Measurement scale in maximum entropy models of species abundance

The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry with regard to measurement scale. By symmetry, I mean that different ecological processes preserve the same measure of information and lose all other information in the aggregation of various perturbations. I frame these explanations of symmetry, measurement, and aggregation in terms of a recently developed extension to the theory of maximum entropy. I show that the natural measurement scale for the species abundance distribution is log-linear: the information in observations at small population sizes scales logarithmically and, as population size increases, the scaling of information grades from logarithmic to linear. Such log-linear scaling leads naturally to a gamma distribution for species abundance, which matches well with the observed patterns. Much of the variation between samples can be explained by the magnitude at which the measurement scale grades from logarithmic to linear. This measurement approach can be applied to the similar problem of allelic diversity in population genetics and to a wide variety of other patterns in biology.     

Competition and species diversity: removal of dominant species increases diversity in Costa Rican butterfly communities

Biological communities are usually dominated by a few species and show characteristically skewed species abundance distributions. Although niche apportionment and resource competition are sometimes implicated in such patterns, few experimental studies have shown direct links between resource limitation, competition with dominant species and their impacts on the overall diversity and composition of large natural communities. Here I report the results of an experiment in which I first studied species diversity and composition in two Costa Rican nectar-feeding butterfly communities numerically dominated by two species of Anartia butterflies. Then I removed Anartia from these communities to study changes in resource availability, species abundance relationships, community diversity and composition as an outcome of the removal of the dominant competitors. In the face of competition with Anartia , nectar was scarce, species abundance distributions were highly skewed, and species diversity was low in both communities. Within two weeks after the removal of Anartia , there were parallel changes in both communities: competition for nectar reduced and the nectar quantity increased substantially, which facilitated increase in community diversity and resulted in significantly less skewed species abundance distributions. Higher nectar quantity also enabled the distribution of body size and proboscis length of constituent species in the communities to expand at both ends. This study thus experimentally showed that resource competition with the dominant species was excluding many species from the communities, lowering their diversity and skewing relative species abundance relationships. These findings are of fundamental importance for competition theory and community ecology because they indicate ways in which diverse communities may be affected by and recover from competition with dominant species.     

Stochastic and deterministic processes together determine alpine meadow plant community composition on the Tibetan Plateau

To predict the consequences of environmental change on the structure and composition of communities, it is necessary to also understand the regional drivers underlying the structuring of these communities. Here, we have taken a hypothesis-based approach to test the relative importance of niche versus neutral processes using niche overlap, species traits and population asynchrony in two crossed treatments of fertilization and grazing in an alpine meadow community. Our results suggested that the observed species biomass overlap was not significantly different between treatments of grazing, grazing × fertilization and grazer exclusion. In contrast, the species biomass overlap was higher than expected in fertilization treatments when grazers were excluded. On the one hand, we found no relationship between species traits and relative abundance in grazing, grazing × fertilization and grazer-exclusion treatments; on the other hand, mechanistic trait-based theory could be used to predict species relative abundance patterns in fertilization treatments when grazers were excluded. From grazing to fertilization, when grazers were excluded, there was a slight increase in species synchrony, which indicated that the complementary dynamic of species gradually changed from complete independence into synchronously fluctuating with increasing fertilization. Based on the above results, we concluded that stochastic and deterministic processes formed ends of a continuum from grazing to fertilization when grazers were excluded in an alpine meadow plant community, and the importance of niche differences between species in structuring grassland communities increased with increasing fertilization and decreased with grazing.     

Maximum entropy,logistic regression,and species abundance

There is considerable debate about the utility of statistical mechanics in predicting diversity patterns in terms of life history traits. Here, I reflect on this debate and show that a community is controlled by the balance of two opposite forces: the entropic part (the natural tendency of the system to be in the configuration with the highest possible entropy) and environmental, ecological and evolutionary constraints maintaining order (reducing entropy). The Boltzmann distribution law that can be derived from the maximum entropy formalism provides a fundamental model for linking species abundance to life history traits and environmental constraining factors. This model predicts a global pattern of diversity evenness along a latitudinal gradient. Although the Boltzmann distribution and the logistic regression models represent two fundamentally different approaches, the two models have an identical mathematical form. Their identical formalisms facilitate the interpretation of logistic regression models with statistical mechanics, and reveal several limitations of the maximum entropy formalism. I argued that although maximum entropy formalism is a promising tool for modeling species abundances and for linking microscopic quantities of individual life history traits to macroscopic patterns of diversity, it is necessary to revise the Boltzmann distribution law for successful prediction of species abundance.     

Climate, energy and diversity

In recent years, a number of species-energy hypotheses have been developed to explain global patterns in plant and animal diversity. These hypotheses frequently fail to distinguish between fundamentally different forms of energy which influence diversity in dissimilar ways. Photosynthetically active radiation (PAR) can be utilized only by plants, though their abundance and growth rate is also greatly influenced by water. The Gibbs free energy (chemical energy) retained in the reduced organic compounds of tissue can be utilized by all heterotrophic organisms. Neither PAR nor chemical energy influences diversity directly. Both, however, influence biomass and/or abundance; diversity may then increase as a result of secondary population dynamic or evolutionary processes. Temperature is not a form of energy, though it is often used loosely by ecologists as a proxy for energy; it does, however, influence the rate of utilization of chemical energy by organisms. It may also influence diversity by allowing a greater range of energetic lifestyles at warmer temperatures (the metabolic niche hypothesis). We conclude that there is no single species/energy mechanism; fundamentally different processes link energy to abundance in plants and animals, and diversity is affected secondarily. If we are to make progress in elucidating these mechanisms, it is important to distinguish climatic effects on species' distribution and abundance from processes linking energy supply to plant and animal diversity.     

广西大青山南亚热带次生林演替过程的种群动态

该文研究了广西大青山南亚热带次生林群落经过26年的自然演替其间的种群结构变化规律。通过对主要种群类型、重要值、生态位宽度和分布格局的测定,分析了演替过程中各种群内部的消长与分布变化趋势,研究发现阳生性优势种由高集群分布变为随机分布,其生态位宽度减小,中生及阴生性树种则由随机分布逐渐变为高集群分布,生态位宽度增大。树种由32种增加到65种,35种中生及阴生树种为后期侵入种,物种多样性比较丰富;通过对现存种群的种间联结与生态位重叠进行分析,揭示了天然次生演替过程中种间关系的相互适应变化规律。原来阳生性的优势树种,如大叶栎(Castannopsis fleuryi)、大叶山楝(Aphanamixis grandifolia)等,与其它种群的生态位重叠值普遍下降,中生性种群生态位重叠值稍有增加,如柃木(Eurya nitida)、血胶树(Eberhardtia aurata)、广西拟肉豆蔻(Knema guangxiensis)等,中生偏阴生性种群生态位重叠值明显增大,其中一些种,如厚叶琼楠(Beilschmiedia percoriacea)、杨桐(Adinandra millettii)、毛黄肉楠(Actinodaphne pilosa)等,成为群落的建群种和优势种。次生群落种群之间的联结程度加强,一些种从零联结变为高度正联结或负联结,正、负联结性均变得更加紧密,高度正联结的种对占较大比例。种间联结与生态位分析结果基本一致,高度正联结的种群之间生态位重叠值较大,也反映出这些种对生境要求的一致性。次生群落由前期阳生性大叶栎群落演替为中后期中生性厚叶琼楠群落,群落接近较稳定的中生性气候顶极阶段。     

Speciation and the neutral theory of biodiversity

The neutral theory of biodiversity purports that patterns in the distribution and abundance of species do not depend on adaptive differences between species (i.e. niche differentiation) but solely on random fluctuations in population size (“ecological drift”), along with dispersal and speciation. In this framework, the ultimate driver of biodiversity is speciation. However, the original neutral theory made strongly simplifying assumptions about the mechanisms of speciation, which has led to some clearly unrealistic predictions. In response, several recent studies have combined neutral community models with more elaborate speciation models. These efforts have alleviated some of the problems of the earlier approaches, while confirming the general ability of neutral theory to predict empirical patterns of biodiversity. However, the models also show that the mode of speciation can have a strong impact on relative species abundances. Future work should compare these results to diversity patterns arising from non‐neutral modes of speciation, such as adaptive radiations.     

天童常绿阔叶林中常绿与落叶物种的物种多度分布格局

物种多度分布是对群落内不同物种多度情况的数量描述, 作为理解群落性质的基石, 其形成机制受到广泛关注。常绿与落叶物种是两类有着不同物候性状与生长策略的物种集合, 它们普遍共存于常绿阔叶林中。在天童20 ha常绿阔叶林动态监测样地内, 虽然常绿物种在物种多度和胸高断面积等指标上占有绝对优势, 但其在物种丰富度上却不及落叶物种。分析两者在常绿阔叶林中的物种多度分布特征, 能够为理解常绿阔叶林内物种多样性的维持机制提供一个全新的视角。为此, 我们基于天童样地的植被调查数据, 一方面利用累积经验分布函数对两类生活型植物的物种多度分布进行描述, 使用Kolmogorov-Smirnov检验(K-S检验)判断其差异性; 另一方面, 采用纯统计模型、生态位模型和中性理论模型对二者的物种多度分布曲线进行拟合, 并基于K-S检验的结果以及AIC值进行最优模型的筛选。结果显示: (1)常绿与落叶物种的物种多度分布曲线间并无显著差异。(2)在选用的3类模型中, 中性理论模型对于两类物种多度分布曲线的拟合效果都最好, 而生态位模型的拟合效果则一般。从上述结果可以看出, 尽管常绿与落叶物种在物种数量和多度等方面均存在差异, 但它们却有着近似的物种多度分布格局以及相近的多样性维持机制。然而, 鉴于模型拟合的结果只能作为理解群落多样性构建机制的必要非充分条件, 故而只能初步判定中性过程对于常绿与落叶物种的物种多样性格局影响更大, 却不能排除或衡量诸如生态位分化等其他过程在两类生活型多样性格局形成中的贡献。     

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。     

Regional patterns of mussel species distributions in North American rivers

North American freshwater mussels are a highly threatened group with half of the fauna already federally listed as threatened or endangered candidates for listing, or believed extinct Using data from 16 river systems I examined distributional attributes of mussel species to gain insight into the importance of regional-scale processes vs local-scale processes to species distribution patterns There was no evidence of density compensation or saturation which would have indirectly indicated that competition was important in structuring mussel communities Rather there was a positive correlation between summed species densities and regional richness, indicating that regional forces may be strongly contributing to community structure Incidence, abundance and nestedness patterns all indicated a hierarchical niche structure for these mussel assemblages I hypothesize that these hierarchical patterns may be the result of differences in colonization potentials among mussel species as a result of different fish-host requirements among mussels, and of the abundance and distribution of those host fishes     

Temporal variability of forest communities: empirical estimates of population change in 4000 tree species

Long‐term surveys of entire communities of species are needed to measure fluctuations in natural populations and elucidate the mechanisms driving population dynamics and community assembly. We analysed changes in abundance of over 4000 tree species in 12 forests across the world over periods of 6–28 years. Abundance fluctuations in all forests are large and consistent with population dynamics models in which temporal environmental variance plays a central role. At some sites we identify clear environmental drivers, such as fire and drought, that could underlie these patterns, but at other sites there is a need for further research to identify drivers. In addition, cross‐site comparisons showed that abundance fluctuations were smaller at species‐rich sites, consistent with the idea that stable environmental conditions promote higher diversity. Much community ecology theory emphasises demographic variance and niche stabilisation; we encourage the development of theory in which temporal environmental variance plays a central role.     

Multi-scale analysis on species diversity within a 40-ha old-growth temperate forest

In order to better explore the maintenance mechanisms of biodiversity,data collected from a 40-ha undisturbed Pinus forest were applied to the Individual SpecieseArea Relationship model (ISAR) to determine distribution patterns for species richness.The ecological processes influencing species abundance distribution patterns were assessed by applying the same data set to five models:a LogNormal Model (LNM),a Broken Stick Model (BSM),a Zipf Model (ZM),a Niche Preemption Model (NPM),and a Neutral Model (NM).Each of the five models was used at six different sampling scales (10 m×10 m,20 m×20 m,40 m×40 m,60 m×60 m,80 m×80 m,and 100 m×100 m).Model outputs showed that:(1) Accumulators and neutral species strongly influenced species diversity,but the relative importance of the two types of species varied across spatial scales.(2) Distribution patterns of species abundance were best explained by the NPM at small scales (10 me20 m),whereas the NM was the best fit model at large spatial scales.(3) Species richness and abundance distribution patterns appeared to be driven by similar ecological processes.At small scales,the niche theory could be applied to describe species richness and abundance,while at larger scales the neutral theory was more applicable.     

The interpretation of biological surveys

Biological surveys provide the raw material for assembling ecological patterns. These include the properties of parameters such as range, abundance, dispersion, evenness and diversity; the relationships between these parameters; the relationship between geographical distributions and landscape structure; and the co-occurrence of species. These patterns have often been used in the past to evaluate the role of ecological processes in structuring natural communities. In this paper, I investigate the patterns produced by simple neutral community models (NCMs) and compare them with the output of systematic biological surveys. The NCM generates qualitatively, and in some cases quantitatively, the same patterns as the survey data. It therefore provides a satisfactory general theory of diversity and distribution, although what patterns can be used to distinguish neutral from adaptationist interpretations of communities, or even whether such patterns exist, remains unclear.     

Taxa-area relationship and neutral dynamics influence the diversity of fungal communities on senesced tree leaves

This study utilized individual senesced sugar maple and beech leaves as natural sampling units within which to quantify saprotrophic fungal diversity. Quantifying communities in individual leaves allowed us to determine if fungi display a classic taxa–area relationship (species richness increasing with area). We found a significant taxa–area relationship for sugar maple leaves, but not beech leaves, consistent with Wright's species‐energy theory. This suggests that energy availability as affected plant biochemistry is a key factor regulating the scaling relationships of fungal diversity. We also compared taxa rank abundance distributions to models associated with niche or neutral theories of community assembly, and tested the influence of leaf type as an environmental niche factor controlling fungal community composition. Among rank abundance distribution models, the zero‐sum model derived from neutral theory showed the best fit to our data. Leaf type explained only 5% of the variability in community composition. Habitat (vernal pool, upland or riparian forest floor) and site of collection explained > 40%, but could be attributed to either niche or neutral processes. Hence, although niche dynamics may regulate fungal communities at the habitat scale, our evidence points towards neutral assembly of saprotrophic fungi on individual leaves, with energy availability constraining the taxa–area relationship.     

塔里木荒漠河岸林不同生境群落物种多度分布格局

为解释塔里木荒漠河岸林群落构建和物种多度分布格局形成的机理, 本文以塔里木荒漠河岸林2个不同生境(沙地、河漫滩) 4 ha固定监测样地为研究对象, 基于两样地物种调查数据, 采用统计模型(对数级数模型、对数正态模型、泊松对数正态分布模型、Weibull分布模型)、生态位模型(生态位优先占领模型、断棍模型)和中性理论模型(复合群落零和多项式模型、Volkov模型)拟合荒漠河岸林群落物种多度分布, 并用K-S检验与赤池信息准则(AIC)筛选最优拟合模型。结果表明: (1)随生境恶化(土壤水分降低), 植物物种多度分布曲线变化减小, 群落物种多样性、多度和群落盖度降低, 常见种数减少。(2)选用的3类模型均可拟合荒漠河岸林不同生境群落物种多度分布格局, 统计模型和中性理论模型拟合效果均优于生态位模型。复合群落零和多项式模型对远离河岸的干旱沙地生境拟合效果最好; 对数正态模型和泊松对数正态模型对洪水漫溢的河漫滩生境拟合效果最优; 中性理论模型与统计模型无显著差异。初步推断中性过程在荒漠河岸林群落构建中发挥着主导作用, 但模型拟合结果只能作为推断群落构建过程的必要非充分条件, 不能排除生态位过程的潜在作用。     

Effects of aerial dispersal, habitat specialisation, and landscape structure on spider distribution across fragmented grey dunes

Species distribution patterns have been explained by Hutchinson's niche theory, metapopulation theory and source-sink theory. Empirical verification of this framework, however, remains surprisingly scant. In this paper, we test the hypothesis that landscape characteristics (patch size and connectivity), aerial dispersal ability and niche breadth interact in explaining distribution patterns of 29 spider species inhabiting fragmented grey dunes. Distribution patterns only depended on aerial dispersal potential, and the interaction between patch connectivity and area. Niche breadth, measured as the degree of habitat specialisation in the total coastal dune system, did not contribute to the observed distribution patterns. Additional variation in patch occupancy frequency was strongly species-dependent and was determined by different responses to the degree of patch connectivity for ballooning dispersal. Results from this study suggest that dispersal ability largely affects our perception of a species "fundamental niche", and that source-sink and metapopulation dynamics may have a major impact on the distribution of species. From a conservation point of view, specialised (and hence intrinsically rare) species can be predicted to become rarer if fragmentation increases and connectivity decreases. This study is, to our knowledge, one of the few linking species distribution (and not patch occupancy, species diversity or richness) to landscape ecological (patch connectivity and area) and auto-ecological (niche breadth, dispersal potential) features.     

北京东灵山辽东栎(Quercus liaotungensis)林沿海拔梯度的物种多度分布

多度格局对理解群落结构具有重要意义。选用5个描述种-多度关系的生态位模型（断棍模型BSM、生态位优先占领模型NPM、生态位重叠模型ONM、随机分配模型RAM、优势优先模型DPM）,分乔、灌、草3层分别对北京东灵山辽东栎林进行了研究。结果表明：在乔木层,沿海拔梯度从低海拔到高海拔,能很好地反映物种多度格局变异的模型有由RAM、NPM向DPM过渡的趋势;NPM和BSM均能较好地模拟灌木层的绝大多数海拔段,但NPM的效果更好;草本层以BSM的模拟效果最好。生态位模型可以反映出辽东栎林乔木层物种多度分布沿海拔存在的明显变异,而灌木层和草本层物种多度分布沿海拔梯度无明显变化或很难由生态位模型反映出来,是否引入新的模型方法,如中性模型、近中性模型,还有待于进一步研究。     

北京东灵山辽东栎(Quercus liaotungensis)林沿海拔梯度的物种多度分布

多度格局对理解群落结构具有重要意义。选用5个描述种-多度关系的生态位模型(断棍模型BSM、生态位优先占领模型NPM、生态位重叠模型ONM、随机分配模型RAM、优势优先模型DPM),分乔、灌、草3层分别对北京东灵山辽东栎林进行了研究。结果表明:在乔木层,沿海拔梯度从低海拔到高海拔,能很好地反映物种多度格局变异的模型有由RAM、NPM向DPM过渡的趋势;NPM和BSM均能较好地模拟灌木层的绝大多数海拔段,但NPM的效果更好;草本层以BSM的模拟效果最好。生态位模型可以反映出辽东栎林乔木层物种多度分布沿海拔存在的明显变异,而灌木层和草本层物种多度分布沿海拔梯度无明显变化或很难由生态位模型反映出来,是否引入新的模型方法,如中性模型、近中性模型,还有待于进一步研究。     

Diversity and diffusion in multidimensional niche space

The results of an earlier effort to provide a geometrical analysis of Hutchinsonian niche space are extended. The concept of diversity of a species in niche space is introduced and the maximization of this diversity provides a rationale for a within-niche fitness distribution which is Gaussian. Niche expansion is seen as a consequence of diffusion in niche space, and an evolutionary version of the Volterra competition equations is proposed as a way to relate niche geometry with population dynamics. Applications to topics in community evolution, species packing and the statistical fitting of species abundance data are mentioned.     

Niche versus neutrality in structuring the beta diversity of damselfly assemblages

1. Differences among communities in taxonomic composition – beta diversity – are frequently expected to result from taxon‐specific responses to spatial variation in ecological conditions, through niche partitioning. Such process‐derived patterns are in sharp contrast to arguments from neutral theory, where taxa are ecologically equivalent and beta diversity results primarily from dispersal limitation. 2. Here, we compared beta diversity among assemblages of damselflies (Odonata: Zygoptera), for which previous experiments have shown that niche differences maintain genera within a community, but patterns of relative abundance for species within each genus are shaped primarily by neutral dynamics. 3. Using null‐model and ordination‐based methods, we find that both genera and (in contrast to neutral theory) species assemblage composition vary across the landscape in a deterministic fashion, shaped by environmental and spatial factors. 4. While the observed patterns in species composition conflict with theory, we suggest that this a result of weak ecological filters acting to produce spatial variation in assemblages of ecologically similar species undergoing ecological drift within communities. Such patterns are especially likely in systems of relatively weak dispersers like damselflies.