A model for range expansion of an introduced species: the common waxbill Estrilda astrild in Portugal

The common waxbill Estrilda astrild was first introduced to Portugal from Africa in 1964, and has spread across much of the country and into Spain. We modelled the expansion of the common waxbill on a 20 × 20 km UTM grid in 4-year periods from 1964 to 1999. The time variation of the square root of the occupied area shows that this expansion process is stabilizing in Portugal, and reasons for this are discussed. Several methods used to model biological expan- sions are not appropriate for the present case, because little quantitative data are available on the species ecology and because this expansion has been spatially heterogeneous. Instead, colon- ization on a grid was modelled as a function of several biophysical and spatio-temporal variables through the fitting of a multivariate autologistic equation. This approach allows examination of the underlying factors affecting the colonization process. In the case of the common waxbill it was associated positively with its occurrence in adjacent cells, and affected negatively by altitude and higher levels of solar radiation.