Skill: population-viability-analysis

Inputs

Outputs

Steps

1. Build the projection matrix Read vital rates from CSV. Confirm all survival rates are in (0, 1] and fecundity ≥ 0. Construct Leslie (age-structured) or Lefkovitch (stage-structured) matrix. If stage boundaries are ambiguous, document choice in decision_log.md.

2. Compute λ and confidence interval (invoke matrix_pva.R) Calculate dominant eigenvalue λ = Re(eigen(A)$values[1]). Bootstrap vital rates (1000 resamples) to obtain 95% CI for λ. If λ < 1.0: population declining. If λ < 0.95: high extinction risk.

3. Sensitivity and elasticity analysis Compute sensitivity matrix S and elasticity matrix E. Identify which vital rate (survival, growth, fecundity) most affects λ. High elasticity for adult survival → management interventions should target adults.

4. Deterministic projection Project N(t) = A^t × N(0) over n_years. If CV of vital rates > 0.30, note that deterministic projection underestimates variance. Plot projection with initial population size.

5. Stochastic simulation (invoke stochastic_pva.R) Draw vital rates from Beta (survival) and Poisson/Normal (fecundity) distributions each time step using CV from input table. Run n_simulations replicates. Track N(t) for each. Calculate P(N(t) < Ne) for each year to produce extinction probability curve.

6. Compute MTE and IUCN assessment Mean time to extinction = mean year of first crossing Ne across simulations. Classify against IUCN criteria:

   • P(extinction in 100 yr) > 50% → Critically Endangered (criterion E)

   • 20% → Endangered; > 10% → Vulnerable.

7. Validate and document Check λ from step 2 is consistent with stochastic simulation trend. Record all vital rate sources, CV assumptions, and IUCN classification rationale in decision_log.md.

Decision Points

Key Decisions to Document

Record the following in decision_log.md after running this skill:

• Source of vital rate estimates (literature, field data, expert elicitation) and associated uncertainty
• Choice of Leslie vs. Lefkovitch structure and age/stage class boundaries
• Quasi-extinction threshold (Ne) and its biological justification
• Distribution assumptions for stochastic vital rate draws (Beta, Poisson, Normal)
• Whether IUCN criterion E classification was performed and the result

Tools and Libraries

R

suppressPackageStartupMessages(library(popbio))    # matrix PVA: lambda, sensitivity, elasticity
suppressPackageStartupMessages(library(dplyr))     # data manipulation
suppressPackageStartupMessages(library(tidyr))     # reshaping
suppressPackageStartupMessages(library(ggplot2))   # plotting trajectories and curves
suppressPackageStartupMessages(library(boot))      # bootstrapping vital rates

Python

import numpy as np           # eigenvalue computation, matrix multiplication
import pandas as pd          # vital rate tables
import matplotlib.pyplot as plt  # trajectory plots
from pathlib import Path     # file system

Resources

• skills/population-viability-analysis/resources/matrix-model-guide.md — Leslie vs. Lefkovitch matrices, λ computation, sensitivity and elasticity reference table
• skills/population-viability-analysis/resources/extinction-risk-thresholds.md — IUCN criteria A–E, quasi-extinction thresholds, MVP concept and literature values
• skills/population-viability-analysis/resources/sensitivity-elasticity-reference.md — Published elasticities by taxon group and management implications

Notes

• λ from a single matrix ignores temporal variation: A single matrix built from pooled data produces a long-run average λ. If vital rates vary strongly between years (drought, disease outbreaks), the stochastic geometric mean growth rate (λ_s) will be lower than the deterministic λ.
• Sensitivity vs. elasticity are complementary: Sensitivity identifies which matrix element has the largest absolute effect on λ; elasticity identifies the proportional effect. For management, elasticity is more interpretable because it accounts for the natural scale of each vital rate.
• Small-population effects are not captured by matrix models: Inbreeding depression, Allee effects, and demographic stochasticity in very small populations (N < 20) require individual-based models (IBM) that are beyond this skill's scope.
• Do not extrapolate beyond data range: If only 5 years of demographic data exist, projections to 100 years carry enormous uncertainty. Report CIs from bootstrapping and note the data limitation explicitly.
• IUCN criterion E requires peer-reviewed vital rates: Self-collected data with < 3 years of monitoring should not be used as the sole basis for an IUCN listing under criterion E without independent validation.