Theory predicts rapid genetic drift during invasions, yet many expanding populations maintain high genetic diversity. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because many more migrants from the diverse, high‐density regions arrive at the expansion edge. When density dependence is weak or negative, the effective population size of the front scales only logarithmically with the carrying capacity. The dependence, however, switches to a sublinear power law and then to a linear increase as the density dependence becomes strongly positive. We develop a unified framework revealing that the transitions between different regimes of diversity loss are controlled by a single, universal quantity: the ratio of the expansion velocity to the geometric mean of dispersal and growth rates at expansion edge. Our results suggest that positive density dependence could dramatically alter evolution in expanding populations even when its contribution to the expansion velocity is small.

Traveling fronts describe the transition between two alternative states in a great number of physical and biological systems. Examples include the spread of beneficial mutations, chemical reactions, and the invasions by foreign species. In homogeneous environments, the alternative states are separated by a smooth front moving at a constant velocity. This simple picture can break down in structured environments such as tissues, patchy landscapes, and microfluidic devices. Habitat fragmentation can pin the front at a particular location or lock invasion velocities into specific values. Locked velocities are not sensitive to moderate changes in dispersal or growth and are determined by the spatial and temporal periodicity of the environment. The synchronization with the environment results in discontinuous fronts that propagate as periodic pulses. We characterize the transition from continuous to locked invasions and show that it is controlled by positive density-dependence in dispersal or growth. We also demonstrate that velocity locking is robust to demographic and environmental fluctuations and examine stochastic dynamics and evolution in locked invasions.

Theory predicts rapid genetic drift in expanding populations due to the serial founder e↵ect at the expansion front. Yet, many natural populations maintain high genetic diversity in the newly colonized regions. Here, we investigate whether density-dependent dispersal could provide a resolution of this paradox. We find that genetic drift is dramatically suppressed when dispersal rates increase with the population density because many more migrants from the diverse, highdensity regions arrive at the expansion edge. When density-dependence is weak or negative, the e↵ective population size of the front scales only logarithmically with the carrying capacity. The dependence, however, switches to a sublinear power law and then to a linear increase as the density-dependence becomes strongly positive. To understand these results, we introduce a unified framework that predicts how the strength of genetic drift depends on the densitydependence in both dispersal and growth. This theory reveals that the transitions between di↵erent regimes of diversity loss are controlled by a single, universal parameter: the ratio of the expansion velocity to the geometric mean of dispersal and growth rates at expansion edge. Importantly, our results suggest that positive density-dependence could dramatically alter evolution in expanding populations even when its contributions to the expansion velocity is small.

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We show that the Olami-Feder-Christensen model exhibits an effective ergodicity breaking transition as the noise is varied. Above the critical noise, the system is effectively ergodic because the time-averaged stress on each site converges to the global spatial average. In contrast, below the critical noise, the stress on individual sites becomes trapped in different limit cycles, and the system is not ergodic. To characterize this transition, we use ideas from the study of dynamical systems and compute recurrence plots and the recurrence rate. The order parameter is identified as the recurrence rate averaged over all sites and exhibits a jump at the critical noise. We also use ideas from percolation theory and analyze the clusters of failed sites to find numerical evidence that the transition, when approached from above, can be characterized by exponents that are consistent with hyperscaling.