Epistasis in the multiple locus symmetric viability model

The n-locus two-allele symmetric viability model is considered in terms of the parameters measuring the additive epistasis in fitness. The dynamics is analysed using a simple linear transformation of the gametic frequencies, and then the recurrence equations depend on the epistatic parameters and Geiringer's recombination distribution only. The model exhibits an equilibrium, the central equilibrium, where the 2 ⁿ gametes are equally frequent. The transformation simplifies the stability analysis of the central point, and provides the stability conditions in terms of the existence conditions of other equilibria. For total negative epistasis (all epistatic parameters are negative) the central point is stable for all recombination distributions. For free recombination either a central point (segregating one, two, ... or n loci) or the n-locus fixation states are stable. For no recombination and some epistatic parameters positive the central point is unstable and several boundary equilibria may be locally stable. The sign structure of the additive epistasis is therefore an important determinant of the dynamics of the n-locus symmetric viability model. The non-symmetric multiple locus models previously analysed are dynamically related, and they all have an epistatic sign structure that resembles that of the multiplicative viability model. A non-symmetric model with total negative epistasis which share dynamical properties with the similar symmetric model is suggested.Supported in part by NIH grant GM 28016, and by grant 81-5458 from the Danish Natural Science Research Council     

Modeling segregation distortion for viability selection I. Reconstruction of linkage maps with distorted markers

Molecular markers have been widely used to map quantitative trait loci (QTL). The QTL mapping partly relies on accurate linkage maps. The non-Mendelian segregation of markers, which affects not only the estimation of genetic distance between two markers but also the order of markers on a same linkage group, is usually observed in QTL analysis. However, these distorted markers are often ignored in the real data analysis of QTL mapping so that some important information may be lost. In this paper, we developed a multipoint approach via Hidden Markov chain model to reconstruct the linkage maps given a specified gene order while simultaneously making use of distorted, dominant and missing markers in an F₂ population. The new method was compared with the methods in the MapManager and Mapmaker programs, respectively, and verified by a series of Monte Carlo simulation experiments along with a working example. Results showed that the adjusted linkage maps can be used for further QTL or segregation distortion locus (SDL) analysis unless there are strong evidences to prove that all markers show normal Mendelian segregation.     

Population trajectories for single locus additive fecundity selection and related selection models

A selection model which comprises models of additive fecundities as well as models of viability, fecundity, or differential mating selection acting only in one sex, is investigated for an autosomal gene locus in a population reproducing in nonoverlapping generations. The recurrence equations and basic properties of the genotypic population trajectories and equilibrium points are formulated for the multiallelic case. For the diallelic case, the trajectory development is discussed in more detail, and it is proven that every population trajectory converges to a Hardy-Weinberg equilibrium point.     

A quantitative genetics model for viability selection

Viability selection will change gene frequencies of loci controlling fitness. Consequently, the frequencies of marker loci linked to the viability loci will also change. In genetic mapping, the change of marker allelic frequencies is reflected by the departure from Mendelian segregation ratio. The non-Mendelian segregation of markers has been used to map viability loci along the genome. However, current methods have not been able to detect the amount of selection (s) and the degree of dominance (h) simultaneously. We developed a method to detect both s and h using an F2 mating design under the classical fitness model. We also developed a quantitative genetics model for viability selection by proposing a continuous liability controlling the viability of individuals. With the liability model, mapping viability loci has been formulated as mapping quantitative trait loci. As a result, nongenetic systematic environmental effects can be easily incorporated into the model and subsequently separated from the genetic effects of the viability loci. The quantitative genetic model has been verified with a series of Monte Carlo simulation experiments.     

A coalescent dual process in a Moran model with genic selection, and the lambda coalescent limit

The genealogical structure of neutral populations in which reproductive success is highly-skewed has been the subject of many recent studies. Here we derive a coalescent dual process for a related class of continuous-time Moran models with viability selection. In these models, individuals can give birth to multiple offspring whose survival depends on both the parental genotype and the brood size. This extends the dual process construction for a multi-type Moran model with genic selection described in Etheridge and Griffiths (2009). We show that in the limit of infinite population size the non-neutral Moran models converge to a Markov jump process which we call the Λ-Fleming-Viot process with viability selection and we derive a coalescent dual for this process directly from the generator and as a limit from the Moran models. The dual is a branching-coalescing process similar to the Ancestral Selection Graph which follows the typed ancestry of genes backwards in time with real and virtual lineages. As an application, the transition functions of the non-neutral Moran and Λ-coalescent models are expressed as mixtures of the transition functions of the dual process.     

Nonlinear frequency-dependent selection at a single locus with two alleles and two phenotypes

 The paper investigates the discrete frequency dynamics of two phenotype diploid models where genotypic fitness is an exponential function of the expected payoff in the matrix game. Phenotypic and genotypic equilibria are defined and their stability compared to frequency-dependent selection models based on linear fitness when there are two possible phenotypes in the population. In particular, it is shown that stable equilibria of both types can exist in the same nonlinear model. It is also shown that period-doubling bifurcations emerge when there is sufficient selection in favor of interactions between different phenotypes. Received: 22 October 1998     

A slow selection analysis of two locus, two allele traits.

A deterministic, continuous time model for the dynamics of two locus, two allele Mendelian traits in a large randomly mating diploid population is derived. The model allows for frequency and time dependent birth and death rates. It is analyzed under the assumption that the selective forces acting in the population are small. Slow selection approximations to the system's solution are then constructed. Two particular cases are studied. First, when linkage between loci is tight, the population is shown to rapidly approach Hardy-Weinberg proportions, which then may vary on a (slow) time scale determined by differential fitness. In the case of constant birth and death rates, a measure of the population's fitness is shown to increase on the slow time scale after an initial rapid adjustment. The second case considered is for loose linkage; a population near linkage equilibrium is studied. It is shown that the epistatic parameters cancel and that the results agree with the tight linkage case to leading order. The linkage disequlibrium is described in both cases.     

A single locus model of selection in permanent translocation heterozygotes

A model for evolution at a single locus in permanent translocation heterozygotes is described. It is also applicable to other permanent structural heterozygotes that possess the mating systems discussed. Recombination occurs between the locus and the chromosomes, which are of two types. The mating system includes selfing and random mating. When recombination is rare, selection will result in almost complete fixation on the single most fit genotype present in a population, regardless of the frequency of selfing. This provides a possible explanation for the ecological success of permanent translocation heterozygotes in some groups of organisms, like Oenothera. It is not necessary to postulate that their success is the result of hybrid vigor. Furthermore, a complete lack of recombination is not necessary for explaining the observed association of alleles with particular segmental arrangements. A small amount of recombination is consistent with the observation that different segmental arrangements often carry different alleles.     

Religion, fertility and genes: a dual inheritance model

Religious people nowadays have more children on average than their secular counterparts. This paper uses a simple model to explore the evolutionary implications of this difference. It assumes that fertility is determined entirely by culture, whereas subjective predisposition towards religion is influenced by genetic endowment. People who carry a certain 'religiosity' gene are more likely than average to become or remain religious. The paper considers the effect of religious defections and exogamy on the religious and genetic composition of society. Defections reduce the ultimate share of the population with religious allegiance and slow down the spread of the religiosity gene. However, provided the fertility differential persists, and people with a religious allegiance mate mainly with people like themselves, the religiosity gene will eventually predominate despite a high rate of defection. This is an example of 'cultural hitch-hiking', whereby a gene spreads because it is able to hitch a ride with a high-fitness cultural practice. The theoretical arguments are supported by numerical simulations.     

The petunia restorer of fertility protein is part of a large mitochondrial complex that interacts with transcripts of the CMS-associated locus

A class of nuclear genes termed "restorers of fertility" (Rf) acts to suppress the expression of abnormal mitochondrial genes associated with cytoplasmic male sterility (CMS). In petunia, both the nuclear Rf gene and mitochondrial CMS-associated gene have previously been identified. The CMS-associated gene is an aberrant chimera in which portions of several mitochondrially encoded genes are fused to an unknown reading frame. The dominant Rf allele reduces the CMS-associated protein to nearly undetectable levels and alters the RNA population derived from the CMS locus, but its mechanism of action has not been determined. The petuniaRf gene is a member of the pentatricopeptide repeat gene family (PPR), an unusually large gene family in Arabidopsis (approximately 450 genes) compared with yeast (five genes) and mammalian genomes (six genes). The PPR gene family has been implicated in the control of organelle gene expression. To gain insight into the mode of action of PPR genes, we generated transgenic petunia plants expressing a functional tagged version of Rf. Analysis of the restorer protein revealed that it is part of a soluble mitochondrial inner-membrane-associated, RNase-sensitive high-molecular-weight protein complex. The complex is associated with mRNA derived from the CMS locus.     

Mathematical model for the study of fertility and viability in inbreeding populations

Granted that a single or complex gene is responsible for inbreeding depression, theoretical expressions for fertility and viability are obtained in different diploid populations: brother-sister, half-brother-sister, cousins and double-cousins. The conclusions of the study of viability variations according to the coefficient of parentage are proved by the results of experiments and lead to a new view of genetic load.     

Density-dependent selection migration model with non-monotone fitness functions

This paper studies the classical single locus, diallelic selection model with diffusion for a continuously reproducing population. The phase variables are population density and allele frequency (or allele density). The genotype fitness depend only on population density but include one-hump functions of the density variable. With mild assumptions on genotype fitnesses, we study the geometry of the nullclines and the asymptotic behavior of solutions of the selection model without diffusion. For the diffusion model with zero Neumann boundary conditions, we use this geometric information to show that if the initial data satisfy certain conditions then the corresponding solution to the reaction-diffusion equation converges to the spatially constant stable equilibrium which is closest to the initial data.Research partially supported by NSF grant DMS-8920597Research supported by funds provided by the USDA-Forest Service, Southeastern Forest Experiment Station, Pioneering (Population Genetics of Forest Trees) Research Unit, Raleigh, North Carolina     

Influence of mating duration on fecundity and fertility in two aphidophagous ladybirds

Abstract:  The influence of different mating durations on fecundity and fertility has been studied in two aphidophagous ladybirds, Cheilomenes sexmaculata and Coelophora saucia . Pre-oviposition period decreased while fecundity and fertility increased with increase in mating duration in both the ladybird species. The increase in fecundity with longer mating durations is probably due to the female response because of cryptic female choice. Mating of 10-s duration resulted in oviposition but of unviable eggs probably because of lack of sperm transfer. A minimum duration of 1 min of mating was probably essential for fertilization of the eggs. Absence of spermatophore in the reproductive tract of females is indicative of direct sperm transfer in both the ladybird species. Trend of fertility (similar fertility at 1 and 5 min followed by increase at 60 min which was again similar to that at complete mating) indicates probable sperm transfer in spurts in C. sexmaculata while continuous transfer in C. saucia is indicated by continuous increase in fertility with increase in mating duration.     

A null mutation at the mouse Phosphoglucomutase-1 locus and a new locus,Pgm-3

A null mutation at the phosphoglucomutase locus (Pgm-1) was discovered by electrophoretic analysis of the inbred mouse strain C57 BL/6J. The null allele (Pgm-1 ⁿ) was shown to segregate as a Mendelian unit alternative to the Pgm-1 ^a and Pgm-1 ^b alleles. Mice expressing the Pgm-1 ⁿ allele, either in the heterozygous or homozygous state, are viable, healthy, and fertile. The occurrence of the Pgm-1 ⁿ mutant revealed a previously unreported genetic locus (Pgm-3) that controls the expression of a third phosphoglucomutase. Two electrophoretically expressed alleles of Pgm-3 (inherited without dominance) are found in the inbred mouse strains C57 BL/6J and DBA/2J. Linkage observed between the Pgm-3 locus, the dilute locus (d) and the cytoplasmic malic enzyme locus (Mod-1) has allowed assignment of the Pgm-3 locus to chromosome 9. A striking tissue specific expression of Pgm-1 and Pgm-3 was observed. Products of the Pgm-3 locus were detected in kidney, testes, brain, and heart. In contrast, Pgm-1 controlled isozymes were present in kidney, spleen, ovaries, and erythrocytes.Financial support for this work was provided in part by Contract #263-78-C-0393 from the National Institute of Environmental Health Sciences to the Research Triangle Institute.     

Fertility and viability at the Sod locus in Drosophila melanogaster: non-additive and asymmetric selection

Experiments were designed to test in Drosophila melanogaster the effect of mating type at the Sod locus on fertility and viability. The experiments show that fertility is neither additive (or multiplicative) nor symmetric, i.e. that the fertility of a mating type cannot be predicted from the average fertility of the two genotypes involved in the mating. There is no significant male x female interaction with respect or progeny viability; but the interaction is significant for productivity, i.e. when fertility and viability are jointly taken into account. There is overdominance with respect to female fertility, but not with respect to male fertility or to viability. There also is alloprocoptic selection with respect to fertility and with respect to productivity, i.e. mating between like homozygotes are less fertile and productive than matings between dissimilar homozygotes. Selection at the Sod locus yields stable polymorphic equilibria, with the frequency of the F allele predicted at P = 0.641 or 0.695, respectively for low and high larval density.     

A flow-cytometric method for determination of yeast viability and cell number in a brewery

A flow-cytometric assay, using the fluorescent dye, oxonol, for the simultaneous determination of yeast cell viability and cell number is described. The assay was optimised, and trialed at a brewery for 6 months. The flow-cytometry assay offered a substantially reduced error in viability determination, compared to methylene blue which is the industry standard for measuring viability. Further, by calculating yeast cell number at the same time, this assay provides a reliable method for determining pitching rate, allowing increased quality control of subsequent fermentations.     

Impact of genomic selection of AI dairy sires on their likely utilization and methods to estimate fertility: a paradigm shift

Breeding of dairy cattle is undergoing a paradigm shift to genomic selection of potential sires and dams. This undoubtedly will affect how bulls are managed in an artificial insemination (AI) center and impact methods to estimate their ‘fertility'. Our goal is to help decision-makers understand the contents of a straw of semen, current estimates of sire fertility, and how estimates might evolve in a genomic era. Sire fertility is estimated from outcome (pregnant or not) after 300 to > 2,000 inseminations and reported in units (U) as a sire's deviation from a population (> 500 bulls) average pregnancy rate (PR). Too often users do not recognize that imprecision of an estimate encompasses a 3-U range, or more. ‘True fertility' of the sire whose semen is inseminated influences outcome far less than ‘true fertility' of each female and a myriad of microenvironment and management factors. Further, AI centers discard substandard collections and intentionally adjust number of sperm per straw so that differences in pregnancy rates achieved by different sires are minimized! For > 80% of Holstein bulls, estimated ‘sire conception rates' are within a 5.4-U range. In the future, most sires will be 15 to 40 mo old and services will accumulate at > 1,000/mo. Estimated sire conception rates still will be a deviation from the population mean, but should be based on records for the most recent 6 or 12 mo, rather than 48 or 60 mo. Repeated ‘snap shots' every 2 mo would allow AI centers to adjust number of sperm per AI straw from genomic-sires in a timely manner, to maintain high pregnancy rates, and to meet market demands with sires producing ∼40% as many sperm as mature ‘proven sires' of yesteryear.     

Hormone-dependent insertional Arabidopsis thaliana mutants with decreased viability and fertility

We present data on the phenotype identification and genetic analysis of offspring in three lines of dominant morphological mutants of Arabidopsis thaliana having drastically reduced fertility (a sterile calluslike mutant, a flower mutant, and a dwarf mutant) and in five lines of recessive morphological mutants (four mutants with lethal seedlings and one pigmentation mutant). The mutants were selected from a collection of transgenic plants that had genomes carrying a T-DNA insertion of plasmid vectors pLD3 and pPCVRN4; the collection was created earlier via agrobacterial transformation of germinating seeds. The results presented here were obtained using compensation of hormonal imbalance in the insertional morphological mutants of A. thaliana by exogenous hormones.