Biology 205Ecology and Adaptation

Lab 8: Competition Models

Dr. Erik D. Davenport

1

Mathematical and Laboratory Models

• Metz summarized models:–Abstractions and simplifications, not

facsimiles of nature.–Man-made construct; partly empirical and

partly deductive.–Used to provide insights into natural

phenomena.

2

What model is used for the intraspecific competition??

dN/dt = rN(1-N/K)

• r = per capita rate of increase under ideal conditions.

• Logistic population growth model.• What term in this model describe the

intraspecific competition???

3

Paramecia Lab Experiments

4

Lab Experiments

• Gause demonstrated resource limitation with Paramecium caudatum and Paramecium aurelia in presence of two different concentrations of Bacillus pyocyaneus.– When grown alone, carrying capacity determined

by intraspecific competition.– When grown together, P. caudatum quickly

declined.– Reduced resource supplies increased competition.

5

Lotka Volterra

• Effect of interspecific competition on population growth of each species:

– dN1 / dt = rm1N1 ((K1-N1- α 12N2) / K1)

– dN2 / dt = rm2N2 ((K2-N2- α 21N1) / K2)

• α12: Effect of individual of species 2 on rate of pop. growth of species 1.• α21: Effect of individual of species 1 on rate of pop.

growth of species 2.6

Lotka Volterra (Alternative)

• Effect of predation on population growth of each species:– dH/dt = rH – aPH– dP/dt = bPH – mP• r : prey per capita rate of increase (birth rate)• a: prey per capita rate of predation (death rate from

predation• b: predator per capita rate of increase (birth rate).• m: predator per capita rate of mortality (death rate)• P: predator population• H: prey population

7

Lotka-Volterra

• The Lotka-Volterra model incorporates interspecific competition by using a parameter called α.

• α is the coefficient of competition (or competition coefficient) and measures the competitive effect of one species on another. (IMPORTANT!!!!)

• For example: α12 is the effect of species 2 on species 1, α21 is the effect of species 1 on species 2.

8

Predicting the outcome of competition

• The outcome of competition, according to the Lotka-Volterra model, is ultimately determined by

• carrying capacity (Ki) and • the competition coefficient (aij) of the two

species

9