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.     

Estimation of false discovery proportion under general dependence

MOTIVATION: Wide-scale correlations between genes are commonly observed in gene expression data, due to both biological and technical reasons. These correlations increase the variability of the standard estimate of the false discovery rate (FDR). We highlight the false discovery proportion (FDP, instead of the FDR) as the suitable quantity for assessing differential expression in microarray data, demonstrate the deleterious effects of correlation on FDP estimation and propose an improved estimation method that accounts for the correlations. METHODS: We analyse the variation pattern of the distribution of test statistics under permutation using the singular value decomposition. The results suggest a latent FDR model that accounts for the effects of correlation, and is statistically closer to the FDP. We develop a procedure for estimating the latent FDR (ELF) based on a Poisson regression model. RESULTS: For simulated data based on the correlation structure of real datasets, we find that ELF performs substantially better than the standard FDR approach in estimating the FDP. We illustrate the use of ELF in the analysis of breast cancer and lymphoma data. AVAILABILITY: R code to perform ELF is available in http://www.meb.ki.se/~yudpaw.     

Correlations between forest stand diversity and landscape pattern in Otepää Nature Park, Estonia

Rank correlations between tree species diversity in forest stands and parameters of landscape pattern were calculated using data from 4933 locations in Otepää Nature Park. Stand diversity was characterised by the number of tree species in the stand formula and by the index of dominance of tree species’ coverage. Landscape diversity was characterised by locally calculated pattern parameters from three categorical map layers (1:10 000 base map, 1:10 000 soil map, combination of these maps) and from six numerical variables (elevation, slope angle, four channels of a Landsat 7 ETM image).A weak trend appeared for more diverse forest stands to be located in more diverse landscapes according to the base map. Forest stand diversity is also higher on steeper slopes and in places surrounded by slopes of varying steepness. The correlation between landscape diversity and biodiversity depends on the radius of the kernel in which landscape characteristics are calculated. Evidence of an indicative neighbourhood could be seen in many spatial relationships. The spatial correlation between stand diversity and indices calculated from the base map was most visible at distances ranging from 400 to 500 m; surface elevation and its variation correlates with stand diversity at distances of 100–200 m. Some relationships between forest diversity and landscape diversity that had a different sign of correlation in proximate and distant kernels can be interpreted as a need to standardise local landscape indices with the index values in a wider neighbourhood as a reference.     

Temporal encoding of place sequences by hippocampal cell assemblies

Both episodic memory and spatial navigation require temporal encoding of the relationships between events or locations. In a linear maze, ordered spatial distances between sequential locations were represented by the temporal relations of hippocampal place cell pairs within cycles of theta oscillation in a compressed manner. Such correlations could arise due to spike "phase precession" of independent neurons driven by common theta pacemaker or as a result of temporal coordination among specific hippocampal cell assemblies. We found that temporal correlation between place cell pairs was stronger than predicted by a pacemaker drive of independent neurons, indicating a critical role for synaptic interactions and precise timing within and across cell assemblies in place sequence representation. CA1 and CA3 ensembles, identifying spatial locations, were active preferentially on opposite phases of theta cycles. These observations suggest that interleaving CA3 neuronal sequences bind CA1 assemblies representing overlapping past, present, and future locations into single episodes.     

Spatial and Space-Time Correlations in Systems of Subpopulations with Genetic Drift and Migration

The geographic distribution of genetic variation is an important theoretical and experimental component of population genetics. Previous characterizations of genetic structure of populations have used measures of spatial variance and spatial correlations. Yet a full understanding of the causes and consequences of spatial structure requires complete characterization of the underlying space-time system. This paper examines important interactions between processes and spatial structure in systems of subpopulations with migration and drift, by analyzing correlations of gene frequencies over space and time. We develop methods for studying important features of the complete set of space-time correlations of gene frequencies for the first time in population genetics. These methods also provide a new alternative for studying the purely spatial correlations and the variance, for models with general spatial dimensionalities and migration patterns. These results are obtained by employing theorems, previously unused in population genetics, for space-time autoregressive (STAR) stochastic spatial time series. We include results on systems with subpopulation interactions that have time delay lags (temporal orders) greater than one. We use the space-time correlation structure to develop novel estimators for migration rates that are based on space-time data (samples collected over space and time) rather than on purely spatial data, for real systems. We examine the space-time and spatial correlations for some specific stepping stone migration models. One focus is on the effects of anisotropic migration rates. Partial space-time correlation coefficients can be used for identifying migration patterns. Using STAR models, the spatial, space-time, and partial space-time correlations together provide a framework with an unprecedented level of detail for characterizing, predicting and contrasting space-time theoretical distributions of gene frequencies, and for identifying features such as the pattern of migration and estimating migration rates in experimental studies of genetic variation over space and time.     

Patterns of spatial autocorrelation of assemblages of birds, floristics, physiognomy, and primary productivity in the central Great Basin, USA

We fitted spatial autocorrelation functions to distance-based data for assemblages of birds and for three attributes of birds' habitats at 140 locations, separated by up to 65 km, in the Great Basin (Nevada, USA). The three habitat characteristics were taxonomic composition of the vegetation, physical structure of the vegetation, and a measure of primary productivity, the normalized difference vegetation index, estimated from satellite imagery. We found that a spherical model was the best fit to data for avifaunal composition, vegetation composition, and primary productivity, but the distance at which spatial correlation effectively was zero differed substantially among data sets ( c . 30 km for birds, 20 km for vegetation composition, and 60 km for primary productivity). A power-law function was the best fit to data for vegetation structure, indicating that the structure of vegetation differed by similar amounts irrespective of distance between locations (up to the maximum distance measured). Our results suggested that the spatial structure of bird assemblages is more similar to vegetation composition than to either vegetation structure or primary productivity, but is autocorrelated over larger distances. We believe that the greater mobility of birds compared with plants may be responsible for this difference.     

Effects of Spatial Pattern Scale of Brain Activity on the Sensitivity of DOT,fMRI, EEG and MEG

The objective of this work is to quantify how patterns of cortical activity at different spatial scales are measured by noninvasive functional neuroimaging sensors. We simulated cortical activation patterns at nine different spatial scales in a realistic head model and propagated this activity to magnetoencephalography (MEG), electroencephalography (EEG), diffuse optical tomography (DOT), and functional magnetic resonance imaging (fMRI) sensors in arrangements that are typically used in functional neuroimaging studies. We estimated contrast transfer functions (CTF), correlation distances in sensor space, and the minimum resolvable spatial scale of cortical activity for each modality. We found that CTF decreases as the spatial extent of cortical activity decreases, and that correlations between nearby sensors depend on the spatial extent of cortical activity. For cortical activity on the intermediate spatial scale of 6.7 cm², the correlation distances (r>0.5) were 1.0 cm for fMRI, 2.0 cm for DOT, 12.8 for EEG, 9.5 cm for MEG magnetometers and 9.7 cm for MEG gradiometers. The resolvable spatial pattern scale was found to be 1.43 cm² for MEG magnetometers, 0.88 cm² for MEG gradiometers, 376 cm² for EEG, 0.75 cm² for DOT, and 0.072 cm² for fMRI. These findings show that sensitivity to cortical activity varies substantially as a function of spatial scale within and between the different imaging modalities. This information should be taken into account when interpreting neuroimaging data and when choosing the number of nodes for network analyses in sensor space.     

Geographic variation of flower traits in Narcissus papyraceus (Amaryllidaceae): do pollinators matter?

Aim The geographic clinal variation of traits in organisms can indicate the possible causes of phenotypic evolution. We studied the correlates of flower trait variation in populations of a style‐dimorphic plant, Narcissus papyraceus Ker‐Gawl., within a region of high biogeographical significance, the Strait of Gibraltar. This species shows a geographic gradient in the style‐morph ratio, suggested to be driven by pollinator shifts. We tested whether parallel geographic variation of perianth traits also exists, concomitant with vegetative trait variation or genetic similarity of plant populations. Location The Strait of Gibraltar region (SG hereafter, including both south‐western Iberian Peninsula and north‐western Morocco). Methods We used univariate and multivariate analyses of flower and vegetative traits in 23 populations. We applied Mantel tests and partial Mantel correlations on vegetative and flower traits and geographic locations of populations to test for spatial effects. We used Moran’s autocorrelation analyses to explore the spatial structure within the range, and performed the analyses with and without the Moroccan samples to test for the effects of the SG on spatial patterns. Amplified fragment length polymorphism data were used to estimate the genetic distance between populations and to ascertain its relationship with morphometric distance. Results There was high variation between and within populations in both flower and vegetative traits. Mantel correlations between geographic and morphometric distances were not significant, but the exclusion of Moroccan populations revealed some distance effect. Partial Mantel correlation did not detect a significant correlation between flower and vegetative morphometric distances after controlling for geographic distance. There were opposite trends in spatial autocorrelograms of flower and vegetative traits. The genetic distance between pairs of populations was directly correlated with geographic distance; however, flower morphometric and genetic distances were not significantly correlated. Main conclusions The SG had some influence on phenotypes, although the causes remain to be determined. The opposite trend of variation in flower and vegetative traits, and the lack of correlation between genetic distance and dissimilarity of flower phenotypes favour the hypothesis of pollinator‐mediated selection on flower morphology, although this may affect only particular traits and populations rather than overall phenotypes. Although stochastic population processes may have a small effect, other factors may account for the high flower variation within and between populations.     

How far do songbirds disperse?

Dispersal distances determine the scales over which many population processes occur. Knowledge of these distances may therefore be crucial in determining the appropriate spatial scales for research and management. However, dispersal distances are difficult to measure, especially for vagile organisms like songbirds. For these species, the use of traditional mark–recapture and radio‐telemetry methods is problematic. We used positive one‐year time‐lagged correlations in abundance to estimate natal dispersal distances. Using the North American Breeding Bird Survey database, we examined one‐year time‐lagged correlations between pairs of North American songbird samples separated by 10–100 km. We submit that consistent positive one‐year time‐lagged correlations reflect the exchange of individuals through dispersal. We found positive one‐year time‐lagged correlations between pairs of samples from 25 different songbird species. The median distances of these correlations ranged from 15 to 95 km, depending on the species. These distances were positively correlated with body size and wing length. Dispersal appears to be the most parsimonious explanation for the time‐lagged correlations we observed in these species. The putative dispersal distances we measured are generally an order of magnitude longer than those reported in the literature.     

genclone: a computer program to analyse genotypic data,test for clonality and describe spatial clonal organization

genclone 1.0 is designed for studying clonality and its spatial components using genotype data with molecular markers from haploid or diploid organisms. genclone 1.0 performs the following tasks. (i) discriminates distinct multilocus genotypes (MLGs), and uses permutation and resampling approaches to test for the reliability of sets of loci and sampling units for estimating genotypic and genetic diversity (a procedure also useful for nonclonal organisms); (ii) computes statistics to test for clonal propagation or clonal identity of replicates; (iii) computes various indices describing genotypic diversity; and (iv) summarizes the spatial organization of MLGs with adapted spatial autocorrelation methods and clonal subrange estimates.     

基于实测高光谱与Sentinel-2B数据的银北土壤Na+含量估测

为了探讨不同传感器对土壤Na⁺含量的估测能力,本研究以宁夏银北地区典型样点土壤实测光谱和Sentinel-2B影像光谱为对象,运用逐步回归(SR)和主成分回归分析(PCA)方法对光谱数据进行敏感参量筛选,然后采用偏最小二乘回归(PLSR)、支持向量机(SVM)和反向传播神经网络模型(BPNN)分别建立实测光谱和影像数据的土壤Na⁺含量估算模型。结果表明: 除Band9外,实测重采样数据与影像数据呈极显著相关。基于SR筛选方式建立的模型估算精度普遍高于PCA(SVM模型除外),PCA-SVM模型为影像最佳Na⁺含量估算模型,预测精度为0.792;SR-BPNN模型为实测最佳Na⁺含量估算模型,预测精度达到0.908。经重采样实测光谱模型校正后的SR-PLSR影像光谱土壤Na⁺含量估算模型精度从0.481提高到0.798,有效提高了较大尺度下的土壤Na⁺含量估算精度。本研究实现了遥感监测土壤Na⁺含量由点向面的空间转换,为Sentinel-2B影像监测盐渍化土壤Na⁺含量提供了科学参考。     

A modified pseudolikelihood approach for analysis of longitudinal data

We consider the analysis of longitudinal data when the covariance function is modeled by additional parameters to the mean parameters. In general, inconsistent estimators of the covariance (variance/correlation) parameters will be produced when the "working" correlation matrix is misspecified, which may result in great loss of efficiency of the mean parameter estimators (albeit the consistency is preserved). We consider using different "working" correlation models for the variance and the mean parameters. In particular, we find that an independence working model should be used for estimating the variance parameters to ensure their consistency in case the correlation structure is misspecified. The designated "working" correlation matrices should be used for estimating the mean and the correlation parameters to attain high efficiency for estimating the mean parameters. Simulation studies indicate that the proposed algorithm performs very well. We also applied different estimation procedures to a data set from a clinical trial for illustration.     

Generalized common spatial factor model

There are often two types of correlations in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two types of correlations are caused by a common spatially correlated underlying factor. Under this hypothesis, we propose a generalized common spatial factor model. The parameters are estimated using the Bayesian method and a Markov chain Monte Carlo computing technique. Our main goals are to determine which observed variables share a common underlying spatial factor and also to predict the common spatial factor. The model is applied to county-level cancer mortality data in Minnesota to find whether there exists a common spatial factor underlying the cancer mortality throughout the state.     

Plankton motility patterns and encounter rates

Many planktonic organisms have motility patterns with correlation run lengths (distances traversed before direction changes) of the same order as their reaction distances regarding prey, mates and predators (distances at which these organisms are remotely detected). At these scales, the relative measure of run length to reaction distance determines whether the underlying encounter is ballistic or diffusive. Since ballistic interactions are intrinsically more efficient than diffusive, we predict that organisms will display motility with long correlation run lengths compared to their reaction distances to their prey, but short compared to the reaction distances of their predators. We show motility data for planktonic organisms ranging from bacteria to copepods that support this prediction. We also present simple ballistic and diffusive motility models for estimating encounter rates, which lead to radically different predictions, and we present a simple criterion to determine which model is the more appropriate in a given case.     

Novel Three-Step Pseudo-Absence Selection Technique for Improved Species Distribution Modelling

Pseudo-absence selection for spatial distribution models (SDMs) is the subject of ongoing investigation. Numerous techniques continue to be developed, and reports of their effectiveness vary. Because the quality of presence and absence data is key for acceptable accuracy of correlative SDM predictions, determining an appropriate method to characterise pseudo-absences for SDM’s is vital. The main methods that are currently used to generate pseudo-absence points are: 1) randomly generated pseudo-absence locations from background data; 2) pseudo-absence locations generated within a delimited geographical distance from recorded presence points; and 3) pseudo-absence locations selected in areas that are environmentally dissimilar from presence points. There is a need for a method that considers both geographical extent and environmental requirements to produce pseudo-absence points that are spatially and ecologically balanced. We use a novel three-step approach that satisfies both spatial and ecological reasons why the target species is likely to find a particular geo-location unsuitable. Step 1 comprises establishing a geographical extent around species presence points from which pseudo-absence points are selected based on analyses of environmental variable importance at different distances. This step gives an ecologically meaningful explanation to the spatial range of background data, as opposed to using an arbitrary radius. Step 2 determines locations that are environmentally dissimilar to the presence points within the distance specified in step one. Step 3 performs K-means clustering to reduce the number of potential pseudo-absences to the desired set by taking the centroids of clusters in the most environmentally dissimilar class identified in step 2. By considering spatial, ecological and environmental aspects, the three-step method identifies appropriate pseudo-absence points for correlative SDMs. We illustrate this method by predicting the New Zealand potential distribution of the Asian tiger mosquito (Aedes albopictus) and the Western corn rootworm (Diabrotica virgifera virgifera).     

Identifying the Threshold of Dominant Controls on Fire Spread in a Boreal Forest Landscape of Northeast China

The relative importance of fuel, topography, and weather on fire spread varies at different spatial scales, but how the relative importance of these controls respond to changing spatial scales is poorly understood. We designed a “moving window” resampling technique that allowed us to quantify the relative importance of controls on fire spread at continuous spatial scales using boosted regression trees methods. This quantification allowed us to identify the threshold value for fire size at which the dominant control switches from fuel at small sizes to weather at large sizes. Topography had a fluctuating effect on fire spread across the spatial scales, explaining 20–30% of relative importance. With increasing fire size, the dominant control switched from bottom-up controls (fuel and topography) to top-down controls (weather). Our analysis suggested that there is a threshold for fire size, above which fires are driven primarily by weather and more likely lead to larger fire size. We suggest that this threshold, which may be ecosystem-specific, can be identified using our “moving window” resampling technique. Although the threshold derived from this analytical method may rely heavily on the sampling technique, our study introduced an easily implemented approach to identify scale thresholds in wildfire regimes.     

毛乌素沙地南缘沙漠化临界区域土壤水分和植被空间格局

应用地统计学和经典统计学方法,对毛乌素沙地南缘沙漠化临界区域土壤水分和植被特征的空间分布格局及其相互关系进行研究,结果表明: 0-5 cm和5-10 cm土壤水分符合指数模型,10-15 cm土壤水分和植物群落物种数、植被盖度、植被密度都符合球状模型;0-5 cm土壤水分、植物群落物种数和植被盖度都具有强空间自相关性,5-10 cm、10-15 cm土壤水分和植被密度都具有中等程度的空间自相关性;从牛枝子群落到黑沙蒿群落,各层土壤水分与植物群落物种数之间具有相似的空间格局,都呈先升高后降低的变化趋势,而植被盖度和植被密度呈逐渐减小的变化趋势;0-5 cm土壤水分与植物群落物种数之间具有显著的正相关,是制约植被物种空间分布的关键因素。     

Effects of landscape and history on diversification of a montane, stream-breeding amphibian

Aim The aim of this study was to understand the roles of landscape features in shaping patterns of contemporary and historical genetic diversification among populations of the Andean tree frog (Hypsiboas andinus) across spatial scales. Location Andes mountains, north‐western Argentina, South America. Methods Mitochondrial DNA control region sequences were utilized to assess genetic differentiation among populations and calculate population pair‐wise genetic distances. Three models of movement, namely traditional straight‐line distance and two effective distances based on habitat classification, were examined to determine which of these explained the most variation in pair‐wise population genetic differentiation. The two habitat classifications were based on digital vegetation and hydrology layers that were generated from a 90‐m resolution digital elevation model (DEM) and known relationships between elevation and habitat. Mantel tests were conducted to test for correlations between geographic and genetic distance matrices and to estimate the percentage variation explained by each type of geographic distance. To investigate the location of possible barriers to gene flow, we used Monmonier’s maximum difference algorithm as implemented in barrier 2.2. Results At both geographic scales, effective distances explained more variation in genetic differentiation than did straight‐line distance. The least‐cost distances based on the simple classification performed better than the more detailed habitat classification. We controlled for the effects of historical range fragmentation determined from previous nested clade analyses, and therefore evaluated the effect of different distances on the genetic variation attributable to more recent factors. Effective distances identified populations that were highly divergent as a result of isolation in unsuitable habitats. The proposed locations of barriers to gene flow identified using Monmonier’s maximum difference algorithm corresponded well with earlier analyses and supported findings from our partial Mantel tests. Main conclusions Our results indicate that landscape features have been important in both historical and contemporary genetic structuring of populations of H. andinus at both large and small spatial scales. A landscape genetic perspective offers novel insights not provided by traditional phylogeographic studies: (1) effective distances can better explain patterns of differentiation in populations, especially in heterogeneous landscapes where barriers to dispersal may be common; and (2) least‐cost path analysis can help to identify corridors of movement between populations that are biologically more realistic.     

内蒙古荒漠草原植被盖度的空间异质性动态分析

利用半方差函数分析法对内蒙古荒漠草原生长盛期(6—8月)的植被盖度时空变异特征的研究表明,荒漠草原生长盛期的植被盖度半方差函数形态符合指数模型,但函数曲线的形态和各参数在不同月份变化较大。其中,6月的植被盖度变程最大,达到100 m;7月植被盖度的半方差函数形态具有巢式等级结构;8月植被盖度的变程最小,仅为15 m,但空间变异程度最高。3个月的结构比介于72%—85%,具有较强的空间自相关。各向异性分析表明,6月植被盖度在135°方向的半方差函数值明显低于其它3个方向(0°、45°、90°),具有各向异性特征;而7月和8月植被盖度的各向异性比接近于1,表现为各向同性。研究结果表明,荒漠草原植被盖度空间异质性的时间动态不容忽视,在野外采样或制图时,要根据时间合理控制采样范围。     

Dispersal, Environmental Correlation, and Spatial Synchrony in Population Dynamics

Many species exhibit widespread spatial synchrony in population fluctuations. This pattern is of great ecological interest and can be a source of concern when the species is rare or endangered. Both dispersal and spatial correlations in the environment have been implicated as possible causes of this pattern, but these two factors have rarely been studied in combination. We develop a spatially structured population model, simple enough to obtain analytic solutions for the population correlation, that incorporates both dispersal and environmental correlation. We ask whether these two synchronizing factors contribute additively to the total spatial population covariance. We find that there is always an interaction between these two factors and that this interaction is small only when one or both of the environmental correlation and the dispersal rate are small. The interaction is opposite in sign to the environmental correlation; so, in the normal case of positive environmental correlation across sites, the population synchrony will be lower than predicted by simply adding the effects of dispersal and environmental correlation. We also find that population synchrony declines as the strength of population regulation increases. These results indicate that dispersal and environmental correlation need to be considered in combination as explanations for observed patterns of population synchrony.