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

Interspecific relationships between the instantaneous rate of natural mortality of fish in a natural population and its surrogates are useful for studies of their population dynamics. In this paper, I derive interspecific models for the instantaneous rate of natural mortality of animals in a natural population as a function of age-, length-, and mass-based surrogates, demonstrate their relationships with existing interspecific models, and fit them 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 populationʹs instantaneous rates of natural and fishing mortalities is in inverse proportion to its characteristic age or approximately to its mean age, thereby decreasing with its observed maximum age and increasing linearly with the rate of its individualʹs growth in length or mass. Fitting of these age-, length-, and mass-based models to data from cetaceans, fishes, and benthic invertebrates showed that the instantaneous rate of natural mortality 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 individuals in a fish population, and 2.4825 (±0.1262) times the growth rate of individuals in a population of benthic invertebrates.