Transcript Competition

Modeling Interspecific Competition
Lotka Volterra
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Effect of interspecific competition on
population growth of each species:
dN1 / dt = rmax1N1 ((K1-N1 -α12N2) / K1)
 dN2 / dt = rmax2N2 ((K2-N2 -α21N1) / K2)
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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
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In general, LV predicts coexistence of two
species when, for both species, interspecific
competition is weaker than intraspecific
competition.
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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
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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
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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.
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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
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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
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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
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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
allopatric
sympatric
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Character Displacement
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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.
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