Herbivore Extinction Due to Poor Food Quality

Stoichiometrically implicit predator-prey and especially plant-herbivore interactions have been built and analyzed, providing some clues as to the role of stoichiometry in system dynamics and species diversity. In these models, consumers respond to food quality determined by element ratios, and nutrients are recycled according to stoichiometry and strict homeostasis.

Recycling provides a feedback between a herbivore and its algal or plant prey. The herbivore's growth and nutrient release rates decline as the prey's C:nutrient ratio increases above its TER. These analyses involve development of versions of the classic Lotka-Volterra predator-prey models in which the homeostatic regulation ofnutrient content varies between predator and prey. When the prey is modeled as a photoautotroph, its nutrient content will be variable and the predatory herbivore will have fixed nutrient.

The effects of introducing stoichiometric constraints to such models of trophic interaction are dramatic (Figure 7). In classical Lotka-Volterra-type models, the predator can always grow whenever prey abundance is above some finite level. This is seen as a vertical, linear nullcline for the predator; the predator's nullcline is the set of points where the predator's net growth rate is zero. There is thus only one possible equilibrium point of plant and herbivore density for the system. However, in a stoichiometric version of these equations, both prey and predator nullclines are hump shaped. The prey's nullcline intersects the x- (prey-) axis due to nutrient limitation. The intersection point is determined by the maximal C:nutrient ratio the prey achieves under nutrient limitation. Stoichiometric models are unusual in that the predator's nullcline also is hump shaped, in this case due to the negative effects of poor food quality when the plant achieves high biomass on a fixed and limited amount of nutrient in the system. At high plant biomass, plants have high C:nutrient ratio, and further additions of biomass (C) can have a depressive effect on herbivore dynamics, a paradoxical result. The herbivore population is inhibited by the addition of bulk food. In fact, the herbivore can shift between positive growth and negative growth by the addition of plant biomass to the system! This counterintuitive aspect of the model has been termed the 'paradox of energy enrichment'.

Stoichiometry alters nullclines so that both are nonlinear, meaning they can intersect each other at more than one point. Depending on the parameters used, there is potential for multiple equilibria, limit cycles, and potentially chaotic dynamics when one includes stoichiometry in such a system. A particularly interesting equilibrium is illustrated in Figure 7b, in which conditions are such that the prey nullcline intersects the prey axis at a high value, beyond the upper intersection of the predator's nullcline. In this situation, a stable equilibrium exists at the prey's intersection on the x-axis, a point where the grazer is extinct and cannot invade from low population levels. This is a grazer extinction point occurring in a 'world' of very high food (plant) biomass! In ecophysiological terms, this situation is more likely to occur for grazers with high body nutrient content and for environmental conditions in which autotrophs develop very high biomass C:nutrient ratios. As described earlier, the latter

Grazer nullcline Algae nullcline

Stable equilibrium Unstable equilibrium

(a)

n

r

log (algae biomass)

log (algae biomass)

Figure 7 Predator (grazer) and prey (algae) nullclines in a theoretical model. Panels (a) and (b) use different parameters for the same model. Stoichiometry makes the grazer nullcline hump shaped, which alters predicted dynamics and makes it possible even for a stable equilibrium point at zero grazer biomass.

occurs when nutrients are severely limiting and when light intensities and perhaps pCO2 levels are high. Indeed, the theory predicts that local deterministic extinction of a herbivore can occur with increased light intensity or with any ecological change that induces high C:nutrient ratio in plant biomass.

A similar model has been built and analyzed where the prey is made to be stoichiometrically variable, but the predators are held to be homeostatic. An analogous situation to this would be the case of bacteria (homeostatic) being fed upon by Protozoa (stoichiometrically variable). When we change the point of strict homeostasis from the predator to the prey, the complex dynamics discussed for Figure 7 disappear. It is both the presence of strict home-ostasis and its location within a food web that influences system dynamics.

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