IPMpack (version 2.1)

makeIntegerFmatrix: Builds P and F matrices built off regressions fitted to discrete variables (with probability mass functions rather than probability density functions).

Description

Uses survival, growth and fecundity objects to construct a matrix defining per-capita contribution to recruitment stages (e.g., propagules [seed, spore], seedlings, calves) by reproductive stages due to sexual reproduction (for the F matrix); and transition probabilities determined from survival and growth to quasi-continuous stages based on integer data (e.g. number of leaves) as opposed to truly continuous data (e.g. mass). NOTE - old createIntegerPmatrix is being deprecated; use makeIntegerPmatrix instead; etc

Usage

makeIntegerFmatrix(fecObj, nEnvClass = 1, meshpoints = 1:20, 
	chosenCov = data.frame(covariate=1), 
	preCensus = TRUE, survObj = NULL, growObj = NULL, offspringObj=NULL)
makeIntegerPmatrix(nEnvClass = 1, 
		meshpoints = 1:20,
		chosenCov = data.frame(covariate = 1), 
		growObj, survObj, 
		discreteTrans = 1)

Arguments

fecObj

fecundity object.

nEnvClass

numeric, number of environmental classes, always = 1 for non-compound matrices.

meshpoints

numeric, identifying meshpoints

chosenCov

data-frame indicating level of the discrete covariate, or range of values where multiple covariates are modeled.

preCensus

logical (TRUE or FALSE), indicating whether the fecundity object should represent an interval between pre-breeding or a post-breeding censuses. defaults to TRUE (pre-breeding census), meaning that all reproduction and offspring rates required for the F matrix are embedded in fecObj. Alternatively, an F matrix based on post-breeding census (preCensus=FALSE) requires additional survObj and growObj, to cover the survival and growth of the parents until the reproductive event.

survObj

survival object, describing the survival of parents from a census until the reproductive event starts (at some point during the inter-census time step). If preCensus = FALSE but no survival object is provided, it is assumed that all individuals survive to the breeding event.

growObj

growth object, describing the growth of parents that survive until the reproductive event starts. Warning: this growth object is still ignored in makeIPMFmatrix in the current version of IPMpack. It will become functional in coming versions. So far it is assumed that at time of breeding the individuals have the same size as at the beginning of the time interval.

discreteTrans

object of class discreteTrans, or numeric.

offspringObj

growth object, describing the size of offspring (this process may alternatively appear in fecObj).

Value

an object of class IPMmatrix with dimensions length(meshpoints)*length(meshpoints), or length(meshpoints)+nrow(discreteTrans).

Details

do check whether the Pmatrix adequately reflects survival by using diagnosticsPmatrix().

References

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

See Also

makeDiscreteTransInteger, makeFecObjInteger

Examples

# Open dataset for the herbaceous perennial Cryptantha flava 
# where the state variable is integer (number of rosettes)
data(dataIPMpackCryptantha)
head(dataIPMpackCryptantha)
d <- dataIPMpackCryptantha

#See the description of the data for information on the variables
help(dataIPMpackCryptantha)

# For this example, focus only on the first annual transition available 
# in the dataset
d1 <- d[d$year==2004, ]

#Make survival, growth and fecundity objects assuming a poisson distribution
so <- makeSurvObj(d1)
go1 <- makeGrowthObj(d1, Formula = sizeNext~size, Family = "poisson")
fo <- makeFecObjInteger(d1, Formula = fec1~size, distOffspring = "poisson")

#Create P and F matrices
Pmatrix1 <- makeIntegerPmatrix(growObj = go1, survObj = so, meshpoints = 1:101, 
    discreteTrans = 1)
Fmatrix <- makeIntegerFmatrix(fecObj = fo, meshpoints = 1:101)

par(mfrow = c(1, 3), bty = "l")

plot(d1$size, d1$sizeNext, xlab = "Stage at t", ylab = "Stage at t+1")

image(Pmatrix1@meshpoints, Pmatrix1@meshpoints, t(Pmatrix1), 
	xlab = "Stage at t", 
		ylab = "Stage at t+1")
image(Fmatrix@meshpoints, Fmatrix@meshpoints, t(Fmatrix), 
	xlab = "Stage at t", 
		ylab = "Stage at t+1")		

#Same approach, but with negative binomial instead of 
# poisson for stage transitions
go2 <- makeGrowthObj(d1, Formula = sizeNext~size, Family = "negbin")

#Recalculate the P matrix
Pmatrix2 <- makeIntegerPmatrix(growObj = go1, survObj = so, 
    meshpoints = 1:101, discreteTrans = 1)

par(mfrow = c(1, 3), bty = "l")
plot(d1$size, d1$sizeNext, xlab = "Stage at t", ylab = "Stage at t+1")
points(1:100, predict(go2@fit[[1]], newdata = data.frame(size = 1:100),
		type = "response"), type = "l", col = 2)

image(Pmatrix2@meshpoints, Pmatrix2@meshpoints, t(Pmatrix2), 
	xlab = "Stage at t", 
		ylab = "Stage at t+1")
image(Fmatrix@meshpoints, Fmatrix@meshpoints, t(Fmatrix), 
	xlab = "Stage at t", 
		ylab = "Stage at t+1")		

#The following repeats the same approach, but with negative binomial 
# instead of poisson for stage transitions
dff <- generateData()
go2 <- makeGrowthObj(d1, Family = "negbin")
Pmatrix2 <- makeIntegerPmatrix(growObj = go2, survObj = so, 
    meshpoints = 1:101, discreteTrans = 1)