Multi-scale methods predict invasion speeds in variable landscapes

Partial differential equation models for invasive species spread in the presence of spatial heterogeneity

Models of invasive species spread often assume that landscapes are spatially homogeneous; thus simplifying analysis but potentially reducing accuracy. We extend a recently developed partial differential equation model for invasive conifer spread to account for spatial heterogeneity in parameter values and introduce a method to obtain key outputs (e.g. spread rates) from computational simulations. Simulations produce patterns of spatial spread which appear qualitatively similar to observed patterns in grassland ecosystems invaded by exotic conifers, validating our spatially explicit strategy. We find that incorporating spatial variation in different parameters does not significantly affect the evolution of invasions (which are characterised by a long quiescent period followed by rapid evolution towards to a constant rate of invasion) but that distributional assumptions can have a significant impact on the spread rate of invasions. Our work demonstrates that spatial variation in site-suitability or other parameters can have a significant impact on invasions and must be considered when designing models of invasive species spread.

Should I Stay or Should I Go: Partially Sedentary Populations Can Outperform Fully Dispersing Populations in Response to Climate-Induced Range Shifts

Global mean temperatures have increased by 0.72 [Formula: see text]C since the 1950s, and climate warming is resulting in geographical shifts in the range limits of many species. Climate velocity is estimated to be 0.42 km/year, and if a species fails to adapt to the new climate, it must track the location of its climatically constrained niche in order to survive. Dispersal has an important role to play in enabling a population to shift is geographical range limits, but many species are partially sedentary, with only a fraction of the population dispersing each year. We ask, can partially sedentary populations keep pace with climate or will such populations be more vulnerable to extinction? Through the development of a moving-habitat integrodifference equation model, we show that, provided climate velocity is not too large, partially sedentary populations can outperform fully dispersing populations in one of two ways: (i) by persisting at climate speeds where a fully dispersing population cannot, and (ii) exhibiting higher population densities. Moreover, we find that positive density-dependent dispersal can further improve the likelihood a population can persist. Our results highlight the positive role that non-dispersers may play in mitigating the effects of overdispersal and facilitating population persistence in a warming world.