Exercise Question (do it by yourself): In a New England Forest gray fox (Urocyon cineroargenteus) and red fox (Vulpes vulpes) are competing for common habitat.

(A) Using the data given below, project the population sizes of two species for next 10 years;

(B) Plot the population curves of both species on a graph paper

(C) predict the outcome of this competition.

gray fox red fox

Initial population 36 individuals 44 individuals

Carrying capacity 100 120

Annual growth rate 0.6 0.4

= 1.2; = 1.8

Year	Gray fox population	Red fox population
0	36	44
1
2
3
4
5
6
7
8
9
10

example equation

Species 1 dN₁/dt = r₁N₁{(K₁ - N₁ - aN₂)/K₁}

Species 2 dN₂/dt = r₂N₂{(K₂ - N₂ - bN₁)/K₂}

In these equations, a measures the effect of N₂ on N₁ in terms of the number of individuals of N₁ to which one individual of N₂ is equal. Similarly, b measures the effect of N₁ on N₂ in terms of the number of individuals of N₂ to which one individual of N₁ is equal. The outcome of competition between two species depends on the ratio of a to K₁/K₂ and of b to K₂/K₁. There are four possible outcomes.

1) a > K₁/K₂; and b > K₂/K₁ Only 1 species survives, depending on initial relative numbers

2) a < K₁/K₂; and b < K₂/K₁ Both species survive

3) a < K₁/K₂; and b > K₂/K₁ Species #1 always wins

4) a > K₁/K₂; and b < K₂/K₁ Species #2 always wins