BIOS 615: Ecology

Dr. S. Malcolm,

Biological Sciences

Week 5: Interspecific Competition

MULTI-SPECIES INTERACTIONS

Lotka-Volterra Competition

Using the Lotka-Volterra Competition model set to run to a steady state and the <altG> (x2) gridding function answer the following questions:

At N₁ = 20 r₁ = 0.5 K₁ = 500 a = 0.5

N₂ = 20 r₂ = 0.5 K₂ = 500 b = 0.5

1) What is the competitive outcome?

2) At what population sizes do the N₁ and N₂ populations end up at when they reach steady state? N₁ =_ _____

N₂ = _ _____

3) Is there a negative impact on the two populations? __________

4) Is K₁ larger or smaller than K₂a (give numbers)? __________

5) Is K₂ larger or smaller than K₁b (give numbers)? __________

At N₁ = 20 r₁ = 0.7 K₁ = 700 a = 0.7

N₂ = 20 r₂ = 0.5 K₂ = 500 b = 0.5

6) At what population sizes do the N₁ and N₂ populations end up at when they reach steady state? N1 =______N2 =______

7) Is K₂ > or < than K₁b (give numbers)?

8) Is K₁ > or < than K₂a (give numbers)?

9) What are the criteria for coexistence in terms of K₁, K₂, a and b?

Give your own values for N, r, K, a and b to satisfy the criteria in the following questions.

10) if K₁ > K₂a and K₁b > K₂ which species wins?

11) if K₂a > K₁ and K₂ > K₁b which species wins?

12) Does changing N or r have any impact on the outcome

of either 10) or 11)?

13) if K₂a > K₁ and K₁b > K₂ which species wins?

14) Does changing N or r have any impact on the outcome

of 13)?