IPMpack (version 2.1)

makeCompoundPmatrix: Builds a compound P matrix.

Description

Uses growth, survival, discreteTrans, and environmental transition objects to construct a matrix defining probabilities for transitions between continuous stages (e.g. size) due to growth and survival given both size and environmental state and discrete stages. NOTE - old createCompoundPmatrix is being deprecated; use makeCompoundPmatrix instead.

Usage

makeCompoundPmatrix(nEnvClass = 2, nBigMatrix = 50,
minSize = -1, maxSize = 50, envMatrix, growObj, survObj,
discreteTrans = 1, integrateType = "midpoint",correction = "none")

Arguments

nEnvClass

numeric, number of environmental classes, defaults to 2.

nBigMatrix

numeric, number of size bins in the P matrix, defaults to 50.

minSize

numeric, minimum size of the P matrix, defaults to -1.

maxSize

numeric, maximum size of the P matrix, defaults to 50.

envMatrix

envMatrix object defining transitions between environmental states for each size.

growObj

growth object.

survObj

survival object.

discreteTrans

object of class discreteTrans, or numeric.

integrateType

integration type, defaults to "midpoint" (which uses probability density function); other option is "cumul" (which uses the cumulative density function).

correction

correction type, defaults to none. The first option is constant which will multiply every column of the IPM by a constant sufficient to adjust values to those predicted for survival at that size. The second option is discretizeExtremes which will place all transitions to sizes smaller than minSize into the smallest bin, and transitions to sizes larger than maxSize into the largest bin.

Value

an object of class IPMmatrix with dimensions nBigMatrix * nEnvClass, or if discrete transitions exist (nBigMatrix + nDisc) * nEnvClass

Details

This structure can also be used to define size x age IPMs, where the transition between ages is reflected by a similar matrix.

References

For information on P matrix: Caswell. 2001. Matrix population models: construction, analysis, and interpretation. 2nd ed. Sinauer. p110-112.

For habitat x stage modeling: Tuljapurkar, Horvitz & Pascarella. 2003. The many growth rates and elasticities of populations in random environments. American Naturalist 162: p489-502. Pascarella & Horvitz. 1998. Hurricane disturbance and the population dynamics of a tropical understory shrub: megamatrix elasticity analysis. Ecology 79: p547-563. Horvitz & Schemske. 1986. Seed dispersal and environmental heterogeneity in a neotropical herb: A model of population and patch dynamics. In Symposium on frugivores and seed dispersal . (Estrada & Fleming, eds.) Dr. W. Junk Publishers, Dordrecht, Netherlands. pp. 169-186.

For age x size modeling: Garcia, Dahlgren and Ehrlen. 2011. No evidence of senescence in a 300-year-old mountain herb. Journal of Ecology 99, p1424-1430.

For general information:

Easterling, Ellner and Dixon. 2000. Size-specific sensitivity: a new structured population model. Ecology 81, p694-708.

Ellner and Rees. 2006. Integral projection models for species with complex demography. The American Naturalist 167, p410-428.

See Also

makeCompoundFmatrix,makeIPMPmatrix

Examples

# Data with only continuous stage and two habitats
dff <- generateData()
Pmatrix <- makeCompoundPmatrix(minSize = min(dff$size,na.rm = TRUE), 
	maxSize = max(dff$size,na.rm = TRUE), envMatrix = makeEnvObj(dff), 
		growObj = makeGrowthObj(dff, Formula = sizeNext~size+size2+covariate), 
			survObj = makeSurvObj(dff, Formula = surv~size+size2+covariate))

image(1:nrow(Pmatrix), 1:ncol(Pmatrix), t(log(Pmatrix)), 
	xlab = "Continuous stage (e.g. size) at t", 
		ylab = "Continuous stage (e.g. size) at t+1", axes = FALSE)
axis(1, at = 1:nrow(Pmatrix), lab = round(rep(Pmatrix@meshpoints,
    Pmatrix@nEnvClass), 2))
axis(2, at = 1:nrow(Pmatrix), lab = round(rep(Pmatrix@meshpoints,
    Pmatrix@nEnvClass), 2))
abline(h = length(Pmatrix@meshpoints) * (1:Pmatrix@nEnvClass))
abline(v = length(Pmatrix@meshpoints) * (1:Pmatrix@nEnvClass))

# Data with continuous and discrete stages
dff <- generateData(type="discrete")
dff$covariate <- sample(1:3, size = nrow(dff), replace = TRUE)
dff$covariateNext <- sample(1:3, size = nrow(dff), replace = TRUE)
discM <- makeDiscreteTrans(dff)
Pmatrix <- makeCompoundPmatrix(minSize = min(dff$size, na.rm = TRUE), 
	maxSize = max(dff$size, na.rm = TRUE), envMatrix = makeEnvObj(dff), 
		growObj = makeGrowthObj(dff, Formula = sizeNext~size+size2+covariate), 
			survObj = makeSurvObj(dff, Formula = surv~size+size2+covariate), 
				discreteTrans = discM)