Inference in MCMC step selection models

Habitat selection models are used in ecology to link the spatial distribution of animals to environmental covariates and identify preferred habitats. The most widely used models of this type, resource selection functions, aim to capture the steady-state distribution of space use of the animal, but they assume independence between the observed locations of an animal. This is unrealistic when location data display temporal autocorrelation. The alternative approach of step selection functions embed habitat selection in a model of animal movement, to account for the autocorrelation. However, inferences from step selection functions depend on the underlying movement model, and they do not readily predict steady-state space use. We suggest an analogy between parameter updates and target distributions in Markov chain Monte Carlo (MCMC) algorithms, and step selection and steady-state distributions in movement ecology, leading to a step selection model with an explicit steady-state distribution. In this framework, we explain how maximum likelihood estimation can be used for simultaneous inference about movement and habitat selection. We describe the local Gibbs sampler, a novel rejection-free MCMC scheme, use it as the basis of a flexible class of animal movement models, and derive its likelihood function for several important special cases. In a simulation study, we verify that maximum likelihood estimation can recover all model parameters. We illustrate the application of the method with data from a zebra.     

Models of nearly neutral mutations with particular implications for nonrandom usage of synonymous codons

Summary The population dynamics of nearly neutral mutations are studied using a single-site and a multisite model. In the latter model, the nucleotides in a sequence are completely linked and the selection schemes employed are additive, multiplicative, and additive with a threshold. Although the third selection scheme is very different from the first two, the three schemes produce identical results for a wide range of parameter values. Thus the present study provides a general theory for the population dynamics of nearly neutral mutations because the results can also be used to draw inferences about other selection schemes such as stabilizing selection and synergistic selection. It is shown that the number of slightly deleterious mutations accumulated in a sequence can be considerably larger under the multisite model than under the single-site model, particularly if the sequence is long or if the mutation rate per site is high. The results show that even a very slight selective difference between synonymous codons can produce a strong bias in codon usage. Three alternative explanations for the strong bias in codon usage in bacterial and yeast genes are considered. The implications of the present results for molecular evolution are discussed.     

Evolution of the environmental component of the phenotypic variance: stabilizing selection in changing environments and the cost of homogeneity

Quantitative traits show abundant genetic, environmental, and phenotypic variance, yet if they are subject to stabilizing selection for an optimal phenotype, both the genetic and environmental components are expected to decline. The mechanisms that determine the level and maintenance of phenotypic variance are not yet fully understood. While there has been extensive study of mechanisms maintaining genetic variability, it has generally been assumed that environmental variance is not dependent on the genotype and therefore not subject to change. However, accumulating data suggest that the environmental variance is under some degree of genetic control. In this study, it is assumed accordingly that both the genotypic value (i.e., mean phenotypic value) and the variance of phenotypic value given genotypic value depend on the genotype. Two models are investigated as potentially able to explain the protected maintenance of environmental variance of quantitative traits under stabilizing selection. One is varying environment among generations, such that both the optimal phenotype and the strength of the stabilizing selection vary between generations. The other is the cost of homogeneity, which is based on an assumption of an engineering cost of minimizing variability in development. It is shown that a small homogeneity cost is enough to maintain the observed levels of environmental variance, whereas a large amount of temporal variation in the optimal phenotype and the strength of selection would be necessary.     

分子标记辅助聚合两个棉纤维高强主效QTLs的选择效果

利用长江流域推广品种泗棉3号和优异纤维种质系7235为育种亲本,配置了系统育种和修饰回交聚合育种两套群体。基于来自7235的2个高强纤维主效QTL的分子标记,在上述育种群体中进行了分子标记辅助选择效率研究。高强纤维主效QTLfs1是利用(7235×TM1)F2分离群体,通过集团混合分离法检测到的,它可解释纤维强度表型变异的30%以上。高强纤维主效QTLfs2最初是利用(HS42710×TM1)F2分离群体检测到的,它可解释纤维强度表型变异的12.5%以上。进一步的研究表明,该QTL也位于7235优质系中,但与QTLfs1非等位。2套育种分离群体的2个高强纤维主效QTL的分子标记辅助选择效果表明:QTLfs1在不同环境条件下均稳定表达,它对不同遗传背景的育种群体均有显著的选择效果。尽管QTLfs2的选择效果低于QTLfs1,它在高世代育种群体中也表现较高的选择效率。利用分子标记辅助选择具有一定遗传距离的QTLfs1区间,其纤维强度的选择效率将大大增强。通过分子标记对位于不同连锁群上的2个QTL聚合选择,其中选单株的纤维强度显著提高。研究结果为利用分子标记辅助聚合优质QTL提供了成功实例。     

Using biological assemblage composition to infer the values of covarying environmental factors

1. Observations of different organisms can often be used to infer environmental conditions at a site. These inferences may be useful for diagnosing the causes of degradation in streams and rivers. 2. When used for diagnosis, biological inferences must not only provide accurate, unbiased predictions of environmental conditions, but also pairs of inferred environmental variables must covary no more strongly than actual measurements of those same environmental variables. 3. Mathematical analysis of the relationship between the measured and inferred values of different environmental variables provides an approach for comparing the covariance between measurements with the covariance between inferences. Then, simulated and field‐collected data are used to assess the performance of weighted average and maximum likelihood inference methods. 4. Weighted average inferences became less accurate as covariance in the calibration data increased, whereas maximum likelihood inferences were unaffected by covariance in the calibration data. In contrast, the accuracy of weighted average inferences was unaffected by changes in measurement error, whilst the accuracy of maximum likelihood inferences decreased as measurement error increased. Weighted average inferences artificially increased the covariance of environmental variables beyond what was expected from measurements, whereas maximum likelihood inference methods more accurately reproduced the expected covariances. 5. Multivariate maximum likelihood inference methods can potentially provide more useful diagnostic information than single variable inference models.     

Correlated response in plasticity to selection for early flowering in Arabidopsis thaliana

Phenotypic plasticity is an important strategy for coping with changing environments. However, environmental change usually results in strong directional selection, and little is known empirically about how this affects plasticity. If genes affecting a trait value also affect its plasticity, selection on the trait should influence plasticity. Synthetic outbred populations of Arabidopsis thaliana were selected for earlier flowering under simulated spring- and winter-annual conditions to investigate the correlated response of flowering time plasticity and its effect on family-by-environment variance (Vg×e) within each selected line. We found that selection affected plasticity in an environmentally dependent manner: under simulated spring-annual conditions, selection increased the magnitude of plastic response but decreased Vg×e; selection under simulated winter-annual conditions reduced the magnitude of plastic response but did not alter Vg×e significantly. As selection may constrain future response to environmental change, the environment for crop breeding and ex situ conservation programmes should be carefully chosen. Models of species persistence under environmental change should also consider the interaction between selection and plasticity.     

Inferring selection in partially sequenced regions

A common approach for identifying loci influenced by positive selection involves scanning large portions of the genome for regions that are inconsistent with the neutral equilibrium model or represent outliers relative to the empirical distribution of some aspect of the data. Once identified, partial sequence is generated spanning this more localized region in order to quantify the site-frequency spectrum and evaluate the data with tests of neutrality and selection. This method is widely used as partial sequencing is less expensive with regard to both time and money. Here, we demonstrate that this approach can lead to biased maximum likelihood estimates of selection parameters and reduced rejection rates, with some parameter combinations resulting in clearly misleading results. Most significantly, for a commonly used sample size in Drosophila population genetics (i.e., n = 12), the estimate of the target of selection has a large mean square error and the strength of selection is severely under estimated when the true selected site has not been sampled. We propose sequencing approaches that are much more likely to accurately localize the target and estimate the strength of selection. Additionally, we examine the performance of a commonly used test of selection under a variety of recurrent and single sweep models.     

Artificially selecting bacterial communities using propagule strategies†

Artificial selection is a promising approach to manipulate microbial communities. Here, we report the outcome of two artificial selection experiments at the microbial community level. Both used “propagule” selection strategies, whereby the best-performing communities are used as the inocula to form a new generation of communities. Both experiments were contrasted to a random selection control. The first experiment used a defined set of strains as the starting inoculum, and the function under selection was the amylolytic activity of the consortia. The second experiment used multiple soil communities as the starting inocula, and the function under selection was the communities’ cross-feeding potential. In both experiments, the selected communities reached a higher mean function than the control. In the first experiment, this was caused by a decline in function of the control, rather than an improvement of the selected line. In the second experiment, this response was fueled by the large initial variance in function across communities, and stopped when the top-performing community “fixed” in the metacommunity. Our results are in agreement with basic expectations from breeding theory, pointing to some of the limitations of community-level selection experiments that can inform the design of future studies.     

Genetic analysis of autosomal and X-linked markers across a mouse hybrid zone

In this paper, we present results of the first comprehensive study of the introgression of both autosomal and sex-chromosome markers across the central European portion of the hybrid zone between two house mouse subspecies, Mus musculus musculus and M. m. domesticus. More than 1800 individuals sampled from 105 sites were analyzed with a set of allozyme loci (hopefully representing neutral or nearly neutral markers) and X-linked loci (which are assumed to be under selection). The zone center is best modeled as a single straight line independent of fine-scale local geographic or climatic conditions, being maintained by a balance between dispersal and selection against hybrids. The width (w) of the multilocus autosomal cline was estimated as 9.6 km whereas the estimate for the compound X-chromosome cline was about 4.6 km only. As the former estimate is comparable to that of the Danish portion of the zone (assumed to be much younger than the central European one), zone width does not appear to be related to its age. The strength (B) of the central barrier was estimated as about 20 km; with dispersal (sigma) of about 1 km/gen(1/2), this means effective selection (s*) is approximately 0.06-0.09 for autosomal loci and about 0.25 for X-linked loci. The number of loci under selection was estimated as N= 56-99 for autosomes and about 380 for X-linked loci. Finally, we highlight some potential pitfalls in hybrid zone analyses and in comparisons of different transects. We suggest that conclusions about parts of the mouse genome involved in reproductive isolation and speciation should be drawn with caution and that analytical approaches always providing some estimates should not be used without due care regarding the support or confidence of such estimates, especially if conclusions are based on the difference between these estimates. Finally, we recommend that analysis in two-dimensional space, dense sampling, and rigorous treatment of data, including inspection of likelihood profiles, are essential for hybrid zone studies.     

Semiparametric inference for a 2-stage outcome-auxiliary-dependent sampling design with continuous outcome

Two-stage design has long been recognized to be a cost-effective way for conducting biomedical studies. In many trials, auxiliary covariate information may also be available, and it is of interest to exploit these auxiliary data to improve the efficiency of inferences. In this paper, we propose a 2-stage design with continuous outcome where the second-stage data is sampled with an "outcome-auxiliary-dependent sampling" (OADS) scheme. We propose an estimator which is the maximizer for an estimated likelihood function. We show that the proposed estimator is consistent and asymptotically normally distributed. The simulation study indicates that greater study efficiency gains can be achieved under the proposed 2-stage OADS design by utilizing the auxiliary covariate information when compared with other alternative sampling schemes. We illustrate the proposed method by analyzing a data set from an environmental epidemiologic study.     

A maximum likelihood approach to the detection of selection from a phylogeny

Summary A large amount of information is contained within the phylogentic relationships between species. In addition to their branching patterns it is also possible to examine other aspects of the biology of the species. The influence that deleterious selection might have is determined here. The likelihood of different phylogenies in the presence of selection is explored to determine the properties of such a likelihood surface. The calculation of likelihoods for a phylogeny in the presence and absence of selection, permits the application of a likelihood ratio test to search for selection. It is shown that even a single selected site can have a strong effect on the likelihood. The method is illustrated with an example fromDrosophila melanogaster and suggests that delerious selection may be acting on transposable elements.     

New Methods for Detecting Positive Selection at Single Amino Acid Sites

Inferring positive selection at single amino acid sites is of particular importance for studying evolutionary mechanisms of a protein. For this purpose, Suzuki and Gojobori (1999) developed a method (SG method) for comparing the rates of synonymous and nonsynonymous substitutions at each codon site in a protein-coding nucleotide sequence, using ancestral codons at interior nodes of the phylogenetic tree as inferred by the maximum parsimony method. In the SG method, however, selective neutrality of nucleotide substitutions cannot be tested at codon sites, where only termination codons are inferred at any interior node or the number of equally parsimonious inferences of ancestral codons at all interior nodes exceeds 10,000. Here I present a modified SG method which is free from these problems. Specifically, I use the distance-based Bayesian method for inferring the single most likely ancestral codon from 61 sense codons at each interior node. In the computer simulation and real data analysis, the modified SG method showed a higher overall efficiency of detecting positive selection than the original SG method, particularly at highly polymorphic codon sites. These results indicate that the modified SG method is useful for inferring positive selection at codon sites where neutrality cannot be tested by the original SG method. I also discuss that the p-distance is preferable to the number of synonymous substitutions for inferring the phylogenetic tree in the SG method, and present a maximum likelihood method for detecting positive selection at single amino acid sites, which produced reasonable results in the real data analysis.     

Competition can maintain genetic but not environmental variance in the presence of stabilizing selection

A population in which there is stabilizing selection acting on quantitative traits toward an intermediate optimum becomes monomorphic in the absence of mutation. Further, genotypes that show least environmental variation are also favored, such that selection is likely to reduce both genetic and environmental components of phenotypic variance. In contrast, intraspecific competition for resources is more severe between phenotypically similar individuals, such that those deviating from prevailing phenotypes have a selective advantage. It has been shown previously that polymorphism and phenotypic variance can be maintained if competition between individuals is "effectively" stronger than stabilizing selection. Environmental variance is generally observed in quantitative traits, so mechanisms to explain its maintenance are sought, but the impact of competition on its magnitude has not previously been studied. Here we assume that a quantitative trait is subject to selection for an optimal value and to selection due to competition. Further, we assume that both the mean and variance of the phenotypic value depend on genotype, such that both may be affected by selection. Theoretical analysis and numerical simulations reveal that environmental variance can be maintained only when the genetic variance (in mean phenotypic value) is constrained to a very low level. Environmental variance will be replaced entirely by genotypic variance if a range of genotypes that vary widely in mean phenotype are present or become so by mutation. The distribution of mean phenotypic values is discrete when competition is strong relative to stabilizing selection; but more genotypes segregate and the distribution can approach continuity as competition becomes extremely strong. If the magnitude of the environmental variance is not under genetic control, there is a complementary relationship between the levels of environmental and genetic variance such that the level of phenotypic variance is little affected.     

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a “canalization limit” is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m. From this result it is concluded that characters with typical mutational variances of about 10^–3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.     

Divergent natural selection alters male sperm competition success in Drosophila melanogaster

Sexually selected traits may also be subject to non‐sexual selection. If optimal trait values depend on environmental conditions, then “narrow sense” (i.e., non‐sexual) natural selection can lead to local adaptation, with fitness in a certain environment being highest among individuals selected under that environment. Such adaptation can, in turn, drive ecological speciation via sexual selection. To date, most research on the effect of narrow‐sense natural selection on sexually selected traits has focused on precopulatory measures like mating success. However, postcopulatory traits, such as sperm function, can also be under non‐sexual selection, and have the potential to contribute to population divergence between different environments. Here, we investigate the effects of narrow‐sense natural selection on male postcopulatory success in Drosophila melanogaster. We chose two extreme environments, low oxygen (10%, hypoxic) or high CO₂ (5%, hypercapnic) to detect small effects. We measured the sperm defensive (P1) and offensive (P2) capabilities of selected and control males in the corresponding selection environment and under control conditions. Overall, selection under hypoxia decreased both P1 and P2, while selection under hypercapnia had no effect. Surprisingly, P1 for both selected and control males was higher under both ambient hypoxia and ambient hypercapnia, compared to control conditions, while P2 was lower under hypoxia. We found limited evidence for local adaptation: the positive environmental effect of hypoxia on P1 was greater in hypoxia‐selected males than in controls. We discuss the implications of our findings for the evolution of postcopulatory traits in response to non‐sexual and sexual selection.     

Using time series analysis to characterize evolutionary and plastic responses to environmental change: a case study of a shift toward earlier migration date in sockeye salmon

Environmental change can shift the phenotype of an organism through either evolutionary or nongenetic processes. Despite abundant evidence of phenotypic change in response to recent climate change, we typically lack sufficient genetic data to identify the role of evolution. We present a method of using phenotypic data to characterize the hypothesized role of natural selection and environmentally driven phenotypic shifts (plasticity). We modeled historical selection and environmental predictors of interannual variation in mean population phenotype using a multivariate state-space model framework. Through model comparisons, we assessed the extent to which an estimated selection differential explained observed variation better than environmental factors alone. We applied the method to a 60-year trend toward earlier migration in Columbia River sockeye salmon Oncorhynchus nerka, producing estimates of annual selection differentials, average realized heritability, and relative cumulative effects of selection and plasticity. We found that an evolutionary response to thermal selection was capable of explaining up to two-thirds of the phenotypic trend. Adaptive plastic responses to June river flow explain most of the remainder. This method is applicable to other populations with time series data if selection differentials are available or can be reconstructed. This method thus augments our toolbox for predicting responses to environmental change.     

Selection response and efficiency of doubled-haploid recurrent selection in a cross-fertilized species

Summary Computer simulation was used to compare the simulated response to doubled-haploid (DH) mass selection with the response predicted by mathematical formulae. The efficiency of DH versus diploid mass selection in a cross-fertilized species was also studied by means of theoretical consideration and computer simulation. Simulated gain was in agreement with the predicted gain in the DH population under both additive and complete dominance models. The simulated variance of response to DH mass selection was close to the predicted variance at both the 5% and 25% selection regimes under additive and complete dominance models. The efficiency of DH over diploid mass selection was shown to be dependent upon the allelic frequency, the degree of dominance, and the amount of environmental variance. In theory the efficiency can range from zero to infinity, but in reality it should be greater than one. The efficiency ranges from 2 to 2 in the absence of dominance; it can be greater than two only in the presence of dominance and a small environmental variance. The variance of response to DH mass selection can be smaller than or up to twice as large as the variance of response to diploid mass selection. Computer simulation results agreed with the predicted efficiency of DH mass selection and with the predicted variance-of-response ratio of DH mass selection to diploid mass selection.Joint Contribution from the Charlottetown Research Station, contribution no. 604 and Department of Crop Science, University of Guelph     

Evaluating environmental impacts of selection for residual feed intake in pigs

To identify a proper strategy for future feed-efficient pig farming, it is required to evaluate the ongoing selection scenarios. Tools are lacking for the evaluation of pig selection scenarios in terms of environmental impacts to provide selection guidelines for a more sustainable pig production. Selection on residual feed intake (RFI) has been proposed to improve feed efficiency and potentially reduce the associated environmental impacts. The aim of this study was thus to develop a model to account for individual animal performance in life cycle assessment (LCA) methods to quantify the responses to selection. Experimental data were collected from the fifth generation of pig lines divergently selected for RFI (low line, more efficient pigs, LRFI; high line, less efficient pigs, HRFI). The average feed conversion ratio (FCR) and daily feed intake of LRFI pigs were 7% lower than the average of HRFI pigs (P < 0.0001). A parametric model was developed for LCA based on the dietary net energy fluxes in a pig system. A nutritional pig growth tool, InraPorc®, was included as a module in the model to embed flexibility for changes in feed composition, animal performance traits and housing conditions and to simulate individual pig performance. The comparative individual-based LCA showed that LRFI had an average of 7% lower environmental impacts per kilogram live pig at farm gate compared to HRFI (P < 0.0001) on climate change, acidification potential, freshwater eutrophication potential, land occupation and water depletion. High correlations between FCR and all environmental impact categories (>0.95) confirmed the importance of improvement in feed efficiency to reduce environmental impacts. Significant line differences in all impact categories and moderate correlations with impacts (>0.51) revealed that RFI is an effective measure to select for improved environmental impacts, despite lower correlations compared to FCR. Altogether more optimal criteria for efficient environment-friendly selection can then be expected through restructuring the selection indexes from an environmental point of view.     

Multiplicity-adjusted inferences in risk assessment: benchmark analysis with quantal response data

A primary objective in quantitative risk or safety assessment is characterization of the severity and likelihood of an adverse effect caused by a chemical toxin or pharmaceutical agent. In many cases data are not available at low doses or low exposures to the agent, and inferences at those doses must be based on the high-dose data. A modern method for making low-dose inferences is known as benchmark analysis, where attention centers on the dose at which a fixed benchmark level of risk is achieved. Both upper confidence limits on the risk and lower confidence limits on the "benchmark dose" are of interest. In practice, a number of possible benchmark risks may be under study; if so, corrections must be applied to adjust the limits for multiplicity. In this short note, we discuss approaches for doing so with quantal response data.     

Drop-the-losers design: normal case

Drop-the-losers designs are statistical designs which have two stages of a trial separated by a data based decision. In the first stage k experimental treatments and a control are administered. During a transition period, the empirically best experimental treatment is selected for continuation into the second phase, along with the control. At the study's end, inference focuses on the comparison of the selected treatment with the control using both stages' data. Traditional methods used to make inferences based on both stages' data can yield tests with higher than advertised levels of significance and confidence intervals with lower than advertised confidence. For normally distributed data, methods are provided to correct these deficiencies, providing confidence intervals with accurate levels of confidence. Drop-the-losers designs are particularly applicable to biopharmaceutical clinical trials where they can allow Phase II and Phase III clinical trials to be conducted under a single protocol with the use of all available data.