Temporal self-similarity created by spatial individual-based population dynamics

We report an individual-based single-species model producing temporal scale-free, self-similar dynamics in time. Individuals in the population renew in an explicit space with a large number of loci. We show that reproduction, subsequent dispersal of the offspring, and mortality will organise population fluctuations such that the emerging dynamics represent power law and scale-free structures. Further, we show that spatially structured population dynamics may show red frequency spectra, a property that the simple nonlinear population models are generally lacking.