Importantly, ALC not only reduces the fluctuation in metapopulation sizes, but also the global extinction probability. Moreover, ALC is effective even when the subpopulations have high extinction rates: conditions under which another control algorithm had previously failed to attain stability. We also show that ALC can stabilize metapopulations even when applied to as low as one-tenth of the total number of subpopulations. We show that at high migration rates, application of ALC does not require a priori information about the population growth rates. Here, we present a detailed numerical investigation of the effects of ALC on the fluctuations and persistence of metapopulations. 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 investigate a control strategy, which works by perturbing the population size, and is robust to reasonable amounts of noise and extinction probability. Moreover, real populations are often noisy and extinction-prone, which can sometimes render such methods ineffective. 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. Unfortunately, most methods proposed to reduce the fluctuations in chaotic systems are not applicable to real, biological populations. Stabilizing the dynamics of complex, non-linear systems is a major concern across several scientific disciplines including ecology and conservation biology. Note that although there is an overall decrease in metapopulation FI, the trends and magnitude of decrease are different. b) Metapopulation stability when three subpopulations are perturbed but in different arrangements. However, perturbing too many subpopulations leads to a lesser reduction in global FI. ALC was able to stabilize metapopulations in general, even when applied in only 1/9 subpopulations. a) Metapopulation stability for different number of perturbed subpopulations (identity of subpopulations in bracket) at different values of c. Each point is a mean of 100 independent simulations and error bars denote the corresponding SEM. All other conditions were similar to the 1-D migrations. The migration rate, initial population size, r, and K were 0.3, 20, 3.5 and 30 respectively. With periodic boundary conditions, the subpopulations thus inhabit the surface of a 3-D torus. Thus, subpopulation #5 exchanged migrants with subpopulation # 2,8,6,4 and so on. Each subpopulation exchanged migrants with four neighbours (above, below, right and left). The inset gives the identity of the individual subpopulations. In these simulations, the 9 subpopulations were arranged on a 3×3 2-D lattice with periodic boundary conditions for migration. Figure S3: FI of 9-patch 2-D metapopulations for different ALC magnitude ( c ).
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