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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 ...
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 ...
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:
I = (PAT) is the mathematical notation of a formula put forward to describe the impact of human activity on the environment . The expression equates human impact on the environment to a function of three factors: population (P), affluence (A) and technology (T). It is similar in form to the Kaya identity which applies specifically to emissions ...
The existence of a global carrying capacity, limiting the amount of life that can live at once, is debated, as is the question of whether such a limit would also cap the number of species. While records of life in the sea show a logistic pattern of growth, life on land (insects, plants and tetrapods) shows an exponential rise in diversity. [19]
Adaptive capacity relates to the capacity of systems, institutions, humans and other organisms to adjust to potential damage, to take advantage of opportunities, or to respond to consequences. [1] In the context of ecosystems, adaptive capacity is determined by genetic diversity of species, biodiversity of particular ecosystems in specific ...
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 ...
Global biocapacity' is a term sometimes used to describe the total capacity of an ecosystem to support various continuous activity and changes. When the ecological footprint of a population exceeds the biocapacity of the environment it lives in, this is called an 'biocapacity deficit'. Such a deficit comes from three sources: overusing one's ...