Function to take a P matrix (either compound or not) and estimate variance in passage time to a chosen continuous stage value.

1 | ```
varPassageTime(chosenSize, IPMmatrix)
``` |

`chosenSize` |
The continuous stage value of interest. |

`IPMmatrix` |
The Pmatrix (compound or not). |

Note how variation in passage time for values exactly equal to the chosen size (targetSize) are low, because of way the conditionals are framed. Passage time from values > than targetSize should be ignored (space to the right of the red vertical line in example below), unless dealing with an organism that is able to display retrogression.

Numeric vector corresponding to variance in passage time from each of the meshpoints in the IPM (so both size, and if a compound matrix, size from different environments).

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

Caswell, 2001. Matrix population models: analysis, construction and interpretation. 2nd ed. Sinauer. p119.

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.

For species with shrinkage: Salguero-Gomez & Casper. 2010. Keeping shrinkage in the demographic loop. Journal of Ecology 98, p313-323.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# With continuous (e.g. size) stage
dff <- generateData()
Pmatrix <- makeIPMPmatrix(minSize = min(dff$size, na.rm = TRUE),
maxSize <- max(dff$size, na.rm = TRUE), growObj = makeGrowthObj(dff),
survObj = makeSurvObj(dff))
targetSize <- 8
vP <- varPassageTime(targetSize, Pmatrix)
plot(Pmatrix@meshpoints, vP, type = "l", xlab="Continuous (e.g. Size) stage",
xlim=c(Pmatrix@meshpoints[1],targetSize),
ylab = "Variance in passage time", col = "dark gray")
abline(v = targetSize, col = "red")
## not sure variance works with this....
``` |

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