IPMpack (version 2.1)

stochGrowthRateManyCov: Estimates stochastic population growth rates (lambda_s) or invasion rate with many varying covariates. Alternatively, tracks population structure in a stochastic environment if trackStruct is TRUE.

Description

Iterates a population vector through a time series of covariates according to growth, survival and fecundity objects, and calculates the stochastic population rate of increase if no density-dependence is specified, or the rate of invasion if density dependence is specified.

Usage

stochGrowthRateManyCov(covariate, nRunIn, tMax,
growthObj, survObj, fecObj, nBigMatrix, minSize, maxSize, 
nMicrosites,integrateType = "midpoint", correction = "none",
trackStruct=FALSE, plot=FALSE, ...)

Arguments

covariate

matrix with tMax rows, and as many columns as there are relevant covariates.

nRunIn

numeric, number of initial samples to discard.

tMax

numeric, total number of time-steps to run (same as ncol(covariate)).

growthObj

a growth object, defined to correspond to covariate definition (indexing used to make the growth object must match up).

survObj

a survival object, defined to correspond to covariate definition in covariate.

fecObj

a fecundity object, defined to correspond to covariate definition in covariate.

nBigMatrix

numeric, number of size bins in the IPM.

minSize

numeric, minimum size in the IPM.

maxSize

numeric, maximum size in the IPM.

nMicrosites

vector, if sum(nMicrosites)> 0 then density dependence is assumed to operate on seedling establishment, and if length(nMicrosites)>1, then the number of microsites available for establishment at time t is nMicrosites[min(t,length(nMicrosites))].

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"; 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 continuous stage value.

trackStruct

Boolean indicating whether you want to track the population structure (beyond simply estimating the growth rate)

plot

Boolean indicating whether a plot of the population structure is desired.

...

extra arguments relating to plotting if trackStruct and plot are TRUE.

Value

Rt

If trackStruct is TRUE, numeric, converging on log lambda_s, or invasion rate (density dependence) for large enough tMax, and if covariate distribution is stationary.

rc

matrix of the numbers of individuals in each size and seed class (row) over time (columns).

IPM.here

IPM constructed corresponding to pop structure and covariates at tMax.

Details

Forms of density dependence beyond density dependence in seedling establishment not yet defined.

References

Ellner & Rees. 2007. Stochastic stable population growth in integral projection models: theory and application. Journal of Mathematical Biology 54, p227-256.

Rees & Ellner. 2009. Integral projection models for populations in temporally varying environments. Ecological Monographs 79, p575-594.

See Also

stochGrowthRateSampleList,

Examples

### NOT RUN - this is hashed out because compiles too slowly ###

# Generate relevant data, build objects
#dff <- generateData(type="stochastic")
#print(head(dff))
#gr1 <- makeGrowthObj(dff, Formula = sizeNext~size+size2+covariate1)
#sv1 <- makeSurvObj(dff, Formula = surv~size+size2+covariate2)
#fv1 <- makeFecObj(dff, Formula = fec~size+size2,Transform="log")

# Generate time series of covariates for which population growth rate 
#is required. Here set to be seasonal environment. 
#Names of covariates must be same as in dff
#tVals <- seq(1,100,by = 1/12)
#covTest <- (1 + 0.5*sin(2*pi*tVals))
#covMatTest <- data.frame(covariate1 = rnorm(length(covTest),covTest,0.5) - 1, 
#covariate2 = rnorm(length(covTest), covTest,0.5) - 1, 
#covariate3 = rnorm(length(covTest), covTest,0.5) - 1, row.names = NULL)

# Calculate

#r <- stochGrowthRateManyCov(covariate = covMatTest, nRunIn = 5*10, 
#tMax = length(tVals), growthObj = gr1, survObj = sv1, fecObj = fv1, 
#nBigMatrix = 100, 
#minSize = 1.1*min(dff$size, na.rm = TRUE), 
#maxSize = 1.1*max(dff$size, na.rm = TRUE), nMicrosites = 0)

#r

# Track population strucuture instead
#st <- stochGrowthRateManyCov(covariate = covMatTest, nRunIn = 5*10, 
#tMax = length(tVals), growthObj = gr1, survObj = sv1, fecObj = fv1, 
#nBigMatrix = 100, 
#minSize = 1.1*min(dff$size, na.rm = TRUE), 
#maxSize = 1.1*max(dff$size, na.rm = TRUE), nMicrosites = 0, 
#trackStruct=TRUE,plot=TRUE)