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

Abstract

1. Improving the understanding, 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. This is especially the case in the field of invasion biology and 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 individual-based methods can valuably be used in conjunction. 3. We use a mechanistic wind dispersal model to generate age-specific dispersal kernels for the invasive shrub, Rhododendron ponticum. To demonstrate the utility of employing both modelling approaches, this information along with demographic parameters is incorporated into an IBMand an analytical, integrodifference model. From both models, the equilibrium rate of spread is calculated. 4. Estimates of wavespeeds were similar for the two models, although slower rates of spread were consistently projected by the IBM. Further, our results demonstrate the 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 wavespeed, which can provide helpful information for management. We gain qualitatively similar results using the IBMbut obtaining the results is time-consuming and, because the model is stochastic, they are noisy and harder to interpret. We argue that analytically derived transient elasticity analyses are needed for the many cases where success of control is measured on a relatively short time horizon. 6. To demonstrate the flexibility of the IBMapproach, we run it on a real landscape comprising different habitat types. The comparison of two different control scenarios is an example of the utility of this approach for more tactical applications. 7. As a general conclusion of the study, we emphasise that analytical and individual-based approaches offer different, but complementary, advantages and suggest how their joint use can facilitate the improvement in biodiversity management at a range of spatial scales.