Abstract
Stabilizing the dynamics of complex, non-linear systems is a major concern across several scientific disciplines including ecology and conservation biology. Unfortunately, most methods proposed to reduce the fluctuations in chaotic systems are not applicable to real, biological populations. This is because such methods typically require detailed knowledge of system specific parameters and the ability to manipulate them in real time; conditions often not met by most real populations. Moreover, real populations are often noisy and extinction-prone, which can sometimes render such methods ineffective. Here, we investigate a control strategy, which works by perturbing the population size, and is robust to reasonable amounts of noise and extinction probability. This strategy, called the Adaptive Limiter Control (ALC), has been previously shown to increase constancy and persistence of laboratory populations and metapopulations of Drosophila melanogaster. Here, we present a detailed numerical investigation of the effects of ALC on the fluctuations and persistence of metapopulations. We show that at high migration rates, application of ALC does not require a priori information about the population growth rates. We also show that ALC can stabilize metapopulations even when applied to as low as one-tenth of the total number of subpopulations. Moreover, ALC is effective even when the subpopulations have high extinction rates: conditions under which another control algorithm had previously failed to attain stability. Importantly, ALC not only reduces the fluctuation in metapopulation sizes, but also the global extinction probability. Finally, the method is robust to moderate levels of noise in the dynamics and the carrying capacity of the environment. These results, coupled with our earlier empirical findings, establish ALC to be a strong candidate for stabilizing real biological metapopulations.
Highlights
Controlling chaotically fluctuating and extinction-prone populations is of major interest to ecologists and conservation biologists and has been an active area of investigation for the last two decades [1]
We further explore the efficacy of Adaptive Limiter Control (ALC) in silico in stabilizing the dynamics of metapopulations governed by coupled Ricker maps
We demonstrate that compared to an unperturbed system, ALC-controlled metapopulations are more stable over a wide range of intrinsic population growth rate, carrying capacity and extinction probability
Summary
Controlling chaotically fluctuating and extinction-prone populations is of major interest to ecologists and conservation biologists and has been an active area of investigation for the last two decades [1]. Substantial progress has been made in terms of ameliorating chaos in the fields of chemical sciences, physical sciences, electrical engineering, medicine and economics (reviewed in [2,3]), few strategies have been demonstrated to be successful in stabilizing biological populations. One reason for this is the fact that short and noisy time series typical of most biological populations make it statistically difficult to distinguish noisy limit cycles from chaotic trajectories. Until recently, there was no empirical support for the efficacy of any of the several limiter control algorithms in the context of biological populations or metapopulations
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