Spatial Null Models Research Articles

Addressing spatial bias in intracranial EEG functional connectivity analyses for epilepsy surgical planning

Objective. To determine the effect of epilepsy on intracranial electroencephalography (EEG) functional connectivity, and the ability of functional connectivity to localize the seizure onset zone (SOZ), controlling for spatial biases. Approach. We analyzed intracranial EEG data from patients with drug-resistant epilepsy admitted for pre-surgical planning. We calculated intracranial EEG functional networks and determined whether changes in functional connectivity lateralized the SOZ using a spatial subsampling method to control for spatial bias. We developed a ‘spatial null model’ to localize the SOZ electrode using only spatial sampling information, ignoring EEG data. We compared the performance of this spatial null model against models incorporating EEG functional connectivity and interictal spike rates. Main results. About 110 patients were included in the study, although the number of patients differed across analyses. Controlling for spatial sampling, the average connectivity was lower in the SOZ region relative to the same anatomic region in the contralateral hemisphere. A model using intra-hemispheric connectivity accurately lateralized the SOZ (average accuracy 75.5%). A spatial null model incorporating spatial sampling information alone achieved moderate accuracy in classifying SOZ electrodes (mean AUC = 0.70, 95% CI 0.63–0.77). A model incorporating intracranial EEG functional connectivity and spike rate data further outperformed this spatial null model (AUC 0.78, p = 0.002 compared to spatial null model). However, a model incorporating functional connectivity without spike rate data did not significantly outperform the null model (AUC 0.72, p = 0.38). Significance. Intracranial EEG functional connectivity is reduced in the SOZ region, and interictal data predict SOZ electrode localization and laterality, however a predictive model incorporating functional connectivity without interictal spike rates did not significantly outperform a spatial null model. We propose constructing a spatial null model to provide an estimate of the pre-implant hypothesis of the SOZ, and to serve as a benchmark for further machine learning algorithms in order to avoid overestimating model performance because of electrode sampling alone.

Rethinking the complexity and uncertainty of spatial networks applied to forest ecology

Characterizing tree spatial patterns and interactions are helpful to reveal underlying processes assembling forest communities. Spatial networks, despite their complexity, are powerful to examine spatial interactions at an individual level using well-defined patterns. However, complex forestation networks introduce uncertainties. Validation methods are needed to assess whether network-based metrics can identify different processes. Here, we constructed three types of networks, which reflect various aspects of tree competition. Based on five spatial null models and 199 Monte-Carlo simulations, we were able to select network-based metrics that exhibited well performance in distinguishing different processes. This technique was then applied to a tropical forest dataset in Costa Rica. We found that the average node degree and the clustering coefficient are good metrics like the paired correlation function. In addition, the network approach can identify fine-scale spatial variations of tree competition and its underlying causes. Our analyzes also indicate that a bit of caution is needed when defining the network structure as well as designing network-based metrics. We suggested that validation techniques using corresponding spatial null models are critically important to reduce the negative effects caused by uncertainties of the network.

Unmasking the perching effect of the pioneer Mediterranean dwarf palm Chamaerops humilis L.

Although farmlands are the most extensive terrestrial biomes, the abandonment of traditional agriculture in many parts of the world has brought opportunities and challenges for the restoration of such human-disturbed habitats. Seed arrival is a crucial necessary ecological process during plant recolonization that can be enhanced by the use of the so-called "perch plants". Little is known, however, about whether the seed arrival via frugivorous birds is affected by the spatial distribution of the perch plants in disturbed habitats. To evaluate several spatial aspects of "perching" effect, we used a spatially explicit approach in two disturbed plots within the Doñana National Park (SW Spain). Specifically, we chose as study system the pioneer Mediterranean dwarf palm Chamaerops humilis L., which is often used as a perch by a variety of frugivorous bird species. A total of 289 C. humilis individuals were sampled in search of bird feces (N = 2998) and dispersed seeds (N = 529). Recorded seeds belonged to six different woody species from five different families. Nine bird species from six different families were recorded using C. humilis as perches. GLMs analyses indicated that taller C. humilis males with higher numbers of spatially associated woody species received more dispersed seeds. We detected a random spatial structure of bird feces and dispersed seeds in one study plot, while a nonrandom spatial structure was found in the other one, where isolated C. humilis received a higher number of bird feces and dispersed seeds than expected under spatial null models. The difference in spatial patterns between both study plots could relate, among other factors, to their different state of development in the ecological succession. Most of dispersed seeds were concentrated in a small number of C. humilis individuals, usually male and large ones, that acted as "hotspots" of seed arrival. The fact that frugivorous birds in one study site visited most often isolated C. humilis questions the aggregated spatial structure of revegetation designs typically used in restoration projects. This study reveals novel spatial aspects of the "perching" effect which could be helpful in the restoration of human-disturbed habitats worldwide.

A simple permutation-based test of intermodal correspondence.

Many key findings in neuroimaging studies involve similarities between brain maps, but statistical methods used to measure these findings have varied. Current state‐of‐the‐art methods involve comparing observed group‐level brain maps (after averaging intensities at each image location across multiple subjects) against spatial null models of these group‐level maps. However, these methods typically make strong and potentially unrealistic statistical assumptions, such as covariance stationarity. To address these issues, in this article we propose using subject‐level data and a classical permutation testing framework to test and assess similarities between brain maps. Our method is comparable to traditional permutation tests in that it involves randomly permuting subjects to generate a null distribution of intermodal correspondence statistics, which we compare to an observed statistic to estimate a p‐value. We apply and compare our method in simulated and real neuroimaging data from the Philadelphia Neurodevelopmental Cohort. We show that our method performs well for detecting relationships between modalities known to be strongly related (cortical thickness and sulcal depth), and it is conservative when an association would not be expected (cortical thickness and activation on the n‐back working memory task). Notably, our method is the most flexible and reliable for localizing intermodal relationships within subregions of the brain and allows for generalizable statistical inference.

Comparing spatial null models for brain maps

Technological and data sharing advances have led to a proliferation of high-resolution structural and functional maps of the brain. Modern neuroimaging research increasingly depends on identifying correspondences between the topographies of these maps; however, most standard methods for statistical inference fail to account for their spatial properties. Recently, multiple methods have been developed to generate null distributions that preserve the spatial autocorrelation of brain maps and yield more accurate statistical estimates. Here, we comprehensively assess the performance of ten published null frameworks in statistical analyses of neuroimaging data. To test the efficacy of these frameworks in situations with a known ground truth, we first apply them to a series of controlled simulations and examine the impact of data resolution and spatial autocorrelation on their family-wise error rates. Next, we use each framework with two empirical neuroimaging datasets, investigating their performance when testing (1) the correspondence between brain maps (e.g., correlating two activation maps) and (2) the spatial distribution of a feature within a partition (e.g., quantifying the specificity of an activation map within an intrinsic functional network). Finally, we investigate how differences in the implementation of these null models may impact their performance. In agreement with previous reports, we find that naive null models that do not preserve spatial autocorrelation consistently yield elevated false positive rates and unrealistically liberal statistical estimates. While spatially-constrained null models yielded more realistic, conservative estimates, even these frameworks suffer from inflated false positive rates and variable performance across analyses. Throughout our results, we observe minimal impact of parcellation and resolution on null model performance. Altogether, our findings highlight the need for continued development of statistically-rigorous methods for comparing brain maps. The present report provides a harmonised framework for benchmarking and comparing future advancements.

Null models for community dynamics: Beware of the cyclic shift algorithm

AbstractAimTemporal patterns of community dynamics are drawing increasing interest due to their potential to shed light on assembly processes and anthropogenic effects. However, interpreting such patterns considerably benefits from comparing observed dynamics to the reference of a null model. For that aim, the cyclic shift permutations algorithm, which generates randomized null communities based on empirically observed time series, has recently been proposed. This algorithm, borrowed from the spatial analysis literature, shifts each species time series randomly in time, and this is claimed to preserve the temporal autocorrelation of single species. Hence it has been used to test the significance of various community patterns, in particular excessive compositional changes, biodiversity trends and community stability.InnovationHere I critically study the properties of the cyclic shift algorithm for the first time. I show that, unlike previously suggested, this algorithm does not preserve temporal autocorrelation due to the need to ‘wrap’ the time series and assign the last observations to the first years. Moreover, this algorithm scrambles the initial state of the community, making any dynamics that result from deviations from equilibrium seem excessive. I exemplify that these two issues lead to a highly elevated type I error rate in tests for excessive compositional changes and richness trends.ConclusionsCaution is needed when using the cyclic shift permutation algorithm and interpreting results obtained using it. Interpretation is further complicated because the algorithm removes all correlations between species. I suggest guidelines for using this method and discuss several possible alternative approaches. The non‐preservation of autocorrelation also raises questions regarding the use of the analogous spatial null model, the torus‐translation.

Spatial autocorrelation inflates niche breadth–range size relationships

AbstractAimSpecies with broader environmental tolerances are expected to be more widely distributed than specialist species, implying a positive correlation between niche breadth and geographic range size. When this relationship is evaluated using data derived from broad‐scale geographic distributions of species, spatial autocorrelation of species distribution data and environments may inflate niche breadth–range size relationships, bringing into question the causal relationship between environmental tolerance and range size. Using null models, we quantify the contribution of spatial autocorrelation to the frequently reported relationship between species’ range size and niche breadth.LocationSouth Africa.Time periodCurrent.Major taxa studiedEighty species in the genus Pelargonium.MethodsUsing phylogenetic least squares regression, we examined the extent to which variation in range size of Pelargonium species is related to temperature and precipitation niche breadths. We developed null models that randomized the spatial distribution of the climatic variables, but retained their broad spatial autocorrelation structure. We tested whether observed niche breadth–range size relationships were stronger than expected, given spatial autocorrelation of climatic variables.ResultsWe found the expected positive relationships between measures of niche breadth and range size, but these were no stronger than expected based on our spatial null models. Including spatial structure in simulations reduced expected niche breadths compared to simulations based on fully randomized environmental variables, resulting in steeper slopes for the simulated niche breadth–range size relationships.Main conclusionOur results indicate that spatial autocorrelation may positively bias niche breadth–range size relationships. This bias suggests that previously reported relationships between range size and niche breadth based on broad‐scale distributional data may be, at least in part, artefactual. Future studies need to explicitly account for spatial autocorrelation, and inferences on the role of environmental tolerance in driving patterns of species range size variation should be derived in conjunction with laboratory and field‐based experiments.

DASSCAN: A Density and Adjacency Expansion-Based Spatial Structural Community Detection Algorithm for Networks

Existing spatial community detection algorithms are usually modularity based. Motivated by different applications, these algorithms build appropriate spatial null models to describe spatial effects on the connection of nodes. Then, by choosing certain modularity maximizing strategies, they try to find interesting community structures hidden behind the null models. In this paper, a novel structural similarity-based spatial network community is defined, which is based on the shared neighbors of nodes. In addition, there are two other special node roles defined: the spatial hub and outlier. Then, a density and adjacency expansion-based spatial structural community detection algorithm for networks (DASSCAN) is proposed for mining these communities, hubs and outliers. DASSCAN uses structural similarity to measure the relationship between nodes, and then, structurally similar and spatially adjacent nodes are merged into communities using a density-based clustering method and spatial adjacency expansion strategy. Comparative experiments on two kinds of Chinese train line networks clarified the accuracy and efficiency of DASSCAN in finding the spatial structural communities, spatial hubs and outliers. The communities found can be used to uncover more interesting spatial structural patterns, and the hubs and outliers are more accurate and have more valuable meanings.

Elevational patterns of non‐volant small mammal species richness in Gyirong Valley, Central Himalaya: Evaluating multiple spatial and environmental drivers

AbstractAimDocumenting the elevational species richness patterns of non‐volant small mammals and assessing the roles of pure spatial factors and spatial structured environmental factors in shaping the elevational richness patterns.LocationGyirong Valley in the Mount Qomolangma National Nature Reserve, located in the southern Himalayas, China.MethodsField surveys were conducted at each of twelve 300‐m elevational bands along a gradient from 1,800 to 5,400 m above sea level (a.s.l). For the pure spatial variables, we calculated area and the spatial null model named MDE (cf. below). For spatial structured environmental variables, we calculated mean annual temperature, mean annual precipitation, mean annual temperature range, potential evapotranspiration (PET), the normalized difference vegetation index, plant species richness and habitat heterogeneity. Multivariate models of species richness against eight factors (excluding PET) for different species groups were used to test the explanatory power of both the spatial structured environmental variables and the pure spatial variables. In addition, mean annual precipitation and potential evapotranspiration were used to test the water–energy dynamics model for each species groups.ResultsSeven hundred and fifty‐five individuals of 22 species were documented over 21,600 trap nights. The elevational species richness pattern for all non‐volant small mammals was hump‐shaped with the highest richness occurring at 2,700–3,300 m a.s.l. Endemic and non‐endemic species as well as two elevational range size categories of small mammals also generally showed hump‐shaped species richness patterns. In most data sets, spatial structured environmental variables played more important roles than the pure spatial variables in shaping the elevational species richness patterns than the pure spatial factors, while the MDE contributed to richness patterns for large‐ranged species. The water–energy dynamics model explained 66% of the variation in all the non‐volant small mammals, 56% for endemic species, 88% for the non‐endemic species, 59% for the large‐ranged species, and 53% for the small‐ranged species.Main conclusionsAlthough no single key factor can explain all species richness patterns, we found that spatial structured environmental variables correlate well with the elevational species richness pattern of non‐volant small mammals. The water–energy dynamics model was found to explain non‐volant small mammal species richness along the Gyirong Valley.

Nematode distributions as spatial null models for macroinvertebrate species richness across environmental gradients: A case from mountain lakes.

Nematode species are widely tolerant of environmental conditions and disperse passively. Therefore, the species richness distribution in this group might largely depend on the topological distribution of the habitats and main aerial and aquatic dispersal pathways connecting them. If so, the nematode species richness distributions may serve as null models for evaluating that of other groups more affected by environmental gradients. We investigated this hypothesis in lakes across an altitudinal gradient in the Pyrenees. We compared the altitudinal distribution, environmental tolerance, and species richness, of nematodes with that of three other invertebrate groups collected during the same sampling: oligochaetes, chironomids, and nonchironomid insects. We tested the altitudinal bias in distributions with t‐tests and the significance of narrow‐ranging altitudinal distributions with randomizations. We compared results between groups with Fisher's exact tests. We then explored the influence of environmental factors on species assemblages in all groups with redundancy analysis (RDA), using 28 environmental variables. And, finally, we analyzed species richness patterns across altitude with simple linear and quadratic regressions. Nematode species were rarely biased from random distributions (5% of species) in contrast with other groups (35%, 47%, and 50%, respectively). The altitudinal bias most often shifted toward low altitudes (85% of biased species). Nematodes showed a lower portion of narrow‐ranging species than any other group, and differed significantly from nonchironomid insects (10% and 43%, respectively). Environmental variables barely explained nematode assemblages (RDA adjusted R2 = 0.02), in contrast with other groups (0.13, 0.19 and 0.24). Despite these substantial differences in the response to environmental factors, species richness across altitude was unimodal, peaking at mid elevations, in all groups. This similarity indicates that the spatial distribution of lakes across altitude is a primary driver of invertebrate richness. Provided that nematodes are ubiquitous, their distribution offers potential null models to investigate species richness across environmental gradients in other ecosystem types and biogeographic regions.

Determination of the complexity of distance weights in Mexican city systems.

This study tests distance weights based on the economic geography assumption of straight lines and the complex networks approach of empirical road segments in the Mexican system of cities to determine the best distance specification. We generated network graphs by using geospatial data and computed weights by measuring shortest paths, thereby characterizing their probability distributions and comparing them with spatial null models. Findings show that distributions are sufficiently different and are associated with asymmetrical beta distributions. Straight lines over- and underestimated distances compared to the empirical data, and they showed compatibility with random models. Therefore, accurate distance weights depend on the type of the network specification.

Null models for community detection in spatially embedded, temporal networks

In the study of networks, it is often insightful to use algorithms to determine mesoscale features such as ‘community structure’, in which densely connected sets of nodes constitute ‘communities’ that have sparse connections to other communities. The most popular way of detecting communities algorithmically is to maximize the quality function known as modularity. When maximizing modularity, one compares the actual connections in a (static or time-dependent) network to the connections obtained from a random-graph ensemble that acts as a null model. The communities are then the sets of nodes that are connected to each other densely relative to what is expected from the null model. Clearly, the process of community detection depends fundamentally on the choice of the null model, so it is important to develop and analyse novel null models that take into account appropriate features of the system under study. In this paper, we investigate the effects of using null models that incorporate spatial information, and we propose a novel null model based on the radiation model of population spread. We also develop novel synthetic spatial benchmark networks in which the connections between entities are based on the distance or flux between nodes, and we compare the performance of static and time-dependent versions of the radiation null model to the standard (‘Newman–Girvan’) null model for modularity optimization and to a recently proposed gravity null model. In our comparisons, we use both the above synthetic benchmarks and time-dependent correlation networks that we construct using countrywide dengue fever incidence data for Peru. Our findings illustrate the need to use appropriate generative models for the development of spatial null models for community detection.

Performance of LAI‐MODIS and the influence on drought simulation in a Mediterranean forest

ABSTRACTThis study investigates the benefits and methodological issues to integrate weekly 1 km Leaf Area Index (LAI) Moderate Resolution Imaging Spectroradiometer (LAI‐MODIS) (MOD15A2) satellite product in a distributed water budget model over a Mediterranean forested ecosystem of about 2553 km2 for drought assessment at regional scale. The high overestimation of LAI‐MODIS compared to field measurements was corrected based on the calibration of high‐resolution Satellites Pour l'Observation de la Terre (SPOT) images combined with ground measurements. The LAI‐MODIS time series over the 2003 to 2009 period has been calibrated and integrated into a spatially explicit water budget model at the regional level using spatial information on vegetation, soil types and topoclimates. Actual LAI‐MODIS scenario was tested against temporal and spatial null models to assess for the benefits of the regional heterogeneity from MODIS and its intra‐annual and interannual variation in a water budget model. From water budget analyses at local and regional scales, we concluded that calibration of LAI‐MODIS images was mandatory to enhance the correlation coefficient between measured and simulated daily actual transpiration. We estimated daily bias in the resulting ‘Water Stress Index’ to be slightly affected between constant and seasonally‐varying LAI datasets. However, the interannual variability in LAI detected by MODIS followed LAI adjustments expected from the ecohydrological equilibrium hypothesis. This can significantly affect the simulated annual drought period features, so that integrating LAI‐MODIS spatial and temporal variability into water budget models for evergreen Mediterranean vegetation can be a useful dataset when carbon allocation schemes in dynamic vegetation models are lacking, but should be carefully calibrated particularly in transitions towards semi‐arid zones. Copyright © 2013 John Wiley & Sons, Ltd.

A nonlinear, low data requirement model for producing spatially explicit fishery forecasts

AbstractSpatial variability can confound accurate estimates of catch per unit effort (CPUE), especially in highly migratory species. The incorporation of spatial structure into fishery stock assessment models should ultimately improve forecasts of stock biomass. Here, we describe a nonlinear time series model for producing spatially explicit forecasts of CPUE that does not require ancillary environmental or demographic data, or specification of a model functional form. We demonstrate this method using spatially resolved (1° × 1° cells) CPUE time series of North Pacific albacore in the California Current System. The spatial model is highly significant (P < 0.00001) and outperforms two spatial null models. We then create a spatial forecast map for years beyond the range of data. Such approaches can guide spatial management of resources and provide a complement to more data‐intensive, highly parameterized population dynamics and ecosystem models currently in use.

Niche breadth and range area in North American trees

Identifying factors affecting species distribution is a longstanding goal in ecology and evolution that is accentuated by our need to anticipate climate change impacts. We sought to test whether any phylogenetic effect can be detected in either the environmental characteristics or range attributes of North American trees, and to explore the existence of a general interspecific pattern in the environmental factors influencing species range size. To do so we tested prevailing hypotheses relating climatic and edaphic characteristics to species range size in the North American arboflora (n = 598), using spatial null models to test for the relevance of observed patterns. We found that interspecific variation in the range area of North American trees is strongly related to the environmental regimes characteristic of the species range. Linear models and phylogenetic regressions involving six environmental characteristics explained 83% of the variance in species range area, and affirmed a positive relationship between niche breadth and range size. Tree species that can tolerate a larger variability in local climatic conditions, deal with harsher edaphic conditions, and weak levels of environmental energy tend to have larger range area; this can account for the greater geographic range of species at higher latitudes, the Rapoport effect. There is a significant phylogenetic signal for both range area and limits in North American trees, and for climatic limits, but not for energy or edaphic characteristics associated with species range. These findings highlight the possibility that species with small geographic ranges may be more sensitive to the effects of climate change.

Disentangling facilitation and seed dispersal from environmental heterogeneity as mechanisms generating associations between savanna plants

Question: How can we disentangle facilitation and seed dispersal from environmental heterogeneity as mechanisms causing spatial associations of plant species? Location: Semi-arid savanna in the Kimberley Thorn Bushveld, South Africa. Methods: We developed a two-step protocol for the statistical differentiation of association-promoting mechanisms in plants based on the Acacia erioloba–Grewia flava association. Individuals of the savanna shrub G. flava and the tree A. erioloba were mapped on four study plots. Disentangling the mechanism causing the association of G. flava and A. erioloba involved tests of three spatial and one non-spatial null model. The spatial null models include homogeneous and heterogeneous Poisson processes for spatial randomness based on the bivariate spatial point patterns of the four plots. With the non-spatial analysis, we determined the relationship between the canopy diameter of A. erioloba trees and presence or absence of G. flava shrubs in the tree understorey to find whether shrub presence requires a minimum tree canopy diameter. Results: We first showed a significant positive spatial association of the two species. Thereafter, the non-spatial analysis supported an exclusion of environmental heterogeneity as the sole cause of this positive association. We found a minimum tree size under which no G. flava shrubs occurred. Conclusions: Our two-step analysis showed that it is unlikely that heterogeneous environmental conditions caused the spatial association of A. erioloba and G. flava. Instead, this association may have been caused by seed dispersal and/or facilitation (e.g. caused by hydraulic lift and/or nitrogen fixation by the host tree).

Identifying significant scale-specific spatial boundaries using wavelets and null models: spruce budworm defoliation in Ontario, Canada as a case study

We combine wavelet analysis and multiple null models to identify significant spatial scales of pattern and spatial boundaries in historical spruce budworm defoliation in Ontario, Canada. Previous analyses of budworm defoliation in Ontario over the last two outbreaks have suggested three distinct zones of defoliation. We asked the following three questions: (1) is there statistical support for the existence of these three zones? (2) Are the locations of these boundaries consistent between outbreak periods? And (3) how does boundary identification depend on the spatial null model used? Defoliation data for the two outbreak periods (1941–1965 and 1966–2001), and the combined period (1941–2001) were analyzed using a 1D continuous wavelet transform. Boundaries were identified through comparison of wavelet power spectra of each outbreak period to reference distributions based on three different spatial null models: (1) a complete spatial randomness model, (2) an autoregressive model, and (3) a Gaussian random field model. The Gaussian random field model identified coarser scales of pattern than the autoregressive model. Locally, the Gaussian random field model found significant boundaries similar to those previously described, whereas the autoregressive model only did so for the first outbreak. These results indicate that the coarse scale spatial factors that influenced defoliation were more consistent between outbreaks relative to fine scale factors, and that previously described boundaries were strongly driven by the first outbreak. Wavelet analysis combined with spatial null models provides a powerful tool for identifying non-arbitrary scales of structure and significant spatial boundaries in non-stationary ecological data.