Description
Extinction Risk Estimation.
Description
Estimates extinction risk from population time series under a drifted Wiener process using the w-z method for accurate confidence intervals.
README.md
extr
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)
#> --- 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, 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