shape_rep: Calculate shape of reproduction over age

In Rage: Life History Metrics from Matrix Population Models

Calculate shape of reproduction over age

Description

Calculates a 'shape' value of distribution of reproduction over age by comparing the area under a cumulative reproduction curve (over age) with the area under a cumulative function describing constant reproduction.

Usage

shape_rep(rep, surv = NULL, xmin = NULL, xmax = NULL, ...)

Arguments

rep	Either 1) a numeric vector describing reproduction over age (mx), 2) a data.frame / list with one column / element titled 'mx' describing a reproduction over age, optionally a column / element 'x' containing age classes (each element a number representing the age at the start of the class), or 3) a matrix, specifically the reproduction submatrix (e.g. F matrix) of a matrix population model. If rep is provided as a matrix, then surv must be provided as the U submatrix of the matrix population model. In case (2), if x is not supplied, the function will assume age classes starting at 0 with time steps of unit. If x ends at maximum longevity, mx[which.max(x)] should equal 0; however it is possible to supply partial reproduction schedules.
surv	An optional argument to be used if rep is provided as a matrix (the reproduction submatrix of the matrix population model.) If rep is provided as a matrix, then surv should also be provided as a the U submatrix of the matrix population model.
xmin, xmax	The minimum and maximum age respectively over which to evaluate shape. If not given, these default to min(x) and max(x) respectively.
...	Additional variables passed to 'mpm_to_mx' when the data are provided as matrices.

Value

a shape value describing symmetry of reproduction over age by comparing the area under a cumulative reproduction curve over age with the area under constant reproduction. May take any real value between -0.5 and +0.5. A value of 0 indicates negligible ageing (neither generally increasing nor generally decreasing reproduction with age); positive values indicate senescence (generally decreasing reproduction with age); negative values indicate negative senescence (generally increasing reproduction with age). A value of +0.5 indicates that (hypothetically) all individuals are born to individuals of age 0; a value of -0.5 indicates that all individuals are born at the age of maximum longevity.

Author(s)

Iain Stott <[e-mail]>

References

Baudisch, A, Stott, I. 2019. A pace and shape perspective on fertility. Methods Ecol Evol. 10: 1941– 1951. <https://doi.org/10.1111/2041-210X.13289>

See Also

Other life history traits: entropy_d(), entropy_k(), gen_time(), life_expect_mean(), longevity(), net_repro_rate(), repro_maturity, shape_surv()

Examples

# increasing mx yields negative shape
mx <- c(0, 0, 0.3, 0.4, 0.5, 0.6)
shape_rep(mx)

# decreasing mx yields positive shape
mx <- c(1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4)
shape_rep(mx)

# constant mx yields shape = 0
mx <- c(0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)
shape_rep(mx)

# calculate mx trajectory first
mpm_to_mx(matU = mpm1$matU, matR = mpm1$matF)


# providing the matrices directly
data(mpm1)
shape_rep(rep = mpm1$matF, surv = mpm1$matU)

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