Age-Structured Population Models

Age-structured models use matrix algebra and eigenanalysis to project population dynamics when vital rates depend on age or stage class.

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Food Web Dynamics

Food webs describe energy flow and species interactions across trophic levels, combining network theory with nonlinear population dynamics.

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Island Biogeography

MacArthur and Wilson's equilibrium theory explains species richness on islands through the balance of immigration and extinction, predicting the species-area relationship.

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Logistic Population Growth

The logistic equation models density-dependent population growth toward a carrying capacity, with rich extensions including chaos, Allee effects, and generalized forms.

differential equations dynamical systems probability theory

Lotka-Volterra Equations

A foundational system of nonlinear ODEs describing predator-prey population dynamics and their oscillatory coexistence.

differential equations dynamical systems

Metapopulation Dynamics

The Levins metapopulation model and its extensions describe how species persist as networks of local populations connected by dispersal.

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Occupancy Models

Occupancy models estimate species occurrence probability while explicitly accounting for imperfect detection, using repeated surveys across sites.

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SIR Epidemic Model

The SIR compartmental model partitions a population into Susceptible, Infected, and Recovered classes to describe epidemic spread through a basic system of ODEs.

differential equations dynamical systems probability theory

Species Distribution Models

Species distribution models (SDMs) relate occurrence records to environmental predictors to estimate and project a species' ecological niche in geographic space.

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Stochastic Population Dynamics

Demographic and environmental stochasticity drive population fluctuations and extinction risk in ways that deterministic models cannot capture.

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