In
population dynamics
Population dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems.
History
Population dynamics has traditionally been the dominant branch of mathematical biology, which has a ...
, depensation is the effect on a
population
Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction usi ...
(such as a
fish stock) whereby, due to certain causes, a decrease in the breeding population (mature individuals) leads to reduced production and survival of eggs or offspring.
The causes may include predation levels rising per offspring (given the same level of overall predator pressure) and the
Allee effect, particularly the reduced likelihood of finding a mate.
Critical depensation
When the level of depensation is high enough that the population is no longer able to sustain itself, it is said to be a critical depensation. This occurs when the population size has a tendency to decline when the population drops below a certain level (known as the "Critical depensation level").
Ultimately this may lead to the population or fishery's collapse (
resource depletion
Resource depletion is the consumption of a resource faster than it can be replenished. Natural resources are commonly divided between renewable resources and non-renewable resources (see also mineral resource classification). Use of eith ...
), or even
local extinction
Local extinction, also known as extirpation, refers to a species (or other taxon) of plant or animal that ceases to exist in a chosen geographic area of study, though it still exists elsewhere. Local extinctions are contrasted with global extinct ...
.
The phenomenon of critical depensation may be modelled or defined by a negative second order
derivative
In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
of population growth rate with respect of population
biomass
Biomass is plant-based material used as a fuel for heat or electricity production. It can be in the form of wood, wood residues, energy crops, agricultural residues, and waste from industry, farms, and households. Some people use the terms bio ...
, which describes a situation where a decline in population biomass is not compensated by a corresponding increase in marginal growth per unit of biomass.
See also
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Abundance (ecology)
In ecology, local abundance is the relative representation of a species in a particular ecosystem. It is usually measured as the number of individuals found per sample. The ratio of abundance of one species to one or multiple other species living ...
*
Conservation biology
Conservation biology is the study of the conservation of nature and of Earth's biodiversity with the aim of protecting species, their habitats, and ecosystems from excessive rates of extinction and the erosion of biotic interactions. It is an in ...
*
Local extinction
Local extinction, also known as extirpation, refers to a species (or other taxon) of plant or animal that ceases to exist in a chosen geographic area of study, though it still exists elsewhere. Local extinctions are contrasted with global extinct ...
*
Overexploitation
Overexploitation, also called overharvesting, refers to harvesting a renewable resource to the point of diminishing returns. Continued overexploitation can lead to the destruction of the resource, as it will be unable to replenish. The term ap ...
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Overfishing
Overfishing is the removal of a species of fish (i.e. fishing) from a body of water at a rate greater than that the species can replenish its population naturally (i.e. the overexploitation of the fishery's existing fish stock), resulting in t ...
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Small population size
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Threatened species
Threatened species are any species (including animals, plants and fungi) which are vulnerable to endangerment in the near future. Species that are threatened are sometimes characterised by the population dynamics measure of '' critical depen ...
References
External links
Optimal harvesting in the presence of critical depensationOn line source of definitions and other fish info
Extinction
Ecological processes
Population dynamics
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