  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 for 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 one other control algorithm has 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.
