Abstract
A series of interrelated models is developed for various types of predator-prey interaction, based on combining the McKendrick equation for a single age-structured population with the Volterra-Lotka or Kolmogorov predator-prey equations. First a single species is studied that cannibalizes its own young. There it is shown by fixed point theory that the population will tend to a stable equilibrium or periodic solution if the birth rate is sufficiently high. Three cases are studied of a two-species system with age-dependent predation: (1) predators eat all ages of prey indiscriminately; (2) predators eat only newborn prey; (3) predators eat all ages with a preference toward the very young and very old. Case (1) is indistinguishable from a system where age is ignored. Case (2) can lead to oscillations of unbounded amplitude, but realistic refinements of the model can be made that eliminate the unboundedness. Case (3) can be analyzed using bifurcation from the situation of Case (1), and shown to have periodic solutions if the age bias in predation is sufficiently small.
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