## 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.

**What does the competitive exclusion principle tell us?**

The competitive exclusion principle says that two species can not occupy the same ecological niche. When a species invades a new island, it encounters, in almost every case, an environment that is different to some degree. The species usually responds by either contracting or expanding its niche.

### How are species’isoclines related in interspecific competition?

The following four graphs include both species’ isoclines, and illustrate the possible outcomes of interspecific competition depending on where each species’ isocline lies in relation to the other. In each graph, the solid yellow line represents the isocline of species 1, and the dashed pink line represents the isocline of species 2.

**How are isoclines used in the Lotka Volterra competition model?**

The values for K 1, K 2, a 12, and a 21 are used to plot the isoclines of zero growth (i.e., where dN 1 /dt or dN 2 /dt equal zero) for both species on the same graph, and the resulting sums of population growth vectors (trajectories) are used to determine the outcome of the competition (Figure 1). Figure 1.

## What happens when a population is below or above its isocline?

These two graphs illustrate what happens to a population when it is below or above its isocline, but they only account for one isocline at a time. The following four graphs include both species’ isoclines, and illustrate the possible outcomes of interspecific competition depending on where each species’ isocline lies in relation to the other.

**Is there an unstable equilibrium point below both isoclines?**

Below both isoclines and above both isoclines the populations increase or decrease as in the first two scenarios, and there is an unstable equilibrium point (closed circle) where the isoclines intersect.