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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} .
Carrying capacity is a commonly used concept for biologists when trying to better understand biological populations and the factors which affect them. [1] When addressing biological populations, carrying capacity can be seen as a stable dynamic equilibrium, taking into account extinction and colonization rates. [ 16 ]
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
However, as the population reaches its maximum (the carrying capacity), intraspecific competition becomes fiercer and the per capita growth rate slows until the population reaches a stable size. At the carrying capacity, the rate of change of population density is zero because the population is as large as possible based on the resources ...
Their theoretical structure suggests that as long as higher income has a positive effect on reproductive success, and land is a limiting factor in resource production, then technological progress has only a temporary effect on income per capita (per person). While in the short run technological progress increases income per capita, resource ...
Limiting factors may be physical or biological. [4]: 417, 8 Limiting factors are not limited to the condition of the species. Some factors may be increased or reduced based on circumstances. An example of a limiting factor is sunlight in the rain forest, where growth is limited to all plants on the forest floor unless more light becomes ...
Using these techniques, Malthus' population principle of growth was later transformed into a mathematical model known as the logistic equation: = (), where N is the population size, r is the intrinsic rate of natural increase, and K is the carrying capacity of the population.
In the r/K-selection model, the first variable r is the intrinsic rate of natural increase in population size and the second variable K is the carrying capacity of a population. [33] Different species evolve different life-history strategies spanning a continuum between these two selective forces.