stochPassageTime: Estimates passage time in a discretely varying environment.
In IPMpack: Builds and analyses Integral Projection Models (IPMs).

Description Usage Arguments Details Value Author(s) References See Also Examples

Estimates the time in units of the chosen time steps (see convertIncrement()) that it will take to reach a chosen continuous stage value for the first time conditional on surviving from each of the meshpoints of the IPM for each starting environment.

1	stochPassageTime(chosenSize, IPMmatrix, envMatrix)

`chosenSize`	numeric, target size for which passage time is desired.
`IPMmatrix`	object of class IPMmatrix describing survival related transitions only.
`envMatrix`	object of class envMatrix describing transitions between discrete environmental states.

Passage time for values exactly equal to the target size are one year, because of how the conditionals are framed. Values slightly less than the target size may on average take longer due to variance in growth, mortality, leading to discontinuities in the pattern of passage time over age. Passage time from values > than the chosenSize should be ignored (space to the right of the red vertical line in example below).

vector containing passage times across size in the first discrete environmental state, then in the second, etc.

C. Jessica E. Metcalf, Sean M. McMahon, Roberto Salguero-Gomez & Eelke Jongejans

Caswell, 2001. Matrix population models: analysis, construction and interpretation. 2nd ed. Sinauer.

Metcalf, Horvitz, Tuljapurkar, Clark. 2009. A time to grow and a time to die: a new way to analyze the dynamics of size, light, age and death of tropical trees. Ecology 90, p2766-2778.

For bias in this estimation where variance in growth is small relative to the size range: Zuidema, Jongejans, Chien, During & Schieving. 2010. Integral Projection Models for trees: a new parameterization method and a validation of model output. Journal of Ecology 98, p345-355.

passageTime

dff <- generateData()
Pmatrix <- makeCompoundPmatrix(minSize = min(dff$size, na.rm = TRUE),
maxSize=max(dff$size, na.rm = TRUE), 
growObj = makeGrowthObj(dff, Formula=sizeNext~size+covariate), 
survObj = makeSurvObj(dff, Formula = surv~size+covariate), 
envMatrix = makeEnvObj(dff), correction="constant")
targetSize <- 8

passage <- stochPassageTime(targetSize, Pmatrix, makeEnvObj(dff))

plot(Pmatrix@meshpoints,passage[1:length(Pmatrix@meshpoints)], 
	ylab = "Passage time", xlab = "Continuous (e.g. size) stage", 
	type = "l", col = "dark gray", 
	xlim=c(Pmatrix@meshpoints[1],targetSize),
	ylim = c(0, max(passage)))
abline(v = targetSize, col = "red")
points(Pmatrix@meshpoints,
	passage[(length(Pmatrix@meshpoints)+1):(2*length(Pmatrix@meshpoints))], 
		type="l",col="green")