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```
#' Derive mean vital rates from a matrix population model
#'
#' @description
#' Derive mean vital rates of survival, growth (or development), shrinkage (or
#' de-development), stasis, dormancy, or reproduction from a matrix population
#' model, by averaging across stage classes. These functions include optional
#' arguments for custom weighting of different stage classes (see
#' \emph{Weighting stages}), excluding certain stage classes from the
#' calculation (see \emph{Excluding stages}), and defining the set of
#' biologically-possible transitions (see \emph{Possible transitions}).
#'
#' These decompositions assume that all transition rates are products of a
#' stage-specific survival term (column sums of \code{matU}) and a lower level
#' vital rate that is conditional on survival (growth/development,
#' shrinkage/de-development, stasis, dormancy, or a/sexual reproduction).
#' Reproductive vital rates that are not conditional on survival (i.e., within a
#' stage class from which there is no survival) are also allowed.
#'
#' @param 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)
#' @param matR The reproductive component of a matrix population model (i.e., a
#' square projection matrix reflecting transitions due to reproduction; either
#' sexual, clonal, or both)
#' @param posU A logical matrix of the same dimension as \code{matU}, with
#' elements indicating whether a given \code{matU} transition is possible
#' (\code{TRUE}) or not (\code{FALSE}). Defaults to \code{matU > 0} (see
#' \emph{Possible transitions}).
#' @param posR A logical matrix of the same dimension as \code{matR}, with
#' elements indicating whether a given \code{matR} transition is possible
#' (\code{TRUE}) or not (\code{FALSE}). Defaults to \code{matR > 0} (see
#' \emph{Possible transitions}).
#' @param exclude Integer, character or logical vector indicating stages for
#' which transitions both \emph{to} and \emph{from} the stage should be
#' excluded from the calculation of vital rates. See section
#' \emph{Excluding stages}.
#' @param exclude_row Integer, character or logical vector indicating stages for
#' which transitions both \emph{to} and \emph{from} the stage should be
#' excluded from the calculation of vital rates. See section
#' \emph{Excluding stages}.
#' @param exclude_col Integer, character or logical vector indicating stages for
#' which transitions both \emph{to} and \emph{from} the stage should be
#' excluded from the calculation of vital rates. See section
#' \emph{Excluding stages}.
#' @param dorm_stages Integer or character vector indicating dormant stage
#' classes.
#' @param weights_row Vector of stage-specific weights to apply while summing
#' vital rates across rows within columns. See section \emph{Weighting
#' stages}.
#' @param weights_col Vector of stage-specific weights to apply while averaging
#' vital rates across columns. See section \emph{Weighting stages}.
#' @param surv_only_na If there is only one possible \code{matU} transition in a
#' given column, should that transition be attributed exclusively to survival?
#' If \code{TRUE}, the vital rate of growth/stasis/shrinkage in that column
#' will be coerced to \code{NA}. If \code{FALSE}, dividing the single
#' transition by the stage-specific survival probability will always yield a
#' value of \code{1}. Defaults to \code{TRUE}.
#'
#' @return Vector of vital rates. Vital rates corresponding to impossible
#' transitions are coerced to \code{NA} (see \emph{Possible transitions}).
#'
#' @section Possible transitions:
#' A transition rate of \code{0} within a matrix population model may indicate
#' that the transition is not possible in the given life cycle (e.g., tadpoles
#' never revert to eggs), or that the transition rate is possible but was
#' estimated to be \code{0} in the relevant population and time period. If vital
#' rates are to be averaged across multiple stage classes, or compared across
#' populations, it may be important to distinguish between these two types of
#' zeros.
#'
#' By default, the \code{vr_} functions assume that a transition rate of
#' \code{0} indicates an impossible transition, in which case a value of
#' \code{NA} will be used in relevant calculations. Specifically, the arguments
#' \code{posU} and \code{posR} are specified by the logical expressions
#' \code{(matU > 0)} and \code{(matR > 0)}, respectively. If the matrix
#' population model includes transitions that are estimated to be \code{0} but
#' still in fact possible, one should specify the \code{posU} and/or \code{posR}
#' arguments manually.
#'
#' @section Weighting stages:
#' In averaging vital rates across stages, it may be desirable to weight stage
#' classes differently (e.g., based on reproductive values or stable
#' distributions). Weights are generally applied when averaging across columns,
#' i.e., across transitions \emph{from} a set of stage classes (e.g., averaging
#' stage-specific survival probabilities across multiple stages). All \code{vr_}
#' functions therefore include an optional argument \code{weights_from}.
#'
#' In principle, particularly for vital rates of reproduction, the user can also
#' apply weights when summing across rows within columns, i.e., across
#' reproductive transitions \emph{to} a set of stage classes (e.g., summing the
#' production of different types of offspring, such as seeds vs. seedlings). The
#' function \code{vr_fecundity} therefore also includes an optional
#' argument \code{weights_to}.
#'
#' If supplied, \code{weights_from} will automatically be scaled to sum to 1
#' over the set of possible transitions, whereas \code{weights_to} will not be
#' rescaled because we wish to enable the use of reproductive values here, which
#' do not naturally sum to 1.
#'
#' @section Excluding stages:
#' It may be desirable to exclude one or more stages from the calculation of
#' certain vital rates. For instance, we might not believe that 'growth' to a
#' dormant stage class really reflects biological growth, in which case we could
#' exclude transitions \emph{to} the dormant stage class using the argument
#' \code{exclude_row}. We may or may not want to ignore 'growth' transitions
#' \emph{from} the dormant stage class, which can be done using
#' \code{exclude_col}. To exclude transitions both \emph{to and from} a given
#' set of stages, use argument \code{exclude}.
#'
#' @author Patrick Barks <patrick.barks@@gmail.com>
#'
#' @family vital rates
#'
#' @examples
#' # create example MPM (stage 4 is dormant)
#' matU <- rbind(
#' c(0.1, 0, 0, 0),
#' c(0.5, 0.2, 0.1, 0.1),
#' c(0, 0.3, 0.3, 0.1),
#' c(0, 0, 0.5, 0.4)
#' )
#'
#' matF <- rbind(
#' c(0, 0.7, 1.1, 0),
#' c(0, 0.3, 0.8, 0),
#' c(0, 0, 0, 0),
#' c(0, 0, 0, 0)
#' )
#'
#' vr_survival(matU, exclude_col = 4)
#' vr_growth(matU, exclude = 4)
#' vr_shrinkage(matU, exclude = 4)
#' vr_stasis(matU, exclude = 4)
#'
#' # `exclude*` and `*_stages` arguments can accept stage names
#' matU <- name_stages(matU)
#' matF <- name_stages(matF)
#' vr_dorm_enter(matU, dorm_stages = "stage_4")
#' vr_dorm_exit(matU, dorm_stages = 4)
#'
#' vr_fecundity(matU, matF, exclude_col = 4)
#'
#' @name vr
NULL
#' @rdname vr
#' @export vr_survival
vr_survival <- function(matU,
posU = matU > 0,
exclude_col = NULL,
weights_col = NULL) {
vr_vec <- vr_vec_survival(
matU = matU,
posU = posU,
exclude_col = exclude_col
)
return(column_weight(vr_vec, weights_col))
}
#' @rdname vr
#' @export vr_growth
vr_growth <- function(matU,
posU = matU > 0,
exclude = NULL,
exclude_row = NULL,
exclude_col = NULL,
weights_col = NULL,
surv_only_na = TRUE) {
vr_vec <- vr_vec_growth(
matU = matU,
posU = posU,
exclude = exclude,
exclude_row = exclude_row,
exclude_col = exclude_col,
surv_only_na = surv_only_na
)
return(column_weight(vr_vec, weights_col))
}
#' @rdname vr
#' @export vr_shrinkage
vr_shrinkage <- function(matU,
posU = matU > 0,
exclude = NULL,
exclude_row = NULL,
exclude_col = NULL,
weights_col = NULL,
surv_only_na = TRUE) {
vr_vec <- vr_vec_shrinkage(
matU = matU,
posU = posU,
exclude = exclude,
exclude_row = exclude_row,
exclude_col = exclude_col,
surv_only_na = surv_only_na
)
return(column_weight(vr_vec, weights_col))
}
#' @rdname vr
#' @export vr_stasis
vr_stasis <- function(matU,
posU = matU > 0,
exclude = NULL,
weights_col = NULL,
surv_only_na = TRUE) {
vr_vec <- vr_vec_stasis(
matU = matU,
posU = posU,
exclude = exclude,
surv_only_na = surv_only_na
)
return(column_weight(vr_vec, weights_col))
}
#' @rdname vr
#' @export vr_dorm_enter
vr_dorm_enter <- function(matU,
posU = matU > 0,
dorm_stages,
weights_col = NULL) {
vr_vec <- vr_vec_dorm_enter(
matU = matU,
posU = posU,
dorm_stages = dorm_stages
)
return(column_weight(vr_vec, weights_col))
}
#' @rdname vr
#' @export vr_dorm_exit
vr_dorm_exit <- function(matU,
posU = matU > 0,
dorm_stages,
weights_col = NULL) {
vr_vec <- vr_vec_dorm_exit(
matU = matU,
posU = posU,
dorm_stages = dorm_stages
)
return(column_weight(vr_vec, weights_col))
}
#' @rdname vr
#' @export vr_fecundity
vr_fecundity <- function(matU,
matR,
posR = matR > 0,
exclude_col = NULL,
weights_row = NULL,
weights_col = NULL) {
vr_vec <- vr_vec_reproduction(
matU = matU,
matR = matR,
posR = posR,
exclude_col = exclude_col,
weights_row = weights_row
)
return(column_weight(vr_vec, weights_col))
}
#' @noRd
column_weight <- function(x, weights) {
if (is.null(weights)) {
out <- mean(x, na.rm = TRUE)
} else {
weights[is.na(x)] <- NA_real_
weights <- weights / sum(weights, na.rm = TRUE)
out <- sum(weights * x, na.rm = TRUE)
}
if (is.nan(out)) out <- NA_real_
return(out)
}
```

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