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The identification of a factor as limiting is possible only in distinction to one or more other factors that are non-limiting. Disciplines differ in their use of the term as to whether they allow the simultaneous existence of more than one limiting factor (which may then be called "co-limiting"), but they all require the existence of at least one non-limiting factor when the terms are used.
There also exists density-independent inhibition, where other factors such as weather or environmental conditions and disturbances may affect a population's carrying capacity. [ citation needed ] An example of a density-dependent variable is crowding and competition.
The first variable is r (the intrinsic rate of natural increase in population size, density independent) and the second variable is K (the carrying capacity of a population, density dependent). [21] It is important to understand the difference between density-independent factors when selecting the intrinsic rate and density-dependent for the ...
However, as N(t) approaches the carrying capacity the second term in the logistic equation becomes smaller, reducing the rate of change of population density. [16] The logistic growth curve is initially very similar to the exponential growth curve. When population density is low, individuals are free from competition and can grow rapidly.
Where two similar species share an overlapping range, competition often causes the distributions to shift to exclude one of the two. [ 17 ] [ 18 ] [ 19 ] The geographic range of one species may be linked to another, where the range of one species cannot extend independent of the other.
Liebig's law states that growth only occurs at the rate permitted by the most limiting factor. [ 2 ] For instance, in the equation below, the growth of population O {\displaystyle O} is a function of the minimum of three Michaelis-Menten terms representing limitation by factors I {\displaystyle I} , N {\displaystyle N} and P {\displaystyle P} .
[171]: 62 The physical environment is external to the level of biological organization under investigation, including abiotic factors such as temperature, radiation, light, chemistry, climate and geology. The biotic environment includes genes, cells, organisms, members of the same species (conspecifics) and other species that share a habitat. [172]
The first principle of population dynamics is widely regarded as the exponential law of Malthus, as modelled by the Malthusian growth model.The early period was dominated by demographic studies such as the work of Benjamin Gompertz and Pierre François Verhulst in the early 19th century, who refined and adjusted the Malthusian demographic model.