Modeling Interspecific Competition Lotka Volterra

1. Modeling Interspecific Competition Lotka Volterra • Effect of interspecific competition on population growth of each species: • dN1 / dt = rmax1N1((K1-N1 -α12N2)/ K1) • dN2 / dt = rmax2N2 ((K2-N2-α21N1) / 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.

2. Lotka Volterra • In general, LV predicts coexistence of two species when, for both species, interspecific competition is weaker than intraspecific competition. • LV predicts population growth for the two species will stop when: • N1=K 1 - α12 N2 and N2 = K 2 - α21 N1

3. Lotka Volterra Zero Growth Isoclines • Above: Population decreasing • Below: Population increasing • Parallel isoclines will result in competitive exclusion of species with lower K value. • Coexistence of two species is only possible when isoclines cross. • Trajectories between isoclines always toward higher K values. (e.g. “c” is unstable coexistance)

4. Paramecia 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. Paramecia Lab Experiments

6. Flour Beetle Experiments • What’s a niche? Collective environmental factors that influence growth, survival, and reproduction. • Tribolium beetles infest stored grain products. • Park studied interspecific competition between T. confusum and T. castaneum under varied environmental conditions. • Had similar fundamental niches; when grown alone the abiotic constraints were similar. • Growing the two species together suggested interspecific competition restricts the realized niches (adds biotic influences) of both species to fewer environmental conditions.

7. Niche Overlap and Competition Between Barnacles • Connell discovered interspecific competition in barnacles. Balanus plays a role in determining lower limit of Chthamalus within intertidal zone. • Did not account for all observed patterns.

8. Competition and Niches of Small Rodents • Brown studied competition among rodents in Chihuahuan Desert. • Predicted if competition among rodents is mainly for food, then small granivorous rodent populations would increase in response to removal of larger granivorous rodents. • Insectivorous rodents would show little or no response. • Results supported hypothesis.

9. Competition and Niches of Small Rodents

10. Character Displacement= evolution of niche divergence by competition • The degree of competition is assumed to depend upon degree of niche overlap, • Interspecific competition has been predicted to lead to directional selection for reduced niche overlap. • Galapagos finch size versus seed size.

11. allopatric Galapagos Finch Character Displacement sympatric

12. Character Displacement • Taper and Case: Necessary criteria for C.D.: • Morphological differences between sympatric populations are statistically greater than differences between allopatric populations. • Differences between sympatric and allopatric populations have genetic basis. • Differences between sympatric and allopatric populations evolved in place, and are not derived from different founder groups already differing in the character.

13. Taper and Case: Characteristics • Variation in the character must have a known effect on use of resources. • Must be demonstrated competition for the resource and competition must be directly correlated with character similarity. • Differences in character cannot be explained by differences in resources available to each of the populations.