Competition at the Mouse t Complex: Rare Alleles Are Inherently Favored

We investigate the competition between alleles at a segregation distorter locus. The focus is on the invasion prospects of rare mutant distorter alleles in a population in which a wildtype and a resident distorter allele are present. The parameters are chosen to reflect the situation at the t complex of the house mouse, one of the best-studied examples of segregation distortion. By analyzing the invasion chances of rare alleles, we provide an analytical justification of earlier simulation results. We show that a new distorter allele can successfully invade even if it is inferior both at the gamete and at the individual level. In fact, newly arising distorter alleles have an inherent rareness advantage if their negative fitness consequences are restricted to homozygous condition. Likewise, rare mutant wildtype alleles may often invade even if their viability or fertility is reduced. As a consequence, the competition between alleles at a segregation distorter locus should lead to a high degree of polymorphism. We discuss the implications of this conclusion for the t complex of the house mouse and for the evolutionary stability of “honest” Mendelian segregation.     

EVOLUTION AT THE MOUSE t COMPLEX: WHY IS THE t HAPLOTYPE PRESERVED AS AN INTEGRAL UNIT?

Abstract Segregation distorters are selfish genetic elements that bias Mendelian segregation in their favor. All well-known segregation distortion systems consist of one or more "distorter" loci that act upon a "responder" locus. At the t complex of the house mouse, segregation distortion is brought about by the harmful effect of t alleles at a number of distorter loci on the wild-type variant of the responder locus. The responder and distorter alleles are closely linked by a number of inversions, thus forming a coherent t haplotype. It has been conjectured that the close integration of the various components into a "complete" t haplotype has been crucial for the evolutionary success of these selfish genetic elements. By means of a population genetical metapopulation model, we show that this intuition may be unfounded. In fact, under most circumstances an "insensitive" t haplotype retaining only the responder did invade and reach a high frequency, despite the fact that this haplotype has a strong segregation disadvantage. For certain population structures, the complete t haplotype was even competitively excluded by partial t haplotypes with lower segregation ratios. Moreover, t haplotypes carrying one or more recessive lethals only prevailed over their nonlethal counterparts if the product of local population size and migration rate ( Nm ) was not much smaller or larger than one. These phenomena occurred for rather realistic fitness, segregation, and recombination values. It is therefore quite puzzling that partial t haplotypes are absent from natural house mousepopulations, and that t haplotypes carrying recessive lethals prevail over nonlethal t haplotypes.     

Segretation distortion in a deme-structured population: opposing demands of gene,individual and group selection

The evolution of segregation distortion is governed by the interplay of selection at different levels. Despite their systematic advantage at the gamete level, none of the well-known segregation distorters spreads to fixation since they induce severe negative fitness effects at the individual level. In a deme-structured population, selection at the population level also plays a role. By means of a population genetical model, we analyse the various factors that determine the success of a segregation distorter in a metapopulation. Our focus is on the question of how the success of a distorter allele is affected by its segregation ratio and its fitness effects at the individual level. The analysis reveals that distorter alleles with high segregation ratios are the best invaders and reach the highest frequencies within single demes. However, the productivity of a deme harbouring a distorter with a high segregation ratio may be significantly reduced. As a consequence, an efficient distorter will be underrepresented in the migrant pool and, moreover, it may increase the probability of deme extinction. In other words, efficient distorters with high segregation ratios may well succumb to their own success. Therefore, distorters with intermediate segregation ratios may reach the highest frequency in the metapopulation as a result of the opposing forces of gamete, individual and group selection. We discuss the implications of this conclusion for the t complex of the house mouse.     

On the evolutionary stability of Mendelian segregation

We present a model of a primary locus subject to viability selection and an unlinked locus that causes sex-specific modification of the segregation ratio at the primary locus. If there is a balanced polymorphism at the primary locus, a population undergoing Mendelian segregation can be invaded by modifier alleles that cause sex-specific biases in the segregation ratio. Even though this effect is particularly strong if reciprocal heterozygotes at the primary locus have distinct viabilities, as might occur with genomic imprinting, it also applies if reciprocal heterozygotes have equal viabilities. The expected outcome of the evolution of sex-specific segregation distorters is all-and-none segregation schemes in which one allele at the primary locus undergoes complete drive in spermatogenesis and the other allele undergoes complete drive in oogenesis. All-and-none segregation results in a population in which all individuals are maximally fit heterozygotes. Unlinked modifiers that alter the segregation ratio are unable to invade such a population. These results raise questions about the reasons for the ubiquity of Mendelian segregation.     

Selection and segregation distortion in a sex-differentiated population

We extend the classical model for selection at an autosomal locus in a sex-differentiated population to include segregation distortion. The equations remain the same, but the fitness parameters are interpreted differently and refer to alleles instead of genotypes. We derive conditions for internal and external stability of the equilibria, i.e., stability with respect to perturbations of alleles that are already present at equilibrium and stability with respect to invasion attempts by newly arising alleles. We show that, in a sex-differentiated population, external stability of an equilibrium can be judged on the basis of Shaw--Mohler criteria. Throughout, we compare the situation in populations with and without sex differentiation. Interestingly, internal stability is more difficult to achieve in a population without sex differentiation than in a population in which selection and segregation distortion are restricted to one sex. In a companion paper we show how the general results of the present paper can lead to new insights into specific systems such as the t complex of the house mouse.     

Evolution of the segregation ratio: modification of gene conversion and meiotic drive

We compare the evolutionary pressures that direct the modification of gene conversion and meiotic drive at loci subject to purifying and overdominant viability selection. Gene conversion differs from meiotic drive in that modifers do not affect their own segregation ratios, even when linked to the viability locus. Segregation distortion generates gametic level disequilibria between alleles at the viability locus and modifiers of gene conversion and meiotic drive: enhancers of segregation distortion become positively associated with driven alleles. Suppression of gene conversion evolves if the driven allele is marginally disadvantageous (overdominant viability selection), and higher rates evolve if the driven alleles are relatively advantageous (purifying viability selection). Gametic disequilibria permit enhancers of meiotic drive that are linked to the driven locus to promote their own segregation. We attribute the failure of genetic modifiers of gene conversion and meiotic drive to maximinize mean fitness to the generation of such associations.     

Sex‐specific recombination rates and allele frequencies affect the invasion of sexually antagonistic variation on autosomes

The introduction and persistence of novel, sexually antagonistic alleles can depend upon factors that differ between males and females. Understanding the conditions for invasion in a two‐locus model can elucidate these processes. For instance, selection can act differently upon the sexes, or sex linkage can facilitate the invasion of genetic variation with opposing fitness effects between the sexes. Two factors that deserve further attention are recombination rates and allele frequencies – both of which can vary substantially between the sexes. We find that sex‐specific recombination rates in a two‐locus diploid model can affect the invasion outcome of sexually antagonistic alleles and that the sex‐averaged recombination rate is not necessarily sufficient to predict invasion. We confirm that the range of permissible recombination rates is smaller in the sex benefitting from invasion and larger in the sex harmed by invasion. However, within the invasion space, male recombination rate can be greater than, equal to or less than female recombination rate in order for a male‐benefit, female‐detriment allele to invade (and similarly for a female‐benefit, male‐detriment allele). We further show that a novel, sexually antagonistic allele that is also associated with a lowered recombination rate can invade more easily when present in the double heterozygote genotype. Finally, we find that sexual dimorphism in resident allele frequencies can impact the invasion of new sexually antagonistic alleles at a second locus. Our results suggest that accounting for sex‐specific recombination rates and allele frequencies can determine the difference between invasion and non‐invasion of novel, sexually antagonistic alleles in a two‐locus model.     

On the evolution of fluctuating segregation distortion

Previous mathematical models of the genetic control by one locus of the segregation at another have all concluded that alleles causing departures from Mendelian segregation should succeed. In this study the segregation ratios induced at the major locus by the modifier locus fluctuate cyclically. It is shown that if initially there is Mendelian segregation and if the rare modifying allele induces symmetric fluctuation about the Mendelian ratios it cannot succeed. It is further proven that if initially there are symmetric fluctuations about Mendelian segregation then an allele reducing the amplitude of the fluctuation will succeed.     

The evolution of costly mate choice against segregation distorters

The evolution of female preference for male genetic quality remains a controversial topic in sexual selection research. One well‐known problem, known as the lek paradox, lies in understanding how variation in genetic quality is maintained in spite of natural selection and sexual selection against low‐quality alleles. Here, we theoretically investigate a scenario where females pay a direct fitness cost to avoid males carrying an autosomal segregation distorter. We show that preference evolution is greatly facilitated under such circumstances. Because the distorter is transmitted in a non‐Mendelian fashion, it can be maintained in the population despite directional sexual selection. The preference helps females avoid fitness costs associated with the distorter. Interestingly, we find that preference evolution is limited if the choice allele induces a very strong preference or if distortion is very strong. Moreover, the preference can only persist in the presence of a signal that reliably indicates a male's distorter genotype. Hence, even in a system where the lek paradox does not play a major role, costly preferences can only spread under specific circumstances. We discuss the importance of distorter systems for the evolution of costly female choice and potential implications for the use of artificial distorters in pest control.     

Nonrandom segregation during meiosis: the unfairness of females

Most geneticists assume that chromosome segregation during meiosis is Mendelian (i.e., each allele at each locus is represented equally in the gametes). The great majority of reports that discuss non-Mendelian transmission have focused on systems of gametic selection, such as the mouse t-haplotype and Segregation distorter in Drosophila, or on systems in which post-fertilization selection takes place. Because the segregation of chromosomes in such systems is Mendelian and unequal representation of alleles among offspring is achieved through gamete dysfunction or embryonic death, there is a common perception that true disturbances in the randomness of chromosome segregation are rare and of limited biological significance. In this review we summarize data on nonrandom segregation in a wide variety of genetic systems. Despite apparent differences between some systems, the basic requirements for nonrandom segregation can be deduced from their shared characteristics: i) asymmetrical meiotic division(s); ii) functional asymmetry of the meiotic spindle poles; and iii) functional heterozygosity at a locus that mediates attachment of a chromosome to the spindle. The frequency with which all three of these requirements are fulfilled in natural populations is unknown, but our analyses indicate that nonrandom segregation occurs with sufficient frequency during female meiosis, and in exceptional cases of male meiosis, that it has important biological, clinical, and evolutionary consequences. Received: 28 December 2000 / Accepted: 23 January 2001     

Gene dosage effects on transmission ratio distortion and fertility in mice that carry t haplotypes

Complete t haplotypes can be transmitted at distorted ratios from heterozygous +/t male mice as a consequence of t-specific alleles at a series of t complex distorter loci (Tcd-1t through Tcd-4t) and a t complex responder locus. Partial t haplotypes that lack the Tcd-2t allele cannot be transmitted at the very high ratios characteristic of complete t haplotypes. The breeding studies reported here tested the possibility that the absence of Tcd-2t could be compensated for by the presence of double doses of other Tcdt alleles. The results indicate that a double dose of Tcd-4t alone will not work, but that a double dose of both Tcd-1t and Tcd-4t can promote a very high transmission ratio in the absence of Tcd-2t. These results suggest that the extent to which transmission ratios are distorted is dependent upon the absolute level of expression of the individual Tcd genes. Further studies of genotypic effects on transmission ratio distortion, as well as fertility, lead to the suggestion of a fifth t complex distorter (Tcd-5) locus within t haplotypes.     

The evolution of recombination in permanent translocation heterozygotes

The evolution of a selectively neutral locus that controls the degree to which alleles at a single selected locus are linked with a particular set of chromosomes in a permanent translocation heterozygote is studied. With complete selfing and fitness overdominance a new allele at the modifying locus will increase in frequency if it increases the linkage of all alleles at the selected locus to a particular set of chromosomes. With random mating a new allele at the modifying locus will increase when rare if it increases the linkage of alleles at the selected locus to a particular set of chromosomes. In addition, a parameter analogous to the coefficient of linkage disequilibrium in usual two-locus models with random mating must be nonzero if a new allele at the modifying locus is to increase in frequency at a geometric rate when rare. With mixed selfing and random mating a new allele at the modifying locus will apparently increase when rare only if it increases the linkage of alleles at the selected locus to a particular set of chromosomes.     

Evolution of dominance under frequency-dependent intraspecific competition

A population-genetic analysis is performed of a two-locus two-allele model, in which the primary locus has a major effect on a quantitative trait that is under frequency-dependent disruptive selection caused by intraspecific competition for a continuum of resources. The modifier locus determines the degree of dominance at the trait level. We establish the conditions when a modifier allele can invade and when it becomes fixed if sufficiently frequent. In general, these are not equivalent because an unstable internal equilibrium may exist and the condition for successful invasion of the modifier is more restrictive than that for eventual fixation from already high frequency. However, successful invasion implies global fixation, i.e., fixation from any initial condition. Modifiers of large effect can become fixed, and also invade, in a wider parameter range than modifiers of small effect. We also study modifiers with a direct, frequency-independent deleterious fitness effect. We show that they can invade if they induce a sufficiently high level of dominance and if disruptive selection on the ecological trait is strong enough. For deleterious modifiers, successful invasion no longer implies global fixation because they can become stuck at an intermediate frequency due to a stable internal equilibrium. Although the conditions for invasion and for fixation if sufficiently frequent are independent of the linkage relation between the two loci, the rate of spread depends strongly on it. The present study provides further support to the view that evolution of dominance may be an efficient mechanism to remove unfit heterozygotes that are maintained by balancing selection. It also demonstrates that an invasion analysis of mutants of very small effect is insufficient to obtain a full understanding of the evolutionary dynamics under frequency-dependent selection.     

Multiple mating,sperm competition and meiotic drive

Most discussions of ‘sperm competition’ have ignored the potential for competition among the different sperm genotypes present in the ejaculate of a single male. Rivalry within ejaculates may limit cooperation among the members of an ejaculate when they compete with sperm produced by other males. A gene that gains an advantage in competition within an ejaculate (a segregation distorter) may increase in frequency even if it is associated with significant costs to organismal fitness. Therefore, selection will favor genes expressed in males that suppress competition within ejaculates. This may explain why sperm function is largely controlled by the diploid genotype of the male progenitor, rather than by the genotypes of individual haploid sperm. Females who mate with multiple males reduce the relative advantage of a segregation distorter whenever the distorter impairs the competitive effectiveness of the ejaculates in which it occurs. If the distorter is associated with costs to organismal fitness, selection will favor female mating behavior that reduces the distorter's equilibrium frequency. Competition within ejaculates may thus be one reason why females choose to mate with multiple males.     

Physical mapping of male fertility and meiotic drive quantitative trait loci in the mouse t complex using chromosome deficiencies

The t complex spans 20 cM of the proximal region of mouse chromosome 17. A variant form, the t haplotype (t), exists at significant frequencies in wild mouse populations and is characterized by the presence of inversions that suppress recombination with wild-type (+) chromosomes. Transmission ratio distortion and sterility are associated with t and affect males only. It is hypothesized that these phenomena are caused by trans-acting distorter/sterility factors that interact with a responder locus (Tcr(t)) and that the distorter and sterility factors are the same because homozygosity of the distorters causes male sterility. One factor, Tcd1, was previously shown to be amorphic using a chromosome deletion. To overcome limitations imposed by recombination suppression, we used a series of deletions within the t complex in trans to t chromosomes to characterize the Tcd1 region. We find that the distorter activity of Tcd1 is distinct from a linked sterility factor, originally called tcs1. YACs mapped with respect to deletion breakpoints localize tcs1 to a 1.1-Mb interval flanked by D17Aus9 and Tctex1. We present evidence for the existence of multiple proximal t complex regions that exhibit distorter activity. These studies demonstrate the utility of chromosome deletions for complex trait analysis.     

Transitions in the evolution of meiosis

Meiosis may have evolved gradually within the eukaryotes with the earliest forms having a one‐step meiosis. It has been speculated that the putative transition from a one‐step meiosis without recombination to one with recombination may have been stimulated by the invasion of Killer alleles. These imaginary selfish elements are considered to act prior to recombination. They prime for destruction (which occurs after cell division) the half of the cell on the opposite side of the meiotic spindle. Likewise the transition from one‐step to two‐step meiosis might have been stimulated by a subtly different sort of imaginary distorter allele, a SisterKiller. These are proposed to act after recombination. It has yet to be established that the presence of such distorter alleles could induce the transitions in question. To investigate these issues we have analysed the dynamics of a modifier (1) of recombination and (2) of the number of steps of meiosis, as they enter a population with one‐step meiosis. For the modifier of recombination, we find that invasion conditions are very broad and that persistence of Killer and modifier is likely through most parameter space, even when the recombination rate is low. However, if we allow a Killer element to mutate into one that is self‐tolerant, the modifier and the nonself‐tolerant alleles are typically both lost from the population. The modifier of the number of steps can invade if the SisterKiller acts at meiosis II. However, a SisterKiller acting at meiosis I, far from promoting the modifier’s spread, actually impedes it. In the former case the invasion is easiest if there is no recombination. The SisterKiller hypothesis therefore fails to provide a reasonable account of the evolution of two‐step meiosis with recombination. As before, the evolution of self‐tolerance on the part of the selfish element destroys the process. We conclude that the conditions under which SisterKillers promote the evolution of two‐step meiosis are very much more limited than originally considered. We also conclude that there is no universal agreement between ESS and modifier analyses of the same transitions.     

COMPETITION BETWEEN SEGREGATION DISTORTERS: COEXISTENCE OF “SUPERIOR” AND “INFERIOR” HAPLOTYPES AT THE t COMPLEX

By means of population genetical models, we investigate the competition between sex-specific segregation distorters. Although the models are quite general, they are motivated by a specific example, the t complex of the house mouse. Some variants at this gene complex, the t haplotypes, distort Mendelian segregation in heterozygous males in their favor. The selective advantage at the gamete level is counterbalanced by strong negative fitness effects at the individual level (male sterility or even lethality in both sexes). A plethora of different t haplotypes has been found, both in the field and in the lab. Up to now, however, models have focused on the equilibrium frequency of a single t haplotype. In contrast, we explicitly model the competition between several t haplotypes. A deterministic model for a large, well-mixed population predicts a surprisingly high degree of polymorphism. Haplotypes with seemingly inferior fitness characteristics may easily coexist with “superior” haplotypes. For instance, a lethal haplotype with a low segregation ratio may stably coexist with a sterile haplotype with a high segregation ratio. Stable coexistence is even possible for haplotypes with a segregation disadvantage. A simple stochastic model shows that the same principles apply in the context of a structured metapopulation. Although counterintuitive at first sight, all our results can be explained by the fact that segregation distorters have an inherent advantage when they are rare. We conclude that fitness comparisons are not sufficient to predict the outcome of competition when selective forces are acting at different levels.     

Co-segregation and heteroplasmy of two coding-region mtDNA mutations within a matrilineal pedigree

The ENG1 Lebers hereditary optic neuropathy (LHON) family spans six generations and comprises more than 90 maternally related individuals. In this pedigree, the G:A LHON mutation at nucleotide position 11778 shows a complex pattern of segregation in which it is homoplasmic mutant in two branches, homoplasmic wildtype in another, and heteroplasmic in a fourth branch. In addition, there is co-segregation of the 11778 mutant allele and of a G:A silent polymorphism at nucleotide position 5471 in 18 of 19 family members. This co-segregation indicates that the two substitutions arose either simultaneously, or nearly so, in the same founder mtDNA molecule. However, the highly divergent mitochondrial allele ratios in the one family member suggest that there has been a complex origin and segregation history of these two substitutions. Taking all of the results into consideration, the evidence supports sequential single mutations at sites 5471 and 11778, in close temporal proximity, with subsequent segregation of the intermediate mutational genotype to high levels in one branch of the ENG1 LHON family. In other branches, either the double wildtype or double mutant genotype has become essentially homoplasmic.     

The vit gene maps to the mi (microphthalmia) locus of the laboratory mouse.

The murine model for human vitiligo (the vit/vit mouse) develops progressive depigmentation of the pelage, skin, and eyes. The vit gene is inherited as an autosomal recessive. We have used classical breeding and isozyme marker analysis to map this vit gene that produces a vitiligo-like condition in the mouse. Crossbreeding the C57BL/6J-vit/vit mice with C57BL/6J mice carrying the Miwh and/or miws alleles at the microphthalmia locus resulted in mutant phenotypes, demonstrating absence of complementation. When vit is heterozygous with the Miwh allele, a "blotched" pigment pattern results. When it is heterozygous with the miws allele, a novel expression of the vitiliginous phenotype results. Further mating analysis of these crossbred populations demonstrates allelic inheritance between vit and the alleles at the microphthalmia locus. Other breeding studies using alleles at the agouti, belted, brown, dominant spotting, extension, mahogany, patch, and piebald loci did not demonstrate pigmentation explainable by allelic inheritance with the vit gene. Also, vit was tested for linkage with isozyme markers located on chromosomes 1, 4, 5, 7, 9, and 11, and results were negative. Therefore, the vit (vitiligo) gene of the laboratory mouse has been mapped to the mi (microphthalmia) locus on chromosome 6. The gene properly should be designated as mivit.     

Localization of the gene for plasma retinol binding protein to the distal half of mouse chromosome 19

A DNA polymorphism for the mouse retinol binding protein has been identified using the enzyme BamHI and a rat partial cDNA probe. Analysis of the polymorphism in DNA from 64 inbred mouse strains demonstrated the presence of a single gene with two alleles, Rbp-4b and Rbp-4d. Comparison of the segregation patterns of these alleles in three sets of recombinant inbred strains with allele segregation patterns of previously characterized loci shows that the Rbp-4 locus is closely linked to the locus for phenobarbital-inducible cytochrome P450-2c (Cyp-2c) that has been shown by in situ hybridization to lie on chromosome 19, bands D1-D2. The Rbp-4 locus is just proximal to Cyp-2c at the distal end of chromosome 19.