Plant traits,species pools and the prediction of relative abundance in plant communities: a maximum entropy approach

Questions: To what extent can Shipley et al.'s original maximum entropy model of trait‐based community assembly predict relative abundances of species over a large (3000 km²) landscape? How does variation in the species pool affect predictive ability of the model? How might the effects of missing traits be detected? How can non‐trait‐based processes be incorporated into the model? Location: Central England. Material and Methods: Using 10 traits measured on 506 plant species from 1308 1‐m² plots collected over 3000 km² in central England, we tested one aspect of Shipley et al.'s original maximum entropy model of “pure” trait‐based community assembly (S₁), and modified it to represent both a neutral (S₂) and a hybrid (S₃) scenario of community assembly at the local level. Predictive ability of the three corresponding models was determined with different species pool sizes (30, 60, 100 and 506 species). Statistical significance was tested using a distribution‐free permutation test. Results: Predictive ability was high and significantly different from random expectations in S₁. Predictive ability was low but significant in S₂. Highest predictive ability occurred when both neutral and trait‐based processes were included in the model (S₃). Increasing the pool size decreased predictive ability, but less so in S₃. Incorporating habitat affinity (to indicate missing traits) increased predictive ability. Conclusions: The measured functional traits were significantly related to species relative abundance. Our results both confirm the generality of the original model but also highlight the importance of (i) taking into account neutral processes during assembly of a plant community, and (ii) properly defining the species pool.     

Ontogenetic trait variation and metacommunity effects influence species relative abundances during tree community assembly

Predicting species abundance is one of the most fundamental pursuits of ecology. Combining the information encoded in functional traits and metacommunities provides a new perspective to predict the abundance of species in communities. We applied a community assembly via trait selection model to predict quadrat-scale species abundances using functional trait variation on ontogenetic stages and metacommunity information for over 490 plant species in a subtropical forest and a lowland tropical forest in Yunnan, China. The relative importance of trait-based selection, mass effects, and stochasticity in shaping local species abundances is evaluated using different null models. We found both mass effects and trait selection contribute to local abundance patterns. Trait selection was detectable at all studied spatial scales (0.04–1 ha), with its strength stronger at larger scales and in the subtropical forest. In contrast, the importance of stochasticity decreased with spatial scale. A significant mass effect of the metacommunity was observed at small spatial scales. Our results indicate that tree community assembly is primarily driven by ontogenetic traits and metacommunity effects. Our findings also demonstrate that including ontogenetic trait variation into predictive frameworks allows ecologists to infer ecological mechanisms operating in community assembly at the individual level.     

Limitations of entropy maximization in ecology: a reply to Haegeman and Loreau

Haegeman and Loreau published a paper that is primarily a criticism of a maximum entropy model of trait-based community assembly (by Shipley et al.) and purports to show the limitations of this method in ecology. However, they misunderstood the basic purpose, logic and justification of the maximum entropy formalism and, because of this, leveled criticisms of Shipley et al. that are unfounded. Part of the confusion can be traced to sloppy presentation of the underlying approach in Shipley et al. The confusion arises because maximum entropy models are justified based on information theory and Bayesian logic while the interpretation that Haegeman and Loreau present is based on substantive empirical assumptions about microstate allocations and a combinatorial argument that do not apply to maximum entropy models and which I do not apply to my model in particular.     

Tree diversity on islands: assembly rules,passive sampling and the theory of island biogeography

Aim Species diversity is distributed heterogeneously through space, for reasons that are poorly understood. We tested three hypotheses to account for spatial variation in coniferous tree species diversity in a temperate island archipelago. The theory of island biogeography (ToIB) predicts that island area affects species diversity both directly (by increasing habitat diversity) and indirectly (by increasing abundances, which in turn reduce extinction rates). The ToIB also predicts that island isolation directly affects species diversity by reducing immigration rates. The passive sampling hypothesis predicts that island area and isolation both affect species diversity indirectly, by increasing and decreasing abundances, respectively. Community assembly rules (i.e. even partitioning of conifer abundances among islands) might also reduce tree species diversity beyond the core predictions of ToIB and the passive sampling hypothesis. Location Barkley Sound, British Columbia, Canada. Methods The abundances of eight coniferous tree species were quantified on 34 islands and two (1 ha) mainland plots. The predictions of the ToIB and the passive sampling hypothesis were tested using path analysis, and null models were used to test for abundance‐based assembly rules and to further test the passive sampling hypothesis. Results Path analysis showed that island area and isolation did not have direct, statistical effects on tree species diversity. Instead, both geographic variables had direct statistical effects on total tree abundances, which in turn predicted tree diversity. Results from several passive sampling null models were correlated with observed patterns in species diversity, but they consistently overestimated the number of tree species inhabiting most islands. A different suite of null models showed support for community assembly rules, or that tree species often reached higher abundances on islands that housed fewer heterospecific trees. Main conclusions Results were inconsistent with the ToIB. Instead, patterns in tree diversity were best explained by a combination of stochastic (passive sampling) and deterministic (assembly rules) processes. Stochastic and deterministic processes are commonly considered to be exclusive explanations for island community structure, but results from this study suggest that they can work synergistically to structure island tree communities.     

Species richness, endemism, and abundance patterns: tests of two fractal models in a serpentine grassland

Although scaling relationships that characterize fractal species distributions offer an exciting potential for unification in biogeography, empirical support for fractal theory remains the subject of debate. We synthesize and test multiple predictions of two interrelated fractal models and a null model of random placement using Californian serpentine grassland data describing the spatial location of over 37 000 individually identified plants. The endemics–area relationship and species‐abundance distribution recently derived from a community‐level fractal property performed poorly because of an inaccurate assumption of homogeneity among species. In contrast, a species‐level fractal model that incorporates species‐level differences predicted abundances well, but systematically overestimated endemism and predicted a species–area relationship that violated the observed power law. These findings indicate that in order to make predictions based on the existence of a power‐law species–area relationship, ecologists need a unifying theory of how the community‐level fractal property arises in the presence of species‐level distributional differences.     

A simple null model predicts fruit-frugivore interactions in a temperate rainforest

Studies of seed dispersal mutualisms typically test for adaptive relationships between fruits and frugivores. Here, I take the opposite approach, and ask what relationships would be expected based on chance encounters between mutualists. I derived a simple null model to predict pair-wise relationships between fruit and frugivore species. I assumed that all frugivores had identical fruit preferences, but allowed for interspecific variation in plant abundances, frugivore abundances and fruit phenologies. Under these conditions, the number of visits each frugivore species makes to each plant species results from the product of plant abundances and frugivore abundances when each plant species produces fruit. I then tested null model predictions with observations in a temperate rainforest in British Columbia, Canada. I measured the abundance and phenology of seven bird-dispersed plant species, seasonal changes in the abundances of six avian frugivore species and 212 interactions between them. Empirical results were generally consistent with predictions, suggesting that relationships between birds and fruits are structured randomly. However, some variation in relationships between observations and predictions was observed, suggesting deterministic processes may also be important. Overall results illustrate that predictable relationships between fruit and frugivore species can result from random encounters between mutualists.     

Community assembly,natural selection and maximum entropy models

The papers in this Forum discussion debate various aspects of my maximum entropy model of community assembly. The questions raised centre around (1) the possible mechanisms generating the patterns predicted by my maxent model of community assembly, and (2) the appropriate statistical methods for testing the patterns. Here I briefly explain the proposed mechanistic basis of the model: natural selection occurring between individuals of different species. If trait differences are linked to differential demographic probabilities (i.e. fitness differences) then natural selection will constrain the average trait values found in the community and such average (‘community‐aggregated’) traits will then possess information that is translated into the maximum entropy probabilities. If community assembly is strictly neutral then the maxent model will have no predictive ability. This also justifies the null model, and the permutation test, proposed by Roxburgh and Mokany.     

Multiple modes in a coral species abundance distribution

Species abundance distributions are an important measure of biodiversity and community structure. These distributions are affected by sampling, and alternative species-abundance models often make similar predictions for small sample sizes. Very large samples reveal the relative abundances of rare species, and thus provide information about species relative abundances that small samples cannot. Here, we present the species-abundance distribution for a sample of > 40,000 coral colonies at a single site, exceeding existing samples of coral local assemblages by over an order of magnitude. This abundance distribution is multimodal when examined on a logarithmic scale. Four different model selection procedures all indicate that the underlying community abundance distribution has at least three modes. We show that the multiple modes are not caused by mixtures of species with different habitat preferences. However, spatial aggregation partially explains our results. We inspect published work on species abundance distributions, and suggest that multimodality may be a common feature of large samples.     

Relationships between survival and habitat suitability of semi‐aquatic mammals

Spatial distribution and habitat selection are integral to the study of animal ecology. Habitat selection may optimize the fitness of individuals. Hutchinsonian niche theory posits the fundamental niche of species would support the persistence or growth of populations. Although niche‐based species distribution models (SDMs) and habitat suitability models (HSMs) such as maximum entropy (Maxent) have demonstrated fair to excellent predictive power, few studies have linked the prediction of HSMs to demographic rates. We aimed to test the prediction of Hutchinsonian niche theory that habitat suitability (i.e., likelihood of occurrence) would be positively related to survival of American beaver (Castor canadensis), a North American semi‐aquatic, herbivorous, habitat generalist. We also tested the prediction of ideal free distribution that animal fitness, or its surrogate, is independent of habitat suitability at the equilibrium. We estimated beaver monthly survival probability using the Barker model and radio telemetry data collected in northern Alabama, United States from January 2011 to April 2012. A habitat suitability map was generated with Maxent for the entire study site using landscape variables derived from the 2011 National Land Cover Database (30‐m resolution). We found an inverse relationship between habitat suitability index and beaver survival, contradicting the predictions of niche theory and ideal free distribution. Furthermore, four landscape variables selected by American beaver did not predict survival. The beaver population on our study site has been established for 20 or more years and, subsequently, may be approaching or have reached the carrying capacity. Maxent‐predicted increases in habitat use and subsequent intraspecific competition may have reduced beaver survival. Habitat suitability‐fitness relationships may be complex and, in part, contingent upon local animal abundance. Future studies of mechanistic SDMs incorporating local abundance and demographic rates are needed.     

Linking grazing response of species abundance to functional traits in the Tibetan alpine meadow

Whether grazing response of species abundance can be predicted by plant functional trait remains a challenge untested in a specific ecosystem. We measured species abundance and relevant functional traits for 30 common component species in a moderately grazed and a control community over 3 years (2005, 2006 and 2007) in a Kobresia capillifolia dominated alpine meadow on the Tibetan Plateau. Our objective was to examine species response to grazing and to test the relationship between the response of species abundance and functional traits in grazed and control habitats. Our results showed: i) in terms of species relative abundance and saturated height (the maximum height of an adult individual), most component species significantly decrease in response to moderate grazing and the effect differed among species and between functional groups. ii) The response of species abundance was significantly negatively correlated with saturated height, but not correlated with specific leaf area or seed size. We concluded that the response direction of species abundance to grazing can be predicted by functional traits, whereas it is a weak predictor of the extent of grazing response in species abundance.     

亚高寒草甸植物群落的中性理论验证

 该文以物种组成较为复杂的青藏高原东部亚高寒草甸为背景,结合最新的群落中性理论,以解释亚高寒草甸草本植物群落的物种分布格局和生物多样性的维持机制。通过对阴坡、阳坡和滩地3个生境进行随机取样调查,用中性模型对所得多样性数据进行拟合,并分别应用置信区间检验、拟合优度检验和多样性指数检验3种方法对拟合效果进行检验。研究结果表明,在拟合优度检验中,3个生境中中性理论预测和实际物种多度分布之间没有显著差异(p>0.05);实际观测值基本全部落入模型预测分布的95%的置信区间之内（仅滩地草本植物群落的63个物种中的1个以及阴坡草本植物群落75个物种中的2个偏离95%的置信区间）;对群落多样性的预测也和实际观测没有显著差异,其中丰富度预测拟合得最好(0.49相似文献   

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.     

The importance of spatial scale for trait–abundance relations

The concept of community assembly through trait‐based environmental filtering has played a key role in our understanding of how communities change over space and time, however, the importance of spatial scale in the filtering process remains unclear. We propose that different environmental filters may operate at different spatial scales, and that filters at finer scales would be nested within those acting at coarser scales. We tested for the existence of spatially nested sets of trait‐based filters in a temperate native grassland by applying the recently proposed maximum entropy (MaxEnt) approach to trait‐based community assembly, which we extend through a trait selection procedure. We found that different traits were important in influencing the abundances of species at the three different spatial scales examined (micro‐habitat, habitat, landscape), supporting the idea that trait based filtering processes operating at coarse spatial scales can be quite distinct from those operating at fine scales. Despite this result, we identified several traits which were frequently related to abundance at all spatial scales. Taken together, our results support the proposition that trait‐based environmental filters at finer spatial scales are nested within those operating at coarser scales. We compared our results to those obtained using a simpler trait‐by‐trait analytical approach (correlation analysis and MaxEnt on individual traits). The capacity for MaxEnt to incorporate multiple traits simultaneously provided unique insights into the important traits at each spatial scale and presents significant advantages over existing univariate and multivariate approaches.     

The Influence of Matrix Size on Statistical Properties of Co-Occurrence and Limiting Similarity Null Models

Null models exploring species co-occurrence and trait-based limiting similarity are increasingly used to explore the influence of competition on community assembly; however, assessments of common models have not thoroughly explored the influence of variation in matrix size on error rates, in spite of the fact that studies have explored community matrices that vary considerably in size. To determine how smaller matrices, which are of greatest concern, perform statistically, we generated biologically realistic presence-absence matrices ranging in size from 3–50 species and sites, as well as associated trait matrices. We examined co-occurrence tests using the C-Score statistic and independent swap algorithm. For trait-based limiting similarity null models, we used the mean nearest neighbour trait distance (NN) and the standard deviation of nearest neighbour distances (SDNN) as test statistics, and considered two common randomization algorithms: abundance independent trait shuffling (AITS), and abundance weighted trait shuffling (AWTS). Matrices as small as three × three resulted in acceptable type I error rates (p < 0.05) for both the co-occurrence and trait-based limiting similarity null models when exclusive p-values were used. The commonly used inclusive p-value (≤ or ≥, as opposed to exclusive p-values; < or >) was associated with increased type I error rates, particularly for matrices with fewer than eight species. Type I error rates increased for limiting similarity tests using the AWTS randomization scheme when community matrices contained more than 35 sites; a similar randomization used in null models of phylogenetic dispersion has previously been viewed as robust. Notwithstanding other potential deficiencies related to the use of small matrices to represent communities, the application of both classes of null model should be restricted to matrices with 10 or more species to avoid the possibility of type II errors. Additionally, researchers should restrict the use of the AWTS randomization to matrices with fewer than 35 sites to avoid type I errors when testing for trait-based limiting similarity. The AITS randomization scheme performed better in terms of type I error rates, and therefore may be more appropriate when considering systems for which traits are not clustered by abundance.     

Neutral processes and species sorting in benthic microalgal community assembly: effects of tidal resuspension

Benthic microalgae (BMA) provide vital food resources for heterotrophs and stabilize sediments with their extracellular secretions. A central goal in ecology is to understand how processes such as species interactions and dispersal, contribute to observed patterns of species abundance and distribution. Our objectives were to assess the effects of sediment resuspension on microalgal community structure. We tested whether taxa‐abundance distributions could be predicted using neutral community models (NCMs) and also specific hypotheses about passive migration: (i) As migration decreases in sediment patches, BMA α‐diversity will decrease, and (ii) As migration decreases, BMA community dissimilarity (β‐diversity) will increase. Co‐occurrence indices (checkerboard score and variance ratio) were also computed to test for deterministic factors, such as competition and niche differentiation, in shaping communities. Two intertidal sites (mudflat and sand bar) differing in resuspension regime were sampled throughout the tidal cycle. Fluorometry and denaturing gradient gel electrophoresis were utilized to investigate diatom community structure. Observed taxa‐abundances fit those predicted from NCMs reasonably well (R² of 0.68–0.93), although comparisons of observed local communities to artificial randomly assembled communities rejected the null hypothesis that diatom communities were assembled solely by stochastic processes. No co‐occurrence tests indicated a significant role for competitive exclusion or niche partitioning in microalgal community assembly. In general, predictions about relationships between migration and species diversity were supported for local community dynamics. BMA at low tide (lowest migration) exhibited reduced α‐diversity as compared to periods of immersion at both mudflat and sand bar sites. β‐diversity was higher during low tide emersion on the mudflat, but did not differ temporally at the sand bar site. In between‐site metacommunity comparisons, low‐ and high‐resuspension sites exhibited distinct community compositions while the low‐energy mudflats contained higher microalgal biomass and greater α‐diversity. To our knowledge this is the first study to test the relevance of neutral processes in structuring marine microalgal communities. Our results demonstrate a prominent role for stochastic factors in structuring local BMA community assembly, although unidentified nonrandom processes also appear to play some role. High passive migration, in particular, appears to help maintain species diversity and structure communities in both sand and muddy habitats.     

Concordant population dynamics of Lepidoptera herbivores in a forest ecosystem

It is frequently assumed that population fluctuations are largely independent within a community of trophically‐similar species, but this need not be so. If population fluctuations are partly synchronized or concordant, this will produce interannual variability in the community's aggregate abundance and generate temporal variance in ecosystem structure. We studied the community of Lepidoptera inhabiting northern hardwood forests in New Hampshire, USA, to evaluate the hypothesis that fluctuations in consumer communities can arise from concordant dynamics of constituent populations. Interannual comparisons of moth abundances for >75 species sampled at three sites over four years revealed that concordant dynamics contribute strongly to interannual variability in the abundance of consumers. A conspicuous decline in community abundance from 2004 to 2005 was the result of predominantly negative population growth rates of the component species, while an increase in community abundance from 2006 to 2007 was the result of predominantly positive population growth rates. Population dynamics most strongly linked species that feed in the early season (perhaps due to shared responses to climatic effects), but not species that might share natural enemies or host plants. The observed concordant dynamics introduced conspicuous temporal variation in the abundance of primary consumers relative to plants and secondary consumers, thereby altering the forest's trophic structure. Such variance in the aggregate abundance of forest primary consumers could generate time‐lagged fluctuations in abundances of secondary consumers and will generally have important consequences for ecosystem properties and processes that are nonlinear functions of consumer abundance, such as plant community structure and nutrient cycling.     

Quantifying trait selection driving community assembly: a test in herbaceous plant communities under contrasted land use regimes

Plant traits are particularly important in determining plant community structure. However, how can one identify which traits are the most important in driving community assembly? Here we propose a method 1) to quantify the direction and strength of trait selection during community assembly and 2) to obtain parsimonious lists of traits that can predict species relative abundances in plant communities. We tested our method using floristic data from 32 plots experiencing different treatments (fertilisation and grazing) in southern France. Twelve functional traits were measured on 68 species. We determined the direction and strength of selection on these 12 traits using a metric derived from a maximum entropy model (i.e. lambda). We then determined our parsimonious list of traits using a backward selection of traits based on these lambda values (for all treatments and in each treatment separately). We finally compared our method to two other methods: one based on iterative RLQ and the other based on an entropy‐based forward selection of traits. We found major differences in the direction and strength of selection across the 12 traits and treatments. From the 12 traits, plant vegetative and reproductive heights, leaf dry matter content leaf nitrogen content, specific leaf area, and leaf phosphorus content were particularly important for predicting species relative abundances when considering all treatments together. Our method yielded results similar to those produced by the entropy‐based approach but differed from those produced by the iterative RLQ, whose selected traits could not significantly predict species relative abundances. Together these results suggest that the assembly of these communities is primarily driven by a small number of key functional traits. We argue that our method provides an objective way of determining a parsimonious list of traits that together accurately predict community structure and which, despite its complementarities with entropy‐based method, offers significant advantages.     

Integrating macroecological metrics and community taxonomic structure

We extend macroecological theory based on the maximum entropy principle from species level to higher taxonomic categories, thereby predicting distributions of species richness across genera or families and the dependence of abundance and metabolic rate distributions on taxonomic tree structure. Predictions agree with qualitative trends reported in studies on hyper‐dominance in tropical tree species, mammalian body size distributions and patterns of rarity in worldwide plant communities. Predicted distributions of species richness over genera or families for birds, arthropods, plants and microorganisms are in excellent agreement with data. Data from an intertidal invertebrate community, but not from a dispersal‐limited forest, are in excellent agreement with a predicted new relationship between body size and abundance. Successful predictions of the original species level theory are unmodified in the extended theory. By integrating macroecology and taxonomic tree structure, maximum entropy may point the way towards a unified framework for understanding phylogenetic community structure.     

Fish and Phytoplankton Exhibit Contrasting Temporal Species Abundance Patterns in a Dynamic North Temperate Lake

Temporal patterns of species abundance, although less well-studied than spatial patterns, provide valuable insight to the processes governing community assembly. We compared temporal abundance distributions of two communities, phytoplankton and fish, in a north temperate lake. We used both 17 years of observed relative abundance data as well as resampled data from Monte Carlo simulations to account for the possible effects of non-detection of rare species. Similar to what has been found in other communities, phytoplankton and fish species that appeared more frequently were generally more abundant than rare species. However, neither community exhibited two distinct groups of “core” (common occurrence and high abundance) and “occasional” (rare occurrence and low abundance) species. Both observed and resampled data show that the phytoplankton community was dominated by occasional species appearing in only one year that exhibited large variation in their abundances, while the fish community was dominated by core species occurring in all 17 years at high abundances. We hypothesize that the life-history traits that enable phytoplankton to persist in highly dynamic environments may result in communities dominated by occasional species capable of reaching high abundances when conditions allow. Conversely, longer turnover times and broad environmental tolerances of fish may result in communities dominated by core species structured primarily by competitive interactions.     

Modelling ecological niches from low numbers of occurrences: assessment of the conservation status of poorly known viverrids (Mammalia, Carnivora) across two continents

The conservation of poorly known species is difficult because of incomplete knowledge on their biology and distribution. We studied the contribution of two ecological niche modelling tools, the Genetic Algorithm for Rule-set Prediction (GARP) and maximum entropy (Maxent), in assessing potential ranges and distributional connectivity among 12 of the least known African and Asian viverrids. The level of agreement between GARP and Maxent predictions was low when < 15 occurrences were available, probably indicating a minimum number below that necessary to obtain models with good predictive power. Unexpectedly, our results suggested that Maxent extrapolated more than GARP in the context of small sample sizes. Predictions were overlapped with current land use and location of protected areas to estimate the conservation status of each species. Our analyses yielded range predictions generally contradicting with extents of occurrence established by the IUCN. We evidenced a high level of disturbance within predicted distributions in West and East Africa, Sumatra, and South-East Asia, and identified within West African degraded lowlands four relatively preserved areas that might be of prime importance for the conservation of rainforest taxa. Knowing whether these species of viverrids may survive in degraded or alternative habitats is of crucial importance for further conservation planning. The level of coverage of species suitable ranges by existing and proposed IUCN reserves was low, and we recommend that the total surface of protected areas be substantially increased on both continents.