A model of growth and development in copepods

We present a model for the growth and development of copepods based on the simple assumption that a constant fraction of assimilated carbon is invested in the formation of a new carapace. The individual molts into the next stage when the weight of the accumulated carapace building bricks is a fixed fraction of the body mass at the beginning of the stage. This simple stage-transition coordinating system is built into an individual growth model. The model predicts decreasing stage duration and increasing body weight with increasing food concentrations. These trends closely agree with published data. Anisochronality, as found in many copepod species, agrees with model predictions. Acartia species usually show isochronal development. The model predicts isochronal development for one particular value of a parameter of the feeding process. Literature data show that this parameter value is realistic for Acartia spp. “Equiproportionality” is predicted by the model. The model thus shows close agreement with observed growth and development patterns. In many freshwater and marine ecosystems, copepods are among the dominant secondary producers. Research on copepods lags work on cladocerans, especially Daphnia species. Physiologically based models of individual growth have been developed for Daphnia. Much insight has been gained into the growth and development of Daphnia individuals. These individual growth models have been used to investigate the physiology of starvation (Lynch 1989; Gurney et al. 1990) and the effects of toxic substances (Kooijman and Metz 1984; Hallam et al. 1990). Some investigators have constructed population models based on such individual growth models (de Roos et al. 1992; Sinko and Steifer 1969). These models reveal how processes at the individual level influence the dynamics of Daphnia populations. In copepods, both the study of growth and development of individuals and of population dynamics could benefit from models of individual growth, as has been done for Daphnia. There are, however, major differ1 Present address: Department of Mathematics, Agricultural University of Wageningen, Dreijenlaan 4, NL6703 HA Wageningen, The Netherlands. Acknowledgments We thank R. C. Hart for helpful discussions. We are grateful to W. R. DeMott and two anonymous referees whose comments improved the paper. We thank N. Zerbath for checking the English. F. van den Bosch acknowledges the Alexander von Humboldt Stiftung for a research stipend and the MaxPlank-Institut fti Limnologie for hospitality and support during his stay. ences between growth and development of copepods and cladocerans that must be considered. These differences necessitate the development of new models. In this paper, we make a first step toward constructing a copepod life-history model. We concentrate on development within a stage and the transitions between stages. Most Daphnia models assume molts occur at preset ages that are not influenced by food conditions (Lynch 1989; Hallam et al. 1990; Gurney et al. 1990). The onset of reproduction is assumed to be triggered by size (length or weight) of the animal (Kooijman and Metz 1984; Kooijman 1986; Gurney et al. 1990). These rules are questionable for Daphnia at low concentrations of food and are not appropriate for copepods. In contrast to Daphnia, copepods reach the adult stage after a fixed number of immature stages. Molting from one stage to the next is not triggered simply by age or size of the animal. Stage duration of some species decreases with increasing food supply, thus ruling out age as the sole trigger for stage transition. Size in a stage for some species increases with increasing food supply, thus ruling out size as the sole trigger (Vidal 1980a, b; Paffenhijfer and Harris 1976; Elmore 1982; Berggreen et al. 1988; Santer and van den Bosch 1994). The when and why of stage transition is thus a central question in modeling the growth and development of copepods. We suggest an answer to this question by proposing a simple molting rule. Based on this idea, we present a copepod growth model.