A Second Example: Vertical Migration and Reproductive Effort in Daphnia

Abstract

This chapter demonstrates the application of state- and prediction-based theory (SPT) to a real biological system, but a system that has been simplified enough to also be addressed by dynamic state variable modeling (DSVM). The Daphnia vertical migration (VM) system allows one to explore ways to use SPT for an adaptive trade-off behavior that clearly is important to population dynamics, and to compare the behavior it produces to behavior predicted by a DSVM model and observed in real organisms. The chapter reproduces the three patterns of observed behavior, in almost all their details, while converting Øyvind Fiksen's DSVM model into a population model that includes mortality and reproduction and could easily include processes that make DSVM intractable—like interaction and variation among individuals. One lesson is that SPT can readily represent contingent decisions, such as Daphnia choice of both depth and reproductive allocation. This is not surprising because such decisions have also been modeled with DSVM.