A theoretical foundation for multi-scale regular vegetation patterns

Empirically validated mathematical models show that a combination of intraspecific competition between subterranean social-insect colonies and scale-dependent feedbacks between plants can explain the spatially periodic vegetation patterns observed in many landscapes, such as the Namib Desert ‘fairy circles’. The many causes of fairy circles Desert grasslands in parts of Namibia are punctuated by regularly patterned patches of bare soil known as fairy circles, the origins of which have remained unclear. Corina Tarnita, Juan Bonachela and colleagues use theoretical modelling and image analysis to show that a combination of scale-dependent feedbacks between plants and territorial competition between subterranean social-insect colonies can explain these features. They conclude that multiple mechanisms of self-organization are probably at play in ecosystems across the world. Self-organized regular vegetation patterns are widespread 1 and thought to mediate ecosystem functions such as productivity and robustness 2 , 3 , 4 , but the mechanisms underlying their origin and maintenance remain disputed. Particularly controversial are landscapes of overdispersed (evenly spaced) elements, such as North American Mima mounds, Brazilian murundus , South African heuweltjies , and, famously, Namibian fairy circles 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 . Two competing hypotheses are currently debated. On the one hand, models of scale-dependent feedbacks, whereby plants facilitate neighbours while competing with distant individuals, can reproduce various regular patterns identified in satellite imagery 1 , 14 , 15 . Owing to deep theoretical roots and apparent generality, scale-dependent feedbacks are widely viewed as a unifying and near-universal principle of regular-pattern formation 1 , 16 , 17 despite scant empirical evidence 18 . On the other hand, many overdispersed vegetation patterns worldwide have been attributed to subterranean ecosystem engineers such as termites, ants, and rodents 3 , 4 , 7 , 19 , 20 , 21 , 22 . Although potentially consistent with territorial competition 19 , 20 , 21 , 23 , 24 , this interpretation has been challenged theoretically and empirically 11 , 17 , 24 , 25 , 26 and (unlike scale-dependent feedbacks) lacks a unifying dynamical theory, fuelling scepticism about its plausibility and generality 5 , 9 , 10 , 11 , 16 , 17 , 18 , 24 , 25 , 26 . Here we provide a general theoretical foundation for self-organization of social-insect colonies, val