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Interspecific Competition
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Population interactions
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Logistic Curve Time # individuals
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Logistic model Logistic equation *dN/dt = rN((K-N)/K) Assumptions of the logistic model: *Each individual has identical ecological properties *Instantaneous response to environmental change *Constant upper limit to population size and rate of gain is directly related to remaining gap *Limited space and constant food supply *Age distribution is stable
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Lotka/Volterra model dN 1 /dt = r 1 N 1 [(K 1 -N 1 - 12 N 2 )/K 1 ] is the competition coefficient 12 is effect of species 2 on species 1 dN 2 /dt = r 2 N 2 [(K 2 -N 2 - 21 N 1 )/K 2 ] if 12 >1, then individuals of sp. 2 have a greater inhibitory effect on individuals of sp. 1 than does species 1 on species 1. if 12 <1, then sp. 2 individuals have less effect
![Lotka/Volterra model dN 1 /dt = r 1 N 1 [(K 1 -N 1 - 12 N 2 )/K 1 ] is the competition coefficient 12 is effect of species 2 on species 1 dN 2 /dt = r 2 N 2 [(K 2 -N 2 - 21 N 1 )/K 2 ] if 12 >1, then individuals of sp.](http://images.slideplayer.com./16/5236948/slides/slide_5.jpg "2 have a greater inhibitory effect on individuals of sp. 1 than does species 1 on species 1. if 12 <1, then sp. 2 individuals have less effect.")
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Lotka/Volterra assumptions Environment is homogeneous and stable Migration is unimportant Coexistence requires a stable equilibrium point Competition is the only important biological interaction
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Model with isocline See Fig. 12.1 and 12.2 Growth is 0 along the line Species 1 growthSpecies 2 growth
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Finding K/ dN 1 /dt = r 1 N 1 [(K 1 -N 1 - 12 N 2 )/K 1 if growth is 0, and r is >0, then the term (K 1 -N 1 - 12 N 2 ) must be 0 therefore N 1 = K 1 - 12 N 2 when N 1 = 0, N 2 = K 1 / 12
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Possible outcomes Fig. 12.3
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Possible outcomes Fig. 12.3
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Competition - 2 species
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Competition - 3 species
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Diffuse competition Effect of several species
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Diffuse competition Effect of several species Exclusion may occur
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How does coexistance occur? Unpredictable gaps: the poorer competitor is a better colonizer Unpredictable gaps: the pre-emption of space Fluctuating environments Ephemeral patches with variable life-spans Aggregated distributions
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If we observe niche differences in the field, what does it mean? Current competition Evolutionary avoidance through competition Evolutionary avoidance (without competition)
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DeWitt diagrams Plants sown at different densities (40:0, 30:10, 20:20, 10:30, 0:40) Seeds harvested
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