Fitting probability distributions to animal movement trajectories: using artificial neural networks to link distance, resources, and memory

Animal movement paths are often thought of as a confluence of behavioral processes and landscape patterns. Yet it has proven difficult to develop frameworks for analyzing animal movement that can test these interactions. Here we describe a novel method for fitting movement models to data that can incorporate diverse aspects of landscapes and behavior. Using data from five elk (Cervus canadensis) reintroduced to central Ontario, we employed artificial neural networks to estimate movement probability kernels as functions of three landscape-behavioral processes. These consisted of measures of the animals' response to the physical spatial structure of the landscape, the spatial variability in resources, and memory of previously visited locations. The results support the view that animal movement results from interactions among elements of landscape structure and behavior, motivating context-dependent movement probabilities, rather than from successive realizations of static distributions, as some traditional models of movement and resource selection assume. Flexible, nonlinear models may thus prove useful in understanding the mechanisms controlling animal movement patterns.     

Spatiotemporal dynamic models of plant populations and communities

The idea of relating spatial patterns and temporal processes in plant community dynamics is not new, but its transformation into realistic spatiotemporal models is the result of quite recent methodological developments. There are now two classes of analytical model and a broad class of simulation models pertaining to the role of spatial structure in vegetation dynamics. They indicate that any community-dynamical theory intended to be predictive should not omit the spatial aspects of plant population dynamics, because these may radically change the conditions of persistence and coexistence.     

Accounting for multi‐scale spatial autocorrelation improves performance of invasive species distribution modelling (iSDM)

Aim Analyses of species distributions are complicated by various origins of spatial autocorrelation (SAC) in biogeographical data. SAC may be particularly important for invasive species distribution models (iSDMs) because biological invasions are strongly influenced by dispersal and colonization processes that typically create highly structured distribution patterns. We examined the efficacy of using a multi‐scale framework to account for different origins of SAC, and compared non‐spatial models with models that accounted for SAC at multiple levels. Location We modelled the spatial distribution of an invasive forest pathogen, Phytophthora ramorum, in western USA. Methods We applied one conventional statistical method (generalized linear model, GLM) and one nonparametric technique (maximum entropy, Maxent) to a large dataset on P. ramorum occurrence (n = 3787) to develop four types of model that included environmental variables and that either ignored spatial context or incorporated it at a broad scale using trend surface analysis, a local scale using autocovariates, or multiple scales using spatial eigenvector mapping. We evaluated model accuracies and amounts of explained spatial structure, and examined the changes in predictive power of the environmental and spatial variables. Results Accounting for different scales of SAC significantly enhanced the predictive capability of iSDMs. Dramatic improvements were observed when fine‐scale SAC was included, suggesting that local range‐confining processes are important in P. ramorum spread. The importance of environmental variables was relatively consistent across all models, but the explanatory power decreased in spatial models for factors with strong spatial structure. While accounting for SAC reduced the amount of residual autocorrelation for GLM but not for Maxent, it still improved the performance of both approaches, supporting our hypothesis that dispersal and colonization processes are important factors to consider in distribution models of biological invasions. Main conclusions Spatial autocorrelation has become a paradigm in biogeography and ecological modelling. In addition to avoiding the violation of statistical assumptions, accounting for spatial patterns at multiple scales can enhance our understanding of dynamic processes that explain ecological mechanisms of invasion and improve the predictive performance of static iSDMs.     

Pushed to the edge: Spatial sorting can slow down invasions

Our ability to understand population spread dynamics is complicated by rapid evolution, which renders simple ecological models insufficient. If dispersal ability evolves, more highly dispersive individuals may arrive at the population edge than less dispersive individuals (spatial sorting), accelerating spread. If individuals at the low-density population edge benefit (escape competition), high dispersers have a selective advantage (spatial selection). These two processes are often described as forming a positive feedback loop; they reinforce each other, leading to faster spread. Although spatial sorting is close to universal, this form of spatial selection is not: low densities can be detrimental for organisms with Allee effects. Here, we present two conceptual models to explore the feedback loops that form between spatial sorting and spatial selection. We show that the presence of an Allee effect can reverse the positive feedback loop between spatial sorting and spatial selection, creating a negative feedback loop that slows population spread.     

Overview: Spatial information and indicators for sustainable management of natural resources

Natural resource management (NRM) is becoming increasingly important at all scales, local, regional, national and global, because of an increasing human population and increasing per capita use of resources and space. Conflicts are intensifying between different interest groups. Production and conservation aspects are particularly debated because conservation often conflicts with economic and social sustainability. There is public demand for objective decision based NRM but limitations are all pervasive due to the spatial and temporal complexity and interdisciplinary nature.This special issue explores the use of spatial data and models to overcome some limitations of NRM decision making. The papers in this issue show modern approaches of natural resources management with a particular focus on spatial data collection, analysis and the development of spatial indicators. This issue presents a balanced mix of review and research papers that give examples of how to find or improve the spatial information base for evidence-based decision making.This overview makes the argument that understanding complex spatial pattern and processes, and the development of spatial indicators, is an essential aspect of evidence-based NRM. If spatial and temporal patterns are complex, ecological evidence from field data or experiments may have limited value for NRM and observational study designs become more appropriate for understanding complex spatial pattern and processes. Data quality should be documented as a combination of accuracy and spatio-temporal representativeness in order to be useful in the NRM decision process.     

Marine systems analysis and modeling

Oceanography and marine ecology have a considerable history in the use of computers for modeling both physical and ecological processes. With increasing stress on the marine environment due to human activities such as fisheries and numerous forms of pollution, the analysis of marine problems must increasingly and jointly consider physical, ecological and socio-economic aspects in a broader systems framework that transcends more traditional disciplinary boundaries. This often introduces difficult-to-quantify, “soft” elements, such as values and perceptions, into formal analysis. Thus, the problem domain combines a solid foundation in the physical sciences, with strong elements of ecological, socio-economic and political considerations. At the same time, the domain is also characterized by both a very large volume of some data, and an extremely datapoor situation for other variables, as well as a very high degree of uncertainty, partly due to the temporal and spatial heterogeneity of the marine environment. Consequently, marine systems analysis and management require tools that can integrate these diverse aspects into efficient information systems that can support research as well as planning and also policy- and decisionmaking processes. Supporting scientific research, as well as decision-making processes and the diverse groups and actors involved, requires better access and direct understanding of the information basis as well as easy-to-use, but powerful tools for analysis. Advanced information technology provides the tools to design and implement smart software where, in a broad sense, the emphasis is on the man-machine interface. Symbolic and analogous, graphical interaction, visual representation of problems, integrated data sources, and built-in domain knowledge can effectively support users of complex and complicated software systems. Integration, interaction, visualization and intelligence are key concepts that are discussed in detail, using an operational software example of a coastal water quality model. The model comprises components of a geographical information and mapping system, data bases, dynamic simulation models, and an integrated expert system. An interactive graphical user interface, dynamic visualization of model results, and a hyper-text-based help-and-explain system illustrate some of the features of new and powerful software tools for marine systems analysis and modeling.     

Computational models of spatial updating in peri-saccadic perception

Perceptual phenomena that occur around the time of a saccade, such as peri-saccadic mislocalization or saccadic suppression of displacement, have often been linked to mechanisms of spatial stability. These phenomena are usually regarded as errors in processes of trans-saccadic spatial transformations and they provide important tools to study these processes. However, a true understanding of the underlying brain processes that participate in the preparation for a saccade and in the transfer of information across it requires a closer, more quantitative approach that links different perceptual phenomena with each other and with the functional requirements of ensuring spatial stability. We review a number of computational models of peri-saccadic spatial perception that provide steps in that direction. Although most models are concerned with only specific phenomena, some generalization and interconnection between them can be obtained from a comparison. Our analysis shows how different perceptual effects can coherently be brought together and linked back to neuronal mechanisms on the way to explaining vision across saccades.     

Spatial dynamics in model plant communities: what do we really know?

A variety of models have shown that spatial dynamics and small-scale endogenous heterogeneity (e.g., forest gaps or local resource depletion zones) can change the rate and outcome of competition in communities of plants or other sessile organisms. However, the theory appears complicated and hard to connect to real systems. We synthesize results from three different kinds of models: interacting particle systems, moment equations for spatial point processes, and metapopulation or patch models. Studies using all three frameworks agree that spatial dynamics need not enhance coexistence nor slow down dynamics; their effects depend on the underlying competitive interactions in the community. When similar species would coexist in a nonspatial habitat, endogenous spatial structure inhibits coexistence and slows dynamics. When a dominant species disperses poorly and the weaker species has higher fecundity or better dispersal, competition-colonization trade-offs enhance coexistence. Even when species have equal dispersal and per-generation fecundity, spatial successional niches where the weaker and faster-growing species can rapidly exploit ephemeral local resources can enhance coexistence. When interspecific competition is strong, spatial dynamics reduce founder control at large scales and short dispersal becomes advantageous. We describe a series of empirical tests to detect and distinguish among the suggested scenarios.     

Linking community and ecosystem dynamics through spatial ecology

Classical approaches to food webs focus on patterns and processes occurring at the community level rather than at the broader ecosystem scale, and often ignore spatial aspects of the dynamics. However, recent research suggests that spatial processes influence both food web and ecosystem dynamics, and has led to the idea of 'metaecosystems'. However, these processes have been tackled separately by 'food web metacommunity' ecology, which focuses on the movement of traits, and 'landscape ecosystem' ecology, which focuses on the movement of materials among ecosystems. Here, we argue that this conceptual gap must be bridged to fully understand ecosystem dynamics because many natural cases demonstrate the existence of interactions between the movements of traits and materials. This unification of concepts can be achieved under the metaecosystem framework, and we present two models that highlight how this framework yields novel insights. We then discuss patches, limiting factors and spatial explicitness as key issues to advance metaecosystem theory. We point out future avenues for research on metaecosystem theory and their potential for application to biological conservation.     

On the role of spatial stochastic models in understanding landscape indices in ecology

Spatial stochastic models play an important role in understanding and predicting the behaviour of complex systems. Such models may be implemented with explicit knowledge of only a limited number of parameters relating to spatial relationships among locations. Consequently, they are often used instead of deterministic‐mechanistic models, which may potentially require an unrealistically large number of parameters. Currently, in contrast to spatial stochastic models, the parameterization of the joint spatial distribution of objects in landscape models is more often implicit than explicit. Here, we investigate the similarities and differences between bona fide spatial stochastic models and landscape models by focusing mostly on the relationships between processes, their realizations (patterns), representation and measurement, and their use in exploratory as well as confirmatory data analysis. One of the most important outcomes of recognizing the importance of stochastic processes is the acknowledgement that the spatial pattern observed in a landscape is only one realization of that process. Hence, while ecologists have been using landscape pattern indices (LPIs) to characterize landscape heterogeneity and/or make inferences about processes shaping the landscape, no stochastic modelling framework has been developed for their proper statistical elucidation. Consequently, several (mis)uses of LPIs draw conclusions about landscapes which are suspect. We show that several reports about sensitivities of LPIs to measurements have common roots that can be made explicitly manageable by adopting stochastic models of spatial structure. The key parameters of these stochastic models are composition and configuration, which, in general, cannot be estimated independently from each other. We outline how to develop the stochastic framework to interpret observations and make some recommendations to practitioners about everyday usage. The conceptual linkages between patterns and processes are particularly important in light of recent efforts to bridge the static‐structural and the dynamic‐analytic traditions of ecology.     

Moving beyond abundance distributions: neutral theory and spatial patterns in a tropical forest

Assessing the relative importance of different processes that determine the spatial distribution of species and the dynamics in highly diverse plant communities remains a challenging question in ecology. Previous modelling approaches often focused on single aggregated forest diversity patterns that convey limited information on the underlying dynamic processes. Here, we use recent advances in inference for stochastic simulation models to evaluate the ability of a spatially explicit and spatially continuous neutral model to quantitatively predict six spatial and non-spatial patterns observed at the 50 ha tropical forest plot on Barro Colorado Island, Panama. The patterns capture different aspects of forest dynamics and biodiversity structure, such as annual mortality rate, species richness, species abundance distribution, beta-diversity and the species–area relationship (SAR). The model correctly predicted each pattern independently and up to five patterns simultaneously. However, the model was unable to match the SAR and beta-diversity simultaneously. Our study moves previous theory towards a dynamic spatial theory of biodiversity and demonstrates the value of spatial data to identify ecological processes. This opens up new avenues to evaluate the consequences of additional process for community assembly and dynamics.     

Spatiotemporally explicit demographic modelling supports a joint effect of historical barriers to dispersal and contemporary landscape composition on structuring genomic variation in a red‐listed grasshopper

Inferring the processes underlying spatial patterns of genomic variation is fundamental to understand how organisms interact with landscape heterogeneity and to identify the factors determining species distributional shifts. Here, we use genomic data (restriction site‐associated DNA sequencing) to test biologically informed models representing historical and contemporary demographic scenarios of population connectivity for the Iberian cross‐backed grasshopper Dociostaurus hispanicus, a species with a narrow distribution that currently forms highly fragmented populations. All models incorporated biological aspects of the focal taxon that could hypothetically impact its geographical patterns of genomic variation, including (a) spatial configuration of impassable barriers to dispersal defined by topographic landscapes not occupied by the species; (b) distributional shifts resulting from the interaction between the species bioclimatic envelope and Pleistocene glacial cycles; and (c) contemporary distribution of suitable habitats after extensive land clearing for agriculture. Spatiotemporally explicit simulations under different scenarios considering these aspects and statistical evaluation of competing models within an Approximate Bayesian Computation framework supported spatial configuration of topographic barriers to dispersal and human‐driven habitat fragmentation as the main factors explaining the geographical distribution of genomic variation in the species, with no apparent impact of hypothetical distributional shifts linked to Pleistocene climatic oscillations. Collectively, this study supports that both historical (i.e., topographic barriers) and contemporary (i.e., anthropogenic habitat fragmentation) aspects of landscape composition have shaped major axes of genomic variation in the studied species and emphasizes the potential of model‐based approaches to gain insights into the temporal scale at which different processes impact the demography of natural populations.     

Regional persistence of locally unstable predator/prey populations

Phytoseiid mites are efficient predators capable of completely destroying colonies of spider mites. Thus, coexistence of phytoseiids and their tetranychid prey at a local scale (typically an individual plant) is not likely for more than a single predator/prey cycle. However, the species may coexist at a regional scale, i.e. in a complex environment consisting of many plants, provided local colonisations, extinctions and recolonisations occur asynchronously. This review investigates some of the factors responsible for establishing and maintaining spatial asynchrony between local populations of prey and predators, such as dispersal, environmental heterogeneity and demographic stochasticity. Existing predator/prey models are considered in order to find agreement between theory and empirical data. Based on our current knowledge of spatial processes and their importance for the overall dynamics and persistence of predator/prey interactions, some consequences and aspects for biological control of crop pests by means of natural enemies are outlined.     

异质种群动态模型:破碎化景观动态模拟的新途径

景观破碎化导致物种以异质种群方式存活,使得基于异质种群动态模拟破碎化景观动态成为可能。异质种群动态模型的发展为景观动态模拟奠定了良好基础。根据空间处理方式的不同,异质种群模型可分为三大类,可不同程度地用于描述破碎化景观动态。(1)空间不确定异质种群模型,假定所有局域种群间均等互联,模型中不包含空间信息,仅能用于景观斑块动态描述;(2)空间确定异质种群模型,假设局域种群在二维空间上以规则格子形式排列,是一种准现实的空间处理方式,可用于景观动态的简单描述;(3)空间现实异质种群模型,包含了破碎化景观中局域种群的几何特征,可直接用于真实景观动态的模拟研究。空间现实的和基于个体的异质种群模型不但是未来异质种群模型发展的主流,也将成为未来破碎化景观动态研究的重要工具。为了更加准确完整地描述破碎化景观动态,不但应该综合运用已有的各种异质种群模型方法,更要引进新模型来刎画多物种、多变量、高维度、复杂连接的破碎化景观格局与过程。     

Decoding complex Ca2+ signals through the modulation of Ras signaling

Calcium (Ca(2+)) is a universal regulator of a wide variety of cellular processes. For such control to be achieved, information is encoded within spatial and temporal components of the underlying Ca(2+) signal. One pathway through which Ca(2+) signals are decoded is the Ras binary switch. Here I describe some recent advances that have shed light on how cells can decode the spatial and temporal aspects of Ca(2+) signals through the regulation of this important signalling switch.     

A pulse-periodic torch in a coaxial waveguide: Formation dynamics and spatial structure

Results are presented from experimental studies of the formation dynamics, spatial structure, and parameters of a pulse-periodic microwave discharge excited in a coaxial waveguide. The experimental setup allows the stable generation of a plasma jet in molecular and atomic gas flows at pressures close to atmospheric pressure without applying additional initiators. The complicated sequence of processes leading to torch formation cannot be adequately described with conventional models of a discharge sustained by a surface electromagnetic wave.     

No evidence of intrinsic spatial processes driving Neotropical savanna vegetation on different substrates

The relationships between floristic patterns and environmental variation in tropical savannas have been the focus of many studies worldwide. However, important aspects of these relationships, such as the role of geographic distance in structuring plant communities, have received little attention. We investigated the individual and combined influences of substrate, climatic, and spatial factors on the floristic‐structural dissimilarity between two savanna physiognomies in the core region of Brazilian savannas: one on plain relief with deep soils and another on steep relief with shallow rocky soils. Ten 1‐ha plots were sampled in each physiognomy. We modeled species abundance using multiple linear models and variance partitioning. Our results indicated that spatial processes that are intrinsically related to species variation have negligible effects on floristic variation. The most important predictors in our models were related to soil characteristics (mainly nutrient availability) and topography (relief and elevation). Consequently, the substrate component exhibited the greatest power (14%) in explaining the floristic‐structural variation in the overall variance partitioning. Our results provide the first demonstration of the individual and combined contributions of substrate, climatic, and spatial factors to the occurrence and abundance of woody species in the most diverse and threatened savanna in the world. We also provide evidence that neutral processes might not be strong predictors of vegetation structure where savanna substrates differ greatly; instead, community structure may be primarily regulated by environmental filters.     

Spatial processes and evolutionary models: a critical review

Evolution is a fundamentally population level process in which variation, drift and selection produce both temporal and spatial patterns of change. Statistical model fitting is now commonly used to estimate which kind of evolutionary process best explains patterns of change through time using models like Brownian motion, stabilizing selection (Ornstein–Uhlenbeck) and directional selection on traits measured from stratigraphic sequences or on phylogenetic trees. But these models assume that the traits possessed by a species are homogeneous. Spatial processes such as dispersal, gene flow and geographical range changes can produce patterns of trait evolution that do not fit the expectations of standard models, even when evolution at the local‐population level is governed by drift or a typical OU model of selection. The basic properties of population level processes (variation, drift, selection and population size) are reviewed and the relationship between their spatial and temporal dynamics is discussed. Typical evolutionary models used in palaeontology incorporate the temporal component of these dynamics, but not the spatial. Range expansions and contractions introduce rate variability into drift processes, range expansion under a drift model can drive directional change in trait evolution, and spatial selection gradients can create spatial variation in traits that can produce long‐term directional trends and punctuation events depending on the balance between selection strength, gene flow, extirpation probability and model of speciation. Using computational modelling that spatial processes can create evolutionary outcomes that depart from basic population‐level notions from these standard macroevolutionary models.     

The time sequence of the relation between mean crowding and mean density with some population processes

Summary The theories of the stochastic processes are applied to construct mathematical models for describing the processes of population change as an ever changing the distribution of individuals in a space. These models consist of two mathematical expressions which are named the spatial distribution probability function (Q _n (t)) and the transition probability function (P _i,n (t)), respectively. The former gives the spatial distribution at any future time. Given an actual spatial distribution at any time, the latter function converts it to the spatial distribution at any future time. According to these models, we discussed the time sequence of the mean crowding-mean density relation (Iwao andKuno, 1971) in some population processes such as mortality, birth, immigration, growth, and their combined processes.