Variation in risk in single-species discrete-time models - Abhyudai Singh; Roger M. Nisbet (Mathematical Biosciences and Engineering)
Simple, discrete-time, population models typically exhibit complex dynamics, like cyclicoscillations and chaos, when the net reproductive rate, $R$, is large. These traditionalmodels generally do not incorporate variability in juvenile 'risk,'' defined to be ameasure of a juvenile's vulnerability to density-dependent mortality. For a broad class of discrete-time models we show that variability in risk across juveniles tends to stabilize the equilibrium. We consider both density-independent and density-dependent risk, and for each, we identify appropriate shapes of the distribution of risk that will stabilize the equilibrium for all values of $R$. In both cases, it is the shape of the distribution of risk and not the amount of variation in risk that is crucial for stability.