# Population ecology

The human population is growing at a logistic rate and has been affecting the populations of other species in return. Chemical pollution, deforestation, and irrigation are examples of means by which humans may influence the population ecology of other species. As the human population increases, its effect on the populations of other species may also increase.
Populations cannot grow indefinitely. Population ecology involves studying factors that affect population growth and survival. Mass extinctions are examples of factors that have radically reduced populations' sizes and populations' survivability. The survivability of populations is critical to maintaining high levels of biodiversity on Earth.

Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment.[1] It is the study of how the population sizes of species change over time and space. The term population ecology is often used interchangeably with population biology or population dynamics.

The development of population ecology owes much to demography and actuarial life tables. Population ecology is important in conservation biology, especially in the development of population viability analysis (PVA) which makes it possible to predict the long-term probability of a species persisting in a given habitat patch. Although population ecology is a subfield of biology, it provides interesting problems for mathematicians and statisticians who work in population dynamics.

## Fundamentals

Terms used to describe natural groups of individuals in ecological studies[2]
Term Definition
Species population All individuals of a species.
Metapopulation A set of spatially disjunct populations, among which there is some immigration.
Population A group of conspecific individuals that is demographically, genetically, or spatially disjunct from other groups of individuals.
Aggregation A spatially clustered group of individuals.
Deme A group of individuals more genetically similar to each other than to other individuals, usually with some degree of spatial isolation as well.
Local population A group of individuals within an investigator-delimited area smaller than the geographic range of the species and often within a population (as defined above). A local population could be a disjunct population as well.
Subpopulation An arbitrary spatially delimited subset of individuals from within a population (as defined above).

The most fundamental law of population ecology is Thomas Malthus' exponential law of population growth.[3]

A population will grow (or decline) exponentially as long as the environment experienced by all individuals in the population remains constant.[3]:18

This principle in population ecology provides the basis for formulating predictive theories and tests that follow:

Simplified population models usually start with four key variables (four demographic processes) including death, birth, immigration, and emigration. Mathematical models used to calculate changes in population demographics and evolution hold the assumption (or null hypothesis) of no external influence. Models can be more mathematically complex where "...several competing hypotheses are simultaneously confronted with the data."[4] For example, in a closed system where immigration and emigration does not take place, the rate of change in the number of individuals in a population can be described as:

${\displaystyle {\frac {dN}{dT}}=B-D=bN-dN=(b-d)N=rN,}$

where N is the total number of individuals in the population, B is the raw number of births, D is the raw number of deaths, b and d are the per capita rates of birth and death respectively, and r is the per capita average number of surviving offspring each individual has. This formula can be read as the rate of change in the population (dN/dT) is equal to births minus deaths (B - D).[3][5]

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

${\displaystyle {\frac {dN}{dT}}=aN\left(1-{\frac {N}{K}}\right),}$

where N is the biomass density, a is the maximum per-capita rate of change, and K is the carrying capacity of the population. The formula can be read as follows: the rate of change in the population (dN/dT) is equal to growth (aN) that is limited by carrying capacity (1-N/K). From these basic mathematical principles the discipline of population ecology expands into a field of investigation that queries the demographics of real populations and tests these results against the statistical models. The field of population ecology often uses data on life history and matrix algebra to develop projection matrices on fecundity and survivorship. This information is used for managing wildlife stocks and setting harvest quotas [5][6]

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