Latitudinal gradients in diversity: real patterns and random models

Mid-domain models have been argued lo provide a default explanation for the best known spatial pattern in biodiversity, namely the latitudinal gradient in species richness. These models assume no environmental gradients, but merely a random latitudinal association between the size and placement of the geographic ranges of species. A mid-domain peak in richness is generated because when the latitudinal extents of species in a given taxonomic group are bounded to north and south, perhaps by a physical constraint such as a continental edge or perhaps by a climatic constraint such as a critical temperature or precipitation threshold, then the number of ways in which ranges can be distributed changes systematically between the bounds. In addition, such models make predictions about latitudinal variation in the latitudinal extents of the distributions of species, and in beta diversity (the spatial turnover in species identities). Here we test how well five mid-domain models predict observed latitudinal patterns of species richness, latitudinal extent and beta diversity in two groups of birds, parrots and woodpeckers, across the New World. Whilst both groups exhibit clear gradients in richness and beta diversity and the general trend in species richness is acceptably predicted (but not accurately, unless substantial empirical information is assumed), the fit of these models is uniformly poor for beta diversity and latitudinal range extent. This suggests either that, at least for these data, as presently formulated mid-domain models are too simplistic, or that in practice the mid-domain effect is not significant in determining geographical variation in diversity.     

Spatial distributions of European Tenebrionidae point to multiple postglacial colonization trajectories

Many studies have found that species richness in the Western Palaearctic follows a latitudinal trend, yet the importance of geographical and ecological factors in shaping species ranges remains obscure. In this article, we present geographical patterns of darkling beetles (Tenebrionidae), a species‐rich group of arthropods. We relate the spatial distributions of species, instead of simply species richness, to spatial and climatic gradients, and test the effects of area (by species–area relationships), latitude (by various climatic gradients) and environmental diversity (by elevation) using simultaneous autoregressive models to identify major correlates of species richness. We then use nestedness and co‐occurrence analyses to identify glacial refugial centres and postglacial dispersal trajectories responsible for current species ranges. Our results indicate the presence of two refugial centres (in the Iberian and Balkan peninsulas) that appear to have been particularly important in shaping extant tenebrionid ranges. Northern countries were selectively colonized by more tolerant and, possibly, more mobile species, which survived in southern refugia during the Pleistocene glacial maxima, whereas the low dispersal capabilities of many species that evolved in these southern isolated areas prevented their spread northwards. High levels of endemism recorded in Spain and Sardinia suggest that the faunas of these regions originated during the Tertiary period and have remained substantially isolated. © 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2012, 105 , 318–329.     

Genes on the edge: A framework to detect genetic diversity imperiled by climate change

Ongoing global warming is disrupting several ecological and evolutionary processes, spanning different levels of biological organization. Species are expected to shift their ranges as a response to climate change, with relevant implications to peripheral populations at the trailing and leading edges. Several studies have analyzed the exposure of species to climate change but few have explored exposure at the intraspecific level. We introduce a framework to forecast exposure to climate change at the intraspecific level. We build on existing methods by combining correlative species distribution models, a model of species range dynamics, and a model of phylogeographic interpolation. We demonstrate the framework by applying it to 20 Iberian amphibian and reptile species. Our aims were to: (a) identify which species and intraspecific lineages will be most exposed to future climate change; (b) test if nucleotide diversity at the edges of species ranges are significantly higher or lower than on the overall range; and (c) analyze if areas of higher species gain, loss, and turnover coincide with those predicted for lineages richness and nucleotide diversity. We found that about 80% of the studied species are predicted to contract their range. Within each species, some lineages were predicted to contract their range, while others were predicted to maintain or expand it. Therefore, estimating the impacts of climate change at the species level only can underestimate losses at the intraspecific level. Some species had significant high amount of nucleotide at the trailing or leading edge, or both, but we did not find a consistent pattern across species. Spatial patterns of species richness, gain, loss, and turnover were fairly concurrent with lineages richness and nucleotide diversity. Our results support the need for increased attention to intraspecific diversity regarding monitoring and conservation strategies under climate change.     

The mid-domain effect in ectomycorrhizal fungi: range overlap along an elevation gradient on Mount Fuji,Japan

Mid-domain effect (MDE) models predict that the random placement of species'' ranges within a bounded geographical area leads to increased range overlap and species richness in the center of the bounded area. These models are frequently applied to study species-richness patterns of macroorganisms, but the MDE in relation to microorganisms is poorly understood. In this study, we examined the characteristics of the MDE in richness patterns of ectomycorrhizal (EM) fungi, an ecologically important group of soil symbionts. We conducted intensive soil sampling to investigate overlap among species ranges and the applicability of the MDE to EM fungi in four temperate forest stands along an elevation gradient on Mount Fuji, Japan. Molecular analyses using direct sequencing revealed 302 EM fungal species. Of 73 EM fungal species found in multiple stands, 72 inhabited a continuous range along the elevation gradient. The maximum overlap in species range and the highest species richness occurred at elevations in the middle of the gradient. The observed richness pattern also fit within the 95% confidence interval of the mid-domain null model, supporting the role of the MDE in EM fungal richness. Deviation in observed richness from the mean of the mid-domain null estimation was negatively correlated with some environmental factors, including precipitation and soil C/N, indicating that unexplained richness patterns could be driven by these environmental factors. Our results clearly support the existence of microbial species'' ranges along environmental gradients and the potential applicability of the MDE to better understand microbial diversity patterns.     

Determinants of tapeworm species richness in elasmobranch fishes: untangling environmental and phylogenetic influences

Parasite species richness is a fundamental characteristic of host species and varies substantially among host communities. Hypotheses aiming to explain observed patterns of richness are numerous, and none is universal. In this study, we use tapeworm parasites of elasmobranch fishes to examine the phylogenetic and environmental influences on the variation in species richness for this specific system. Tapeworms are the most diverse group of helminths to infect elasmobranchs. Elasmobranchs are cosmopolitan in distribution and their tapeworm parasites are remarkably host specific; therefore, making this an ideal system in which to examine global patterns in species diversity. Here, we 1) quantify the tapeworm richness in elasmobranch fishes, 2) identify the host features correlated with tapeworm richness, and 3) determine whether tapeworm richness follows a latitudinal gradient. The individual and combined effects of host size, factors associated with water temperatures (influenced by latitude and depth), host habitat, and type of elasmobranch (shark or batoid) on measures of species diversity were assessed using general linear models. These analyses included tapeworm host records for 317 different elasmobranch species (124 species were included in our analyses) and were conducted with and without taking into account phylogenetic relationships between host species. Since sharks and batoids differ substantially in body form, analyses were repeated for each host subset. On average, batoids harboured significantly more tapeworm species than shark hosts. Tapeworm richness in sharks was influenced by median depth, whereas no predictor variable included in our models could adequately account for interspecific variation in tapeworm richness in batoid hosts. The taxonomic diversity of tapeworm assemblages of sharks and batoids was influenced by median depth and median latitude, respectively. When the influence of host phylogeny is accounted for, larger hosts harbour a greater tapeworm richness, whereas hosts exploiting wider latitudinal ranges harbour more taxonomically distinct tapeworm assemblages. Species richness and taxonomic diversity of tapeworm assemblages in elasmobranch fishes are influenced by different evolutionary pressures, including host phylogenetic relationships, space constraints and geographical area. Our results suggest that ca 3600 tapeworm species have yet to be described from elasmobranch fishes.     

Co-diversity and co-distribution in phyllostomid bats: Evaluating the relative roles of climate and niche conservatism

Explaining the causes of geographic gradients in biodiversity remains an elusive task. Traditionally, correlative approaches have been used to relate species richness with contemporary climate, without actually explaining the causal factors. Recent approaches propose simulation models as more appropriate tools for assessing potential causes of macroecological patterns. Here we developed stochastic models to assess the relative contribution of climate and niche conservatism in determining compositional similarity among sites (co-diversity) and geographic association among species (co-distribution) in the bat family Phyllostomidae. We used range-diversity plots and variance-ratio tests to describe and evaluate such patterns. Our results supported a strong effect of climate in determining cohesive ranges causing positive co-diversity and co-distribution. We also demonstrated a marginal effect of niche conservatism, as modeled here, among species in shaping these patterns. However, climate and niche conservatism are not sufficient and other processes are still required to explain observed patterns. Our study highlights the importance of historical processes and demonstrates the usefulness of a simulation framework in testing biogeographical hypothesis to understand the relationship between diversity and distribution.     

Richness patterns, species distributions and the principle of extreme deconstruction

Aim To analyse the global patterns in species richness of Viperidae snakes through the deconstruction of richness into sets of species according to their distribution models, range size, body size and phylogenetic structure, and to test if environmental drivers explaining the geographical ranges of species are similar to those explaining richness patterns, something we called the extreme deconstruction principle. Location Global. Methods We generated a global dataset of 228 terrestrial viperid snakes, which included geographical ranges (mapped at 1° resolution, for a grid with 7331 cells world‐wide), body sizes and phylogenetic relationships among species. We used logistic regression (generalized linear model; GLM) to model species geographical ranges with five environmental predictors. Sets of species richness were also generated for large and small‐bodied species, for basal and derived species and for four classes of geographical range sizes. Richness patterns were also modelled against the five environmental variables through standard ordinary least squares (OLS) multiple regressions. These subsets are replications to test if environmental factors driving species geographical ranges can be directly associated with those explaining richness patterns. Results Around 48% of the total variance in viperid richness was explained by the environmental model, but richness sets revealed different patterns across the world. The similarity between OLS coefficients and the primacy of variables across species geographical range GLMs was equal to 0.645 when analysing all viperid snakes. Thus, in general, when an environmental predictor it is important to model species geographical ranges, this predictor is also important when modelling richness, so that the extreme deconstruction principle holds. However, replicating this correlation using subsets of species within different categories in body size, range size and phylogenetic structure gave more variable results, with correlations between GLM and OLS coefficients varying from –0.46 up to 0.83. Despite this, there is a relatively high correspondence (r = 0.73) between the similarity of GLM‐OLS coefficients and R² values of richness models, indicating that when richness is well explained by the environment, the relative importance of environmental drivers is similar in the richness OLS and its corresponding set of GLMs. Main conclusions The deconstruction of species richness based on macroecological traits revealed that, at least for range size and phylogenetic level, the causes underlying patterns in viperid richness differ for the various sets of species. On the other hand, our analyses of extreme deconstruction using GLM for species geographical range support the idea that, if environmental drivers determine the geographical distribution of species by establishing niche boundaries, it is expected, at least in theory, that the overlap among ranges (i.e. richness) will reveal similar effects of these environmental drivers. Richness patterns may be indeed viewed as macroecological consequences of population‐level processes acting on species geographical ranges.     

Global habitat suitability models of terrestrial mammals

Detailed large-scale information on mammal distribution has often been lacking, hindering conservation efforts. We used the information from the 2009 IUCN Red List of Threatened Species as a baseline for developing habitat suitability models for 5027 out of 5330 known terrestrial mammal species, based on their habitat relationships. We focused on the following environmental variables: land cover, elevation and hydrological features. Models were developed at 300 m resolution and limited to within species' known geographical ranges. A subset of the models was validated using points of known species occurrence. We conducted a global, fine-scale analysis of patterns of species richness. The richness of mammal species estimated by the overlap of their suitable habitat is on average one-third less than that estimated by the overlap of their geographical ranges. The highest absolute difference is found in tropical and subtropical regions in South America, Africa and Southeast Asia that are not covered by dense forest. The proportion of suitable habitat within mammal geographical ranges correlates with the IUCN Red List category to which they have been assigned, decreasing monotonically from Least Concern to Endangered. These results demonstrate the importance of fine-resolution distribution data for the development of global conservation strategies for mammals.     

Continental and regional ranges of North American mammals: Rapoport's rule in real and null worlds

Aim To assess the relationship between species richness and distribution within regions arranged along a latitudinal gradient we use the North American mammalian fauna as a study case for testing theoretical models. Location North America. Methods We propose a conceptual framework based on a fully stochastic mid‐domain model to explore geographical patterns of range size and species richness that emerge when the size and position of species ranges along a one‐dimensional latitudinal gradient are randomly generated. We also analyse patterns for the mammal fauna of North America by comparing empirical results from a biogeographical data base with predictions based on randomization null models. Results We confirmed the validity of Rapoport's rule for the mammals of North America by documenting gradients in the size of the continental ranges of species. Additionally, we demonstrated gradients of mean regional range size that parallel those of continental range. Our data also demonstrated that mean range size, measured both as a continental or a regional variable, is significantly correlated with the geographical pattern in species richness. All these patterns deviated sharply from null models. Main conclusions Rapoport's statement of an areographic relationship between species distribution and richness is highly relevant in modern discussions about ecological patterns at the geographical scale.     

The diversity field of New World leaf‐nosed bats (Phyllostomidae)

Aim To analyse how the patterns of species richness for the whole family Phyllostomidae determine the structure of diversity fields (sets of species‐richness values) within the ranges of individual bat species. Location The range of the family Phyllostomidae in North and South America. Methods We generated a database of the occurrence of 143 phyllostomid bat species in 6794 quadrats, analysing the species‐richness frequency distribution for all sites, and for subsets of sites defined by the geographic ranges of species. Range–diversity plots, depicting simultaneously the size and the mean species richness of ranges, were built to explore the patterns of co‐occurrence in widespread and restricted species. We compared the empirical patterns against two null models: (1) with scattered (non‐cohesive) ranges, and (2) with cohesive ranges modelled with the spreading‐dye algorithm. Diversity fields were analysed with richness maps for individual species and with comparisons of species‐richness frequency distributions. Results Overall richness frequency distribution showed a multimodal pattern, whereas simulated distributions showed lower values of variance, and were unimodal (for model 1) and bimodal (for model 2). Range–diversity plots for the empirical data and for the cohesive‐ranges simulation showed a strong tendency of species to co‐occur in high‐diversity sites. The scattered‐ranges simulation showed no such tendency. Diversity fields varied according to idiosyncratic features of species generating particular geographic patterns and richness frequency distributions. Main conclusions Phyllostomid bats show a higher level of co‐occurrence than expected from null models. That tendency in turn implies a higher variance in species richness among sites, generating a wider species‐richness frequency distribution. The diversity field of individual species results from the size, shape and location of ranges, but also depends on the general pattern of richness for the whole family.     

Type and spatial structure of distribution data and the perceived determinants of geographical gradients in ecology: the species richness of African birds

Aim Studies exploring the determinants of geographical gradients in the occurrence of species or their traits obtain data by: (1) overlaying species range maps; (2) mapping survey‐based species counts; or (3) superimposing models of individual species’ distributions. These data types have different spatial characteristics. We investigated whether these differences influence conclusions regarding postulated determinants of species richness patterns. Location Our study examined terrestrial bird diversity patterns in 13 nations of southern and eastern Africa, spanning temperate to tropical climates. Methods Four species richness maps were compiled based on range maps, field‐derived bird atlas data, logistic and autologistic distribution models. Ordinary and spatial regression models served to examine how well each of five hypotheses predicted patterns in each map. These hypotheses propose productivity, temperature, the heat–water balance, habitat heterogeneity and climatic stability as the predominant determinants of species richness. Results The four richness maps portrayed broadly similar geographical patterns but, due to the nature of underlying data types, exhibited marked differences in spatial autocorrelation structure. These differences in spatial structure emerged as important in determining which hypothesis appeared most capable of explaining each map's patterns. This was true even when regressions accounted for spurious effects of spatial autocorrelation. Each richness map, therefore, identified a different hypothesis as the most likely cause of broad‐scale gradients in species diversity. Main conclusions Because the ‘true’ spatial structure of species richness patterns remains elusive, firm conclusions regarding their underlying environmental drivers remain difficult. More broadly, our findings suggest that care should be taken to interpret putative determinants of large‐scale ecological gradients in light of the type and spatial characteristics of the underlying data. Indeed, closer scrutiny of these underlying data — here the distributions of individual species — and their environmental associations may offer important insights into the ultimate causes of observed broad‐scale patterns.     

Spatial diversity patterns of Pristimantis frogs in the Tropical Andes

Although biodiversity gradients have been widely documented, the factors governing broad‐scale patterns in species richness are still a source of intense debate and interest in ecology, evolution, and conservation biology. Here, we tested whether spatial hypotheses (species–area effect, topographic heterogeneity, mid‐domain null model, and latitudinal effect) explain the pattern of diversity observed along the altitudinal gradient of Andean rain frogs of the genus Pristimantis. We compiled a gamma‐diversity database of 378 species of Pristimantis from the tropical Andes, specifically from Colombia to Bolivia, using records collected above 500 m.a.s.l. Analyses were performed at three spatial levels: Tropical Andes as a whole, split in its two main domains (Northern and Central Andes), and split in its 11 main mountain ranges. Species richness, area, and topographic heterogeneity were calculated for each 500‐m‐width elevational band. Spatial hypotheses were tested using linear regression models. We examined the fit of the observed diversity to the mid‐domain hypothesis using randomizations. The species richness of Pristimantis showed a hump‐shaped pattern across most of the altitudinal gradients of the Tropical Andes. There was high variability in the relationship between area and species richness along the Tropical Andes. Correcting for area effects had little impact in the shape of the empirical pattern of biodiversity curves. Mid‐domain models produced similar gradients in species richness relative to empirical gradients, but the fit varied among mountain ranges. The effect of topographic heterogeneity on species richness varied among mountain ranges. There was a significant negative relationship between latitude and species richness. Our findings suggest that spatial processes partially explain the richness patterns of Pristimantis frogs along the Tropical Andes. Explaining the current patterns of biodiversity in this hot spot may require further studies on other possible underlying mechanisms (e.g., historical, biotic, or climatic hypotheses) to elucidate the factors that limit the ranges of species along this elevational gradient.     

The river domain: why are there more species halfway up the river?

Biologists have long noted higher levels of species diversity in the longitudinal middle‐courses of river systems and have proposed many explanations. As a new explanation for this widespread pattern, we suggest that many middle‐course peaks in richness may be, at least in part, a consequence of geometric constraints on the location of species’ ranges along river courses, considering river headwaters and mouths as boundaries for the taxa considered. We demonstrate this extension of the mid‐domain effect (MDE) to river systems for riparian plants along two rivers in Sweden, where a previous study found a middle‐course peak in richness of natural (non‐ruderal) species. We compare patterns of empirical richness of these species to null model predictions of species richness along the two river systems and to spatial patterns for six environmental variables (channel width, substrate fineness, substrate heterogeneity, ice scour, bank height, and bank area). In addition, we examine the independent prediction of mid‐domain effects models that species with large ranges, because the location of their ranges is more constrained, are more likely to produce a mid‐domain peak in richness than are species with small ranges. Species richness patterns of riparian plants were best predicted by models including both null model predictions and environmental variables. When species were divided into large‐ranged and small‐ranged groups, the mid‐domain effect was more prominent and the null model predictions were a better fit to the empirical richness patterns of large‐ranged species than those of small‐ranged species. Our results suggest that the peak in riparian plant species richness in the middle courses of the rivers studied can be explained by an underlying mid‐domain effect (driven by geometric constraints on large‐ranged species), together with environmental effects on richness patterns (particularly on small‐ranged species). We suggest that the mid‐domain effect may help to explain similar middle‐course richness peaks along other rivers.     

Challenges in the application of geometric constraint models

Discerning the processes influencing geographical patterns of species richness remains one of the central goals of modern ecology. Traditional approaches to exploring these patterns have focused on environmental and ecological correlates of observed species richness. Recently, some have suggested these approaches suffer from the lack of an appropriate null model that accounts for species ranges being constrained to occur within a bounded domain. Proponents of these null geometric constraint models (GCMs), and the mid-domain effect these models produce, argue their utility in identifying meaningful gradients in species richness. This idea has generated substantial debate. Here we discuss what we believe are the three major challenges in the application of GCMs. First, we argue that there are actually two equally valid null models for the random placement of species ranges within a domain, one of which actually predicts a uniform distribution of species richness. Second, we highlight the numerous decisions that must be made to implement a GCM that lead to marked differences in the predictions of the null model. Finally, we discuss challenges in evaluating the importance of GCMs once they have been implemented.     

One,two and three‐dimensional geometric constraints and climatic correlates of North American tree species richness

The ‘mid‐domain effect’ (MDE) has received much attention recently as a candidate explanation for patterns in species richness over large geographic areas. Mid‐domain models generate a central peak in richness when species ranges are randomly placed within a bounded geographic area (i.e. the domain). The most common terrestrial mid‐domain models published to date have been 1‐D latitude or elevation models and 2‐D latitude‐longitude models. Here, we test 1‐D, 2‐D and 3‐D mid‐domain models incorporating latitude, longitude and elevation, and assess independent and concurrent effects of geometric constraints and climatic variables on species richness of North American trees. We use both the traditional ‘global’ regression models as well as geographically weighted regressions (‘local’ models) to examine local variation in the contribution of MDE and climatic variables to species richness across the domain. Our results show that in some dimensions the contribution of MDE to patterns of species richness can be quite substantial, and we show that in most cases a combination of MDE and climate predicted empirical species richness best in both local and global models. For the North American domain, MDE in the elevation dimension is clearly important in describing patterns of empirical species richness. We also show that the assumption of stationarity in global models is not met in the North American domain and that results of these models mask complex patterns in both the effect of MDE on richness and the response of species richness to climate. In particular we show the increased explanatory role of MDE in predicting species richness as domain edges are approached. Our results support the hypothesis that geometric constraints contribute to species richness patterns and we suggest the mid‐domain effect should be considered alongside more traditional environmental correlates in understanding patterns of species diversity.     

When does diversity fit null model predictions? Scale and range size mediate the mid‐domain effect

Aim  Recently, a flurry of studies have focused on the extent to which geographical patterns of diversity fit mid-domain effect (MDE) null models. While some studies find strong support for MDE null models, others find little. We test two hypotheses that might explain this variation among studies: small-ranged groups of species are less likely than large-ranged species to show mid-domain peaks in species richness, and mid-domain null model predictions are less robust for smaller spatial extents than for larger spatial extents.
Location  We analyse data sets from elevational, riverine, continental and other domains from around the world.
Methods  We use a combination of Spearman rank correlations and binomial tests to examine whether differences within and among studies and domains in the predictive power of MDE null models vary with spatial scale and range size.
Results  Small-ranged groups of species are less likely to fit mid-domain predictions than large-ranged groups of species. At large spatial extents, diversity patterns of taxonomic groups with large mean range sizes fit MDE null model predictions better than did diversity patterns of groups with small mean range sizes. MDE predictions were more explanatory at larger spatial extents than at smaller extents. Diversity patterns at smaller spatial extents fit MDE predictions poorly across all range sizes. Thus, MDE predictions should be expected to explain patterns of species richness when ranges and the scale of analysis are both large.
Main conclusions  Taken together, the support for these hypotheses offers a more sophisticated model of when MDE predictions should be expected to explain patterns of species richness, namely when ranges and the scale of analysis are both large. Thus the circumstances in which the MDE is important are finite and apparently predictable.     

Process-based models of species distributions and the mid-domain effect

Null models that place species ranges at random within a bounded geographical domain produce hump-shaped species richness gradients (the "mid-domain effect," or MDE). However, there is debate about the extent to which these models are a suitable null expectation for effects of environmental gradients on species richness. Here, I present a process-based framework for modeling species distributions within a bounded geographical domain. Analysis of null models consistent with the mid-domain hypothesis shows that MDEs are indeed likely to be ubiquitous consequences of geographical domain boundaries. Comparing the probability distributions of range locations for the process-based and randomization-based models reveals that randomization models probably overestimate the contribution of MDEs to empirical patterns of species richness, but it also indicates that other testable predictions from randomization models are likely to be robust. I also show how this process-based framework can be extended beyond null models to incorporate effects of environmental gradients within the domain. This study provides a first step toward an ecological theory of species distributions in geographical space that can incorporate both "geometric constraints" and effects of environmental gradients, and it shows how such a theory can inform our understanding of species richness gradients in nature.     

Geographical patterns in species richness of the benthic polychaetes in the continental shelf of the Gulf of California, Mexican Pacific

The present study is the first attempt to describe meso-scale patterns in the species richness of polychaetes along the Gulf of California, which stretches from about 23°N to 31°N. We examine herein the spatial changes in species distribution and explore the overlapping of species’ ranges towards the centre of the Gulf, to test whether the mid-domain effect (MDE) could explain an expected mid-domain peak in species richness. The faunal composition and the latitudinal range of 244 species of polychaetes recorded along the continental shelf of the Gulf of California were analysed in latitude bands of 1°. The species composition changes around the Gulf’s archipelago (~29°N), and the highest values of species richness are found at the 25° (197 species) and 26° (193 species) of latitude. Although the species richness pattern could be described by a parabolic shape, the regional trend was not strongly consistent with the peak of diversity at 27°N (176–191 species) predicted by the mid-domain effect: the random sorting of species’ ranges within spatial domain does not explain satisfactorily the geographical patterns of diversity. Nevertheless, a partial contribution of MDE to these natural patterns of diversity could be detected, and the increase in species richness towards middle latitudes was basically determined by species with distribution ranges larger than 6°. The low level of significance between the empirical species richness pattern and the mid-domain model prediction for polychaetes in the Gulf does not restrict their use as a model for exploring the randomness of the diversity patterns.     

The mid-domain effect and species richness patterns:what have we learned so far?

If species' ranges are randomly shuffled within a bounded geographical domain free of environmental gradients, ranges overlap increasingly toward the center of the domain, creating a "mid-domain" peak of species richness. This "mid-domain effect" (MDE) has been controversial both in concept and in application. Empirical studies assess the degree to which the evolutionary, ecological, and historical processes that undeniably act on individual species and clades produce geographical patterns that resemble those produced by MDE models. MDE models that resample empirical range size frequency distributions (RSFDs) balance the risk of underestimating and overestimating the role of MDE, whereas theoretical RSFDs are generally biased toward underestimating MDE. We discuss the inclusion of nonendemic species in MDE models, rationales for setting domain limits, and the validity of one- and two-dimensional MDE models. MDE models, though null models, are not null hypotheses to be simplistically rejected or accepted. They are a means of estimating the expected effect of geometric constraints within the context of multiple causality. We call for assessment of MDE on an equal statistical footing with other candidate explanations for richness gradients. Although some critics have categorically dismissed MDE, an overview of the 21 MDE studies published to date reveals a substantial signature of MDE in natural patterns and justifies continued work.     

Three-dimensional mid-domain predictions: geometric constraints in North American amphibian, bird, mammal and tree species richness patterns

The "mid-domain effect" (MDE) has received much attention as a candidate explanation for patterns in species richness over large geographic areas. Mid-domain models generate a central peak in richness when species ranges are placed randomly within a bounded geographic area (i.e. the domain). Until now, domain limits have been described mostly in one-dimension, usually latitude or elevation, and only occasionally in two-dimensions. Here we test 1-D, 2-D and, for the first time, 3-D mid-domain models and assess the effects of geometric constraints on species richness in North American amphibian, bird, mammal and tree species. Using spatially lagged simultaneous autoregressive models, empirical richness was predicted quite well by the mid-domain predictions and the spatial autoregressive term (45–92% R²). However, our results show that empirical species richness peaks do deviate from those of the MDE predictions in 3 dimensions. Variation explained (R²) by MDE predictions generally increased with increasing mean range size of the different biotic groups (from amphibian, to tree, mammal and finally bird data), and decreased with increasing dimensions being accounted for in the models. The results suggest geometric constraints alone can explain much of the variation in species richness with elevation, specifically with respect to the larger-range taxa, birds and mammals. Our analysis addresses many of the recent methodological criticisms directed at studies testing the MDE, and our results support the hypothesis that species diversity patterns are influenced by geometric constraints.