Population dynamics

Population dynamics is the study of marginal and long-term changes in the numbers, individual weights and age composition of individuals in one or several populations, and biological and environmental processes influencing those changes.

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.

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 (e.g. Jahn et al. 2005).

A more general model formulation was proposed by F.J. Richards in 1959, by which the models of Gompertz, Pierre François Verhulst and also Ludwig von Bertalanffy are covered as special cases of the general formulation. The computer game SimCity and the MMORPG Ultima Online, among others, tried to simulate some of these population dynamics. Population dynamics also attempts to study topics such as aging populations or population decline.

In fisheries and wildlife management, population is affected by three dynamic rate functions. Density of individuals in a population affects all three rate functions.

Immigration and emigration are present, but are usually not measured.
 * Natality or birth rate, often recruitment, which means reaching a certain size or reproductive stage. Usually refers to the age a fish can be caught and counted in nets
 * Growth rate, which measures the growth of individuals in size and length. More important in fisheries, where population is often measured in biomass.
 * Mortality, which includes harvest mortality and natural mortality. Natural mortality includes non-human predation, disease and old age.

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. 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.