Coexistence in neutral theories: interplay of criticality and mild local preferences

Abstract: Neutral theories have played a crucial and revolutionary role in fields such as population genetics and biogeography. These theories are critical by definition, in the sense that the overall growth rate of each single allele/species/type vanishes. Thus each species in a neutral model sits at the edge between invasion and extinction, allowing for the coexistence of symmetric/neutral types. However, in finite systems, mono-dominated states are ineludibly reached in relatively short times owing to demographic fluctuations, thus leaving us with an unsatisfactory framework to rationalize empirically-observed long-term coexistence. Here, we scrutinize the effect of heterogeneity in quasi-neutral theories, in which there can be a local mild preference for some of the competing species at some sites, even if the overall species symmetry is maintained. As we show here, mild biases at a small fraction of locations suffice to induce overall robust and durable species coexistence, even in regions arbitrarily far apart from the biased locations. This result stems from the long-range nature of the underlying critical bulk dynamics and has a number of implications, for example, in conservation ecology as it suggests that constructing local specific "sanctuaries" for different competing species can result in global enhancement of biodiversity, even in regions arbitrarily distant from the protected refuges.