Linkage Disequilibrium and Genetic Variances under Mutation-Selection Balance

I determine the contribution of linkage disequilibrium to genetic variances using results for two loci and for induced or marginal systems. The analysis allows epistasis and dominance, but assumes that mutation is weak relative to selection. The linkage disequilibrium component of genetic variance is shown to be unimportant for unlinked loci if the gametic mutation rate divided by the harmonic mean of the pairwise recombination rates is much less than one. For tightly linked loci, linkage disequilibrium is unimportant if the gametic mutation rate divided by the (induced) per locus selection is much less than one.     

Mutation-Selection Balance and Metabolic Control Theory

The evolution of metabolic control is examined with models that unify approaches of classical quantitative genetics and metabolic control theory. The quantitative traits considered are the activities of enzymes embedded within metabolic pathways. In the models, polygenic mutation alters the enzyme activities (Vmax/Km) according to prescribed distributions, and the population evolves following classical haploid viability selection. Stabilizing selection operates on global properties of the metabolic pathway, including either flux or metabolite pool concentration. Analytical results and numerical simulations demonstrate several important properties of these characters, including skewed, non-Gaussian equilibrium distributions, and an expected positive correlation between activities of enzymes flanking a substrate pool undergoing stabilizing selection. The house-of-cards approximation proved to be accurate in predicting the equilibrium distribution of allelic effects for a biologically reasonable segment of the parameter space. Further experimental and theoretical work is needed before a clear assessment can be made whether the observed variance in enzyme activities is explicable by a mutation-selection balance, and this system provides an excellent opportunity for such a test.     

Effects of Pleiotropy on Predictions concerning Mutation-Selection Balance for Polygenic Traits

Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P1 and P2. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, can be compared to a prediction based solely on observations of P1. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10(-4), the widely used gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.     

Repression/Depression of Conjugative Plasmids and Their Influence on the Mutation-Selection Balance in Static Environments

We study the effect that conjugation-mediated Horizontal Gene Transfer (HGT) has on the mutation-selection balance of a population in a static environment. We consider a model whereby a population of unicellular organisms, capable of conjugation, comes to mutation-selection balance in the presence of an antibiotic, which induces a first-order death rate constant for genomes that are not resistant. We explicitly take into consideration the repression/de-repression dynamics of the conjugative plasmid, and assume that a de-repressed plasmid remains temporarily de-repressed after copying itself into another cell. We assume that both repression and de-repression are characterized by first-order rate constants and , respectively. We find that conjugation has a deleterious effect on the mean fitness of the population, suggesting that HGT does not provide a selective advantage in a static environment, but is rather only useful for adapting to new environments. This effect can be ameliorated by repression, suggesting that while HGT is not necessarily advantageous for a population in a static environment, its deleterious effect on the mean fitness can be negated via repression. Therefore, it is likely that HGT is much more advantageous in a dynamic landscape. Furthermore, in the limiting case of a vanishing spontaneous de-repression rate constant, we find that the fraction of conjugators in the population undergoes a phase transition as a function of population density. Below a critical population density, the fraction of conjugators is zero, while above this critical population density the fraction of conjugators rises continuously to one. Our model for conjugation-mediated HGT is related to models of infectious disease dynamics, where the conjugators play the role of the infected (I) class, and the non-conjugators play the role of the susceptible (S) class.     

Tissue Culture-Induced Heritable Genomic Variation in Rice,and Their Phenotypic Implications

Background

Somaclonal variation generally occurs in plants regenerated from tissue culture. However, fundamental issues regarding molecular characteristics, mutation rates and mutation spectra of plant somatic variation as well as their phenotypic relevance have been addressed only recently. Moreover, these studies have reported highly discrepant results in different plant species and even in the same plant genotype.

Methodology/principal findings

We investigated heritable genomic variation induced by tissue culture in rice by whole genome re-sequencing of an extensively selfed somaclonal line (TC-reg-2008) and its wild type (WT) donor (cv. Hitomebore). We computed the overall mutation rate, single nucleotide polymorphisms (SNPs), small scale insertions/deletions (Indels) and mobilization of transposable elements (TEs). We assessed chromosomal distribution of the various types of genomic variations, tested correlations between SNPs and Indels, and examined concomitancy between TE activity and its cytosine methylation states. We also performed gene ontology (GO) analysis of genes containing nonsynonymous mutations and large-effect mutations, and assayed effects of the genomic variations on phenotypes under both normal growing condition and several abiotic stresses. We found that heritable somaclonal genomic variation occurred extensively in rice. The genomic variations distributed non-randomly across each of the 12 rice chromosomes, and affected a large number of functional genes. The phenotypic penetrance of the genomic variations was condition-dependent.

Conclusions/significance

Tissue culture is a potent means to generate heritable genetic variations in rice, which bear distinct difference at least in space (chromosomal distribution) from those occurred under natural settings. Our findings have provided new information regarding the mutation rate and spectrum as well as chromosomal distribution pattern of somaclonal variation in rice. Our data also suggest that rice possesses a strong capacity to canalize genetic variations under normal growing conditions to maintain phenotypic robustness, which however can be released by certain abiotic stresses to generate variable phenotypes.     

Temporal Hierarchies of Variation and the Maintenance of Diversity

Abstract A general model shows how the long-term growth rate of a population can be partitioned into components representing various mechanisms of maintenance of species diversity. One component summarises the effects of fluctuation-independent mechanisms, which include classical resource partitioning and frequency-dependent herbivory. Two other components represent fluctuation-dependent mechanisms, the storage effect and relative nonlinearity of competition.
The general model shows how a community will track an equilibrium set by fluctuation-independent mechanisms and the environmental state when community dynamics are faster than the rate of environmental change. Fluctuation-dependent mechanisms can be important for diversity maintenance with or without such tracking, but on long timescales their effects are indistinguishable from those of fluctuation-independent mechanisms.
These considerations lead to a hierarchical view of mechanisms of diversity maintenance where the effects of different timescales are partitioned or merged depending on the timescale of observation. These issues are illustrated with model examples involving various combinations of resource partitioning, fluctuations in recruitment rates, variation in the timing of germination, and seasonality. The very long timescales associated with climate change contain many complexities but nevertheless many ideas applicable to shorter timescales may be useful in a modified form.     

A Computer Model Allowing Maintenance of Large Amounts of Genetic Variability in Mendelian Populations. II. the Balance of Forces between Linkage and Random Assortment

It is shown, through theory and computer simulations of outbreeding Mendelian populations, that there may be conditions under which a balance is struck between two facotrs. The first is the advantage of random assortment, which will, when multilocus selection is for intermediate equilibrium values, lead to higher average heterozygosity than when linkage is introduced. There is some indication that random assortment is also advantageous when selection is toward a uniform distribution of equilibrium values. The second factor is the advantage of linkage between loci having positive epistatic interactions. When multilocus selection is for a bimodal distribution of equilibrium values an early advantage of random assortment is replaced by a later disadvantage. Linkage disequilibrium, which in finite populations is increased only by random or selective sampling, may hinder the movement of alleles to their selective equilibria, thus leading to the advantage of random assortment.-Some consequences of this approach to the structure of natural populations are discussed.     

Variation of the Linkage of Root Function with Root Branch Order

Mounting evidence has shown strong linkage of root function with root branch order. However, it is not known whether this linkage is consistent in different species. Here, root anatomic traits of the first five branch order were examined in five species differing in plant phylogeny and growth form in tropical and subtropical forests of south China. In Paramichelia baillonii, one tree species in Magnoliaceae, the intact cortex as well as mycorrhizal colonization existed even in the fifth-order root suggesting the preservation of absorption function in the higher-order roots. In contrast, dramatic decreases of cortex thickness and mycorrhizal colonization were observed from lower- to higher-order roots in three other tree species, Cunninghamia lanceolata, Acacia auriculiformis and Gordonia axillaries, which indicate the loss of absorption function. In a fern, Dicranopteris dichotoma, there were several cortex layers with prominently thickened cell wall and no mycorrhizal colonization in the third- and fourth-order roots, also demonstrating the loss of absorptive function in higher-order roots. Cluster analysis using these anatomic traits showed a different classification of root branch order in P. baillonii from other four species. As for the conduit diameter-density relationship in higher-order roots, the mechanism underpinning this relationship in P. baillonii was different from that in other species. In lower-order roots, different patterns of coefficient of variance for conduit diameter and density provided further evidence for the two types of linkage of root function with root branch order. These linkages corresponding to two types of ephemeral root modules have important implication in the prediction of terrestrial carbon cycling, although we caution that this study was pseudo-replicated. Future studies by sampling more species can test the generality of these two types of linkage.     

Effect of Mating Structure on Variation in Linkage Disequilibrium

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size (N_e) and the mating structure. Second, there is sampling of a finite number (n) of individuals to estimate the population disequilibrium.——Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of N_e, mating structure, n, and linkage or recombination parameter.——The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci.     

Extrafloral Nectaries in Aspen (Populus tremuloides): Heritable Genetic Variation and Herbivore-induced Expression

Annals of Botany 100:     

Pleiotropic Overdominance and the Maintenance of Genetic Variation in Polygenic Characters

A model of selection is described in which optimizing phenotypic selection is combined with pleiotropic overdominance. Thus, the role that mutation commonly plays in models of phenotypic evolution is replaced by balancing selection. Expressions are provided for the equilibrium genetic variance in phenotype and for the heterozygosity. An approximate analysis of the transient properties of the model shows that, in certain circumstances, the behavior is quite similar to that of models based on the interaction of mutation and selection.     

Heritable Variation in a Polypeptide Subunit of the Major Storage Protein of the Bean, Phaseolus vulgaris L

Electrophoretic analysis of the major seed protein, G1 globulin, from four strains of Phaseolus vulgaris L. revealed a three-banded pattern for two strains having a high methionine content (BBL 240 and PI 302,542). The other two strains (PI 207,227 and PI 229,815) known to have a lower seed methionine content, had a two-banded subunit pattern for the G1 globulin. Analytical ultracentrifugation confirmed that globulin from the two-banded strains underwent pH-dependent reversible dissociation similar to that previously found for a three-banded cultivar; additionally, the protomer molecular weight showed that three subunits of about 50,000 molecular weight each were present in the G1 globulin of the two-banded strain. Gel patterns of G1 globulin from the two strains used as parents, BBL 240 and PI 229,815, showed differences in the largest subunit, which appeared as either a 53,000 molecular weight polypeptide known to be present in the three-banded strain, or as a shorter polypeptide having a molecular weight close to 47,000. Analysis of G1 protein from portions of single hybrid seeds showed a banding pattern intermediate between the two- and three-banded types. The subunit pattern from all seeds with intermediate-banded parents segregated in a manner consistent with that expected for control of the polypeptide by a single Mendelian gene. The remaining portions of the seeds were grown to confirm that they represented true crosses. The procedures used are essentially nondestructive, and can be used as a basis for selecting seeds having different protein characters.     

Allozymic Variation and Linkage Disequilibrium in Some Laboratory Populations of DROSOPHILA MELANOGASTER

Nine laboratory populations of D. melanogaster were surveyed by starch gel electrophoresis for variation at 17 enzyme loci. A single-fly extract could be assayed for all 17 enzymes, so that the data consist of 17-locus genotypes.--Pairwise linkage disequilibria were estimated from the multilocus genotypic frequencies, using both Burrows' and Hill's methods. Large amounts of linkage disequilibrium were found, in contrast to the results reported for natural populations.-Knowledge of the approximate sizes of these populations was used to compare the observed heterozygosities and linkage disequilibria with predictions of the neutral allele hypothesis. The relatively large amount of linkage disequilibrium is consistent with the small sizes of the populations. However, the levels of heterozygosity in at least some populations suggest that some mechanism has been operating to retard the rate of decay by random drift. Several examples of significant deviation from Hardy-Weinberg frequencies and the large amount of linkage disequilibrum present in these populations indicate that a likely mechanism is selective effects associated with neutral alleles because of linkage disequilibrium with selected loci (e.g., "associative overdominance"). The results are therefore consistent with both neutralist, and selectionist hypotheses, but suggest the importance of considering linkage disequilibrium between neutral and selected loci when attempting to explain the dynamics of enzyme polymorphisms.     

Deleterious Mutations, Apparent Stabilizing Selection and the Maintenance of Quantitative Variation

Apparent stabilizing selection on a quantitative trait that is not causally connected to fitness can result from the pleiotropic effects of unconditionally deleterious mutations, because as N. Barton noted, "...individuals with extreme values of the trait will tend to carry more deleterious alleles...." We use a simple model to investigate the dependence of this apparent selection on the genomic deleterious mutation rate, U; the equilibrium distribution of K, the number of deleterious mutations per genome; and the parameters describing directional selection against deleterious mutations. Unlike previous analyses, we allow for epistatic selection against deleterious alleles. For various selection functions and realistic parameter values, the distribution of K, the distribution of breeding values for a pleiotropically affected trait, and the apparent stabilizing selection function are all nearly Gaussian. The additive genetic variance for the quantitative trait is kQa2, where k is the average number of deleterious mutations per genome, Q is the proportion of deleterious mutations that affect the trait, and a2 is the variance of pleiotropic effects for individual mutations that do affect the trait. In contrast, when the trait is measured in units of its additive standard deviation, the apparent fitness function is essentially independent of Q and a2; and beta, the intensity of selection, measured as the ratio of additive genetic variance to the "variance" of the fitness curve, is very close to s = U/k, the selection coefficient against individual deleterious mutations at equilibrium. Therefore, this model predicts appreciable apparent stabilizing selection if s exceeds about 0.03, which is consistent with various data. However, the model also predicts that beta must equal Vm/VG, the ratio of new additive variance for the trait introduced each generation by mutation to the standing additive variance. Most, although not all, estimates of this ratio imply apparent stabilizing selection weaker than generally observed. A qualitative argument suggests that even when direct selection is responsible for most of the selection observed on a character, it may be essentially irrelevant to the maintenance of variation for the character by mutation-selection balance. Simple experiments can indicate the fraction of observed stabilizing selection attributable to the pleiotropic effects of deleterious mutations.     

Linkage Disequilibrium in Natural Populations of DROSOPHILA MELANOGASTER. Seasonal Variation

Linkage disequilibrium among ten polymorphic allozyme loci and polymorphic inversions on chromosomes 2 and 3 in a natural population of Drosophila melanogaster was examined early and late in the annual season. Similar to previous studies, little linkage disequilibrium was observed among allozymes. The two significant cases that were observed in the first sample behaved in a contradictory way. One declined much more rapidly than expected due simply to recombination; the other declined slowly as expected. There was little change in allozyme or inversion frequencies during the season.