PSPMequi {PSPManalysis}

Bifurcation analysis of a structured population model

Description

PSPMequi computes bifurcation curves for a physiologically structured population model as a function of one or two parameters and detects bifurcation points along these curves. When computing equilibrium curves of a physiologically structured population model as a function of one parameter, PSPMequi can detect transcritical bifurcation points (branching points, BP) of both the structured populations as well as environment variables (BPE), limit points (LP) in the equilibrium curve and evolutionary stationary points (ESS). The location of these bifurcation points can subsequently be computed as a function of second parameter. In addition PSPMequi can compute the pairwise invasion plot (PIP) as a function of the resident and a mutant value for one evolving parameter.

Usage

PSPMequi(
  modelname = NULL,
  biftype = NULL,
  startpoint = NULL,
  stepsize = NULL,
  parbnds = NULL,
  parameters = NULL,
  minvals = NULL,
  maxvals = NULL,
  options = NULL,
  clean = FALSE,
  force = FALSE,
  debug = FALSE,
  silent = FALSE
)

Arguments

modelname

(string, required)

Basename of the file with the model specification. The file should have an extension ".h". For example, the model "PNAS2002" is specified in the file "PNAS2002.h". If the model is specified in R include the .R extension explicitly, i.e. specify the model name as "PNAS2002.R"

biftype

(string, required)

Type of bifurcation to compute: "BP", "BPE", "EQ", "LP", "ESS" or "PIP"

startpoint

(row vector, required)

The initial point from which to start the continuation of the curve

stepsize

(double value, required)

Value of the step size in the first bifurcation parameter

parbnds

(row vector, required)

Vector of length 3 for EQ continuation, length 6 for BP, BPE, LP and PIP continuation and 3+4*N for ESS continuation. The first triplet specifies: Each triples specifies:

⁠parbnds[1]⁠: the index of the first bifurcation parameter (in case the model is specified in R, this can be a string with the name of the parameter as specified in the variable 'DefaultParameters')

⁠parbnds[2]⁠: lower threshold, below which value of the first bifurcation parameter the computation stops

⁠parbnds[3]⁠: upper threshold, above which value of the first bifurcation parameter the computation stops

In case of two-parameter bifurcations, the second triplet specifies:

⁠parbnds[4]⁠: the index of the second bifurcation parameter (in case the model is specified in R, this can be a string with the name of the parameter as specified in the variable 'DefaultParameters')

⁠parbnds[5]⁠: lower threshold, below which value of the second bifurcation parameter the computation stops

⁠parbnds[6]⁠: upper threshold, above which value of the second bifurcation parameter the computation stops

In case of ESS continuation, consecutive sets of 4 values specify:

⁠parbnds[4*n]⁠: the index of population that is impacted by the parameter at its ESS value (in case the model is specified in R, this can be a string with the name of the parameter as specified in the variable 'DefaultParameters') ⁠parbnds[4*n+1]⁠: the index of the parameter at its ESS value ⁠parbnds[4*n+2]⁠: lower threshold, below which value of this ESS parameter the computation stops ⁠parbnds[4*n+3]⁠: upper threshold, above which value of this ESS parameter the computation stops

parameters

(row vector, optional, can be left equal to its default NULL)

Vector of length PARAMETER_NR (set in the model program file; This is the length of the variable 'DefaultParameters' if the model is specified in R), specifying the values for the model parameters to use in the computation. Vectors of other lengths, including an empty vector will be ignored.

minvals

(row vector, optional, can be left equal to its default NULL)

Vector of length (ENVIRON_DIM + POPULATION_NR), specifying minimum values for the environmental variables and the population birth rates, at which computations will stop. Vectors of other lengths, including an empty vector will be ignored.

maxvals

(row vector, optional, can be left equal to its default NULL)

Vector of length (ENVIRON_DIM + POPULATION_NR), specifying maximum values for the environmental variables and the population birth rates, at which computations will stop. Vectors of other lengths, including an empty vector will be ignored.

options

(row vector of strings, optional, can be left equal to its default NULL)

Vector with pairs of strings, consisting of an option name and a value (for example c("popBP", "1")) or single options (i.e. c("test")). Possible option names and their values are:

⁠"envBP", "<index>"⁠: Index of environment variable, of which to continue the transcritical bifurcation

⁠"popBP", "<index>"⁠: Index of structured population, of which to continue the transcritical bifurcation

⁠"popEVO", "<index>"⁠: Index of structured population, for which to compute the selection gradient or perform PIP continuation

⁠"parEVO", "<index>"⁠: Index of parameter, for which to compute the selection gradient

⁠"envZE", "<index>"⁠: Index of environment variable in trivial equilibrium (can be used multiple times)

⁠"popZE", "<index>"⁠: Index of structured population in trivial equilibrium (can be used multiple times)

⁠"isort", "<index>"⁠: Index of i-state variable to use as ruling variable for sorting the structured populations

⁠"report", "<value>"⁠: Interval between consecutive output of computed points to the console ( >= 1). Minimum value of 1 implies output of every point

⁠"noBP"⁠: Do not check for branching points while computing equilibrium curves

⁠"noLP"⁠: Do not check for limit points while computing equilibrium curves

⁠"single"⁠: Only compute the first point of the solution curve, do not continue the curve

⁠"test"⁠: Perform only a single integration over the life history, reporting dynamics of survival, R0, i-state and interaction variables

clean

(Boolean, optional argument)

Specify clean = TRUE as argument to remove all the result files of the model before the computation

force

(Boolean, optional argument)

Specify force = TRUE as argument to force a rebuilding of the model before the computation

debug

(Boolean, optional argument)

Specify debug = TRUE as argument to compile the model in verbose mode and with debugging flag set

silent

(Boolean, optional argument)

Specify silent = TRUE as argument to suppress reporting of compilation commands and results on the console

Details

output <- PSPMequi(modelname = NULL, biftype = NULL, startpoint = NULL, stepsize = NULL, parbnds = NULL, parameters = NULL, minvals = NULL, maxvals = NULL, options = NULL, clean = FALSE, force = FALSE, debug = FALSE, silent = FALSE)

Value

The output is a list containing the following elements:

⁠curvepoints⁠: Matrix with output for all computed points along the curve

⁠curvedesc⁠: Column vector with strings, summarizing the numerical details of the computed curve (i.e., initial point, parameter values, numerical settings used)

⁠bifpoints⁠: Matrix with the located bifurcation points along the curve

⁠biftypes⁠: Column vector of strings, containing a description of the type of bifurcation for each of the located bifurcation points

Examples

## Not run: 
PSPMequi("Indet_growth", "EQ", c(1, 0.22, 0), -0.1, c(6, 0.8, 1.0),
         options = c("popEVO", "0"), silent = TRUE)

## End(Not run)