 Population dynamics

Population dynamics studies changes in the abundance and composition of a biological population through births, deaths, movement and interactions. The first step is a balance: count gains and losses over the same time interval and within the same population boundary. If each individual gives birth at constant per capita rate $b$ and dies at rate $d$, with no movement across that boundary, the deterministic abundance $N$ obeysThe coefficients have units of inverse time, so $b>d$ gives exponential growth rather than addition of a fixed number each generation.

Resources and crowding can introduce density dependence. For example, the logistic differential equation uses $\dot{N}=rN(1-N/K)$, with carrying capacity $K$. An age-structured population equation or stage-structured population model separates individuals whose survival and reproduction differ. At low abundance, a birth-death process also represents demographic stochasticity: a positive deterministic growth rate does not prevent a finite population from going extinct. Repeated counts and survival or reproductive observations test which rates and state variables the model actually needs.

Population dynamics is a branch of ecology that studies the changes in population size and composition over time and the biological and environmental factors that influence these changes. It encompasses the examination of how populations of organisms—such as animals, plants, or microorganisms—grow, decline, and interact. Key aspects of population dynamics include: 1. **Population Size**: Refers to the number of individuals within a specific population at a given time.