An improved null model for assessing the net effects of multiple stressors on communities

Ecological stressors (i.e., environmental factors outside their normal range of variation) can mediate each other through their interactions, leading to unexpected combined effects on communities. Determining whether the net effect of stressors is ecologically surprising requires comparing their cumulative impact to a null model that represents the linear combination of their individual effects (i.e., an additive expectation). However, we show that standard additive and multiplicative null models that base their predictions on the effects of single stressors on community properties (e.g., species richness or biomass) do not provide this linear expectation, leading to incorrect interpretations of antagonistic and synergistic responses by communities. We present an alternative, the compositional null model, which instead bases its predictions on the effects of stressors on individual species, and then aggregates them to the community level. Simulations demonstrate the improved ability of the compositional null model to accurately provide a linear expectation of the net effect of stressors. We simulate the response of communities to paired stressors that affect species in a purely additive fashion and compare the relative abilities of the compositional null model and two standard community property null models (additive and multiplicative) to predict these linear changes in species richness and community biomass across different combinations (both positive, negative, or opposite) and intensities of stressors. The compositional model predicts the linear effects of multiple stressors under almost all scenarios, allowing for proper classification of net effects, whereas the standard null models do not. Our findings suggest that current estimates of the prevalence of ecological surprises on communities based on community property null models are unreliable, and should be improved by integrating the responses of individual species to the community level as does our compositional null model.     

USING PHYLOGENETIC TREES TO STUDY SPECIATION AND EXTINCTION

One tool in the study of the forces that determine species diversity is the null, or simple, model. The fit of predictions to observations, good or bad, leads to a useful paradigm or to knowledge of forces not accounted for, respectively. It is shown how simple models of speciation and extinction lead directly to predictions of the structure of phylogenetic trees. These predictions include both essential attributes of phylogenetic trees: lengths, in the form of internode distances; and topology, in the form of internode links. These models also lead directly to statistical tests which can be used to compare predictions with phylogenetic trees that are estimated from data. Two different models and eight data sets are considered. A model without species extinction consistently yielded predictions closer to observations than did a model that included extinction. It is proposed that it may be useful to think of the diversification of recently formed monophyletic groups as a random speciation process without extinction.     

Generating and testing predictions about community structure: Which theory is relevant and can it be tested with observational data?

Three issues are discussed relevant to the controversy over using null models and observational data on guild structure to test community-level predictions based on limiting similarity theory. First, I argue that most limiting similarity theory is not based on reasonable assumptions for plants and that the theory that is relevant does not generate any predictions about expected guild proportionality on a small spatial scale. Therefore, regardless of adequacy of the statistical methods, the predictions being tested by the body of literature using null models to test for niche limitation are unlikely to be relevant in most plant comunities. Second, assuming that the predictions are after all worth being tested, I argue that most tests using the guild approach do not provide adequate explanations of how the defined guilds could lead to greater competition within vs. between guilds. If this is not true for the particular guilds used, the predictions of guild proportionality or size constancy will not be valid. Third, I address the controversy over whether field experiments can provide more solid evidence than observational data about the role of competition in determining community structure by (1) suggesting methods of dealing with potential drawbacks of field experiments, and (2) suggesting alternative experimental approaches for directly addressing issues about community structure.     

When does diversity fit null model predictions? Scale and range size mediate the mid‐domain effect

Aim  Recently, a flurry of studies have focused on the extent to which geographical patterns of diversity fit mid-domain effect (MDE) null models. While some studies find strong support for MDE null models, others find little. We test two hypotheses that might explain this variation among studies: small-ranged groups of species are less likely than large-ranged species to show mid-domain peaks in species richness, and mid-domain null model predictions are less robust for smaller spatial extents than for larger spatial extents.
Location  We analyse data sets from elevational, riverine, continental and other domains from around the world.
Methods  We use a combination of Spearman rank correlations and binomial tests to examine whether differences within and among studies and domains in the predictive power of MDE null models vary with spatial scale and range size.
Results  Small-ranged groups of species are less likely to fit mid-domain predictions than large-ranged groups of species. At large spatial extents, diversity patterns of taxonomic groups with large mean range sizes fit MDE null model predictions better than did diversity patterns of groups with small mean range sizes. MDE predictions were more explanatory at larger spatial extents than at smaller extents. Diversity patterns at smaller spatial extents fit MDE predictions poorly across all range sizes. Thus, MDE predictions should be expected to explain patterns of species richness when ranges and the scale of analysis are both large.
Main conclusions  Taken together, the support for these hypotheses offers a more sophisticated model of when MDE predictions should be expected to explain patterns of species richness, namely when ranges and the scale of analysis are both large. Thus the circumstances in which the MDE is important are finite and apparently predictable.     

Simultaneous inference in general parametric models

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here.     

Current caveats and further directions in the analysis of density-dependent population regulation

An important issue in population ecology is to disentangle different density-dependent mechanisms that may limit or regulate animal populations. This goal is further complicated when studying long-lived species for which experimental approaches are not feasible, in whose cases density-dependence hypotheses are tested using long-term monitored populations. Here we respond to some criticisms and identify additional problems associated with these kinds of observational studies. Current caveats are related to the temporal and spatial scales covered by population monitoring data, which may question its suitability for density-dependence tests, and to statistical flaws such as the incorrect control for confounding variables, low statistical power, the distribution of demographic variables, the interpretation of spurious correlations, and the often used stepwise series of univariate analyses. Generalised linear mixed models are recommended over other more traditional approaches, since they help to solve the above statistical problems and, more importantly, allow to properly test several hypotheses simultaneously. Finally, several management actions aimed to recover endangered species, such as supplementary feeding, might be considered as field experiments for further testing density-dependence hypotheses in long-lived study models. We expect these opportunities, together with the most adequate statistical tools now available, will help to better our understanding of density-dependent effects in wild populations.     

Forest savanna ecotone dynamics in India as revealed by carbon isotope ratios of soil organic matter

Linear programming models of diet selection (LP) have been criticized as being too sensitive to variations in parameter values that have not been or may not be able to be measured with a high degree of precision (small standard error). Therefore, LP's predictions have been questioned, even though the predicted diet choices agree very well with observations in 400 published tests. The philosophical and statistical aspects of this criticism of LP are reviewed in light of the ability to test any nontrivial ecological theory. It is argued that measures of error in field data may not meet simple statistical definitions, and thereby, may make sensitivity analyses that use the error measures overly conservative. Furthermore, the important issue in testing ecological theory may not be the statistical confidence in a single test, but whether or not the theory withstands repeated tests.     

Presenting Scientific Theories Within Risk Assessments

We propose a structure for presenting risk assessments with the purpose of enhancing the transparency of the selection process of scientific theories and models derived from them. The structure has two stages, with 7 steps, where the stages involve two types of theories: core and auxiliary, which need to be identified in order to explain and evaluate observations and predictions. Core theories are those that are “fundamental” to the phenomena being observed, whereas auxiliary theories are those that describe or explain the actual observation process of the phenomena. The formulation of a scientific theory involves three constitutive components or types of judgments: explanative, evaluative, and regulative or aesthetic, driven by reason. Two perspectives guided us in developing the proposed structure: (1) In a risk assessment explanations based on notions of causality can be used as a tool for developing models and predictions of possible events outside the range of direct experience. The use of causality for development of models is based on judgments, reflecting regulative or aesthetic conceptualizations of different phenomena and how they (should) fit together in the world. (2) Weight of evidence evaluation should be based on falsification principles for excluding models, rather than validation or justification principles that select the best or nearly best-fitting models. Falsification entails discussion that identifies challenges to proposed models, and reconciles apparent inconsistencies between models and data. Based on the discussion of these perspectives the 7 steps of the structure are: the first stage for core theories, (A) scientific concepts, (B) causality network, and (C) mathematical model; and the second stage for auxiliary theories, (D) data interpretation, (E) statistical model, (F) evaluation (weight of evidence), and (G) reconciliation, which includes the actual decision formulation.     

Comparison of probability and likelihood models for peptide identification from tandem mass spectrometry data

We evaluate statistical models used in two-hypothesis tests for identifying peptides from tandem mass spectrometry data. The null hypothesis H(0), that a peptide matches a spectrum by chance, requires information on the probability of by-chance matches between peptide fragments and peaks in the spectrum. Likewise, the alternate hypothesis H(A), that the spectrum is due to a particular peptide, requires probabilities that the peptide fragments would indeed be observed if it was the causative agent. We compare models for these probabilities by determining the identification rates produced by the models using an independent data set. The initial models use different probabilities depending on fragment ion type, but uniform probabilities for each ion type across all of the labile bonds along the backbone. More sophisticated models for probabilities under both H(A) and H(0) are introduced that do not assume uniform probabilities for each ion type. In addition, the performance of these models using a standard likelihood model is compared to an information theory approach derived from the likelihood model. Also, a simple but effective model for incorporating peak intensities is described. Finally, a support-vector machine is used to discriminate between correct and incorrect identifications based on multiple characteristics of the scoring functions. The results are shown to reduce the misidentification rate significantly when compared to a benchmark cross-correlation based approach.     

假说检验和科学方法

本文的意图是让研究者审视研究方法,并在研究设计中充分使用假说检验,并在选择模式物种时充分理解其自然史.我们的总前提是,按照"强推论"(指假定拒绝某一假说而不是支持某一偏爱假说)的逻辑,科学能够进展得更快、更可观、更有确定性.我们强调并提供了符合逻辑的一系列步骤,即确定科学问题或确定具有未知生物学意义的问题;列出所有可靠的、能解释所观察现象的假说,每个假说列出其可检验的、可证明其无根据的预测;然后是符合预测检验的实验或研究设计.我们也强调,模式物种对于解决科学的理论问题以及得出推论是很重要的.本文所展示的不是新思想,只是提醒研究者要注意遵循的基本研究途径.     

Ecologists should not use statistical significance tests to interpret simulation model results

Simulation models are widely used to represent the dynamics of ecological systems. A common question with such models is how changes to a parameter value or functional form in the model alter the results. Some authors have chosen to answer that question using frequentist statistical hypothesis tests (e.g. ANOVA). This is inappropriate for two reasons. First, p‐values are determined by statistical power (i.e. replication), which can be arbitrarily high in a simulation context, producing minuscule p‐values regardless of the effect size. Second, the null hypothesis of no difference between treatments (e.g. parameter values) is known a priori to be false, invalidating the premise of the test. Use of p‐values is troublesome (rather than simply irrelevant) because small p‐values lend a false sense of importance to observed differences. We argue that modelers should abandon this practice and focus on evaluating the magnitude of differences between simulations. Synthesis Researchers analyzing field or lab data often test ecological hypotheses using frequentist statistics (t‐tests, ANOVA, etc.) that focus on p‐values. Field and lab data usually have limited sample sizes, and p‐values are valuable for quantifying the probability of making incorrect inferences in that situation. However, modern ecologists increasingly rely on simulation models to address complex questions, and those who were trained in frequentist statistics often apply the hypothesis‐testing approach inappropriately to their simulation results. Our paper explains why p‐values are not informative for interpreting simulation models, and suggests better ways to evaluate the ecological significance of model results.     

Selection of evolutionary models for phylogenetic hypothesis testing using parametric methods

Recent molecular studies have incorporated the parametric bootstrap method to test a priori hypotheses when the results of molecular based phylogenies are in conflict with these hypotheses. The parametric bootstrap requires the specification of a particular substitutional model, the parameters of which will be used to generate simulated, replicate DNA sequence data sets. It has been both suggested that, (a) the method appears robust to changes in the model of evolution, and alternatively that, (b) as realistic model of DNA substitution as possible should be used to avoid false rejection of a null hypothesis. Here we empirically evaluate the effect of suboptimal substitution models when testing hypotheses of monophyly with the parametric bootstrap using data sets of mtDNA cytochrome oxidase I and II (COI and COII) sequences for Macaronesian Calathus beetles, and mitochondrial 16S rDNA and nuclear ITS2 sequences for European Timarcha beetles. Whether a particular hypothesis of monophyly is rejected or accepted appears to be highly dependent on whether the nucleotide substitution model being used is optimal. It appears that a parameter rich model is either equally or less likely to reject a hypothesis of monophyly where the optimal model is unknown. A comparison of the performance of the Kishino–Hasegawa (KH) test shows it is not as severely affected by the use of suboptimal models, and overall it appears to be a less conservative method with a higher rate of failure to reject null hypotheses.     

Fish–prey interactions in,and associated data from,a temperate stream of the Yura River,Kyoto, Japan

Although quantitative data on interspecific interactions within complex food webs are essential for evaluation of assumptions, hypotheses, and predictions of ecological theories; empirical studies yielding quantitative data on complex food webs are very limited. Ecological information on body size, habitat use, and seasonality of the component species of food webs aids in determining the mechanisms of food web structures. Ideally, ecological information on component species should be obtained contemporaneously when used to describe quantitative food webs, but such observations and sampling strategies are labor intensive and thus have been rarely described. We conducted year-round samplings of, and performed observations on, a temperate stream: the upper reaches of the Yura River, Kyoto, Japan. We derived quantitative data on the abundance, biomass, body mass, microhabitat use, and those seasonality of 7 fish species and 167 invertebrate taxa of the temperate stream food web. In addition, we estimated the per mass consumption rates of 7 predatory fish species, consuming 183 prey invertebrates, and the ratios between the per mass consumption rates of the 7 predatory fish species and the production rates of 78 prey invertebrates in each trophic link. All fishes and aquatic invertebrates were identified to species or lowest possible taxon. Our data may contribute to the construction of mathematical models explaining the behavior of stream communities/ecosystems.     

生态学中的点格局研究概况及其在国内的应用

点格局分析是研究生态学格局的工具之一,近年来在生态学中的应用越来越多。为深入了解点格局分析方法在国内的研究与应用情况,以所总结的研究进展、一般步骤和基本要点为背景,分析评述了1996—2015年期间以点格局为主题的国内中文核心期刊文献。结果表明,在国内生态学格局研究中,应用研究占据主导地位,研究对象广泛,包括以树木为主的乔、灌、草等不同生活型的植物,甚至包括景观;基础研究,包括概括性统计量、零模型与点过程模型等方面,以及专用软件工具包的开发等研究薄弱。在应用中存在一定问题,主要表现为:概括性统计量使用单一,且以Ripley的K-函数及其变形为主;零模型(或点过程模型)是科学问题的统计表达,但是有一半以上的研究未明确给出零模型。建议在未来应用研究中重视多种统计量的组合使用和原假设的建立,在探讨热带、亚热带森林等具有复杂空间结构系统的多样性格局时,考虑对象的不同世代和系统的不同垂直层次,并加强多变量或三维概括性统计量的开发、点格局分析方法与动态过程模型的结合研究等工作。     

Empirical Relationships between Species Richness, Evenness, and Proportional Diversity

Diversity (or biodiversity) is typically measured by a species count (richness) and sometimes with an evenness index; it may also be measured by a proportional statistic that combines both measures (e.g., Shannon-Weiner index or H'). These diversity measures are hypothesized to be positively and strongly correlated, but this null hypothesis has not been tested empirically. We used the results of Caswell's neutral model to generate null relationships between richness (S), evenness (J'), and proportional diversity (H'). We tested predictions of the null model against empirical relationships describing data in a literature survey and in four individual studies conducted across various scales. Empirical relationships between log S or J' and H' differed from the null model when <10 species were tested and in plants, vertebrates, and fungi. The empirical relationships were similar to the null model when >10 and <100 species were tested and in invertebrates. If >100 species were used to estimate diversity, the relation between log S and H' was negative. The strongest predictive models included log S and J'. A path analysis indicated that log S and J' were always negatively related, that empirical observations could not be explained without including indirect effects, and that differences between the partials may indicate ecological effects, which suggests that S and J' act like diversity components or that diversity should be measured using a compound statistic.     

A generalized model for overdispersed count data

Overdispersed count data are very common in ecology. The negative binomial model has been used widely to represent such data. Ecological data often vary considerably, and traditional approaches are likely to be inefficient or incorrect due to underestimation of uncertainty and poor predictive power. We propose a new statistical model to account for excessive overdisperson. It is the combination of two negative binomial models, where the first determines the number of clusters and the second the number of individuals in each cluster. Simulations show that this model often performs better than the negative binomial model. This model also fitted catch and effort data for southern bluefin tuna better than other models according to AIC. A model that explicitly and properly accounts for overdispersion should contribute to robust management and conservation for wildlife and plants.     

Niches versus neutrality: uncovering the drivers of diversity in a species-rich community

Ecological models suggest that high diversity can be generated by purely niche-based, purely neutral or by a mixture of niche-based and neutral ecological processes. Here, we compare the degree to which four contrasting hypotheses for coexistence, ranging from niche-based to neutral, explain species richness along a body mass niche axis. We derive predictions from these hypotheses and confront them with species body-mass patterns in a highly sampled marine phytoplankton community. We find that these patterns are consistent only with a mechanism that combines niche and neutral processes, such as the emergent neutrality mechanism. In this work, we provide the first empirical evidence that a niche-neutral model can explain niche space occupancy pattern in a natural species-rich community. We suggest this class of model may be a useful hypothesis for the generation and maintenance of species diversity in other size-structured communities.     

Statistical mechanical treatment of α-helices and extended structures in proteins with inclusion of short- and medium-range interactions

A statistical mechanical model of protein conformation with medium-range interactions between theith and (i+k)^th residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interactionk; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameterss and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as inall empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.