IPMpack (version 1.6)

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 <- createIPMPmatrix(minSize = min(dff$size, na.rm = TRUE), 
	maxSize = max(dff$size, na.rm = TRUE), growObj = makeGrowthObj(dff), survObj = makeSurvObj(dff))
Fmatrix <- createIPMFmatrix(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))