A spatially explicit model of patchy stomatal responses to humidity

Stomata of leaves can exhibit either temporally stable, spatially homogeneous behaviour or complex spatial and temporal dynamics, depending on environmental and physiological conditions. To test the ability of accepted physiological mechanisms to describe these patterns, we developed a simple, spatially explicit model of stomatal responses to humidity that incorporated hydraulic interactions among stomata. Model results showed qualitative agreement with experimental evidence for a number of phenomena: (1) at high humidities, whole-leaf steady-state conductance is a monotonic function of humidity; (2) the initial stomatal response following a perturbation in humidity is in the direction opposite to the final response, and (3) spatial dynamics include patch formation and self-organization similar to that observed in actual leaves. These comparisons do not eliminate other explanations, but do suggest that novel mechanisms need not be invoked to explain the diversity of spatial and temporal patterns of stomatal behaviour in leaves.     

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.     

Spatial and temporal heterogeneity explain disease dynamics in a spatially explicit network model

There is an increasing recognition that individual-level spatial and temporal heterogeneity may play an important role in metapopulation dynamics and persistence. In particular, the patterns of contact within and between aggregates (e.g., demes) at different spatial and temporal scales may reveal important mechanisms governing metapopulation dynamics. Using 7 years of data on the interaction between the anther smut fungus (Microbotryum violaceum) and fire pink (Silene virginica), we show how the application of spatially explicit and implicit network models can be used to make accurate predictions of infection dynamics in spatially structured populations. Explicit consideration of both spatial and temporal organization reveals the role of each in spreading risk for both the host and the pathogen. This work suggests that the application of spatially explicit network models can yield important insights into how heterogeneous structure can promote the persistence of species in natural landscapes.     

昆虫种群动态时空回归预测方法及应用研究

根据昆虫种群内个体空间相互作用的特点,提出分析昆虫种群时空相关的三维相关图方法及种群动态预测的时空混合回归模型,对马尾松毛虫幼虫密切分布的预测采用了时空自回归加空趋势面的形式,预测的马尾松毛虫幼虫的平均密度和实测的平均密度在时空变化的趋势上是完全一致的,而且预测结果给出了马尾松毛虫的幼虫密度分布的图形形式,给防治决策提供了方便。     

Autoregressive spatial smoothing and temporal spline smoothing for mapping rates

This article proposes generalized additive mixed models for the analysis of geographic and temporal variability of mortality rates. This class of models accommodates random spatial effects and fixed and random temporal components. Spatiotemporal models that use autoregressive local smoothing across the spatial dimension and B-spline smoothing over the temporal dimension are developed. The objective is the identification of temporal treads and the production of a series of smoothed maps from which spatial patterns of mortality risks can be monitored over time. Regions with consistently high rate estimates may be followed for further investigation. The methodology is illustrated by analysis of British Columbia infant mortality data.     

Temporally and Spatially Constrained ICA of fMRI Data Analysis

Constrained independent component analysis (CICA) is capable of eliminating the order ambiguity that is found in the standard ICA and extracting the desired independent components by incorporating prior information into the ICA contrast function. However, the current CICA method produces constraints that are based on only one type of prior information (temporal/spatial), which may increase the dependency of CICA on the accuracy of the prior information. To improve the robustness of CICA and to reduce the impact of the accuracy of prior information on CICA, we proposed a temporally and spatially constrained ICA (TSCICA) method that incorporated two types of prior information, both temporal and spatial, as constraints in the ICA. The proposed approach was tested using simulated fMRI data and was applied to a real fMRI experiment using 13 subjects who performed a movement task. Additionally, the performance of TSCICA was compared with the ICA method, the temporally CICA (TCICA) method and the spatially CICA (SCICA) method. The results from the simulation and from the real fMRI data demonstrated that TSCICA outperformed TCICA, SCICA and ICA in terms of robustness to noise. Moreover, the TSCICA method displayed better robustness to prior temporal/spatial information than the TCICA/SCICA method.     

Measuring fast dynamics in solutions and cells with a laser scanning microscope

Single-point fluorescence correlation spectroscopy (FCS) allows measurements of fast diffusion and dynamic processes in the microsecond-to-millisecond time range. For measurements on living cells, image correlation spectroscopy (ICS) and temporal ICS extend the FCS approach to diffusion times as long as seconds to minutes and simultaneously provide spatially resolved dynamic information. However, ICS is limited to very slow dynamics due to the frame acquisition rate. Here we develop novel extensions to ICS that probe spatial correlations in previously inaccessible temporal windows. We show that using standard laser confocal imaging techniques (raster-scan mode) not only can we reach the temporal scales of single-point FCS, but also have the advantages of ICS in providing spatial information. This novel method, called raster image correlation spectroscopy (RICS), rapidly measures during the scan many focal points within the cell providing the same concentration and dynamic information of FCS as well as information on the spatial correlation between points along the scanning path. Longer time dynamics are recovered from the information in successive lines and frames. We exploit the hidden time structure of the scan method in which adjacent pixels are a few microseconds apart thereby accurately measuring dynamic processes such as molecular diffusion in the microseconds-to-seconds timescale. In conjunction with simulated data, we show that a wide range of diffusion coefficients and concentrations can be measured by RICS. We used RICS to determine for the first time spatially resolved diffusions of paxillin-EGFP stably expressed in CHOK1 cells. This new type of data analysis has a broad application in biology and it provides a powerful tool for measuring fast as well as slower dynamic processes in cellular systems using any standard laser confocal microscope.     

Characterising the temporal variability of the spatial distribution of animals: an application to seabirds at sea

Understanding the patterns of spatial and temporal variations in animal abundance is a fundamental question in ecology. Here, we propose a method to quantify temporal variations in animal spatial patterns and to determine the spatial scale at which such temporal variability is expressed. The methodology extends from the approach proposed by Taylor (Taylor, L. R. 1961. Aggregation, variance and the mean. Nature 189: 732–735) and relies on models of the relationship between temporal mean and variance in animal abundance. Repeated observations of the spatial distribution of populations are used to construct spatially explicit models of Taylor's power law. The resulting slope parameters of the Taylor power law provide local measures of the temporal variability in animal abundance. We investigate if the value of the slope varies significantly with spatial location and with spatial scale. The method is applied to seabirds distribution in the Bay of Biscay. We study four taxa (northern gannets, large gulls, auks and kittiwakes) that display distinct geographical distribution, spatial structure and foraging strategy. Our results show that the temporal variability associated to the spatial distribution of northern gannets is high and spatially homogeneous. By contrast, kittiwakes present large geographical areas associated with high and low variability. The temporal variability of auk's spatial distribution is strongly scale-dependent: at fine scale high variability is associated to high abundance, but at large scale high variability is associated to the external border of their distribution range. The method provides satisfactory results and useful information on species spatio-temporal distribution.     

Range expansion through fragmented landscapes under a variable climate

Ecological responses to climate change may depend on complex patterns of variability in weather and local microclimate that overlay global increases in mean temperature. Here, we show that high‐resolution temporal and spatial variability in temperature drives the dynamics of range expansion for an exemplar species, the butterfly Hesperia comma. Using fine‐resolution (5 m) models of vegetation surface microclimate, we estimate the thermal suitability of 906 habitat patches at the species' range margin for 27 years. Population and metapopulation models that incorporate this dynamic microclimate surface improve predictions of observed annual changes to population density and patch occupancy dynamics during the species' range expansion from 1982 to 2009. Our findings reveal how fine‐scale, short‐term environmental variability drives rates and patterns of range expansion through spatially localised, intermittent episodes of expansion and contraction. Incorporating dynamic microclimates can thus improve models of species range shifts at spatial and temporal scales relevant to conservation interventions.     

Dispersal, colored environmental noise, and spatial synchrony in population dynamics: analyzing a discrete host–parasitoid population model

Spatial synchrony is common, and its influences and causes have attracted the interest of ecologists. Spatially correlated environmental noise, dispersal, and trophic interactions have been considered as the causes of spatial synchrony. In this study, we developed a spatially structured population model, which is described by coupled-map lattices. Our recent investigation showed that trophic correlation of environmental noise was another important factor that affects spatial synchrony. As a supplement, we considered the influence of the color of the environmental noise on the spatial synchrony in this study. The noise color refers to the temporal correlation in the time series data of the noise, and is expressed as the degree of (first-order) autocorrelation for autoregressive noise. Patterns of spatial synchrony were considered for stable, periodic (quasi-periodic), and chaotic population dynamics. Numerical simulations verified that the color of the environmental noise is another mechanism that causes spatial synchrony. Generally, the effect of the color of the noise on the synchrony is dependent on the type of dynamics (stable, cyclic, chaotic) present in the population. For cyclic dynamics, simulation results clearly demonstrate that reddened noise has higher synchrony than white noise. The importance of our research is that it enriches the theory of potential causes of spatial synchrony.     

Stabilization through spatial pattern formation in metapopulations with long-range dispersal

Many studies of metapopulation models assume that spatially extended populations occupy a network of identical habitat patches, each coupled to its nearest neighbouring patches by density-independent dispersal. Much previous work has focused on the temporal stability of spatially homogeneous equilibrium states of the metapopulation, and one of the main predictions of such models is that the stability of equilibrium states in the local patches in the absence of migration determines the stability of spatially homogeneous equilibrium states of the whole metapopulation when migration is added. Here, we present classes of examples in which deviations from the usual assumptions lead to different predictions. In particular, heterogeneity in local habitat quality in combination with long-range dispersal can induce a stable equilibrium for the metapopulation dynamics, even when within-patch processes would produce very complex behaviour in each patch in the absence of migration. Thus, when spatially homogeneous equilibria become unstable, the system can often shift to a different, spatially inhomogeneous steady state. This new global equilibrium is characterized by a standing spatial wave of population abundances. Such standing spatial waves can also be observed in metapopulations consisting of identical habitat patches, i.e. without heterogeneity in patch quality, provided that dispersal is density dependent. Spatial pattern formation after destabilization of spatially homogeneous equilibrium states is well known in reaction–diffusion systems and has been observed in various ecological models. However, these models typically require the presence of at least two species, e.g. a predator and a prey. Our results imply that stabilization through spatial pattern formation can also occur in single-species models. However, the opposite effect of destabilization can also occur: if dispersal is short range, and if there is heterogeneity in patch quality, then the metapopulation dynamics can be chaotic despite the patches having stable equilibrium dynamics when isolated. We conclude that more general metapopulation models than those commonly studied are necessary to fully understand how spatial structure can affect spatial and temporal variation in population abundance.     

Synchrony of spatial populations induced by colored environmental noise and dispersal

Spatial synchrony of oscillating populations has been observed in many ecological systems, and its influences and causes have attracted the interest of ecologists. Spatially correlated environmental noises, dispersal, and trophic interactions have been considered as the causes of spatial synchrony. In this study, we develop a spatially structured population model, which is described by coupled-map lattices and incorporates both dispersal and colored environmental noise. A method for generating time series with desired spatial correlation and color is introduced. Then, we use these generated time series to analyze the influence of noise color on synchrony in population dynamics. The noise color refers to the temporal correlation in the time series data of the noise, and is expressed as the degree of (first-order) autocorrelation for autoregressive noise. Patterns of spatial synchrony are considered for stable, periodic and chaotic population dynamics. Numerical simulations verify that environmental noise color has a major influence on the level of synchrony, which depends strongly on how noise is introduced into the model. Furthermore, the influence of noise color also depends on patterns of dispersal between local populations. In addition, the desynchronizing effect of reddened noise is always weaker than that of white noise. From our results, we notice that the role of reddened environmental noise on spatial synchrony should be treated carefully and cautiously, especially for the spatially structured populations linked by dispersal.     

Environmental colour intensifies the Moran effect when population dynamics are spatially heterogeneous

Evidence for synchronous fluctuations of spatially separated populations is ubiquitous in the literature, including accounts within and across taxa. Among the few mechanisms explaining this phenomenon is the Moran effect, whereby independent populations are synchronized by spatially correlated environmental disturbances. The body of research on the Moran effect predominantly assumes that environmental disturbances within a local site are serially uncorrelated; that is, successive observations in time at a particular local site are independent. Yet, many environmental variables are known to possess strong temporal autocorrelation – a character which has often been described as 'colour'. The omission of environmental colour from research on the Moran effect may be due in part to the lack of methods capable of generating sets of time series with a desired colour and spatial correlation. Here I present a novel and simple method designated as 'phase partnering' to generate such sets of time series and I investigate the combined impact of spatial correlation and environmental colour on population synchrony in two common models of population dynamics. For linear population dynamics, and for a subset of nonlinear population dynamics, coloured environments intensify the Moran effect when population dynamics are spatially heterogeneous; in coloured environments the spatial correlation between populations more closely mimics the spatial correlation between their respective environments. Given that most environmental variables are coloured, these results imply that the Moran effect may be a far more significant driver of regional-scale population and interspecific synchrony than is currently believed.     

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.     

Modeling longitudinal spatial periodontal data: a spatially adaptive model with tools for specifying priors and checking fit

Summary .   Attachment loss (AL), the distance down a tooth's root that is no longer attached to surrounding bone by periodontal ligament, is a common measure of periodontal disease. In this article, we develop a spatiotemporal model to monitor the progression of AL. Our model is an extension of the conditionally autoregressive (CAR) prior, which spatially smooths estimates toward their neighbors. However, because AL often exhibits a burst of large values in space and time, we develop a nonstationary spatiotemporal CAR model that allows the degree of spatial and temporal smoothing to vary in different regions of the mouth. To do this, we assign each AL measurement site its own set of variance parameters and spatially smooth the variances with spatial priors. We propose a heuristic to measure the complexity of the site-specific variances, and use it to select priors that ensure parameters in the model are well identified. In data from a clinical trial, this model improves the fit compared to the usual dynamic CAR model for 90 of 99 patients' AL measurements.     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。     

Nonlinear visuoauditory integration in the mouse superior colliculus

Sensory information from different modalities is processed in parallel, and then integrated in associative brain areas to improve object identification and the interpretation of sensory experiences. The Superior Colliculus (SC) is a midbrain structure that plays a critical role in integrating visual, auditory, and somatosensory input to assess saliency and promote action. Although the response properties of the individual SC neurons to visuoauditory stimuli have been characterized, little is known about the spatial and temporal dynamics of the integration at the population level. Here we recorded the response properties of SC neurons to spatially restricted visual and auditory stimuli using large-scale electrophysiology. We then created a general, population-level model that explains the spatial, temporal, and intensity requirements of stimuli needed for sensory integration. We found that the mouse SC contains topographically organized visual and auditory neurons that exhibit nonlinear multisensory integration. We show that nonlinear integration depends on properties of auditory but not visual stimuli. We also find that a heuristically derived nonlinear modulation function reveals conditions required for sensory integration that are consistent with previously proposed models of sensory integration such as spatial matching and the principle of inverse effectiveness.     

A tunable fluorescent timer method for imaging spatial‐temporal protein dynamics using light‐driven photoconvertible protein

Cellular function is largely determined by protein behaviors occurring in both space and time. While regular fluorescent proteins can only report spatial locations of the target inside cells, fluorescent timers have emerged as an invaluable tool for revealing coupled spatial‐temporal protein dynamics. Existing fluorescent timers are all based on chemical maturation. Herein we propose a light‐driven timer concept that could report relative protein ages at specific sub‐cellular locations, by weakly but chronically illuminating photoconvertible fluorescent proteins inside cells. This new method exploits light, instead of oxygen, as the driving force. Therefore its timing speed is optically tunable by adjusting the photoconverting laser intensity. We characterized this light‐driven timer method both in vitro and in vivo and applied it to image spatiotemporal distributions of several proteins with different lifetimes. This novel timer method thus offers a flexible “ruler” for studying temporal hierarchy of spatially ordered processes with exquisite spatial‐temporal resolution. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Viability analyses with habitat-based metapopulation models

Population viability analysis (PVA) models incorporate spatial dynamics in different ways. At one extreme are the occupancy models that are based on the number of occupied populations. The simplest occupancy models ignore the location of populations. At the other extreme are individual-based models, which describe the spatial structure with the location of each individual in the population, or the location of territories or home ranges. In between these are spatially structured metapopulation models that describe the dynamics of each population with structured demographic models and incorporate spatial dynamics by modeling dispersal and temporal correlation among populations. Both dispersal and correlation between each pair of populations depend on the location of the populations, making these models spatially structured. In this article, I describe a method that expands spatially structured metapopulation models by incorporating information about habitat relationships of the species and the characteristics of the landscape in which the metapopulation exists. This method uses a habitat suitability map to determine the spatial structure of the metapopulation, including the number, size, and location of habitat patches in which subpopulations of the metapopulation live. The habitat suitability map can be calculated in a number of different ways, including statistical analyses (such as logistic regression) that find the relationship between the occurrence (or, density) of the species and independent variables which describe its habitat requirements. The habitat suitability map is then used to calculate the spatial structure of the metapopulation, based on species-specific characteristics such as the home range size, dispersal distance, and minimum habitat suitability for reproduction. Received: April 1, 1999 / Accepted: October 29, 1999     

Evolution under Spatially Heterogeneous Selection in Solid Tumors

Spatial genetic and phenotypic diversity within solid tumors has been well documented. Nevertheless, how this heterogeneity affects temporal dynamics of tumorigenesis has not been rigorously examined because solid tumors do not evolve as the standard population genetic model due to the spatial constraint. We therefore, propose a neutral spatial (NS) model whereby the mutation accumulation increases toward the periphery; the genealogical relationship is spatially determined and the selection efficacy is blunted (due to kin competition). In this model, neutral mutations are accrued and spatially distributed in manners different from those of advantageous mutations. Importantly, the distinctions could be blurred in the conventional model. To test the NS model, we performed a three-dimensional multiple microsampling of two hepatocellular carcinomas. Whole-genome sequencing (WGS) revealed a 2-fold increase in mutations going from the center to the periphery. The operation of natural selection can then be tested by examining the spatially determined clonal relationships and the clonal sizes. Due to limited migration, only the expansion of highly advantageous clones can sweep through a large part of the tumor to reveal the selective advantages. Hence, even multiregional sampling can only reveal a fraction of fitness differences in solid tumors. Our results suggest that the NS patterns are crucial for testing the influence of natural selection during tumorigenesis, especially for small solid tumors.