Effect of cannibalism on a predator-prey system with nutritional value: a model based study

摘要

Enrichment of a simple predator-prey system results in the destruction of stable steady state and further enrichment leads to the extinction of the species, which is a classical problem in ecology and known as the paradox of enrichment. The Paradox of enrichment is a controversial issue. Most theoretical studies show the destabilization of predator-prey system due to enrichment, but there is a discrepancy between the empirical evidence and theoretical predictions. In spite of the debate and cross-debate, research is still being carried out on the paradox of enrichment (16 papers and nearly 500 citations in 2008), which in general does not include the effect of cannibalism. Here we present a simple predator-prey system in the presence of cannibalism among predators and offer a novel resolution to the paradox of enrichment. The concept of nutritional value is introduced by many authors to resolve the issue. It is observed that even in the face of sufficient enrichment the system remains stable in the vicinity of critical nutritional value. In the case of a lower cannibalism rate we also observe similar kinds of behaviour, but for a higher cannibalism rate, the system remains always stable and does not depend upon the nutritional value of prey, i.e. paradox of enrichment does not hold at all in such a situation. We also observe that cannibalism can have a positive as well as a negative effect on population abundance, depending on the cannibalism rate.