Abstract
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.
Keywords
Ecological stoichiometry; Imperfectly substitutable resources; Liebig's Law; Numerical response; Omnivory
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