IPMpack (version 2.1)

largeMatrixCalc: Calculates population growth rate (lambda) and stable stage distribution in a computationally efficient way when the number of bins in the IPM is large.

Description

Method to calculate population growth rate (lambda) and stable stage distribution where a large number of bins are used in the IPM, as it may be the case with species that vary largely in size, or models that include size x age interactions.

Usage

largeMatrixCalc(Pmatrix, Fmatrix, tol = 1e-08)

Arguments

Pmatrix

object of class IPMmatrix describing survival transitions.

Fmatrix

object of class IPMmatrix describing fecundity transitions.

tol

tolerance for convergence, defaults to 1e-08.

Value

lambda

Population rate of increase.

stableDist

Stable stage distribution.

h1

size bin width.

References

Rees and Ellner. 2009. Integral projection models for populations in temporally varying environments. The American Naturalist 79, p575-594.

Caswell. 2001. Matrix population models: construction, analysis, and interpretation. 2nd ed. Sinauer. p377-502.

Garcia, Dahlgren, Ehrlen. 2011. No evidence of senescence in a 300-year-old mountain herb. Journal of Ecology 99, p1424-1430.

Examples

dff <- generateData()
Pmatrix <- makeIPMPmatrix(minSize = min(dff$size, na.rm = TRUE), 
	maxSize = max(dff$size, na.rm = TRUE), growObj = makeGrowthObj(dff), 
	  survObj = makeSurvObj(dff))
Fmatrix <- makeIPMFmatrix(minSize = min(dff$size, na.rm = TRUE), 
	maxSize = max(dff$size, na.rm = TRUE),fecObj = makeFecObj(dff))

largeMatrixCalc(Pmatrix, Fmatrix)

par(mfrow=c(1,2),pty="s")

plot(largeMatrixCalc(Pmatrix, Fmatrix)$stableDist, 
    ylab = "Stable stage distribution", 
	xlab = "Continuous (e.g. size) stage", 
	type = "l", col = "blue", lty = 1, ylim = c(0:1))

#Note that this will not always run - as tolerance levels 
# for convergence are set to be quite high
#plot(largeMatrixCalc(Pmatrix, Fmatrix)$reprodValue, 
#    ylab = "Reproductive value", 
#	xlab = "Continuous (e.g. size) stage", type = "l", col = "red", 
#    lty = 1, ylim = c(0:1))