Estimating Breeding Values With Molecular Relatedness and Reconstructed Pedigrees in Natural Mating Populations of Common Sole,Solea Solea

Captive populations where natural mating in groups is used to obtain offspring typically yield unbalanced population structures with highly skewed parental contributions and unknown pedigrees. Consequently, for genetic parameter estimation, relationships need to be reconstructed or estimated using DNA marker data. With missing parents and natural mating groups, commonly used pedigree reconstruction methods are not accurate and lead to loss of data. Relatedness estimators, however, infer relationships between all animals sampled. In this study, we compared a pedigree relatedness method and a relatedness estimator (“molecular relatedness”) method using accuracy of estimated breeding values. A commercial data set of common sole, Solea solea, with 51 parents and 1953 offspring (“full data set”) was used. Due to missing parents, for 1338 offspring, a pedigree could be reconstructed with 10 microsatellite markers (“reduced data set”). Cross-validation of both methods using the reduced data set showed an accuracy of estimated breeding values of 0.54 with pedigree reconstruction and 0.55 with molecular relatedness. Accuracy of estimated breeding values increased to 0.60 when applying molecular relatedness to the full data set. Our results indicate that pedigree reconstruction and molecular relatedness predict breeding values equally well in a population with skewed contributions to families. This is probably due to the presence of few large full-sib families. However, unlike methods with pedigree reconstruction, molecular relatedness methods ensure availability of all genotyped selection candidates, which results in higher accuracy of breeding value estimation.To estimate genetic parameters, additive genetic relationships between individuals are inferred from known pedigrees (Falconer and Mackay 1996; Lynch and Walsh 1997). However, in natural populations (Ritland 2000; Thomas et al. 2002) and in captive species where natural mating in groups is used to obtain offspring (Brown et al. 2005; Fessehaye et al. 2006; Blonk et al. 2009) pedigrees are reconstructed. In these populations there is no control on mating structure, and typically unbalanced population structures with highly skewed parental contributions are obtained (Bekkevold et al. 2002; Brown et al. 2005; Fessehaye et al. 2006; Blonk et al. 2009). To reconstruct pedigrees, parental allocation methods are often used (Marshall et al. 1998; Avise et al. 2002; Duchesne et al. 2002). These methods require that all parents be known. For situations where parental information is not available, numerous DNA-marker-based methods for estimating molecular relatedness have been developed (Lynch 1988; Queller and Goodnight 1989; Ritland 2000; Toro et al. 2002). These relatedness estimators determine relationship values between individuals on a continuous scale. Evaluation of relatedness estimators within real and simulated data in both plants and animals (e.g., see Van de Casteele et al. 2001 ; Milligan 2003; Oliehoek et al. 2006; Rodríguez-Ramilo et al. 2007; Bink et al. 2008) has generally focused on bias and sampling error of estimated genetic variances or relatedness values. Relatively little attention has been paid to their efficiency for estimation of breeding values.Two types of relatedness estimators are currently available: method-of-moments estimators and maximum-likelihood estimators. Method-of-moments estimators (e.g., Queller and Goodnight 1989; Li et al. 1993; Ritland 1996; Lynch and Ritland 1999; Toro et al. 2002) determine relationships while calculating sharing of alleles between pairs in different ways. A variant of method-of-moments estimators is the transformation of continuous relatedness values to categorical genealogical relationships using “explicit pedigree reconstruction” (Fernández and Toro 2006) or thresholds (Rodríguez-Ramilo et al. 2007). However, correlations of transformed coancestries with known genealogical coancestries are low (Rodríguez-Ramilo et al. 2007). Several studies have compared different method-of-moments estimators but none revealed one single best estimator (Van de Casteele et al. 2001; Oliehoek et al. 2006; Rodríguez-Ramilo et al. 2007; Bink et al. 2008).Maximum-likelihood (ML) approaches classify animals into a limited number of relationship classes (Mousseau et al. 1998; Thomas et al. 2002; Wang 2004; Herbinger et al. 2006; Anderson and Weir 2007). For each pair a likelihood to fall into a possible relatedness class (e.g., full sib vs. unrelated) is calculated given its genotype and phenotype. ML techniques combined with a Markov chain Monte Carlo approach reconstruct groups with specific relationships jointly and are therefore more efficient than other ML approaches. To minimize standard errors, all discussed ML methods require balanced population structures, large sibling groups, and a large variance of relatedness (Thomas et al. 2002; Wang 2004; Anderson and Weir 2007). Therefore, these methods may not be suitable for natural mating systems.Unlike parental allocation methods, a benefit from relatedness estimators is that essentially all selection candidates are maintained for breeding value estimation, even with missing parents. The question is, however, whether such relatedness estimators also give accurate breeding values to perform selection.In this study, we test suitability of a relatedness estimator to obtain breeding values in a population of common sole, Solea solea (n = 1953) obtained by natural mating. First, we estimate breeding values using pedigree relatedness of animals for which a pedigree could be reconstructed (using parental allocation). This data set (n = 1338) is further referred to as “reduced data set.” We compare results with estimated breeding values using a simple but robust method-of-moments relatedness estimator: “molecular relatedness” (Toro et al. 2002, 2003). Next, we estimate breeding values using molecular relatedness in the full data set (n = 1953). Results show that accuracies of estimated breeding values obtained with molecular relatedness and pedigree relatedness are comparable. Accuracy increases when breeding values are estimated with molecular relatedness in the full data set. This implies that a molecular relatedness estimator can be used to estimate breeding values in captive natural mating populations.     

On the inference of complex phylogenetic networks by Markov Chain Monte-Carlo

For various species, high quality sequences and complete genomes are nowadays available for many individuals. This makes data analysis challenging, as methods need not only to be accurate, but also time efficient given the tremendous amount of data to process. In this article, we introduce an efficient method to infer the evolutionary history of individuals under the multispecies coalescent model in networks (MSNC). Phylogenetic networks are an extension of phylogenetic trees that can contain reticulate nodes, which allow to model complex biological events such as horizontal gene transfer, hybridization and introgression. We present a novel way to compute the likelihood of biallelic markers sampled along genomes whose evolution involved such events. This likelihood computation is at the heart of a Bayesian network inference method called SnappNet, as it extends the Snapp method inferring evolutionary trees under the multispecies coalescent model, to networks. SnappNet is available as a package of the well-known beast 2 software.Recently, the MCMC_BiMarkers method, implemented in PhyloNet, also extended Snapp to networks. Both methods take biallelic markers as input, rely on the same model of evolution and sample networks in a Bayesian framework, though using different methods for computing priors. However, SnappNet relies on algorithms that are exponentially more time-efficient on non-trivial networks. Using simulations, we compare performances of SnappNet and MCMC_BiMarkers. We show that both methods enjoy similar abilities to recover simple networks, but SnappNet is more accurate than MCMC_BiMarkers on more complex network scenarios. Also, on complex networks, SnappNet is found to be extremely faster than MCMC_BiMarkers in terms of time required for the likelihood computation. We finally illustrate SnappNet performances on a rice data set. SnappNet infers a scenario that is consistent with previous results and provides additional understanding of rice evolution.     

Maximum-likelihood estimation of relatedness

Relatedness between individuals is central to many studies in genetics and population biology. A variety of estimators have been developed to enable molecular marker data to quantify relatedness. Despite this, no effort has been given to characterize the traditional maximum-likelihood estimator in relation to the remainder. This article quantifies its statistical performance under a range of biologically relevant sampling conditions. Under the same range of conditions, the statistical performance of five other commonly used estimators of relatedness is quantified. Comparison among these estimators indicates that the traditional maximum-likelihood estimator exhibits a lower standard error under essentially all conditions. Only for very large amounts of genetic information do most of the other estimators approach the likelihood estimator. However, the likelihood estimator is more biased than any of the others, especially when the amount of genetic information is low or the actual relationship being estimated is near the boundary of the parameter space. Even under these conditions, the amount of bias can be greatly reduced, potentially to biologically irrelevant levels, with suitable genetic sampling. Additionally, the likelihood estimator generally exhibits the lowest root mean-square error, an indication that the bias in fact is quite small. Alternative estimators restricted to yield only biologically interpretable estimates exhibit lower standard errors and greater bias than do unrestricted ones, but generally do not improve over the maximum-likelihood estimator and in some cases exhibit even greater bias. Although some nonlikelihood estimators exhibit better performance with respect to specific metrics under some conditions, none approach the high level of performance exhibited by the likelihood estimator across all conditions and all metrics of performance.     

Estimating Relatedness in the Presence of Null Alleles

Studies of genetics and ecology often require estimates of relatedness coefficients based on genetic marker data. However, with the presence of null alleles, an observed genotype can represent one of several possible true genotypes. This results in biased estimates of relatedness. As the numbers of marker loci are often limited, loci with null alleles cannot be abandoned without substantial loss of statistical power. Here, we show how loci with null alleles can be incorporated into six estimators of relatedness (two novel). We evaluate the performance of various estimators before and after correction for null alleles. If the frequency of a null allele is <0.1, some estimators can be used directly without adjustment; if it is >0.5, the potency of estimation is too low and such a locus should be excluded. We make available a software package entitled PolyRelatedness v1.6, which enables researchers to optimize these estimators to best fit a particular data set.     

Identity-by-Descent Matrix Decomposition Using Latent Ancestral Allele Models

Genetic linkage and association studies are empowered by proper modeling of relatedness among individuals. Such relatedness can be inferred from marker and/or pedigree information. In this study, the genetic relatedness among n inbred individuals at a particular locus is expressed as an n × n square matrix Q. The elements of Q are identity-by-descent probabilities, that is, probabilities that two individuals share an allele descended from a common ancestor. In this representation the definition of the ancestral alleles and their number remains implicit. For human inspection and further analysis, an explicit representation in terms of the ancestral allele origin and the number of alleles is desirable. To this purpose, we decompose the matrix Q by a latent class model with K classes (latent ancestral alleles). Let P be an n × K matrix with assignment probabilities of n individuals to K classes constrained such that every element is nonnegative and each row sums to 1. The problem then amounts to approximating Q by PP^T, while disregarding the diagonal elements. This is not an eigenvalue problem because of the constraints on P. An efficient algorithm for calculating P is provided. We indicate the potential utility of the latent ancestral allele model. For representative locus-specific Q matrices constructed for a set of maize inbreds, the proposed model recovered the known ancestry.HIGH-THROUGHPUT techniques allow extensive genotyping of individuals for thousands of SNP markers (Gibbs et al. 2003) and thereby provide accurate information about the genetic diversity within a population at many chromosomal loci. If two individuals within this population carry the same DNA sequence at a locus, and this sequence can be traced to the same common ancestor, the individuals are said to be identical by descent (IBD) for this segment (Chapman and Thompson 2003). Quite often, however, the ancestral source of a chromosomal segment is ambiguous and thus IBD relationships between haplotypes are given as probabilities. Various methods have been described to estimate the IBD probability of pairs of chromosomal segments (Meuwissen and Goddard 2001; Leutenegger et al. 2003). When pedigree relationships are known, these can be included to estimate IBD probabilities (Wang et al. 1995; Heath 1997; George et al. 2000; Meuwissen and Goddard 2000; Besnier and Carlborg 2007).In quantitative genetic analysis we seek to find and characterize associations between the large number of SNPs that are now available for many organisms and phenotypic variation for traits of interest (e.g., grain yield and time to flowering). Many current methods developed for this purpose make use of IBD information. For example, a locus-specific matrix of IBD probabilities can be incorporated into restricted maximum-likelihood (REML) procedures for fine mapping quantitative trait loci (Bink and Meuwissen 2004) as well as for marker-based genetic evaluation (Fernando and Grossman 1989) using mixed models. The IBD matrix takes the role of a covariance matrix in the REML procedure.Other approaches, however, require that chromosome segments (also referred to here as haplotypes or alleles) are assigned to independent ancestors. These approaches include regression approaches with genetic predictors (Malosetti et al. 2006) and Bayesian oligo-allelic approaches that sample the ancestral origin of each chromosomal segment (Heath 1997; Uimari and Sillanpaa 2001; Bink et al. 2008a). In the IBD matrix representation the ancestral alleles and their number remain implicit. For these approaches, the locus-specific matrix of IBD probabilities must therefore be decomposed into a matrix that links the chromosomal segments to independent ancestral alleles. This decomposition is addressed in this article.The individuals that we consider in this article are inbred. For n inbred individuals the IBD matrix at a given chromosomal position is thus n × n, because there is no need to distinguish between identical chromosomes. In diploid, outbred populations, each individual would be represented by two haplotypes (alleles) and the matrix would be 2n × 2n (Fernando and Grossman 1989). This is feasible if any phase ambiguity can be resolved. From now on, the term “individual” thus means chromosomal segment or haplotype. Analogously, ancestor will be shorthand for ancestral allele (ancestral haplotype).We propose two models of IBD matrix decomposition, a simple threshold model (TIBD) and a more sophisticated latent ancestral allele model (LAAM), that provide (1) an estimate of the number of independent ancestral alleles, (2) a concise, easy-to-interpret, summary of the relatedness, (3) an explicit (probabilistic) representation of the descent of alleles, and (4) the ability to sample alleles for each individual from a set of ancestral alleles in such a way that the probability that a pair of individuals shares the same allele corresponds to their IBD probability.The last two features of the model are essential for its use in Bayesian oligo-allelic approaches to quantitative trait locus (QTL) analysis (Uimari and Sillanpaa 2001; Bink et al. 2008a).     

The Role of a d-Mannosyl-Lipid as an Intermediate in the Synthesis of Polysaccharide in Phaseolus aureus Seedlings

Particulate preparations from Phaseolus aureus produce a d-mannosyl-lipid when treated with GDP-d-mannose. This lipid complex appears to be an active d-mannose donor, and some investigators have proposed that its role might be an obligatory intermediate in mannan synthesis of higher plants. When the partially purified d-mannosyl-lipids, isotopically labeled in the d-mannose moiety, were treated with particulate enzymes under a variety of conditions, a negligible amount of material was produced that behaved as a polysaccharide. Endogenous, particle-bound d-mannosyl-¹⁴C-lipid prepared from P. aureus particles readily transferred d-mannose to GDP to yield GDP-d-mannose and was hydrolyzed to free d-mannose when treated briefly with 0.01 n HCl at 100 C. The d-mannosyl-lipid, therefore, exhibits active d-mannose transfer potential in its endogenous state. When endogenous glycosyl-lipid was incubated in the absence of GDP-d-mannose-¹⁴C, little or no polysaccharide was produced. It was, instead, slowly degraded to d-mannose. Addition of several different unlabeled sugar nucleotides had no effect on the results. Our studies to date, therefore, offer no evidence that the mannosyl-lipid is an obligatory precursor of polysaccharide.     

Age Structure,Changing Demography and Effective Population Size in Atlantic Salmon (Salmo salar)

Effective population size (N_e) is a central evolutionary concept, but its genetic estimation can be significantly complicated by age structure. Here we investigate N_e in Atlantic salmon (Salmo salar) populations that have undergone changes in demography and population dynamics, applying four different genetic estimators. For this purpose we use genetic data (14 microsatellite markers) from archived scale samples collected between 1951 and 2004. Through life table simulations we assess the genetic consequences of life history variation on N_e. Although variation in reproductive contribution by mature parr affects age structure, we find that its effect on N_e estimation may be relatively minor. A comparison of estimator models suggests that even low iteroparity may upwardly bias N_e estimates when ignored (semelparity assumed) and should thus empirically be accounted for. Our results indicate that N_e may have changed over time in relatively small populations, but otherwise remained stable. Our ability to detect changes in N_e in larger populations was, however, likely hindered by sampling limitations. An evaluation of N_e estimates in a demographic context suggests that life history diversity, density-dependent factors, and metapopulation dynamics may all affect the genetic stability of these populations.THE effective size of a population (N_e) is an evolutionary parameter that can be informative on the strength of stochastic evolutionary processes, the relevance of which relative to deterministic forces has been debated for decades (e.g., Lande 1988). Stochastic forces include environmental, demographic, and genetic components, the latter two of which are thought to be more prominent at reduced population size, with potentially detrimental consequences for average individual fitness and population persistence (Newman and Pilson 1997; Saccheri et al. 1998; Frankham 2005). The quantification of N_e in conservation programs is thus frequently advocated (e.g., Luikart and Cornuet 1998; Schwartz et al. 2007), although gene flow deserves equal consideration given its countering effects on genetic stochasticity (Frankham et al. 2003; Palstra and Ruzzante 2008).Effective population size is determined mainly by the lifetime reproductive success of individuals in a population (Wright 1938; Felsenstein 1971). Variance in reproductive success, sex ratio, and population size fluctuations can reduce N_e below census population size (Frankham 1995). Given the difficulty in directly estimating N_e through quantification of these demographic factors (reviewed by Caballero 1994), efforts have been directed at inferring N_e indirectly through measurement of its genetic consequences (see Leberg 2005, Wang 2005, and Palstra and Ruzzante 2008 for reviews). Studies employing this approach have quantified historical levels of genetic diversity and genetic threats to population persistence (e.g., Nielsen et al. 1999b; Miller and Waits 2003; Johnson et al. 2004). N_e has been extensively studied in (commercially important) fish species, due to the common availability of collections of archived samples that facilitate genetic estimation using the temporal method (e.g., Hauser et al. 2002; Shrimpton and Heath 2003; Gomez-Uchida and Banks 2006; Saillant and Gold 2006).Most models relating N_e to a population''s genetic behavior make simplifying assumptions regarding population dynamics. Chiefly among these is the assumption of discrete generations, frequently violated in practice given that most natural populations are age structured with overlapping generations. Here, theoretical predictions still apply, provided that population size and age structure are constant (Felsenstein 1971; Hill 1972). Ignored age structure can introduce bias into temporal genetic methods for the estimation of N_e, especially for samples separated by time spans that are short relative to generation interval (Jorde and Ryman 1995; Waples and Yokota 2007; Palstra and Ruzzante 2008). Moreover, estimation methods that do account for age structure (e.g., Jorde and Ryman 1995) still assume this structure to be constant. Population dynamics will, however, likely be altered as population size changes, thus making precise quantifications of the genetic consequences of acute population declines difficult (Nunney 1993; Engen et al. 2005; Waples and Yokota 2007). This problem may be particularly relevant when declines are driven by anthropogenic impacts, such as selective harvesting regimes, that can affect age structure and N_e simultaneously (Ryman et al. 1981; Allendorf et al. 2008). Demographic changes thus have broad conservation implications, as they can affect a population''s sensitivity to environmental stochasticity and years of poor recruitment (Warner and Chesson 1985; Ellner and Hairston 1994; Gaggiotti and Vetter 1999). Consequently, although there is an urgent need to elucidate the genetic consequences of population declines, relatively little is understood about the behavior of N_e when population dynamics change (but see Engen et al. 2005, 2007).Here we focus on age structure and N_e in Atlantic salmon (Salmo salar) river populations in Newfoundland and Labrador. The freshwater habitat in this part of the species'' distribution range is relatively pristine (Parrish et al. 1998), yet Atlantic salmon in this area have experienced demographic declines, associated with a commercial marine fishery, characterized by high exploitation rates (40–80% of anadromous runs; Dempson et al. 2001). A fishery moratorium was declared in 1992, with rivers displaying differential recovery patterns since then (Dempson et al. 2004b), suggesting a geographically variable impact of deterministic and stochastic factors, possibly including genetics. An evaluation of those genetic consequences thus requires accounting for potential changes in population dynamics as well as in life history. Life history in Atlantic salmon can be highly versatile (Fleming 1996; Hutchings and Jones 1998; Fleming and Reynolds 2004), as exemplified by the high variation in age-at-maturity displayed among and within populations (Hutchings and Jones 1998), partly reflecting high phenotypic plasticity (Hutchings 2004). This diversity is particularly evident in the reproductive biology of males, which can mature as parr during juvenile freshwater stages (Jones and King 1952; Fleming and Reynolds 2004) and/or at various ages as anadromous individuals, when returning to spawn in freshwater from ocean migration. Variability in life history strategies is further augmented by iteroparity, which can be viewed as a bet-hedging strategy to deal with environmental uncertainty (e.g., Orzack and Tuljapurkar 1989; Fleming and Reynolds 2004). Life history diversity and plasticity may allow salmonid fish populations to alter and optimize their life history under changing demography and population dynamics, potentially acting to stabilize N_e. Reduced variance in individual reproductive success at low breeder abundance (genetic compensation) will achieve similar effects and might be a realistic aspect of salmonid breeding systems (Ardren and Kapuscinski 2003; Fraser et al. 2007b). Little is currently known about the relationships between life history plasticity, demographic change and N_e, partly due to scarcity of the multivariate data required for these analyses.Our objective in this article is twofold. First, we use demographic data for rivers in Newfoundland to quantify how life history variation influences age structure in Atlantic salmon and hence N_e and its empirical estimation from genetic data. We find that variation in reproductive contribution by mature parr has a much smaller effect on the estimation of N_e than is often assumed. Second, we use temporal genetic data to estimate N_e and quantify the genetic consequences of demographic changes. We attempt to account for potential sources of bias, associated with (changes in) age structure and life history, by using four different analytical models to estimate N_e: a single-sample estimator using the linkage disequilibrium method (Hill 1981), the temporal model assuming discrete generations (Nei and Tajima 1981; Waples 1989), and two temporal models for species with overlapping generations (Waples 1990a,b; Jorde and Ryman 1995) that differ principally in assumptions regarding iteroparity. A comparison of results from these different estimators suggests that iteroparity may often warrant analytical consideration, even when it is presumably low. Although sometimes limited by statistical power, a quantification and comparison of temporal changes in N_e among river populations suggests a more prominent impact of demographic changes on N_e in relatively small river populations.     

Structural Features of Sugars That Trigger or Support Conidial Germination in the Filamentous Fungus Aspergillus niger

The asexual spores (conidia) of Aspergillus niger germinate to produce hyphae under appropriate conditions. Germination is initiated by conidial swelling and mobilization of internal carbon and energy stores, followed by polarization and emergence of a hyphal germ tube. The effects of different pyranose sugars, all analogues of d-glucose, on the germination of A. niger conidia were explored, and we define germination as the transition from a dormant conidium into a germling. Within germination, we distinguish two distinct stages, the initial swelling of the conidium and subsequent polarized growth. The stage of conidial swelling requires a germination trigger, which we define as a compound that is sensed by the conidium and which leads to catabolism of d-trehalose and isotropic growth. Sugars that triggered germination and outgrowth included d-glucose, d-mannose, and d-xylose. Sugars that triggered germination but did not support subsequent outgrowth included d-tagatose, d-lyxose, and 2-deoxy-d-glucose. Nontriggering sugars included d-galactose, l-glucose, and d-arabinose. Certain nontriggering sugars, including d-galactose, supported outgrowth if added in the presence of a complementary triggering sugar. This division of functions indicates that sugars are involved in two separate events in germination, triggering and subsequent outgrowth, and the structural features of sugars that support each, both, or none of these events are discussed. We also present data on the uptake of sugars during the germination process and discuss possible mechanisms of triggering in the absence of apparent sugar uptake during the initial swelling of conidia.     

Amino Acid Isomerization in the Production of l-Phenylalanine from d-Phenylalanine by Bacteria

To establish an advantageous method for the production of l-amino acids, microbial isomerization of d- and dl-amino acids to l-amino acids was studied. Screening experiments on a number of microorganisms showed that cell suspensions of Pseudomonas fluorescens and P. miyamizu were capable of isomerizing d- and dl-phenylalanines to l-phenylalanine. Various conditions suitable for isomerization by these organisms were investigated. Cells grown in a medium containing d-phenylalanine showed highest isomerization activity, and almost completely converted d- or dl-phenylalanine into l-phenylalanine within 24 to 48 hr of incubation. Enzymatic studies on this isomerizing system suggested that the isomerization of d- or dl-phenylalanine is not catalyzed by a single enzyme, “amino acid isomerase,” but the conversion proceeds by a two step system as follows: d-pheylalanine is oxidized to phenylpyruvic acid by d-amino acid oxidase, and the acid is converted to l-phenylalanine by transamination or reductive amination.     

The Genetic Signature of Conditional Expression

Conditionally expressed genes have the property that every individual in a population carries and transmits the gene, but only a fraction, φ, expresses the gene and exposes it to natural selection. We show that a consequence of this pattern of inheritance and expression is a weakening of the strength of natural selection, allowing deleterious mutations to accumulate within and between species and inhibiting the spread of beneficial mutations. We extend previous theory to show that conditional expression in space and time have approximately equivalent effects on relaxing the strength of selection and that the effect holds in a spatially heterogeneous environment even with low migration rates among patches. We support our analytical approximations with computer simulations and delineate the parameter range under which the approximations fail. We model the effects of conditional expression on sequence polymorphism at mutation–selection–drift equilibrium, allowing for neutral sites, and show that sequence variation within and between species is inflated by conditional expression, with the effect being strongest in populations with large effective size. As φ decreases, more sites are recruited into neutrality, leading to pseudogenization and increased drift load. Mutation accumulation diminishes the degree of adaptation of conditionally expressed genes to rare environments, and the mutational cost of phenotypic plasticity, which we quantify as the plasticity load, is greater for more rarely expressed genes. Our theory connects gene-level relative polymorphism and divergence with the spatial and temporal frequency of environments inducing gene expression. Our theory suggests that null hypotheses for levels of standing genetic variation and sequence divergence must be corrected to account for the frequency of expression of the genes under study.IN genetically and ecologically subdivided populations, some individuals will experience a local environment very different from others, making it difficult to evolve a single adaptation adequate for all local conditions. Phenotypic plasticity allows organisms to respond adaptively to spatially and temporally varying environments by developing alternative phenotypes that enhance fitness under local conditions (Scheiner 1993; Via et al. 1995). Examples of alternative phenotypes, i.e., polyphenisms, include the defensive morphologies in Daphnia and algae induced by the presence of predators (e.g., Lively 1986; DeWitt 1998; Harvell 1998; Hazel et al. 2004); the winged and wingless morphs of bean beetles responding to resource variation (e.g., Abouheif and Wray 2002; Roff and Gelinas 2003; Lommen et al. 2005); and bacterial genes involved in traits such as quorum sensing, antibiotic production, biofilm formation, and virulence (Fuqua et al. 1996). The developmental basis of such alternative phenotypes often lies in the inducible expression of some genes in some individuals by environmental variables. That is, all individuals carry and transmit the conditionally expressed genes but only a fraction of individuals, φ, express them when environmental conditions are appropriate.The genes underlying plastic traits should experience relaxed selection due to conditional expression. Wade and co-workers have shown that genes hidden from natural selection in a fraction of individuals in the population by X-linked (Whitlock and Wade 1995; Linksvayer and Wade 2009) or sex-limited expression (Wade 1998; Demuth and Wade 2007) experience relaxed selective constraint. In Drosophila spp., sequence data for genes with maternally limited expression quantitatively support the theoretical predictions both for within-species polymorphism (Barker et al. 2005; Cruickshank and Wade 2008) and for between-species divergence (Barker Et Al 2005; Demuth and Wade 2007; Cruickshank and Wade 2008). Furthermore, male-specific genes in the facultatively sexual pea aphid have been shown to have elevated levels of sequence variation due to relaxed selection (Brisson and Nuzhdin 2008). Genes with spatially restricted expression in a heterogeneous environment should likewise experience relaxed selection. Adaptation to the most common environment in an ecologically subdivided population (Rosenzweig 1987; Holt and Gaines 1992; Holt 1996) allows deleterious mutations to accumulate in traits expressed in rare environments (Kawecki 1994; Whitlock 1996).Here we extend these results by quantifying the consequences of relaxed selection on conditionally expressed genes. Specifically, we show that, with weak selection, spatial and temporal fluctuations in selection intensity generate approximately equivalent effects on mean trait fitness, even with low rates of migration between habitats, resulting in a great simplification of analytical results. Our analytical approximations are supported with deterministic and stochastic simulations, and we note the conditions under which the approximations fail. We then derive general expressions for (1) the expected level of sequence polymorphism within populations under mutation, migration, drift, and purifying selection with conditional gene expression; (2) the rate of sequence divergence among populations, for dominant and recessive mutations; and (3) the reduction in mean population fitness due to accumulation of deleterious mutations at conditionally expressed loci. We find that the rate of accumulation of deleterious mutations for conditionally expressed genes is accelerated and the probability of fixation of beneficial mutations is reduced, causing a reduction in the fitness of conditional traits and an inflation in sequence variation within and between species. Our results suggest that evolutionary null hypotheses must be adjusted to account for the frequency of expression of genes under study, such that signatures of elevated within- or between-species sequence variation are not necessarily evidence of the action of diversifying natural selection. Furthermore, if conditional expression is due to spatial heterogeneity, we show that the level of genetic variation in a sample will often depend on whether or not genotypes were sampled from the selective habitat, the neutral habitat, or both. In the discussion we address the scope and limitations of our theory, as well as its implications for the maintenance of genetic variation, adaptive divergence between species, constraints on phenotypic plasticity, and evolutionary inference from sequence data.     

Accumulation of d-Glucose from Pentoses by Metabolically Engineered Escherichia coli

Escherichia coli that is unable to metabolize d-glucose (with knockouts in ptsG, manZ, and glk) accumulates a small amount of d-glucose (yield of about 0.01 g/g) during growth on the pentoses d-xylose or l-arabinose as a sole carbon source. Additional knockouts in the zwf and pfkA genes, encoding, respectively, d-glucose-6-phosphate 1-dehydrogenase and 6-phosphofructokinase I (E. coli MEC143), increased accumulation to greater than 1 g/liter d-glucose and 100 mg/liter d-mannose from 5 g/liter d-xylose or l-arabinose. Knockouts of other genes associated with interconversions of d-glucose-phosphates demonstrate that d-glucose is formed primarily by the dephosphorylation of d-glucose-6-phosphate. Under controlled batch conditions with 20 g/liter d-xylose, MEC143 generated 4.4 g/liter d-glucose and 0.6 g/liter d-mannose. The results establish a direct link between pentoses and hexoses and provide a novel strategy to increase carbon backbone length from five to six carbons by directing flux through the pentose phosphate pathway.     

Inositol Metabolism in Plants. V. Conversion of Myo-inositol to Uronic Acid and Pentose Units of Acidic Polysaccharides in Root-tips of Zea mays

The metabolism of myo-inositol-2-¹⁴C, d-glucuronate-1-¹⁴C, d-glucuronate-6-¹⁴C, and l-methionine-methyl-¹⁴C to cell wall polysaccharides was investigated in excised root-tips of 3 day old Zea mays seedlings. From myo-inositol, about one-half of incorporated label was recovered in ethanol insoluble residues. Of this label, about 90% was solubilized by treatment, first with a preparation of pectinase-EDTA, then with dilute hydrochloric acid. The only labeled constituents in these hydrolyzates were d-galacturonic acid, d-glucuronic acid, 4-O-methyl-d-glucuronic acid, d-xylose, and l-arabinose, or larger oligosaccharide fragments containing these units. Medium external to excised root-tips grown under sterile conditions in myo-inositol-2-¹⁴C contained labeled polysaccharide.     

Frequency Spectrum Neutrality Tests: One for All and All for One

Neutrality tests based on the frequency spectrum (e.g., Tajima''s D or Fu and Li''s F) are commonly used by population geneticists as routine tests to assess the goodness-of-fit of the standard neutral model on their data sets. Here, I show that these neutrality tests are specific instances of a general model that encompasses them all. I illustrate how this general framework can be taken advantage of to devise new more powerful tests that better detect deviations from the standard model. Finally, I exemplify the usefulness of the framework on SNP data by showing how it supports the selection hypothesis in the lactase human gene by overcoming the ascertainment bias. The framework presented here paves the way for constructing novel tests optimized for specific violations of the standard model that ultimately will help to unravel scenarios of evolution.THE standard models of population genetics (i.e., the Wright–Fisher model and related ones) constitute null models for which an amazing amount of theory has been developed. Population geneticists have used some aspect of the theory (e.g., summary statistics) to test the goodness-of-fit of the standard model on a given data set. Rejection of the standard model typically suggests that alternative hypotheses, such as selection or demographic history, have to be accounted for. Although they test for more than neutrality, tests that compute the goodness-of-fit of the standard model have been referred to as “neutrality tests.” Since different neutrality tests have varying sensitivity to different violations of the standard model, one typically uses a plethora of tests on the data set of interest. One then hopes that the evolutionary processes that generated the data set will be, at least partially, uncovered by the tests. Although neutrality tests based on population samples exhibit important diversity, they can be assigned to families such as “haplotype tests” (e.g., Fu 1997; Depaulis and Veuille 1998) that use the distribution of haplotypes, “tree shape tests” that try to capture specific tree deformations (e.g., Ramos-Onsins and Rozas 2002), and “frequency spectrum tests” that are based on the frequency spectrum (e.g., Tajima 1989; Fu and Li 1993b; Fay and Wu 2000; Achaz 2008).In this study, I investigate neutrality tests based on the frequency spectrum (hereafter referred to simply as neutrality tests) and show that they are all specific instances of a general framework. Neutrality tests compare two estimators of the population mutation parameter θ that characterizes the mutation–drift equilibrium. It is defined as θ = 2pN_eμ, where p is the ploidy (1 for haploids and 2 for diploids), N_e is the effective population size, and μ is the locus neutral mutation rate. When the standard model is true, the expectations of the several unbiased estimators of θ are equal.Typical estimators of θ, in a sample of n sequences, are , where S is the number of polymorphic sites and (Watterson 1975), and , where π is the average pairwise difference between all sequences in the sample (Tajima 1983). If an outgroup is available, mutations at frequency i/n can be distinguished from mutations at frequency 1 − i/n. Following Fu (1995)''s notations, ξ is a vector that represents the unfolded frequency spectrum composed of ξ_i, the number of polymorphic sites at frequency i/n in the sample (i ∈ [1, n − 1]). When no outgroup is available, the frequency spectrum is folded and is given by a vector η, composed of η_i, the number of polymorphic sites at both frequencies i/n and 1 − i/n. Accordingly, it has been shown that θ can be estimated from , with ξ₁ the number of derived singletons (Fu and Li 1993b), from , with η₁ the total number of singletons (derived and ancestral) (Fu and Li 1993b), and from (Fay and Wu 2000). Recently, it has been suggested that singletons should be ignored when θ is estimated in samples with sequencing errors; this leads to estimators such as , and (Achaz 2008). Other estimators of θ, such as and , were designed to minimize their variance (Fu 1994b), although they can be computed using recursions only for a given value of θ.Neutrality tests compute the goodness-of-fit of a statistic T, which is the difference between two estimators of θ, normalized by its standard deviation:(1)For a given θ, under the standard model, T has a mean of E[T] = 0 and a variance of Var[T] = 1. Lowercase letters (e.g., t) denote the absolute difference (i.e., the numerator only) and uppercase letters (e.g., T) denote the normalized difference (Equation 1) throughout this work. Interestingly, the variance in the denominator is a function of both θ and θ². Because θ is unknown, the denominator cannot be computed as such. In practice, unbiased estimators of θ and θ² must be used instead. Because the variance of vanishes asymptotically in a very large sample (), θ and θ² are, in practice, substituted by estimators based on S (Tajima 1989), which changes the mean and the variance of T to E[T] ≈ 0 and Var[T] ≈ 1.Tajima''s D (Tajima 1989) is defined by ; the statistics proposed by Fu and Li (1993b) are , , , and . Another classical statistic is (Fay and Wu 2000), even though its variance was not given by the authors. Finally, two other related neutrality tests that are, a priori, immune to sequencing errors were proposed: and (Achaz 2008). Other tests based on θ_ξ and θ_η (which are optimized for a given θ-value) as well as the difference between the observed and the expected values of the frequency spectrum were also proposed (Fu 1996).Here, I show that when using a general weighted linear combination of (or when no outgroup is available), any estimators of θ [i.e., ] and consequently any neutrality tests can be derived. Nawa and Tajima (2008) recently advocated the use of the spectrum, which is expected to be uniform under the standard model, as a visual test for neutrality instead of the classical frequency spectrum. This last proposal is in complete agreement with the current work. Importantly, it has been previously reported that some θ-estimators and neutrality tests could be expressed as specific linear combinations of ξ_i or η_i (Tajima 1997; Wakeley 2009). Furthermore, Fu (1997) shows that several θ-estimators can be expressed as specific linear combinations of () or in a related framework that uses instead of . was subsequently designed as (Fay and Wu 2000). However, some estimators (like , , or ) cannot be expressed using the Fu (1997) framework. To the best of my knowledge, no previous study has explicitly derived the framework presented here. No work has yet highlighted the striking simplicity of θ-estimators and related tests, when expressed in this framework. I further show how the use of such a simple framework greatly facilitates the study of previous θ-estimators and their related neutrality tests and how it opens the door for constructing yet undiscovered interesting θ-estimators and neutrality tests with enhanced power.     

Glutamate, glutamine, aspartate, asparagine, glucose and ketone-body metabolism in chick intestinal brush-border cells

1. Suspensions of isolated chick jejunal columnar absorptive (brush-border) cells respired on endogenous substrates at a rate 40% higher than that shown by rat brush-border cells. 2. Added d-glucose (5 or 10mm), l-glutamine (2.5mm) and l-glutamate (2.5mm) were the only individual substrates which stimulated respiration by chick cells; l-aspartate (2.5 or 6.7mm), glutamate (6.7mm), glutamine (6.7mm), l-alanine (1 or 10mm), pyruvate (1 or 2mm), l-lactate (5 or 10mm), butyrate (10mm) and oleate (1mm) did not stimulate chick cell respiration; l-asparagine (6.7mm) inhibited slightly; glucose (5mm) stimulated more than did 10mm-glucose. 3. Acetoacetate (10mm) and d-3-hydroxybutyrate (10mm) were rapidly consumed but, in contrast to rat brush-border cells, did not stimulate respiration. 4. Glucose (10mm) was consumed more slowly than 5mm-glucose; the dominant product of glucose metabolism during vigorous respiration was lactate; the proportion of glucose converted to lactate was greater with 10mm- than with 5mm-glucose. 5. Glutamate and aspartate consumption rates decreased, and alanine and glutamine consumption rates increased when their initial concentrations were raised from 2.5 to 6.7 or 10mm. 6. The metabolic fate of glucose was little affected by concomitant metabolism of any one of aspartate, glutamate or glutamine except for an increased production of alanine; the glucose-stimulated respiration rate was unaffected by concomitant metabolism of these individual amino acids. 7. Chick cells produced very little alanine from aspartate and, in contrast to rat cells, likewise produced very little alanine from glutamate or glutamine; in chick cells alanine appeared to be predominantly a product of transmination of pyruvate derived from glucose metabolism. 8. In chick cells, glutamate and glutamine were formed from aspartate (2.5 or 6.7mm); aspartate and glutamine were formed from glutamate (2.5mm) but only aspartate from 6.7mm-glutamate; glutamate was the dominant product formed from glutamine (6.7mm) but aspartate only was formed from 2.5mm-glutamine. 9. Chick brush-border cells can thus both catabolize and synthesize glutamine; glutamine synthesis is always diminished by concomitant metabolism of glucose, presumably by allosteric inhibition of glutamine synthetase by alanine. 10. Proline was formed from glutamine (2.5mm) but not from glutamine (2.5mm)+glucose (5mm) and not from 2.5mm-glutamate; ornithine was formed from glutamine (2.5mm)+glucose (5.0mm) but not from glutamine alone; serine was formed from glutamine (2.5mm)+glucose (5mm) and from these two substrates plus aspartate (2.5mm). 11. Total intracellular adenine nucleotides (22μmol/g dry wt.) remained unchanged during incubation of chick cells with glucose. 12. Intracellular glutathione (0.7–0.8mm) was depleted by 40% during incubation of respiring chick cells without added substrates for 75min at 37°C; partial restoration of the lost glutathione was achieved by incubating cells with l-glutamate+l-cysteine+glycine.     

Utilization of d-Lactate as an Energy Source Supports the Growth of Gluconobacter oxydans

d-Lactate was identified as one of the few available organic acids that supported the growth of Gluconobacter oxydans 621H in this study. Interestingly, the strain used d-lactate as an energy source but not as a carbon source, unlike other lactate-utilizing bacteria. The enzymatic basis for the growth of G. oxydans 621H on d-lactate was therefore investigated. Although two putative NAD-independent d-lactate dehydrogenases, GOX1253 and GOX2071, were capable of oxidizing d-lactate, GOX1253 was the only enzyme able to support the d-lactate-driven growth of the strain. GOX1253 was characterized as a membrane-bound dehydrogenase with high activity toward d-lactate, while GOX2071 was characterized as a soluble oxidase with broad substrate specificity toward d-2-hydroxy acids. The latter used molecular oxygen as a direct electron acceptor, a feature that has not been reported previously in d-lactate-oxidizing enzymes. This study not only clarifies the mechanism for the growth of G. oxydans on d-lactate, but also provides new insights for applications of the important industrial microbe and the novel d-lactate oxidase.     

Nested Association Mapping for Identification of Functional Markers

Identification of functional markers (FMs) provides information about the genetic architecture underlying complex traits. An approach that combines the strengths of linkage and association mapping, referred to as nested association mapping (NAM), has been proposed to identify FMs in many plant species. The ability to identify and resolve FMs for complex traits depends upon a number of factors including frequency of FM alleles, magnitudes of their genetic effects, disequilibrium among functional and nonfunctional markers, statistical analysis methods, and mating design. The statistical characteristics of power, accuracy, and precision to identify FMs with a NAM population were investigated using three simulation studies. The simulated data sets utilized publicly available genetic sequences and simulated FMs were identified using least-squares variable selection methods. Results indicate that FMs with simple additive genetic effects that contribute at least 5% to the phenotypic variability in at least five segregating families of a NAM population consisting of recombinant inbred progeny derived from 28 matings with a single reference inbred will have adequate power to accurately and precisely identify FMs. This resolution and power are possible even for genetic architectures consisting of disequilibrium among multiple functional and nonfunctional markers in the same genomic region, although the resolution of FMs will deteriorate rapidly if more than two FMs are tightly linked within the same amplicon. Finally, nested mating designs involving several reference parents will have a greater likelihood of resolving FMs than single reference designs.THE primary purpose for identifying functional markers (FMs) associated with complex traits in plant species is to provide molecular genetic information underlying variability upon which both artificial and natural selection are based. FMs are defined as polymorphic sites within genomes that causally affect phenotypic trait variability (Andersen and Lubberstedt 2003). This definition is a pragmatic recognition that phenotypic variability can be due to genomic variability located outside of open reading frames. Forward genetics approaches to associate naturally occurring structural genomic variants with phenotypic variability can be broadly categorized as (1) linkage mapping, also referred to as quantitative trait locus (QTL) mapping, (2) association genetic mapping, also known as linkage disequilibrium (LD) mapping, and (3) designs that combine linkage and LD mapping.The third approach based on the concept of combining LD with QTL mapping is a natural extension of the multifamily QTL approach and has been referred as joint linkage and linkage disequilibrium mapping (JLLDM) (Xiong and Jin 2000; Farnir et al. 2002; Wu et al. 2002; Perez-Enciso 2003; Jung et al. 2005) in samples from natural populations. The combined approach also has been applied to designed mapping families sampled from plant breeding populations (Xu 1998a; Jannink and Jansen 2000; Jannink and Wu 2003; Jansen et al. 2003). A special case of designed mapping families that are interconnected, known as nested association mapping (NAM), was proposed by Yu et al. (2008). As originally proposed, a NAM population consists of multiple families of recombinant inbred lines (RILs) derived from multiple inbred lines crossed to a single reference inbred line. Implicitly, genomic information is composed of high-density genotypes of parental inbred lines and low-density genotypes from segregating progeny. If the segregating progeny are RILs or doubled haploid lines (DHLs), then the genomic information can be “immortalized” for associations with phenotypes obtained through long-term longitudinal studies (Nordborg and Weigel 2008).A NAM population consisting of 25 families with 200 RILs for each family has been developed and released as a genetic resource for identification of FMs in maize (Yu et al. 2008). Other publicly available NAM populations are being developed for several species including Arabidopsis thaliana (Buckler and Gore 2007), barley (R. Wise, personal communication), sorghum (J. Yu, personal communication), and soybean (B. Diers, personal communication).The power, accuracy, and precision of identifying FMs in experimental NAM populations have not been investigated for complex genetic architectures. These statistical properties depend upon a number of factors including the following:

1. Data analysis method: Some methods are more powerful than others; however, experimental biologists prefer methods implemented in existing software packages. Are least-squares methods sufficiently powerful to identify FMs in established and developing NAM populations?
2. Frequency of functional markers and magnitudes of genetic effects: Development of a NAM population will change the allele frequencies of the FM relative to the reference population from which the lines are sampled. How will allele frequency and magnitude of genetic effects in a typical NAM population affect the ability to identify FMs?
3. Disequilibrium among functional and nonfunctional markers: Disequilibrium may exist among alleles within subpopulations even when there is no physical basis for genetic linkage. To what extent can the NAM design address consequences of gametic disequilibrium (population structure) in the reference population?
4. Multiple FMs in the same genomic region: If multiple FMs are physically located in the same genomic region, will equilibrium among the parental lines enable resolution of multiple FMs?
5. Mating design: An appropriate mating design can maximize the number of families that are informative for FMs. Will multiple-reference mating designs improve the probability of identifying FMs?

These five questions were addressed.     

Nuclear Compartmentalization of Serine Racemase Regulates d-Serine Production: IMPLICATIONS FOR N-METHYL-d-ASPARTATE (NMDA) RECEPTOR ACTIVATION*

d-Serine is a physiological co-agonist that activates N-methyl d-aspartate receptors (NMDARs) and is essential for neurotransmission, synaptic plasticity, and behavior. d-Serine may also trigger NMDAR-mediated neurotoxicity, and its dysregulation may play a role in neurodegeneration. d-Serine is synthesized by the enzyme serine racemase (SR), which directly converts l-serine to d-serine. However, many aspects concerning the regulation of d-serine production under physiological and pathological conditions remain to be elucidated. Here, we investigate possible mechanisms regulating the synthesis of d-serine by SR in paradigms relevant to neurotoxicity. We report that SR undergoes nucleocytoplasmic shuttling and that this process is dysregulated by several insults leading to neuronal death, typically by apoptotic stimuli. Cell death induction promotes nuclear accumulation of SR, in parallel with the nuclear translocation of GAPDH and Siah proteins at an early stage of the cell death process. Mutations in putative SR nuclear export signals (NESs) elicit SR nuclear accumulation and its depletion from the cytosol. Following apoptotic insult, SR associates with nuclear GAPDH along with other nuclear components, and this is accompanied by complete inactivation of the enzyme. As a result, extracellular d-serine concentration is reduced, even though extracellular glutamate concentration increases severalfold. Our observations imply that nuclear translocation of SR provides a fail-safe mechanism to prevent or limit secondary NMDAR-mediated toxicity in nearby synapses.