Statistical mechanics unifies different ecological patterns

Recently there has been growing interest in the use of maximum relative entropy (MaxREnt) as a tool for statistical inference in ecology. In contrast, here we propose MaxREnt as a tool for applying statistical mechanics to ecology. We use MaxREnt to explain and predict species abundance patterns in ecological communities in terms of the most probable behaviour under given environmental constraints, in the same way that statistical mechanics explains and predicts the behaviour of thermodynamic systems. We show that MaxREnt unifies a number of different ecological patterns: (i) at relatively local scales a unimodal biodiversity-productivity relationship is predicted in good agreement with published data on grassland communities, (ii) the predicted relative frequency of rare vs. abundant species is very similar to the empirical lognormal distribution, (iii) both neutral and non-neutral species abundance patterns are explained, (iv) on larger scales a monotonic biodiversity-productivity relationship is predicted in agreement with the species-energy law, (v) energetic equivalence and power law self-thinning behaviour are predicted in resource-rich communities. We identify mathematical similarities between these ecological patterns and the behaviour of thermodynamic systems, and conclude that the explanation of ecological patterns is not unique to ecology but rather reflects the generic statistical behaviour of complex systems with many degrees of freedom under very general types of environmental constraints.     

The wealth of species: ecological communities, complex systems and the legacy of Frank Preston

General statistical patterns in community ecology have attracted considerable recent debate. Difficulties in discriminating among mathematical models and the ecological mechanisms underlying them are likely related to a phenomenon first described by Frank Preston. He noted that the frequency distribution of abundances among species was uncannily similar to the Boltzmann distribution of kinetic energies among gas molecules and the Pareto distribution of incomes among wage earners. We provide additional examples to show that four different 'distributions of wealth' (species abundance distributions, species–area and species–time relations, and distance decay of compositional similarity) are not unique to ecology, but have analogues in other physical, geological, economic and cultural systems. Because these appear to be general statistical patterns characteristic of many complex dynamical systems they are likely not generated by uniquely ecological mechanistic processes.     

Native drivers of fish life history traits are lost during the invasion process

Rapid adaptation to global change can counter vulnerability of species to population declines and extinction. Theoretically, under such circumstances both genetic variation and phenotypic plasticity can maintain population fitness, but empirical support for this is currently limited. Here, we aim to characterize the role of environmental and genetic diversity, and their prior evolutionary history (via haplogroup profiles) in shaping patterns of life history traits during biological invasion. Data were derived from both genetic and life history traits including a morphological analysis of 29 native and invasive populations of topmouth gudgeon Pseudorasbora parva coupled with climatic variables from each location. General additive models were constructed to explain distribution of somatic growth rate (SGR) data across native and invasive ranges, with model selection performed using Akaike's information criteria. Genetic and environmental drivers that structured the life history of populations in their native range were less influential in their invasive populations. For some vertebrates at least, fitness‐related trait shifts do not seem to be dependent on the level of genetic diversity or haplogroup makeup of the initial introduced propagule, nor of the availability of local environmental conditions being similar to those experienced in their native range. As long as local conditions are not beyond the species physiological threshold, its local establishment and invasive potential are likely to be determined by local drivers, such as density‐dependent effects linked to resource availability or to local biotic resistance.     

Consistent abundance distributions of marine fishes in an old,climatically buffered,infertile seascape

Aim Macroecological theory predicts that along direct physiological gradients there will be unimodal abundance distributions of species and consistent rates of assemblage turnover. However, the majority of marine studies that have investigated the realized distribution of species along latitudinal or temperature gradients have generally found unimodal distributions to be rare. We assess fish distributions along a temperature gradient in a stable oligotrophic seascape and suggest that unimodal distributions will be more common. Location Nearshore demersal fish habitat extending 1500 km along the coast of south‐western Australia. Methods The relative abundances of demersal fish species were sampled off the coast of south‐western Australia along a temperature gradient. The confounding influence of other environmental variables was tested, and the assemblage was found to be highly correlated with temperature. For the 20 most abundant species, quantile regression spline models were used to construct a model within which 95% of their abundance was expected to fall. We compared the results from this study with the proportion of unimodal species abundance distributions observed in other studies. Results Of the 20 most abundant species, 19 displayed patterns that indicated temperature was an important factor influencing their range and relative abundance; with 15 species exhibiting unimodal abundance distributions, four having ramped distribution to one end of the sampled range and one showing no consistent pattern. Main conclusions The high diversity and percentage of endemic species in terrestrial and marine habitats of south‐western Australia is likely to be due to the stable geological and oceanographic history of the region. In comparison, studies of abundance distribution in other marine systems have been conducted in relatively heterogeneous and productive environments. The old, climatically buffered, oligotrophic seascape of south‐western Australia has provided a simple system in which the consistent influence of physiological gradients on the abundance distribution of fish species can be observed.     

Distribution, ecology, life history, genetic variation, and risk of extinction of nonhuman primates from Costa Rica

We examined the association between geographic distribution, ecological traits, life history, genetic diversity, and risk of extinction in nonhuman primate species from Costa Rica. All of the current nonhuman primate species from Costa Rica are included in the study; spider monkeys (Ateles geoffroyi), howling monkeys (Alouatta palliata), capuchins (Cebus capucinus), and squirrel monkeys (Saimiri oerstedii). Geographic distribution was characterized accessing existing databases. Data on ecology and life history traits were obtained through a literature review. Genetic diversity was characterized using isozyme electrophoresis. Risk of extinction was assessed from the literature. We found that species differed in all these traits. Using these data, we conducted a Pearson correlation between risk of extinction and ecological and life history traits, and genetic variation, for widely distributed species. We found a negative association between risk of extinction and population birth and growth rates; indicating that slower reproducing species had a greater risk of extinction. We found a positive association between genetic variation and risk of extinction; i.e., species showing higher genetic variation had a greater risk of extinction. The relevance of these traits for conservation efforts is discussed.     

Geographical patterns of hoverfly (Diptera,Syrphidae) functional groups in Europe: inconsistency in environmental correlates and latitudinal trends

Abstract 1. Relationships between species richness in higher taxa and large‐scale environmental variables have been widely studied over the past 15 years. Much less is known about how different functional groups (FGs) of species with similar biological and life‐history traits contribute to the overall trends, or how they differ in species‐richness patterns. 2. Multivariate analysis clustered 641 species of Syrphidae into eight FGs on the basis of 10 life‐history features, revealing feeding strategy as the main factor separating the groups. 3. Geographical trends in species richness and determinants of species richness within the FGs were compared across Europe. 4. Total species richness showed no latitudinal trend. However, the richness of individual FGs revealed variable relationships with latitude, including positive, negative, and hump‐shaped ones. This appeared to be related to how different environmental factors affected species richness within FGs. 5. Functional groups differed in their responses to the environmental variables. Annual temperature, evapotranspiration, and elevation span were the most important variables separating the FGs in ordination analysis. The multiple regression models showed further differences between FGs and their responses to the environment. 6. The FG approach revealed important inconsistencies in latitudinal diversity gradients and diversity‐climate relationships.     

Terrestrial gastropod diversity in an alpine region: disentangling effects of elevation,area, geometric constraints,habitat type and land‐use intensity

Elevational gradients have proven to be useful to examine key factors shaping species diversity patterns. This study examines the effects of elevation, area, geometric constraints, habitat type, environmental factors and land‐use intensity on terrestrial gastropod diversity patterns in Val Müstair, an alpine region influenced by different types of agricultural land use in the eastern Alps, Switzerland. Gastropods were sampled using a standardized method in 180 sites spanning an elevational range from 1215 to 2770 m and covering 11 different habitat types. A total of 11 102 specimens representing 70 species were recorded. Observed species richness, statistically estimated true richness (Chao) and geographically interpolated observed richness were used as measures of local species richness. The comparison of three alternative models (environmental, geometric constraints and gastropod abundance models) revealed that the environmental model explained most of the variation in all measures of local diversity. The best model combining the predictors of all three models showed that elevation, soil pH and habitat type affected all measures of local species richness. Similar analyses conducted at the level of 150‐m elevational bands showed that elevation was again the best predictor of species richness, while the area of the elevational band did not have any influence. However, in one out of the two measures of band species richness, the best model indicated that geometric constraints may also contribute to the observed pattern. At both spatial scales, all measures of species richness decreased with increasing elevation. An analysis of species‐specific life‐history traits showed that adult shell size of land snails decreased with increasing elevation. Most species with large shells were confined to lower elevations. The results indicate that environmental factors might be most important in shaping the observed patterns.     

Understanding ecological community succession: Causal models and theories,a review

Critical review of explanations for patterns of natural succession suggests a strong, common basis for theoretical understanding, but also suggests that several well known models are incomplete as explanations of succession. A universal, general cause for succession is unlikely, since numerous aspects of historical and environmental circumstances will impinge on the process in a unique manner. However, after disturbance, occupation of a site by any species causes changes in the conditions at the site. Sorting of species may result, since different species are adapted to different regions of environmental gradients. Such sorting can generate several patterns of species abundance in time, but commonly results in sequential replacements of species adapted to the varying conditions. This may be due to constraints on species' strategies, or life history traits, placed by the limited resources available to the organism. These constraints often result in inverse correlation between traits which confer success during early and late stages of succession. Facilitatory or inhibitory effects of species on each other are best understood in terms of these life history interactions, perhaps as restrictions on, or as moderation of, these processes.Strong support for the importance of correlations in life history traits stems from comparisons of simulated succession with and without these correlations. These simulations are reviewed in some detail, and followed by brief reviews of other prominent models for succession. Several aspects of the confusion and controversies in the successional literature are then discussed, with a view to a more optimistic synthesis and direction for successional ecology.     

揭示群落结构及其环境响应的联合物种分布模型的研究进展

物种分布模型通常用于基础生态和应用生态研究,用来确定影响生物分布和物种丰富度的因素,量化物种与非生物条件的关系,预测物种对土地利用和气候变化的反应,并确定潜在的保护区.在传统的物种分布模型中,生物的相互作用很少被纳入,而联合物种分布模型(JSDMs)作为近年提出的一种新的可行方法,可以同时考虑环境因素和生物交互作用,因而成为分析生物群落结构和种间相互作用过程的有力工具.JSDMs以物种分布模型(SDMs)为基础,通常采用广义线性回归模型建立物种对环境变量的多变量响应,以随机效应的形式获取物种间的关联,同时结合隐变量模型(LVMs),并基于Laplace近似和马尔科夫蒙脱卡罗模拟的最大似然估计或贝叶斯方法来估算模型参数.本文对JSDMs的产生及理论基础进行归纳总结,重点介绍了不同类型JSDMs的特点及其在现代生态学中的应用,阐述了JSDMs的应用前景、使用过程中存在的问题及发展方向.随着对环境因素与多物种种间关系研究的深入,JSDMs将是今后物种分布模型研究的重点.     

When no catches matter: Coping with zeros in environmental assessments

The environmental legislation of many countries increasingly requires the continuous monitoring of fish assemblages to evaluate the success of river and stream restorations. Predicting species–environment relationships on the basis of monitoring data is central in the evaluation of ecological integrity and planning of rehabilitation strategies. Monitoring data are, however, often plagued by a substantial proportion of zeros (no catch at single sampling points) which are caused by relevant ecological processes, but complicate the use of commonly used statistical methods. This study compares mere count regression models, mixture and hurdle models based on Poisson and negative binomial distribution and logistic regressions with respect to their ability to cope with large zero-inflated data sets obtained by point abundance sampling of young-of-the-year fish from three large German rivers. Only mixture and hurdle models based on negative binomial distribution could satisfactorily be fitted to the zero-inflated and overdispersed count data. The logistic regression models applied to transliterated catch data simplified the computational procedure and yielded qualitative similar results to the count regression models indicating that the use of more complex count data did not generally provide better predictions. Therefore, presence/absence sampling may be a suitable and less costly alternative to abundance surveys for identifying environmental factors which affect the spatial distribution of fish populations at least if information on subtly abundance fluctuations is not needed. Mixture or hurdle models are particularly worth the additional effort if it is reasonable to distinguish between those environmental factors influencing the occurrence probability and others affecting the abundance. All models showed low sensitivity to rare guilds pointing to the need for a further development of statistical models for rare species whose management is a matter of growing environmental concern.     

Cryptic diversity in a fig wasp community—morphologically differentiated species are sympatric but cryptic species are parapatric

A key debate in ecology centres on the relative importance of niche and neutral processes in determining patterns of community assembly with particular focus on whether ecologically similar species with similar functional traits are able to coexist. Meanwhile, molecular studies are increasingly revealing morphologically indistinguishable cryptic species with presumably similar ecological roles. Determining the geographic distribution of such cryptic species provides opportunities to contrast predictions of niche vs. neutral models. Discovery of sympatric cryptic species increases alpha diversity and supports neutral models, while documentation of allopatric/parapatric cryptic species increases beta diversity and supports niche models. We tested these predictions using morphological and molecular data, coupled with environmental niche modelling analyses, of a fig wasp community along its 2700‐km latitudinal range. Molecular methods increased previous species diversity estimates from eight to eleven species, revealing morphologically cryptic species in each of the four wasp genera studied. Congeneric species pairs that were differentiated by a key morphological functional trait (ovipositor length) coexisted sympatrically over large areas. In contrast, morphologically similar species, with similar ovipositor lengths, typically showed parapatric ranges with very little overlap. Despite parapatric ranges, environmental niche models of cryptic congeneric pairs indicate large regions of potential sympatry, suggesting that competitive processes are important in determining the distributions of ecologically similar species. Niche processes appear to structure this insect community, and cryptic diversity may typically contribute mostly to beta rather than alpha diversity.     

Environmental,spatial and phylogenetic determinants of fish life‐history traits and functional composition of Australian rivers

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Species distribution modelling in low‐interaction environments: Insights from a terrestrial Antarctic system

It is widely acknowledged that in the terrestrial Antarctic, interspecific interactions are typically unimportant in determining species distributions and community structure. Therefore, correlative models should prove useful for predicting current and future spatial variation in species abundance patterns. However, this idea has not been formally tested, and the utility of such models, which have shown value for understanding the distribution of diversity elsewhere, for investigating biodiversity patterns in Antarctica remains unclear. Here we make a start at such tests by using generalized linear and simultaneous autoregressive models to demonstrate that simple environmental variables and information about the spatial structure of the environment can explain more than 90% of the variation in the abundance of Maudheimia wilsoni (Oribatida; Maudheimiidae), a representative of one of the most significant groups of Antarctic terrestrial arthropods, the mites. We show that a single environmental variable, maximum soil moisture content, can account for as much as 80% of the variance in the abundance of the mite, and that linear models with only a few environmental and spatial terms can be used to forecast the species abundance at the landscape scale. Given ongoing calls for better understanding of the distribution of Antarctic diversity and its likely future change, this initial test indicates that such modelling procedures, and more sophisticated versions thereof, hold much promise for the region and should be tested for other taxa with different life forms and habitat requirements.     

Unraveling the habitat preferences of two closely related bumble bee species in Eastern Europe

Co‐occurrence of closely related species is often explained through resource partitioning, where key morphological or life‐history traits evolve under strong divergent selection. In bumble bees (genus Bombus), differences in tongue lengths, nest sites, and several life‐history traits are the principal factors in resource partitioning. However, the buff‐tailed and white‐tailed bumble bee (Bombus terrestris and B. lucorum respectively) are very similar in morphology and life history, but their ranges nevertheless partly overlap, raising the question how they are ecologically divergent. What little is known about the environmental factors determining their distributions stems from studies in Central and Western Europe, but even less information is available about their distributions in Eastern Europe, where different subspecies occur. Here, we aimed to disentangle the broad habitat requirements and associated distributions of these species in Romania and Bulgaria. First, we genetically identified sampled individuals from many sites across the study area. We then not only computed species distributions based on presence‐only data, but also expanded on these models using relative abundance data. We found that B. terrestris is a more generalist species than previously thought, but that B. lucorum is restricted to forested areas with colder and wetter climates, which in our study area are primarily found at higher elevations. Both vegetation parameters such as annual mean Leaf Area Index and canopy height, as well as climatic conditions, were important in explaining their distributions. Although our models based on presence‐only data suggest a large overlap in their respective distributions, results on their relative abundance suggest that the two species replace one another across an environmental gradient correlated to elevation. The inclusion of abundance enhances our understanding of the distribution of these species, supporting the emerging recognition of the importance of abundance data in species distribution modeling.     

长白山森林／沼泽生态交错带群落和环境梯度分析

揭示了森林－沼泽过渡带群落的结构、生产力、植物多样性等群落梯度和交错环境梯度的相关规律,并结合交错区环境梯度分析这些群落特征形成机制,为维持、保护与经营管理这一交错带生物资源提供了理论依据。将长白山地区森林和高、中、低位沼泽所形成的三大类型过渡带研究对象,采用样带网格的调查方法,并应用系统软件分析方法建立了经验回归模型,研究了森林／沼泽生态交错带群落的种类组成、群落建群种径级结构与年龄结构、植物多样性、群落生产力及其随生态交错带环境梯度变化趋势。结果表明,森林／沼泽生态交错带群落结构特征、植物多样性、群落生产力均随着交错带环境梯度的变化而呈现有规律的分布格局,沿着沼泽至森林方向的交错区环境梯度,群落建种种发生更替现象;群落种类数目呈现指数递增趋势;群落的径级结构呈现双曲线分布规律性;年龄结构一般呈三次式分布规律;揿样性呈二次式梯增分布趋势;群落生物量均呈现三次函数曲线递增趋势,表现出群落梯度和环境梯度的高度相关性。     

The maximum entropy formalism and the idiosyncratic theory of biodiversity

Why does the neutral theory, which is based on unrealistic assumptions, predict diversity patterns so accurately? Answering questions like this requires a radical change in the way we tackle them. The large number of degrees of freedom of ecosystems pose a fundamental obstacle to mechanistic modelling. However, there are tools of statistical physics, such as the maximum entropy formalism (MaxEnt), that allow transcending particular models to simultaneously work with immense families of models with different rules and parameters, sharing only well‐established features. We applied MaxEnt allowing species to be ecologically idiosyncratic, instead of constraining them to be equivalent as the neutral theory does. The answer we found is that neutral models are just a subset of the majority of plausible models that lead to the same patterns. Small variations in these patterns naturally lead to the main classical species abundance distributions, which are thus unified in a single framework.     

Landscape-scale patterns of shrub-species abundance in California chaparral – The role of topographically mediated resource gradients

We examine the degree to which landscape-scale spatial patterns of shrub-species abundance in California chaparral reflect topographically mediated environmental conditions, and evaluate whether these patterns correspond to known ecophysiological plant processes. Regression tree models are developed to predict spatial patterns in the abundance of 12 chaparral shrub and tree species in three watersheds of the Santa Ynez Mountains, California. The species response models are driven by five variables: average annual soil moisture, seasonal variability in soil moisture, average annual photosynthetically active radiation, maximum air temperature over the dry season (May–October), and substrate rockiness. The energy and moisture variables are derived by integrating high resolution (10 m) digital terrain data and daily climate observations with a process-based hydro-ecological model (RHESSys). Field-sampled data on species abundance are spatially integrated with the distributed environmental variables for developing and evaluating the species response models.The species considered are differentially distributed along topographically-mediated environmental gradients in ways that are consistent with known ecophysiological processes. Spatial patterns in shrub abundance are most strongly associated with annual soil moisture and solar radiation. Substrate rockiness is also closely associated with the establishment of certain species, such as Adenostoma fasciculatum and Arctostaphylos glauca. In general, species that depend on fire for seedling recruitment (e.g., Ceanothous megacarpus) occur at high abundance in xeric environments, whereas species that do not depend on fire (e.g., Heteromeles arbutifolia) occur at higher abundance in mesic environments. Model performance varies between species and is related to life history strategies for regeneration. The scale of our analysis may be less effective at capturing the processes that underlie the establishment of species that do not depend on fire for recruitment. Analysis of predication errors in relation to environmental conditions and the abundance of potentially competing species suggest factors not explicitly considered in the species response models.     

山西霍山油松林的物种多度分布格局

物种多度格局分析对理解群落结构具有重要的意义。该文首次选用描述种-多度关系的生态位模型(生态位优先模型NPM、分割线段模型BSM、生态位重叠模型ONM)、生物统计模型(对数级数分布模型LSD、对数正态分布模型LN)以及中性理论模型NT, 对山西霍山油松(Pinus tabulaeformis)林的物种数量关系进行了拟合研究, 并采用卡方(χ²)检验、Likelihood-ratios (L-R)检验、Kolmogorov-Smirnov (K-S)检验和赤池信息量准则(AIC)选择最适合模型, 结果表明: (1)描述乔木层物种多度格局的最优生态位模型为NPM (3种检验方法均接受该模型, p > 0.05, 且该模型具有最小的 AIC值), ONM的拟合效果次之, 不服从BSM; 三种生态位模型均可较好地拟合灌木层物种多度格局; ONM是草本层最佳生态位模型, BSM、NPM拟合效果较差; LSD可以描述油松林各层物种多度结构; LN可以很好地解释灌草层物种数量关系; NT不能解释油松林任何层次的物种多度结构。(2)霍山油松林乔木层和灌木层的物种丰富度和物种多样性均明显小于草本层; 该群落物种富集种少而稀疏种多, 且群落的均匀度相对较小。(3)从该区油松林种-多度分布来看, 同一个模型可以拟合不同的物种多度数据, 相同的数据可以由不同的模型来解释。因此, 研究森林群落物种分布时, 应采用多个模型进行拟合, 同时选用多种方法筛选最优模型。     

Habitat distribution models,spatial autocorrelation,functional traits and dispersal capacity of alpine plant species

Abstract. We evaluate the potential influence of disturbance on the predictability of alpine plant species distribution from equilibrium‐based habitat distribution models. Firstly, abundance data of 71 plant species were correlated with a comprehensive set of environmental variables using ordinal regression models. Subsequently, the residual spatial autocorrelation (at distances of 40 to 320 m) in these models was explored. The additional amount of variance explained by spatial structuring was compared with a set of functional traits assumed to confer advantages in disturbed or undisturbed habitats. We found significant residual spatial autocorrelation in the habitat models of most of the species that were analysed. The amount of this autocorrelation was positively correlated with the dispersal capacity of the species, levelling off with increasing spatial scale. Both trends indicate that dispersal and colonization processes, whose frequency is enhanced by disturbance, influence the distribution of many alpine plant species. Since habitat distribution models commonly ignore such spatial processes they miss an important driver of local‐ to landscape‐scale plant distribution.