Generation length for IUCN Red List assessments — rl_generation

Compute generation length, the average age of reproducing individuals in a population, using one of the four definitions given in the IUCN Red List guidance. Generation length sets the time window used by criteria A and C.

Usage

rl_generation_length(
  data,
  method = c("mean_parent", "mean_reproduction", "half_reproduction", "replacement"),
  age = NULL,
  year = NULL,
  id = NULL,
  output = NULL,
  lx = NULL,
  mx = NULL,
  na_rm = TRUE
)

Arguments

data: A data frame or tibble holding the columns the chosen method needs.
method: One of "mean_parent", "mean_reproduction", "half_reproduction", "replacement".
age: Column of ages, unquoted. Used by every method (as x in replacement).
year: Optional grouping column for mean_parent when the population is not at a stable age distribution. Unquoted.
id: Optional individual identifier for half_reproduction. Unquoted.
output: Reproductive output at each age for half_reproduction: offspring produced, or a count of breeding events as a proxy. If omitted, each row counts as one unit of output. Unquoted.
lx, mx: Survivorship and age-specific fecundity columns, unquoted. Required for method = "replacement", and for the life-table form of method = "mean_reproduction".
na_rm: Logical; drop missing values before computing. Default TRUE.

Value

A single numeric value: the generation length.

Details

Each method needs different input columns. Pass the relevant columns unquoted (tidy-style); only the columns a method actually uses need to be present.

"mean_parent" (mean age of parents)

One row per newborn, holding the age of its parent when the newborn was produced. Generation length is the mean parental age. If the population is not at a stable age distribution, supply year: the mean is then taken within each year and averaged across years. Columns: age (required), year (optional).

"mean_reproduction" (mean age of reproduction)

Two input shapes are accepted:

event form: one cohort followed over life, one row per breeding event with the age at which it happened. Generation length is the mean of those ages. Columns: age.
life-table form: one row per age with survivorship lx and age-specific fecundity mx. Generation length is the weighted mean age of reproduction sum(x * lx * mx) / sum(lx * mx), which reproduces the result of the official IUCN generation length calculator. Columns: age, lx, mx.

Supply lx and mx to use the life-table form; omit both for the event form.

"half_reproduction" (50% of reproductive output)

Age at which an individual reaches half of its lifetime reproductive output, averaged over individuals. Output is measured in offspring produced; supply that as output. A count of breeding events works as a proxy when every event yields the same number of offspring. Two input shapes are accepted:

event form: one row per breeding event with an age column (and id to separate individuals); each row counts as one unit of output when output is not supplied;
summarised form: one row per (id, age) with an output column giving the offspring produced at that age.

The 50% age is the weighted median age: the smallest age at which the running total of output reaches half of the individual's lifetime total. Reproductive output happens at an age, so no value between age classes is invented. Columns: age (required), id (required with more than one individual), output (optional; omit for the one-event-per-row form).

"replacement" (replacement rate)

Time for the population to grow by its net reproductive rate R0 = sum(lx * mx). With intrinsic growth rate r the population multiplies by exp(r * t) each unit of time, so T = log(R0) / r, where r solves the Euler-Lotka equation sum(exp(-r * x) * lx * mx) = 1. When the population is essentially stationary (R0 close to 1, r close to 0) the limit is the mean age of reproduction sum(x * lx * mx) / sum(lx * mx), which is returned instead. Columns: age, lx, mx (all required).

References

IUCN Standards and Petitions Committee. 2024. Guidelines for Using the IUCN Red List Categories and Criteria. Version 16. Prepared by the Standards and Petitions Committee. Pages 30-32. https://www.iucnredlist.org/documents/RedListGuidelines.pdf

Examples

# Mean age of parents at a stable age distribution
parents <- data.frame(age = c(5, 5, 3, 3, 4, 6, 6, 4, 5))
rl_generation_length(parents, "mean_parent", age = age)
#> [1] 4.555556

# Mean age of reproduction for one cohort
cohort <- data.frame(age_of_breeding = c(5, 5, 3, 8, 5, 6, 3, 8, 9, 4))
rl_generation_length(cohort, "mean_reproduction", age = age_of_breeding)
#> [1] 5.6

# Same definition from a life table, reproducing the official IUCN
# calculator (this input returns 10.5, as the IUCN workbook does)
# https://www.iucnredlist.org/resources/generation-length-calculator
life_table <- data.frame(
  age = 0:19,
  lx = c(1, 0.1, rep(0.01, 17), 0),
  mx = c(0, 0, 0, rep(30, 16), 0)
)
rl_generation_length(life_table, "mean_reproduction", age = age, lx = lx, mx = mx)
#> [1] 10.5

# 50% of reproductive output, several mothers, weighted by breeding counts
rep_data <- data.frame(
  mother = rep(c("m1", "m2"), each = 3),
  age = c(2, 3, 4, 2, 3, 4),
  n_offspring = c(2, 3, 2, 2, 2, 2)
)
rl_generation_length(rep_data, "half_reproduction",
                     age = age, id = mother, output = n_offspring)
#> [1] 3

# Replacement rate from a life table
life_table <- data.frame(
  age = 1:4,
  lx = c(1, 0.6, 0.3, 0.1),
  mx = c(0, 1.5, 2, 1)
)
rl_generation_length(life_table, "replacement", age = age, lx = lx, mx = mx)
#> [1] 2.465397