# resample: Resample a projection matrix In popbio: Construction and Analysis of Matrix Population Models

## Description

Resample a projection matrix using a multinomial distribution for transitions and a log normal distribution for fertilities

## Usage

 `1` ```resample(A, n, fvar = 1.5, ...) ```

## Arguments

 `A` a projection matrix `n` either a stage vector with the number of transitions to sample in each column or a single value that is applied to all columns `fvar` either a vector of different fertility variances or a single variance of fertility (default 1.5) that is applied to all rates `...` additional items are passed to `splitA` and are used to split A into T and F matrices

## Details

The projection matrix A is first split into separate transition and fertility matrices. Dead fates are added to the transtion matrix and the columns are then sampled from a `Multinomial` distribution based on the size in each corresponding stage class in `n`.

The fertility rates are sample from a Log Normal distribution using the `lnorms` function. The variance can be a single value which is applied to all rates, or vector of different values to apply to each rate. In this case, the values are recycled to match the number of non-zero fertilities.

## Value

A resampled projection matrix

## Note

see section 12.1.5.2 on parametric bootsrap in Caswell (2001)

## Author(s)

Chris Stubben

`boot.transitions`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```data(hudsonia) A<-hudsonia[[1]] lambda(A) ## NOTE fertilities are in first two rows, so use r=1:2 for splitting this matrix ## resample transitions 100 times each resample(A, 100, r=1:2) ## set higher fvar in stage 4 and 6 ##because there are two fertilities per stage (8 total), need to repeat values resample(A,1000, fvar=c(1.5, 1.5, 3, 3), r=1:2) ## OR resample based on number of plants surveyed # data from table 6.4 and box 7.3) n<-c(4264,3, 30, 16, 24,5) ## create a list with 1000 resampled matrices x<-lapply(1:1000, function(x) resample(A,n, r=1:2)) mean(x) ## use var2 to check variances, especially if using differnt fvar values var2(x) ## growth rates y<-sapply(x, lambda) quantile( y, c(0.025, .975) ) hist(y, br=30, col="palegreen", xlab="Lambda", main="1985 Hudsonia growth rates") abline(v=quantile(y, c(0.025, .975)), lty=3) ## double the sample size (and quadruple seedlings) and you may be able to detect a decline n<-n*2 n[2]<-n[2]*2 x<-lapply(1:1000, function(x) resample(A, n*2, r=1:2)) quantile( sapply(x, lambda), c(0.025, .975) ) ```