Improving prediction and management of range expansions by combining analytical and individual-based modelling approaches

Summary
1. Improving understanding and the prediction and management of range expansions is a key challenge for ecology. Over recent years there has been a rapid increase in modelling effort focussed on range expansions and a shift from predominantly theoretical developments towards application especially in the field of invasion biology, but also in relation to reintroductions and species’ responses to climate change.
2. While earlier models were exclusively analytical, individual-based models (IBMs) are now increasingly widely used. We argue that, instead of being viewed as competing methodologies, analytical and simulation methods can valuably be used in conjunction.
3. In order to demonstrate the utility of employing both modelling approaches, we first use a mechanistic wind dispersal model to generate age-specific dispersal kernels for the invasive shrub, Rhododendron ponticum. This information along with demographic parameters is incorporated both within an IBM and an analytical, integrodifference model.
4. Estimates of equilibrium wavespeeds are similar for the two models, although slower rates of spread are consistently projected by the IBM. Comparing results provides an important cross-validation. Importantly our results demonstrate the equilibrium wavespeed to be sensitive to the characterisation of age structure in the model; when few age classes are used much higher rates of spread are projected.
5. The analytical model is extremely efficient at providing elasticity analysis of the equilibrium wavespeed and this information can help inform management. We gain qualitatively similar results using the IBM but obtaining the results is time consuming and, because the model is stochastic, they are noisy and harder to interpret. We argue that such elasticity analyses are needed for the many cases where success of control is measured on a relatively short time horizon.
6. We run the IBM on a real landscape (represented using GIS) comprising different habitat types, and compare two different control scenarios. This highlights the flexibility of the IBM approach and clearly demonstrates the utility of this approach for more tactical applications.
7. We emphasise that analytical and individual-based approaches offer different, but complementary, advantages and suggest how their joint use can facilitate the improvement of biodiversity management at a range of spatial scales.