Spreading information in a network of interacting neighbours.

Dispersed individuals can coordinate the onset of life history events, like reproduction or migration, on a large (population) spatial scale. However, the mechanism of this synchronisation has not yet been identified. In many species signals produced by one individual stimulate signalling activity of immediate neighbours. I propose that such local focuses of signalling could transform into waves propagating in space. This hypothesis predicts that signalling self-organizes into bursts, because neighbours tend to enter activity and refractory periods together. Temporal characteristics of such pulses should be more similar in locations proximate to one another than in distant ones. Finally, denser populations should produce relatively more complex wave patterns, since the number of propagating waves is proportional to the number of individuals. These predictions were tested in an analysis of time series of numbers of territorial songs in chaffinches, Fringilla coelebs, and the results supported the hypothesis. Time series of singing activity had memory of their past states: they were autoregressive processes with spectra in which low frequency oscillations predominated. The degree of similarity in two synchronously sampled time series, measured as a Euclidean distance between their spectra, decreased with the increasing physical distance of sampling spots and the number of signalling males. It is concluded that networks of interacting neighbours may integrate populations synchronising life cycles of dispersed individuals.