Statistical Versus Biological Hypothesis Testing: Response to Steidl

ABSTRACT In spite of the wide use and acceptance of information theoretic approaches in the wildlife sciences, debate continues on the correct use and interpretation of Akaike's Information Criterion as compared to frequentist methods. Misunderstandings as to the fundamental nature of such comparisons continue. Here we agree with Steidl's argument about situation-specific use of each approach. However, Steidl did not make clear the distinction between statistical and biological hypotheses. Certainly model selection is not statistical, or null, hypothesis testing; importantly, it represents a more effective means to test among competing biological, or research, hypotheses. Employed correctly, it leads to superior strength of inference and reduces the risk that favorite hypotheses are uncritically accepted.     

The neutral theory is dead. Long live the neutral theory

The neutral theory of molecular evolution has been instrumental in organizing our thinking about the nature of evolutionary forces shaping variation at the DNA level. More importantly, it has provided empiricists with a strong set of testable predictions and hence, a useful null hypothesis against which to test for the presence of selection. Evidence indicates that the neutral theory cannot explain key features of protein evolution nor patterns of biased codon usage in certain species. Whereas we now have a reasonable model of selection acting on synonymous changes in Drosophila, protein evolution remains poorly understood. Despite limitations in the applicability of the neutral theory, it is likely to remain an integral part of the quest to understand molecular evolution.     

An information-theoretical approach to phylogeography

Data analysis in phylogeographic investigations is typically conducted in either a qualitative manner, or alternatively via the testing of null hypotheses. The former, where inferences about population processes are derived from geographical patterns of genetic variation, may be subject to confirmation bias and prone to overinterpretation. Testing the predictions of null hypotheses is arguably less prone to bias than qualitative approaches, but only if the tested hypotheses are biologically meaningful. As it is difficult to know a priori if this is the case, there is the general need for additional methodological approaches in phylogeographic research. Here, we explore an alternative method for analysing phylogeographic data that utilizes information theory to quantify the probability of multiple hypotheses given the data. We accomplish this by augmenting the model‐selection procedure implemented in ima with calculations of Akaike Information Criterion scores and model probabilities. We generate a ranking of 17 models each representing a set of historical evolutionary processes that may have contributed to the evolution of Plethodon idahoensis, and then quantify the relative strength of support for each hypothesis given the data using metrics borrowed from information theory. Our results suggest that two models have high probability given the data. Each of these models includes population divergence and estimates of ancestral θ that differ from estimates of descendent θ, inferences consistent with prior work in this system. However, the models disagree in that one includes migration as a parameter and one does not, suggesting that there are two regions of parameter space that produce model likelihoods that are similar in magnitude given our data. Results of a simulation study suggest that when data are simulated with migration, most of the optimal models include migration as a parameter, and further that when all of the shared polymorphism results from incomplete lineage sorting, most of the optimal models do not. The results could also indicate a lack of precision, which may be a product of the amount of data that we have collected. In any case, the information‐theoretic metrics that we have applied to the analysis of our data are statistically rigorous, as are hypothesis‐testing approaches, but move beyond the ‘reject/fail to reject’ dichotomy of conventional hypothesis testing in a manner that provides considerably more flexibility to researchers.     

The demography and population genomics of evolutionary transitions to self-fertilization in plants

The evolution of self-fertilization from outcrossing has occurred on numerous occasions in flowering plants. This shift in mating system profoundly influences the morphology, ecology, genetics and evolution of selfing lineages. As a result, there has been sustained interest in understanding the mechanisms driving the evolution of selfing and its environmental context. Recently, patterns of molecular variation have been used to make inferences about the selective mechanisms associated with mating system transitions. However, these inferences can be complicated by the action of linked selection following the transition. Here, using multilocus simulations and comparative molecular data from related selfers and outcrossers, we demonstrate that there is little evidence for strong bottlenecks associated with initial transitions to selfing, and our simulation results cast doubt on whether it is possible to infer the role of bottlenecks associated with reproductive assurance in the evolution of selfing. They indicate that the effects of background selection on the loss of diversity and efficacy of selection occur rapidly following the shift to high selfing. Future comparative studies that integrate explicit ecological and genomic details are necessary for quantifying the independent and joint effects of selection and demography on transitions to selfing and the loss of genetic diversity.     

Detecting the molecular signature of social conflict: theory and a test with bacterial quorum sensing genes

Extending social evolution theory to the molecular level opens the door to an unparalleled abundance of data and statistical tools for testing alternative hypotheses about the long-term evolutionary dynamics of cooperation and conflict. To this end, we take a collection of known sociality genes (bacterial quorum sensing [QS] genes), model their evolution in terms of patterns that are detectable using gene sequence data, and then test model predictions using available genetic data sets. Specifically, we test two alternative hypotheses of social conflict: (1) the "adaptive" hypothesis that cheaters are maintained in natural populations by frequency-dependent balancing selection as an evolutionarily stable strategy and (2) the "evolutionary null" hypothesis that cheaters are opposed by purifying kin selection yet exist transiently because of their recurrent introduction into populations by mutation (i.e., kin selection-mutation balance). We find that QS genes have elevated within- and among-species sequence variation, nonsignificant signatures of natural selection, and putatively small effect sizes of mutant alleles, all patterns predicted by our evolutionary null model but not by the stable cheater hypothesis. These empirical findings support our theoretical prediction that QS genes experience relaxed selection due to nonclonality of social groups, conditional expression, and the individual-level advantage enjoyed by cheaters. Furthermore, cheaters are evolutionarily transient, persisting in populations because of their recurrent introduction by mutation and not because they enjoy a frequency-dependent fitness advantage.     

Statistical challenges in null model analysis

This review identifies several important challenges in null model testing in ecology: 1) developing randomization algorithms that generate appropriate patterns for a specified null hypothesis; these randomization algorithms stake out a middle ground between formal Pearson–Neyman tests (which require a fully‐specified null distribution) and specific process‐based models (which require parameter values that cannot be easily and independently estimated); 2) developing metrics that specify a particular pattern in a matrix, but ideally exclude other, related patterns; 3) avoiding classification schemes based on idealized matrix patterns that may prove to be inconsistent or contradictory when tested with empirical matrices that do not have the idealized pattern; 4) testing the performance of proposed null models and metrics with artificial test matrices that contain specified levels of pattern and randomness; 5) moving beyond simple presence–absence matrices to incorporate species‐level traits (such as abundance) and site‐level traits (such as habitat suitability) into null model analysis; 6) creating null models that perform well with many sites, many species pairs, and varying degrees of spatial autocorrelation in species occurrence data. In spite of these challenges, the development and application of null models has continued to provide valuable insights in ecology, evolution, and biogeography for over 80 years.     

A comment on testing for a decline in upper Cretaceous dinosaur diversity

A common problem in ecology is to determine whether the diversity of a biological community has changed over time or in response to a disturbance. This involves testing the null hypothesis that diversity is constant against the alternative hypothesis that it has changed. As the power of this test may be low, Fritsch and Hsu (1999, Biometrics 55, 1300-1305) proposed reversing the null and alternative hypothesis. Here, I return to the original formulation and point out that power can be improved by adopting a parametric model for relative abundances and by testing against an ordered alternative.     

基于DNA分子的现代人起源研究35年回顾与展望

1983年,有学者首次发表现代人线粒体DNA进化树,认为现代人可能起源自亚洲。1987年,又有学者按照分子钟假说得到线粒体在10-20万年前出自非洲的推论。随后,以分子钟为前提的Y染色体和常染色体DNA研究也支持了出非洲的结论,该结论逐渐成为分子进化领域的主流理论。2010年,对尼安德特人常染色体基因组的研究指出其对现代人有遗传贡献,这颠覆了人们先前关于现代人只来源自非洲,其他大洲的当地古人被完全取代的认知。目前,单地区起源说已经被修正为同化说。尽管学界对非洲人遗传多样性最高这一现象有共识,但是对该现象的不同解读却可以得出两种迥然不同的结果,现代人出亚洲说和出非洲说。大量研究证实基因组的大部分序列是有功能的,并处在遗传变异水平的饱和态,这质疑了中性理论以及由它推导的现代人出非洲说的合理性,而中性理论的提出恰恰是用来解释并非普遍存在的分子钟的。近年来已经有研究者从新理论的角度解读遗传多样性的饱和态和线性态,人们对现代人起源的认识将会进一步加深完善。     

生态学假说试验验证的原假说困境

试验方法是生态学假说的主要验证方法之一,但也存在由原假说引发的质疑.Quinn和Dunham(1983)通过对Platt(1964)的假说-演绎模型进行分析,主张生态学不可能存在可以严格被试验验证的原假说.Fisher的证伪主义与Neyman-Pearson(N-P)的非判决性使得统计学原假说不能被严格验证;而生态过程中存在的不同于经典物理学的原假说H₀(α=1,β=0)与不同的备假说H₁′(α′=1,β′=0)的情况,使得生态学原假说也很难得到严格的实验验证.通过降低P值、谨慎选择原假说、对非原假说采取非中心化和双侧验证可分别缓解上述的原假说困境.但统计学的原假说显著性验证(NHST)不应等同于生态学假说中有关因果关系的逻辑证明方法.因此,现有大量基于NHST的生态学假说的方法研究和试验验证的结果与结论都不是绝对的逻辑可靠的.     

Saccharomyces sensu stricto as a model system for evolution and ecology

Baker's yeast, Saccharomyces cerevisiae, is not only an extensively used model system in genetics and molecular biology, it is an upcoming model for research in ecology and evolution. The available body of knowledge and molecular techniques make yeast ideal for work in areas such as evolutionary and ecological genomics, population genetics, microbial biogeography, community ecology and speciation. As long as ecological information remains scarce for this species, the vast amount of data that is being generated using S. cerevisiae as a model system will remain difficult to interpret in an evolutionary context. Here we review the current knowledge of the evolution and ecology of S. cerevisiae and closely related species in the Saccharomyces sensu stricto group, and suggest future research directions.     

Analysis of a Schnute postulate-based unified growth model for model selection in evolutionary computations

In order to evaluate the feasibility of a combined evolutionary algorithm-information theoretic approach to select the best model from a set of candidate invasive species models in ecology, and/or to evolve the most parsimonious model from a suite of competing models by comparing their relative performance, it is prudent to use a unified model that covers a myriad of situations. Using Schnute's postulates as a starting point [Schnute, J., 1981. A versatile growth model with statistically stable parameters, Can. J. Fish Aquat. Sci. 38, 1128-1140], we present a single, unified model for growth that can be successfully utilized for model selection in evolutionary computations. Depending on the parameter settings, the unified equation can describe several growth mechanisms. Such a generalized model mechanism, which encompasses a suite of competing models, can be successfully implemented in evolutionary computational algorithms to evolve the most parsimonious model that best fits ground truth data. We have done exactly this by testing the effectiveness of our reaction-diffusion-advection (RDA) model in an evolutionary computation model selection algorithm. The algorithm was validated (with success) against field data sets of the Zebra mussel invasion of Lake Champlain in the United States.     

Mutation-selection models of codon substitution and their use to estimate selective strengths on codon usage

Current models of codon substitution are formulated at the levels of nucleotide substitution and do not explicitly consider the separate effects of mutation and selection. They are thus incapable of inferring whether mutation or selection is responsible for evolution at silent sites. Here we implement a few population genetics models of codon substitution that explicitly consider mutation bias and natural selection at the DNA level. Selection on codon usage is modeled by introducing codon-fitness parameters, which together with mutation-bias parameters, predict optimal codon frequencies for the gene. The selective pressure may be for translational efficiency and accuracy or for fine-tuning translational kinetics to produce correct protein folding. We apply the models to compare mitochondrial and nuclear genes from several mammalian species. Model assumptions concerning codon usage are found to affect the estimation of sequence distances (such as the synonymous rate d(S), the nonsynonymous rate d(N), and the rate at the 4-fold degenerate sites d(4)), as found in previous studies, but the new models produced very similar estimates to some old ones. We also develop a likelihood ratio test to examine the null hypothesis that codon usage is due to mutation bias alone, not influenced by natural selection. Application of the test to the mammalian data led to rejection of the null hypothesis in most genes, suggesting that natural selection may be a driving force in the evolution of synonymous codon usage in mammals. Estimates of selection coefficients nevertheless suggest that selection on codon usage is weak and most mutations are nearly neutral. The sensitivity of the analysis on the assumed mutation model is discussed.     

Proceedings of the SMBE Tri-National Young Investigators' Workshop 2005. Control of the false discovery rate applied to the detection of positively selected amino acid sites

In this article, we consider the probabilistic identification of amino acid positions that evolve under positive selection as a multiple hypothesis testing problem. The null hypothesis "H0,s: site s evolves under a negative selection or under a neutral process of evolution" is tested at each codon site of the alignment of homologous coding sequences. Standard hypothesis testing is based on the control of the expected proportion of falsely rejected null hypotheses or type-I error rate. As the number of tests increases, however, the power of an individual test may become unacceptably low. Recent advances in statistics have shown that the false discovery rate--in this case, the expected proportion of sites that do not evolve under positive selection among those that are estimated to evolve under this selection regime--is a quantity that can be controlled. Keeping the proportion of false positives low among the significant results generally leads to an increase in power. In this article, we show that controlling the false detection rate is relevant when searching for positively selected sites. We also compare this new approach to traditional methods using extensive simulations.     

Testing alternative vicariance scenarios in Western Mediterranean discoglossid frogs

Dated molecular phylogenies are often used to interpret evolutionary history with respect to paleogeographic events. Where more than one interpretation is possible, it is desirable but difficult to assess the alternatives in an objective manner. The present work demonstrates a formalized method for testing molecular clock calibrations and biogeographic scenarios based on them. We assessed the plausibility of several previously published biogeographic hypotheses, using the frog genera Alytes, Discoglossus, and Bombina as model groups. Our data set comprised ca. 900bp of partial mitochondrial 16S and 12S rRNA gene sequences (both genes evolved in a clock-like manner across genera) from nearly all the species and subspecies in the three genera. We tested several calibrations of a molecular clock, which resulted in competing temporal settings for the evolution of taxa. Although only one scenario was in complete accordance with paleogeographic data, statistical testing did not reject the alternatives. Limitations encountered with the present approach may be overcome by more comprehensive analyses in future.     

Can You Sequence Ecology? Metagenomics of Adaptive Diversification

Few areas of science have benefited more from the expansion in sequencing capability than the study of microbial communities. Can sequence data, besides providing hypotheses of the functions the members possess, detect the evolutionary and ecological processes that are occurring? For example, can we determine if a species is adapting to one niche, or if it is diversifying into multiple specialists that inhabit distinct niches? Fortunately, adaptation of populations in the laboratory can serve as a model to test our ability to make such inferences about evolution and ecology from sequencing. Even adaptation to a single niche can give rise to complex temporal dynamics due to the transient presence of multiple competing lineages. If there are multiple niches, this complexity is augmented by segmentation of the population into multiple specialists that can each continue to evolve within their own niche. For a known example of parallel diversification that occurred in the laboratory, sequencing data gave surprisingly few obvious, unambiguous signs of the ecological complexity present. Whereas experimental systems are open to direct experimentation to test hypotheses of selection or ecological interaction, the difficulty in “seeing ecology” from sequencing for even such a simple system suggests translation to communities like the human microbiome will be quite challenging. This will require both improved empirical methods to enhance the depth and time resolution for the relevant polymorphisms and novel statistical approaches to rigorously examine time-series data for signs of various evolutionary and ecological phenomena within and between species.     

Local spatial autocorrelation in biological variables

Spatial autocorrelation (SA) methods have recently been extended to include the detection of local spatial autocorrelation at individual sampling stations. We review the formulas for these statistics and report on the results of an extensive population-genetic simulation study we have published elsewhere to test the applicability of these methods in spatially distributed biological data. We find that most biological variables exhibit global SA, and that in such cases the methods proposed for testing the significance of local SA coefficients reject the null hypothesis excessively. When global SA is absent, permutational methods for testing significance yield reliable results. Although standard errors have been published for the local SA coefficients, their employment using an asymptotically normal approach leads to unreliable results; permutational methods are preferred. In addition to significance tests of suspected non-stationary localities, we can use these methods in an exploratory manner to find and identify hotspots (places with positive local SA) and coldspots (negative local SA) in a dataset. We illustrate the application of these methods in three biological examples from plant population biology, ecology and population genetics. The examples range from the study of single variables to the joint analysis of several variables and can lead to successful demographic and evolutionary inferences about the populations studied.     

Empirical problems of the hierarchical likelihood ratio test for model selection

Advocates of maximum likelihood (ML) approaches to phylogenetics commonly cite as one of their primary advantages the use of objective statistical criteria for model selection. Currently, a particular implementation of the likelihood ratio test (LRT) is the most commonly used model-selection criterion in phylogenetics. This approach requires the choice of a starting point and a parameter addition (or removal) sequence that can affect all ML inferences (i.e., topology, model, and all evolutionary parameters). Here, several alternative starting points and parameter sequences are tested in empirical data sets to assess their influence on model selection and optimal topology. In the studied data sets, varying model-selection protocols leads to selection of different models that, in some cases, lead to different ML trees. Given the sensitivity of the LRT, some possible solutions to model selection (within the hypothesis testing approach) are outlined, and alternative model-selection criteria are discussed. Some of the suggested alternatives seem to lack these problems, although their behavior and adequacy for phylogenetics needs to be further explored.     

Mainstreaming Caenorhabditis elegans in experimental evolution

Experimental evolution provides a powerful manipulative tool for probing evolutionary process and mechanism. As this approach to hypothesis testing has taken purchase in biology, so too has the number of experimental systems that use it, each with its own unique strengths and weaknesses. The depth of biological knowledge about Caenorhabditis nematodes, combined with their laboratory tractability, positions them well for exploiting experimental evolution in animal systems to understand deep questions in evolution and ecology, as well as in molecular genetics and systems biology. To date, Caenorhabditis elegans and related species have proved themselves in experimental evolution studies of the process of mutation, host–pathogen coevolution, mating system evolution and life-history theory. Yet these organisms are not broadly recognized for their utility for evolution experiments and remain underexploited. Here, we outline this experimental evolution work undertaken so far in Caenorhabditis, detail simple methodological tricks that can be exploited and identify research areas that are ripe for future discovery.     

Pitfalls of hypothesis tests and model selection on bootstrap samples: Causes and consequences in biometrical applications

The bootstrap method has become a widely used tool applied in diverse areas where results based on asymptotic theory are scarce. It can be applied, for example, for assessing the variance of a statistic, a quantile of interest or for significance testing by resampling from the null hypothesis. Recently, some approaches have been proposed in the biometrical field where hypothesis testing or model selection is performed on a bootstrap sample as if it were the original sample. P‐values computed from bootstrap samples have been used, for example, in the statistics and bioinformatics literature for ranking genes with respect to their differential expression, for estimating the variability of p‐values and for model stability investigations. Procedures which make use of bootstrapped information criteria are often applied in model stability investigations and model averaging approaches as well as when estimating the error of model selection procedures which involve tuning parameters. From the literature, however, there is evidence that p‐values and model selection criteria evaluated on bootstrap data sets do not represent what would be obtained on the original data or new data drawn from the overall population. We explain the reasons for this and, through the use of a real data set and simulations, we assess the practical impact on procedures relevant to biometrical applications in cases where it has not yet been studied. Moreover, we investigate the behavior of subsampling (i.e., drawing from a data set without replacement) as a potential alternative solution to the bootstrap for these procedures.     

THE LANDE–KIRKPATRICK MECHANISM IS THE NULL MODEL OF EVOLUTION BY INTERSEXUAL SELECTION: IMPLICATIONS FOR MEANING,HONESTY, AND DESIGN IN INTERSEXUAL SIGNALS

The Fisher‐inspired, arbitrary intersexual selection models of Lande (1981) and Kirkpatrick (1982) , including both stable and unstable equilibrium conditions, provide the appropriate null model for the evolution of traits and preferences by intersexual selection. Like the Hardy–Weinberg equilibrium, the Lande–Kirkpatrick (LK) mechanism arises as an intrinsic consequence of genetic variation in trait and preference in the absence of other evolutionary forces. The LK mechanism is equivalent to other intersexual selection mechanisms in the absence of additional selection on preference and with additional trait‐viability and preference‐viability correlations equal to zero. The LK null model predicts the evolution of arbitrary display traits that are neither honest nor dishonest, indicate nothing other than mating availability, and lack any meaning or design other than their potential to correspond to mating preferences. The current standard for demonstrating an arbitrary trait is impossible to meet because it requires proof of the null hypothesis. The LK null model makes distinct predictions about the evolvability of traits and preferences. Examples of recent intersexual selection research document the confirmationist pitfalls of lacking a null model. Incorporation of the LK null into intersexual selection will contribute to serious examination of the extent to which natural selection on preferences shapes signals.