The paradoxical sustainability of periodic migration and habitat destruction
Some species and societies engage in sustainable habitat destruction by periodically alternating between a low-growth migratory lifestyle and high-growth but destructive behavior. Examples include nomadic pastoralism and shifting cultivation, practiced by humans for millenia. Although specific models have been developed for species or societies which practice periodic migration and habitat destruction, theoretical insight into such phenomena as a whole is lacking. Here we present a general model of populations which alternate between migratory but negative-growth nomadism and destructive colonialism which yields high but short-term growth. Despite both strategies individually resulting in extinction, we demonstrate that a population can sustainably colonize an arbitrarily large network of habitats by alternating between the two. This counter-intuitive result can be interpreted in terms of both Parrondos paradox and the exploration-exploitation dilemma, suggesting answers to the question of sustainable development.