Adding energy gradients and long‐distance dispersal to a neutral model improves predictions of Madagascan bird diversity

Macroecological patterns are likely the result of both stochastically neutral mechanisms and deterministic differences between species. In Madagascar, the simplest stochastically neutral hypothesis – the mid‐domain effects (MDE) hypothesis – has already been rejected. However, rejecting the MDE hypothesis does not necessarily refute the existence of all other neutral mechanisms. Here, we test whether adding complexity to a basic neutral model improves predictions of biodiversity patterns. The simplest MDE model assumes that: (1) species' ranges are continuous and unfragmented, (2) are randomly located throughout the landscape, and (3) can be stacked independently and indefinitely. We designed a simulation based on neutral theory that allowed us to weaken each of these assumptions incrementally by adjusting the habitat capacity as well as the likelihood of short‐ and long‐distance dispersal. Simulated outputs were compared to four empirical patterns of bird diversity: the frequency distributions of species richness and range size, the within‐island latitudinal diversity gradient, and the distance‐decay of species compositional similarity. Neutral models emulated empirical diversity patterns for Madagascan birds accurately. The frequency distribution of range size, latitudinal diversity gradient, and the distance‐decay of species compositional similarity could be attributed to stochastic long‐distance migration events and zero‐sum population dynamics. However, heterogenous environmental gradients improved predictions of the frequency distribution of species richness. Patterns of bird diversity in Madagascar can broadly be attributed to stochastic long‐distance migration events and zero‐sum population dynamics. This implies that rejecting simple hypotheses, such as MDE, does not serve as evidence against stochastic processes in general. However, environmental gradients were necessary to explain patterns of species richness and deterministic differences between species are probably important for explaining the distributions of narrow‐range and endemic species.     

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.     

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.     

Intraspecific application of the mid-domain effect model: spatial and temporal nest distributions of green turtles, Chelonia mydas, at Tortuguero, Costa Rica

The mid‐domain effect (MDE) model was developed to evaluate patterns of species richness. We applied the MDE model to intraspecific distribution patterns – the spatial and temporal nest distributions of green turtles, Chelonia mydas, at Tortuguero, Costa Rica, from 1972 to 2000. Spatial and temporal distributions of green turtle nests at Tortuguero did not exhibit significant annual variation over this time period. The spatial and temporal distribution of nests largely conformed to the predictions of the MDE model, although the spatial model has a better fit. Environmental factors that may cause deviations from the MDE model are discussed. The model also indirectly provided a first estimate of the mean spatial nesting range of individual green turtles at Tortuguero: 10.1 km (SD 8.7 km). The MDE model provides insight into intraspecific as well as interspecific distribution patterns.     

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.     

The determinants of land snail diversity along a tropical elevational gradient: insularity,geometry and niches

Aim We investigated the patterns of species richness in land snails and slugs along a tropical elevational gradient and whether these patterns correlate with area, elevation, geographic constraints, and productivity. We did so both at the scale at which land snail population processes take place and at the coarser scale of elevational zones. Location Mount Kinabalu (4096 m) and the adjacent Mount Tambuyukon (2588 m) in Kinabalu Park, Sabah, Malaysian Borneo. Methods We used an effort‐controlled sampling protocol to determine land snail and slug species richness in 142 plots of 0.04 ha at elevations ranging from 570 to 4096 m. Extents of elevational ranges were determined by interpolation, extended where appropriate at the lower end with data from lowlands outside the study area. We used regression analysis to study the relationships between species density and richness on the one hand and elevation and area on the other. This was done for point data as well as for data combined into 300‐m elevational intervals. Results Species density (based on the individual samples) showed a decline with elevation. Elevational range length profiles revealed that range lengths are reduced at greater elevations and that a Rapoport effect is absent. Diversity showed a mild mid‐domain effect on Kinabalu, but not on Tambuyukon. When the data were combined into 300‐m elevational intervals, richness correlated more strongly with elevation than with area. Ecomorphospace was seen to shrink with increasing elevation. Main conclusions The elevational species richness patterns show the combined effects of (1) reduced niche diversity at elevations with lower productivity and (2) historical events in which the upward migration of lowland species as well as the speciation of highland endemics took place.     

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.     

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.     

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.     

Ecological interpretations of the mid-domain effect

The suggestion that spatial gradients in species richness are influenced by geometric constraints resulting in the mid‐domain effect has been investigated by null models. The technical aspects of making such null models are well explored, but the implicit ecological assumptions behind these models are less explored. Four ecological models that all assume that species ranges are constrained by hard boundaries are made: evolutionary model, source‐sink model, dynamic‐environment model, and range‐size model. These models give different predictions that make it possible to separate the models from each other, and from a model that assumes that hard boundaries are not important.     

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.     

Neutral community dynamics, the mid-domain effect and spatial patterns in species richness

The mid‐domain effect (MDE) aims to explain spatial patterns in species richness invoking only stochasticity and geometrical constraints. In this paper, we used simulations to show that its main qualitative prediction, a hump‐shaped pattern in species richness, converges to the expectation of a spatially bounded neutral model when communities are linked by short‐distance migration. As these two models can be linked under specific situations, neutral theory may provide a mechanistic population level basis for MDE. This link also allows establishing in which situations MDE patterns are more likely to be found. Also, in this situation, MDE models could be used as a first approximation to understand the role of both stochastic (ecological drift and migration) and deterministic (adaptation to environmental conditions) processes driving the spatial structure of species richness.     

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.     

Midpoint attractors and species richness: Modelling the interaction between environmental drivers and geometric constraints

We introduce a novel framework for conceptualising, quantifying and unifying discordant patterns of species richness along geographical gradients. While not itself explicitly mechanistic, this approach offers a path towards understanding mechanisms. In this study, we focused on the diverse patterns of species richness on mountainsides. We conjectured that elevational range midpoints of species may be drawn towards a single midpoint attractor – a unimodal gradient of environmental favourability. The midpoint attractor interacts with geometric constraints imposed by sea level and the mountaintop to produce taxon‐specific patterns of species richness. We developed a Bayesian simulation model to estimate the location and strength of the midpoint attractor from species occurrence data sampled along mountainsides. We also constructed midpoint predictor models to test whether environmental variables could directly account for the observed patterns of species range midpoints. We challenged these models with 16 elevational data sets, comprising 4500 species of insects, vertebrates and plants. The midpoint predictor models generally failed to predict the pattern of species midpoints. In contrast, the midpoint attractor model closely reproduced empirical spatial patterns of species richness and range midpoints. Gradients of environmental favourability, subject to geometric constraints, may parsimoniously account for elevational and other patterns of species richness.     

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.     

What drives elevational patterns of diversity? A test of geometric constraints,climate and species pool effects for pteridophytes on an elevational gradient in Costa Rica

Aim We studied pteridophyte species richness between 100 m and 3400 m along a Neotropical elevational gradient and tested competing hypotheses for patterns of species richness. Location Elevational transects were situated at Volcán Barva in the Braulio Carrillo National Park and La Selva Biological Station (100–2800 m) and Cerro de la Muerte (2700–3400 m), both on the Atlantic slope of Costa Rica, Central America. Method We analysed species richness on 156 plots of 20 × 20 m and measured temperature and humidity at four elevations (40, 650, 1800 and 2800 m). Species richness patterns were regressed against climatic variables (temperature, humidity, precipitation and actual evapotranspiration), regional species pool, area and predicted species number of a geometric null model (the mid‐domain effect, MDE). Results The species richness of the 484 recorded species showed a hump‐shaped pattern with elevation with a richness peak at mid‐elevations (c. 1700 m). The MDE was the single most powerful explanatory variable in linear regression models, but species richness was also associated strongly with climatic variables, especially humidity and temperature. Area and species pool were associated less strongly with observed richness patterns. Main conclusions Geometric models and climatic models exclusive of geometric constraints explained comparable amounts of the elevational variation in species richness. Discrimination between these two factor complexes is not possible based on model fits. While overall fits of geometric models were high, large‐ and small‐ranged species were explained by geometric models to different extents. Species with narrow elevational ranges clustered at both ends of the gradient to a greater extent than predicted by the MDE null models used here. While geometric models explained much of the pattern in species richness, we cannot rule out the role of climatic factors (or vice versa) because the predicted peak in richness from geometric models, the empirical peak in richness and the overlap in favourable environmental conditions all coincide at middle elevations. Mid‐elevations offer highest humidity and moderate temperatures, whereas at high elevations richness is reduced due to low temperatures, and at low elevations by reduced water availability due to high temperatures.     

Do Rapoport's rule,the mid‐domain effect or the source–sink hypotheses predict bathymetric patterns of polychaete richness on the Pacific coast of South America?

Aim We evaluated the bathymetric gradient of benthic polychaete species richness from the Chilean coast, as well as its possible underlying causes. We tested three possible hypotheses to explain the richness gradient: (1) Rapoport's effect; (2) the mid‐domain effect (MDE); and (c) the source–sink hypothesis. Location South‐eastern Pacific coast of Chile. Methods The bathymetric gradient in richness was evaluated using the reported ranges of bathymetric distribution of 498 polychaete species, from the intertidal to abyssal zone (c. 4700 m). Rapoport's effect was evaluated by examining the relationship between bathymetric mid‐point and bathymetric range extent, and species richness and depth. The MDE was tested using the Monte Carlo simulation program. The source–sink hypothesis was tested through nestedness analysis. Results Species richness shows significant exponential decay across the bathymetric gradient. The pattern is characterized by a high presence of short‐ranged species on the continental shelf area; while only a few species reach abyssal depths, and they tend to show extremely wide bathymetric ranges. Our simulation analyses showed that, in general, the pattern is robust to sampling artefacts. This pattern cannot be reproduced by the MDE, which predicts a parabolic richness gradient. Rather, results agree with the predictions of Rapoport's effect. Additionally, the data set is significantly nested at species, genus and family levels, supporting the source–sink hypothesis. Main conclusions The sharp exponential decay in benthic polychaete richness across the bathymetric gradient supports the general idea that abyssal environments should harbour fewer species than shallower zones. This pattern may be the result of colonization–extinction dynamics, characterized by abyssal assemblages acting as ‘sinks’ maintained mainly by shallower ‘sources’. The source–sink hypothesis provides a conceptual and methodological framework that may shed light on the search for general patterns of diversity across large spatial scales.     

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.     

A global comparative analysis of elevational species richness patterns of ferns

Aim Elevational gradients offer an outstanding opportunity to assess factors determining patterns of species richness, but along single transects potential explanatory factors often covary, making it difficult to distinguish between competing hypotheses. Many previous studies on plants have interpreted their results as supporting the mid‐domain effect (MDE) as a major determinant of species richness, even when climatic factors showed similarly high explanatory power. We compared fern species richness along 20 elevational transects to quantify the relative contribution of climate and MDE as drivers of elevational richness patterns. Location Twenty transects world‐wide. Methods Ferns were sampled in 1039 plots of 400–2500 m² each. Mean annual precipitation and temperature, epiphytic bryophyte cover (as a proxy for air humidity) and MDE predictions were included as independent variables. For each transect, we calculated multiple linear models and partitioned the variance to assess the relative contribution of the independent variables, selecting the most parsimonious models based on Akaike weights and multi‐model inference. Results Along most individual gradients, nearly all variance of fern species richness that could be attributed to either space or MDEs was collinear with climatic factors. Yet, the comparison across transects showed that elevational richness patterns are most parsimoniously accounted for by climatic conditions, especially by low water availability at low elevations and in dry regions in general, and by low temperatures at high elevations and in extra‐tropical regions. Main conclusions Fern species richness is most closely related to climatic factors, and while MDE, surface area and metapopulation processes may somewhat modify the patterns, their importance has been overstated in the past. Future research challenges include determining whether the richness–climate relationship reflects: (1) a direct relationship through the physiological tolerance of the plants, (2) an indirect influence of climate on ecosystem productivity, or (3) an evolutionary legacy of longer or faster diversification processes under certain climatic conditions.     

Phylogeny can make the mid-domain effect an inappropriate null model

The mid-domain effect (MDE), a bias in species richness towards the midpoint of a given geographical dimension, has been used as a null model in macro-ecological studies. Departures from a MDE are often thought of as interesting. The MDE is a product of the interaction between geometric boundaries and range locations, with species being forced to occupy more central positions in proportion to their range size. We criticize this mechanism for assuming species' locations to be wholly independent from their evolutionary past. We present a simple simulation model that shows how range locations arising as part of a phylogenetic process depart from a MDE. The amount of departure is positively correlated with phylogenetic imbalance (tree shape), but a deviation from an equal-rates Markov speciation model is not necessary to negate a MDE. We suggest that the MDE is an appropriate ecological null model only when phylogenetic influence on range location is demonstrably low or non-existent.