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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 ...
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 ...
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. Thus the competitive Lotka–Volterra equations are:
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 ...
Ecology (from Ancient Greek οἶκος (oîkos) 'house', and -λογία ( -logía) 'study of') [A] is the natural science of the relationships among living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere levels.
r. /. K. selection theory. A North Atlantic right whale with solitary calf. Whale reproduction follows a K -selection strategy, with few offspring, long gestation, long parental care, and a long period until sexual maturity. In ecology, r/K selection theory relates to the selection of combinations of traits in an organism that trade off between ...
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation. where. , the value of the function's midpoint; , the supremum of the values of the function; , the logistic growth rate or steepness of the curve. [1] Standard logistic function where. For values of in the domain of real numbers from to , the S ...
Overshoot (population) In environmental science, a population "overshoots" its local carrying capacity — the capacity of the biome to feed and sustain that population — when that population has not only begun to outstrip its food supply in excess of regeneration, but actually shot past that point, setting up a potentially catastrophic crash ...