Formulae for calculating the instantaneous rate of natural mortality of animals from its surrogates

Interspecific relationships between the instantaneous rate of natural morta lity of fish in a natural population and its surrogates are useful for stud ies of their population dynamics. In this paper, I derive interspecific mod els for the instantaneous rate of natural mortality of animals in a natural population as a function of age-, length-, and mass-based surrogates, demo nstrate their relationships with existing interspecific models, and fit the m into data from three groups of animals. At temporal equilibrium, and for the most stable distribution of individuals of a population, the sum of the population's instantaneous rates of natural and fishing mortalities is in inverse proportion to its characteristic age or approximately to its mean a ge, thereby decreasing with its observed maximum age and increasing linearl y with the rate of its individual's growth in length or mass. Fitting of th ese age-, length-, and mass-based models to data from cetaceans, fishes, an d benthic invertebrates showed that the instantaneous rate of natural morta lity is 4.7725 (+/-0.1365) times the reciprocal of the observed maximum age of a cetacean population, 1.2718 (+/-0.1944) times the growth rate of indi viduals in a fish population, and 2.4825 (+/-0.1262) times the growth rate of individuals in a population of benthic invertebrates. (C) 2001 Elsevier Science Ltd. All rights reserved.