Stochastic optimization

Surprising heterogeneity of profit distribution under a simple Beverton-Holt model

Usually I expect the alternate stable state dynamics to be the ones producing bimodal distribution of profit:

The pattern is driven by a costs to harvesting making harvest unprofitable most of the time, while chance fluctuations push some populations across this threshold again and again. The ensemble variation in harvest is suggestive of this:

but we really see what is going on when we color-code the population dynamics of the most profitable and least profitable realizations of the stochastic dynamics:

Maximizing expected profit when it means 1:4 chance of no profit might not be, well, optimal? Haven’t seen this kind of dynamic before.