Toxicant-induced fecundity compensation: A model of population responses

Abstract

/ A mathematical model widely applied in population studies and in assessment of the impact of exploitation on fish populations was applied to assess cadmium toxicity in laboratory populations of Daphnia galeata mendotae. Over a range of toxicant concentrations, the birth rate of the population increased to balance the death rate and the population compensated for the increased mortality. The model describes the relation between toxicant concentration, toxicant-induced mortality, and equilibrium population size. Compensation for increased mortality is described in terms of the decrease in population size necessary to produce an increase in the birth rate that will balance the increased death rate. The relative capacity of different aquatic organisms to compensate for toxicant-induced mortality is examined and a relation between compensatory capacity and the innate capacity for increase is developed.Populations subjected to mortality induced by exposure to toxicants compensate to offset this mortality so that its impact on populations will not be as severe as observations of individuals indicate. Compensation provides a margin of safety, but its results are gradual and more difficult to detect. In this study a mathematical mode) is developed and applied to describe the toxic impact, of cadmium on laboratory populations of Daphnia and the responses of the populations to this impact. The model is applied to examine the relations among the levels of stress, population size, birth rate, and death rate. The ModelA mortality equation for some concentration of a toxicant that increases the death rate iswhere D is the number of toxicant-induced deaths, N is the population size, and Z is the toxicant-induced mortality rate per individual. The toxicant-induced mortality rate is a function of toxicant concentration; the simplest relation isKEY WORDS Toxicant-induced mortality; Environmental modeling; Fecundity compensation lWork performed under the auspices of the United States Environmental Protection Agency. 9 Work completed while on sabbatical leave at Argonne National Laboratory.for C --Co, where h is the toxicant-induced mortali*.yin #g/L, and Co is the threshold toxicant concentration (which might be zero).To apply the toxicant mortality equation, an equation must be developed for change in population size. The capacity of a population to compensate for increased mortality is a function of population size with the compensatory capacity low at both low and high population sizes and a maximum at some intermediate population size. Application of a parabola to describe the relation between the capacity to increase and population size, which is the simplest approach, gives the modelwhere the new symbols are r is the innate capacity for the population to increase (time) -l, and K which is the environmental carrying capacity in numbers. The above population growth equation is the logistic equation. The toxicity of a chemical under a particular set of conditions and the sensitivity of the individuals tested determines...

Dynamics of fisheries that affect the population growth rate coefficient

“…This logistic surplus production model was developed by Volterra (1928), Hjort and others (1933), Graham (1935), and Schaefer (1954). It has been widely applied for stock assessment (Ricker 1975, Gulland 1972and 1977, Jensen 1976and 1978, Abramson and Tomlinson 1972, and MacCall and others 1976, for environmental impact assessment (Jensen 1982, Jensen andothers 1982), and for assessment of the impact of toxicants on populations Marshall 1982 and1983).…”