Bayesian modelling of daphnid responses to time-varying cadmium exposure in laboratory aquatic microcosms

Experiments were carried out to test the effects of cadmium on five aquatic species in 2-L indoor freshwater/sediment microcosms. Experimental data were collected over 21 days in static conditions, i.e. the microcosms evolved without water renewal. Because of speciation, the total cadmium concentration in water decreased with time. Here we present a focus on Daphnia magna responses. For the three life history traits we considered (survival, growth and reproduction), mathematical effect models were built based on threshold stress functions involving no effect concentrations (NECs). These models took the time-varying conditions of exposure into account through a time-recurrent formalism. Within a Bayesian framework, four kinds of data were fitted simultaneously (exposure, survival, growth and reproduction), using an appropriate error model for each endpoint. Hence, NECs were determined as well as their associated estimation uncertainty. Through this modelling approach, we demonstrate that thresholds for stress functions can be successfully inferred even in experimental setup more complex than standard bioassays.