IPMpack (version 1.6)

sensParams: Estimates sensitivity and elasticity of lambda (or R0, or Life expectancy of a chosen bin) to parameters underlying an IPM.

Description

Uses perturbation to estimate the sensitivity and elasticity of all the parameters underlying an IPM. s

Usage

sensParams(growObj, survObj, fecObj, nBigMatrix, minSize, maxSize,  chosenCov = data.frame(covariate = 1),discreteTrans = 1, integrateType = "midpoint", correction = "none", preCensus = TRUE, delta=1e-4)
sensParamsR0(growObj, survObj, fecObj, nBigMatrix, minSize, maxSize, 
discreteTrans = 1, integrateType = "midpoint", correction = "none", preCensus = TRUE, chosenCov = data.frame(covariate=1),delta=1e-4)
sensParamsLifeExpect(growObj, survObj, nBigMatrix, minSize, maxSize,  chosenCov = data.frame(covariate = 1),
    discreteTrans = 1, integrateType = "midpoint", correction = "none", preCensus = TRUE, 
	delta=1e-4,chosenBin=1)

Arguments

growObj

a growth object.

survObj

a survival object.

fecObj

a fecundity object (not necessary for life expectancy analysis).

nBigMatrix

numeric, number of bins of size used in the IPM matrix.

minSize

numeric, minimum size used for meshpoints of the IPM matrix.

maxSize

numeric, maximum size used for meshpoints of the IPM matrix.

discreteTrans

matrix of discrete transitions; or 1 if there is none

integrateType

integration type.

correction

correction.

preCensus

boolean saying if preCensus fertility or not (not necessary for life expectancy analysis)

delta

size of the perturbation desired

chosenBin

for analysis of life expectancy, which bin in the IPM Life expectancy should be compared for

chosenCov

level or value of the covariate(s) at which sensitivity estimation is desired

Value

• slam
  a vector of sensitivities of lambda with names corresponding to parameters.
• elam
  a vector of elasticities to lambda with names corresponding to parameters.

Details

The values returned by sensParam are calculated by first calculating lambda for the chosen IPM; then modifying the focal parameter c by a very small amount, c.new=c*(1+delta) (the default for delta =1e-4, but users may specify the value that they want). The function then rebuilds the T and F matrices, and re-calculates lambda. Sensitivity is calculated as: sens = df(x)/dx = (lam.new-lam)/(c*delta) i.e., the function estimates the degree to which a small change in the parameter results in a small change in lambda; and elasticity is calculated as: elas = sens*c/lam = (lam.new-lam)/(lam*delta) which corresponds to the proportional change in lambda as an outcome of the proportional change in the parameter; analagous calculations are used for R0 and life expectancy.

References

Rees & Rose. 2002. Evolution of flowering strategies in Oenothera glazioviana: an integral projection model approach. Proceedings of the Royal Society London Seres B 269, p1509-1515.

See Also

sens, elas

Examples

dff <- generateData()

#lambda
res <- sensParams(growObj = makeGrowthObj(dff), 
survObj = makeSurvObj(dff), fecObj = makeFecObj(dff, Transform="log"), nBigMatrix = 50, 
minSize = min(dff$size, na.rm=TRUE), maxSize = max(dff$size, na.rm = TRUE))

par(mfrow = c(2, 1), bty = "l", pty = "m") 
barplot(res$slam, 
main = expression("Parameter sensitivity of population growth rate "* lambda), 
las = 2, cex.names = 0.5) 
barplot(res$elam, 
main = expression("Parameter elasticity of population growth rate "* lambda), 
las = 2, cex.names = 0.5) 

#R0
resR0 <- sensParamsR0(growObj = makeGrowthObj(dff), 
survObj = makeSurvObj(dff), fecObj = makeFecObj(dff, Transform="log"), nBigMatrix = 50, 
minSize = min(dff$size, na.rm=TRUE), maxSize = max(dff$size, na.rm = TRUE))

par(mfrow = c(2, 1), bty = "l", pty = "m") 
barplot(resR0$slam, 
main = expression("Parameter sensitivity of net reproductive rate R"[0]), 
las = 2, cex.names = 0.5) 
barplot(resR0$elam, 
main = expression("Parameter elasticity of net reproductive rate R"[0]), 
las = 2, cex.names = 0.5) 

#life expectancy
resLE <- sensParamsLifeExpect (growObj = makeGrowthObj(dff), 
survObj = makeSurvObj(dff),  nBigMatrix = 50, 
minSize = min(dff$size, na.rm=TRUE), maxSize = max(dff$size, na.rm =
TRUE), chosenBin=1)

par(mfrow = c(2, 1), bty = "l", pty = "m") 
barplot(resLE$slam, 
main = expression("Parameter sensitivity of Life Expectancy"*eta[0]), 
las = 2, cex.names = 0.5) 
barplot(resLE$elam, 
main = expression("Parameter elasticity of Life expectancy"*eta[0]), 
las = 2, cex.names = 0.5) 

# Same as lambda above, but with two fecundity functions
dff$fec2 <- dff$fec>0 #create binomial describing e.g., prob of flowering
dff$fec[dff$fec==0] <- NA #take out zeros to avoid infinity when fit on a log scale
fv1 <- makeFecObj(dff, Formula = c(fec~size+size2,fec2~size), Transform=c("log","none"),
Family = c("gaussian","binomial"))

res <- sensParams(growObj=makeGrowthObj(dff), survObj = makeSurvObj(dff), 
fecObj = fv1, nBigMatrix = 50, minSize = min(dff$size, na.rm = TRUE), 
maxSize = max(dff$size, na.rm = TRUE))

par(mfrow = c(2, 1), bty = "l", pty = "m") 
barplot(res$slam, 
main = expression("Parameter sensitivity of population growth rate " *lambda), 
las = 2, cex.names = 0.5) 
barplot(res$elam, 
main = expression("Parameter elasticity of population growth rate " *lambda), 
las = 2, cex.names = 0.5) 

# Same but with two fecundity functions and a constant
fv1@fecConstants[1] <-0.5
res <- sensParams(growObj = makeGrowthObj(dff), survObj = makeSurvObj(dff), 
fecObj = fv1, nBigMatrix = 50, minSize = min(dff$size, na.rm = TRUE), 
maxSize = max(dff$size, na.rm = TRUE))

par(mfrow = c(2, 1), bty = "l", pty = "m") 
barplot(res$slam, 
main = expression("Parameter sensitivity of population growth rate " *lambda), 
las = 2, cex.names = 0.5) 
barplot(res$elam, 
main = expression("Parameter elasticity of population growth rate " *lambda), 
las = 2, cex.names = 0.5)