Modelling ecological invasion includes a number of approaches, from mechanistics approaches that generally require a detailed understanding of key life-history parameters of the invaders (e.g. growth rate, diffusion processes, biotic and abiotic interactions), to empirical statistical models that analyse the spatio-temporal patterns of invasions in order to quantify some of their key features (e.g. rate of spread, correlation between date of first invasion and external predictor variables). In our work, we mainly focus on empirical statistical approaches to analyze spatio-temporal data of ecological invasions. In particular, invading organisms spreading though a heterogeneous landscape are difficult to study using conventional statistical models, and there is no established methodology to analyse those space-time data sets. We aim to develop new methodology to study type of data, to review existing methods, and to compare all methods in their capacity to detect the influence of landscape heterogeneity on the pattern of spread.
To date, the statistical analysis of spread rates can broadly be divided in two categories. In one hand, boundary displacement methods (BD) are based on the division of the invasion in different and discrete time steps, the spatial distribution of the invaded area and of the invasion front-line is established at each time step, and the local spread rate is measured locally as the distance separating the invasion front-line of two sequential time step. In the other hand, trend-surface analysis methods (TSA) treat the date of first invasion as a continuous dependent variable, fit a surface model to the observed date of first invasion as a function of spatial coordinates, and finally estimate the local rate of spread as the inverse of the local slope of the surface. Analyzing the resulting local spread rates estimates in relation with the heterogenous environment has not been much investigated so far. We approach this problem through simulating the spread of invading organisms with known parameters, and build a data set that we can then use as training data to compare statistical methods. The two figures below illustrate how the travelling wave of invasion can be interpreted in terms of spread rate.
Once our methods will have been evaluated, they will be tested on empirical data sets. In addition, we aim to assessing the effect of long-range dispersal on the accuracy of local spread rate estimates, and try to evaluate the extent by which invasions can be forecasted through the study of past invasions.
Our current research activities on this topic are supported by the EDENext FP7 project, and we work in collaboration with Renaud Lancelot (CIRAD, Montpellier, France), William Wint & Guy Hendrickx (Euro-AEGIS, Belgium) A. Conte (IZS, Teramo, Italy) S. Napp & A. Allepuz (CRESA, Barcelona, Spain). Previous research on the topic were made in collaboration with Sandy Liebhold (USDA Forest Service) & Sylvie Augustin (INRA, France).