Predicting the outcome of competition

The outcome of competition can be predicted if we know how the population sizes of species 1 and species 2 are likely to change over time. For example, if the population size of species 2 is likely to increase while that of species 1 is likely to decrease to zero, then species 2 should drive its competitor to extinction, thus “winning” the competitive interaction.

We begin by determining when the population size of each competing species would stop changing in size. This approach, which we also used for the Lotka- Volterra predator-prey model (see Concept 12.3), is based on the idea that the population size (N) does not change when the population growth rate (dN∕dt) equals zero (or reaches an equilibrium). For example, based on the Lotka- Volterra competition model (Equation 14.1), the population size of species 1 does not change when dN₁∕dt = 0. When we set dN₁∕dt equal to zero, we find that the population size of species 1 (N₁) does not change when

(14.2)

Likewise, the population size of species 2 (N₂) does not change when

(14.3)

Notice that Equations 14.2 and 14.3 are straight lines, written with N₁ as a function of N₂ and N₂ as a function of N₁, respectively. Each of these lines is called the zero population growth isocline (or simply isocline), so named because a population does not increase or decrease in size for any combination of N₁ and N₂ that lies on these lines.

for species 2, the abundance does not change when dN₂∕dt = 0, which occurs when N₁ = K₂∕β and N₂ = K₂.

Once we determine K₁∕α and K₂∕β, we can then plot the isoclines for both species 1 (x-axis) and species 2 (ó-axis) in graphical form. For species 1, the isocline will be a diagonal line originating at the value N₂ = K₁∕α and ending at the value N₁ = K₁ (FIGURE 14.13A). This isocline represents the number of individuals of species 2 that would keep species 1's population from changing (or at equilibrium). For example, in Figure 14.13A, because a point to the right of the N₁ isocline represents more individuals than zero population growth will allow, the population size of species 1 will decrease until it reaches the isocline. This is true for the entire region shaded in blue: the population size of species 1 decreases for all points to the right of the N₁ isocline. In contrast, when the population size of species 1 is to the left of the N₁ isocline, the population size of species 1 increases. Similar reasoning applies to species 2's isocline, which can be plotted as the diagonal line originating at the value N₁ = K₂∕β and ending at the value N₂ = K₂ (FIGURE 14.13B). This isocline represents the number of individuals of species 1 that would keep species 2's population from changing (or at equilibrium). Here the population size of species 2 decreases in regions above the N₂ isocline and increases in regions below the N₂ isocline.

FIGURE 14.13 GraphicalAnalysesofCompetition Thezeropopulationgrowthisoclines from the Lotka-Volterra competition model can be used to predict changes in the population sizes of competing species.

The graphical approach we have just described can be used to predict the end result of competition between species. To do this, we plot the N₁ and N₂ isoclines together. Because there are four possible ways that the N₁ and N₂ isoclines can be arranged relative to each other, we must make four different graphs. In two of these graphs, the isoclines do not cross, and competitive exclusion results: depending on which isocline is above the other, either species 1 (FIGURE 14.14A) or species 2 (FIGURE 14.14B) always drives the other to extinction. Note that in the regions shaded in blue, the population sizes of both species are greater than the population sizes on their isoclines, and hence both species decrease in number (as indicated by the thick black arrows). Similarly, in the regions shaded in yellow, the population sizes of both species are less than those on their isoclines, and hence both species increase in number. In the regions shaded in light or dark gray, one species increases in number (because its

population sizes are less than those on its isocline) while the other decreases until the species that increases reaches its carrying capacity (K) and the species that decreases reaches zero and becomes extinct.

FIGURE 14.14 Outcome of Competition in the Lotka-Volterra Competition Model The outcome of competition depends on how the N1 and isoclines are positioned relative to one

another. (A) Competitive exclusion of species 2 by species 1; species 1 always wins.

In (B), if K₂ = 1,000 and if species 1 went extinct when N₂ = 1,200, how would the population size of species 2 change after the extinction of species 1?

View larger image

Competitive exclusion also occurs in the third graph (FIGURE 14.14C), but which species “wins” depends on whether the changing population sizes of the two species first enter the region shown in dark gray (in which case, species 2 drives species 1 to extinction) or the region shown in light gray (in which case, species 1 drives species 2 to extinction). Finally, FIGURE 14.14D shows the only case in which the two species coexist, and hence competitive exclusion does not occur. Although in this case neither species drives the other to extinction, competition still has an effect: the final or equilibrium population size of each species (indicated by the box in the figure) is lower than its carrying capacity, as in Gause's experiments with Paramecium (see Figure 14.9A).

Researchers have used the graphical approach described in Figure 14.14 to predict the outcome of competition under different ecological conditions. For example, Livdahl and Willey (1991) used this approach to predict whether competition with a native species of mosquito could prevent the invasion of an introduced mosquito species. You can explore their results in ANALYZING DATA 14.1.

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ANALYZING DATA 14.1

Will Competition with a Native Mosquito Species Prevent the Spread of an Introduced Mosquito?

The mosquito Aedes albopictus breeds in small volumes of water, such as those in tree holes (cavities in trees that can hold water) and in abandoned tires.

Livdahl and Willey (1991)* sought to predict the outcome of competition between A. albopictus and the native mosquito A. triseriatus, a predominant member of tree hole communities. To do this, they estimated competition coefficients and carrying capacities for A. albopictus and A. triseriatus mosquito larvae developing in water obtained from tree holes and from tires. Their results are shown in the table.

1. Using Equation 14.1, designate A. triseriatus as species 1 and A. albopictus as species 2. Use the data in the table to plot the N₁ and N₂ isoclines (see Equations 14.2 and 14.3) for these two species competing in tree hole communities. Predict the equilibrium population density (no. individuals per 100 ml of water) for each species. Describe the likely outcome of competition between these two species in tree hole communities.

2. On a separate graph, plot the N₁ and N₂ isoclines for these two species competing in tires. Predict the equilibrium population density (no. individuals per 100 ml of water) for each species. Describe the likely outcome of competition between these two species in tires.

3. Is it likely that competition with the native species (A. triseriatus) will prevent the spread of the introduced species (A. albopictus)? Explain.

*Livdahl, T. P., and M. S. Willey. 1991. Prospects for an invasion: Competition between Aedes albopictus and native Aedes triseriatus. Science 253: 189-191.