Population Ecology Calculators

0 calculators tagged with “Population Ecology”

Population ecology studies the dynamics of single-species groups — how populations grow, decline, and are regulated over time. Core models include exponential growth (unlimited resources: N(t) = N₀e^(rt)) and logistic growth (density-dependent regulation: dN/dt = rN(1−N/K), where K is the carrying capacity). Population size is determined by births, deaths, immigration, and emigration. Life tables quantify age-specific survival (lₓ) and fecundity (mₓ). Mark-recapture (Lincoln-Petersen: N̂ = MC/R) estimates population size in the field. Population viability analysis (PVA) assesses extinction risk using stochastic models.

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Population Growth Models

Exponential: N(t) = N₀ × e^(rt). Doubling time = 0.693/r. J-shaped curve; unlimited resources. Logistic: dN/dt = rN(1 − N/K). S-shaped curve; density-dependent. Population grows fastest at N = K/2; stabilizes at K. Integrated: N(t) = K / (1 + ((K−N₀)/N₀) × e^(−rt)).

Demographic Parameters

r = intrinsic rate of increase = b − d (birth rate − death rate). R₀ = net reproductive rate = Σlₓmₓ. T = generation time = Σxlₓmₓ / R₀. r ≈ ln(R₀)/T.

Density-Dependent vs. Independent Regulation

Density-dependent: food competition, predation, disease — effects strengthen as N increases → negative feedback → N regulated toward K. Density-independent: weather extremes, catastrophes — affect population regardless of N.

Glossary

Carrying Capacity (K)
The maximum sustainable population size in a given environment; logistic growth stabilizes at N = K; determined by food, water, space, and shelter; varies seasonally and with habitat quality.
Intrinsic Rate of Increase (r)
r = birth rate − death rate; determines exponential growth rate; doubling time = 0.693/r; relates to net reproductive rate: r ≈ ln(R₀)/T.
Lincoln-Petersen Estimator
N̂ = MC/R; mark-recapture method; M = marked released; C = second sample size; R = marked in second sample; assumes closed population and random mixing; Chapman modification used for small samples.

Frequently Asked Questions

Population ecology studies how single-species populations change over time — their size, density, growth rate, age structure, and regulation. Key models: Exponential growth: N(t) = N₀e^(rt); assumes unlimited resources; J-shaped; r = intrinsic rate of increase. Logistic growth: dN/dt = rN(1−N/K); adds density-dependent regulation via carrying capacity K; S-shaped sigmoidal curve; population stabilizes at K. Life table models: lₓmₓ table → R₀ and r. Matrix population models: age-structured projections; elasticity analysis identifies which life stage most affects population growth.

Carrying capacity (K) is the maximum sustainable population size in a given environment, determined by food, water, space, and shelter availability. As N → K in logistic growth: per-capita growth rate (r × (1−N/K)) declines toward zero. Density-dependent mechanisms that reduce growth as N increases: food competition → reduced per-capita resources → lower birth rate, higher death rate. Predation → prey populations increase → predators increase → predation rate rises → prey population regulated. Disease → higher density → easier pathogen transmission → higher mortality. K is not fixed — it changes seasonally and with habitat quality.

Lincoln-Petersen estimator: N̂ = MC/R. M = individuals marked and released in first sample. C = total individuals captured in second sample. R = marked individuals in second sample. Assumptions: closed population (no births/deaths/migration between samples); random mixing; equal catchability of marked and unmarked. Chapman modification (less biased for small samples): N̂ = [(M+1)(C+1)/(R+1)] − 1. Example: tag 50 fish; recapture 40; 8 are tagged: N̂ = 50×40/8 = 250 fish.

A life table tracks a cohort of individuals from birth to death. Key columns: x = age class; nₓ = number alive at age x; lₓ = nₓ/n₀ (survivorship); dₓ = deaths in age class x; qₓ = age-specific mortality = dₓ/nₓ; mₓ = mean female offspring per female at age x; lₓmₓ = contribution to R₀. Demographic parameters: R₀ = Σlₓmₓ (net reproductive rate); R₀ > 1: growing; = 1: stable; < 1: declining. T = Σxlₓmₓ/R₀ (generation time). Survivorship curves: Type I (low early mortality, humans); Type II (constant mortality, birds); Type III (high early mortality, fish, trees).