1 Modeling Interspecific Competition Lotka Volterra Effect of interspecific competition on...

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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.

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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

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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)

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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.

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Paramecia Lab Experiments

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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.

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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.

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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.

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Competition and Niches of Small Rodents

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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.

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Galapagos Finch Character Displacement

sympatric

allopatric

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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.

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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.