An integrated, spatio-temporal modelling framework for analysing biological invasions

Evaluating the predictive performance of presence-absence models: Why can the same model appear excellent or poor?

When comparing multiple models of species distribution, models yielding higher predictive performance are clearly to be favored. A more difficult question is how to decide whether even the best model is "good enough". Here, we clarify key choices and metrics related to evaluating the predictive performance of presence-absence models. We use a hierarchical case study to evaluate how four metrics of predictive performance (AUC, Tjur's R 2, max-Kappa, and max-TSS) relate to each other, the random and fixed effects parts of the model, the spatial scale at which predictive performance is measured, and the cross-validation strategy chosen. We demonstrate that the very same metric can achieve different values for the very same model, even when similar cross-validation strategies are followed, depending on the spatial scale at which predictive performance is measured. Among metrics, Tjur's R 2 and max-Kappa generally increase with species' prevalence, whereas AUC and max-TSS are largely independent of prevalence. Thus, Tjur's R 2 and max-Kappa often reach lower values when measured at the smallest scales considered in the study, while AUC and max-TSS reaching similar values across the different spatial levels included in the study. However, they provide complementary insights on predictive performance. The very same model may appear excellent or poor not only due to the applied metric, but also how predictive performance is exactly calculated, calling for great caution on the interpretation of predictive performance. The most comprehensive evaluation of predictive performance can be obtained by evaluating predictive performance through the combination of measures providing complementary insights. Instead of following simple rules of thumb or focusing on absolute values, we recommend comparing the achieved predictive performance to the researcher's own a priori expectations on how easy it is to make predictions related to the same question that the model is used for.

Climate and habitat configuration limit range expansion and patterns of dispersal in a non-native lizard

Invasive species are one of the main causes of biodiversity loss worldwide. As introduced, populations increase in abundance and geographical range, so does the potential for negative impacts on native communities. As such, there is a need to better understand the processes driving range expansion as species become established in recipient landscapes. Through an investigation into capacity for population growth and range expansion of introduced populations of a non-native lizard (Podarcis muralis), we aimed to demonstrate how multi-scale factors influence spatial spread, population growth, and invasion potential in introduced species. We collated location records of P. muralis presence in England, UK through data collected from field surveys and a citizen science campaign. We used these data as input for presence-background models to predict areas of climate suitability at a national-scale (5 km resolution), and fine-scale habitat suitability at the local scale (2 m resolution). We then integrated local models into an individual-based modeling platform to simulate population dynamics and forecast range expansion for 10 populations in heterogeneous landscapes. National-scale models indicated climate suitability has restricted the species to the southern parts of the UK, primarily by a latitudinal cline in overwintering conditions. Patterns of population growth and range expansion were related to differences in local landscape configuration and heterogeneity. Growth curves suggest populations could be in the early stages of exponential growth. However, annual rates of range expansion are predicted to be low (5-16 m). We conclude that extensive nationwide range expansion through secondary introduction is likely to be restricted by currently unsuitable climate beyond southern regions of the UK. However, exponential growth of local populations in habitats providing transport pathways is likely to increase opportunities for regional expansion. The broad habitat niche of P. muralis, coupled with configuration of habitat patches in the landscape, allows populations to increase locally with minimal dispersal.

The Epidemiological Framework for Biological Invasions (EFBI): an interdisciplinary foundation for the assessment of biosecurity threats

Emerging microparasite (e.g. viruses, bacteria, protozoa and fungi) epidemics and the introduction of non-native pests and weeds are major biosecurity threats worldwide. The likelihood of these threats is often estimated from probabilities of their entry, establishment, spread and ease of prevention. If ecosystems are considered equivalent to hosts, then compartment disease models should provide a useful framework for understanding the processes that underpin non-native species invasions. To enable greater cross-fertilisation between these two disciplines, the Epidemiological Framework for Biological Invasions (EFBI) is developed that classifies ecosystems in relation to their invasion status: Susceptible, Exposed, Infectious and Resistant. These states are linked by transitions relating to transmission, latency and recovery. This viewpoint differs markedly from the species-centric approaches often applied to non-native species. It allows generalisations from epidemiology, such as the force of infection, the basic reproductive ratio R0, super-spreaders, herd immunity, cordon sanitaire and ring vaccination, to be discussed in the novel context of non-native species and helps identify important gaps in the study of biological invasions. The EFBI approach highlights several limitations inherent in current approaches to the study of biological invasions including: (i) the variance in non-native abundance across ecosystems is rarely reported; (ii) field data rarely (if ever) distinguish source from sink ecosystems; (iii) estimates of the susceptibility of ecosystems to invasion seldom account for differences in exposure to non-native species; and (iv) assessments of ecosystem susceptibility often confuse the processes that underpin patterns of spread within -and between- ecosystems. Using the invasion of lakes as a model, the EFBI approach is shown to present a new biosecurity perspective that takes account of ecosystem status and complements demographic models to deliver clearer insights into the dynamics of biological invasions at the landscape scale. It will help to identify whether management of the susceptibility of ecosystems, of the number of vectors, or of the diversity of pathways (for movement between ecosystems) is the best way of limiting or reversing the population growth of a non-native species. The framework can be adapted to incorporate increasing levels of complexity and realism and to provide insights into how to monitor, map and manage biological invasions more effectively.