# Estimates variation in passage time.

### Description

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

### Usage

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

### Arguments

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

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

### Details

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.

### Value

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).

### Author(s)

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

### References

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.

### See Also

`passageTime`

, `makeIPMPmatrix`

### Examples

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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