilities: When the user wants to ignore the use of probabilities: [ ]
years	Eeach year represents a matrix and therefore characterizes a period of transition. The respective years must be filled one by one. In the tutorial, we have 6 matrices (see 5.2.2 Input data) that represent 6 years (e.g.: 1987 =data interval between 1987 and 1988; 1988= data interval between 1988 and 1989).
threshold	The quasi-extinction threshold, express as a density. The entries in the inicial population vector represent densities, but quasi-extinction thresholds are typically expressed in terms of numbers of individuals (Morris and Doak 2002). Thus when we ask whether the summed densities across all or a subset of the classes has fallen below the quasi-extinction threshold, we first need to be sure that a numerical threshold has been converted to a density. For example, let's assume that the densities in the population vector represent mean numbers of individuals per hectare, that the population occupies 1,000 hectares, and that we have decided to set the quasiextinction threshold at a total of 100 individuals in the reproductive classes. One hundred reproductive individuals in the entire population represents an average density of 0.1 individuals per hectare summed across the reproductive classes, so we would consider the population to have hit the threshold if this sum hits 0.1, not 100. Alternatively, we could multiply the starting densities by 1,000 to arrive at an estimate of total numbers and set the quasiextinction threshold to 100 (Morris and Doak 2002).
max_runs	The number of times to simulate CDF (cumulative distribution function).
sumweight	Summed density to compare the quasi-extinction threshold. A vector of ones and zeroes used to omit stage classes when checking quasiextinction threshold (0 = omit a stage, 1= include). Use sumweight, ignore stages: In this tutorial, matrices have 5 stages, therefore 5 sumweight data must be used, the sumweight values must follow the same order as the submitted stages. In this example, the zero instruct the workflow to ignore seedlings (S is the first stage, see Stages) when summing the densities across classes to compare to the quasi-extinction threshold (Figure 9). Ignore sumweight: When the user wants to ignore the use of sumweight: [ ]

Processors (15)

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) png(quasiextinction_plot) if (length(probabilities) == 0) { probabilities<- NULL } if (length(weight) == 0) { weight<- NULL } x<-stoch.quasi.ext(matrices, abundances, Nx=threshold, tmax=intervals, maxruns=max_runs, nreps=iterations, prob=probabilities, sumweight=weight) matplot(x, xlab="Years", ylab="Quasi-extinction probability", type='l', lty=1, col=rainbow(10), las=1, main=graph_title, cex.main=1) 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
false	stringconstant	Value false
Year	stringconstant	Value Year
AddNames	rshell	Script names(expr) <- labels R Server localhost:6311
OutputFundamentalMatrix_3	workflow
Initial_Population_Vector	stringconstant	Value Set initial population vector
FirstListElement	beanshell	Script elem = list.get(0);
Select_a_matrix	stringconstant	Value Select a matrix
forceEqualNumberMatricesPerField	stringconstant	Boolean to force or not that the user introduces the same number of matrices in each field. Possible values: true => all elements should have the same number of matrices false => the elements can have different number of matrices from one to anot Value false
minMatricesPerField	stringconstant	Minimum number of matrices per field Value 1

Beanshells (1)

Name	Description	Inputs	Outputs
FirstListElement		list	elem

Outputs (2)

Name	Description
quasiextinction_threshold_graph	Plots the numeric results of the Quasi-extinction threshold numeric results.
quasiextinction_threshold	This text has been adapted to the Gentiana exampled following Morris and Doak (2002). The Figure 19 and 20 are the numeric and graphic results of 50 separate runs of this workflow, each with 5,000 separate realizations of population growth and a quasi-extinction threshold of 100. Figure 20 shows little variation among the separate runs, indicating that in this example, 5,000 realizations provide a reasonably good estimate of the extinction time CDF (Morris and Doak 2002, advocate increasing the number of realizations per run until separate runs yield very similar estimates for the CDF). Starting with a population density of 344 individual plants, the probability of hitting a threshold density of 50 individual plants reaches a value of 0.1 after only about 7.5 years, and exceeds 0.8 by year 25 (see Morris and Doak 2002). In this tutorial, it is computed the probability that the total density over all classes except seedlings (S) falls below 50. In this example the quasi-extinction threshold is applied to a subset of the stages (J, V, G and D). For this purpose, the sumweights were [0 1 1 1 1 1] (see input ports example Sumweight ignoring seedlings (S) when summing the densities across classes to compare to the quasi-extinction threshold (Morris and Doak 2002). The entries in the Initial population vector (see interactions) represent densities, but quasi-extinction thresholds are typically expressed in terms of numbers of individuals. Thus when it is asked whether the summed densities across all or a subset of the classes has fallen below the quasi-extinction threshold, first it is necessary to be sure that a numerical threshold has been converted to a density. For example, let's assume that the densities in the population vector represent mean numbers of individuals per hectare, that the population occupies 100 hectares, and that we have decided to set the quasiextinction threshold at a total of 50 individuals. One hundred reproductive individuals in the entire population represents an average density of 0.5 individuals per hectare summed across the J, V, G and D stages, so it would be considered the population to have hit the threshold if this sum hits 0.5, not 50. Alternatively, it could be multiplied the starting densities by 100 to arrive at an estimate of total numbers and set the quasiextinction threshold to 50 (Morris and Doak 2002).

Name

Description

quasiextinction_threshold_graph

Plots the numeric results of the Quasi-extinction threshold numeric results.

quasiextinction_threshold

This text has been adapted to the Gentiana exampled following Morris and Doak (2002). The Figure 19 and 20 are the numeric and graphic results of 50 separate runs of this workflow, each with 5,000 separate realizations of population growth and a quasi-extinction threshold of 100. Figure 20 shows little variation among the separate runs, indicating that in this example, 5,000 realizations provide a reasonably good estimate of the extinction time CDF (Morris and Doak 2002, advocate increasing the number of realizations per run until separate runs yield very similar estimates for the CDF). Starting with a population density of 344 individual plants, the probability of hitting a threshold density of 50 individual plants reaches a value of 0.1 after only about 7.5 years, and exceeds 0.8 by year 25 (see Morris and Doak 2002). In this tutorial, it is computed the probability that the total density over all classes except seedlings (S) falls below 50. In this example the quasi-extinction threshold is applied to a subset of the stages (J, V, G and D). For this purpose, the sumweights were [0 1 1 1 1 1] (see input ports example Sumweight ignoring seedlings (S) when summing the densities across classes to compare to the quasi-extinction threshold (Morris and Doak 2002). The entries in the Initial population vector (see interactions) represent densities, but quasi-extinction thresholds are typically expressed in terms of numbers of individuals. Thus when it is asked whether the summed densities across all or a subset of the classes has fallen below the quasi-extinction threshold, first it is necessary to be sure that a numerical threshold has been converted to a density. For example, let's assume that the densities in the population vector represent mean numbers of individuals per hectare, that the population occupies 100 hectares, and that we have decided to set the quasiextinction threshold at a total of 50 individuals. One hundred reproductive individuals in the entire population represents an average density of 0.5 individuals per hectare summed across the J, V, G and D stages, so it would be considered the population to have hit the threshold if this sum hits 0.5, not 50. Alternatively, it could be multiplied the starting densities by 100 to arrive at an estimate of total numbers and set the quasiextinction threshold to 50 (Morris and Doak 2002).

Datalinks (29)

Source	Sink
years	RequestStageMatrices:values_L
false:value	RequestStageMatrices:multiple
Year:value	RequestStageMatrices:field
Select_a_matrix:value	RequestStageMatrices:title
forceEqualNumberMatricesPerField:value	RequestStageMatrices:forceEqualNumberMatricesPerField
minMatricesPerField:value	RequestStageMatrices:minMatricesPerField
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
threshold	graph:threshold
max_runs	graph:max_runs
sumweight	graph:weight
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:x	OutputFundamentalMatrix_3:input
years	FirstListElement:list
graph:quasiextinction_plot	quasiextinction_threshold_graph
OutputFundamentalMatrix_3:output	quasiextinction_threshold