Local dispersal, trophic interactions and handling times mediate contrasting effects in prey-predator dynamics

Trophic interactions between prey and predator species are an ubiquitous force in nature and it is reckoned to be one of the most important factors that can shape species geographical range limits. To better understand how local dispersal and predator handling times affect community dynamics, we perform a bifurcation analysis of a partial differential equations model consisting of environmental gradients, trophic (generalist, specialist predator and prey species) interactions and spatial diffusion components. Our co-dimension one bifurcation results depict the existence of numerous threshold values corresponding to supercritical and subcritical Hopf bifurcations, saddle-node bifurcation of cycles and transcritical bifurcation, as the magnitude of handling times and the generalist predation-induced mortality force change in this ecological system with local dispersal. It is discovered that the interaction between these distinct local bifurcations leads to higher codimension (two) bifurcation such as a generalised Hopf bifurcation, which acts as an organising centre of the dynamics. Ecologically, we also observe that: (i) without dispersal, higher levels of generalist predation (which acts as a mortality agent) require shorter specialist predator handling times to promote the maintenance of biodiversity through coexistence steady state of prey-predator species and oscillatory dynamics; however, lower forces of generalist predation result in longer specialist predator handling times and this situation induces destabilisation of species biodiversity; (ii) local dispersal stabilises the trophic dynamics and mediates more species diversity outcomes; (iii) dispersal interacts with lower magnitudes of generalist predator-induced mortality to generate bistability phenomenon between stable limit cycles and coexistence steady state; (iv) interestingly, higher intensities of mortality factor combined with dispersal may destroy some interior attractors, and exclude bistability-oscillatory dynamics in this trophic system; consequently, this situation leads to the extinction of specialist predator species and jeopardises species biodiversity. Taken together, our findings illustrate the influential roles of local dispersal, trophic interactions and handling times in determining community dynamics and these insights may have important consequences in conservation management and biological control strategies.