Using one predator-two prey systems with different prey profitability, I theoretically examined the effects of enrichment on stability and population abundances at equilibrium. In any feeding type of predator, the effects were shown to depend critically on the profitability of the less profitable prey which had been unknown in natural systems and not been clearly dealt with by previous models.

In Chapter 2, I analysed the stability of a system involving an optimally selective feeding predator as a possible resolution of the paradox of enrichment. A less profitable but edible prey species sharply reduced the amplitude of population oscillations and firmly prevented the minimum abundances of species from falling below certain values. The presence of such an unpalatable prey guaranteed the robustness of the system against enrichment.

In Chapter 3, using a system involving a generalist predator I clarified the response of the more profitable prey abundance at equilibrium to enrichment which had been various among previous models. These models had assumed the less profitable prey as inedible, though its actual profitability was unknown. Relaxing this assumption, I showed that the response of the more profitable prey abundance to enrichment depended critically on the profitability of the less profitable prey. Specifically, the more profitable prey increased in abundance with enrichment if the profitability of the less profitable prey was lower than a critical value so that it was unable to support the predator population by itself even at high densities, and decreased otherwise. This established a more general rule, which unified the previous works and resolved the indeterminacy, on the response of the more profitable prey.

In Chapter 4, I analysed the stability of the system considered in Chapter 3. I conducted numerical analyses of stability along a gradient of enrichment using Daphnia-algal systems with realistic parameter values. It was shown to depend on combination of algal prey species whether or not all species were able to coexist stably. In systems with proper combination of prey species, if the profitability of less profitable prey was close to a critical value, it was further shown that the Daphnia-algal systems can hold a stable equilibrium even at high degrees of enrichment with no change in the abundance of more profitable prey. This accounted simultaneously for the response of population abundance and stability to enrichment in natural systems.

The results with regard to stability in Chapters 2 and 4 indicate a potential that predator-prey systems are robust with regard to stability against a recently serious trend of enrichment, irrespective of the type of predator.