Universal scaling of species‐abundance distributions across multiple scales

The scale‐dependent species abundance distribution (SAD) is fundamental in ecology, but few spatially explicit models of this pattern have thus far been studied. Here we show spatially explicit neutral model predictions for SADs over a wide range of spatial scales, which appear to match empirical patterns qualitatively. We find that the assumption of a log‐series SAD in the metacommunity made by spatially implicit neutral models can be justified with a spatially explicit model in the large area limit. Furthermore, our model predicts that SADs on multiple scales are characterized by a single, compound parameter that represents the ratio of the survey area to the species’ average biogeographic range (which is in turn set by the speciation rate and the dispersal distance). This intriguing prediction is in line with recent empirical evidence for a universal scaling of the species‐area curve. Hence we hypothesize that empirical SAD patterns will show a similar universal scaling for many different taxa and across multiple spatial scales.     

Aggregate statistical measures and metapopulation dynamics

There are two main types of metapopulation models. Spatially implicit models are analytically tractable but neglect spatial heterogeneities. Spatially explicit models are more realistic but too complex. In this paper, I build a bridge between both approximations. I derive a new metapopulation model using a well-known technique in population genetics. Spatial heterogeneities are captured by an aggregate statistical measure of spatial correlation. When this correlation is zero, i.e., space is homogeneous, the model becomes the well-known Levins' model. As spatial correlation increases, equilibrium patch occupancy decreases from what would be expected under the spatially homogeneous assumption. I proceed by testing how well spatial complexities from a spatially explicit simulation can be encapsulated by such an aggregate statistical measure.     

Effects of perceptual and movement ranges on joint predator–prey distributions

We developed a spatially‐explicit individual‐based model to study how limited perceptual and movement ranges affect spatial predator–prey interactions. Earlier models of ‘predator–prey space games’ were often developed by modifying ideal free distribution models, which are spatially‐implicit and also assume that individuals are omniscient, although some more recent models have relaxed these assumptions. We found that under some conditions, the spatially‐explicit model generated similar predictions to previous models. However, the model showed that limited range in a spatially‐explicit context generated different predictions when 1) predator density and range are both small, and 2) when the predator movement range varied while the prey range was small. The model suggests that the differences were the result of 1) movement range changing the value of information sources and thus changing the behavior of individual predators and prey and 2) movement range limiting the ability of individuals to exploit the environment.     

Importance of spatial autocorrelation in modeling bird distributions at a continental scale

Spatial autocorrelation in species' distributions has been recognized as inflating the probability of a type I error in hypotheses tests, causing biases in variable selection, and violating the assumption of independence of error terms in models such as correlation or regression. However, it remains unclear whether these problems occur at all spatial resolutions and extents, and under which conditions spatially explicit modeling techniques are superior. Our goal was to determine whether spatial models were superior at large extents and across many different species. In addition, we investigated the importance of purely spatial effects in distribution patterns relative to the variation that could be explained through environmental conditions. We studied distribution patterns of 108 bird species in the conterminous United States using ten years of data from the Breeding Bird Survey. We compared the performance of spatially explicit regression models with non-spatial regression models using Akaike's information criterion. In addition, we partitioned the variance in species distributions into an environmental, a pure spatial and a shared component. The spatially-explicit conditional autoregressive regression models strongly outperformed the ordinary least squares regression models. In addition, partialling out the spatial component underlying the species' distributions showed that an average of 17% of the explained variation could be attributed to purely spatial effects independent of the spatial autocorrelation induced by the underlying environmental variables. We concluded that location in the range and neighborhood play an important role in the distribution of species. Spatially explicit models are expected to yield better predictions especially for mobile species such as birds, even in coarse-grained models with a large extent.     

Modeling bird species distribution change in fire prone Mediterranean landscapes: incorporating species dispersal and landscape dynamics

Species distribution models (SDMs) have traditionally been founded on the assumption that species distributions are in equilibrium with environmental conditions and that these species–environment relationships can be used to estimate species responses to environmental changes. Insight into the validity of this assumption can be obtained from comparing the performance of correlative species distribution models with more complex hybrid approaches, i.e. correlative and process‐based models that explicitly include ecological processes, thereby accounting for mismatches between habitat suitability and species occupancy patterns. Here we compared the ability of correlative SDMs and hybrid models, which can accommodate non‐equilibrium situations arising from dispersal constraints, to reproduce the distribution dynamics of the ortolan bunting Emberiza hortulana in highly dynamic, early successional, fire driven Mediterranean landscapes. Whereas, habitat availability was derived from a correlative statistical SDM, occupancy was modeled using a hybrid approach combining a grid‐based, spatially‐explicit population model that explicitly included bird dispersal with the correlative model. We compared species occupancy patterns under the equilibrium assumption and different scenarios of species dispersal capabilities. To evaluate the predictive capability of the different models, we used independent species data collected in areas affected to different degree by fires. In accordance with the view that disturbance leads to a disparity between the suitable habitat and the occupancy patterns of the ortolan bunting, our results indicated that hybrid modeling approaches were superior to correlative models in predicting species spatial dynamics. Furthermore, hybrid models that incorporated short dispersal distances were more likely to reproduce the observed changes in ortolan bunting distribution patterns, suggesting that dispersal plays a key role in limiting the colonization of recently burnt areas. We conclude that SDMs used in a dynamic context can be significantly improved by using combined hybrid modeling approaches that explicitly account for interactions between key ecological constraints such as dispersal and habitat suitability that drive species response to environmental changes.     

Non-additive and non-stationary properties in the spatial distribution of a large marine fish population

Density-independent and density-dependent variables both affect the spatial distributions of species. However, their effects are often separately addressed using different analytical techniques. We apply a spatially explicit regression framework that incorporates localized, interactive and threshold effects of both density-independent (water temperature) and density-dependent (population abundance) variables, to study the spatial distribution of a well-monitored flatfish population in the eastern Bering Sea. Results indicate that when population biomass was beyond a threshold a further increase in biomass-promoted habitat expansion in a non-additive fashion with water temperature. In contrast, during years of low population size, habitat occupancy was affected positively only by water temperature. These results reveal the spatial signature of intraspecific abundance distribution relationships as well as the non-additive and non-stationary responses of species spatial dynamics. Furthermore, these results underscore the importance of implementing analytical techniques that can simultaneously account for density-dependent and density-independent sources of variability when studying geographical distribution patterns.     

Can niche‐based distribution models outperform spatial interpolation?

Aim Distribution modelling relates sparse data on species occurrence or abundance to environmental information to predict the population of a species at any point in space. Recently, the importance of spatial autocorrelation in distributions has been recognized. Spatial autocorrelation can be categorized as exogenous (stemming from autocorrelation in the underlying variables) or endogenous (stemming from activities of the organism itself, such as dispersal). Typically, one asks whether spatial models explain additional variability (endogenous) in comparison to a fully specified habitat model. We turned this question around and asked: can habitat models explain additional variation when spatial structure is accounted for in a fully specified spatially explicit model? The aim was to find out to what degree habitat models may be inadvertently capturing spatial structure rather than true explanatory mechanisms. Location We used data from 190 species of the North American Breeding Bird Survey covering the conterminous United States and southern Canada. Methods We built 13 different models on 190 bird species using regression trees. Our habitat‐based models used climate and landcover variables as independent variables. We also used random variables and simulated ranges to validate our results. The two spatially explicit models included only geographical coordinates or a contagion term as independent variables. As another angle on the question of mechanism vs. spatial structure we pitted a model using related bird species as predictors against a model using randomly selected bird species. Results The spatially explicit models outperformed the traditional habitat models and the random predictor species outperformed the related predictor species. In addition, environmental variables produced a substantial R² in predicting artificial ranges. Main conclusions We conclude that many explanatory variables with suitable spatial structure can work well in species distribution models. The predictive power of environmental variables is not necessarily mechanistic, and spatial interpolation can outperform environmental explanatory variables.     

Abundance, spatial variance and occupancy: arthropod species distribution in the Azores

1. The positive abundance-occupancy and abundance-variance relationships are two of the most widely documented patterns in population and community ecology. 2. Recently, a general model has been proposed linking the mean abundance, the spatial variance in abundance, and the occupancy of species. A striking feature of this model is that it consists explicitly of the three variables abundance, variance and occupancy, and no extra parameters are involved. However, little is known about how well the model performs. 3. Here, we show that the abundance-variance-occupancy model fits extremely well to data on the abundance, variance and occupancy of a large number of arthropod species in natural forest patches in the Azores, at three spatial extents, and distinguishing between species of different colonization status. Indeed, virtually all variation about the bivariate abundance-occupancy and abundance-variance relationships is effectively explained by the third missing variable (variance in abundance in the case of the abundance-occupancy relationship, and occupancy in the case of the abundance-variance relationship). 4. Introduced species tend to exhibit lower densities, less spatial variance in these densities, and occupy fewer sites than native and endemic species. None the less, they all lie on the same bivariate abundance-occupancy and abundance-variance, and trivariate abundance-variance-occupancy, relationships. 5. Density, spatial variance in density, and occupancy appear to be all the things one needs to know to describe much of the spatial distribution of species.     

Spatial scaling of mountain pine beetle infestations

1. The relationship between occupancy and spatial contagion during the spread of eruptive and invasive species demands greater study, as it could lead to improved prediction of ecosystem damage. 2. We applied a recently developed model that links occupancy and its fractal dimension to model the spatial distribution of mountain pine beetle infestations in British Columbia, Canada. We showed that the distribution of infestation was scale-invariant in at least 24 out of 37 years (mostly in epidemic years), and presented some degree of scale-invariance in the rest. There was a general logarithmic relationship between fractal dimension and infestation occupancy. Based on the scale-invariance assumption, we further assessed the interrelationships for several landscape metrics, such as correlation length, maximum cluster size, total edge length and total number of clusters. 3. The scale-invariance assumption allows fitting the above metrics, and provides a framework to establish the scaling relationship between occupancy and spatial contagion. 4. We concluded that scale-invariance dominates the spread of mountain pine beetle. In this context, spatial aggregation can be predicted from occupancy, hence occupancy is the only variable one needs to know in order to predict the spatial distributions of populations. This supports the hypothesis that fractal dispersal kernels may be abundant among outbreaks of pests and invasive species.     

Hierarchical models facilitate spatial analysis of large data sets: a case study on invasive plant species in the northeastern United States

Many critical ecological issues require the analysis of large spatial point data sets – for example, modelling species distributions, abundance and spread from survey data. But modelling spatial relationships, especially in large point data sets, presents major computational challenges. We use a novel Bayesian hierarchical statistical approach, 'spatial predictive process' modelling, to predict the distribution of a major invasive plant species, Celastrus orbiculatus , in the northeastern USA. The model runs orders of magnitude faster than traditional geostatistical models on a large data set of c . 4000 points, and performs better than generalized linear models, generalized additive models and geographically weighted regression in cross-validation. We also use this approach to model simultaneously the distributions of a set of four major invasive species in a spatially explicit multivariate model. This multispecies analysis demonstrates that some pairs of species exhibit negative residual spatial covariation, suggesting potential competitive interaction or divergent responses to unmeasured factors.     

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     

Mechanistic home range models capture spatial patterns and dynamics of coyote territories in Yellowstone

Patterns of space-use by individuals are fundamental to the ecology of animal populations influencing their social organization, mating systems, demography and the spatial distribution of prey and competitors. To date, the principal method used to analyse the underlying determinants of animal home range patterns has been resource selection analysis (RSA), a spatially implicit approach that examines the relative frequencies of animal relocations in relation to landscape attributes. In this analysis, we adopt an alternative approach, using a series of mechanistic home range models to analyse observed patterns of territorial space-use by coyote packs in the heterogeneous landscape of Yellowstone National Park. Unlike RSAs, mechanistic home range models are derived from underlying correlated random walk models of individual movement behaviour, and yield spatially explicit predictions for patterns of space-use by individuals. As we show here, mechanistic home range models can be used to determine the underlying determinants of animal home range patterns, incorporating both movement responses to underlying landscape heterogeneities and the effects of behavioural interactions between individuals. Our analysis indicates that the spatial arrangement of coyote territories in Yellowstone is determined by the spatial distribution of prey resources and an avoidance response to the presence of neighbouring packs. We then show how the fitted mechanistic home range model can be used to correctly predict observed shifts in the patterns of coyote space-use in response to perturbation.     

Modeling species distributions by breaking the assumption of self-similarity

Species distributions are commonly measured as the number of sites, or geographic grid cells occupied. These data may then be used to model species distributions and to examine patterns in both intraspecific and interspecific distributions. Harte et al. (1999) used a model based on a bisection rule and assuming self-similarity in species distributions to do so. However, this approach has also been criticized for several reasons. Here we show that the self-similarity in species distributions breaks down according to a power relationship with spatial scales, and we therefore adopt a power-scaling assumption for modeling species occupancy distributions. The outcomes of models based on these two assumptions (self-similar and power-scaling) have not previously been compared. Based on Harte's bisection method and an occupancy probability transition model under these two assumptions (self-similar and power-scaling), we compared the scaling pattern of occupancy (also known as the area-of-occupancy) and the spatial distribution of species. The two assumptions of species distribution lead to a relatively similar interspecific occupancy frequency distribution pattern, although the spatial distribution of individual species and the scaling pattern of occupancy differ significantly. The bimodality in occupancy frequency distributions that is common in species communities, is confirmed to a result for certain mathematical and statistical properties of the probability distribution of occupancy. The results thus demonstrate that the use of the bisection method in combination with a power-scaling assumption is more appropriate for modeling species distributions than the use of a self-similarity assumption, particularly at fine scales.     

Population dynamics, disturbance, and pattern evolution: identifying the fundamental scales of organization in a model ecosystem

We used auto- and cross-correlation analysis and Ripley's K-function analysis to analyze spatiotemporal pattern evolution in a spatially explicit simulation model of a semiarid shrubland (Karoo, South Africa) and to determine the impact of small-scale disturbances on system dynamics. Without disturnities bance, local dynamics were driven by a pattern of cyclic succession, where 'colonizer' and 'successor' species alternately replaced each other. This results in a strong pattern of negative correlation in the temporal distribution of colonizer and successor species. As disturbance rates were increased, the relationship shifted from being negatively correlated in time to being positively correlated-the dynamics became decoupled from the ecologically driven cyclic succession and were increasingly influenced by abiotic factors (e.g., rainfall events). Further analysis of the spatial relationships among colonizer and successor species showed that, without disturbance, periods of attraction and repulsion between colonizer and successor species alternate cyclically at intermediate spatial scales. This was due to the spatial 'memory' embedded in the system through the process of cyclic succession. With the addition of disturbance, this pattern breaks down, although there is some indication of increasing ecological organization at broader spatial scales. We suggest that many of the insights that can be gained through spatially explicit models will only be obtained through a direct analysis of the spatial patterns produced.     

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.     

An allometric model of home range formation explains the structuring of animal communities exploiting heterogeneous resources

Understanding and predicting the composition and spatial structure of communities is a central challenge in ecology. An important structural property of animal communities is the distribution of individual home ranges. Home range formation is controlled by resource heterogeneity, the physiology and behaviour of individual animals, and their intra‐ and interspecific interactions. However, a quantitative mechanistic understanding of how home range formation influences community composition is still lacking. To explore the link between home range formation and community composition in heterogeneous landscapes we combine allometric relationships for physiological properties with an algorithm that selects optimal home ranges given locomotion costs, resource depletion and competition in a spatially‐explicit individual‐based modelling framework. From a spatial distribution of resources and an input distribution of animal body mass, our model predicts the size and location of individual home ranges as well as the individual size distribution (ISD) in an animal community. For a broad range of body mass input distributions, including empirical body mass distributions of North American and Australian mammals, our model predictions agree with independent data on the body mass scaling of home range size and individual abundance in terrestrial mammals. Model predictions are also robust against variation in habitat productivity and landscape heterogeneity. The combination of allometric relationships for locomotion costs and resource needs with resource competition in an optimal foraging framework enables us to scale from individual properties to the structure of animal communities in heterogeneous landscapes. The proposed spatially‐explicit modelling concept not only allows for detailed investigation of landscape effects on animal communities, but also provides novel insights into the mechanisms by which resource competition in space shapes animal communities.     

Modelling forest dynamics: a perspective from point process methods

This paper reviews the main applications of (marked) point process theory in forestry including functions to analyse spatial variability and the main (marked) point process models. Although correlation functions do describe spatial variability at distinct range of scale, they are clearly restricted to the analysis of few dominant species since they are based on pairwise analysis. This has over-simplified the spatial analysis of complex forest dynamics involving "large" number of species. Moreover, although process models can reproduce, to some extent, real forest spatial patterns of trees, the biological forest-ecological interpretation of the resulting spatial structures is difficult since these models usually lack of biological realism. This problem gains in strength as usually most of these point process models are defined in terms of purely spatial relationships, though in real life, forest develop through time. We thus aim to discuss the applicability of such formulations to analyse and simulate "real" forest dynamics and unwrap their shortcomes. We present a unified approach of modern spatially explicit forest growth models. Finally, we focus on a continuous space-time stochastic process as an alternative approach to generate marked point patterns evolving through space and time.     

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.     

Weak climatic associations among British plant distributions

Aim Species distribution models (SDMs) are used to infer niche responses and predict climate change‐induced range shifts. However, their power to distinguish real and chance associations between spatially autocorrelated distribution and environmental data at continental scales has been questioned. Here this is investigated at a regional (10 km) scale by modelling the distributions of 100 plant species native to the UK. Location UK. Methods SDMs fitted using real climate data were compared with those utilizing simulated climate gradients. The simulated gradients preserve the exact values and spatial structure of the real ones, but have no causal relationships with any species and so represent an appropriate null model. SDMs were fitted as generalized linear models (GLMs) or by the Random Forest machine‐learning algorithm and were either non‐spatial or included spatially explicit trend surfaces or autocovariates as predictors. Results Species distributions were significantly but erroneously related to the simulated gradients in 86% of cases (P < 0.05 in likelihood‐ratio tests of GLMs), with the highest error for strongly autocorrelated species and gradients and when species occupied 50% of sites. Even more false effects were found when curvilinear responses were modelled, and this was not adequately mitigated in the spatially explicit models. Non‐spatial SDMs based on simulated climate data suggested that 70–80% of the apparent explanatory power of the real data could be attributable to its spatial structure. Furthermore, the niche component of spatially explicit SDMs did not significantly contribute to model fit in most species. Main conclusions Spatial structure in the climate, rather than functional relationships with species distributions, may account for much of the apparent fit and predictive power of SDMs. Failure to account for this means that the evidence for climatic limitation of species distributions may have been overstated. As such, predicted regional‐ and national‐scale impacts of climate change based on the analysis of static distribution snapshots will require re‐evaluation.