A strong test of a maximum entropy model of trait-based community assembly

We evaluate the predictive power and generality of Shipley's maximum entropy (maxent) model of community assembly in the context of 96 quadrats over a 120-km2 area having a large (79) species pool and strong gradients. Quadrats were sampled in the herbaceous understory of ponderosa pine forests in the Coconino National Forest, Arizona, U.S.A. The maxent model accurately predicted species relative abundances when observed community-weighted mean trait values were used as model constraints. Although only 53% of the variation in observed relative abundances was associated with a combination of 12 environmental variables, the maxent model based only on the environmental variables provided highly significant predictive ability, accounting for 72% of the variation that was possible given these environmental variables. This predictive ability largely surpassed that of nonmetric multidimensional scaling (NMDS) or detrended correspondence analysis (DCA) ordinations. Using cross-validation with 1000 independent runs, the median correlation between observed and predicted relative abundances was 0.560 (the 2.5% and 97.5% quantiles were 0.045 and 0.825). The qualitative predictions of the model were also noteworthy: dominant species were correctly identified in 53% of the quadrats, 83% of rare species were correctly predicted to have a relative abundance of < 0.05, and the median predicted relative abundance of species actually absent from a quadrat was 5 x 10(-5).     

Wetlands as an alternative stable state in desert streams

Historically, desert drainages of the American southwest supported productive riverine wetlands (ciénegas). Region-wide erosion of ciénegas during the late 19th and early 20th century dramatically reduced the abundance of these ecosystems, but recent reestablishment of wetlands in Sycamore Creek, Arizona, USA, provides an opportunity to evaluate the mechanisms underlying wetland development. A simple model demonstrates that density-dependent stabilization of channel substrate by vegetation results in the existence of alternative stable states in desert streams. A two-year (October 2004-September 2006) field survey of herbaceous cover and biomass at 26 sites located along Sycamore Creek is used to test the underlying assumption of this model that vegetation cover loss during floods is density dependent, as well as the prediction that the distribution of vegetation abundance should shift toward bimodality in response to floods. Observations of nonlinear, negative relationships between herbaceous biomass prior to flood events and the proportion of persistent vegetation cover were consistent with the alternative stable state model. In further support of the alternative-state hypothesis, vegetation cover diverged from an approximately normal distribution toward a distinctly bimodal distribution during the monsoon flood season of 2006. These results represent the first empirically supported example of alternative-state behavior in stream ecosystems. Identification of alternative stable states in desert streams supports recent hypotheses concerning the importance of strong abiotic-disturbance regimes and biogeomorphic mechanisms in multiple-state ecosystems.     

Characterizing species abundance distributions across taxa and ecosystems using a simple maximum entropy model

The species abundance distribution (SAD) is one of themost studied patterns in ecology due to its potential insights into commonness and rarity, community assembly, and patterns of biodiversity. It is well established that communities are composed of a few common and many rare species, and numerous theoretical models have been proposed to explain this pattern. However, no attempt has been made to determine how well these theoretical characterizations capture observed taxonomic and global-scale spatial variation in the general form of the distribution. Here, using data of a scope unprecedented in community ecology, we show that a simple maximum entropy model produces a truncated log-series distribution that can predict between 83% and 93% of the observed variation in the rank abundance of species across 15 848 globally distributed communities including birds, mammals, plants, and butterflies. This model requires knowledge of only the species richness and total abundance of the community to predict the full abundance distribution, which suggests that these factors are sufficient to understand the distribution for most purposes. Since geographic patterns in richness and abundance can often be successfully modeled, this approach should allow the distribution of commonness and rarity to be characterized, even in locations where empirical data are unavailable.     

Use of Community‐Composition Data to Predict the Fecundity and Abundance of Species

Abstract: Species distribution models are critical tools for the prediction of invasive species spread and conservation of biodiversity. The majority of species distribution models have been built with environmental data. Community ecology theory suggests that species co‐occurrence data could also be used to predict current and potential distributions of species. Species assemblages are the products of biotic and environmental constraints on the distribution of individual species and as a result may contain valuable information for niche modeling. We compared the predictive ability of distribution models of annual grassland plants derived from either environmental or community‐composition data. Composition‐based models were built with the presence or absence of species at a site as predictors of site quality, whereas environment‐based models were built with soil chemistry, moisture content, above‐ground biomass, and solar radiation as predictors. The reproductive output of experimentally seeded individuals of 4 species and the abundance of 100 species were used to evaluate the resulting models. Community‐composition data were the best predictors of both the site‐specific reproductive output of sown individuals and the site‐specific abundance of existing populations. Successful community‐based models were robust to omission of data on the occurrence of rare species, which suggests that even very basic survey data on the occurrence of common species may be adequate for generating such models. Our results highlight the need for increased public availability of ecological survey data to facilitate community‐based modeling at scales relevant to conservation.     

A methodological framework for integrating computational fluid dynamics and ecological models applied to juvenile freshwater mussel dispersal in the Upper Mississippi River

Interdisciplinary research in hydraulics and ecology for river management and restoration must integrate processes that occur over a wide range of spatial and temporal scales, which presents a challenge to ecohydraulics modelers. Computational fluid dynamics (CFD) models are being more widely used to determine flow fields for ecohydraulics applications. In the Upper Mississippi River (UMR), the mussel dynamics model was developed as a tool for management and conservation of freshwater mussels (Unionidae), which are benthic organisms, imperiled in North America, that are inextricably linked with the hydraulics of river flow. We updated the juvenile dispersal component of the mussel dynamics model by using stochastic Lagrangian particle tracking in a three dimensional flow field output from CFD models of reaches in the UMR. We developed a methodological framework to integrate hydrodynamic data with the mussel dynamics model, and we demonstrate the use of the juvenile dispersal model employed within the methodological framework in two reaches of the UMR. The method was used to test the hypothesis that impoundment affects the relationship of some hydraulic parameters with juvenile settling distribution. Simulation results were consistent with this hypothesis, and the relationships of bed shear stress and Froude number with juvenile settling were altered by impoundment most likely through effects on local hydraulics. The methodological framework is robust, integrates Eulerian and Lagrangian reference frameworks, and incorporates processes over a wide range of temporal and spatial scales, from watershed scale hydrologic processes (decades), to reach scale (km) processes that occur over hours or days, and turbulent processes on spatial scales of meter to millimeter and times scales of seconds. The methods are presently being used to assess the impacts of pre- and early post-settlement processes on mussel distributions, including the effects of bed shear stress, and the sensitivity of the location of the host fish when juveniles excyst, on juvenile settling distribution.     

Lifting a veil on diversity: a Bayesian approach to fitting relative-abundance models.

Bayesian methods incorporate prior knowledge into a statistical analysis. This prior knowledge is usually restricted to assumptions regarding the form of probability distributions of the parameters of interest, leaving their values to be determined mainly through the data. Here we show how a Bayesian approach can be applied to the problem of drawing inference regarding species abundance distributions and comparing diversity indices between sites. The classic log series and the lognormal models of relative- abundance distribution are apparently quite different in form. The first is a sampling distribution while the other is a model of abundance of the underlying population. Bayesian methods help unite these two models in a common framework. Markov chain Monte Carlo simulation can be used to fit both distributions as small hierarchical models with shared common assumptions. Sampling error can be assumed to follow a Poisson distribution. Species not found in a sample, but suspected to be present in the region or community of interest, can be given zero abundance. This not only simplifies the process of model fitting, but also provides a convenient way of calculating confidence intervals for diversity indices. The method is especially useful when a comparison of species diversity between sites with different sample sizes is the key motivation behind the research. We illustrate the potential of the approach using data on fruit-feeding butterflies in southern Mexico. We conclude that, once all assumptions have been made transparent, a single data set may provide support for the belief that diversity is negatively affected by anthropogenic forest disturbance. Bayesian methods help to apply theory regarding the distribution of abundance in ecological communities to applied conservation.     

Hierarchical linear mixed models in multi-stage sampling soil studies

The issue of variances of different soil variables prevailing at different sampling scales is addressed. This topic is relevant for soil science, agronomy and landscape ecology. In multi-stage sampling there are randomness components in each stage of sampling which can be taken into account by introducing random effects in analysis through the use of hierarchical linear mixed models (HLMM). Due to the nested sampling scheme, there are several hierarchical sub-models. The selection of the best model can be carried out through likelihood ratio tests (LRTs) or Wald tests, which are asymptotically equivalent under standard conditions. However, when the comparison leads to a restricted hypothesis of variance components, standard conditions are not maintained, which leads to more elaborated versions of LRTs. These versions are not disseminated among environmental scientists. The present study shows the modeling of soil data from a sampling where sites, fields within sites, transects within fields, and sampling points within transects were selected in order to take samples from different vegetation types (open and shade). For soil data, several sub-models were compared using Wald tests, classic LRTs and adjusted LRTs where the distribution of the test statistic under the null hypothesis is the Chi-square mixture of Chi-square distributions. The inclusion of random effects via HLMM and suggested by the latest version of LRT allowed us to detect effects of vegetation type on soil properties that were not detected under a classical ANOVA.     

Invasive species distribution modeling (iSDM): Are absence data and dispersal constraints needed to predict actual distributions?

Species distribution models (SDMs) based on statistical relationships between occurrence data and underlying environmental conditions are increasingly used to predict spatial patterns of biological invasions and prioritize locations for early detection and control of invasion outbreaks. However, invasive species distribution models (iSDMs) face special challenges because (i) they typically violate SDM's assumption that the organism is in equilibrium with its environment, and (ii) species absence data are often unavailable or believed to be too difficult to interpret. This often leads researchers to generate pseudo-absences for model training or utilize presence-only methods, and to confuse the distinction between predictions of potential vs. actual distribution. We examined the hypothesis that true-absence data, when accompanied by dispersal constraints, improve prediction accuracy and ecological understanding of iSDMs that aim to predict the actual distribution of biological invasions. We evaluated the impact of presence-only, true-absence and pseudo-absence data on model accuracy using an extensive dataset on the distribution of the invasive forest pathogen Phytophthora ramorum in California. Two traditional presence/absence models (generalized linear model and classification trees) and two alternative presence-only models (ecological niche factor analysis and maximum entropy) were developed based on 890 field plots of pathogen occurrence and several climatic, topographic, host vegetation and dispersal variables. The effects of all three possible types of occurrence data on model performance were evaluated with receiver operating characteristic (ROC) and omission/commission error rates. Results show that prediction of actual distribution was less accurate when we ignored true-absences and dispersal constraints. Presence-only models and models without dispersal information tended to over-predict the actual range of invasions. Models based on pseudo-absence data exhibited similar accuracies as presence-only models but produced spatially less feasible predictions. We suggest that true-absence data are a critical ingredient not only for accurate calibration but also for ecologically meaningful assessment of iSDMs that focus on predictions of actual distributions.     

Monotonicity-constrained species distribution models

Flexible modeling frameworks for species distribution models based on generalized additive models that allow for smooth, nonlinear effects and interactions are of increasing importance in ecology. Commonly, the flexibility of such smooth function estimates is controlled by means of penalized estimation procedures. However, the actual shape remains unspecified. In many applications, this is not desirable as researchers have a priori assumptions on the shape of the estimated effects, with monotonicity being the most important. Here we demonstrate how monotonicity constraints can be incorporated in a recently proposed flexible framework for species distribution models. Our proposal allows monotonicity constraints to be imposed on smooth effects and on ordinal, categorical variables using an additional asymmetric L2 penalty. Model estimation and variable selection for Red Kite (Milvus milvus) breeding was conducted using the flexible boosting framework implemented in R package mboost.     

Landscape ecology of eastern coyotes based on large-scale estimates of abundance.

Since their range expansion into eastern North America in the mid-1900s, coyotes (Canis latrans) have become the region's top predator. Although widespread across the region, coyote adaptation to eastern forests and use of the broader landscape are not well understood. We studied the distribution and abundance of coyotes by collecting coyote feces from 54 sites across a diversity of landscapes in and around the Adirondacks of northern New York. We then genotyped feces with microsatellites and found a close correlation between the number of detected individuals and the total number of scats at a site. We created habitat models predicting coyote abundance using multi-scale vegetation and landscape data and ranked them with an information-theoretic model selection approach. These models allow us to reject the hypothesis that eastern forests are unsuitable habitat for coyotes as their abundance was positively correlated with forest cover and negatively correlated with measures of rural non-forest landscapes. However, measures of vegetation structure turned out to be better predictors of coyote abundance than generalized "forest vs. open" classification. The best supported models included those measures indicative of disturbed forest, especially more open canopies found in logged forests, and included natural edge habitats along water courses. These forest types are more productive than mature forests and presumably host more prey for coyotes. A second model with only variables that could be mapped across the region highlighted the lower density of coyotes in areas with high human settlement, as well as positive relationships with variables such as snowfall and lakes that may relate to increased numbers and vulnerability of deer. The resulting map predicts coyote density to be highest along the southwestern edge of the Adirondack State Park, including Tug Hill, and lowest in the mature forests and more rural areas of the central and eastern Adirondacks. Together, these results support the need for a nuanced view of how eastern coyotes use forested habitats.     

Composite forces shape population dynamics of copepod crustaceans

Understanding the processes that control species abundance and distribution is a major challenge in ecology, yet for a large number of potentially important organisms, we know little about the biotic and abiotic factors that influence population size. One group of aquatic organisms that defies traditional demographic analyses is the Crustacea, particularly those with complex life cycles. We used likelihood techniques and information theoretics to evaluate a suite of models representing alternative hypotheses on factors controlling the abundance of two copepod crustaceans in a small, tropical floodplain lake. Quantitative zooplankton samples were collected at three stations in a Venezuelan floodplain lake from June through December 1984; the average sampling interval was two days. We constructed a series of models with stage structure that incorporated six biotic and abiotic covariates in various combinations to account for temporal changes in abundance of these target species and in their population growth rates. Our analysis produced several novel insights into copepod population dynamics. We found that multiple forces affected the abundance of particular stages, that these factors differed between species as well as among stages within each species, and that biotic processes had the largest effects on copepod population dynamics. Density dependence had a large effect on the survival of Oithona amazonica copepodites and on population growth rate of Diaptomus negrensis.     

On the random placement hypothesis

A traditional method of summarizing spatial distribution of species is the observed species-area curve. Often the observed species-area curve is surprisingly close to the expected species-area curve under the hypothesis of random placement of individuals. This has been used as evidence supporting the hypothesis. In this paper, we argue that using the observed species-area curve to test the general random placement hypothesis is highly inefficient. We present a testing method based on the classical ² test for over-dispersion which is not only more efficient but also applicable to situations where complete abundance information are unavailable. We also discuss three alternatives of the hypothesis. The focus of this paper is on these and other general issues relevant to communities of different types. No applications are included in this paper.     

Identifying landscape scale patterns from individual scale processes

Extrapolating across scales is a critical problem in ecology. Explicit mechanistic models of ecological systems provide a bridge from measurements of processes at small and short scales to larger scales; spatial patterns at large scales can be used to test the outcomes of these models. However, it is necessary to identify patterns that are not dependent on initial conditions, because small scale initial conditions will not normally be measured at large scales. We examined one possible pattern that could meet these conditions, the relationship between mean and variance in abundance of a parasitic tick in an individual based model of a lizard tick interaction. We scaled discrepancies between the observed and simulated patterns with a transformation of the variance–covariance matrix of the observed pattern to objectively identify patterns that are “close”.     

Alternatives to statistical hypothesis testing in ecology: a guide to self teaching.

Statistical methods emphasizing formal hypothesis testing have dominated the analyses used by ecologists to gain insight from data. Here, we review alternatives to hypothesis testing including techniques for parameter estimation and model selection using likelihood and Bayesian techniques. These methods emphasize evaluation of weight of evidence for multiple hypotheses, multimodel inference, and use of prior information in analysis. We provide a tutorial for maximum likelihood estimation of model parameters and model selection using information theoretics, including a brief treatment of procedures for model comparison, model averaging, and use of data from multiple sources. We discuss the advantages of likelihood estimation, Bayesian analysis, and meta-analysis as ways to accumulate understanding across multiple studies. These statistical methods hold promise for new insight in ecology by encouraging thoughtful model building as part of inquiry, providing a unified framework for the empirical analysis of theoretical models, and by facilitating the formal accumulation of evidence bearing on fundamental questions.     

Sexual selection based on egg colour: physiological models and egg discrimination experiments in a cavity-nesting bird

It has been proposed that the blue-green bird egg colourations of many avian species may constitute a sexually selected female signal that males can use to modulate their parental investment. A fundamental untested assumption for the validation of this hypothesis is that males can accurately assess differences in the colour of eggs. A recent review suggests that this could be particularly problematic when egg clutches were located within a dimly lit nest cavity, due to limitations of the visual system in low light conditions. Here, we first used a photoreceptor noise-limited model of colour discrimination ability that accounts for visual performance under low light conditions to study whether a typical cavity-nesting passerine, the spotless starling Sturnus unicolor, can discriminate their eggs under the ambient illumination in their nest-holes. Secondly, we tested the validity of model predictions with behavioural data collected in two egg discrimination experiments performed in this species. Estimated egg detectability depended entirely on model assumptions about visual limitations linked to light intensity. Starlings would not be able to discriminate egg differences in their nests if the model was based on the assumption that light intensity limited detectability, whereas they could potentially perceive as different many possible pairwise clutch comparisons if the model assumption was that light intensity did not limit detectability. Results of behavioural experiments fitted the prediction of the visual model where light intensity did not limit detectability. Our results suggest that photoreceptor noise-limited colour models based on stimulation of single photoreceptors cannot, at present, be used to predict egg discrimination ability in spotless starlings under low light conditions. Future studies aiming to test egg discrimination constraints in the frame of the sexual selection hypothesis should therefore combine both modelling and behavioural experiments to determine which are the components of the models that produce the mismatch with the behavioural conditions.     

Geospatial variability of krill and top predators within an Antarctic submarine canyon system

The spatial distribution patterns of krill, seabirds (penguin, petrel and albatross), fur seals and baleen whales were mapped in nearshore waters (<50 km from land) to investigate their habitat selection within two adjacent submarine canyons near Livingston Island, Antarctica. Three shipboard surveys were conducted (February 2005–2007), and an echosounder was used to measure the distribution and abundance of krill while simultaneously conducting visual surveys to map seabird and marine mammals. Using a multispecies approach, we test the hypothesis that spatial organization of krill and top predators co-vary according to fine-scale changes in bathymetry in the nearshore marine environment. GAMs are used to examine the effect of sea depth, slope and distance to isobaths on the spatial distribution and abundance of krill and predators. Spatial distribution patterns of krill and predators relate to fine-scale (1–10 km) changes in bathymetry and exhibit cross-shelf gradients in abundance. Krill were concentrated along the shelf-break and abundant within both submarine canyons. Predators exhibited different preferences for locations within the submarine canyon system that relates to their foraging behavior. Penguins concentrated closer to shore and within the head of the east submarine canyon immediately adjacent to a breeding colony. Whales were also concentrated over the head of the east canyon (overlapping with penguins), whereas albatrosses and fur seals were concentrated in the west canyon. Fur seals also showed preference for steep slopes and were concentrated along the shelf-break. Petrels exhibited peaks in abundance throughout both submarine canyons. Owing to their orientation, size and proximity to the coastline, submarine canyons provide important habitat heterogeneity for krill and a variety of predators. This study highlights the multispecies approach for studying spatial ecology of top predators and krill and has implications for marine spatial management of the Scotia Sea.     

Reserve design to optimize functional connectivity and animal density

Ecological distance-based spatial capture–recapture models (SCR) are a promising approach for simultaneously estimating animal density and connectivity, both of which affect spatial population processes and ultimately species persistence. We explored how SCR models can be integrated into reserve-design frameworks that explicitly acknowledge both the spatial distribution of individuals and their space use resulting from landscape structure. We formulated the design of wildlife reserves as a budget-constrained optimization problem and conducted a simulation to explore 3 different SCR-informed optimization objectives that prioritized different conservation goals by maximizing the number of protected individuals, reserve connectivity, and density-weighted connectivity. We also studied the effect on our 3 objectives of enforcing that the space-use requirements of individuals be met by the reserve for individuals to be considered conserved (referred to as home-range constraints). Maximizing local population density resulted in fragmented reserves that would likely not aid long-term population persistence, and maximizing the connectivity objective yielded reserves that protected the fewest individuals. However, maximizing density-weighted connectivity or preemptively imposing home-range constraints on reserve design yielded reserves of largely spatially compact sets of parcels covering high-density areas in the landscape with high functional connectivity between them. Our results quantify the extent to which reserve design is constrained by individual home-range requirements and highlight that accounting for individual space use in the objective and constraints can help in the design of reserves that balance abundance and connectivity in a biologically relevant manner.     

物种多度对数正态分布模型的一种数值计算方法

物种多度分布格局是生物多样性研究的重要内容．本文针对物种多度分布的对数正态模型计算方法的缺陷,首次提出应用遗传算法计算对数正态模型参数,并与前人计算方法进行了比较,证明遗传算法具有较强的数值计算能力,对生态学中诸多非线性曲线的参数估计具有普遍意义．     

Tree cover in sub-Saharan Africa: rainfall and fire constrain forest and savanna as alternative stable states

Savannas are known as ecosystems with tree cover below climate-defined equilibrium values. However, a predictive framework for understanding constraints on tree cover is lacking. We present (a) a spatially extensive analysis of tree cover and fire distribution in sub-Saharan Africa, and (b) a model, based on empirical results, demonstrating that savanna and forest may be alternative stable states in parts of Africa, with implications for understanding savanna distributions. Tree cover does not increase continuously with rainfall, but rather is constrained to low (<50%, "savanna") or high tree cover (>75%, "forest"). Intermediate tree cover rarely occurs. Fire, which prevents trees from establishing, differentiates high and low tree cover, especially in areas with rainfall between 1000 mm and 2000 mm. Fire is less important at low rainfall (<1000 mm), where rainfall limits tree cover, and at high rainfall (>2000 mm), where fire is rare. This pattern suggests that complex interactions between climate and disturbance produce emergent alternative states in tree cover. The relationship between tree cover and fire was incorporated into a dynamic model including grass, savanna tree saplings, and savanna trees. Only recruitment from sapling to adult tree varied depending on the amount of grass in the system. Based on our empirical analysis and previous work, fires spread only at tree cover of 40% or less, producing a sigmoidal fire probability distribution as a function of grass cover and therefore a sigmoidal sapling to tree recruitment function. This model demonstrates that, given relatively conservative and empirically supported assumptions about the establishment of trees in savannas, alternative stable states for the same set of environmental conditions (i.e., model parameters) are possible via a fire feedback mechanism. Integrating alternative stable state dynamics into models of biome distributions could improve our ability to predict changes in biome distributions and in carbon storage under climate and global change scenarios.     

The Importance of Being Spatial (and Reserved): Assessing Northern Spotted Owl Habitat Relationships with Hierarchical Bayesian Models

Abstract:  Regional conservation planning increasingly draws on habitat suitability models to support decisions regarding land allocation and management. Nevertheless, statistical techniques commonly used for developing such models may give misleading results because they fail to account for 3 factors common in data sets of species distribution: spatial autocorrelation, the large number of sites where the species is absent (zero inflation), and uneven survey effort. We used spatial autoregressive models fit with Bayesian Markov Chain Monte Carlo techniques to assess the relationship between older coniferous forest and the abundance of Northern Spotted Owl nest and activity sites throughout the species' range. The spatial random-effect term incorporated in the autoregressive models successfully accounted for zero inflation and reduced the effect of survey bias on estimates of species–habitat associations. Our results support the hypothesis that the relationship between owl distribution and older forest varies with latitude. A quadratic relationship between owl abundance and older forest was evident in the southern portion of the range, and a pseudothreshold relationship was evident in the northern portion of the range. Our results suggest that proposed changes to the network of owl habitat reserves would reduce the proportion of the population protected by up to one-third, and that proposed guidelines for forest management within reserves underestimate the proportion of older forest associated with maximum owl abundance and inappropriately generalize threshold relationships among subregions. Bayesian spatial models can greatly enhance the utility of habitat analysis for conservation planning because they add the statistical flexibility necessary for analyzing regional survey data while retaining the interpretability of simpler models.