Evaluating methods to quantify spatial variation in the velocity of biological invasions

Invading species rarely spread homogeneously through a landscape and invasion patterns typically display irregular frontal boundaries as the invasion progresses through space. Those irregular patterns are generally produced by local environmental factors that may slow or accelerate movement of the frontal boundary. While there is an abundant literature on species distribution modelling methods that quantify local suitability for species establishment, comparatively few studies have examined methods for measuring the local velocity of invasions that can then be statistically analysed in relation to spatially variable environmental factors. Previous studies have used simulations to compare different methods for estimating the overall rate of spread of an invasion. We adopted a similar approach of simulating invasions that resemble two real case‐studies, both in terms of their spatial resolution (i.e. considering the size of one cell as one km) and their spatial extent (> 600 000 km²). Simulations were sampled to compare how different methods used to measure local spread rate, namely the neighbouring, nearest distance and Delaunay methods, perform for spatio‐temporal comparisons. We varied the assessment using three levels of complexity of the spatio‐temporal pattern of invasion, three sample sizes (500, 1000 and 2000 points), three different spatial sampling patterns (stratified, random, aggregated), three interpolation methods (generalized linear model, kriging, thin plate spline regression) and two spatio‐temporal modelling structures (trend surface analysis and boundary displacement), resulting in a total of 486 different scenarios. The thin plate spline regression interpolation method, in combination with trend surface analysis, was found to provide the most robust local spread rate quantification as it was able to reliably accommodate different sampling conditions and invasion patterns. This best approach was successfully applied to two case‐studies, the invasion of France by the horse‐chestnut leafminer Cameraria ohridella and by the bluetongue virus, generally in agreement with previously published values of spread rates. Potential avenues for further research are discussed.