quality:corruption
Population ecology

Population ecology studies the dynamics of species populations and how these populations interact with the wider environment. A population consists of individuals of the same species that live, interact, and migrate through the same niche and habitat.

A primary law of population ecology is the Malthusian growth model which states, "a population will grow (or decline) exponentially as long as the environment experienced by all individuals in the population remains constant." Simplified population models usually starts with four variables: death, birth, immigration, and emigration.

An example of an introductory population model describes a closed population, such as on an island, where immigration and emigration does not take place. Hypotheses are evaluated with reference to a null hypothesis which states that random processes create the observed data. In these island models, the rate of population change is described by:

where N is the total number of individuals in the population, b and d are the per capita rates of birth and death respectively, and r is the per capita rate of population change.

Using these modeling techniques, Malthus' population principle of growth was later transformed into a model known as the logistic equation by Pierre Verhulst:

where N(t) is the number of individuals measured as biomass density as a function of time, t, r is the maximum per-capita rate of change commonly known as the intrinsic rate of growth, and α {\displaystyle \alpha } is the crowding coefficient, which represents the reduction in population growth rate per individual added. The formula states that the rate of change in population size (d N (t) / d t {\displaystyle \mathrm {d} N(t)/\mathrm {d} t}) will grow to approach equilibrium, where (d N (t) / d t = 0 {\displaystyle \mathrm {d} N(t)/\mathrm {d} t=0}), when the rates of increase and crowding are balanced, r / α {\displaystyle r/\alpha }. A common, analogous model fixes the equilibrium, r / α {\displaystyle r/\alpha } as K, which is known as the "carrying capacity."

Population ecology builds upon these introductory models to further understand demographic processes in real study populations. Commonly used types of data include life history, fecundity, and survivorship, and these are analyzed using mathematical techniques such as matrix algebra. The information is used for managing wildlife stocks and setting harvest quotas. In cases where basic models are insufficient, ecologists may adopt different kinds of statistical methods, such as the Akaike information criterion, or use models that can become mathematically complex as "several competing hypotheses are simultaneously confronted with the data."