MBI Publications

MBI Publications for Ross Cressman (2)

  • V. Krivan and R. Cressman
    Competition in di-and tri-trophic food web modules
    Journal of Theoretical BiologyVol. 343 (2013) pp. 127-137


    Competition in di-and tri-trophic food web modules with many competing species is studied.The food web modules considered are apparent competition between n species sharing a single predator and a diamond-like food web with a single resource,a single top predator and many competing middle species.The predators have either fixed preferences for their prey,or they switch between available prey in away that maximizes their fitness. Dependence of these food web dynamics on environmental carrying capacity and food web connectance is studied.The results predict that optimal flexible for aging strongly weakens apparent competition and promotes species coexistence. Food web robustness (defined here as the proportion of surviving species) does not decrease with increased connectance in these food-webs. Moreover, it is shown that flexible prey switching leads to the same population equilibria as in corresponding food webs with highly specialized predators. The results show that flexible for aging behavior by predators can have very strong impact on species richness, as well as the response of communities to changes in resource enrichment and food web connectance when compared to the same food-web topology with inflexible top predators. Several results on global stability using Lyapunov functions areprovided.
  • R. Cressman and V. Krivan
    Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds
    J. Math. Biol.Vol. 67 (2013) pp. 329–358


    The population-dispersal dynamics for predator–prey interactions and two competing species in a two patch environment are studied. It is assumed that both species (i.e., either predators and their prey, or the two competing species) are mobile and their dispersal between patches is directed to the higher fitness patch. It is proved that such dispersal, irrespectively of its speed, cannot destabilize a locally stable predator–prey population equilibrium that corresponds to no movement at all. In the case of two competing species, dispersal can destabilize population equilibrium. Conditions are given when this cannot happen, including the case of identical patches.

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