Gametic conflict versus contact in the evolution of anisogamy

Anisogamy refers to gametes that differ in size, and characterizes the difference between males and females. The evolution of aniosgamy is widely interpreted as involving conflict between gamete producers with small sperm parasitizing on the investment made by the eggs. Using a population genetic model for evolution at a locus that codes jointly for sperm and egg sizes of a hermaphrodite, we show that the origin of anisogamy in an externally spawning population need not involve conflict between gamete producers. Gamete size dimorphism may be an adaptation that increases gamete encounter rates when large zygotes are selected, and we show this in a mechanistically general individual selection model. We use the Vance survival function without specific allometric assumptions to model the zygote fitness dependence on its size, and hence obtain ecological and life-history correlates of isogamy and anisogamy, which we successfully compare with data from Volvocales.     

Descent measures for two loci with some applications

For any four genes, two at each of two loci, in a population, a 15 component descent measure has been introduced. These components are the probabilities of the 15 possible arrangements on a set of initial gametes of those genes of which the four of interest are copies. Since identity by descent of genes is equivalent to their being copies of a single gene on an initial gamete, descent measures have inbreeding coefficients as special cases. The individual descent measure, defined for four genes on two uniting gametes can be evaluated for any pedigree by means of an algorithm developed here. If initial gametic frequencies are specified, descent measures allow genotypic frequencies and disequilibria functions at one and two loci to be found. The procedures are illustrated for selfing and for sib mating. Several applications of the descent measures are discussed.     

Lines of descent in the diffusion approximation of neutral Wright-Fisher models

This paper studies lines of descent in the diffusion approximation of neutral Wright-Fisher models where the mutation rate away from each gene per generation is the same. Here a line of descent begins with a single gene and has branches at each generation where genes are reproduced from a parent in the line. New mutations are not included in a line of descent but are considered to begin a new line. The joint distribution of the number of lines of descent surviving in a population from time 0 to time t and the frequencies in these lines is derived. Expected times between loss of lines of descent are found. The distribution of the number of lines of descent in a sample from the population is derived. This leads to the distribution of the number of types in a sample from a nonstationary infinite alleles population.     

The iso1 gene of Chlamydomonas is involved in sex determination.

Sexual differentiation in the heterothallic alga Chlamydomonas reinhardtii is controlled by two mating-type loci, mt+ and mt-, which behave as a pair of alleles but contain different DNA sequences. A mutation in the mt minus-linked imp11 gene has been shown previously to convert a minus gamete into a pseudo-plus gamete that expresses all the plus gametic traits except the few encoded by the mt+ locus. Here we describe the iso1 mutation which is unlinked to the mt- locus but is expressed only in minus gametes (sex-limited expression). A population of minus gametes carrying the iso1 mutation behaves as a mixture of minus and pseudo-plus gametes: the gametes isoagglutinate but they do not fuse to form zygotes. Further analysis reveals that individual gametes express either plus or minus traits: a given cell displays one type of agglutinin (flagellar glycoprotein used for sexual adhesion) and one type of mating structure. The iso1 mutation identifies a gene unlinked to the mating-type locus that is involved in sex determination and the repression of plus-specific genes.     

Prediction of effects of genetic drift on variance components under a general model of epistasis

For a model of diallelic loci with arbitrary epistasis, Barton and Turelli [2004. Effects of genetic drift on variance components under a general model of epistasis. Evolution 58, 2111-2132] gave results for variances among and within replicate lines obtained by inbreeding without selection. Here, we discuss the relation between their population genetic methods and classical quantitative genetic arguments. In particular, we consider the case of no dominance using classical identity by descent arguments, which generalizes their results from two alleles to multiple alleles. To clarify the connections between the alternative methods, we obtain the same results using an intermediate method, which explicitly identifies the statistical effects of sets of loci. We also discuss the effects of population bottlenecks on covariances among relatives.     

Evolution of hierarchical cytoplasmic inheritance in the plasmodial slime mold Physarum polycephalum

A striking linear dominance relationship for uniparental mitochondrial transmission is known between many mating types of plasmodial slime mold Physarum polycephalum. We herein examine how such hierarchical cytoplasmic inheritance evolves in isogamous organisms with many self-incompatible mating types. We assume that a nuclear locus determines the mating type of gametes and that another nuclear locus controls the digestion of mitochondria DNAs (mtDNAs) of the recipient gamete after fusion. We then examine the coupled genetic dynamics for the evolution of self-incompatible mating types and biased mitochondrial transmission between them. In Physarum, a multiallelic nuclear locus matA controls both the mating type of the gametes and the selective elimination of the mtDNA in the zygotes. We theoretically examine two potential mechanisms that might be responsible for the preferential digestion of mitochondria in the zygote. In the first model, the preferential digestion of mitochondria is assumed to be the outcome of differential expression levels of a suppressor gene carried by each gamete (suppression-power model). In the second model (site-specific nuclease model), the digestion of mtDNAs is assumed to be due to their cleavage by a site-specific nuclease that cuts the mtDNA at unmethylated recognition sites. Also assumed is that the mtDNAs are methylated at the same recognition site prior to the fusion, thereby being protected against the nuclease of the same gamete, and that the suppressor alleles convey information for the recognition sequences of nuclease and methylase. In both models, we found that a linear dominance hierarchy evolves as a consequence of the buildup of a strong linkage disequilibrium between the mating-type locus and the suppressor locus, though it fails to evolve if the recombination rate between the two loci is larger than a threshold. This threshold recombination rate depends on the number of mating types and the degree of fitness reduction in the heteroplasmic zygotes. If the recombination rate is above the threshold, suppressor alleles are equally distributed in each mating type at evolutionary equilibrium. Based on the theoretical results of the site-specific nuclease model, we propose that a nested subsequence structure in the recognition sequence should underlie the linear dominance hierarchy of mitochondrial transmission.     

Analyse des pedigrees et calcul des coefficients d'identité par les arbres géniques

Two genes in a pedigree are identical by descent if they are two copies of a common ancestor gene. To obtain an unambiguous definition of the set of genes, at some autosomal locus, any gene is defined as an ordered pair of zygotes: the zygote who carries the gene, and the parent who transmitted it. The natural ordered structure on the set of zygotes yields an ordered structure upon the set of genes. Any event of the mendelian segregation splits down the set of genes into non-overlaping classes of identical genes: when considered as an ordered sub-set of genes, each class is shown to have the algebraic properties of a tree. Given a sub-set ?? of genes, a family of exclusive events ensuring identity between all genes of ?? is identified as a family of genic trees with some property. This relationship between segregational events and genic trees is extended to the case where two sub-sets ?? and ??′ of genes are considered together. As a consequence, a general method is obtained to compute either identity coefficients involving any number of genes splitted into one or two identity classes, or the fifteen coefficients defined among four genes, whichever the relationships between zygotes and genes might be. Using this approach to deal with the allelic structure in a set of genes carried by related zygotes is suggested.     

Impact on Reindeer (Rangifer tarandus) Genetic Diversity from Two Parallel Population Bottlenecks Founded from a Common Source

Population bottlenecks and founder events reduce genetic diversity through stochastic processes associated with the sampling of alleles at the time of the bottleneck, and the recombination of alleles that are identical by descent. At the same time bottlenecks and founder events can structure populations through the stochastic distortion of allele frequencies. Here we undertake an empirical assessment of the impact of two independent bottlenecks of known size from a known source, and consider inference about evolutionary process in the context of simulations and theoretical expectations. We find a similar level of reduced variation in the parallel bottleneck events, with the greater impact on the population that began with the smaller number of females. The level of diversity remaining was consistent with model predictions, but only if re-growth of the population was essentially exponential and polygeny was minimal at the early stages. There was a high level of differentiation seen compared to the source population and between the two bottlenecked populations, reflecting the stochastic distortion of allele frequencies. We provide empirical support for the theoretical expectations that considerable diversity can remain following a severe bottleneck event, given rapid demographic recovery, and that populations founded from the same source can become quickly differentiated. These processes may be important during the evolution of population genetic structure for species affected by rapid changes in available habitat.     

Modeling extent and distribution of zygotic disequilibrium: implications for a multigenerational canine pedigree

Unlike gametic linkage disequilibrium defined for a random-mating population, zygotic disequilibrium describes the nonrandom association between different loci in a nonequilibrium population that deviates from Hardy-Weinberg equilibrium. Zygotic disequilibrium specifies five different types of disequilibria simultaneously that are (1) Hardy-Weinberg disequilibria at each locus, (2) gametic disequilibrium (including two alleles in the same gamete, each from a different locus), (3) nongametic disequilibrium (including two alleles in different gametes, each from a different locus), (4) trigenic disequilibrium (including a zygote at one locus and an allele at the other), and (5) quadrigenic disequilibrium (including two zygotes each from a different locus). However, because of the uncertainty on the phase of the double heterozygote, gametic and nongametic disequilibria need to be combined into a composite digenic disequilibrium and further define a composite quadrigenic disequilibrium together with the quadrigenic disequilibrium. To investigate the extent and distribution of zygotic disequilibrium across the canine genome, a total of 148 dogs were genotyped at 247 microsatellite markers located on 39 pairs of chromosomes for an outbred multigenerational pedigree, initiated with a limited number of unrelated founders. A major portion of zygotic disequilibrium was contributed by the composite digenic and quadrigenic disequilibrium whose values and numbers of significant marker pairs are both greater than those of trigenic disequilibrium. All types of disequilibrium are extensive in the canine genome, although their values tend to decrease with extended map distances, but with a greater slope for trigenic disequilibrium than for the other types of disequilibrium. Considerable variation in the pattern of disequilibrium reduction was observed among different chromosomes. The results from this study provide scientific guidance about the determination of the number of markers used for whole-genome association studies.     

Some observations on the fine structure of the gametes and zygotes of Acetabularia

Summary Gametes and zygotes of Acetabularia have been studied with the electron microscope. The two flagella of the gamete enter the cell obliquely and the roots run near the surface of the organism. No connexion between the eyespot and the flagella was found nor was there regular relationship between the two eyespots of the zygote. When zygotes were fixed some hours after fusion of the gametes the eyespots appeared to be within the same chloroplast.Some zygotes had two nuclei or dumb-bell shaped nuclei suggesting stages of fusion. The initial contact between nuclei appeared to be through a narrow gap formed by fusion of the two nuclear membranes.     

The 230-kDa gamete surface protein of Plasmodium falciparum is also a target for transmission-blocking antibodies

Immunization with extracellular sexual stages of the malaria parasites can induce the production of antibodies which block the development of the parasites in the midgut of a mosquito after a blood meal. We have generated a number of monoclonal antibodies against gametes and zygotes of the human malaria Plasmodium falciparum. Two monoclonal antibodies (mAb) reacting with a 230-kDa gamete surface protein (mAb 1B3 and 2B4 both isotype IgG2a) were found to block transmission of P. falciparum to mosquitoes. Blocking was complement dependent and this was verified in vitro by the rapid lysis of newly formed gametes and zygotes in the presence of the mAb and active complement. Both mAb reacted by immunofluorescence with the surface of gametes and zygotes from isolates of P. falciparum from various geographical areas. Each mAb immunoprecipitated a 230-kDa protein from 125I-labeled surface proteins of newly formed gametes and zygotes and immunoblotted a protein doublet of about molecular mass 260 and 230 kDa from gametocytes and gametes of P. falciparum. Only the 230-kDa protein is expressed on the surface of newly formed macrogametes and zygotes. The 230-kDa gamete surface protein forms a molecular complex with two proteins of 48 and 45 kDa. The 48- and 45-kDa gamete surface proteins have previously been shown to be targets of mAb which block infectivity of P. falciparum to mosquitoes. The present study now demonstrates that antibodies against the 230-kDa gamete surface protein block transmission of P. falciparum to mosquitoes. The 230-kDa gamete protein is thus a potential candidate for a gamete vaccine.     

The population genetics of anisogamy

This paper analyses the population genetics of anisogamy controlled by a single locus, in both the haploid and diploid cases. The conclusions of Parker et al. (1972), based on computer calculations, are confirmed analytically. The effects of the existence of two mating types on the evolution of anisogamy are examined. Close linkage between a mating type locus and the gamete size locus may produce non-random associations of alleles, leading to disassortative fusion with respect to gamete size. With loose linkage, there is random association of alleles, but selection favours closer linkage.     

The fate of chloroplast DNA during cell fusion, zygote maturation and zygote germination in Chlamydomonas reinhardi as revealed by DAPI staining

Chlamydomonas reinhardi, a haploid isogamous green alga, presents a classic case of uniparental inheritance of chloroplast genes. Since the molecular basis of this phenomenon is poorly understood, an examination of the cytology of the C. reinhardi plastid DNA was made in gametes, newly formed zygotes, maturing zygotes, and at zygote germination.The single plastid per cell of Chlamydomonas contains a small number of DNA aggregates (‘nucleoids’) which can be seen after staining with DNA-binding fluorochromes. In zygotes formed by pre-stained gametes, the fluorescing nucleoids disappear from the plastid of mating type minus (male) gamete plastids but not from the plastid of mating type plus (female) gamete plastids about 1 h after zygote formation. Subsequently, nucleoids aggregate slowly to a final average of two or three in the single plastid of the mature zygote.Quantitative microspectrofluorimetry indicates that gametes of both mating types have equal amounts of plastid DNA, and that zoospores arising from zygotes have 3.5 × as much as gametes. Assuming degradation of male plastid DNA, there must be a very major synthesis of plastid DNA between zygote formation and zoospore release when zygotes produce the typical 8–16 zoospores. That synthesis appears to occur at germination, where there is a massive increase in plastid DNA and nucleoid number beginning just prior to meiosis. The results support the theory that uniparental inheritance results from degradation of plastid DNA entering the zygote via the male gamete and suggest further studies, using mutants and altered conditions, which might explain how male plastid DNA sometimes survives.     

Selection, subdivision and extinction and recolonization

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.     

QUANTITATIVE GENETIC VARIANCE MAINTAINED BY FLUCTUATING SELECTION WITH OVERLAPPING GENERATIONS: VARIANCE COMPONENTS AND COVARIANCES

The quantitative genetic variance-covariance that can be maintained in a random environment is studied, assuming overlapping generations and Gaussian stabilizing selection with a fluctuating optimum. The phenotype of an individual is assumed to be determined by additive contributions from each locus on paternal and maternal gametes (i.e., no epistasis and no dominance). Recurrent mutation is ignored, but linkage between loci is arbitrary. The genotype distribution in the evolutionarily stable population is generically discrete: only a finite number of polymorphic alleles with distinctly different effects are maintained, even though we allow a continuum of alleles with arbitrary phenotypic contributions to invade. Fluctuating selection maintains nonzero genetic variance in the evolutionarily stable population if the environmental heterogeneity is larger than a certain threshold. Explicit asymptotic expressions for the standing variance-covariance components are derived for the population near the threshold, or for large generational overlap, as a function of environmental variability and genetic parameters (i.e., number of loci, recombination rate, etc.), using the fact that the genotype distribution is discrete. Above the threshold, the population maintains considerable genetic variance in the form of positive linkage disequilibrium and positive gamete covariance (Hardy-Weinberg disequilibrium) as well as allelic variance. The relative proportion of these disequilibrium variances in the total genetic variance increases with the environmental variability.     

Recombination and clonal groupings within Helicobacter pylori from different geographical regions.

A collection of 20 strains of Helicobacter pylori from several regions of the world was studied to better understand the population genetic structure and diversity of this species. Sequences of fragments from seven housekeeping genes (atpA, efp, mutY, ppa, trpC, ureI, yphC ) and two virulence-associated genes (cagA, vacA) showed high levels of synonymous sequence variation (mean percentage Ks of 10-27%) and lower levels of non-synonymous variation (mean percentage Ka of 0.2-5.6%). Cluster analysis of pairwise differences between alleles revealed the existence of two weakly clonal groupings, which included half of the strains investigated. All six strains isolated from Japanese and coastal Chinese were assigned to the 'Asian' clonal grouping, probably reflecting descent from a distinct common ancestor. The clonal groupings were not totally uniform; recombination, as measured by the homoplasy test and compatibility matrices, was extremely common within all genes tested, except cagA. The fact that clonal descent could still be discerned despite such frequent recombination possibly reflects founder effects and geographical separation and/or selection for particular alleles of these genes.     

Selection on non-random fusion of gametes during the evolution of anisogamy

Correction of an error in earlier simulations which show how anisogamy could evolve by selection on individuals (Parker et al., 1971) now indicates that anisogamy can evolve when the range of gamete size is very much smaller than previously thought. These models assumed random fusion of gametes, external fertilization, and that zygote viability is dependent on the volume of provisioning it receives from one or both gametes.The present analysis concerns the success of strategies for selective fusion of gametes arising in a randomly-fusing parental population. On a priori grounds selection is expected to favour assortative fusion in ova but disassortative fusion in sperm; anisogamy can persist only if genes for assortative fusion of ova will not spread, and “perfect” anisogamy where genes for disassortative fusion fixate. Mutant strategies for assortatively-fusing ova may not be successful if such ova must compete with sperm for fusions with the randomly-fusing ova. Particularly at high levels of anisogamy, very few of the mutant ova will be fused by the time all other ova have become zygotes; hence their spread may be checked by the enhanced chances of death before fusion, or by problems associated with selfing if they do manage to fuse. In contrast, disassortatively-fusing sperm generally have an advantage when anisogamy would be favoured under random fusion. Genetic simulations (involving two loci, one with alleles for fusion behaviour and the other with alleles for gamete size) were used to confirm these conclusions. Where there is some degree of asynchrony of spawning, disassortative fusion alleles do even better than with perfect synchrony.Simulations with various sex-limited fusion strategies show that non-limited disassortative fusion, i.e. for both ova and sperm, is likely to be an ESS at high anisogamy against all strategies but the one which plays random fusion in ova, disassortative fusion in sperm. This is the ultimate ESS and it does not disrupt anisogamy, but at high anisogamy it has an extremely small advantage over non-limited disassortative fusion. The reasons for the establishment of non-limited disassortative fusion are probably related to avoiding selfing, and to the cost of maintaining random-fusion in ova (in terms of motility, etc.) outweighing the benefits of becoming obligatorily disassortative (non-motile).     

Target antigens in malaria transmission blocking immunity

Malaria transmission blocking immunity has been found to operate against two distinct phases of development of malaria parasites in the mosquito midgut: (i) against the extracellular gametes and newly fertilized zygotes shortly after ingestion by a mosquito of parasitized blood and (ii) against the zygotes during their subsequent development into ookinetes. Immunity is antibody-mediated and stage-specific. A set of three proteins, synthesized in the gametocytes, expressed on the surface of the gametes and newly fertilized zygotes and subsequently shed during later transformation of the zygotes, has been identified as the target antigens of anti-gamete fertilization blocking antibodies. A single protein, synthesized and expressed on the zygote surface during its development to ookinetes, has been identified as the target of antibodies which block the development of the fertilized parasites in the mosquito. Immunization of human populations against gamete or zygote antigens, while not directly protecting an immunized individual from inflection, would reduce the transfer of malaria within the population. Such immunity, in addition to reducing the overall rate of malaria transmission, would, if combined with a vaccine against the asexual (disease-causing) stages, reduce the chance of selection of parasites that are resistant to the asexual vaccine by preventing their entry into the mosquito population.     

A Monte Carlo algorithm for computing the IBD matrices using incomplete marker information

Identity-By-Descent (IBD) is a general measurement of the relationship between two groups of genes. If the two groups consist of two homologous genes, one from each individual, the IBD is called the coancestry between the two individuals. Coancestry is an important concept in both population and quantitative genetics. It is the probability that both genes are copies of the same gene in the genealogy. The average coancestry value at a random locus in a population reflects the level of population diversity, effective population size, the level of inbreeding and other attributes. Coancestry is also the building block for the covariance structure used to estimate the additive genetic variance component for a quantitative trait. There are many other types of IBD matrices, depending on the natures of the genes included in each group, and these IBD matrices vary from locus to locus. Molecular markers distributed along the genome provide information that can be used to infer these locus-specific IBD matrices. As a result, we can estimate and test the variance components of a quantitative trait contributed by these loci using the inferred IBD matrices. In this study, we develop the concept of locus-specific epistatic IBD matrices and a Monte Carlo method to infer these IBD matrices. The method is suitable for large pedigrees with arbitrary complexity and various levels of missing marker information. With these locus-specific IBD matrices, we are ready to search for quantitative trait loci along the genome in complicated pedigrees.     

The average number of sites separating DNA sequences drawn from a subdivided population

The "infinite sites" model in the absence of recombination is examined in a subdivided population in which there is arbitrary migration among demes. It is shown that, if the migration matrix is symmetric and irreducible, the average number of sites that differ in two alleles chosen from the same deme depends only on an effective size of the whole population and not on either the elements of the migration matrix or the size of each deme separately. If there are n demes all of size N, the average number of sites that differ in two alleles chosen from the same deme is 4nN mu, where mu is the average mutation rate per site. This is the same value as for two alleles drawn from a panmictic population of size nN. The average number of sites that differ in alleles drawn from the same and from different demes can provide some information about the degree of population subdivision, as is illustrated by using the data of Kreitman and Aquadé (1986, Proc. Nat. Acad. Sci. U.S.A., 83, 3562) on Drosophila melanogaster.