Individual and Global Adaptation in Networks

The structure of complex biological and socio-economic networks affects the selective pressures or behavioural incentives of components in that network, and reflexively, the evolution/behaviour of individuals in those networks changes the structure of such networks over time. Such ‘adaptive networks’ underlie how gene-regulation networks evolve, how ecological networks self-organise, and how networks of strategic agents co-create social organisations. Although such domains are different in the details, they can each be characterised as networks of self-interested agents where agents alter network connections in the direction that increases their individual utility. Recent work shows that such dynamics are equivalent to associative learning, wellunderstood in the context of neural networks. Associative learning in neural substrates is the result of mandated learning rules (e.g. Hebbian learning), but in networks of autonomous agents ‘associative induction’ occurs as a result of local individual incentives to alter connections. Using results from a number of recent studies, here we review the theoretical principles that can be transferred between disciplines as a result of this isomorphism, and the implications for the organisation of genetic, social and ecological networks. Neural (Adaptive) Networks The Hopfield network [6] is a well-understood example of a dynamical system based on pairwise interactions (Eq. 1). It has provided a vehicle for studying dynamical behaviour across many disciplines from neural networks, to spin-glass models, to ecosystems. For example, it can be relabelled to represent strategic choices of agents rather than activation responses of neurons. Specifically, each agent in a network, repeatedly, one at a time in random order, adopts one of two discrete behaviours or states, si = ±1 (e.g. trait-a/trait-A, tradex/trade-y, vote-A/vote-B), so as to maximise an individual pay-off, fitness or utility, ui, which is a weighted sum of interactions between the state it adopts and the states of other agents in the network,