Code and Data for: Importance of environmental productivity and diet quality in intraguild predation

In the intricate network of ecological interactions, intraguild predation
emerges as a fundamental community module incorporating omnivory.
Classical equilibrium theory predicts the exclusion of the intraguild
predator and prey at low and high environmental productivity,
respectively, with the coexistence of both species occurring only at
intermediate productivity levels. However, empirical studies challenge
this theoretical prediction, particularly concerning the extinction of
intraguild prey in highly productive environments. To address this
enigmatic issue, Diehl (2003) and Abrams and Fung (2010a) explore the
impact of food quality and propose that low nutritional quality of the
basal resource stabilizes omnivorous systems. Yet, the influence of
intermediate consumer quality remains inadequately explored. This study
employs analytical and numerical bifurcation studies to investigate the
effects of the quality of two diet types. Various bifurcations, including
supercritical and subcritical Hopf bifurcations, saddlenode bifurcations
of periodic solutions, and transcritical bifurcations of periodic
solutions are observed. These bifurcations are directly linked to the
destinies of intraguild prey and predators. The results reveal that, in
highly productive environments, it may not be the intermediate consumer
but the omnivore that faces extinction. This discovery holds significant
implications for the conservation and management of omnivorous systems.