  Stoichiometric constraints play a role in the dynamics of natural
populations, but are not explicitly considered in most mathematical models.
Recent theoretical works suggest that these constraints can have a significant
impact and should not be neglected. However, it is not yet resolved how
stoichiometry should be integrated in population dynamical models, as different
modeling approaches are found to yield qualitatively different results. Here we
investigate a unifying framework that reveals the differences and commonalities
between previously proposed models for producer-grazer systems. Our analysis
reveals that stoichiometric constraints affect the dynamics mainly by
increasing the intraspecific competition between producers and by introducing a
variable biomass conversion efficiency. The intraspecific competition has a
strongly stabilizing effect on the system, whereas the variable conversion
efficiency resulting from a variable food quality is the main determinant for
the nature of the instability once destabilization occurs. Only if the food
quality is high an oscillatory instability, as in the classical paradox of
enrichment, can occur. While the generalized model reveals that the generic
insights remain valid in a large class of models, we show that other details
such as the specific sequence of bifurcations encountered in enrichment
scenarios can depend sensitively on assumptions made in modeling stoichiometric
constraints.
