Population dynamics is the branch of life sciences that studies short and longterm changes in the size and age composition of populations, and the biological and environmental processes influencing those changes. Population dynamics deals with the way populations are affected by birth and death rates, and by immigration and emigration, and studies topics such as aging populations or population decline.
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Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 210 years, although more recently the scope of mathematical biology has greatly expanded. The first principle of population dynamics is widely regarded as the exponential law of Malthus, as modelled by the Malthusian growth model. The early period was dominated by demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic model.
A more general model formulation was proposed by F.J. Richards in 1959, further expanded by Simon Hopkins, in which the models of Gompertz, Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation. The Lotka–Volterra predatorprey equations are another famous example. The computer game SimCity and the MMORPG Ultima Online, among others, tried to simulate some of these population dynamics.
In the past 30 years, population dynamics has been complemented by evolutionary game theory, developed first by John Maynard Smith. Under these dynamics, evolutionary biology concepts may take a deterministic mathematical form. Population dynamics overlap with another active area of research in mathematical biology: mathematical epidemiology, the study of infectious disease affecting populations. Various models of viral spread have been proposed and analysed, and provide important results that may be applied to health policy decisions.
In fisheries and wildlife management, population is affected by three dynamic rate functions.
If N_{1} is the number of individuals at time 1 then
where N_{0} is the number of individuals at time 0, B is the number of individuals born, D the number that died, I the number that immigrated, and E the number that emigrated between time 0 and time 1.
If we measures these rates over many time intervals, we can determine how a population's density changes over time. Immigration and emigration are present, but are usually not measured.
All of these are measured to determine the harvestable surplus, which is the number of individuals that can be harvested from a population without affecting long term stability, or average population size. The harvest within the harvestable surplus is considered compensatory mortality, where the harvest deaths are substituting for the deaths that would occur naturally. It started in Europe. Harvest beyond that is additive mortality, harvest in addition to all the animals that would have died naturally. These terms are not the universal good and evil of population management, for example, in deer, the DNR are trying to reduce deer population size overall to an extent, since hunters have reduced buck competition and increased deer population unnaturally.
The rate at which a population increases in size, i.e. the change in population size over a particular period of time is known as the intrinsic rate of increase. The concept is commonly used in insect population biology to determine how environmental factors affect the rate at which pest populations increase.^{[1]}
