Mathematical and theoretical biology

Mathematical and theoretical biology uses equations, computation, and abstract models to explain biological systems, processes, and patterns.

Population dynamics: The study of how population sizes and structures change over time. Growth, competition, and environmental limits become explicit in population models.
Ordinary differential equation: An equation relating a function of one variable to its derivatives. It represents rates of change in quantities such as population size or chemical concentration.
Population genetics: The study of genetic variation and its change within and between populations. Mathematical models quantify how mutation, selection, drift, and migration alter gene frequencies.
Pierre François Verhulst: A Belgian mathematician who introduced the logistic equation for population growth. His model made limited-resource population growth a tractable mathematical problem.
Phenomenological model: A model that describes observed patterns without specifying all underlying mechanisms. It can fit biological data efficiently, unlike models built from detailed mechanisms.
Lotka–Volterra equations: A pair of differential equations modeling interactions between predator and prey populations. They show how simple interaction rules generate coupled population cycles.
Partial differential equation: An equation involving derivatives with respect to multiple independent variables. It allows a model to track biological quantities across both space and time.
Epidemiological modeling: The use of mathematical models to describe infectious disease spread and control. Compartment models turn transmission assumptions into estimates of epidemic trajectories.
Alfred J. Lotka: An American mathematician and physical chemist who developed models of population and chemical dynamics. His work helped establish mathematical approaches to predator–prey dynamics.
Mechanistic model: A model that represents processes through explicit causal mechanisms and interactions. It explains outcomes through proposed biological processes rather than pattern-fitting alone.

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