Stunted Growth and Stepwise Die-Off in Animal Cohorts

A model of an animal cohort foraging on logistically growing food is analyzed. The problem is captured in three differential equations, one for food density and two for the state of the animal cohort, keeping track of body weight and number of individuals, respectively. When the animals efficiently exploit their food to low densities, the model produces cycles. The cycles differ markedly from those produced by traditional predator-prey models. Consumer decline is associated with starvation mortality when individuals lose too much weight. This condition causes a stepwise decline in individual number, each step corresponding to one cycle. Because the survivors of each starvation period grow and because larger animals have lower weight-specific metabolic rates, the nature of the cycles changes over time. They acquire a slow-fast character because of the increasing difference between food and consumer speed and show distinct catastrophic features, as the fast phases are caused by jumping between an over-and underexploited state of the food population. The cycles may either continue toward extinction of the cohort or damp out in a stable state characterized by stunted individual growth. Data from fish communities are closely in line with the specific predictions from this generic model about patterns of die-off and stunted growth. The model behavior is robust. It does not depend on the type of functional response or the way in which mortality increases with individual loss. Furthermore, the same patterns are obtained from an elaborate, realistic individual-based model, which indicates that the results are not artifacts of simplifications like considering all individuals equal and assuming only one food source.