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Population density is the number of people per unit of area, usually transcribed as "per square kilometer" or square mile, and which may include or exclude, for example, areas of water or glaciers. Commonly this is calculated for a county, city, country, another territory or the entire world . The world's population is around 8,000,000,000 [3 ...
where N is the biomass density, a is the maximum per-capita rate of change, and K is the carrying capacity of the population. The formula can be read as follows: the rate of change in the population (dN/dT) is equal to growth (aN) that is limited by carrying capacity (1 − N/K).
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 ...
The McKendrick–von Foerster equation is a linear first-order partial differential equation encountered in several areas of mathematical biology – for example, demography [1] and cell proliferation modeling; it is applied when age structure is an important feature in the mathematical model. [2] It was first presented by Anderson Gray ...
Beverton–Holt model. The Beverton–Holt model is a classic discrete-time population model which gives the expected number n t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation, Here R0 is interpreted as the proliferation rate per generation and K = ( R0 − 1) M is the ...
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation of the probabilities of the outcomes of any measurement performed upon this system, using the Born rule. It is a generalization of the more usual state vectors or wavefunctions: while ...
Ricker model. The Ricker model, named after Bill Ricker, is a classic discrete population model which gives the expected number N t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation, [1] Here r is interpreted as an intrinsic growth rate and k as the carrying capacity of the ...
Together, Lotka and Volterra formed the Lotka–Volterra model for competition that applies the logistic equation to two species illustrating competition, predation, and parasitism interactions between species. In 1939 contributions to population modeling were given by Patrick Leslie as he began work in biomathematics.