BIO 360  Ecology

Lecture 25:  Competition -- classic theory
 

I.  Background
    A.  How do we predict the outcome of competition?
        1.  One successful approach has been  to represent competition mathematically, in a manner that derives directly from models that we have already learned in class.

         2.  Begin with exponential growth and logistic growth
 

         3.  With simple modifications to this model, we can represent mathematically the effects of competition between two species.
 

        4.  The easiest way is to have the competitor influence the population level of a species in the same way that the species influences its own density.
             --  in the absence of a competitor, the population grows to K
 

        5.  Thus, change in population size equals the intrinsic rate of growth, minus density-dependent effects, minus effects due to competition



    B.  Lotka Volterra competition models (won't reproduce  in the notes, but can be found on page 374-378 in your book)
 
 
 

        1. The only terms that differ from the exponential and logistic equations are:
            alpha  = which is the effect of an individual of species 2 on the exponential growth rate of the population of species 1.
            Likewise, beta is simply the effect of an individual of species 1 on the exponential growth rate of the population of species 2.
            K1, K2, N1, and N2 are the same as in previous equations, but the subscript stands for each different population of a different species
 
 


II.  Predicting the outcome of competition
    A.  What is the outcome of competition?  Four possibilities sp1 wins, sp2 wins, both coexist, or both go extinct.

    B.  To determine which species wins in competition, we will use a graphical approach
 
    C.  First ask:  What are equilibrium conditions?

        1.  Solve Lotka-Volterra equations  one species at a time for solutions at equilibrium (when population size is not changing) -- Start with species one
 
 
 
 
 

        2.  Graph the line represented by the equilibrium solutions
 
 
 
 
 
 
 

                Note: an ISOCLINE is a line that defines all of the possible equilibrium population sizes of one species, given the population size of a second species
 

        3.  Determine population growth from any initial population size



 
 

VI.  The outcomes of competition in words:

    A.  Species 1 wins when it inhibits species 2 more than it inhibits itself AND
                  When species 2 inhibits itself more than it inhibits species 1

    B.  Species 2 wins when it inhibits species 1 more than it inhibits itself AND
                  When species 1 inhibits itself more than it inhibits species 2

     C.  When each species inhibits itself more than it inhibits the other species:
          STABLE COEXISTENCE

     D.  When each species inhibits the other species more than it inhibits itself:
          UNSTABLE COEXISTENCE