Optimal nutrient foraging strategy of an omnivore: Liebig's law determining numerical response.

The paper is aimed at a theoretical explanation of the following phenomenon. In biological pest control in greenhouses, if an omnivore agent is released before the arrival of the pest, the agent may be able to colonize, feeding only on plant and then control its arriving prey to a low density. If the pest arrives before the release of the agent, then it tends to reach a high density, in spite of the action of the agent. This means that according to the initial state, the system displays different stable equilibria, i.e. bistable coexistence is observed. Based on the biological situation, the explaining theoretical model must take into account the stoichiometry of different nutrients and the optimal foraging of the omnivore agent. We introduce an optimal numerical response which depends on the optimal functional responses and on the 'mixed diet-fitness' correspondence determined by 'egg stoichiometry', in our case by Liebig's Law; moreover we also study the dynamical consequences of the latter when the plant is "inexhaustible". In our model, we found that under Holling type II functional response, the omnivore-prey system has a unique equilibrium, while for Holling type III, we obtained bistable coexistence. The latter fact also explains the above phenomenon that an omnivore agent may control the pest to different levels, according to the timing of the release of the agent.