Modeling the Spatial and Temporal Dependence in fMRI Data

Summary Functional magnetic resonance imaging (fMRI) data sets are large and characterized by complex dependence structures driven by highly sophisticated neurophysiology and aspects of the experimental designs. Typical analyses investigating task‐related changes in measured brain activity use a two‐stage procedure in which the first stage involves subject‐specific models and the second‐stage specifies group (or population) level parameters. Customarily, the first‐level accounts for temporal correlations between the serial scans acquired during one scanning session. Despite accounting for these correlations, fMRI studies often include multiple sessions and temporal dependencies may persist between the corresponding estimates of mean neural activity. Further, spatial correlations between brain activity measurements in different locations are often unaccounted for in statistical modeling and estimation. We propose a two‐stage, spatio‐temporal, autoregressive model that simultaneously accounts for spatial dependencies between voxels within the same anatomical region and for temporal dependencies between a subject's estimates from multiple sessions. We develop an algorithm that leverages the special structure of our covariance model, enabling relatively fast and efficient estimation. Using our proposed method, we analyze fMRI data from a study of inhibitory control in cocaine addicts.     

A Method of Moments Estimator for Random Effect Multivariate Meta‐Analysis

Summary Meta‐analysis is a powerful approach to combine evidence from multiple studies to make inference about one or more parameters of interest, such as regression coefficients. The validity of the fixed effect model meta‐analysis depends on the underlying assumption that all studies in the meta‐analysis share the same effect size. In the presence of heterogeneity, the fixed effect model incorrectly ignores the between‐study variance and may yield false positive results. The random effect model takes into account both within‐study and between‐study variances. It is more conservative than the fixed effect model and should be favored in the presence of heterogeneity. In this paper, we develop a noniterative method of moments estimator for the between‐study covariance matrix in the random effect model multivariate meta‐analysis. To our knowledge, it is the first such method of moments estimator in the matrix form. We show that our estimator is a multivariate extension of DerSimonian and Laird’s univariate method of moments estimator, and it is invariant to linear transformations. In the simulation study, our method performs well when compared to existing random effect model multivariate meta‐analysis approaches. We also apply our method in the analysis of a real data example.     

The stability of the G‐matrix: The role of spatial heterogeneity

The temporal stability of the genetic variance‐covariance matrix ( G ) has been discussed for a long time in the evolutionary literature. A common assumption in all studies, including empirical ones, is that spatial heterogeneity is minor such that the population can be represented by a single mean and variance. We use the well‐established allocation‐acquisition model to analyze the effect of relaxing of this assumption, simulating a case where the population is divided into patches with a variance in quality between patches. This variance can in turn differ between years. We found that changes in spatial variance in patch quality over years can make the G ‐matrix vary substantially over years and that the estimated genetic correlations, evolvability, and response to selection are different dependent on whether spatial heterogeneity is taken into account or not. This will have profound implications for our ability to predict evolutionary change and understanding of the evolutionary process.     

Spatio‐temporal Modelling of Weeds by Shot‐noise G Cox processes

Tractable space‐time point processes models are needed in various fields. For example in weed science for gaining biological knowledge, for prediction of weed development in order to optimize local treatments with herbicides or in epidemiology for prediction of the risk of a disease. Motivated by the spatio‐temporal point patterns for two weed species, we propose a spatio‐temporal Cox model with intensity based on gamma random fields. The model is an extension of Neyman–Scott and shot‐noise Cox processes to the space‐time domain and it allows spatial and temporal inhomogeneity. We use the weed example to give a first intuitive interpretation of the model and then show how the model is constructed more rigorously and how to estimate the parameters. The weed data are analysed using the proposed model, and both spatially and temporally the model shows a good fit to the data using classical goodness‐of‐fit tests.     

Spatio‐temporal variation in European starling reproductive success at multiple small spatial scales

Understanding population dynamics requires spatio‐temporal variation in demography to be measured across appropriate spatial and temporal scales. However, the most appropriate spatial scale(s) may not be obvious, few datasets cover sufficient time periods, and key demographic rates are often incompletely measured. Consequently, it is often assumed that demography will be spatially homogeneous within populations that lack obvious subdivision. Here, we quantify small‐scale spatial and temporal variation in a key demographic rate, reproductive success (RS), within an apparently contiguous population of European starlings. We used hierarchical cluster analysis to define spatial clusters of nest sites at multiple small spatial scales and long‐term data to test the hypothesis that small‐scale spatio‐temporal variation in RS occurred. RS was measured as the number of chicks alive ca. 12 days posthatch either per first brood or per nest site per breeding season (thereby incorporating multiple breeding attempts). First brood RS varied substantially among spatial clusters and years. Furthermore, the pattern of spatial variation was stable across years; some nest clusters consistently produced more chicks than others. Total seasonal RS also varied substantially among spatial clusters and years. However, the magnitude of variation was much larger and the pattern of spatial variation was no longer temporally consistent. Furthermore, the estimated magnitude of spatial variation in RS was greater at smaller spatial scales. We thereby demonstrate substantial spatial, temporal, and spatio‐temporal variation in RS occurring at very small spatial scales. We show that the estimated magnitude of this variation depended on spatial scale and that spatio‐temporal variation would not have been detected if season‐long RS had not been measured. Such small‐scale spatio‐temporal variation should be incorporated into empirical and theoretical treatments of population dynamics.     

Understanding species distribution in dynamic populations: a new approach using spatio‐temporal point process models

Understanding and predicting a species’ distribution across a landscape is of central importance in ecology, biogeography and conservation biology. However, it presents daunting challenges when populations are highly dynamic (i.e. increasing or decreasing their ranges), particularly for small populations where information about ecology and life history traits is lacking. Currently, many modelling approaches fail to distinguish whether a site is unoccupied because the available habitat is unsuitable or because a species expanding its range has not arrived at the site yet. As a result, habitat that is indeed suitable may appear unsuitable. To overcome some of these limitations, we use a statistical modelling approach based on spatio‐temporal log‐Gaussian Cox processes. These model the spatial distribution of the species across available habitat and how this distribution changes over time, relative to covariates. In addition, the model explicitly accounts for spatio‐temporal dynamics that are unaccounted for by covariates through a spatio‐temporal stochastic process. We illustrate the approach by predicting the distribution of a recently established population of Eurasian cranes Grus grus in England, UK, and estimate the effect of a reintroduction in the range expansion of the population. Our models show that wetland extent and perimeter‐to‐area ratio have a positive and negative effect, respectively, in crane colonisation probability. Moreover, we find that cranes are more likely to colonise areas near already occupied wetlands and that the colonisation process is progressing at a low rate. Finally, the reintroduction of cranes in SW England can be considered a human‐assisted long‐distance dispersal event that has increased the dispersal potential of the species along a longitudinal axis in S England. Spatio‐temporal log‐Gaussian Cox process models offer an excellent opportunity for the study of species where information on life history traits is lacking, since these are represented through the spatio‐temporal dynamics reflected in the model.     

Spatio-temporal modeling of localized brain activity

Functional neuroimaging, including positron emission tomography (PET) and functional magnetic resonance imaging (fMRI), plays an important role in identifying specific brain regions associated with experimental stimuli or psychiatric disorders such as schizophrenia. PET and fMRI produce massive data sets that contain both temporal correlations from repeated scans and complex spatial correlations. Several methods exist for handling temporal correlations, some of which rely on transforming the response data to induce either a known or an independence covariance structure. Despite the presence of spatial correlations between the volume elements (voxels) comprising a brain scan, conventional methods perform voxel-by-voxel analyses of measured brain activity. We propose a two-stage spatio-temporal model for the estimation and testing of localized activity. Our second-stage model specifies a spatial auto-regression, capturing correlations within neural processing clusters defined by a data-driven cluster analysis. We use maximum likelihood methods to estimate parameters from our spatial autoregressive model. Our model protects against type-I errors, enables the detection of both localized and regional activations (including volume of interest effects), provides information on functional connectivity in the brain, and establishes a framework to produce spatially smoothed maps of distributed brain activity for each individual. We illustrate the application of our model using PET data from a study of working memory in individuals with schizophrenia.     

Zero‐inflated spatio‐temporal models for disease mapping

In this paper, our aim is to analyze geographical and temporal variability of disease incidence when spatio‐temporal count data have excess zeros. To that end, we consider random effects in zero‐inflated Poisson models to investigate geographical and temporal patterns of disease incidence. Spatio‐temporal models that employ conditionally autoregressive smoothing across the spatial dimension and B‐spline smoothing over the temporal dimension are proposed. The analysis of these complex models is computationally difficult from the frequentist perspective. On the other hand, the advent of the Markov chain Monte Carlo algorithm has made the Bayesian analysis of complex models computationally convenient. Recently developed data cloning method provides a frequentist approach to mixed models that is also computationally convenient. We propose to use data cloning, which yields to maximum likelihood estimation, to conduct frequentist analysis of zero‐inflated spatio‐temporal modeling of disease incidence. One of the advantages of the data cloning approach is that the prediction and corresponding standard errors (or prediction intervals) of smoothing disease incidence over space and time is easily obtained. We illustrate our approach using a real dataset of monthly children asthma visits to hospital in the province of Manitoba, Canada, during the period April 2006 to March 2010. Performance of our approach is also evaluated through a simulation study.     

Widespread evidence for incipient ecological speciation: a meta‐analysis of isolation‐by‐ecology

Ecologically mediated selection has increasingly become recognised as an important driver of speciation. The correlation between neutral genetic differentiation and environmental or phenotypic divergence among populations, to which we collectively refer to as isolation‐by‐ecology (IBE), is an indicator of ecological speciation. In a meta‐analysis framework, we determined the strength and commonality of IBE in nature. On the basis of 106 studies, we calculated a mean effect size of IBE with and without controlling for spatial autocorrelation among populations. Effect sizes were 0.34 (95% CI 0.24–0.42) and 0.26 (95% CI 0.13–0.37), respectively, indicating that an average of 5% of the neutral genetic differentiation among populations was explained purely by ecological contrast. Importantly, spatial autocorrelation reduced IBE correlations for environmental variables, but not for phenotypes. Through simulation, we showed how the influence of isolation‐by‐distance and spatial autocorrelation of ecological variables can result in false positives or underestimated correlations if not accounted for in the IBE model. Collectively, this meta‐analysis showed that ecologically induced genetic divergence is pervasive across time‐scales and taxa, and largely independent of the choice of molecular marker. We discuss the importance of these results in the context of adaptation and ecological speciation and suggest future research avenues.     

A stage‐wise approach for the analysis of multi‐environment trials

Plant breeders and variety testing agencies routinely test candidate genotypes (crop varieties, lines, test hybrids) in multiple environments. Such multi‐environment trials can be efficiently analysed by mixed models. A single‐stage analysis models the entire observed data at the level of individual plots. This kind of analysis is usually considered as the gold standard. In practice, however, it is more convenient to use a two‐stage approach, in which experiments are first analysed per environment, yielding adjusted means per genotype, which are then summarised across environments in the second stage. Stage‐wise approaches suggested so far are approximate in that they cannot fully reproduce a single‐stage analysis, except in very simple cases, because the variance–covariance matrix of adjusted means from individual environments needs to be approximated by a diagonal matrix. This paper proposes a fully efficient stage‐wise method, which carries forward the full variance–covariance matrix of adjusted means from the individual environments to the analysis across the series of trials. Provided the variance components are known, this method can fully reproduce the results of a single‐stage analysis. Computations are made efficient by a diagonalisation of the residual variance–covariance matrix, which necessitates a corresponding linear transformation of both the first‐stage estimates (e.g. adjusted means and regression slopes for plot covariates) and the corresponding design matrices for fixed and random effects. We also exemplify the extension of the general approach to a three‐stage analysis. The method is illustrated using two datasets, one real and the other simulated. The proposed approach has close connections with meta‐analysis, where environments correspond to centres and genotypes to medical treatments. We therefore compare our theoretical results with recently published results from a meta‐analysis.     

Bayesian Spatiotemporal Inference in Functional Magnetic Resonance Imaging

Mapping of the human brain by means of functional magnetic resonance imaging (fMRI) is an emerging field in cognitive and clinical neuroscience. Current techniques to detect activated areas of the brain mostly proceed in two steps. First, conventional methods of correlation, regression, and time series analysis are used to assess activation by a separate, pixelwise comparison of the fMRI signal time courses to the reference function of a presented stimulus. Spatial aspects caused by correlations between neighboring pixels are considered in a separate second step, if at all. The aim of this article is to present hierarchical Bayesian approaches that allow one to simultaneously incorporate temporal and spatial dependencies between pixels directly in the model formulation. For reasons of computational feasibility, models have to be comparatively parsimonious, without oversimplifying. We introduce parametric and semiparametric spatial and spatiotemporal models that proved appropriate and illustrate their performance applied to visual fMRI data.     

The genetic variance but not the genetic covariance of life‐history traits changes towards the north in a time‐constrained insect

Seasonal time constraints are usually stronger at higher than lower latitudes and can exert strong selection on life‐history traits and the correlations among these traits. To predict the response of life‐history traits to environmental change along a latitudinal gradient, information must be obtained about genetic variance in traits and also genetic correlation between traits, that is the genetic variance‐covariance matrix, G . Here, we estimated G for key life‐history traits in an obligate univoltine damselfly that faces seasonal time constraints. We exposed populations to simulated native temperatures and photoperiods and common garden environmental conditions in a laboratory set‐up. Despite differences in genetic variance in these traits between populations (lower variance at northern latitudes), there was no evidence for latitude‐specific covariance of the life‐history traits. At simulated native conditions, all populations showed strong genetic and phenotypic correlations between traits that shaped growth and development. The variance–covariance matrix changed considerably when populations were exposed to common garden conditions compared with the simulated natural conditions, showing the importance of environmentally induced changes in multivariate genetic structure. Our results highlight the importance of estimating variance–covariance matrixes in environments that mimic selection pressures and not only trait variances or mean trait values in common garden conditions for understanding the trait evolution across populations and environments.     

Metacommunity‐scale biodiversity regulation and the self‐organised emergence of macroecological patterns

There exist a number of key macroecological patterns whose ubiquity suggests that the spatio‐temporal structure of ecological communities is governed by some universal mechanisms. The nature of these mechanisms, however, remains poorly understood. Here, we probe spatio‐temporal patterns in species richness and community composition using a simple metacommunity assembly model. Despite making no a priori assumptions regarding biotic spatial structure or the distribution of biomass across species, model metacommunities self‐organise to reproduce well‐documented patterns including characteristic species abundance distributions, range size distributions and species area relations. Also in agreement with observations, species richness in our model attains an equilibrium despite continuous species turnover. Crucially, it is in the neighbourhood of the equilibrium that we observe the emergence of these key macroecological patterns. Biodiversity equilibria in models occur due to the onset of ecological structural instability, a population‐dynamical mechanism. This strongly suggests a causal link between local community processes and macroecological phenomena.     

Classical metapopulation dynamics and eco‐evolutionary feedbacks in dendritic networks

Eco‐evolutionary dynamics are now recognized to be highly relevant for population and community dynamics. However, the impact of evolutionary dynamics on spatial patterns, such as the occurrence of classical metapopulation dynamics, is less well appreciated. Here, we analyse the evolutionary consequences of spatial network connectivity and topology for dispersal strategies and quantify the eco‐evolutionary feedback in terms of altered classical metapopulation dynamics. We find that network properties, such as topology and connectivity, lead to predictable spatio‐temporal correlations in fitness expectations. These spatio‐temporally stable fitness patterns heavily impact evolutionarily stable dispersal strategies and lead to eco‐evolutionary feedbacks on landscape level metrics, such as the number of occupied patches, the number of extinctions and recolonizations as well as metapopulation extinction risk and genetic structure. Our model predicts that classical metapopulation dynamics are more likely to occur in dendritic networks, and especially in riverine systems, compared to other types of landscape configurations. As it remains debated whether classical metapopulation dynamics are likely to occur in nature at all, our work provides an important conceptual advance for understanding the occurrence of classical metapopulation dynamics which has implications for conservation and management of spatially structured populations.     

Monitoring temporal trends in spatially structured populations: how should sampling effort be allocated between space and time?

Estimating temporal trends in spatially structured populations has a critical role to play in understanding regional changes in biological populations and developing management strategies. Designing effective monitoring programmes to estimate these trends requires important decisions to be made about how to allocate sampling effort among spatial replicates (i.e. number of sites) and temporal replicates (i.e. how often to survey) to minimise uncertainty in trend estimates. In particular, the optimal mix of spatial and temporal replicates is likely to depend upon the spatial and temporal correlations in population dynamics. Although there has been considerable interest in the ecological literature on understanding spatial and temporal correlations in species’ population dynamics, little attention has been paid to its consequences for monitoring design. We address this issue using model‐based survey design to identify the optimal allocation of sampling effort among spatial and temporal replicates for estimating population trends under different levels of spatial and temporal correlation. Based on linear trends, we show that how we should allocate sampling effort among spatial and temporal replicates depends crucially on the spatial and temporal correlations in population dynamics, environmental variation, observation error and the spatial variation in temporal trends. When spatial correlation is low and temporal correlation is high, the best option is likely to be to sample many sites infrequently, particularly when observation error and/or spatial variation in temporal trends are high. When spatial correlation is high and temporal correlation is low, the best option is likely to be to sample few sites frequently, particularly when observation error and/or spatial variation in temporal trends are low. When abundances are spatially independent, it is always preferable to maximise spatial replication. This provides important insights into how spatio‐temporal monitoring programmes should be designed to estimate temporal trends in spatially structured populations.     

Modeling Inter‐Subject Variability in fMRI Activation Location: A Bayesian Hierarchical Spatial Model

Summary The aim of this article is to develop a spatial model for multi‐subject fMRI data. There has been extensive work on univariate modeling of each voxel for single and multi‐subject data, some work on spatial modeling of single‐subject data, and some recent work on spatial modeling of multi‐subject data. However, there has been no work on spatial models that explicitly account for inter‐subject variability in activation locations. In this article, we use the idea of activation centers and model the inter‐subject variability in activation locations directly. Our model is specified in a Bayesian hierarchical framework which allows us to draw inferences at all levels: the population level, the individual level, and the voxel level. We use Gaussian mixtures for the probability that an individual has a particular activation. This helps answer an important question that is not addressed by any of the previous methods: What proportion of subjects had a significant activity in a given region. Our approach incorporates the unknown number of mixture components into the model as a parameter whose posterior distribution is estimated by reversible jump Markov chain Monte Carlo. We demonstrate our method with a fMRI study of resolving proactive interference and show dramatically better precision of localization with our method relative to the standard mass‐univariate method. Although we are motivated by fMRI data, this model could easily be modified to handle other types of imaging data.     

Toward spatio‐temporal delineation of positive interactions in ecology

Given unprecedented rates of biodiversity loss, there is an urgency to better understand the ecological consequences of interactions among organisms that may lost or altered. Positive interactions among organisms of the same or different species that directly or indirectly improve performance of at least one participant can structure populations and communities and control ecosystem process. However, we are still in need of synthetic approaches to better understand how positive interactions scale spatio‐temporally across a range of taxa and ecosystems. Here, we synthesize two complementary approaches to more rigorously describe positive interactions and their consequences among organisms, across taxa, and over spatio‐temporal scales. In the first approach, which we call the mechanistic approach, we make a distinction between two principal mechanisms of facilitation—habitat modification and resource modification. Considering the differences in these two mechanisms is critical because it delineates the potential spatio‐temporal bounds over which a positive interaction can occur. We offer guidance on improved sampling regimes for quantification of these mechanistic interactions and their consequences. Second, we present a trait‐based approach in which traits of facilitators or traits of beneficiaries can modulate their magnitude of effect or how they respond to either of the positive interaction mechanisms, respectively. Therefore, both approaches can be integrated together by quantifying the degree to which a focal facilitator's or beneficiary's traits explain the magnitude of a positive effect in space and time. Furthermore, we demonstrate how field measurements and analytical techniques can be used to collect and analyze data to test the predictions presented herein. We conclude by discussing how these approaches can be applied to contemporary challenges in ecology, such as conservation and restoration and suggest avenues for future research.     

The spatio‐temporal forest patch dynamics inferred from the fine‐scale synchronicity in growth chronology

Question: Abrupt increments in tree radial growth chronology are associated with gap formations derived from disturbances. If a forest has been primarily controlled by fine‐scale disturbances such as single tree‐fall, do these release events spatio‐temporally synchronize at a fine scale such as 10 m and 5 years? Is it possible to quantify spatio‐temporal patterns of synchronicity from tree rings and long‐term inventories, and associate them with spatial forest patch dynamics? How and to what extent can we reconstruct the fine‐scale synchronized growth and spatio‐temporal forest patch dynamics from currently available information? Location: Cores were taken from Abies sachalinensis trees in a coniferous/deciduous mixed forest in the Shiretoko Peninsula, Hokkaido, northern Japan. Methods: We first eliminated short‐term fluctuations and highlighted growth trends over the mid‐term using a time‐series smoothing technique. This helped identify release events, we then conducted fine‐scale spatial analyses on released A. sachalinensis primarily with cluster analysis. Results: We specified the unit scale of synchronicity at 10 m, and classified released A. sachalinensis trees into spatially separated regions. Only once during the recent 50 years was extensive synchronicity over 40 m found. Most of the released A. sachalinensis were isolated, with non‐released A. sachalinensis present in nearby, implying imperfect synchronization. The ambiguous 20–30 m A. sachalinensis patches present in the current forest were the result of connected and overlapping patches smaller than 10 m associated with different disturbances and different responses of understorey trees. Conclusion: Tree‐ring series, long‐term census and fine‐scale spatio‐temporal analyses revealed that this forest community has been controlled by two types of disturbance: frequent small disturbances such as single tree‐fall and less frequent multiple tree‐falls.     

Resting‐state networks of the neonate brain identified using independent component analysis

Resting‐state functional magnetic resonance imaging (rs‐fMRI) has been successfully used to probe the intrinsic functional organization of the brain and to study brain development. Here, we implemented a combination of individual and group independent component analysis (ICA) of FSL on a 6‐min resting‐state data set acquired from 21 naturally sleeping term‐born (age 26 ± 6.7 d), healthy neonates to investigate the emerging functional resting‐state networks (RSNs). In line with the previous literature, we found evidence of sensorimotor, auditory/language, visual, cerebellar, thalmic, parietal, prefrontal, anterior cingulate as well as dorsal and ventral aspects of the default‐mode‐network. Additionally, we identified RSNs in frontal, parietal, and temporal regions that have not been previously described in this age group and correspond to the canonical RSNs established in adults. Importantly, we found that careful ICA‐based denoising of fMRI data increased the number of networks identified with group‐ICA, whereas the degree of spatial smoothing did not change the number of identified networks. Our results show that the infant brain has an established set of RSNs soon after birth.