Range-size heritability has sparked an intense debate in the literature in the last years, although no clear conclusions have been drawn, partly because of the variability in the methods employed and the quality of the data used [12, 13, 67, 68] (see  for a review). If geographic range sizes are determined by life-history, ecological or physiological characters, it may be expected to find some degree of phylogenetic signal through the cladogenetic process [7, 70, 71]. Evidence of low phylogenetic signal in range size has been reported in a number of previous studies for different taxonomic groups [14, 16, 25, 29, 72–74], the conclusion being that range size is an extremely labile trait. However, as showed by Pigot et al. , low phylogenetic signal cannot be taken as strong evidence for the lability of geographic ranges. In our case, both the randomization test  and the PVR method  showed some positive significant phylogenetic signal for several lineages. This phylogenetic signal was relatively weak when compared with other range properties, but still strong enough to be kept as a relevant factor in the multiple regression models (see below). The low taxonomic level of the studied phylogenies could contribute to the lack of significance in the randomization tests of phylogenetic signal for some of the groups , as well as the low number of species in some of them (computer simulations demonstrate that this test requires approximately 20 species to achieve a statistical power of 80%, ). Nevertheless, the values of the K statistic do not depend on sample size, and it is considered a valid descriptive statistic of the amount of phylogenetic signal even for small data sets . The PVR method has a good performance with small phylogenies , and in consequence our results from this approach could be more reliable.
The geographic location of the species had the strongest phylogenetic signal of all the variables tested. With the question of the heritability of the size of geographic ranges monopolizing all the attention in the literature, the role of phylogenetic constraints on other attributes of species' ranges, such as geographic position, have remained nearly unexplored (but see ). Our results show that, in general, the geographic position of species' ranges display a stronger phylogenetic signal than their size. This is what would be expected under a vicariant mode of speciation in which the ancestral range is split almost randomly (hence partly erasing the phylogenetic signal of range size), but the resulting species maintain the geographic centroid of their ranges through time, so that range movements do not erase completely the geographic signal of speciation. This would justify the use of the present distribution of species to infer speciation processes (e.g., [46, 77]), contrary to the view that rapid changes to species geographic ranges effectively eliminate any relationship between the geography of speciation and contemporary locations of geographic ranges . In the case of water beetles, a review of the direct evidence provided by Quaternary remains also support a general pattern of range stability through the last Glacial cycle, contrary to the extended view of generalized major range shifts due to climatic change .
When biogeographic, phylogenetic and ecological factors were combined to explain range size differences, the northern limit of the geographic range was generally the main determinant of geographic range size. In a number of terrestrial groups range sizes are known to strongly increase with latitude in the Palearctic and Nearctic above 40°-50°N , in agreement with Rapoport's rule (see  for a review). In the Western Palearctic, widespread species tend to have a central and north European distribution, and among the water beetles in these areas there are few, if any, species with restricted distributions . In the same way, there are many examples of water beetle lineages including narrow endemics in which the widespread species have the southern limit of their ranges at the edge of the southern peninsulas.
The strong role of geographic location in determining range size can be grounded in different lines of argument. From an ecological perspective, latitudinal/longitudinal gradients can represent a particular case of the more general relationship between the niche breadth of a species and the size of its geographic range (e.g., [2, 21, 81–83]). Climatic changes and the drastic changes in ecological conditions were specially dramatic in northern latitudes of the Palearctic region, and might have operated as ecological filters , with only those species displaying broad ecological niches (and consequently wide ranges) being able to persist in northern regions or re-colonize northern areas from southern refugia after the glaciations. In the studied lineages, maximum latitude was usually highly correlated with niche breadth (Additional file 1, Table S3), showing that those species reaching more northern latitudes display broader ecological niches. Species with narrow niches would have remained restricted to southern areas, less affected by the climatic changes. This is valid also for longitude, with species reaching the more continental parts of Eurasia being more affected by climatic changes. The absence of fossil remains of southern species of aquatic Coleoptera among the abundant central and northern European Quaternary records  would support this view, as well as the recognition of the Mediterranean peninsulas as an area of endemism, not as a source of postglacial colonisation (e.g., ).
The Western Palearctic has strong ecological constraints in the south and the west (the seas and oceans), which might result in most species having a distribution centre towards the east or the north. The larger range size of the species with a more northern and eastern distribution could thus be the result of a geometric constraint. The species with the largest ranges necessarily include the largest available surfaces, i.e. from central Europe to the east. Any species expanding its range to cover the biogeographical area of the lineages included here will end up with a distribution centroid in the north-east, as species with large distributions approaching the size of a bounded domain are constrained to have their centroid near the centre of the domain . The general negative correlation between minimum latitude and range size (Table 2) is compatible with this geometric effect, showing that widespread species also expand their ranges to the south. But this geometric constraint cannot be the sole explanation for the patterns we found, as this would not explain the phylogenetic signal for both range size and geographical position. The strong positive relationship between maximum latitude and range size shows the asymmetry of the range expansions, with an origin in southern refugia, as also found for European land snails . A more uniform distribution of the ancestral ranges may result in a similar position of the final centroids of the species with expanding ranges, but not in a strong positive relationship between maximum latitude and range size.
Two additional biogeographic factors emerged as highly correlated with range size, the spatial extent and the number of biomes in which species are found. If species can expand their distribution more easily within than across biogeographic boundaries, then species found in biogeographic biomes with a large spatial extent should have larger range sizes than species found in small biomes ([26, 88–90]; see [14, 25] for examples of application in range-size analyses). The number of biomes can be related with niche breadth differences, since some species are restricted to one (or few) biomes due to habitat specificity while others are able to expand easily their distribution across biomes (Additional file 2), although in this case results are confounded by the unavoidable circularity of the relationship between range size and number of biomes. The heterogeneity of biomes is certainly not uniform over the whole continent, with more climatic and ecological variety in the south associated with the main mountain ranges and the influence of the Mediterranean.
Habitat type was also positively correlated with range-size in those lineages with both lotic and lentic species (the only exception was the genus Hydrochus), showing that in the same lineage, and after accounting for possible phylogenetic effects, species inhabiting lentic water bodies display larger distributional ranges than those inhabiting lotic ones, with species inhabiting both types of environments with intermediate range sizes. This is in agreement with previous studies across multiple lineages of freshwater invertebrates, which have shown that lotic species have on average smaller geographical ranges than the lentic species [22, 23]. Although most of species included here are winged, there is no information about the flying capacity across species within each one of the lineages, so direct measures of dispersal ability are not available. The differences in spatial and temporal persistence between lotic and lentic habitats (small lentic water bodies tend to fill with sediment over a time period of decades or centuries, while rivers and streams persist over geologically defined time periods) have been postulated as resulting in consistent differences in dispersal strategies and colonization abilities between species living in both types of aquatic environments (see  for an overview), providing a surrogate measure of dispersal ability. Since colonization rates depend not only on dispersal abilities, but also on the geographic configuration of habitats, a potential confounding factor could be the differential distribution of suitable habitat between lotic and lentic environments (e.g., a contrasting degree of spatial clustering or a spatial correlation of habitat availability with latitude). Nevertheless, different recent studies have consistently provided evidence against differences in habitat availability, lending further support to the hypothesis that lentic species have a higher propensity for dispersal than lotic species [91–93]. Although dispersal abilities are among the more commonly cited potential determinants of a species' range (see e.g., ), this relation has rarely been assessed correcting for phylogeny.
We did not find evidence to support a clear pattern of range size change over time in water beetle lineages. The relationship between age vs. range-size plots suggested that species' time since divergence is positively correlated with geographic range size, in agreement with the "range and area" model , but the values of the slopes of the lines that best predicted range-size from species age were for most groups not significantly different from zero. Thus, our results are compatible with a "stasis"  or an idiosyncratic model, were there is no reason to expect a directional change in geographic range size through time. In any case, the amount of variance in geographic range size explained by phylogenetic age was generally low, as shown by r
2 values. The lack of a general pattern of the changes in geographic range size over evolutionary time is a common result across a wide range of clades (e.g., [15, 29, 31, 95]. The variability of the type and quality of data used and analyses performed has been viewed as a possible explanation for this lack of consistency [29, 95], but our results, using different lineages and a common methodology and dataset, proved to be equally variable and clade-specific, pointing to a true lack of relationship between age and area, despite the uncertainties in the sampling and the delimitation of the ranges (see below).
Other factors not considered in this study may be of relevance in determining geographic range sizes, such as thermal tolerance, body size, population abundance or colonization and extinction dynamics . Similarly, we are aware that our analyses could be weakened by incomplete taxon sampling in some groups and uncertainties in the estimated geographic range sizes. Uncertainties associated to phylogenies are another possible source of error, as missing or extinct taxa would result in the overestimation of the phylogenetic age of the related species. Despite these obvious limitations, the consistency of the results and the high percentage of variance explained by the factors included (between ca. 60 and 98%, Table 5) allows to draw firm conclusions applicable to a wide range of phylogenetically independent groups of Coleoptera.