# Bootstrap observed census transitions Calculate bootstrap distributions of population growth rates (lambda), stage vectors, and projection matrix elements by randomly sampling with replacement from a stage-fate data frame of observed transitions ```r boot.transitions(transitions, iterations, by.stage.counts = FALSE, ...) ``` ## Arguments - `transitions`: a stage-fate data frame with stage or age class in the current census, fate in the subsequent census, and one or more fertility columns - `iterations`: Number of bootstrap iterations - `by.stage.counts`: Resample transitions with equal probability (default) or by subsets of initial stage counts - ``...``: additional options passed to `projection.matrix` ## Returns A list with 3 items - **lambda**: A vector containing bootstrap values for lambda - **matrix**: A matrix containing bootstrap transtion matrices with one projection matrix per row. - **vector**: A matrix containing bootstrap stage vectors with one stage vector per row. ## Examples ```r ## create stage-fate dataframe using merge and subset trans01 <- subset( merge(test.census, test.census, by="plant", sort=FALSE), year.x==2001 & year.y==2002) ## format column and row names trans01 <- trans01[,c(1:4,6)] colnames(trans01)[2:5] <- c("year", "stage", "fruits", "fate") rownames(trans01) <- 1:nrow(trans01) # order stage columns corresponding to matrix trans01$stage <- ordered(trans01$stage, levels = c("seedling", "vegetative", "reproductive")) ## add individual fertilities using prebreeding census with no seed bank ## based on the proportional reproductive outputs of flowering plants ## and the total number of seedlings at the end of the projection interval seedlings <- nrow(subset(test.census, year==2002 & stage=="seedling")) trans01$seedling <- trans01$fruits/sum(trans01$fruits) * seedlings trans01 ## Step by step instructions for bootstrapping dataframe n <- nrow(trans01) n set.seed(77) x <- sample(n, replace=TRUE) x bt <- trans01[x,] bt projection.matrix(bt) ## or respample by stage class counts lapply(split(trans01, trans01$stage, drop=TRUE), function(x) x[sample(nrow(x), replace=TRUE),]) ## using boot.transitions boot.transitions(trans01, 5) boot.transitions(trans01, 5, by.stage=TRUE) ## Aquilegia example x <- subset(aq.trans, year==1996) # calculate lamda, seed survival and recruitment rate using aq.matrix rec <- nrow(subset(aq.trans, year==1997 & stage == "recruit")) aq.96 <- aq.matrix(x, rec) # add individual fertilities to data frame only aq.96.trans <- aq.matrix(x, rec, summary=FALSE) # pass estimated transitions in aq.96 to projection matrix aq.96.boot <- boot.transitions(aq.96.trans, 200, add=c(1,1, aq.96$seed.survival, 2,1, aq.96$recruitment.rate) ) # calculate percentile intervals using quantile() ci <- quantile(aq.96.boot$lambda, c(0.025,0.975) ) aq.96$lambda ci # plot histogram hist(aq.96.boot$lambda, col="green", xlab="Lambda", main=paste('Bootstrap estimates of population\ngrowth rate from 1996-1997')) abline(v=ci, lty=3) ``` ## References see Morris and Doak 2005 in [http://esapubs.org/Archive/mono/M075/004/appendix-A.htm](http://esapubs.org/Archive/mono/M075/004/appendix-A.htm) for resampling by stage class counts ## See Also `projection.matrix` ## Author(s) Chris Stubben

boot.transitions function