Accounting for uncertainty in colonisation times: a novel approach to modelling the spatio‐temporal dynamics of alien invasions using distribution data

Abstract

A novel, yet generic, Bayesian approach to parameter inference in a stochastic, spatio‐temporal model of dispersal and colonisation is developed and applied to the invasion of a region by an alien plant species. The method requires species distribution data from multiple time points, and accounts for temporal uncertainty in colonisation times inherent in such data. Covariates, such as climate parameters, altitude and land use, which capture variation in the suitability of sites for plant colonisation, are easily incorporated into the model. The method assumes no local extinction of occupied sites and thus is primarily applicable to modelling distribution data at relatively coarse spatial resolutions of plant species whose range is expanding over time. The implementation of the model and inference algorithm are illustrated through application to British floristic atlas data for the widespread alien Heracleum mantegazzianum (giant hogweed) assessed at a 10 × 10 km resolution in 1970 and 2000. We infer key characteristics of this species, predict its future spread, and use the resulting fitted model to inform a simulation‐based assessment of the methodology. Simulated distribution data are used to validate the inference algorithm. Our results suggest that the accuracy of inference is not sensitive to the number of distribution time points, requiring only that there are at least two points in time when distributions are mapped. We demonstrate the utility of the modelling approach by making future forecasts and historic hindcasts of the distribution of giant hogweed in Great Britain. Giant hogweed is one of the worst alien plants in Britain and has rapidly increased its range since 1970, yet we highlight that a further 20% of land area remains susceptible to colonisation by this species. We use the robustness of this case study to discuss the potential for modelling distribution data for other species and at different spatial scales.

New model diagnostics for spatio-temporal systems in epidemiology and ecology

“…Heracleum mantegazzianum (giant hogweed) causes significant problems in Great Britain and has rapidly spread since 1970 [27]. We apply our testing framework to British floristic atlas data which assess the presence of giant hogweed over a square lattice of 10 Â 10 km resolution in 1970, 1987 and 2000.…”

“…It is now standard practice to conduct Bayesian analyses of partially observed epidemics using the process of data augmentation supported by computational techniques such as Markov chain Monte Carlo (MCMC) methods [5,20,27,28]. Given partial data y, these approaches involve simulating from the joint posterior distribution pðu, zjyÞ, where z represents the complete epidemic data as above.…”

Bayesian hierarchical statistical SIRS models

“…Bayesian percolation models have proven popular for modeling spatio-temporal dynamical processes (e.g., Catterall et al, 2012;Gibson et al, 2006) and have been applied to epidemics (e.g., Cook et al, 2007), but they ignore the true process hidden behind the noisy data. More recent Bayesian hierarchical models, which are widely used for mapping non-infectious diseases, aim to capture the true spatial process (e.g., Besag et al, 1991;Carlin and Banerjee, 2002), but their process models and parameter models are not appropriate for epidemics.…”

Modelling the spread of European buckthorn in the Region of Waterloo

“…Grid-based models are commonly used in hybrid models where one model is used to predict the suitability of the habitat in each grid cell while another model is used to predict the likelihood of a propagule arriving at that cell (Smolik et al, 2010;Fennell et al, 2012;Catterall et al, 2012;Cook et al, 2007). Hybrid models have been developed using various methods to model spread.…”

“…Fennel et al (2012) uses a mechanistic individual based model using experimental knowledge to parameterize the model, which predicts the spread from the initial introduction point. Catterall et al (2012) and Cook et al (2007) use a Bayesian model to parameterize a grid-based model, which uses distribution data from multiple time points and suitability factors to model the spread of an invasive plant. Similarly, Smolik et al (2010) used logistic regression to model habitat suitability and combined it with a grid-based model parameterized using numerical optimization based on a time series of distribution data for an invasive plant.…”