longevity {Rage}

Calculate longevity from a matrix population model

Description

Calculate longevity (the age x at which survivorship for a synthetic cohort falls below some critical proportion) from a matrix population model

Usage

longevity(matU, start = 1L, x_max = 1000, lx_crit = 0.01)

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). Optionally with named rows and columns indicating the corresponding life stage names.

start

The index (or stage name) of the first stage at which the author considers the beginning of life. Defaults to 1. Alternately, a numeric vector giving the starting population vector (in which case length(start) must match ncol(matU)). See section Starting from multiple stages.

x_max

The maximum age, in units of the MPM projection interval, to which survivorship will be calculated. Defaults to 1000.

lx_crit

Proportion of initial cohort remaining before all are considered dead (a value between 0 and 1). Defaults to 0.01.

Value

Returns longevity, the integer age at which expected survivorship falls below lx_crit. If survivorship doesn't reach lx_crit by x_max, returns NA and prints a warning message.

Starting from multiple stages

Rather than specifying argument start as a single stage class from which all individuals start life, it may sometimes be desirable to allow for multiple starting stage classes. For example, if we want to start our calculation of longevity from reproductive maturity (i.e., first reproduction), we should account for the possibility that there may be multiple stage classes in which an individual could first reproduce.

To specify multiple starting stage classes, specify argument start as the desired starting population vector, giving the proportion of individuals starting in each stage class (the length of start should match the number of columns in the relevant MPM).

Note

Note that the units of time in returned values are the same as the (ProjectionInterval) of the MPM.

Author(s)

Roberto Salguero-Gomez <[e-mail]>

Hal Caswell <[e-mail]>

References

Caswell, H. 2001. Matrix Population Models: Construction, Analysis, and Interpretation. Sinauer Associates; 2nd edition. ISBN: 978-0878930968

Morris, W. F. & Doak, D. F. 2003. Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis. Sinauer Associates, Sunderland, Massachusetts, USA

See Also

mature_distrib for calculating the proportion of individuals achieving reproductive maturity in each stage class.

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

Examples

data(mpm1)

longevity(mpm1$matU, start = 2)
longevity(mpm1$matU, start = "small") # equivalent using named life stages
longevity(mpm1$matU, start = 2, lx_crit = 0.05)

# starting from first reproduction
repstages <- repro_stages(mpm1$matF)
n1 <- mature_distrib(mpm1$matU, start = 2, repro_stages = repstages)
longevity(mpm1$matU, start = n1)