Speeding up the simulation of population spread models

A unifying theory for two-dimensional spatial redistribution kernels with applications in population spread modelling

When building models to explain the dispersal patterns of organisms, ecologists often use an isotropic redistribution kernel to represent the distribution of movement distances based on phenomenological observations or biological considerations of the underlying physical movement mechanism. The Gaussian, two-dimensional (2D) Laplace and Bessel kernels are common choices for 2D space. All three are special (or limiting) cases of a kernel family, the Whittle-Matérn-Yasuda (WMY), first derived by Yasuda from an assumption of 2D Fickian diffusion with gamma-distributed settling times. We provide a novel derivation of this kernel family, using the simpler assumption of constant settling hazard, by means of a non-Fickian 2D diffusion equation representing movements through heterogeneous 2D media having a fractal structure. Our derivation reveals connections among a number of established redistribution kernels, unifying them under a single, flexible modelling framework. We demonstrate improvements in predictive performance in an established model for the spread of the mountain pine beetle upon replacing the Gaussian kernel by the Whittle-Matérn-Yasuda, and report similar results for a novel approximation, the product-Whittle-Matérn-Yasuda, that substantially speeds computations in applications to large datasets.

Integrating an individual-based model with approximate Bayesian computation to predict the invasion of a freshwater fish provides insights into dispersal and range expansion dynamics

Short-distance dispersal enables introduced alien species to colonise and invade local habitats following their initial introduction, but is often poorly understood for many freshwater taxa. Knowledge gaps in range expansion of alien species can be overcome using predictive approaches such as individual based models (IBMs), especially if predictions can be improved through fitting to empirical data, but this can be challenging for models having multiple parameters. We therefore estimated the parameters of a model implemented in the RangeShifter IBM platform by approximate Bayesian computation (ABC) in order to predict the further invasion of a lowland river (Great Ouse, England) by a small-bodied invasive fish (bitterling Rhodeus sericeus). Prior estimates for parameters were obtained from the literature and expert opinion. Model fitting was conducted using a time-series (1983 to 2018) of sampling data at fixed locations and revealed that for 5 of 11 model parameters, the posterior distributions differed markedly from prior assumptions. In particular, sub-adult maximum emigration probability was substantially higher in the posteriors than priors. Simulations of bitterling range expansion predicted that following detection in 1984, their early expansion involved a relatively high population growth rate that stabilised after 5 years. The pattern of bitterling patch occupancy was sigmoidal, with 20% of the catchment occupied after 20 years, increasing to 80% after 30 years. Predictions were then for 95% occupancy after 69 years. The development of this IBM thus successfully simulated the range expansion dynamics of this small-bodied invasive fish, with ABC improving the simulation precision. This combined methodology also highlighted that sub-adult dispersal was more likely to contribute to the rapid colonisation rate than expert opinion suggested. These results emphasise the importance of time-series data for refining IBM parameters generally and increasing our understanding of dispersal behaviour and range expansion dynamics specifically.