Using survival regression to study patterns of expansion of invasive species: will the common waxbill expand with global warming?

Different approaches can be used to model the spread of invasive species. Here we demonstrate the use of survival regression, an approach that can be used to study a variety of events, not just death, to model the time to colonization. The advantage of survival regression to study colonisation of new areas is that information on those areas that have not been invaded by the end of a study can be included in the analysis, thus potentially increasing the accuracy of parameter estimation. We use proportional hazards regression (PHR; a type of survival regression) to model the spread of the common waxbill Estrilda astrild in Portugal. The species invaded Portugal in two peaks of invasion between 1964 and 1999. We built a PHR model with the information available up to the first invasion peak, then used this model to predict the pattern of invasion in the second peak. PHR had useful forecasting capabilities: areas that were actually colonised by 1999 had significantly higher hazards of colonization based on information from the first wave of invasion than areas that were not colonised. We then built a final model of expansion of the common waxbill that combined all available data up to 1999. Among climate variables, the most important predictor of colonization was temperature, followed by relative humidity. We used this model to estimate the invasion potential of the species under climate change scenarios, observing that an increase of 1°C in mean annual temperature increased the risk of a new invasion by 47%. Our analyses suggest that survival regression may be a useful tool for studying the geographical spread of invasive species. However, PHR was conceived as a descriptive technique rather than as a predictive tool, and thus further research is needed to empirically test the predictive capabilities of PHR.