Figure 3
Onset of sexual production (a) and width w of the transition zone (b) between complete worker and complete sexual production as a function of the width of a uniform distribution of season length (B). w is defined as the number of time steps between the time when the strategy variable u i surpasses a value of 0.05 for the first time and the time when u i has finally reached at least 0.95 (and stays above this value for all remaining time steps). As long as w = 0, the reproduction strategy is bang-bang (as in the deterministic case), but the optimal switching time moves to earlier points in time when variance increases (a). Model parameters: worker productivity rate c = 0.15, survival rate q = 0.95, mean season length μ = 50. The single emphasised point in the right figure denotes the combination of strategy transition and estimation of environmental variance observed for L. malachurum at Wuerzburg. The bars indicate the 95% confidence interval for the estimation of the mean w (between colonies, n1 = 5 colonies) and the estimation of B (between years, n2 = 48).