Testing the grain-size model for the evolution of phenotypic plasticity

Phenotypic plasticity is the ability of a genotype to modify its phenotypic characteristics in response to different environments. Theory predicts that adaptive plasticity should primarily evolve in organisms that experience heterogeneous environments. An organism's dispersal rate is a key component in these models, because the degree of dispersal partly determines the extent of environmental heterogeneity. Here, I provide the first large-scale test of the theoretical prediction that phenotypic plasticity evolves in association with dispersal rate using meta-analysis of data from 258 experiments from the literature on plasticity in marine invertebrates. In line with predictions, phenotypic plasticity is generally greater in species with higher dispersal rates, suggesting that dispersal and environmental heterogeneity are important selective agents for evolution of plasticity in marine habitats.     

A statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci

Non-equivalent expression of alleles at a locus results in genomic imprinting. In this article, a statistical framework for genome-wide scanning and testing of imprinted quantitative trait loci (iQTL) underlying complex traits is developed based on experimental crosses of inbred line species in backcross populations. The joint likelihood function is composed of four component likelihood functions with each of them derived from one of four backcross families. The proposed approach models genomic imprinting effect as a probability measure with which one can test the degree of imprinting. Simulation results show that the model is robust for identifying iQTL with various degree of imprinting ranging from no imprinting, partial imprinting to complete imprinting. Under various simulation scenarios, the proposed model shows consistent parameter estimation with reasonable precision and high power in testing iQTL. When a QTL shows Mendelian effect, the proposed model also outperforms traditional Mendelian model. Extension to incorporate maternal effect is also given. The developed model, built within the maximum likelihood framework and implemented with the EM algorithm, provides a quantitative framework for testing and estimating iQTL involved in the genetic control of complex traits.     

Dissecting the pleiotropic consequences of a quantitative trait nucleotide

The downstream consequences of a single quantitative trait polymorphism can provide important insight into the molecular basis of a trait. However, the molecular consequences of a polymorphism may be complex and only a subset of these may influence the trait of interest. In natural isolates of Saccharomyces cerevisiae , a nonsynonymous polymorphism in cystathione β-synthase ( CYS4 ) causes a deficiency in both cysteine and glutathione that results in rust-colored colonies and drug-dependent growth defects. Using a single-nucleotide allele replacement, we characterized the effects of this polymorphism on gene expression levels across the genome. To determine whether any of the differentially expressed genes are necessary for the production of rust-colored colonies, we screened the yeast deletion collection for genes that enhance or suppress rust coloration. We found that genes in the sulfur assimilation pathway are required for the production of rust color but not the drug-sensitivity phenotype. Our results show that a single quantitative trait polymorphism can generate a complex set of downstream changes, providing a molecular basis for pleiotropy.     

A statistical model for under- or overdispersed clustered and longitudinal count data

We propose a likelihood-based model for correlated count data that display under- or overdispersion within units (e.g. subjects). The model is capable of handling correlation due to clustering and/or serial correlation, in the presence of unbalanced, missing or unequally spaced data. A family of distributions based on birth-event processes is used to model within-subject underdispersion. A computational approach is given to overcome a parameterization difficulty with this family, and this allows use of common Markov Chain Monte Carlo software (e.g. WinBUGS) for estimation. Application of the model to daily counts of asthma inhaler use by children shows substantial within-subject underdispersion, between-subject heterogeneity and correlation due to both clustering of measurements within subjects and serial correlation of longitudinal measurements. The model provides a major improvement over Poisson longitudinal models, and diagnostics show that the model fits well.     

Genes affecting phenotypic plasticity in Arabidopsis: pleiotropic effects and reproductive fitness of photomorphogenic mutants

Many plants exhibit characteristic photomorphogenic shade ’avoidance’ responses to crowding and vegetation shade; this plasticity is often hypothesized to be adaptive. We examined the contribution of specific photomorphogenic loci to plastic shade avoidance responses in the annual crucifer Arabidopsis thaliana by comparing single-gene mutants defective at those loci with wild type plants exhibiting normal photomorphogenesis. The hy1 and hy2 mutants, deficient in all functional phytochromes, were less plastic than the wild type in response to a nearby grass canopy or to a low-red/far-red light ratio characteristic of vegetation shade. These mutants displayed constitutively shade-avoiding phenotypes throughout the life cycle regardless of the treatment: they bolted at an earlier developmental stage and were characterized by reduced branching. In contrast, the hy4 mutant, deficient in blue light reception, exhibited greater plasticity than the wild type in response to vegetation shade after the seedling stage. This mutant produced more leaves before bolting and more basal branches under normal light conditions when compared to the wild type. These results indicate that specific photomorphogenic loci have different and sometimes antagonistic pleiotropic effects on the plastic response to vegetation shade throughout the life cycle of the plant. The fitness of the constitutively shade-avoiding phytochrome-deficient mutants was lower than that of the plastic wild type under normal light, but was not different in the vegetation shade treatments, where all genotypes converged toward similar shade avoidance phenotypes. This outcome supports one key prediction of the adaptive plasticity hypothesis: that inappropriate expression of shade avoidance traits is maladaptive.     

A statistical framework for quantitative trait mapping

We describe a general statistical framework for the genetic analysis of quantitative trait data in inbred line crosses. Our main result is based on the observation that, by conditioning on the unobserved QTL genotypes, the problem can be split into two statistically independent and manageable parts. The first part involves only the relationship between the QTL and the phenotype. The second part involves only the location of the QTL in the genome. We developed a simple Monte Carlo algorithm to implement Bayesian QTL analysis. This algorithm simulates multiple versions of complete genotype information on a genomewide grid of locations using information in the marker genotype data. Weights are assigned to the simulated genotypes to capture information in the phenotype data. The weighted complete genotypes are used to approximate quantities needed for statistical inference of QTL locations and effect sizes. One advantage of this approach is that only the weights are recomputed as the analyst considers different candidate models. This device allows the analyst to focus on modeling and model comparisons. The proposed framework can accommodate multiple interacting QTL, nonnormal and multivariate phenotypes, covariates, missing genotype data, and genotyping errors in any type of inbred line cross. A software tool implementing this procedure is available. We demonstrate our approach to QTL analysis using data from a mouse backcross population that is segregating multiple interacting QTL associated with salt-induced hypertension.     

A role for phenotypic plasticity in the evolution of aposematism

The evolution of warning coloration (aposematism) has been difficult to explain because rare conspicuous mutants should suffer a higher cost of discovery by predators relative to the cryptic majority, while at frequencies too low to facilitate predator aversion learning. Traditional models for the evolution of aposematism have assumed conspicuous prey phenotypes to be genetically determined and constitutive. By contrast, we have recently come to understand that warning coloration can be environmentally determined and mediated by local prey density, thereby reducing the initial costs of conspicuousness. The expression of density-dependent colour polyphenism is widespread among the insects and may provide an alternative pathway for the evolution of constitutive aposematic phenotypes in unpalatable prey by providing a protected intermediate stage. If density-dependent aposematism can function as an adaptive intermediate stage for the evolution of constitutive aposematic phenotypes, differential reaction norm evolution is predicted among related palatable and unpalatable prey populations. Here, I present empirical evidence that indicates that (i) the expression of density-dependent colour polyphenism has differentially evolved between palatable and unpalatable populations of the grasshopper Schistocerca emarginata (= lineata) (Orthoptera: Acrididae), and (ii) variation in plasticity between these populations is commensurate with the expected costs of conspicuousness.     

Fluctuations in population composition dampen the impact of phenotypic plasticity on trait dynamics in superb fairy-wrens

1. In structured populations, phenotypic change can result from changes throughout an individual's lifetime (phenotypic plasticity, age-related changes), selection and changes in population composition (environment- or density-driven fluctuations in age-structure). 2. The contribution of population dynamics to phenotypic change has often been ignored. However, for understanding trait dynamics, it is important to identify both the individual- and population-level mechanisms responsible for trait change, because they potentially reinforce or counteract each other. 3. We use 22 years of field data to investigate the dynamics of a sexually selected phenological trait, the timing of nuptial moult in superb fairy-wrens Malurus cyaneus. 4. We show that trait expression is both climate- and age-dependent, but that phenotypic plasticity in response to climate variability also varies with age. Old males can acquire nuptial plumage very early after high rainfall, but 1- to 2-year-olds cannot. However, males of all ages that defer moult to later in the year acquire nuptial plumage earlier when conditions are warmer. 5. The underlying mechanism appears to be that old males may risk moulting in the most challenging period of the year: in autumn, when drought restricts food abundance and during the cold winter. By contrast, young males always moult during the spring transition to benign - warmer and generally wetter - conditions. Temperature changes dominate this transition that heralds the breeding season, thereby causing both young and late-moulting older birds to be temperature sensitive. 6. Climate and age also affect trait dynamics via a population dynamical pathway. The same high rainfall that triggers early moulting in old males concurrently increases offspring recruitment and thereby reduces the average age of males in the population. Consequently, effects of rainfall on trait dynamics through phenotypic plasticity of old males are dampened by synchronous rejuvenation of the age-structure. 7. A long-term trend towards drier environments prompted phenotypic change because of plasticity, but this was masked by climate-driven demographic change (causing apparent stasis). This suggests a novel explanation for why trait change may fail to reflect the observed pattern of directional selection or phenotypic plasticity.     

A bivariate quantitative genetic model for a threshold trait and a survival trait

Many of the functional traits considered in animal breeding can be analyzed as threshold traits or survival traits with examples including disease traits, conformation scores, calving difficulty and longevity. In this paper we derive and implement a bivariate quantitative genetic model for a threshold character and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted in which model parameters were augmented with unobserved liabilities associated with the threshold trait. The fully conditional posterior distributions associated with parameters of the threshold trait reduced to well known distributions. For the survival trait the two baseline Weibull parameters were updated jointly by a Metropolis-Hastings step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. The Gibbs sampler was tested in a simulation study and illustrated in a joint analysis of calving difficulty and longevity of dairy cattle. The simulation study showed that the estimated marginal posterior distributions covered well and placed high density to the true values used in the simulation of data. The data analysis of calving difficulty and longevity showed that genetic variation exists for both traits. The additive genetic correlation was moderately favorable with marginal posterior mean equal to 0.37 and 95% central posterior credibility interval ranging between 0.11 and 0.61. Therefore, this study suggests that selection for improving one of the two traits will be beneficial for the other trait as well.     

Zero-inflated generalized Poisson regression mixture model for mapping quantitative trait loci underlying count trait with many zeros

Phenotypes measured in counts are commonly observed in nature. Statistical methods for mapping quantitative trait loci (QTL) underlying count traits are documented in the literature. The majority of them assume that the count phenotype follows a Poisson distribution with appropriate techniques being applied to handle data dispersion. When a count trait has a genetic basis, “naturally occurring” zero status also reflects the underlying gene effects. Simply ignoring or miss-handling the zero data may lead to wrong QTL inference. In this article, we propose an interval mapping approach for mapping QTL underlying count phenotypes containing many zeros. The effects of QTLs on the zero-inflated count trait are modelled through the zero-inflated generalized Poisson regression mixture model, which can handle the zero inflation and Poisson dispersion in the same distribution. We implement the approach using the EM algorithm with the Newton-Raphson algorithm embedded in the M-step, and provide a genome-wide scan for testing and estimating the QTL effects. The performance of the proposed method is evaluated through extensive simulation studies. Extensions to composite and multiple interval mapping are discussed. The utility of the developed approach is illustrated through a mouse F₂ intercross data set. Significant QTLs are detected to control mouse cholesterol gallstone formation.     

Quantitative trait loci mapping of phenotypic plasticity and genotype-environment interactions in plant and insect performance

Community genetic studies generally ignore the plasticity of the functional traits through which the effect is passed from individuals to the associated community. However, the ability of organisms to be phenotypically plastic allows them to rapidly adapt to changing environments and plasticity is commonly observed across all taxa. Owing to the fitness benefits of phenotypic plasticity, evolutionary biologists are interested in its genetic basis, which could explain how phenotypic plasticity is involved in the evolution of species interactions. Two current ideas exist: (i) phenotypic plasticity is caused by environmentally sensitive loci associated with a phenotype; (ii) phenotypic plasticity is caused by regulatory genes that simply influence the plasticity of a phenotype. Here, we designed a quantitative trait loci (QTL) mapping experiment to locate QTL on the barley genome associated with barley performance when the environment varies in the presence of aphids, and the composition of the rhizosphere. We simultaneously mapped aphid performance across variable rhizosphere environments. We mapped main effects, QTL × environment interaction (QTL×E), and phenotypic plasticity (measured as the difference in mean trait values) for barley and aphid performance onto the barley genome using an interval mapping procedure. We found that QTL associated with phenotypic plasticity were co-located with main effect QTL and QTL×E. We also located phenotypic plasticity QTL that were located separately from main effect QTL. These results support both of the current ideas of how phenotypic plasticity is genetically based and provide an initial insight into the functional genetic basis of how phenotypically plastic traits may still be important sources of community genetic effects.     

A bivariate quantitative genetic model for a linear Gaussian trait and a survival trait

With the increasing use of survival models in animal breeding to address the genetic aspects of mainly longevity of livestock but also disease traits, the need for methods to infer genetic correlations and to do multivariate evaluations of survival traits and other types of traits has become increasingly important. In this study we derived and implemented a bivariate quantitative genetic model for a linear Gaussian and a survival trait that are genetically and environmentally correlated. For the survival trait, we considered the Weibull log-normal animal frailty model. A Bayesian approach using Gibbs sampling was adopted. Model parameters were inferred from their marginal posterior distributions. The required fully conditional posterior distributions were derived and issues on implementation are discussed. The two Weibull baseline parameters were updated jointly using a Metropolis-Hasting step. The remaining model parameters with non-normalized fully conditional distributions were updated univariately using adaptive rejection sampling. Simulation results showed that the estimated marginal posterior distributions covered well and placed high density to the true parameter values used in the simulation of data. In conclusion, the proposed method allows inferring additive genetic and environmental correlations, and doing multivariate genetic evaluation of a linear Gaussian trait and a survival trait.     

A history of phenotypic plasticity accelerates adaptation to a new environment

Can a history of phenotypic plasticity increase the rate of adaptation to a new environment? Theory suggests it can be through two different mechanisms. Phenotypically plastic organisms can adapt rapidly to new environments through genetic assimilation, or the fluctuating environments that result in phenotypic plasticity can produce evolvable genetic architectures. In this article, I studied a model of a gene regulatory network that determined a phenotypic character in one population selected for phenotypic plasticity and a second population in a constant environment. A history of phenotypic plasticity increased the rate of adaptation in a new environment, but the amount of this increase was dependent on the strength of selection in the original environment. Phenotypic variance in the original environment predicted the adaptive capacity of the trait within, but not between, plastic and nonplastic populations. These results have implications for invasive species and ecological studies of rapid adaptation.     

Development of a statistical model of knee kinetics for applications in pre-clinical testing

Pre-clinical computational testing of total knee replacements (TKRs) often only considers a single patient model with simplified applied loads. In studies of multiple patients, most only take into account geometric differences, especially in studies on the knee. Limited availability of kinetic data means that it is difficult to account for inter-patient variability. Principal component analysis (PCA) based statistical models have been used to capture the variation of a set of data and generate new instances of the data. This study presents a method to create a statistical model of kinetic waveform data. A PCA based statistical model was created of the tibiofemoral joint loads for level gait of preoperative TKR patients using data predicted from a musculoskeletal model. A reconstruction test showed that, using principal components (PCs) representing 95% variance, the median root-mean-squared (RMS) error was <0.1 body weight (BW) for the forces and <0.001 BWm for the moments. Leave-one-out tests were also performed and although the median RMS error increased for each load in comparison to the reconstruction error (maximum was 0.2 BW for the axial force and 0.012 BWm for the varus-valgus moment) these were considered within an acceptable limit. The purpose of creating a statistical model is to be able to sample a large set of data representing a population from a small set of clinical data. Such models can potentially be used in population based studies of TKRs incorporating inter-patient variability.     

Evolution of environmental cues for phenotypic plasticity

Phenotypically plastic characters may respond to multiple variables in their environment, but the evolutionary consequences of this phenomenon have rarely been addressed theoretically. We model the evolution of linear reaction norms in response to several correlated environmental variables, in a population undergoing stationary environmental fluctuations. At evolutionary equilibrium, the linear combination of environmental variables that acts as a developmental cue for the plastic trait is the multivariate best linear predictor of changes in the optimum. However, the reaction norm with respect to any single environmental variable may exhibit nonintuitive patterns. Apparently maladaptive, or hyperadaptive plasticity can evolve with respect to single environmental variables, and costs of plasticity may increase, rather than reduce, plasticity in response to some variables. We also find conditions for the evolution of an indirect environmental indicator that affects expression of a plastic phenotype, despite not influencing natural selection on it.     

A modular concept of phenotypic plasticity in plants

Based on empirical evidence from the literature we propose that, in nature, phenotypic plasticity in plants is usually expressed at a subindividual level. While reaction norms (i.e. the type and the degree of plant responses to environmental variation) are a property of genotypes, they are expressed at the level of modular subunits in most plants. We thus contend that phenotypic plasticity is not a whole-plant response, but a property of individual meristems, leaves, branches and roots, triggered by local environmental conditions. Communication and behavioural integration of interconnected modules can change the local responses in different ways: it may enhance or diminish local plastic effects, thereby increasing or decreasing the differences between integrated modules exposed to different conditions. Modular integration can also induce qualitatively different responses, which are not expressed if all modules experience the same conditions. We propose that the response of a plant to its environment is the sum of all modular responses to their local conditions plus all interaction effects that are due to integration. The local response rules to environmental variation, and the modular interaction rules may be seen as evolving traits targeted by natural selection. Following this notion, whole-plant reaction norms are an integrative by-product of modular plasticity, which has far-reaching methodological, ecological and evolutionary implications.     

On the generalized poisson regression mixture model for mapping quantitative trait loci with count data

Statistical methods for mapping quantitative trait loci (QTL) have been extensively studied. While most existing methods assume normal distribution of the phenotype, the normality assumption could be easily violated when phenotypes are measured in counts. One natural choice to deal with count traits is to apply the classical Poisson regression model. However, conditional on covariates, the Poisson assumption of mean-variance equality may not be valid when data are potentially under- or overdispersed. In this article, we propose an interval-mapping approach for phenotypes measured in counts. We model the effects of QTL through a generalized Poisson regression model and develop efficient likelihood-based inference procedures. This approach, implemented with the EM algorithm, allows for a genomewide scan for the existence of QTL throughout the entire genome. The performance of the proposed method is evaluated through extensive simulation studies along with comparisons with existing approaches such as the Poisson regression and the generalized estimating equation approach. An application to a rice tiller number data set is given. Our approach provides a standard procedure for mapping QTL involved in the genetic control of complex traits measured in counts.     

The relationship between the pleiotropic phenotypic effects of a mutation fixed by selection

A pleiotropic model of mutation is presented that allows for correlations between the effects of a new mutation and for the distribution of mutational effects to vary from being leptokurtic to normally distributed. Using this model I quantify how selection transforms the correlation between the effects of a new (random) mutation into the correlation between the effects of a mutation that is fixed by selection and contributes to an adaptation. Results suggest that under most conditions the correlation between the effects of a fixed mutation is less than the correlation between the effects of a new mutation. I also generalize previous results that quantified the expected size of a fixed mutation's effect on a character given an observed effect of that mutation on another character. In agreement with previous results, work here suggests that as the observed effect becomes large and beneficial the expected effect on another character approaches the expected effect of a new (random) mutation given the observed effect. Lastly, these theoretical results are related to recent empirical work that found beneficial mutations had a positive correlation in their pleiotropic effects.     

A unified model for functional and statistical epistasis and its application in quantitative trait Loci analysis

Interaction between genes, or epistasis, is found to be common and it is a key concept for understanding adaptation and evolution of natural populations, response to selection in breeding programs, and determination of complex disease. Currently, two independent classes of models are used to study epistasis. Statistical models focus on maintaining desired statistical properties for detection and estimation of genetic effects and for the decomposition of genetic variance using average effects of allele substitutions in populations as parameters. Functional models focus on the evolutionary consequences of the attributes of the genotype-phenotype map using natural effects of allele substitutions as parameters. Here we provide a new, general and unified model framework: the natural and orthogonal interactions (NOIA) model. NOIA implements tools for transforming genetic effects measured in one population to the ones of other populations (e.g., between two experimental designs for QTL) and parameters of statistical and functional epistasis into each other (thus enabling us to obtain functional estimates of QTL), as demonstrated numerically. We develop graphical interpretations of functional and statistical models as regressions of the genotypic values on the gene content, which illustrates the difference between the models--the constraint on the slope of the functional regression--and when the models are equivalent. Furthermore, we use our theoretical foundations to conceptually clarify functional and statistical epistasis, discuss the advantages of NOIA over previous theory, and stress the importance of linking functional and statistical models.