Interspecific Competition

Population interactions

Logistic Curve Time # individuals

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

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 assumptions Environment is homogeneous and stable Migration is unimportant Coexistence requires a stable equilibrium point Competition is the only important biological interaction

Model with isocline See Fig and 12.2 Growth is 0 along the line Species 1 growthSpecies 2 growth

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

Possible outcomes Fig. 12.3

Possible outcomes Fig. 12.3

Competition - 2 species

Competition - 3 species

Diffuse competition Effect of several species

Diffuse competition Effect of several species Exclusion may occur

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

If we observe niche differences in the field, what does it mean? Current competition Evolutionary avoidance through competition Evolutionary avoidance (without competition)

DeWitt diagrams Plants sown at different densities (40:0, 30:10, 20:20, 10:30, 0:40) Seeds harvested