Use of a mathematical model in the analysis of survival of Daphnia magna exposed to toxicants

Chronic toxicity tests carried out on species of the genus Daphnia (Crustacea:Cladocera) are bioassays commonly used in ecotoxicology. Mortality in the cohorts exposed to toxicants can be examined by the analysis of survival curves. The shape of these curves may be very different because of inter-individual heterogeneity: the less rectangular is the shape the more different is the probability of dying of daphnids in the cohort. Aim of this paper is to analyze the characteristics — in particular the shape — of survival curves of cohorts of Daphnia magna exposed to heavy metals in chronic toxicity tests. Experimental curves were fitted by a mathematical model recently proposed, which puts emphasis just on this heterogeneity, described by the parameter of the model S0. The information contained in S0 is very useful for the present purposes: the higher the value of S0 the less rectangular the shape of the curve and, as a consequence, the higher the age-at-death heterogeneity of the cohort is thought to be. The model contains a second parameter, omega, representing the maximum potential ability of the individuals to survive in a specific environment and is related with the maximal life span. The model fitted well the survival curves in most cases and both S0 and omega showed statistically different values between treatments, useful for comparisons. It was concluded that S0 provides a quantitative estimation of curve ‘‘rectangularization’’, useful to check different sensitivities to a specific toxicant concentration among daphnids belonging to the same cohort, while omega provides an estimate of maximal life span.