Diallelic Model Research Articles

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.

Multiplicative vs. arbitrary gene action in heterosis.

In this article we investigate multiplicative effects between genes in relation to heterosis. The extensive literature on heterosis due to multiplicative effects between characters is reviewed, as is earlier work on the genetic description of heterosis. A two-locus diallelic model of arbitrary gene action is used to derive linear parameters for two multiplicative models. With multiplicative action between loci, epistatic effects are nonlinear functions of one-locus effects and the mean. With completely multiplicative action, the mean and additive effects form similar restrictions for all the rest of the effects. Extensions to more than two loci are indicated. The linear parameters of various models are then used to describe heterosis, which is taken as the difference between respective averages of a cross (F1) and its two parent populations (P). The difference (F2 - P) is also discussed. Two parts of heterosis are distinguished: part I arising from dominance, and part II due to additive x additive (a x a)-epistasis. Heterosis with multiplicative action between loci implies multiplicative accumulation of heterosis present at individual loci in part I, in addition to multiplicative (a x a)-interaction in part II. Heterosis with completely multiplicative action can only be negative (i.e., the F1 values must be less than the midparent), but the difference (F2 - P) can be positive under certain conditions. Heterosis without dominance can arise from multiplicative as well as any other nonadditive action between loci, as is exemplified by diminishing return interaction. The discussion enlarges the scope in various directions: the genetic significance of multiplicative models is considered.(ABSTRACT TRUNCATED AT 250 WORDS)

Sex ratio genetics and the competitiveness of parasitic wasps

In the first part of the paper we analyse dynamics of the genetic mechanisms responsible for maintaining biased sex ratios in host-parasitoid interactions. We begin by reviewing recent results relating to the maintenance of sibmating in haplo-diploid populations. We then investigate the evolutionary stable sex ratio in populations in which all or some of the females mate with their brothers. In particular, we derive a diallelic one-locus model for studying evolutionary stable sex ratios in partially sibmating haplo-diploid populations. In the second part of the paper we review the impact of sex ratio on host-parasitoid populations. We then analyse how the sex ratio strategy of one parasitoid species may affect its interaction with another parasitoid species competing for the same host. In particular we show that, although a female biased sex ratio may enhance the inherent competitiveness of one species, it may also destabilize the ecological interaction of the three species so that all become extinct.

PLOIDY AND EVOLUTION BY SEXUAL SELECTION: A COMPARISON OF HAPLOID AND DIPLOID FEMALE CHOICE MODELS NEAR FIXATION EQUILIBRIA

We compare the stability properties of haploid and diploid models of Fisherian sexual selection (with male contribution limited to sperm) by examining both models at equilibria for which a male trait is fixed or absent. Haploid and diploid two locus diallelic models share the property that the stability of such fixation equilibria is determined by the relationship between the harmonic mean of relative preference values for the common male trait, weighted by the frequency of the preferences, and the relative viability associated with the common male trait. When diploid females with heterozygotic-based preferences express preference strengths intermediate between homozygote-based preferences, then boundary equilibria of haploid and diploid models share many stability properties. However, even with intermediate heterozygote preferences, haploid and diploid models do differ: (1) for a particular frequency of the preference allele, both fixation boundaries can be stable for the diploid model, and (2) with over- or underdominance at the preference locus (a possibility precluded in the haploid model), a fixation boundary in the diploid model may show two switches in its stability state for increasing frequencies of one of the preference alleles. These differences are due not just to the impossibility of dominance in haploid models, but also to the larger number of diploid genotypes.

ANALYSIS OF AGRONOMIC CHARACTERS FOR AN ELEVEN-PARENT DIALLEL OF EARLY-MATURING SOYBEAN GENOTYPES IN EASTERN CANADA

Information on the genetic behavior of early-maturing soybeans (Glycine max (L.) Merr.) in northern latitudes is important for the formulation of appropriate selection schemes. The Gardner-Eberhart diallel model was used to study genetic effects and combining abilities of 11 early-maturing genotypes (maturity Groups 00 and 000) of soybean grown in Quebec and eastern Ontario. Agronomic characters were measured on spaced F1 plants at one site, and on F2 populations in replicated row plots at three sites. Cultivar (additive) effects were predominant for all characters. Three of eleven lines had positive but unstable varietal parameters for seed yield. Average heterosis was significant for seed yield and plant height at every location. Contrary to other reports, significant negative heterosis for oil content was observed at two locations. Varietal and specific heterosis were significant for most characters.Key words: Soybean, Glycine max (L.) Merr., diallel, Gardner-Eberhart, yield, oil, protein

The affected sib method. V. Testing the assumptions.

The affected sib methods, which are used to make inferences about the genetic components of HLA associated diseases, have many underlying assumptions which may not always be realistic. These include no selective disadvantage of affected individuals, little or no recombination between the marker loci and the 'disease' locus, a single panmictic population, Mendelian segregation of the disease locus alleles and random distribution of individuals over environments. The effects of breaking these assumptions have been investigated. We have explicitly derived the haplotype sharing identity by descent (IBD) expectations for the cases of selection against affected individuals and recombination between the HLA marker loci and the 'disease' predisposing locus for affected sib trios (as was previously done for affected sib pairs). We have also derived, for both affected sib pairs and trios, the haplotype sharing expectations for non-random mating (positive assortative), admixture, meiotic drive (of disease allele carrying haplotypes), and a random versus shared environmental component for sibs. In order to assess the sensitivity of the affected sib methods to perturbations in the assumptions, the expectation spaces of haplotype sharing in affected sib pairs and sib trios under the single diallelic locus model with varying penetrances and allele frequencies are fully described. The effects on haplotype sharing and subsequent disease parameter estimation are different for each of the factors we have considered. The affected sib methods are found to be robust in many situations.

Diallelic model combining selection and incomplete penetrance

In this paper, the concept of penetrance is generalized into a transitional matrix. Models combining selection and incomplete penetrance are analysed by reducing them to the classical selection model.

Quantitative Genetic Aspects of Nitrogen Fixation in Peanuts (Arachis hypogaea L.)1,2

Abstract Manipulation of the host genotype has been proposed as a method of increasing biological nitrogen fixation by rhizobia in symbiosis with the peanut (Arachis hypogaea L.). The F1 generation of a diallel cross of 10 South American cultivars was evaluated in the greenhouse in an analysis of gene action for traits related to nitrogen fixation. The parents represented five secondary centers of diversity and effects in the diallel model were partitioned into among- and within-center components. Variation of center effects was significant for several characters but was smaller in magnitude than within-center variation. Specific combining abilities were significant and accounted for more variability than general combining abilities for nodule number, nodule mass, specific nitrogenase activity, shoot weight, and total nitrogen, indicating non-additive types of gene action. Maternal effects were observed for the same characters. The parents with the highest general combining abilities (GCA's) for nitrogen fixation were both fastigiate types, while Virginia-type parents had generally low GCA's. Correlations between parental and GCA effects were nonsignificant for all traits, so simple evaluation of lines for nitrogen-fixing capacity may not identify superior parents for use in breeding programs.

Detection of genic interactions by analyzing the F2 generation of diallel crosses

The ability of the Hayman and Jinks method of analysis of diallel crosses to detect genic interactions was studied in peanuts. Six traits, measured in the F2 generation of a diallel cross of four cultivars, were analyzed. In F2 analyses of the diallel, least squares estimates of variance components D, H1 , H2, F, E, were used as an additional criteria for the adequacy of the diallel model. They were found to be in substantial agreement with the tests based on Wr and Vr values, and probably more reliable. The regression of Wr on Vr was shown to be unsuitable to detect 'duplicate gene' type of interactions; it was detected, however, by the ratio of the mean within-F2 - family variance and the variance among the parents. Using the different criteria, 'duplicate genes' type of interactions was detected for two traits, 'complementary genes' type was detected for one trait and three traits were found to fit the additive-dominance model without any genic interactions.

Quadratic Analyses of Reciprocal Crosses

Three different models, a two-way factorial model for familiarity, an orthogonalizing transform of this model to a diallel model, and a bio model more representative of the biological situation, are interrelated in terms of their components of variance and covariance. It is clarified that there are five components that can be reckoned with in the analysis of reciprocal crosses, including distinct maternal and paternal variances. Estimation of the components and tests of hypotheses concerning them are outlined for two types of mating designs with reciprocals. One deisgn involves a factorial mating design between two distinct sets of parents or parental lines and the other a diallel of all crosses from a single set of parents or parental lines. Both designs provide the same types of information and similar tests of hypotheses. At least some parts of the analyses corresponding to the factorial model are required to separate the maternal and paternal variances. A least squares partitioning of the sums of squares according to the diallel model, but with expectations expressed in terms of the bio model, provides most of the tests of hypotheses of interest. Worked examples are given.

Modification of the Variety Cross Diallel Model for Evaluating Cycles of Selection1

A general model for the analysis of variety cross diallels was modified for use when the populations represent different cycles of selection from one parent variety. The a and d parameters in the improved populations are functions of a and d in the parent variety assuming negligible mutation effects. The modified model permits the simultaneous estimation of a polynomial regression in a and in d. The regression equation in homozygous effects (a) is a direct measure of weighted average change in gene frequency, and the equation in heterozygous effects (d) is a measure of the approach to fixation of the favorable alleles. If favorable genes are dominant, the first derivative of the equation in heterozygous effects evaluated at zero gives the cycle at which the weighted average gene frequency will be 0.5.A parent population and selected cycles of selection were generated on an IBM 360 computer to illustrate the theory. Crosses and related populations were generated according to the Gardner‐Eberhart model and estimates obtained were compared to known parametric values. From the idealized diallel and related populations, change in gene frequency was determined as well as time to fixation and expected response at the endpoint of selection, when gene frequencies are changing at a linear rate.

Sulla Genetica del DiabeteAnalisi di nove casi famigliari

SummaryNine family cases of diabetes are genetically interpreted on account of a polygenic model of inheritance, with each allele being characterized by a different probability of chronological stability of the normal information. This model provides a satisfactory interpretation of the clinical and subclinical variability of diabetes — which the diallelic model is unable to do — and has on the polygenic model the advantage of a higher fitness to a case of discontinuous variability, such as diabetes. Both pedigrees characterized by apparent recessive inheritance and those characterized by apparent dominant one may equally be interpreted on account of the polyallelic model.The origin of polyallelism is attributed to the hereditary variability of the gene's temporal unit (chronon). As a result, the phenomenon of “anticipation” may also be interpreted, and the one-origin clinical and sub-clinical variability of diabetes be demonstrated.