mpm_standardize: Transform a matrix population model to a standardized form

In Rage: Life History Metrics from Matrix Population Models

Transform a matrix population model to a standardized form

Description

Transform a matrix population model to a standardized set of stage classes (e.g., propagule, pre-reproductive, reproductive, and post-reproductive). The transition rates in the standardized matrix are a weighted mean of the transition rates and per-capita reproductive values from the relevant stages of the original matrix, weighted by the relative proportion of each stage class expected at the stable distribution.

Usage

mpm_standardize(matU, matF, matC = NULL, repro_stages, matrix_stages)

mpm_standardise(matU, matF, matC = NULL, repro_stages, matrix_stages)

Arguments

matU	The survival component of a matrix population model (i.e., a square projection matrix reflecting survival-related transitions; e.g. progression, stasis, and retrogression).
matF	The sexual component of a matrix population model (i.e., a square projection matrix reflecting transitions due to sexual reproduction).
matC	The clonal component of a matrix population model (i.e., a square projection matrix reflecting transitions due to clonal reproduction). Defaults to NULL, indicating no clonal reproduction (i.e., matC is a matrix of zeros).
repro_stages	Logical vector of length ncol(matU) indicating which stages are reproductive. Alternatively, a vector of stage indices or stage names of the reproductive classes.
matrix_stages	Character vector of matrix stage types (e.g., "propagule", "active", or "dormant").

Details

This function is a wrapper for the functions mpm_rearrange, standard_stages and mpm_collapse, which it calls in sequence.

Value

A list with four elements reflecting the standardized matrix and its components:

matA	Standardized projection matrix
matU	Survival component of the standardized projection matrix
matF	Sexual reproduction component of the standardized projection matrix
matC	Clonal reproduction component of the standardized projection matrix

Missing Stages

The returned standardized matrix will always be of dimension 4, even if one or more standardized stages is missing from the original matrix population model. If a standardized stage is missing, the corresponding row/column of the standardized matrix will be coerced to NA.

Note

The method used by this function to collapse a matrix population model preserves the equilibrium population growth rate (\lambda) and relative stable distribution, but is not expected to preserve other demographic characteristics such as relative reproductive value, sensitivities, net reproductive rate, life expectancy, etc.

Author(s)

Rob Salguero-Gomez <[e-mail]>

See Also

Other transformation: is_leslie_matrix(), leslie_collapse(), mpm_collapse(), mpm_rearrange(), mpm_split(), name_stages(), repro_stages(), standard_stages()

Examples

matU <- rbind(
  c(0.1, 0, 0, 0, 0),
  c(0.5, 0.2, 0.1, 0, 0),
  c(0, 0.3, 0.3, 0.1, 0),
  c(0, 0, 0.4, 0.4, 0.1),
  c(0, 0, 0, 0.1, 0.4)
)

matF <- rbind(
  c(0, 1.1, 0, 1.6, 0),
  c(0, 0.8, 0, 0.4, 0),
  c(0, 0, 0, 0, 0),
  c(0, 0, 0, 0, 0),
  c(0, 0, 0, 0, 0)
)

matC <- rbind(
  c(0, 0.6, 0, 0.5, 0),
  c(0, 0.1, 0, 0.3, 0),
  c(0, 0, 0, 0, 0),
  c(0, 0, 0, 0, 0),
  c(0, 0, 0, 0, 0)
)

repro_stages <- c(2, 4)
matrix_stages <- c("prop", "active", "active", "active", "active")

mpm_standardize(matU, matF, matC, repro_stages, matrix_stages)

Rage documentation built on Sept. 30, 2023, 1:06 a.m.