On the Evolution of Genetic Incompatibility Systems. VI. a Three-Locus Modifier Model for the Origin of Gametophytic Self-Incompatibility

Recent genetic analyses have demonstrated that self-incompatibility in flowering plants derives from the coordinated expression of a system of loci. To address the selective mechanisms through which a genetic system of this kind evolves, I present a three-locus model for the origin of gametophytic self-incompatibility. Conventional models assume that a single locus encodes all physiological effects associated with self-incompatibility and that the viability of offspring depends only on whether they were derived by selfing or outcrossing. My model explicitly represents the genetic determination of offspring viability by a locus subject to symmetrically overdominant selection. Initially, the level of expression of the proto-S locus is insufficient to induce self-incompatibility. Weak gametophytic self-incompatibility arises upon the introduction of a rare allele at an unlinked modifier locus which enhances the expression of the proto-S locus. While conventional models predict that the origin of self-incompatibility requires at least two- to threefold levels of inbreeding depression, I find that the comparatively low levels of inbreeding depression generated by a single overdominant locus can ensure the invasion of an enhancer of self-incompatibility under sufficiently high rates of receipt of self-pollen. Associations among components of the incompatibility system promote the origin of self-incompatibility. Enhancement of heterozygosity at the initially neutral proto-S locus improves offspring viability through associative overdominance. Further, the modifier that enhances the expression of self-incompatibility develops a direct association with heterozygosity at the overdominant viability locus. These results suggest that the evolutionary processes by which incompatibility systems originate may differ significantly from those associated with their breakdown. The genetic mechanism explored here may apply to the evolution of other systems that restrict reproduction, including maternal-fetal incompatibility in mammals.     

Properties of Equilibria in Multi-Locus Genetic Systems

The classical mathematical theory of population genetics considered, for simplicity, almost exclusively one-locus systems. In the last two decades much work has been done on two-locus and, less frequently, multi-locus systems. This research has usually involved investigating properties of systems with given, and usually rather special, fitness parameters. Real genetic fitness systems are undoubtedly multi-locus and seldom will possess simplifying characteristics. One aim of this paper is to study generalized systems where no special assumptions are made about fitness structure, the number of alleles at each locus, the number of loci involved or the recombination structure between loci. A second aim is to consider marginal properties (often one-locus properties) of complex systems: the fact that many observations involve data from only on locus makes this second aim relevant.     

The Maintenance of Single-Locus Polymorphism. I. Numerical Studies of a Viability Selection Model

The ability of viability selection to maintain single-locus polymorphism is investigated with two models in which the population is bombarded with a series of mutations with random fitnesses. In the first model, the population is allowed to reach equilibrium before mutation resumes; in the second the iterations and mutation occur simultaneously. Monte Carlo simulations of these models show that viability selection is easily able to maintain stable 6- or 7-allele polymorphisms and that monomorphisms and diallelic polymorphisms are uncommon. The question of how monomorphisms arise is also discussed.     

Central Equilibria in Multilocus Systems. II. Bisexual Generalized Nonepistatic Selection Models

This paper is a continuation of the paper "Central Equilibria in Multilocus Systems I," concentrating on existence and stability properties accruing to central H-W type equilibria in multilocus bisexual systems acted on by generalized nonepistatic selection forces coupled to recombination events. The stability conditions are discussed and interpreted in three perspectives, and the influence of sexual differences in linkage relationships together with sex-dependent selection is appraised. In this case we deduce that the stability conditions of the H-W polymorphism in the bisexual model coincide exactly with the conditions for the corresponding monoecious model, provided that the recombination distribution imposed is that of the arithmetic mean of the male and female recombination distributions. A second concern has the same recombination distribution for both sexes, but contrasting selection regimes between sexes. It is then established that, with respect to discerning the relevance of the H-W equilibrium, there is an equivalent monoecious selection regime which is an appropriate "weighted combination" of the male and female selection forms. Finally, in the case where the selection and recombination structures are both sex dependent, a hierarchy of comparisons is elaborated, seeking to unravel the nature of selection-recombination interaction for monoecious versus diocecious systems.     

Respiratory Complex I in Brain Development and Genetic Disease

A study is presented on the expression and activity of complex I, as well as of other complexes of the respiratory chain, in the course of brain development and inherited encephalopathies. Investigations on mouse hippocampal cells show that differentiation of these cells both in vivo and in cell cultures is associated with the expression of a functional complex I, whose activity markedly increases with respect to that of complexes III and IV. Data are presented on genetic defects of complex I in six children with inborn encephalopathy associated with isolated deficiency of the complex. Mutations have been identified in nuclear and mitochondrial genes coding for subunits of the complex. Different mutations were found in the nuclear NDUFS4 gene coding for the 18 kD (IP, AQDQ) subunit of complex I. All the NDUFS4 mutations resulted in impairment of the assembly of a functional complex. The observations presented provide evidence showing a critical role of complex I in differentiation and functional activity of brain cells.     

Response to Selection Under Non-Random Mating I. Partitioning Genetic Variance

In analogy to the concept of breeding value defined for random mating equilibrium populations, the “transmittable genetic value” of an individual is defined as the average value of its expected progeny for any system of mating. The genotypic value is then characterised in terms of transmittable and residual genetic values and components of genetic variance redefined which can be estimated by the conventional procedure based on resemblance between relatives.     

Model Selection in Systems Biology Depends on Experimental Design

Experimental design attempts to maximise the information available for modelling tasks. An optimal experiment allows the inferred models or parameters to be chosen with the highest expected degree of confidence. If the true system is faithfully reproduced by one of the models, the merit of this approach is clear - we simply wish to identify it and the true parameters with the most certainty. However, in the more realistic situation where all models are incorrect or incomplete, the interpretation of model selection outcomes and the role of experimental design needs to be examined more carefully. Using a novel experimental design and model selection framework for stochastic state-space models, we perform high-throughput in-silico analyses on families of gene regulatory cascade models, to show that the selected model can depend on the experiment performed. We observe that experimental design thus makes confidence a criterion for model choice, but that this does not necessarily correlate with a model''s predictive power or correctness. Finally, in the special case of linear ordinary differential equation (ODE) models, we explore how wrong a model has to be before it influences the conclusions of a model selection analysis.     

Correlations in Multi-Locus Genetic Systems: A Mathematical Model

A spin model with parallels to a multi-locus genetic model is presented which makes it possible to calculate the correlation between allelic states at any two loci in a population at equilibrium. The main features are: (1) The decay of correlation with distance may be expressed essentially as a linear combination of two exponentials, one of which dominates when the two loci are sufficiently far apart. (2) The correlation between two loci a specified distance apart is increased as the number of loci in the entire system increases. The results are compared with those of other theoretical models and discussed in the light of available experimental data. Possible ways of generalizing the model are outlined. However, additional experimental data is clearly needed to indicate the genetic relevance of work of this nature.     

A Genetic Analysis of Phototactic Behavior in DROSOPHILA MELANOGASTER I. Selection in the Presence of Inversions

The effectiveness of selection for positive and negative phototactic behavior in populations of Drosophila melanogaster heterozygous for various multiple inversions was compared using the method of realized heritability. Selection in the presence of FM6, SM1 or TM3 alone was as effective as in populations carrying no inversions. However, the presence of FM6 and TM3 together reduced the effectiveness of selection for photopositive behavior and FM6 and SM1 and TM3 restricted the response to selection for negative phototactic behavior. The results are discussed in terms of the organization of genes influencing phototactic behavior in this species.     

The Scent of Genetic Compatibility: Sexual Selection and the Major Histocompatibility Complex

Individuals in some species prefer mates carrying dissimilar genes at the major histocompatibility complex (MHC), which may function to increase the MHC or overall heterozygosity of progeny. Here I review the evidence for MHC-dependent mating preferences from recent studies, including studies on the underlying olfactory mechanisms and evolutionary functions. Many studies indicate that MHC genes influence odour, and some work is beginning to examine the potential role of MHC-linked olfactory receptor genes in mating preferences. MHC-dependent mating preference increases the MHC-heterozygosity of progeny, which is suspected to confer resistance to infectious diseases. In humans, heterozygosity at MHC loci is associated with increased resistance to hepatitis and HIV infections, but experimental evidence for the heterozygote advantage hypothesis has been lacking. Here I re-analyse data from previously published experimental infection studies with mice. I show that although overdominance is rare, resistance is often dominant, suggesting that heterozygotes are often protected. A second (nonmutually exclusive) possibility is that MHC-disassortative mating preferences promotes inbreeding avoidance. This hypothesis is supported by recent evidence that MHC genes play a role in kin recognition, and that mating with close kin has rather deleterious fitness consequences. In conclusion, I discuss other ways that MHC genes might influence sexual selection. The research on MHC-mediated mating preferences is integrating the study of animal behaviour with other seemingly disparate fields, including sensory biology and immunogenetics.     

The Impact of Population Demography and Selection on the Genetic Architecture of Complex Traits

Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequency, and effect sizes of mutations that contribute risk to complex traits. Because researchers are performing exome sequencing studies aimed at uncovering the role of low-frequency variants in the risk of complex traits, this topic is of critical importance. Here I use simulations under population genetic models where a proportion of the heritability of the trait is accounted for by mutations in a subset of the exome. I show that recent population growth increases the proportion of nonsynonymous variants segregating in the population, but does not affect the genetic load relative to a population that did not expand. Under a model where a mutation''s effect on a trait is correlated with its effect on fitness, rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand. Further, when using a single-marker test, for a given false-positive rate and sample size, recent population growth decreases the expected number of significant associations with the trait relative to the number detected in a population that did not expand. However, in a model where there is no correlation between a mutation''s effect on fitness and the effect on the trait, common variants account for much of the additive genetic variance, regardless of demography. Moreover, here demography does not affect the number of significant associations detected. These findings suggest recent population history may be an important factor influencing the power of association tests and in accounting for the missing heritability of certain complex traits.     

A Study of Conformational Equilibria in Chain Molecules. I. Liquid n-Butane

Abstract

We have performed molecular dynamics simulations for liquid n-butane in order to understand liquid structures in terms of both inter- and intra-molecular interactions. Each n-butane molecule consists of four sites interacting with LJ potential and only a dihedral angle is taken into account as the internal degree of freedom. The population of gauche conformations with respect to the ideal gas state is found to increase in the liquid state. To investigate how the intermolecular interaction affects the dihedral angle distribution, we also adopt the repulsive LJ potential (RLJ) model. It is found that the nearest neighbor packing of the methyl and/or methylene groups can be approximately represented by using only the repulsive interaction. From the dihedral angle distribution, however, the rate of the shift of RLJ model to gauche is larger than that of LJ model and the attractive force also plays a significant role in the conformational equilibrium.     

Genetic Variation in a Heterogeneous Environment. I. Temporal Heterogeneity and the Absolute Dominance Model

The conditions for a stable polymorphism and the equilibrium gene frequency in an infinite population are compared when there is spatial or temporal environmental heterogeneity for the absolute dominance model. For temporal variation the conditions for stability are more restrictive and the equilibrium gene frequency is often at a low gene frequency. In a finite population, temporal environmental heterogeneity for the absolute dominance model was found to be quite ineffective in maintaining genetic variation and is often less effective than no selection at all. For comparison, the maximum maintenance for temporal variation is related to the overdominant model. In general, cyclic environmental variation was found to be more effective at maintaining genetic variation than where the environment varies stochastically. The importance of temporal environmental variation and the maintenance of genetic variation is discussed.     

Natural Selection with Nuclear and Cytoplasmic Transmission. I. a Deterministic Model

A deterministic model allowing variation at a nuclear genetic locus in a population segregating two cytoplasmic types is formulated. Additive, multiplicative and symmetric viability matrices are analyzed for existence and stability of equilibria. The protectedness of polymorphisms in both nuclear genes and cytoplasmic types is also investigated in the general model. In no case is a complete polymorphism protected with this deterministic model. Results are discussed in light of the extensive variation in mtDNA that has recently been reported.     

Analysis of the Albino-Locus Region of the Mouse. I. Origin and Viability

Numerous specific-locus experiments designed to test the mutagenic effect of external radiation have yielded, in over 3,600,000 animals observed, altogether 119 presumed mutations involving the c locus. Of these, 55 were viable and albino (cav), 13 were viable and of various intermediate pigment types (cxv), four were subvital (cas and cxs), seven were neonatally lethal albinos (cal), 28 prenatally lethal albinos (cal); 12 died untested. All of the prenatally lethal and at least one of the neonatally lethal c-locus mutations (cal classes) are probably deficiencies that we have analyzed extensively in other experiments. Since absence of the locus mimics albino in phenotype, the intermediates (cxv and cxs groups) probably resulted from intragenic changes. The class of viable albino mutants (cav) might include, in addition to intragenic changes, some extremely small deficiencies. --The effects on viability of c-locus lethals (cal's) in heterozygous condition are not drastic enough to be perceived in stocks of mixed genetic background except in the case of the two longest known deficiencies and a few others. --Analysis of the relation between radiation treatment and type of c-locus mutants obtained shows that the relative frequency of viable mutations, for each germ-cell type, is greater for low-LET than for neutron irradiation; however, the difference for any individual cell type is not significant. The majority (66.7%) of mutations derived from X- or gamma-ray irradiated spermatogonia are viable, and the proportion of "intermediates" among these viables is similar to that among presumed spontaneous c-locus mutations. No significant dose-rate effect on the proportion of lethals could be demonstrated within the set of mutants induced by low-LET irradiation of spermatogonia. Although sets from other germ-cell stages are too small for statistical tests, the results for oocytes are similar, as far as they go. Furthermore, most of the c-locus mutations induced in spermatogonia, even by high-dose-rate X-ray or gamma irradiation, are of a type most likely to result from single-tract events (62% cxv, cxs, and cav; plus 16% presumed deficiencies not involving the closest marker). These results support the view that most of the reduction in mutation frequency at low dose rates is not due to a change in relative proportion of two-track and one-track ionizing events.