README

The goal of extr is to provide tools for estimating extinction probabilities and confidence intervals for stochastic population models.

Installation

install.packages("extr_1.0.0.tar.gz", repos = NULL, type = "source")

# install.packages("remotes") # if needed
remotes::install_github("hakoyamah/extr")

Function

ext_di()

Estimates demographic parameters and extinction probability under a density-independent (drifted Wiener) model. From a time series of population sizes, it computes MLEs of growth rate and environmental variance, then evaluates extinction risk over a horizon \(t^{\ast}\). Confidence intervals are constructed by the \(w\)-\(z\) method, which achieve near-nominal coverage across the full parameter space.

Example

library(extr)

dat <- data.frame(
  Time = 1959:1987,
  Population = c(
    44, 47, 46, 44, 46, 45, 46, 40, 39, 39, 42, 44, 41, 40,
    33, 36, 34, 39, 35, 34, 38, 36, 37, 41, 39, 51, 47, 57, 47
  )
)

ext_di(dat, th = 100)
#> --- Estimates ---
#>                                                       Estimate
#> Probability of decline to 1 within 100 years (MLE): 9.4128e-05
#> Growth rate (MLE):                                   0.0023556
#> Variance (MLE):                                        0.01087
#> Unbiased variance:                                    0.011273
#> AIC for the distribution of N:                          165.06
#>                                                                        CI
#> Probability of decline to 1 within 100 years (MLE):  (1.4586e-13, 0.5653)
#> Growth rate (MLE):                                  (-0.038814, 0.043525)
#> Variance (MLE):                                     (0.0070464, 0.020885)
#> Unbiased variance:                                                      -
#> AIC for the distribution of N:                                          -
#> 
#> --- Data Summary ---
#>                               Value
#> Current population size, nq:     47
#> xd = ln(nq / ne):            3.8501
#> Sample size, q + 1:              29
#> 
#> --- Input Parameters ---
#>                                                         Parameter
#> Time unit:                                                  years
#> Extinction threshold of population size, ne:                    1
#> Time window for extinction risk evaluation (years), th:     100.0
#> Significance level, alpha:                                   0.05

ext_di(dat, th = 100, ne = 10)
#> --- Estimates ---
#>                                                       Estimate
#> Probability of decline to 10 within 100 years (MLE):  0.096852
#> Growth rate (MLE):                                   0.0023556
#> Variance (MLE):                                        0.01087
#> Unbiased variance:                                    0.011273
#> AIC for the distribution of N:                          165.06
#>                                                                         CI
#> Probability of decline to 10 within 100 years (MLE):  (1.0699e-05, 0.9898)
#> Growth rate (MLE):                                   (-0.038814, 0.043525)
#> Variance (MLE):                                      (0.0070464, 0.020885)
#> Unbiased variance:                                                       -
#> AIC for the distribution of N:                                           -
#> 
#> --- Data Summary ---
#>                               Value
#> Current population size, nq:     47
#> xd = ln(nq / ne):            1.5476
#> Sample size, q + 1:              29
#> 
#> --- Input Parameters ---
#>                                                         Parameter
#> Time unit:                                                  years
#> Extinction threshold of population size, ne:                   10
#> Time window for extinction risk evaluation (years), th:     100.0
#> Significance level, alpha:                                   0.05

ext_di(dat, th = 100, qq_plot = TRUE)

ext_di(dat, th = 100, digits = 9)
#> --- Estimates ---
#>                                                           Estimate
#> Probability of decline to 1 within 100 years (MLE): 9.41283994e-05
#> Growth rate (MLE):                                   0.00235564171
#> Variance (MLE):                                       0.0108702457
#> Unbiased variance:                                    0.0112728474
#> AIC for the distribution of N:                          165.058678
#>                                                                                CI
#> Probability of decline to 1 within 100 years (MLE): (1.45860729e-13, 0.565298682)
#> Growth rate (MLE):                                  (-0.0388142081, 0.0435254915)
#> Variance (MLE):                                     (0.00704642493, 0.0208851222)
#> Unbiased variance:                                                              -
#> AIC for the distribution of N:                                                  -
#> 
#> --- Data Summary ---
#>                                   Value
#> Current population size, nq:         47
#> xd = ln(nq / ne):                3.8501
#> Sample size, q + 1:                  29
#> 
#> --- Input Parameters ---
#>                                                          Parameter
#> Time unit:                                                   years
#> Extinction threshold of population size, ne:                     1
#> Time window for extinction risk evaluation (years), th:      100.0
#> Significance level, alpha:                                    0.05