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Population dynamics is the type of mathematics used to model and study the size ... We can calculate the doubling time of a geometric population using the equation: ...
Population models are used to determine maximum harvest for agriculturists, to understand the dynamics of biological invasions, and for environmental conservation. Population models are also used to understand the spread of parasites, viruses, and disease. [2] Another way populations models are useful are when species become endangered.
The model can also be written in the form of a differential equation: = with initial condition: P(0)= P 0. This model is often referred to as the exponential law. [5] It is widely regarded in the field of population ecology as the first principle of population dynamics, [6] with Malthus as the founder.
An extension to these are the competitive Lotka–Volterra equations, which provide a simple model of the population dynamics of species competing for some common resource. In the 1930s Alexander Nicholson and Victor Bailey developed a model to describe the population dynamics of a coupled predator–prey system. The model assumes that ...
A typical application of the logistic equation is a common model of population growth (see also population dynamics), originally due to Pierre-François Verhulst in 1838, where the rate of reproduction is proportional to both the existing population and the amount of available resources, all else being equal.
Lotka–Volterra equations. The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear 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 ...
Competitive Lotka–Volterra equations. The competitive Lotka–Volterra equations are a simple model of the population dynamics of species competing for some common resource. They can be further generalised to the generalized Lotka–Volterra equation to include trophic interactions.
where x n is a number between zero and one, which represents the ratio of existing population to the maximum possible population. This nonlinear difference equation is intended to capture two effects: reproduction, where the population will increase at a rate proportional to the current population when the population size is small,