• demography;
  • density dependence;
  • logistic;
  • marine mammal;
  • nonlinear dynamics;
  • odontocete;
  • pinniped;
  • population dynamics

Abstract: Ranges of the ratio of maximum net productivity level (MNPL) to carrying capacity (K) are explored in general models for pinnipeds and odontocetes. MNPL/K is used in management of marine mammals but no empirical evidence exists to limit the range of values expected. Density dependent changes in age-specific birth and death rates have been used to infer MNPL/K. Non-linearities in these rates do not translate directly to population growth curves. The simple models demonstrate: (1) density dependence is likely to involve more than a single parameter (such as birth rate), (2) MNPL/K can be greatly reduced from that inferred from one strongly non-linear parameter when changes in other parameters are linear, (3) ranges of MNPL/K depend on biological limits on ranges of fecundity and survival rates, and (4) the magnitude and sign of bias incurred by inferring MNPL/K from functional forms of single parameters cannot be determined. Given current empirical evidence the range of MNPL/K for marine mammals as a group is large. Although MNPL/K should not be inferred from single parameter non-linearities, distributions of MNPL/K values can be generated through models which account for single species ranges for birth and death rates and maximum population growth rate.