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Carrying capacity. The carrying capacity of an environment is the maximum population size of a biological species that can be sustained by that specific environment, given the food, habitat, water, and other resources available. The carrying capacity is defined as the environment 's maximal load, [clarification needed] which in population ...
Here x is the size of the population at a given time, r is inherent per-capita growth rate, and K is the carrying capacity.. Two species. Given two populations, x 1 and x 2, with logistic dynamics, the Lotka–Volterra formulation adds an additional term to account for the species' interactions.
In a population, carrying capacity is known as the maximum population size of the species that the environment can sustain, which is determined by resources available. In many classic population models, r is represented as the intrinsic growth rate, where K is the carrying capacity, and N0 is the initial population size.
The most famous example of an overshoot-and-crash may be from St. Matthew Island. In 1944, 29 reindeer were introduced to the island, which by 1963 had grown to a peak population of roughly 6000 individuals — well past the estimated carrying capacity. At next count, in 1965, the population had plummeted and only 42 reindeer were left alive.
By contrast, K-selected species display traits associated with living at densities close to carrying capacity and typically are strong competitors in such crowded niches, that invest more heavily in fewer offspring, each of which has a relatively high probability of surviving to adulthood (i.e., low r, high K).
An example of direct competition. Intraspecific competition is an interaction in population ecology, whereby members of the same species compete for limited resources. This leads to a reduction in fitness for both individuals, but the more fit individual survives and is able to reproduce. [1] By contrast, interspecific competition occurs when ...
Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, [1] although over the last century the scope of mathematical biology has greatly expanded. [citation needed] The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the ...
The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear [disambiguation needed] differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time ...
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