Interictal stereo-electroencephalography features below 45 Hz are sufficient for correct localization of the epileptogenic zone and postsurgical outcome prediction.

OBJECTIVE: Evidence suggests that the most promising results in interictal localization of the epileptogenic zone (EZ) are achieved by a combination of multiple stereo-electroencephalography (SEEG) biomarkers in machine learning models. These biomarkers usually include SEEG features calculated in standard frequency bands, but also high-frequency (HF) bands. Unfortunately, HF features require extra effort to record, store, and process. Here we investigate the added value of these HF features for EZ localization and postsurgical outcome prediction. METHODS: In 50 patients we analyzed 30 min of SEEG recorded during non-rapid eye movement sleep and tested a logistic regression model with three different sets of features. The first model used broadband features (1-500 Hz); the second model used low-frequency features up to 45 Hz; and the third model used HF features above 65 Hz. The EZ localization by each model was evaluated by various metrics including the area under the precision-recall curve (AUPRC) and the positive predictive value (PPV). The differences between the models were tested by the Wilcoxon signed-rank tests and Cliff's Delta effect size. The differences in outcome predictions based on PPV values were further tested by the McNemar test. RESULTS: The AUPRC score of the random chance classifier was .098. The models (broad-band, low-frequency, high-frequency) achieved median AUPRCs of .608, .582, and .522, respectively, and correctly predicted outcomes in 38, 38, and 33 patients. There were no statistically significant differences in AUPRC or any other metric between the three models. Adding HF features to the model did not have any additional contribution. SIGNIFICANCE: Low-frequency features are sufficient for correct localization of the EZ and outcome prediction with no additional value when considering HF features. This finding allows significant simplification of the feature calculation process and opens the possibility of using these models in SEEG recordings with lower sampling rates, as commonly performed in clinical routines.

Forest disturbance increases functional diversity but decreases phylogenetic diversity of an arboreal tropical ant community.

Tropical rainforest trees host a diverse arthropod fauna that can be characterised by their functional diversity (FD) and phylogenetic diversity (PD). Human disturbance degrades tropical forests, often coinciding with species invasion and altered assembly that leads to a decrease in FD and PD. Tree canopies are thought to be particularly vulnerable, but rarely investigated. Here, we studied the effects of forest disturbance on an ecologically important invertebrate group, the ants, in a lowland rainforest in New Guinea. We compared an early successional disturbed plot (secondary forest) to an old-growth plot (primary forest) by exhaustively sampling their ant communities in a total of 852 trees. We expected that for each tree community (1) disturbance would decrease FD and PD in tree-dwelling ants, mediated through species invasion. (2) Disturbance would decrease ant trait variation due to a more homogeneous environment. (3) The main drivers behind these changes would be different contributions of true tree-nesting species and visiting species. We calculated FD and PD based on a species-level phylogeny and 10 ecomorphological traits. Furthermore, we assessed by data exclusion the influence of species, which were not nesting in individual trees (visitors) or only nesting species (nesters), and of non-native species on FD and PD. Primary forests had higher ant species richness and PD than secondary forest. However, we consistently found increased FD in secondary forest. This pattern was robust even if we decoupled functional and phylogenetic signals, or if non-native ant species were excluded from the data. Visitors did not contribute strongly to FD, but they increased PD and their community weighted trait means often varied from nesters. Moreover, all community-weighted trait means changed after forest disturbance. Our finding of contradictory FD and PD patterns highlights the importance of integrative measures of diversity. Our results indicate that the tree community trait diversity is not negatively affected, but possibly even enhanced by disturbance. Therefore, the functional diversity of arboreal ants is relatively robust when compared between old-growth and young trees. However, further study with higher plot-replication is necessary to solidify and generalise our findings.

Different feeding preferences for macronutrients across seasons and sites indicate temporal and spatial nutrient limitation in the black bog ant.

How the resource use by consumers vary in different environments and time scales is one of the fundamental ecological questions. Replicated field studies are rare, however; so the extent to which nutrient use varies and why is uncertain. We studied an endangered tyrphobiotic species, the black bog ant (Formica picea), and its feeding preferences in temperate peatlands. We conducted a baiting experiment at three different sites with high nest densities, repeated over three years and three periods of growing season. Preferences for three main macronutrients (carbohydrates, proteins and lipids) were assessed. We hypothesised that if nutrient limitation plays a role, ants will have an increased need for proteins and lipids in early seasons when brood is raised, while carbohydrates use will increase in late seasons. We also expected that site identity would influence nutrient preferences, but not year. Our results supported the nutrient limitation hypothesis for proteins that were consumed more in the early season. In contrast, preference for carbohydrates was rather high and did not increase consistently through season. Although the occupancy of lipid baits was low overall, it increased at colder temperatures, in contrast to carbohydrate and protein baits. Nutrient preferences varied more among sites than years, with the lowest nutrient use observed in a diverse fen-meadow, consistent with the nutrient limitation hypothesis. Year affected ant abundance, but not bait occupancy. Our results suggest that black bog ants flexibly adapt their diet to environmental conditions and that an interplay between nutrient limitation and climate determines their feeding behaviour.

Relative entropy is an easy-to-use invasive electroencephalographic biomarker of the epileptogenic zone.

OBJECTIVE: High-frequency oscillations are considered among the most promising interictal biomarkers of the epileptogenic zone in patients suffering from pharmacoresistant focal epilepsy. However, there is no clear definition of pathological high-frequency oscillations, and the existing detectors vary in methodology, performance, and computational costs. This study proposes relative entropy as an easy-to-use novel interictal biomarker of the epileptic tissue. METHODS: We evaluated relative entropy and high-frequency oscillation biomarkers on intracranial electroencephalographic data from 39 patients with seizure-free postoperative outcome (Engel Ia) from three institutions. We tested their capability to localize the epileptogenic zone, defined as resected contacts located in the seizure onset zone. The performance was compared using areas under the receiver operating curves (AUROCs) and precision-recall curves. Then we tested whether a universal threshold can be used to delineate the epileptogenic zone across patients from different institutions. RESULTS: Relative entropy in the ripple band (80-250 Hz) achieved an average AUROC of .85. The normalized high-frequency oscillation rate in the ripple band showed an identical AUROC of .85. In contrast to high-frequency oscillations, relative entropy did not require any patient-level normalization and was easy and fast to calculate due to its clear and straightforward definition. One threshold could be set across different patients and institutions, because relative entropy is independent of signal amplitude and sampling frequency. SIGNIFICANCE: Although both relative entropy and high-frequency oscillations have a similar performance, relative entropy has significant advantages such as straightforward definition, computational speed, and universal interpatient threshold, making it an easy-to-use promising biomarker of the epileptogenic zone.

Interictal high-frequency oscillations, spikes, and connectivity profiles: A fingerprint of epileptogenic brain pathologies.

OBJECTIVE: Focal cortical dysplasia (FCD), hippocampal sclerosis (HS), nonspecific gliosis (NG), and normal tissue (NT) comprise the majority of histopathological results of surgically treated drug-resistant epilepsy patients. Epileptic spikes, high-frequency oscillations (HFOs), and connectivity measures are valuable biomarkers of epileptogenicity. The question remains whether they could also be utilized for preresective differentiation of the underlying brain pathology. This study explored spikes and HFOs together with functional connectivity in various epileptogenic pathologies. METHODS: Interictal awake stereoelectroencephalographic recordings of 33 patients with focal drug-resistant epilepsy with seizure-free postoperative outcomes were analyzed (15 FCD, 8 HS, 6 NT, and 4 NG). Interictal spikes and HFOs were automatically identified in the channels contained in the overlap of seizure onset zone and resected tissue. Functional connectivity measures (relative entropy, linear correlation, cross-correlation, and phase consistency) were computed for neighboring electrode pairs. RESULTS: Statistically significant differences were found between the individual pathologies in HFO rates, spikes, and their characteristics, together with functional connectivity measures, with the highest values in the case of HS and NG/NT. A model to predict brain pathology based on all interictal measures achieved up to 84.0% prediction accuracy. SIGNIFICANCE: The electrophysiological profile of the various epileptogenic lesions in epilepsy surgery patients was analyzed. Based on this profile, a predictive model was developed. This model offers excellent potential to identify the nature of the underlying lesion prior to resection. If validated, this model may be particularly valuable for counseling patients, as depending on the lesion type, different outcomes are achieved after epilepsy surgery.

A multi-scale cortical wiring space links cellular architecture and functional dynamics in the human brain.

The vast net of fibres within and underneath the cortex is optimised to support the convergence of different levels of brain organisation. Here, we propose a novel coordinate system of the human cortex based on an advanced model of its connectivity. Our approach is inspired by seminal, but so far largely neglected models of cortico-cortical wiring established by postmortem anatomical studies and capitalises on cutting-edge in vivo neuroimaging and machine learning. The new model expands the currently prevailing diffusion magnetic resonance imaging (MRI) tractography approach by incorporation of additional features of cortical microstructure and cortico-cortical proximity. Studying several datasets and different parcellation schemes, we could show that our coordinate system robustly recapitulates established sensory-limbic and anterior-posterior dimensions of brain organisation. A series of validation experiments showed that the new wiring space reflects cortical microcircuit features (including pyramidal neuron depth and glial expression) and allowed for competitive simulations of functional connectivity and dynamics based on resting-state functional magnetic resonance imaging (rs-fMRI) and human intracranial electroencephalography (EEG) coherence. Our results advance our understanding of how cell-specific neurobiological gradients produce a hierarchical cortical wiring scheme that is concordant with increasing functional sophistication of human brain organisation. Our evaluations demonstrate the cortical wiring space bridges across scales of neural organisation and can be easily translated to single individuals.

Cortical network organization reflects clinical response to subthalamic nucleus deep brain stimulation in Parkinson's disease.

The degree of response to subthalamic nucleus deep brain stimulation (STN-DBS) is individual and hardly predictable. We hypothesized that DBS-related changes in cortical network organization are related to the clinical effect. Network analysis based on graph theory was used to evaluate the high-density electroencephalography (HDEEG) recorded during a visual three-stimuli paradigm in 32 Parkinson's disease (PD) patients treated by STN-DBS in stimulation "off" and "on" states. Preprocessed scalp data were reconstructed into the source space and correlated to the behavioral parameters. In the majority of patients (n = 26), STN-DBS did not lead to changes in global network organization in large-scale brain networks. In a subgroup of suboptimal responders (n = 6), identified according to reaction times (RT) and clinical parameters (lower Unified Parkinson's Disease Rating Scale [UPDRS] score improvement after DBS and worse performance in memory tests), decreased global connectivity in the 1-8 Hz frequency range and regional node strength in frontal areas were detected. The important role of the supplementary motor area for the optimal DBS response was demonstrated by the increased node strength and eigenvector centrality in good responders. This response was missing in the suboptimal responders. Cortical topologic architecture is modified by the response to STN-DBS leading to a dysfunction of the large-scale networks in suboptimal responders.

Sleep Disruption in Epilepsy: Ictal and Interictal Epileptic Activity Matter.

OBJECTIVE: Disturbed sleep is common in epilepsy. The direct influence of nocturnal epileptic activity on sleep fragmentation remains poorly understood. Stereo-electroencephalography paired with polysomnography is the ideal tool to study this relationship. We investigated whether sleep-related epileptic activity is associated with sleep disruption. METHODS: We visually marked sleep stages, arousals, seizures, and epileptic bursts in 36 patients with focal drug-resistant epilepsy who underwent combined stereo-electroencephalography/polysomnography during presurgical evaluation. Epileptic spikes were detected automatically. Spike and burst indices (n/sec/channel) were computed across four 3-second time windows (baseline sleep, pre-arousal, arousal, and post-arousal). Sleep stage and anatomic localization were tested as modulating factors. We assessed the intra-arousal dynamics of spikes and their relationship with the slow wave component of non-rapid eye-movement sleep (NR) arousals. RESULTS: The vast majority of sleep-related seizures (82.4%; 76.5% asymptomatic) were followed by awakenings or arousals. The epileptic burst index increased significantly before arousals as compared to baseline and postarousal, irrespective of sleep stage or brain area. A similar pre-arousal increase was observed for the spike index in NR stage 2 and rapid eye-movement sleep. In addition, the spike index increased during the arousal itself in neocortical channels, and was strongly correlated with the slow wave component of NR arousals (r = 0.99, p < 0.0001). INTERPRETATION: Sleep fragmentation in focal drug-resistant epilepsy is associated with ictal and interictal epileptic activity. The increase in interictal epileptic activity before arousals suggests its participation in sleep disruption. An additional increase in the spike rate during arousals may result from a sleep-wake boundary instability, suggesting a bidirectional relationship. ANN NEUROL 2020;88:907-920.

Thalamic oscillatory activity may predict response to deep brain stimulation of the anterior nuclei of the thalamus.

We hypothesized that local/regional properties of stimulated structure/circuitry contribute to the effect of deep brain stimulation (DBS). We analyzed intracerebral electroencephalographic (EEG) recordings from externalized DBS electrodes targeted bilaterally in the anterior nuclei of the thalamus (ANT) in 12 patients (six responders, six nonresponders) with more than 1 year of follow-up care. In the bipolar local field potentials of the EEG, spectral power (PW) and power spectral entropy (PSE) were calculated in the passbands 1-4, 4-8, 8-12, 12-20, 20-45, 65-80, 80-200 and 200-500 Hz. The most significant differences between responders and nonresponders were observed in the BRIDGE area (bipolar recordings with one contact within the ANT and the second contact in adjacent tissue). In responders, PW was significantly decreased in the frequency bands of 65-80, 80-200, and 200-500 Hz (p < .05); PSE was significantly increased in all frequency bands (p < .05) except for 200-500 Hz (p = .06). The local EEG characteristics of ANT recorded after implantation may play a significant role in DBS response prediction.

Spatial covariance of herbivorous and predatory guilds of forest canopy arthropods along a latitudinal gradient.

In arthropod community ecology, species richness studies tend to be prioritised over those investigating patterns of abundance. Consequently, the biotic and abiotic drivers of arboreal arthropod abundance are still relatively poorly known. In this cross-continental study, we employ a theoretical framework in order to examine patterns of covariance among herbivorous and predatory arthropod guilds. Leaf-chewing and leaf-mining herbivores, and predatory ants and spiders, were censused on > 1000 trees in nine 0.1 ha forest plots. After controlling for tree size and season, we found no negative pairwise correlations between guild abundances per plot, suggestive of weak signals of both inter-guild competition and top-down regulation of herbivores by predators. Inter-guild interaction strengths did not vary with mean annual temperature, thus opposing the hypothesis that biotic interactions intensify towards the equator. We find evidence for the bottom-up limitation of arthropod abundances via resources and abiotic factors, rather than for competition and predation.

Suboptimal response to STN-DBS in Parkinson's disease can be identified via reaction times in a motor cognitive paradigm.

Although deep brain stimulation of the subthalamic nucleus (STN-DBS) in Parkinson's disease (PD) is generally a successful therapy, adverse events and insufficient clinical effect can complicate the treatment in some patients. We studied clinical parameters and cortical oscillations related to STN-DBS to identify patients with suboptimal responses. High-density EEG was recorded during a visual oddball three-stimuli paradigm in DBS "off" and "on" conditions in 32 PD patients with STN-DBS. Pre-processed data were reconstructed into the source space and the time-frequency analysis was evaluated. We identified a subgroup of six patients with longer reaction times (RT) during the DBS "on" state than in the DBS "off" state after target stimuli. These subjects had lower motor responsiveness to DBS and decreased memory test results compared to the other subjects. Moreover, the alpha and beta power decrease (event-related desynchronizations, ERD), known as an activation correlate linked to motor and cognitive processing, was also reduced in the DBS "on" condition in these patients. A subgroup of PD patients with a suboptimal response to STN-DBS was identified. Evaluation of RT could potentially serve as a biomarker for responsiveness to STN-DBS.

Cognitive task-related functional connectivity alterations in temporal lobe epilepsy.

OBJECTIVE: We investigated cognitive task-related functional connectivity (FC) in patients with temporal lobe epilepsy (TLE). Using a visual three-stimulus paradigm (VTSP), we studied cognitive large-scale networks and the impact of TLE on connectivity outside the temporal lobe. METHODS: High-density electroencephalography (EEG) was recorded during the paradigm from nineteen patients with epilepsy with hippocampal sclerosis (HS) and ten healthy controls (HCs). Scalp data were reconstructed into the source space, and FC was computed. Correlating with the neuropsychological data, possible compensatory mechanisms were investigated. RESULTS: Significant changes were found in the FC of regions outside the epileptogenic network, particularly in the attentional network. These changes were more widespread in left TLE (LTLE). There were no significant differences in task performance (accuracy, time response) in comparison with HCs, implying that there must be some mechanism reducing the impact of connectivity changes on brain functions. When correlated with neuropsychological data, we found stronger compensatory mechanisms in right TLE (RTLE). SIGNIFICANCE: Our findings confirm the hypothesis that LTLE is the more pervasive form of the disease. Even though the network alterations in TLE are severe, some mechanisms reduce the impact of epilepsy on cognitive functions; these mechanisms are more potent in RTLE. We also suggest that there are maladaptive mechanisms in LTLE.

NREM sleep is the state of vigilance that best identifies the epileptogenic zone in the interictal electroencephalogram.

OBJECTIVE: Interictal epileptiform anomalies such as epileptiform discharges or high-frequency oscillations show marked variations across the sleep-wake cycle. This study investigates which state of vigilance is the best to localize the epileptogenic zone (EZ) in interictal intracranial electroencephalography (EEG). METHODS: Thirty patients with drug-resistant epilepsy undergoing stereo-EEG (SEEG)/sleep recording and subsequent open surgery were included; 13 patients (43.3%) had good surgical outcome (Engel class I). Sleep was scored following standard criteria. Multiple features based on the interictal EEG (interictal epileptiform discharges, high-frequency oscillations, univariate and bivariate features) were used to train a support vector machine (SVM) model to classify SEEG contacts placed in the EZ. The performance of the algorithm was evaluated by the mean area under the receiver-operating characteristic (ROC) curves (AUCs) and positive predictive values (PPVs) across 10-minute sections of wake, non-rapid eye movement sleep (NREM) stages N2 and N3, REM sleep, and their combination. RESULTS: Highest AUCs were achieved in NREM sleep stages N2 and N3 compared to wakefulness and REM (P < .01). There was no improvement when using a combination of all four states (P > .05); the best performing features in the combined state were selected from NREM sleep. There were differences between good (Engel I) and poor (Engel II-IV) outcomes in PPV (P < .05) and AUC (P < .01) across all states. The SVM multifeature approach outperformed spikes and high-frequency oscillations (P < .01) and resulted in results similar to those of the seizure-onset zone (SOZ; P > .05). SIGNIFICANCE: Sleep improves the localization of the EZ with best identification obtained in NREM sleep stages N2 and N3. Results based on the multifeature classification in 10 minutes of NREM sleep were not different from the results achieved by the SOZ based on 12.7 days of seizure monitoring. This finding might ultimately result in a more time-efficient intracranial presurgical investigation of focal epilepsy.

Very high-frequency oscillations: Novel biomarkers of the epileptogenic zone.

OBJECTIVE: In the present study, we aimed to investigate depth electroencephalographic (EEG) recordings in a large cohort of patients with drug-resistant epilepsy and to focus on interictal very high-frequency oscillations (VHFOs) between 500Hz and 2kHz. We hypothesized that interictal VHFOs are more specific biomarkers for epileptogenic zone compared to traditional HFOs. METHODS: Forty patients with focal epilepsy who underwent presurgical stereo-EEG (SEEG) were included in the study. SEEG data were recorded with a sampling rate of 25kHz, and a 30-minute resting period was analyzed for each patient. Ten patients met selected criteria for analyses of correlations with surgical outcome: detection of interictal ripples (Rs), fast ripples (FRs), and VHFOs; resective surgery; and at least 1 year of postoperative follow-up. Using power envelope computation and visual inspection of power distribution matrixes, electrode contacts with HFOs and VHFOs were detected and analyzed. RESULTS: Interictal very fast ripples (VFRs; 500-1,000Hz) were detected in 23 of 40 patients and ultrafast ripples (UFRs; 1,000-2,000Hz) in almost half of investigated subjects (n = 19). VFRs and UFRs were observed only in patients with temporal lobe epilepsy and were recorded exclusively from mesiotemporal structures. The UFRs were more spatially restricted in the brain than lower-frequency HFOs. When compared to R oscillations, significantly better outcomes were observed in patients with a higher percentage of removed contacts containing FRs, VFRs, and UFRs. INTERPRETATION: Interictal VHFOs are relatively frequent abnormal phenomena in patients with epilepsy, and appear to be more specific biomarkers for epileptogenic zone when compared to traditional HFOs. Ann Neurol 2017;82:299-310.

Dominance-diversity relationships in ant communities differ with invasion.

The relationship between levels of dominance and species richness is highly contentious, especially in ant communities. The dominance-impoverishment rule states that high levels of dominance only occur in species-poor communities, but there appear to be many cases of high levels of dominance in highly diverse communities. The extent to which dominant species limit local richness through competitive exclusion remains unclear, but such exclusion appears more apparent for non-native rather than native dominant species. Here we perform the first global analysis of the relationship between behavioral dominance and species richness. We used data from 1,293 local assemblages of ground-dwelling ants distributed across five continents to document the generality of the dominance-impoverishment rule, and to identify the biotic and abiotic conditions under which it does and does not apply. We found that the behavioral dominance-diversity relationship varies greatly, and depends on whether dominant species are native or non-native, whether dominance is considered as occurrence or relative abundance, and on variation in mean annual temperature. There were declines in diversity with increasing dominance in invaded communities, but diversity increased with increasing dominance in native communities. These patterns occur along the global temperature gradient. However, positive and negative relationships are strongest in the hottest sites. We also found that climate regulates the degree of behavioral dominance, but differently from how it shapes species richness. Our findings imply that, despite strong competitive interactions among ants, competitive exclusion is not a major driver of local richness in native ant communities. Although the dominance-impoverishment rule applies to invaded communities, we propose an alternative dominance-diversification rule for native communities.

Network reorganization and breakdown of an ant-plant protection mutualism with elevation.

Both the abiotic environment and the composition of animal and plant communities change with elevation. For mutualistic species, these changes are expected to result in altered partner availability, and shifts in context-dependent benefits for partners. To test these predictions, we assessed the network structure of terrestrial ant-plant mutualists and how the benefits to plants of ant inhabitation changed with elevation in tropical forest in Papua New Guinea. At higher elevations, ant-plants were rarer, species richness of both ants and plants decreased, and the average ant or plant species interacted with fewer partners. However, networks became increasingly connected and less specialized, more than could be accounted for by reductions in ant-plant abundance. On the most common ant-plant, ants recruited less and spent less time attacking a surrogate herbivore at higher elevations, and herbivory damage increased. These changes were driven by turnover of ant species rather than by within-species shifts in protective behaviour. We speculate that reduced partner availability at higher elevations results in less specialized networks, while lower temperatures mean that even for ant-inhabited plants, benefits are reduced. Under increased abiotic stress, mutualistic networks can break down, owing to a combination of lower population sizes, and a reduction in context-dependent mutualistic benefits.

A global database of ant species abundances.

What forces structure ecological assemblages? A key limitation to general insights about assemblage structure is the availability of data that are collected at a small spatial grain (local assemblages) and a large spatial extent (global coverage). Here, we present published and unpublished data from 51 ,388 ant abundance and occurrence records of more than 2,693 species and 7,953 morphospecies from local assemblages collected at 4,212 locations around the world. Ants were selected because they are diverse and abundant globally, comprise a large fraction of animal biomass in most terrestrial communities, and are key contributors to a range of ecosystem functions. Data were collected between 1949 and 2014, and include, for each geo-referenced sampling site, both the identity of the ants collected and details of sampling design, habitat type, and degree of disturbance. The aim of compiling this data set was to provide comprehensive species abundance data in order to test relationships between assemblage structure and environmental and biogeographic factors. Data were collected using a variety of standardized methods, such as pitfall and Winkler traps, and will be valuable for studies investigating large-scale forces structuring local assemblages. Understanding such relationships is particularly critical under current rates of global change. We encourage authors holding additional data on systematically collected ant assemblages, especially those in dry and cold, and remote areas, to contact us and contribute their data to this growing data set.

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.