Stabilizing Populations with Adaptive Limiters: Prospects and Fallacies

Adaptive limiter control has been proposed as a method for stabilizing fluctuations in unstable population dynamics. This method invokes a dynamic thresholding and restocks the population if it falls below a certain proportion of its previous size. The reference state for the adaptive threshold can be the previous population size after (ALC) or before (ALCb) intervention. The former has been tested experimentally and analyzed theoretically, whereas the latter has been proposed for biological populations but not yet studied. Here, we investigate the consequences of choosing a different basis for adaptive limiter control. We thoroughly explain the mechanisms that allow ALCb to reduce the magnitude of population fluctuations under certain conditions. However, we also find that ALCb may be counterproductive in other situations, actually increasing fluctuations and extinction risk. We show that this effect is further promoted by an alternative attractor with undesirable properties. The bistability is triggered by basing the adaptive threshold on a different reference population size. The results in this paper highlight the importance of making correct references to system states in the past and the dramatic consequences this can have in chaos control schemes. In the ecological application, a desirable support intervention might backfire into unintended extinction.