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.     

The missing Madagascan mid-domain effect

Species richness varies enormously across geographical gradients, a well-known phenomenon for which there are many hypothesized explanations. One recent hypothesis uses null models to demonstrate that random re-distribution of species' ranges within a given domain leads to a 'mid-domain effect' (MDE): increasing species richness towards the centre of the area. Madagascar is especially well-suited for empirical evaluation of mid-domain models by virtue of its large endemic fauna and its clearly defined boundaries. Lees et al. [ Biol. J. Linn. Soc. 67 (1999) 529] observed patterns of species richness consistent with MDEs in the Madagascan rainforest (a slim, north–south belt). In this study, we test one-dimensional and two-dimensional mid-domain model predictions for the birds and mammals of the entire island of Madagascar. When only latitudinal extents of species' distribution are considered, patterns of richness in Madagascar show an MDE. However, this pattern disappears for both taxa after accounting for the tendency of latitudinal bands nearer the middle of the country to be larger. Two-dimensional mid-domain model predictions of species richness are qualitatively opposite to observed patterns. Instead, island-wide spatial gradients of species richness in Madagascar relate strongly to patterns of primary productivity and amount of remaining natural habitat. Earlier work that showed a mid-domain peak within the rainforest biome (effectively after controlling for climate and natural habitat) seems likely to have reflected methodological artefacts. The classic case in which MDEs should occur is, in fact, inconsistent with the mid-domain hypothesis.     

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.     

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.     

Reconsidering null models of diversity: Do geometric constraints on species ranges necessarily cause a mid‐domain effect?

Recent null models that place species ranges randomly within a bounded domain have produced controversial results. Many such geometric constraint models predict a peak in species richness in the centre of domains in the absence of underlying environmental gradients or interspecific interactions. We used two-dimensional simulation models to explore different ways that species ranges could interact with the domain boundary. In the rejection model, a randomly generated range that overlaps a domain boundary is removed from the simulation. In the reshaping model, a range that overlaps the domain boundary is reshaped so that the entire range is placed within the domain. The truncation model allows potential ranges to extend across the boundary, but only that portion of the range within the domain is included in the realized range. Both rejection and reshaping models produced a drop in species richness near domain boundaries, though the effect was less pronounced in the reshaping model. Our truncation model did not produce any spatial pattern in species richness. Thus the random placement of species ranges within a bounded domain does not necessarily lead to a mid-domain effect.
  Range truncation is consistent with bioclimate envelope models, which can successfully predict a species range in response to the availability of appropriate climate conditions. We argue that such flexible range sizes are more realistic than the assumption that range size is an unvarying characteristic of a species. Other range characteristics, including size and shape, can change near domain boundaries in the null models, including the truncation model. A broader consideration of range characteristics near domain boundaries could be productive.     

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.     

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 mid-domain effect: geometric constraints on the geography of species richness

Geographic patterns of species richness are influenced by many factors, but the role of shared physiographical and physiological boundaries in relation to range-size distributions has been surprisingly neglected, in spite of the fact that such geometric constraints lead to mid-domain richness peaks even without environmental gradients (the mid-domain effect). Relying on null models, several recent studies have begun to quantify this problem using simulated and empirical data. This approach promises to transform how we perceive geographic variation in diversity, including the long unresolved latitudinal gradient in species richness. The question is not whether geometry affects such patterns, but by how much.     

The mid-domain effect revisited

We revisit the proposition that boundary constraints on species' ranges cause species richness gradients (the mid-domain effect [MDE] hypothesis). In the absence of environmental gradients, species should not retain their observed range sizes as assumed by MDE models. Debate remains regarding the definition of domain limits, valid predictions for testing the models, and their statistical assessment. Empirical support for the MDE is varied but often weak, suggesting that geometric constraints on species' ranges do not provide a general explanation for richness gradients. Criticism of MDE model assumptions does not, however, imply opposition to the use of null models in ecology.     

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.     

Environmental and geometric constraints on Indo-Pacific coral reef biodiversity

The Indo-Australian Archipelago supports the world's richest coral reef biodiversity hotspot. Traditional hypotheses that account for such exceptional biodiversity have highlighted the importance of environmental variables such as habitat area and energy input. Recently, however, an additional explanation has been proposed based on geometric constraints in the placement of geographical ranges within a bounded domain, which cause a mid-domain peak in species richness; the mid-domain effect (MDE). Here, for the first time, we examine the relative importance of area, energy and MDE jointly on species richness patterns. Model selection indicates that the best model incorporates MDE and reef area, but no energy effect; moreover, this best-fit model captures all major features of reef fish and coral species richness patterns. Habitat area is the major environmental factor influencing species richness. The prevention of further fragmentation and loss of habitat area is of critical importance for the conservation of coral reef biodiversity.     

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.     

Range size in mid-domain models of species diversity

Geographical patterns of species diversity have been examined using mid-domain null models, in which the ranges of individual species are simulated by randomly arranging them on a bounded one- or two-dimensional continent. These models have shown that structured patterns in the geographical distribution of biodiversity can arise even under a fully stochastic procedure. In particular, mid-domain models have demonstrated that the random generation of ranges of different sizes and locations can produce a gradient of species diversity similar to the one found in real assemblages, with a peak at the middle of a continent. A less explored feature of mid-domain models is the pattern of range-size frequency distribution. Numerical simulations have provided some insights about the geographic pattern of average range size, but no exploration of the shape of range-size frequency distributions has been carried out. Here I present analytical and numerical models that generate explicit predictions for patterns of range size under the assumptions of mid-domain models of species diversity. Some generalizations include: (1) Mid-domain models predict no geographic gradient of average range size; the mean range size of species occurring at any point on a continent is constant (0.5 of the extent of the continent in the one-dimensional model, 0.25 of the area of the continent in the two-dimensional case); (2) Variance in range size is lowest at the middle of a continent and highest near the corners of a square-shaped continent; (3) The range-size frequency distribution is highly right-skewed at any point of a continent, but the skewness is highest near the corners. Despite their alleged weaknesses, mid-domain models are adequate null models against which real-world patterns can be contrasted.     

Using potential distributions to explore determinants of Western Palaearctic migratory songbird species richness in sub-Saharan Africa

Aim  Although the breeding ranges of most Western Palaearctic migratory passerines are well documented in Europe, their overwintering ranges and patterns of species richness in Africa remain poorly understood. To illustrate potential patterns of species richness despite severely limited data, we extrapolated species ranges from a new and unique data bank of locality records that documents overwintering locations of these birds in Africa.
Location  Sub-Saharan Africa.
Methods  We predicted potential geographical distributions of 60 species of passerine birds based on overwintering records using bioclimatic models. We then combined these predictions to estimate potential species richness and explored response shapes using spatial linear regression. We also evaluated the evidence for a mid-domain effect using a one-dimensional null model.
Results  Spatial linear regression analyses of the species richness pattern revealed non-linear relationships to seasonality in precipitation, minimum net primary productivity, minimum average temperature, habitat heterogeneity, percentage of tree cover, distance from the Sahara Desert and inter-annual variability in net primary productivity. The explanatory power of these variables decreased with geographic range size. The one-dimensional null model of species richness based on distance from the Sahara Desert did not show evidence of a mid-domain effect.
Main conclusions  Distributions of migrants seem generally strongly determined by distance from the Sahara Desert working in concert with climatic effects, but this cannot adequately explain richness patterns of species with small ranges in Africa, many of which are of substantial conservation concern.     

Fish distributions along depth gradients of a sea mountain range conform to the mid‐domain effect

Species richness often peaks in the middle of bounded geographic domains (e.g. latitude, altitude or depth). Hump‐shaped richness distributions may be due to deterministic processes, such as adaptations to environmental variation. Alternatively, such distributions might also be due to stochastic process. The mid‐domain effect (MDE) posits that hump‐shaped richness distributions arise when species ranges are randomly arranged within the limits of the domain. We tested whether the MDE could account for the richness of bottom‐associated (demersal) fishes between 200 and 800 m on the Chatham Rise, New Zealand. We quantified the depth distributions of 59 fish species from 1891 research trawl catches made between 1991 and 2007. Results showed a broad plateau of high species richness near the centre of the domain (between 300 and 700 m), which was consistent with expectations of the MDE. Further, empirical species richness was better explained statistically by predictions of the MDE than models incorporating additional abiotic predictor variables. Our results deviated from previous studies that identified a greater richness of fishes in warmer, shallower depths with higher primary production. However, our study was conducted entirely below the euphotic zone, at depths where gradients are relatively weak, suggesting that support for the mid‐domain effect may increase across oceanic domains characterised by weak environmental gradients.     

The mid-domain effect and diversity gradients: is there anything to learn?

The mid-domain effect (MDE) has been proposed as a null model for diversity gradients and an explanation for observed patterns. Here we respond to a recent defense of the concept, explaining that it cannot represent a viable model in either real or null worlds. First, the MDE misrepresents the nature of species ranges. There is also an internal logical inconsistency underlying the MDE because the range size frequency distribution, necessary to generate a hump-shaped pattern under randomization, cannot exist in the absence of environmental gradients and is generated by the ecological and historical processes that the MDE claims to exclude.     

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.     

Climatic and geometric constraints as driving factors of butterfly species richness along a Neotropical elevational gradient

We tested the effects of temperature, humidity and geographical constraints upon butterfly species richness along an elevational gradient covering an altitude ranging from 117 to 3,104 m above sea level (m. a.s.l.), in Southern Mexico. Ten transect sites were sampled 219 times from May 2010 to May 2011, along the elevational gradient to estimate range and population abundance of butterfly species. The effects of temperature, humidity and geometric constraints (mid-domain effects) on species richness along the study gradient were assessed using ordinary least squares regression. A total of 7,005 specimens representing 193 species were recorded. Species richness was relatively higher at elevations between 117 and 1,000 m. a.s.l. with an observed decline in richness values as elevation increased. Butterfly species richness along the study environmental gradient was predominantly determined by climatic constraints, rather than geometric constraints—a mid-domain model fit well only for large-ranged Pieridae species. Temperature and humidity explained the variation species richness for the entire butterfly community and for the three families evaluated; however the effect of predictor variables varied according to the measure of species richness and taxonomic family. This discrepancy in the response of butterfly richness to temperature, humidity and geometric constraints emphasizes the need to evaluate the response of different taxa to elevational gradients, to establish general patterns that help us to prioritize conservation measures that reduce population declines and local extinctions predicted by climate change in highly diverse tropical mountain ecosystems.     

Can stochastic geographical evolution re‐create macroecological richness–environment correlations?

Aim Richness gradients are frequently correlated with environmental characteristics at broad geographic scales. In particular, richness is often associated with energy and climate, while environmental heterogeneity is rarely its best correlate. These correlations have been interpreted as evidence in favour of environmental determinants of diversity gradients, particularly energy and climate. This interpretation assumes that the expected‐by‐random correlation between richness and environment is zero, and that this is equally true for all environmental characteristics. However, these expectations might be unrealistic. We investigated to what degree basic evolutionary/biogeographical processes occurring independently of environment could lead to richness gradients that correlate with environmental characteristics by chance alone. Location Africa, Australia, Eurasia and the New World. Methods We produced artificial richness gradients based on a stochastic simulation model of geographic diversification of clades. In these simulations, species speciate, go extinct and expand or shift their distributions independently of any environmental characteristic. One thousand two hundred repetitions of this model were run, and the resulting stochastic richness gradients were regressed against real‐world environmental variables. Stochastic species–environment relationships were then compared among continents and among three environmental characteristics: energy, environmental heterogeneity and climate seasonality. Results Simulations suggested that a significant degree of correlation between richness gradients and environment is expected even when clades diversify and species distribute stochastically. These correlations vary considerably in strength; but in the best cases, environment can spuriously account for almost 80% of variation in stochastic richness. Additionally, expected‐by‐chance relationships were different among continents and environmental characteristics, producing stronger spurious relationships with energy and climate than with heterogeneity. Main conclusions We conclude that some features of empirical species–environment relationships can be reproduced just by chance when taking into account evolutionary/biogeographical processes underlying the construction of species richness gradients. Future tests of environmental effects on richness should consider structure in richness–environment correlations that can be produced by simple evolutionary null models. Research should move away from the naive non‐biological null hypotheses that are implicit in traditional statistical tests.     

Autoregressive modelling of species richness in the Brazilian Cerrado.

Spatial autocorrelation is the lack of independence between pairs of observations at given distances within a geographical space, a phenomenon commonly found in ecological data. Taking into account spatial autocorrelation when evaluating problems in geographical ecology, including gradients in species richness, is important to describe both the spatial structure in data and to correct the bias in Type I errors of standard statistical analyses. However, to effectively solve these problems it is necessary to establish the best way to incorporate the spatial structure to be used in the models. In this paper, we applied autoregressive models based on different types of connections and distances between 181 cells covering the Cerrado region of Central Brazil to study the spatial variation in mammal and bird species richness across the biome. Spatial structure was stronger for birds than for mammals, with R(2) values ranging from 0.77 to 0.94 for mammals and from 0.77 to 0.97 for birds, for models based on different definitions of spatial structures. According to the Akaike Information Criterion (AIC), the best autoregressive model was obtained by using the rook connection. In general, these results furnish guidelines for future modelling of species richness patterns in relation to environmental predictors and other variables expressing human occupation in the biome.