Polygenic inheritance is not necessary for sympatric speciation by sexual selection

 The theoretical possibility of sympatric speciation by sexual selection has been demonstrated by a number of mathematical models. Although these models assumed that sexually selected traits are additively determined by many genes, recent empirical studies suggest that many sexually selected traits are determined by major gene inheritance. Thus, using a mathematical simulation model, this article examines whether sympatric speciation by sexual selection can occur when sexually selected traits are determined by major gene inheritance. The model reveals that speciation can occur with major gene inheritance of sexually selected traits. Simulations show that speciation from an initially monomorphic population occurs via two successive Fisher's runaway processes of sexual selection. The first runaway causes the unidirectional evolution of male secondary sexual character toward one extreme in the trait space and of female mate preference for such a character. The second runaway then drives the male character and female preference of a part of the population toward the other extreme in the trait space, splitting the population into two reproductively isolated subgroups. The current results reinforce the plausibility of sympatric speciation by sexual selection. Received: January 30, 2002 / Accepted: June 27, 2002     

Selection against Heteroplasmy Explains the Evolution of Uniparental Inheritance of Mitochondria

Why are mitochondria almost always inherited from one parent during sexual reproduction? Current explanations for this evolutionary mystery include conflict avoidance between the nuclear and mitochondrial genomes, clearing of deleterious mutations, and optimization of mitochondrial-nuclear coadaptation. Mathematical models, however, fail to show that uniparental inheritance can replace biparental inheritance under any existing hypothesis. Recent empirical evidence indicates that mixing two different but normal mitochondrial haplotypes within a cell (heteroplasmy) can cause cell and organism dysfunction. Using a mathematical model, we test if selection against heteroplasmy can lead to the evolution of uniparental inheritance. When we assume selection against heteroplasmy and mutations are neither advantageous nor deleterious (neutral mutations), uniparental inheritance replaces biparental inheritance for all tested parameter values. When heteroplasmy involves mutations that are advantageous or deleterious (non-neutral mutations), uniparental inheritance can still replace biparental inheritance. We show that uniparental inheritance can evolve with or without pre-existing mating types. Finally, we show that selection against heteroplasmy can explain why some organisms deviate from strict uniparental inheritance. Thus, we suggest that selection against heteroplasmy explains the evolution of uniparental inheritance.     

A genetic linkage map of the human genome

We report the construction of a linkage map of the human genome, based on the pattern of inheritance of 403 polymorphic loci, including 393 RFLPs, in a panel of DNAs from 21 three-generation families. By a combination of mathematical linkage analysis and physical localization of selected clones, it was possible to arrange these loci into linkage groups representing 23 human chromosomes. We estimate that the linkage map is detectably linked to at least 95% of the DNA in the human genome.     

The significance of specific distributions and functions in models of quantitative inheritance

The main purpose of this paper is to attract attention to the fact that a mathematical model of quantitative inheritance can lead to qualitatively different results, if distributions and functions which in the model represent biological processes are assumed to take analytically different (even though qualitatively similar) forms. A simple model of the effect of environmental variation on the post-selection genotypic variance in a population under phenotypic stabilizing selection is considered. It is demonstrated that this model leads to qualitatively different conclusions depending on whether the phenotypic fitness function is assumed in a Gaussian or in a quadratic form.     

Plasticity,memory and the adaptive landscape of the genotype

The adaptive value of epigenetic inheritance systems is investigated in a simple mathematical framework. These systems enable the environmentally induced phenotypes to be transmitted between generations. The frequencies of the different epigenetic variants are determined by the plasticity and the efficiency of transmission (called memory). Plasticity and memory are genetically determined. This paper studies the evolution of a quantitative character, its plasticity and memory, on the adaptive landscape. Due to the dual inheritance of the character, selection acts on two levels: on the phenotypes of the same genotype, and on the different genotypes. Plasticity generates the raw material, and memory increases the strength of phenotypic selection. If the character is far from the peak of the landscape, then dual inheritance of the character can be advantageous for the genotype. Near the peak it is more favourable to suppress phenotypic variation. This would lead to genetic assimilation.     

Homology across inheritance systems

Recent work on inheritance systems can be divided into inclusive conceptions, according to which genetic and non-genetic inheritance are both involved in the development and transmission of nearly all animal behavioral traits, and more demanding conceptions of what it takes for non-genetic resources involved in development to qualify as a distinct inheritance system. It might be thought that, if a more stringent conception is adopted, homologies could not subsist across two distinct inheritance systems. Indeed, it is commonly assumed that homology relations cannot survive a shift between genetic and cultural inheritance systems, and substantial reliance has been placed on that assumption in debates over the phylogenetic origins of hominin behavioral traits, such as male-initiated intergroup aggression. However, in the homology literature it is widely accepted that a trait can be homologous—that is, inherited continuously in two different lineages from a single common ancestor—despite divergence in the mechanisms involved in the trait’s development in the two lineages. In this paper, we argue that even on an extremely stringent understanding of what it takes for developmental resources to form a separate inheritance system, homologies can nonetheless subsist across shifts between distinct inheritance systems. We argue that this result is a merit of this way of characterizing what it is to be an inheritance system, that it has implications for adjudicating between alternative accounts of homology, and that it offers an important cautionary lesson about how (not) to reason with the homology concept, particularly in the context of cultural species.     

Inheritance of epigenetic chromatin silencing

Maintenance of alternative chromatin states through cell divisions pose some fundamental constraints on the dynamics of histone modifications. In this paper, we study the systems biology of epigenetic inheritance by defining and analyzing general classes of mathematical models. We discuss how the number of modification states involved plays an essential role in the stability of epigenetic states. In addition, DNA duplication and the consequent dilution of marked histones act as a large perturbation for a stable state of histone modifications. The requirement that this large perturbation falls into the basin of attraction of the original state sometimes leads to additional constraints on effective models. Two such models, inspired by two different biological systems, are compared in their fulfilling the requirements of multistability and of recovery after DNA duplication. We conclude that in the presence of multiple histone modifications that characterize alternative epigenetic stable states, these requirements are more easily fulfilled.     

Parental genetic effects in a cavefish adaptive behavior explain disparity between nuclear and mitochondrial DNA

Epigenetic parental genetic effects are important in many biological processes but their roles in the evolution of adaptive traits and their consequences in naturally evolving populations remain to be addressed. By comparing two divergent blind cave-dwelling cavefish populations with a sighted surface-dwelling population (surface fish) of the teleost Astyanax mexicanus, we report here that convergences in vibration attraction behavior (VAB), the lateral line sensory receptors underlying this behavior, and the feeding benefits of this behavior are controlled by parental genetic effects, either maternal or paternal inheritance. From behavioral studies and mathematical evolutionary simulations, we further demonstrate that disparity in nuclear and mitochondrial DNA in one of these cavefish populations that has hybridized with surface fish can be explained by paternal inheritance of VAB. The results suggest that parental genetic effects in adaptive behaviors may be important factors in biasing mitochondrial DNA inheritance in natural populations that are subject to introgression.     

Mathematical and biological intermediacy in bone shape. Fourier analysis of cervical and upper thoracic vertebrae in the mouse

We have used Fourier transforms and discriminant analysis to look at the shapes of cervical and upper thoracic vertebrae from two pairs of mouse strains and biological intermediates (the F₁s) between them. We have also constructed mathematically intermediate shapes and compared mathematical and biological intermediates.
Mathematical and biological intermediates did not correspond in any of the 18 cases studied. We suggest that failure in correspondence is due to complex genetical and environmental factors acting on the F₁ phenotype, and that multivariate shape inheritance may be modelled in a similar way to univariate inheritance. Both depend on a large number of genetic loci.     

Cortical progenitor expansion, self-renewal and neurogenesis-a polarized perspective

Neural stem and progenitor cells giving rise to neurons in developing mammalian neocortex fall into two principal classes with regard to location of mitosis-apical and basal, and into three principal classes in terms of cell polarity during mitosis-bipolar, monopolar, and nonpolar. Insight has been gained into how inheritance of polarized, apical and basal, cell constituents is related to symmetric versus asymmetric divisions of these progenitors, and how this inheritance is linked to their expansion, self-renewal, and neurogenesis. Retention and inheritance of the basal process emerge as key for self-renewal, notably for the monopolar progenitors of prospective gyrencephalic neocortex that undergo asymmetric mitoses at basal locations. The resulting expansion of the neocortex during evolution is proposed to be associated with an increased cone-shape of radial units.     

Selection for mitonuclear co-adaptation could favour the evolution of two sexes

Mitochondria are descended from free-living bacteria that were engulfed by another cell between one and a half to two billion years ago. A redistribution of DNA led to most genetic information being lost or transferred to a large central genome in the nucleus, leaving a residual genome in each mitochondrion. Oxidative phosphorylation, the most critical function of mitochondria, depends on the functional compatibility of proteins encoded by both the nucleus and mitochondria. We investigate whether selection for adaptation between the nuclear and mitochondrial genomes (mitonuclear co-adaptation) could, in principle, have promoted uniparental inheritance of mitochondria and thereby the evolution of two mating types or sexes. Using a mathematical model, we explore the importance of the radical differences in ploidy levels, sexual and asexual modes of inheritance, and mutation rates of the nucleus and mitochondria. We show that the major features of mitochondrial inheritance, notably uniparental inheritance and bottlenecking, enhance the co-adaptation of mitochondrial and nuclear genes and therefore improve fitness. We conclude that, under a wide range of conditions, selection for mitonuclear co-adaptation favours the evolution of two distinct mating types or sexes in sexual species.     

Non-mendelian inheritance of mitochondrial DNA and ribosomal DNA in the myxomycete, Didymium iridis

Summary The inheritance of both the mitochondrial DNA (mtDNA) and the nuclear-encoded extrachromosomal ribosomal DNA (rDNA) has been studied in the myxomycete, Didymium iridis, by DNA-DNA hybridization of labeled probes to total DNA at various stage of the life cycle. Both the mtDNA and rDNA populations rapidly become homogeneous in individuals, but there is a qualitative difference in the patterns of inheritance of these two molecules. One parental rDNA type was preferentially inherited in all crosses; selective replication of this molecule is tentatively proposed as the mechanism of inheritance. In contrast, either parental mtDNA type could be inherited. Since the inherited population of parental mtDNA molecules are not partitioned into cells in this coenocytic organism, no known mechanism of inheritance can explain the rapid and apparently random loss of one parental mtDNA type in individuals.     

A unified approach to the evolutionary consequences of genetic and nongenetic inheritance

Inheritance-the influence of ancestors on the phenotypes of their descendants-translates natural selection into evolutionary change. For the past century, inheritance has been conceptualized almost exclusively as the transmission of DNA sequence variation from parents to offspring in accordance with Mendelian rules, but advances in cell and developmental biology have now revealed a rich array of inheritance mechanisms. This empirical evidence calls for a unified conception of inheritance that combines genetic and nongenetic mechanisms and encompasses the known range of transgenerational effects, including the transmission of genetic and epigenetic variation, the transmission of plastic phenotypes (acquired traits), and the effects of parental environment and genotype on offspring phenotype. We propose a unified theoretical framework based on the Price equation that can be used to model evolution under an expanded inheritance concept that combines the effects of genetic and nongenetic inheritance. To illustrate the utility and generality of this framework, we show how it can be applied to a variety of scenarios, including nontransmissible environmental noise, maternal effects, indirect genetic effects, transgenerational epigenetic inheritance, RNA-mediated inheritance, and cultural inheritance.     

From correlation to causation: The new frontier of transgenerational epigenetic inheritance

While heredity is predominantly controlled by what deoxyribonucleic acid (DNA) sequences are passed from parents to their offspring, a small but growing number of traits have been shown to be regulated in part by the non-genetic inheritance of information. Transgenerational epigenetic inheritance is defined as heritable information passed from parents to their offspring without changing the DNA sequence. Work of the past seven decades has transitioned what was previously viewed as rare phenomenology, into well-established paradigms by which numerous traits can be modulated. For the most part, studies in model organisms have correlated transgenerational epigenetic inheritance phenotypes with changes in epigenetic modifications. The next steps for this field will entail transitioning from correlative studies to causal ones. Here, we delineate the major molecules that have been implicated in transgenerational epigenetic inheritance in both mammalian and non-mammalian models, speculate on additional molecules that could be involved, and highlight some of the tools which might help transition this field from correlation to causation.     

Epigenetically facilitated mutational assimilation: epigenetics as a hub within the inclusive evolutionary synthesis

After decades of debate about the existence of non‐genetic inheritance, the focus is now slowly shifting towards dissecting its underlying mechanisms. Here, we propose a new mechanism that, by integrating non‐genetic and genetic inheritance, may help build the long‐sought inclusive vision of evolution. After briefly reviewing the wealth of evidence documenting the existence and ubiquity of non‐genetic inheritance in a table, we review the categories of mechanisms of parent–offspring resemblance that underlie inheritance. We then review several lines of argument for the existence of interactions between non‐genetic and genetic components of inheritance, leading to a discussion of the contrasting timescales of action of non‐genetic and genetic inheritance. This raises the question of how the fidelity of the inheritance system can match the rate of environmental variation. This question is central to understanding the role of different inheritance systems in evolution. We then review and interpret evidence indicating the existence of shifts from inheritance systems with low to higher transmission fidelity. Based on results from different research fields we propose a conceptual hypothesis linking genetic and non‐genetic inheritance systems. According to this hypothesis, over the course of generations, shifts among information systems allow gradual matching between the rate of environmental change and the inheritance fidelity of the corresponding response. A striking conclusion from our review is that documented shifts between types of inherited non‐genetic information converge towards epigenetics (i.e. inclusively heritable molecular variation in gene expression without change in DNA sequence). We then interpret the well‐documented mutagenicity of epigenetic marks as potentially generating a final shift from epigenetic to genetic encoding. This sequence of shifts suggests the existence of a relay in inheritance systems from relatively labile ones to gradually more persistent modes of inheritance, a relay that could constitute a new mechanistic basis for the long‐proposed, but still poorly documented, hypothesis of genetic assimilation. A profound difference between the genocentric and the inclusive vision of heredity revealed by the genetic assimilation relay proposed here lies in the fact that a given form of inheritance can affect the rate of change of other inheritance systems. To explore the consequences of such inter‐connection among inheritance systems, we briefly review published theoretical models to build a model of genetic assimilation focusing on the shift in the engraving of environmentally induced phenotypic variation into the DNA sequence. According to this hypothesis, when environmental change remains stable over a sufficient number of generations, the relay among inheritance systems has the potential to generate a form of genetic assimilation. In this hypothesis, epigenetics appears as a hub by which non‐genetically inherited environmentally induced variation in traits can become genetically encoded over generations, in a form of epigenetically facilitated mutational assimilation. Finally, we illustrate some of the major implications of our hypothetical framework, concerning mutation randomness, the central dogma of molecular biology, concepts of inheritance and the curing of inherited disorders, as well as for the emergence of the inclusive evolutionary synthesis.     

Julia Bell and the Treasury of Human Inheritance

The Treasury of Human Inheritance represents the most extensive, and one of the earliest series of documentations and analyses of human genetic disorders. Published between 1909 and 1958, from The Galton Laboratory, London, most of the numerous sections were written by Julia Bell, who represents a key figure in the development of human and medical genetics. Her combination of mathematical training, genetic knowledge and clinical expertise yielded numerous important insights into human inheritance first appearing in the Treasury; it remains a valuable scientific as well as an historical record of the genetics of a range of important inherited disorders.     

Quantitative and spatio‐temporal features of protein aggregation in Escherichia coli and consequences on protein quality control and cellular ageing

The aggregation of proteins as a result of intrinsic or environmental stress may be cytoprotective, but is also linked to pathophysiological states and cellular ageing. We analysed the principles of aggregate formation and the cellular strategies to cope with aggregates in Escherichia coli using fluorescence microscopy of thermolabile reporters, EM tomography and mathematical modelling. Misfolded proteins deposited at the cell poles lead to selective re‐localization of the DnaK/DnaJ/ClpB disaggregating chaperones, but not of GroEL and Lon to these sites. Polar aggregation of cytosolic proteins is mainly driven by nucleoid occlusion and not by an active targeting mechanism. Accordingly, cytosolic aggregation can be efficiently re‐targeted to alternative sites such as the inner membrane in the presence of site‐specific aggregation seeds. Polar positioning of aggregates allows for asymmetric inheritance of damaged proteins, resulting in higher growth rates of damage‐free daughter cells. In contrast, symmetric damage inheritance of randomly distributed aggregates at the inner membrane abrogates this rejuvenation process, indicating that asymmetric deposition of protein aggregates is important for increasing the fitness of bacterial cell populations.     

A model of proliferating cell populations with inherited cycle length

A mathematical model of cell population growth introduced by J. L. Lebowitz and S. I. Rubinow is analyzed. Individual cells are distinguished by age and cell cycle length. The cell cycle length is viewed as an inherited property determined at birth. The density of the population satisfies a first order linear partial differential equation with initial and boundary conditions. The boundary condition models the process of cell division of mother cells and the inheritance of cycle length by daughter cells. The mathematical analysis of the model employs the theory of operator semigroups and the spectral theory of linear operators. It is proved that the solutions exhibit the property of asynchronous exponential growth.     

Organelle inheritance in the yeast cell cycle

Cell proliferation requires the inheritance of subcellular organelles, yet little is known of the molecular basis of this essential process. Recent microscopy studies of the yeast Saccharomyces cerevisiae have characterized the cellular distribution of mitochondria, vacuoles and elements of the endoplasmic reticulum and Golgi complex. In addition, genetic and microscopical approaches have allowed the isolation and analysis of mutants defective in the inheritance of mitochondria and vacuoles. These investigations are leading to the identification of molecular components mediating the movement of organelles into daughter cells and have revealed that the inheritance of organelles is coordinated with other events of the cell division cycle.     

When parameters in dynamic models become phenotypes: a case study on flesh pigmentation in the chinook salmon (Oncorhynchus tshawytscha)

The Pacific chinook salmon occurs as both white- and red-fleshed populations, with the flesh color type (red or white) seemingly under strong genetic influence. Previously published data on crosses between red- and white-fleshed individuals cannot be reconciled with a simple Mendelian two-locus, two-allele model, pointing to either a more complex inheritance pattern or the existence of gene interactions. Here we show that a standard single-locus, three-allele model can fully explain these data. Moreover, by implementing the single-locus model at the parameter level of a previously developed mathematical model describing carotenoid dynamics in salmon, we show that variation at a single gene involved in the muscle uptake of carotenoids is able to explain the available data. This illustrates how such a combined approach can generate biological understanding that would not be possible in a classical population genetic explanatory structure. An additional asset of this approach is that by allowing parameters to become phenotypes obeying a given genetic model, biological interpretations of mechanisms involved at a resolution level far beyond what is built into the original dynamic model are made possible. These insights can in turn be exploited in experimental studies as well as in construction of more detailed models.