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 Weighting stages), excluding certain stage classes from the calculation (see Excluding stages), and defining the set of biologically-possible transitions (see Possible transitions).
These decompositions assume that all transition rates are products of a
stage-specific survival term (column sums of 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.
vr_survival(matU, posU = matU > 0, exclude_col = NULL, weights_col = NULL)
vr_growth(
matU,
posU = matU > 0,
exclude = NULL,
exclude_row = NULL,
exclude_col = NULL,
weights_col = NULL,
surv_only_na = TRUE
)
vr_shrinkage(
matU,
posU = matU > 0,
exclude = NULL,
exclude_row = NULL,
exclude_col = NULL,
weights_col = NULL,
surv_only_na = TRUE
)
vr_stasis(
matU,
posU = matU > 0,
exclude = NULL,
weights_col = NULL,
surv_only_na = TRUE
)
vr_dorm_enter(matU, posU = matU > 0, dorm_stages, weights_col = NULL)
vr_dorm_exit(matU, posU = matU > 0, dorm_stages, weights_col = NULL)
vr_fecundity(
matU,
matR,
posR = matR > 0,
exclude_col = NULL,
weights_row = NULL,
weights_col = NULL
)The survival component of a matrix population model (i.e., a square projection matrix reflecting survival-related transitions; e.g., progression, stasis, and retrogression)
A logical matrix of the same dimension as matU, with
elements indicating whether a given matU transition is possible
(TRUE) or not (FALSE). Defaults to matU > 0 (see
Possible transitions).
Integer, character or logical vector indicating stages for which transitions both to and from the stage should be excluded from the calculation of vital rates. See section Excluding stages.
Vector of stage-specific weights to apply while averaging vital rates across columns. See section Weighting stages.
Integer, character or logical vector indicating stages for which transitions both to and from the stage should be excluded from the calculation of vital rates. See section Excluding stages.
Integer, character or logical vector indicating stages for which transitions both to and from the stage should be excluded from the calculation of vital rates. See section Excluding stages.
If there is only one possible matU transition in a
given column, should that transition be attributed exclusively to survival?
If TRUE, the vital rate of growth/stasis/shrinkage in that column
will be coerced to NA. If FALSE, dividing the single
transition by the stage-specific survival probability will always yield a
value of 1. Defaults to TRUE.
Integer or character vector indicating dormant stage classes.
The reproductive component of a matrix population model (i.e., a square projection matrix reflecting transitions due to reproduction; either sexual, clonal, or both)
A logical matrix of the same dimension as matR, with
elements indicating whether a given matR transition is possible
(TRUE) or not (FALSE). Defaults to matR > 0 (see
Possible transitions).
Vector of stage-specific weights to apply while summing vital rates across rows within columns. See section Weighting stages.
Vector of vital rates. Vital rates corresponding to impossible
transitions are coerced to NA (see Possible transitions).
A transition rate of 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 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 vr_ functions assume that a transition rate of
0 indicates an impossible transition, in which case a value of
NA will be used in relevant calculations. Specifically, the arguments
posU and posR are specified by the logical expressions
(matU > 0) and (matR > 0), respectively. If the matrix
population model includes transitions that are estimated to be 0 but
still in fact possible, one should specify the posU and/or posR
arguments manually.
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 from a set of stage classes (e.g., averaging
stage-specific survival probabilities across multiple stages). All vr_
functions therefore include an optional argument 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 to a set of stage classes (e.g., summing the
production of different types of offspring, such as seeds vs. seedlings). The
function vr_fecundity therefore also includes an optional
argument weights_to.
If supplied, weights_from will automatically be scaled to sum to 1
over the set of possible transitions, whereas weights_to will not be
rescaled because we wish to enable the use of reproductive values here, which
do not naturally sum to 1.
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 to the dormant stage class using the argument
exclude_row. We may or may not want to ignore 'growth' transitions
from the dormant stage class, which can be done using
exclude_col. To exclude transitions both to and from a given
set of stages, use argument exclude.
Other vital rates:
vital_rates(),
vr_mat,
vr_vec
# 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)
#> [1] 0.6666667
vr_growth(matU, exclude = 4)
#> [1] 0.7166667
vr_shrinkage(matU, exclude = 4)
#> [1] 0.1111111
vr_stasis(matU, exclude = 4)
#> [1] 0.3
# `exclude*` and `*_stages` arguments can accept stage names
matU <- name_stages(matU)
matF <- name_stages(matF)
vr_dorm_enter(matU, dorm_stages = "stage_4")
#> [1] 0.5555556
vr_dorm_exit(matU, dorm_stages = 4)
#> [1] 0.3333333
vr_fecundity(matU, matF, exclude_col = 4)
#> [1] 2.055556