## Predator Prey Interactions

Predator-prey interactions, especially between planktonic herbivores and algae, have been studied extensively from the perspective of ecological stoichiometry. Therefore, this presentation will emphasize only those principles strongly related to those elaborated above for other interactions. There is a close analogy between a population that produces a substance inhibitory to itself and other populations, and one that supports a predator. In either case, the population produces something that decreases its net potential to grow, and as a result the population must consume more of whatever resource(s) limit its growth. The stoichiometry relating production of the growth-reducing factor to consumption of the resource then has profound effects on how a focal population interacts with others.

Consider a prey population (N) whose growth is limited by a nutrient resource (R) and which supports a predator population (P). In a closed environment where recycling of nutrients is the only supply process, a simple mass-conservation constraint applies to this interaction. This constraint partitions total nutrient (S) into free nutrient, nutrient bound in prey, and bound in predators:

where Qis the nutrient content of prey and q the nutrient content of predators. It is often convenient to measure prey and predator populations as biomass densities of carbon, so that Qand q are nutrient:carbon ratios.

The dynamics of this predator-prey interaction can be conveniently represented on the RP-plane (Figure 8). The ZNGI graph for the prey population is a forward sloping curve: as predator density and hence mortality increase, maintaining a steady-state population of prey, requires more nutrient consumption to support higher reproduction. Given certain simplifying assumptions about predation, the steady-state prey density, N*, is fixed. Then, at steady state, the mass-conservation constraint (eqn [7]) plots as a straight line with elevation proportional to the total nutrient supply, and negative slope equal to the predator's organismal

carbon:nutrient ratio. The intersection of the ZNGI graph and this line shows the steady-state nutrient concentration and predator density. These quantities are thus predicted to increase with increasing nutrient supply while prey density remains constant.

Adding another prey species to this system, which depends on the same nutrient resource and is preyed upon by the same predator, generates a potentially complex interaction. The two prey populations compete by consuming the nutrient, but also engage in apparent competition by supporting the predator which attacks their competitor. Intersection of the ZNGI graphs for the two prey populations implies that coexistence of all three species is possible, and requires a tradeoff in which one prey species is a superior nutrient competitor in the absence of the predator, but is also more susceptible to predation.

In Figure 9, prey species 1 plays this role, and additional conditions for feasibility and stability of steady-state coexistence are shown. The feasible region for steady-state coexistence lies between bounds derived from the mass-conservation constraints associated with

Figure 9 Two prey populations that share a predator and compete for a nutrient. ZNGI graphs (indicated by Z) intersect at the circled point, making steady-state coexistence possible. The shaded feasible region for steady states is superimposed, bounded by mass-conservation constraints for populations 1 and 2 (indicated by Mi), as are impact vectors implying stable coexistence (indicated by I,).

Figure 9 Two prey populations that share a predator and compete for a nutrient. ZNGI graphs (indicated by Z) intersect at the circled point, making steady-state coexistence possible. The shaded feasible region for steady states is superimposed, bounded by mass-conservation constraints for populations 1 and 2 (indicated by Mi), as are impact vectors implying stable coexistence (indicated by I,).

each prey species. Each prey species also has impact vectors related to dynamical stability, but in contrast to interactions examined previously, these vectors are not parallel to the mass-conservation constraints. Slopes of the latter express only the predator's organismal stoichio-metry, but slopes of the impact vectors are also determined by the predator's conversion efficiencies when consuming each prey species. Stability arises when, as illustrated, the more susceptible prey population (species 1) supports greater predator productivity in proportion to prey nutrient consumption, a relationship depending on both stoichiometry and trophic efficiency.

Stable coexistence of two competing prey as illustrated here cannot occur if we take away the predator, because then the prey compete for one resource, and the competitor with the lower R* drives the other to exclusion. A predator that mediates coexistence of its competing prey species, increasing the diversity of the prey community, is called a keystone predator. Although many observations suggest that keystone predators are common in ecological communities, few studies have sufficient information to construct and test fully parametrized models. An exception involves the phage viruses that prey on bacteria (Figure 10).

Glucose (ig ml 1)

Figure 10 Competition for glucose between two strains of Escherichia coli, one more susceptible to predation by phage (strain 1), and one less susceptible (strain 2). The ZNGI graphs (Z,) and impact vectors (I,) predict that stable coexistence is possible. The mass conservation constraints labeled 'M low' represent one of the nutrient supply conditions tested, for which exclusion of the less susceptible strain was predicted, while the mass conservation constraints labeled 'M high' represent the other nutrient supply condition tested, for which exclusion of the more susceptible strain was predicted. Trends toward these predictions were observed, but were often slowerthan predicted, probably due to adaptive evolution of the inferior strain during the experiments. Adapted from Bohannan BJM and Lenski RE (2000) The relative importance of competition and predation varies with productivity in a model community. American Naturalist 156: 329-340, with permission from University of Chicago Press.© 2000 by the University of Chicago Press.

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