![]() Α \alpha α - The natural reproduction rate of the prey in absence of predation. We can assign names to the parameters of the equations: Notice how this factor properly models the natural behavior of predators' populations, and it doesn't apply to the prey one. Here we assume that the predator population is subject to a decrease due to natural death or other causes. Γ y \gamma y γ y - The reduction of the size of the predator population depends on this term. As the food supply is limited, we must consider this (when the prey population dwindles, the predator one also follows suit). Δ x y \delta x y δ x y - In the case of the variation of the predator population, we model a growth that depends on the size of both the prey and the predator population. Its magnitude depends on the size of both the prey and the predator population. Β x y \beta x y β x y - This factor models the rate of predation. ![]() ![]() We discussed a similar quantity in our exponential growth calculator. Α x \alpha x αx - This term represents the exponential growth of a population under an unlimited supply of resources. On the right-hand side, we see the populations in their familiar form: instantaneous number of individuals here we can also identify four characteristic quantities of the Lotka-Volterra model) and their interactions with the populations: While technically, we can find the instantaneous value of these quantities (it would correspond to the variation of a given population for a set of parameters), we are more interested in calculating the Lotka-Volterra model as it evolves with time. As these equations are differential equations, we are studying the evolution of the population in time. The first thing we notice is that on the left-hand side, the populations appear differentiated in time. Let's take a deeper look at these equations.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |