What is the Lotka-Volterra competition model?

The Lotka-Volterra competition model describes the outcome of competition between two species over ecological time. Because one species can competitively exclude another species (Figure 1) in ecological time, the competitively-inferior species may increase the range of food types that it eats in order to survive.

How do you solve Lotka-Volterra?

The Lotka–Volterra model in case of two species is a prey predator equation which is defined as follows: dN 1 dt = N 1 ( α – β N 2 ) , dN 2 dt = N 2 ( δ N 1 – γ ) , where the parameters α, β, γ, δ are all positive and N(0) > 0 and N1 is a population size of prey species and N2 is a population size of predator species.

How do you calculate predation rate?

Specifically, PR = (KR × P)/N, where P is the total number of predators and N is the total number of prey.

Which population growth model is the Lotka-Volterra competition model based on?

logistic growth of populations
The classical Lotka-Volterra set of equations is based on the logistic growth of populations and incorporates explicitly both intra- and interspecific growth limitation. It is an extension of the Verhulst’s logistic equation, which only included intraspecific competition as a density-dependent growth limitation.

How do you calculate Isoclines?

In an equation of the form y’ = f(x, y), the isoclines are lines in the (x, y) plane obtained by setting f(x, y) equal to a constant. This gives a series of lines (for different constants) along which the solution curves have the same gradient.

What is a zero net growth isocline?

Remember a Zero Net Growth Isocline is a visual description of all the points in which the species can grow (at one paritcular loss or dilution rate). All the points above and to the right of the isocline are excess growth and the line is the isocline. Below and to the left are regions in which the algae won’t survive.

What is Alpha in Lotka-Volterra?

The Lotka-Volterra model incorporates interspecific competition by using a parameter called alpha. Alpha is the coefficient of competition (or competition coefficient) and measures the competitive effect of one species on another.

Is the Lotka-Volterra model stable?

These studies have demonstrated that the dynamics of Lotka-Volterra (LV) systems are not stable, that is, exhibiting either cyclic oscillation or divergent extinction of one species. Stochastic versions of the deterministic cyclic oscillations also exhibit divergent extinction.

What is a predation rate?

Predation rate is the proportion of the prey population killed by predation and represents the pressure of predation on the prey population. In this sense, PR is the prey population’s perspective of predation.

What is the difference between additive and compensatory mortality?

If a given mortality factor (Factor X, such as harvest, poisoning or predation) causes an immediate reduction in total survival, it is considered an additive mortality factor. A compensatory factor, in contrast, causes no reduction in total survival (until it reaches some threshold value, C*).