Abstract We use data from the French national butterfly atlas to compare the potential of direct geographical and neighbourhood models to account for numbers of species and incidence of species in French departements. Direct geographical models use data on latitude, longitude and altitude, whereas neighbourhood models use information from adjacent areas. Both geographical models and neighbourhood models account for a large proportion of the variance in species richness (68–78%). However, neighbourhood models are more successful than models based solely on simple geographical variables. A large number of individual species distributions are accounted for by logistic and autologistic regression models (222 of 246 species, 90.2%). The autologistic models incorporate information on neighbouring areas. The exceptions are rare species, five of six of which occur in a single administrative unit only (2.4%), or virtually ubiquitous species found in >90% of units (7.3%). Autologistic models dominate logistic models in accounting for species incidences using stepwise logit regressions, neighbourhood variables appearing in 64.5% of successful species models (absent in 22.8%) and then always entering first. A simple neighbourhood (distance-unweighted) measure (C2) dominates more models (89 of 246 species, 36.2%) than a distance-weighted neighbourhood measure (C1; 77 of 246 species, 31.3%). The models are here demonstrated to be potentially valuable for identifying under-recording and losses from regional extinction and for filling gaps in recording. The findings reveal substantial, apparent, losses of species in western and northern France as well as substantial discrepancies (differences) in numbers of species, for some administrative units (departements) and for both post-1970 and total records, compared with numbers predicted to occur. We use two distinct approaches on total species and individual species to provide comparative estimates of the numbers of species expected within spatial units and we present the number of additional units in which species are expected to occur. The probabilities for these species in French departements are available on Web site: http://www.brookes.ac.uk/schools/bms/research/data/ecology/butterfly.html .

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