Low predictive power of mid-domain effect to explain geographic species richness patterns in Palearctic songbirds

In the study of diversity patterns, the Mid-domain effect (MDE), which explains gradients in diversity solely on the basis of geometric constraints, has emerged as a null-model against which other hypotheses can be tested. The effectiveness, measured by its predictive power, of these MDE models appears to depend on the size of the study area and the range-sizes of the taxa consid-ered. Here we test the predictive power of MDE on the species richness patterns of birds and assess its effectiveness for a variety of species range sizes. We digitised distribution maps of 889 species of songbird endemic to the Palearctic, and analysed the emergent biogeographic patterns with WORLDMAP software. MDE had a predictive power of 20% when all songbirds were included. Major hotspots were located south of the area where MDE predicted the highest species-richness, and some of the observed coldspots were in the centre of the Palearctic, contra-dicting the predictions of the MDE. MDE had little explanatory power (3-19%) for all but the largest range sizes, whereas MDE performed equal or better for the large-ranged species (20-34%) compared to the overall model. Overall MDE did not accurate explain species-richness patterns in Palearctic songbirds. Subsets of larger-range species did not always have a larger predictive power than smaller-range species or the overall model. Despite their predictive MDE models can have a role to in explaining biogeographic patterns but other variables

As the most prominent representative of the fi fth category above, the mid-domain effect (MDE) provides explanations of gradients in species diversity based solely on geometric constraint on species ranges, without the incorporation of underlying biological mechanisms, and thus can serve as a null-model against which other hypotheses can be tested. Under the MDE model, a mid-domain peak in richness is generated in the centre of the domain purely by chance, as this is the area where there is an increasing overlap in species ranges. The initial models of the mid-domain effect were constructed in uni-dimensional space and in the context of a latitudinal gradient in diversity (and associated Rapoport effect, i.e., a decrease in species range sizes towards the equator). Bokma and Monk-konen (2000) extended this analytical model to cover the distribution of species by taking account of both latitudinal and longitudinal dimensions. As such, these bi-dimensional models have been tested with different taxa and in different continental and inter-continental settings with varying degrees of success (reviewed by Colwell et al., 2004).
MDE model predictions depend critically on the range size frequency distribution of individual species within the domain. In general, the range overlap produces a pattern of increasing species richness from the boundaries toward the centre of the domain, and if the ratio of maximum attainable range size to domain size increases the MDE increases and tends to converge towards a parabolic pattern (Colwell and Hurtt, 1994;Lees et al., 1999;Zapata et al., 2003). Large-ranged species necessarily overlap in the middle of the domain whereas small-ranged species are unobstructed by geometric constraints and are free to occur virtually anywhere within the domain . Thus, MDE are hypothesised to explain a larger proportion of the observed variation for large-ranged species than small-ranged species. Hence, when large-ranged species are excluded from analysis, it is hypothesised that the MDE models will be a weak predictor for the observed pattern of species richness in the remaining (small-ranged) species (Colwell and Lees, 2000).
In birds, theoretical and empirical evidence for MDE has been obtained for a variety of taxa on different continents (Jetz and Rahbek, 2001;Hawkins and Diniz-Filho 2002;Diniz-Filho et al., 2003;Colwell et al., 2004). These analyses have shown that, at least for birds, the predictive power of bi-dimensional MDE models explains less than a quarter of the observed variation, whereas models that invoke environmental factors typically explain over three-quarters of the observed variation (Balmford et al., 2001;Boone and Krohn, 2000;Hawkins and Diniz-Filho, 2002).
Here we test a bi-dimensional MDE model on the geographic pattern of species richness of songbirds (Passeriformes) in the Palearctic Region. Its large size, heterogeneous environment and the large number of songbirds occurring in the Palearctic Region make it an interesting test-case to assess the predictive power of the MDE models. MDE models are predicted to perform best in homogenous, single-biome domains in which a substantial proportion of the species have ranges more than half the size of the domain (Lees et al., 1999;Colwell et al., 2004Colwell et al., , 2005. The Palearctic Region is arguably the most climatically and topographically diverse heterogeneous landmass on the planet, with relatively few birds having large distribution ranges, making it an excellent case for testing the performance of MDE models. Furthermore, we test the effect of species-range sizes on how well the MDE performs using two different approaches.

The data set
The full database consists of breeding distribution maps for all 1108 traditional biological or isolation species (3032 taxa in total, i.e. species and subspecies) of songbirds in the Palearctic Region (Europe, N. Africa and Asia: 30º-170ºW, 86º-18ºN), which have been digitized using WORLDMAP software (Williams, 2000), identical to that in Aliabadian et al. (2005) and Roselaar et al. (2007). The geographic distributions were plotted over a one degree longitude equal area map (grid-cell area: 4062 km 2 ) of the Palearctic Region. The distribution data were compiled from standard reference works, supplemented by data obtained from numerous zoological collections (see Roselaar et al., 2007). Nomenclature and taxonomy follows Roselaar and Shirihai (in press).
The empirical diversity gradient was generated by recording whenever a grid cell was within the reported range of a species. Since the logic of the MDE hypothesis assumes that species ranges are found entirely within the domain we limited our analysis to those taxa whose breeding ranges are confi ned to the Palearctic Region, the so-called Palearctic endemics. This data set contains 889 biological species comprising 680,586 presence records across 14,714 grid-cells.
To explore the role of range size frequency distribution on geometric constraints we applied the following two approaches that have been used previously, i.e. by Diniz-Filho and colleagues and by Jetz and Rahbek. (1) Hawkins and Diniz-Filho (2002) and Rangel and Diniz-Filho (2003) classifi ed species ranges into three classes based on the percentage of all sample points occupied by individual species, i.e. small (<25% of all sample points), medium (26-50%), and large (>50%). Following this approach we classifi ed the 680,586 species presence records of breeding songbirds across 14,714 grid cells into small-range species (n = 846), medium-range species (n = 36), and largerange species (n = 7).

Null model
The predictions of the mid-domain effect have been tested by a variety of null models, including fully stochastic distribution and both range and midpoint-constrained models . To avoid an artifi cial reduction in dimensionality, which imposes a simplifi cation of the patterns and a concomitant loss of information (Bokma et al., 2001), we tested observed pattern of species richness with a bi-dimensional model. The species richness for each point of the grid cells (P) is estimated by a pure stochastic process, and is a function of its position relative to boundaries across northern (p), southern (q), western (r), and eastern (t) end points of a domain. The species richness expected at P is then given by 4pqstS, where S is the total species richness in the domain (Bokma et al., 2001). Under this model some areas like peninsular regions, which do not contact the main body of the landmass, will show a large expected diversity because the value of p, q, r, and t are calculated from each point to the immediate boundaries and not the entire landmass. To reduce the peninsular diversity peaks, we followed the 'area corrected' version of Willing and Lyons (1998), taking the absolute distance of a point to the Palearctic border into account (Hawkins and Diniz-Filho, 2002). Then the p, q, r, and t proportions in the null model were estimated for each point of the grid based on the maximum N-S and E-W axes.

Statistical analysis
Biogeographical data, such as species richness, which are derived from geographical range maps, are not independent and tend to be strongly spatially auto-correlated Legendre et al., 2002). As such there is a serious overestimate of the degrees of freedom and therefore the signifi cance levels of the regression coeffi cient are raised upward, in essence making signifi cance tests too liberal . As to preclude this we restrict our comparisons to coeffi cient of determination (R 2 ) of linear regression (r s ), without presenting signifi cance levels between observed and expected species richness at each grid cells of the Palearctic map (cf Jetz and Rahbek, 2001;Williams et al., 2006). Following Aliabadian et al. (2005) values in the null model were only calculated for those grid cells that were actually occupied by one or more species in the real data set; this approach is conservative because any MDE prediction of the presence of species in other grid cells would lower the fi t of the model.

Results
Species richness patterns of all breeding songbirds recorded within the boundaries of the Palearctic (n = 1108 species) and species endemic to the Palearctic (n = 889) are highly correlated (r s = 91%). Since most of the extra-limital species occur in the Ethiopian and Oriental Regions, the Palearctic endemics dataset de-emphasizes the hotspot in Southeast Asia. In both analyses, major hotspots are located in the area from the Caspian Sea Basin extending northeastwards to Hindu-Kush, Pamir, Tien-Shan, and Altai, as well as in central Siberia. Smaller hotspots occur south of the Caspian Sea, curving northwestwards towards the Caucasus and the mountains of southern and eastern Turkey. In Western Europe, a hotspot occurs on the Balkan Peninsula ( Fig. 1a; see also Roselaar et al., 2007). The observed pattern of songbirds' richness clearly varied from that predicted by geometric constraints (Fig. 1b), which placed the highest species richness in the centre of the Palearctic, corresponding to the Gobi desert, Altai and Tien-Shan systems, with a gradual decrease when departing from the midpoint of the Pale-arctic. For all Palearctic endemics MDE explains 20.0% of variation in species richness.
The predictive power of the MDE decreases with smaller range sizes, ranging from 20.0% for largerange species to 18.9 and 9.1% for medium-range and small-range species, respectively (Table 1; Figure 2a, Fig. 2. Species richness pattern of the Palearctic endemic songbirds. a) small-range species (n=846, 67.5% records); b) medium-range species (n=36, 24.2% records); c) large-range species (n=7, 8.4% records); d) fi rst quartile range species (n=223, 1.1% records); e) second quartile range species (n=222, 4.8% records); f) third quartile range species (n=222, 14.3% records); g) fourth quartile range species (n=222, 79.86% records). b, c). The observed pattern of species richness for all Palearctic endemics is most strongly correlated with that of the small-range species, and less so for medium-range and large-range species (Table 1). Hotspot patterns for the small-range and medium-range species differ qualitatively from the large-range species, with an increasing emphasis on northern and western regions.
Partitioning the songbirds into range size quartiles, it is clear that the pattern of species richness for the fourth-quartile species (i.e. those with the largest ranges) (Fig. 2g) differ qualitatively from that of the fi rst-, second-and third-quartile species (Figs 2d, e, f). For the latter species, hotspots are located mainly in Southeast Asia and gradually move northwestwards from the fi rst-, to the third-quartile species. The fourthquartile species, in contrast, do not show a hotspot in Southeast Asia but only in central Siberia and Europe. The predictive power of MDE is low for the fi rst-, second-and third-quartile range species, whereas MDE explains about a third of the observed variation in the fourth-quartile species (Table 1). The observed pattern of species richness for all Palearctic endemics is weakly correlated with that of the fi rst-quartile species, and increases progressively with increasing range-sizes (Table 1).

Discussion
Under a geographic constraint model such as MDE, species richness is expected to be highest in the central Palearctic with a gradual decrease towards the continental edges. Our data of the songbirds, however, shows that hotspots of species richness are not only located in the central parts of the Palearctic but also in southwestern Asia, southern Europe, and especially Southeast Asia. Within these regions especially mountain areas contain high numbers of species, with hotspots clearly following the main mountain ranges (cf. Roselaar et al., 2007;Aliabadian et al., 2005). Moreover, some of the coldspots observed in the songbird distribution are in the centre of the Palearctic and as such contradict the predictions from the MDE model. Overall, the MDE had a low explanatory power of around 20% for almost 900 species of songbirds endemic to the Palearctic Region.
Geometric constraints are expected to affect the distribution of large-ranged species more than they affect small-ranged species as species with small ranges are free to occur (or not to occur) virtually anywhere within the domain, whereas range centres of large-ranged species must cluster near mid-domain . In other words, the strength of the MDE decreases and tends to converge towards a uniform pattern as the ratio of maximum attainable range size to domain size decreases (Zapata et al., 2003).
We assessed the effects of species range sizes on the MDE by creating different range-size classes, one based on number of occupied grid-cells and one based on range-size quartiles. In the fi rst approach, smallranged species show a species-richness pattern similar to that of all Palearctic songbirds but the explanatory power of MDE was halved. The medium-and large ranged species made up only a small part of the overall species pool, and although the explanatory power of MDE was better than that of the smallranged species, unlike Hawkins and Diniz-Filho's analysis (2002), it did not perform better than when all endemic Palearctic songbirds were included. Following a second approach, based on range-size quartiles, similar to Jetz and Rahbek (2002) we found that although MDE had little explanatory power for the fi rst-to third-quartile species, MDE performed well for the fourth-quartile range sizes. In fact, it clearly outperformed the all endemic Palearctic songbirds dataset, and confi rms the notion that MDE performs best for species with large ranges (Colwell and Hurtt, Subdivision Species ( Hawkins and Diniz-Filho (2002) and Rahbek (2001), respectively. 1994;Lees et al., 1999). As such the two approaches led to different results suggesting that how large or small range species are defi ned is an important factor when testing the MDE. As noted by Lees et al. (1999) and Colwell et al. (2004Colwell et al. ( , 2005, MDE models are predicted to perform best in homogenous, single-biome domains in which a substantial proportion of the species have ranges more than half the size of the domain, and this is clearly not the case with songbirds in the Palearctic (with many species with narrow ranges and geographically great climatic and topographic variability). Much attention has been paid to the distribution patterns of restricted range species or centres of endemism, as these are important from a conservation perspective (e.g., Stattersfi eld et al., 1998;Mittermeier et al., 1999) or from an evolutionary and biogeographical perspective (Jetz et al., 2004;Orme et al., 2005). What defi nes a restricted range species differs between studies, but in general it refers to species that have a distribution or breeding range below a certain threshold, ranging from 50,000 km 2 (Stattersfi eld et al., 1998) to c. 960,000 km 2 (Dillon and Fjeldså, 2005). For Palearctic songbirds, the distribution pattern of fi rst-quartile range species (with a breeding range of <325,000 km 2 ) can thus be considered the distribution pattern of centres of endemism.
In interpreting patterns of species distributions these centres of endemism have repeatedly been regarded as areas where the overall species richness is higher than elsewhere, regardless of the particular restricted range species within them (Jetz et al., 2004). Jetz et al., (2004) found supportive evidence for the hypothesis that centres of endemism indeed do contain an unexpectedly greater number of species than other regions in Sub-Saharan African birds and found that environmental factors such as productivity are a better predictor for the observed patterns than MDE. We showed that MDE is a poor predictor for patterns of restricted range species (Table 1). In the Palearctic, all restricted range species hotspots are also hotspots of overall species richness (compare Figs 2d with 1a). Subtracting the restricted range species from the overall species pool does not alter the pattern of species richness (Fig. 3), confi rming the observation that centres of endemism indeed do contain a larger than average number of species.
Our analysis revealed a distinctly uneven geographical distribution of songbirds in the Palearctic region, irrespective of the range size classes included or excluded. This may be related to its large climatic and topographic heterogeneity. In general MDE failed to explain a signifi cant proportion of the observed variation, although for selected subsets of large-range species the explanatory power was larger than in other subsets. However, not even in the best subset MDE did not explain more than 35% of the variance. Hawkins and Diniz-Filho (2002) and Zapata et al. (2003) concluded that (1) there were both theoretical and empirical arguments undermining the validity of the hypothesis behind the MDE, (2) MDE models had failed to predict the observed patterns of species richness in a variety of taxa, and (3) that the practical usefulness of MDE models were limited. Despite these conclusions, we agree with Colwell et al., (2005), that process-based models (e.g., Connolly, 2005;Davies et al., 2005;Rangel and Diniz-Filho, 2005) that mechanistically integrate geometric constraints with environmental gradients and/or evolutionary processes in bounded domains offer a way forward from the correlative approaches of both classic MDE analyses and conventional, regression-based analyses of richness in relation to environmental variables.