knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
Regardless of whether the stage classes of a matrix population model (MPM) are based on age, size, and/or ontogeny, it's possible to obtain age-specific schedules of survivorship (lx) and reproduction (mx) using 'age-from-stage' methods, as described by Caswell (2001).
We'll start by loading a few packages and a dataset that we'll be using throughout this vignette.
library(Rage) # load Rage data(mpm1) # load data object 'mpm1' mpm1 # display the contents
This MPM has 5 stage class, and it's apparent from the dimnames
attribute that the stages are not based solely on age. Nonetheless, we can estimate age-schedules of survivorship and reproduction using the functions mpm_to_lx()
and mpm_to_mx()
from Rage
.
dimnames(mpm1$matU) # extract U and F matrices mat_U <- mpm1$matU mat_F <- mpm1$matF # calculate lx lx <- mpm_to_lx(mat_U, start = 1, xmax = 30) # calculate mx mx <- mpm_to_mx(mat_U, mat_F, start = 1, xmax = 30)
In addition to the relevant matrix components, the mpm_to_*
functions require two extra arguments. The first, start
, is an integer indicating which stage reflects the 'start of life'. Usually this will be 1
, but sometimes we might want to skip over stages that are propagule (i.e. seed) or dormant. The MPM we selected begins with a seed stage, so we may want to start from the second stage, corresponding to start = 2
. The second argument, N
is the number of time steps to calculate over.
# calculate lx lx <- mpm_to_lx(mat_U, start = 1, xmax = 30) # calculate mx mx <- mpm_to_mx(mat_U, mat_F, start = 1, xmax = 30)
Let's take a look at the trajectories.
plot(lx, ylim = c(0, 1), type = "l", xlab = "Age") plot(mx, type = "l", xlab = "Age")
Now we'll extend the basic approach above to many models. Specifically, we'll examine trajectories of survivorship for all of the tree species in Compadre
. Compadre
is a database of matrix population models. You can read more about it here, and the associated R package here. The Rcompadre
package contains a subset of the database that we can use to demonstrate computations on many models simultaneously.
First, we'll subset Compadre
to our group of interest (OrganismType == "Tree"
). We'll also remove matrices with missing values, and limit our selection to matrices with a periodicity (i.e. transition interval) of 1 year.
library(Rcompadre) data(Compadre) # In older versions of Com(p)adre the ProjectionInterval column was called # AnnualPeriodicity. if ("AnnualPeriodicity" %in% names(Compadre)) { Compadre$ProjectionInterval <- Compadre$AnnualPeriodicity } comp_flag <- cdb_flag(Compadre, "check_NA_U") comp_use <- subset(comp_flag, OrganismType == "Tree" & check_NA_U == FALSE & ProjectionInterval == 1)
Let's take a look at the species/populations that made the cut.
CompadreData(comp_use)[, c( "SpeciesAccepted", "MatrixPopulation", "MatrixTreatment" )]
Notice that there are 3 matrices for the species Phyllanthus indofischeri, reflecting different treatment groups. Let's collapse these replicates down to a single matrix per species, by averaging the relevant MPMs using cdb_collapse()
. We'll also use the function cdb_id_stages()
, to make sure we're only collapsing matrices that have the same stage class definitions.
# add column ID-ing matrices with same MatrixClassAuthor vector comp_use$stage_id <- cdb_id_stages(comp_use) # collapse database to single matrix per species * MatrixClassAuthor comp_collapse <- cdb_collapse(comp_use, "stage_id") # check species/populations again CompadreData(comp_collapse)[, c( "SpeciesAccepted", "MatrixPopulation", "MatrixTreatment" )]
Next, let's look at the organized stage classes for each MPM. If any of our MPMs include propagule or dormant stage classes, we may want to account for them when calculating lx.
MatrixClassOrganized(comp_collapse)
Indeed, 1 MPM includes a propagule stage. So let's use the function mpm_first_active()
to determine the first 'active' stage class for each MPM, which we'll use to define the start of life.
comp_collapse$start_life <- mpm_first_active(comp_collapse)
Finally, we'll use lapply()
to apply the function mpm_to_lx
to each row of comp_collapse
. By default, lapply()
will return a vector for each row, and the length of which is xmax
. We can convert the output to an matrix, with columns representing each row from comp_collapse
using do.call
. After that, we'll use the function matplot()
to plot age-trajectories of survivorship for each species.
lx_list <- lapply(seq_len(nrow(comp_collapse)), function(x, comp_collapse) { U <- matU(comp_collapse$mat[[x]]) rownames(U) <- colnames(U) # ensure row and col names are present mpm_to_lx( matU = U, start = comp_collapse$start_life[x], xmax = 40 ) }, comp_collapse = comp_collapse ) lx_array <- do.call(cbind, lx_list) matplot(lx_array, type = "l", lty = 1, log = "y", ylim = c(0.0001, 1), lwd = 1.5, xlab = "Age (years)", ylab = "lx" )
Caswell, H. (2001). Matrix Population Models: Construction, Analysis, and Interpretation. 2nd edition. Sinauer Associates, Sunderland, MA. ISBN-10: 0878930965
Any scripts or data that you put into this service are public.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.