WLF 448: Fish & Wildlife Population Ecology

Lab 11: Competition

Fall 2004

I. Objectives of Lab

  1. Use a computer model based on the Lotka-Volterra competition equations to gain a more intimate understanding of the factors that can influence the outcome of competition in a simple environment.

  2. Learn Tilman's resource competition model can evaluate how resource dynamics can influence the outcome of competition.

II. Definitions and Concepts

A. Intraspecific competition

Theoretically, intraspecific competition may produce within-species patterns of differential resource use (i.e., habitat generalists).

B. Interspecific competition

Theoretically, interspecific competition leads to resource specialization and separation of species along some resource gradient (i.e., interspecific competition influences the realized niche of a species).
Theoretically, each species should evolve to a form in which inter- and intraspecific competition are optimally offset (Begon and Mortimer 1986).

There are 3 important points associated with this definition:

  1. The interaction between two species will be reciprocal, i.e., causing demonstrable reductions in survival, growth, or fecundity of each species. However, one species often is more negatively affected than the other.

  2. A resource is in short supply. Even if animals overlap completely in resource utilization, competition usually does not occur unless a resource is limited in some way.

  3. The implication of #2 is that competition is density dependent.

C. Types of Competition (Park 1962)

III. Lotka-Volterra Model of Competition

A. Intraspecific competition

dN/dt = rm N (1 - N/K)

B. Interspecific competition (i.e., competition coefficients)

a12 is the effect of species 1 on species 2.

a21 is the effect of species 2 on species 1.

Note: the notation for competition coefficients is not consistent among textbooks or computer programs (output). For example, Begon and Mortimer (1986) define a12 as the effect of species 2 on species 1, which is opposite of the definition stated above. Some computer programs may use Greek symbols such alpha and beta to represent a12 and a21, respectively. The bottom line is to make sure you understand the notation used by a particular author or computer model.

If one elk (species 1) is equivalent to 3 deer (species 2) in terms of its use of the resource and its effect on species 2, then a12 = 3.0. If the effect of species 2 on species 1 is reciprocal (i.e., if 1 deer is equivalent to 0.33 elk), then a21 = 0.33. Note: the alpha's of each species do not have to be reciprocal.

C. Interspecific competition based on the logistic growth model:

Remember the logistic growth model:

Population growth of species 1 in the presence of species 2:

Population growth of species 2 in the presence of species 1:

D. Zero-growth isoclines for species 1 and species 2

The zero-growth isocline describes expected equilibrium population sizes of one species if abundance of the second species is held constant, and vice versa. The relationship between the two species is assumed to be linear, i.e., the isoclines for species 1 and species 2 can be written as equations for a straight line (y = a + bx).

1. Plot N2 on the y-axis and N1 on the x=axis (to be consistent with output from the simulation program that you will use in lab today).

2. Determine the zero-growth isocline for species 1:



 3. Determine the zero-growth isocline for species 2:

Thus, the growth of species 1 will be zero when N2 = 0 and N1 = K1 , or when N1 is close to zero and N2 = K1/a21. Likewise, the growth of species 2 will be zero when N1=0 and N2 = K2 , or when N2 is close to zero and N1 = K2/a12 .

E. Predicting the outcome of competition (using the L-V model):

The outcome of competition, according to the Lotka-Volterra model, is ultimately determined by carrying capacity (Ki) and the competition coefficient (aij) of the two species. We will use POPULUS to explore the logistic-competition theory.

Assumptions of the Lotka-Volterra logistic-competition model:

  1. All of the assumptions of the logistic-growth model.

  2. The effect of one species on the other is linear.

  3. The environment is stable and carrying capacities are constant.

IV. Tilman's Resource Competition Model(s)

There are many different ways that a species can respond to 2 resources. One possible response is that of plants to nitrogen and light. These resources are essential. For perfectly essential resources, the growth rate of a plant is determined by the one resource in lowest supply compared to its need. Thus, the growth rate of a plant is determined by the concentration of the one resource that leads to the lowest growth rate.

Two species can coexist when consuming 2 essential resources if each is limited by a different resource and each, relative to the other species, consumes more of the resource which limits it.

Note: Both Tilman's and Lotka-Volterra's model of competition lead to a similar conclusion: coexistence is made possible by ecological segregation, at least in theory!

V. In-class Exercises

VI. Problem Set

VII. Selected References

Revised: 16 November 2004