Inference from Clines Stabilized by Frequency-Dependent Selection

Frequency-dependent selection against rare forms can maintain clines. For weak selection, s, in simple linear models of frequency-dependence, single locus clines are stabilized with a maximum slope of between square root of s/square root of 8 sigma and square root of s/square root of 12 delta, where sigma is the dispersal distance. These clines are similar to those maintained by heterozygote disadvantage. Using computer simulations, the weak-selection analytical results are extended to higher selection pressures with up to three unlinked genes. Graphs are used to display the effect of selection, migration, dominance, and number of loci on cline widths, speeds of cline movements, two-way gametic correlations ("linkage disequilibria"), and heterozygote deficits. The effects of changing the order of reproduction, migration, and selection, are also briefly explored. Epistasis can also maintain tension zones. We show that epistatic selection is similar in its effects to frequency-dependent selection, except that the disequilibria produced in the zone will be higher for a given level of selection. If selection consists of a mixture of frequency-dependence and epistasis, as is likely in nature, the error made in estimating selection is usually less than twofold. From the graphs, selection and migration can be estimated using knowledge of the dominance and number of genes, of gene frequencies and of gametic correlations from a hybrid zone.     

Population dynamics of a gametophytic factor controlling selective fertilization

The population behavior of a gametophytic factor (Ga) which involves gametic selection due to failure ofga pollen onGa Ga orGa ga styles in competition withGa pollen, was investigated by computer simulation. A constant versus randomly varying gametic selection parameter (k) and four different schemes of zygotic selection were introduced in this model for analyzing conditions favorable for the maintenance of locusGa polymorphic in a large, mixed selfing and random mating population. Stable polymorphism was obtained only with rather substantial heterozygote advantage at locusGa whereas the opposing pressures of gametic and zygotic selection yielded fixation of alleleGa orga around a critical value of k instead of a range of k-values allowing nontrivial equilibria. With weak selection and stochastic k, however, very slow rates of change in the genotypic proportions allowed transient polymorphism. In these cases, the rate of outcrossing (t) and the initial frequency ofGa were critical in determining the rate of allelic substitution. Moreover, low values of t allowed the replacement of alleleGa byga even with rather weak zygotic selection. These findings on the balance between gametic and zygotic selection and a markedly frequency-dependent process are briefly discussed in relation to the dynamics of similar factors involving the mating system.     

Inbreeding depression and multiple regions showing heterozygote advantage in Drosophila melanogaster exposed to stress

Recent studies that reveal a correlation between heterozygosity and fitness in natural populations have rekindled interest in whether balancing selection is widespread or an evolutionary oddity. We therefore quantified heterozygote advantage at 12 microsatellite markers in both inbred and outbred crosses of Drosophila grown under different forms of environmental stress. As expected, inbreeding depression reduces fitness relative to the outbred controls. In addition, many loci exhibit heterozygote advantage over and above any effect due to inbreeding, with approximately 30% of markers showing an effect in any given culture condition and approximately 75% of markers showing an effect in at least one of the four culture conditions. To explore the extent of linkage disequilibrium surrounding these loci we further typed four new markers close to each of the three strongest hits. We find a pattern where the extent of heterozygote excess tends to decline to nonsignificance within around 1.5 megabases (Mb) either side of the original hit. Crude extrapolation suggests 12 genes or regions experience detectable levels of heterozygote advantage in any one condition and as many as 25 overall. Thus, balancing selection is widespread and is likely to play an important role in maintaining genetic variability.     

Environment-specific heterozygote deficiency and developmental instability in hybrid Mytilus

The multiple discrete hybrid zones that characterize Mytilus blue mussels allow a novel, non-manipulative, examination of the selective pressures that create and maintain species. If endogenous genetic incompatibility is solely responsible for post-zygotic isolation, then individuals of a specified hybrid genotype are expected to show similar average fitness across environments. However, if hybrid fitness differs across environments, then exogenous selection is implicated, either via ecological selection or environment-specific expression of intrinsic genetic incompatibilities. Correspondence between developmental instability of hybrids and heterozygote deficiency, estimated in two M. trossulus×M. galloprovincialis hybrid zones on the coast of North America, indicates that environment-dependent selection against hybrids may contribute to reproductive isolation among Pacific Mytilus species.     

Major histocompatibility complex (MHC) heterozygote superiority to natural multi-parasite infections in the water vole (Arvicola terrestris)

The fundamental role of the major histocompatibility complex (MHC) in immune recognition has led to a general consensus that the characteristically high levels of functional polymorphism at MHC genes is maintained by balancing selection operating through host–parasite coevolution. However, the actual mechanism by which selection operates is unclear. Two hypotheses have been proposed: overdominance (or heterozygote superiority) and negative frequency-dependent selection. Evidence for these hypotheses was evaluated by examining MHC–parasite relationships in an island population of water voles (Arvicola terrestris). Generalized linear mixed models were used to examine whether individual variation at an MHC class II DRB locus explained variation in the individual burdens of five different parasites. MHC genotype explained a significant amount of variation in the burden of gamasid mites, fleas (Megabothris walkeri) and nymphs of sheep ticks (Ixodes ricinus). Additionally, MHC heterozygotes were simultaneously co-infected by fewer parasite types than homozygotes. In each case where an MHC-dependent effect on parasite burden was resolved, the heterozygote genotype was associated with fewer parasites, and the heterozygote outperformed each homozygote in two of three cases, suggesting an overall superiority against parasitism for MHC heterozygote genotypes. This is the first demonstration of MHC heterozygote superiority against multiple parasites in a natural population, a mechanism that could help maintain high levels of functional MHC genetic diversity in natural populations.     

An improved method for heterozygote detection of cystinosis, using polymorphonuclear leukocytes.

Heterozygotes for the autosomal recessive disease cystinosis are currently detected by measuring the cystine content of mixed-leukocyte preparations. The present study was designed to reassess the accuracy of this method and to determine whether measuring the cystine content of purified polymorphonuclear leukocytes would improve heterozygote detection. Blood samples were obtained from 29 obligate heterozygotes for nephropathic cystinosis, one obligate heterozygote for benign cystinosis, and 18 individuals presumed to be normal. When the cystine content of mixed-leukocyte preparations was measured, three heterozygote values overlapped the normal range. When polymorphonuclear-leukocyte cystine content was measured, no heterozygote values were within the normal range. Measurement of the cystine content of purified preparations of polymorphonuclear leukocytes affords a simple method that improves the sensitivity of heterozygote detection for cystinosis.     

Meiotic analysis by FISH of a human male 46,XY,t(15;20)(q11.2;q11.2) translocation heterozygote: quadrivalent configuration,orientation and first meiotic segregation

Understanding the segregational behaviour of reciprocal tranlocations in man is of both theoretical and clinical importance. Generally, information for genetic counselling is obtained from empirical data although knowledge of gametic output can now be obtained by karyotyping individual human spermatozoa. However, neither empirical studies nor sperm karyotyping data provide detailed information on how the combinations of normal, balanced and unbalanced gametes arise. For this knowledge of quadrivalent orientation and first meiotic segregation is required. We have used dual colour fluorescence in situ hybridisation (FISH) to identify normal and derived chromosomes during meiosis in testicular biopsy material from a 46,XY,t(15;20)(q11.2;q11.2) heterozygote. We were able to determine the frequencies of different quadrivalent structures at first metaphase (MI) and the proportion of first meiotic divisions subject to interstitial chiasmata. Having identified all 2:2, 3:1 and 4:0 segregation products at second metaphase, it was possible to correlate segregation categories with the various forms of MI quadrivalent possibly indicating their modes of orientation. Finally the ratios of normal:balanced:unbalanced gametes expected to be produced by this translocation heterozygote were calculated.by T.C. Hsu     

Inbreeding,heterozygote advantage and the evolution of neo-X and neo-Y sex chromosomes

Associations between heterozygosities at different loci are generated by inbreeding. This can cause a fusion or translocation involving a sex chromosome and an autosome to have a selective advantage, when there is selection in favour of heterozygotes. Population genetic models of Y-autosome and X-autosome rearrangments in populations mating by a mixture of full sib-matings and random mating are described, in which the rearrangements cause an autosomal locus with heterozygote advantage to become linked to the true sex chromosomes. Such rearrangements gain a selective advantage under a wide range of conditions. If they can invade, Y-autosome rearrangements always spread to fixation, whereas X-autosome rearrangements may be maintained as stable polymorphisms. The results are discussed in relation to data on breeding systems and karyotypic evolution in termites.     

Nature of the heterozygote blood catalase in a hypocatalasemic mouse mutant

The blood catalase of a hypocatalasemic mouse mutant has been compared with that of the wild-type (normal) animal and with that of the heterozygote. Comparison is on the basis of stability to heat and to urea. Electrophoretic evidence is of no value, because all forms tested show the same mobility. Because the heterozygote heat and urea inactivation curves differ from those of the two parental forms, and because the curves are smoothly S-shaped, with no shoulders or other irregularities, it is suggested that this heterozygote produces only a single molecular form of the enzyme.Work supported under the auspices of the U.S. Atomic Energy Commission.     

Maladaptive mate choice maintained by heterozygote advantage

Common buzzards (Buteo buteo) show a plumage polymorphism that appears to be maintained by heterozygote advantage and allows a maladaptive form of mate choice to persist. The light and dark morphs have a much lower fitness than the presumed heterozygous intermediate morph, but are replenished through Mendelian segregation in intermediate-intermediate pairs. Light and dark morphs could maximize their fitness by mating light with dark to produce all intermediate offspring, but instead choose partners of their own color, thereby producing broods of minimally fit homozygotes. Such maladaptive behavior argues forcefully against mate choice based on "good genes," and its persistence is best explained by heterozygote advantage maintaining the polymorphism coupled with nongenetic mate choice based on sexual imprinting. Modeling different patterns of mate choice shows that random mating and preference for own morph fit our data poorly, whereas preference for mother's morph yields a good fit.     

Isoenzymes of serum N-acetyl-beta-D-glucosaminidase in the I cell disease heterozygote

Summary Serum N-acetyl-beta-D-hexosaminidase is compared quantitatively and qualitatively in 14 obligate heterozygotes for the mutant gene causing I cell disease (ICD) or mucolipidosis II and in 31 normal controls. The average specific activity in either group is significantly different but reliable heterozygote detection cannot be achieved because of some overlapping of the ranges of individual results. Fractionation of the enzyme either by DEAE cellulose column chromatography, or by heat inactivation, yields a typical average result for each genotype. Also, mere expression of the various components as percentages of the total activity is not useful for certain identification of the ICD heterozygote. There is considerable overlapping of the percents hexosaminidase I₁ and A in both groups of sera. If enzymatic hydrolysis by any component is expressed as a partial activity, a much between though not absolute distinction between the ICD heterozygote and the normal control becomes possible. Only the latter way of expression of hexosaminidase results makes distinction between the ICD heterozygote and the Tay-Sachs heterozygote very probable.The experimental work here presented was supported in part by grant No. 20.057 from the FGWO, Brussels, Belgium.     

Alkaptonuria caused by compound heterozygote mutations

Alkaptonuria is a rare autosomal recessive disorder of inborn errors of metabolism. It is characterised by the deposition of "ochronotic pigment" especially in connective tissue as a result of deficieny of the "homogentisic acid oxidase" enzyme which has a role in the catabolism of tyrosine and phenylalanine. A compound heterozygote alkaptonuria patient, with manifestations in adulthood, without infantile and childhood signs is presented. The described alkaptonuria mutations are reported for the first time in the Turkish population.     

Biased sex‐ratio and sex‐biased heterozygote disadvantage affect the maintenance of a genetic polymorphism and the properties of hybrid zones

The evolution of biodiversity is a major issue of modern biology, and it is becoming increasingly topical as the ongoing erosion of diversity puts serious threats on human well‐being. An elementary mechanism that allows maintaining diversity is the interplay between dispersal and heterozygote selective disadvantage, which can lead to self‐sustainable spatial genetic structures and is central to the stability of hybrid zones. Theoretical studies supporting the importance of this mechanism assume a balanced sex‐ratio and a heterozygote disadvantage equally affecting both sexes, despite the multiplicity of empirical evidence that (i) adult sex‐ratio is usually biased towards either male or female and that (ii) heterozygote disadvantage often affects a single sex. We expanded the existing theory by weighting the strength of selection against heterozygote according to the biased in sex‐ratio and in heterozygote disadvantage. The range of conditions allowing for the maintenance of polymorphism can then either double or vanish. We discuss the implications of such finding for birds, mammals and insects diversity. Finally, we provide simple analytical predictions about the effect of those biased on the width and speed of hybrid zones and on the time for the spread of beneficial mutations through such zones.     

Multilocus allozyme heterozygote deficiencies in Crepidula onyx: geographic and temporal patterns among adult snails in Mission Bay, California

Although the phenomenon of multilocus heterozygote deficienciesin numerous taxonomically diverse molluscs has been studiedfor over 30 years it has resisted general explanation. Herewe describe a case in Crepidula onyx Sowerby, a common protandrousslipper limpet on the Pacific coast of southern California.Spatial and temporal differentiation at 16 polymorphic allozymeloci were examined in samples of adult snails from three orfour seasons and six localities in Mission Bay, San Diego. Thepopulations were highly polymorphic (proportion of polymorphicloci P_L=0.65–0.69; mean individual heterozygosity H_O=0.13–0.29)and although there were slightly more changes in allele frequencybetween autumn and winter than between winter and spring, statisticallysignificant spatial and temporal change or patterning was notdetected. If the larvae are passive dispersers the lack of populationstructure is attributable to the fact that during any three-weekperiod that they are in the plankton, the waters of MissionBay are completely mixed by tidal currents. In marked contrast,statistically significant heterozygote deficiencies were foundin all samples (locality and season) and subsamples (males andfemales). At each locality and season, deficiencies were aspronounced in males as in females. Furthermore, at each locality,there was no increase in level of multilocus deficiency betweenmales in one season and females in a subsequent season. We concludethat the heterozygotes had been lost in the larval planktonicstage or at the time of metamorphosis and settlement. Severalhypotheses to explain the heterozygote deficiencies in adultsare discussed: inbreeding, self-fertilization, presence of nullalleles, allele scoring bias, aneuploidy, parental imprinting,spatial and temporal Wahlund effects, age-effects, and directnatural selection on the marker loci. Although we can rejectsome of these hypotheses, others like inbreeding, require testingwith markers with greater statistical power. Wahlund effectsdue to inadvertent mixing of two cryptic species and/or micro-spatialpopulation genetic structuring due to reproductive asynchroniesappear unlikely causes. Natural selection against heterozygotesin the larval phase of life may account for the observations,but selection does not appear to operate directly on any ofthe individual loci studied. An hypothesis is offered to explainthe general selection against heterozygotes during the pelagiclarval stage, and for the reverse during the sessile adult stage.Selection coefficients would, however, have to be unusuallyhigh and we conclude that we are unable satisfactorily to explainour observations. (Received 5 December 2005; accepted 30 March 2006)     

Evolution of Zygotic Linkage Disequilibrium in a Finite Local Population

One crucial feature of zygotic linkage disequilibrium (LD) analysis is its direct use of diploid genotyping data, irrespective of the type of mating system. Previous theories from an evolutionary perspective mainly focus on gametic LD, but the equivalent development for zygotic LD is not available. Here I study the evolution of zygotic LD and the covariances between gametic and zygotic LDs or between distinct zygotic LDs in a finite local population under constant immigration from a continent population. I derive the analytical theory under genetic hitchhiking effects or in a neutral process. Results indicate that zygotic LDs (diploid level) are more informative than gametic LD (haploid level) in indicating the effects of different evolutionary forces. Zygotic LDs may be greater than or comparable to gametic LD under the epistatic selection process, but smaller than gametic LD under the non epistatic selection process. The covariances between gametic and zygotic LDs are strongly affected by the mating system, linkage distance, and genetic drift effects, but weakly affected by seed and pollen flow and natural selection. The covariances between different zygotic LDs are generally robust to the effects of gene flow, selection, and linkage distance, but sensitive to the effects of genetic drift and mating system. Consistent patterns exist for the covariances between the zygotic LDs for the two-locus genotypes with one common genotype at one locus or without any common genotype at each locus. The results highlight that zygotic LDs can be applied to detecting natural population history.     

A general multilocus two-allele model for epistatic selection

Observations show that evolutionary processes often relate to multilocus epistatic selection. Here we develop further the approach suggested earlier by Zhivotovsky and Gavrilets to admit arbitrary multilocus epistasis. The obtained dynamic equations for allelic frequencies and gametic disequilibria are represented in a simple form. If selection is weak, this result extends Wright’s evolutionary equation to the case of cis-trans effects and sex differences in both recombination rates and genotypic fitnesses. Additionally to Wright’s equations for allelic frequencies, we derive equations for the gametic disequilibrium terms. We also give a general expression for the gametic disequilibria in a quasi-linkage state.     

The multiple-locus symmetric fertility model

Selection due to variation in the fecundity among matings of genotypes with respect to many loci each with two alleles is studied. The fitness of a mating depends only on the genotypic distinction between homozygote and heterozygote at each locus in the two individuals, and differences among loci are allowed. This symmetric fertility model is therefore a generalization of the multiple-locus symmetric viability model. The phenomena seen in the two-locus symmetric fertility model generalize—e.g., the possibility of joint stability of equilibria with linkage equilibrium and with linkage disequilibrium, and the existence of different types of totally polymorphic equilibria with the gametic proportions in linkage equilibrium. The central equilibrium with genotypic frequencies in Hardy-Weinberg proportions and gametic frequencies in Robbins proportions exists for all symmetric fertility models. For some symmetric fertility regimes additional equilibria exist with gametic frequencies in linkage equilibrium and with genotypic frequencies in Hardy-Weinberg proportions at all except one locus. These equilibria may exist in the dioecious symmetric viability model, and then they will be locally stable. For free recombination the stable equilibria show linkage equilibrium, but several of these with different numbers of polymorphic loci may be stable simultaneously.     

Hair follicle initiation in reciprocal recombinations of downless homozygote and heterozygote mouse tail epidermis and dermis

In the development of structures formed by the interaction of an epithelium and its underlying mesenchyme, the mesenchyme appears to be generally responsible for inducing the initiation of development. On the other hand, the epithelium must be competent to respond to the inductive stimulus if a structure is to be produced. One of the effects of the autosomal recessive mouse mutation downless is to suppress tail hair follicle initiation. Failure of initiation could therefore be due to failure in either the epidermal or the dermal component of the system, or both. Reciprocal recombinations between downless homozygote and heterozygote tail epidermis and dermis were made prior to the time when the first signs of follicle formation are visible in the tails of normal mice, and the recombined elements were allowed to continue growth and differentiation on the chick chorioallantoic membrane. The results suggest that the primary mutant effect is restricted to the epidermis. Explants composed of heterozygote epidermis with either heterozygote or homozygote dermis produced follicles, whereas explants composed of homozygote epidermis with either homozygote or heterozygote dermis did not.     

Reliable selfing rate estimates from imperfect population genetic data

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies (FIS) and obtain the selfing rate s from FIS = s/(2 - s), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of FIS and free of technical biases. Their statistical power and precision are comparable to those of FIS, although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not FIS. We analyse four real data sets spanning a range of mating systems. In two examples, we obtain s = 0 despite positive FIS, strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and user-friendly software called rmes (robust multilocus estimate of selfing) available at http://ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progeny-array approaches, to investigate selfing rates.