Allee effects change how other population parameters affect rates of spread in expanding populations

Background/Question/Methods

Species are arriving to novel locations and subsequently spreading at unprecedented rates due to human-activities around the world.  Understanding the population factors that facilitate and reduce spread rates is critical to managing invading species and mitigating the negative effects. Theoretical and empirical studies have identified a number of population parameters that affect rates of spread, such as dispersal rate, dispersal kernel, intrinsic rate of increase, and population synchrony. In addition, recent work has focused on the profound role Allee effects can have at reducing and even preventing range expansion. In this study I explored how Allee effects change the quantitative and qualitative effects of other population parameters on rates of spread. The analyses were performed in a theoretical framework in the Matlab computer environment using a Ricker-type model with and without an explicit Allee threshold. The model was spatially extended into a two-dimensional grid and simulated for 50 time steps. I analyzed how Allee effects moderated the effects of carrying capacity, intrinsic rate of increase, long distance dispersal probability, long distance dispersal kernel, nearest neighbor dispersal probability, total stochasticity, and regional stochasticity.   

Results/Conclusions

Allee effects consistently reduced spread rates regardless of the other population parameter values. Carrying capacity had a positive effect on the rate of spread, likely due to both a larger buffer from the Allee threshold and increases in the number of dispersers to nascent patches, which in turn would increase persistence and establishment probabilities, respectively. The effect of intrinsic rate of increase was dependent on the strength of the Allee effect; for example, the intrinsic rate of increase positively affected the spread rate in the absence of Allee effects, but had little effect when Allee effects were strong. The proportional effect of nearest neighbor dispersal was greatest when Allee effects were high. In contrast, the long distance dispersal probability and the value of the dispersal kernel had large positive effects on spread rates when Allee effects were absent, but little effect when Allee effects were strong. Total stochasticity had a relatively small negative effect on rate of spread regardless of Allee effect. Synchrony and regional stochasticity had little effect on rate of spread regardless of Allee effects. These results suggest that Allee effects can have large effects on how other population parameters affect spread rates.