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Biomedical subjects

U Liberman

Publications and source records attributed to U Liberman.

29 records · Page 2Linked to original sources
PubMed1986

An evolutionary reduction principle for genetic modifiers.

The joint evolution of major genes under viability selection and a modifier locus that controls recombination between the major genes, mutation at the major gene, or migration between two demes is studied. The modifying locus is selectively neutral and may have an arbitrary number of alleles. For each case a class of polymorphic equilibria exists in which the frequencies of the modifying alleles are those computed by assuming that the recombination, mutation, or migration rates were viabilities and in which the major and modifier loci are not statistically associated. These are called viability-analogous Hardy-Weinberg (VAHW) equilibria. A new allele introduced near these equilibria will enter the population if its marginal average rate of recombination, mutation, or migration (whichever applies) is less than the population average prior to its introduction. Stability properties of these VAHW equilibria are also reported.

Biological Evolution↗
PubMed1985

A symmetric two-locus fertility model.

A model in which selection is mediated by differential fertilities among the genotypes at two diallelic loci is proposed. Fertility depends only on the number of heterozygous loci participating in the mating. Classes analogous to symmetric equilibria in symmetric viability models are determined explicitly and shown to exhibit stability behavior very different from the viability results. Linkage equilibrium is shown to occur in a relatively asymmetric fashion and to overlap in stability with linkage disequilibrium. In many cases single-locus or two-locus polymorphism is shown to be stable simultaneously with chromosome fixation even under very tight linkage. It is suggested that historical effects may be of great significance in the evolution of systems in which fertility is the primary agent of natural selection.

Alleles↗
PubMed1985

A symmetric two locus model with viability and fertility selection.

A two locus deterministic population genetic model is analysed. One locus is under viability selection, the other under fertility selection with both forms of selection completely symmetric. It is shown that linkage equilibrium may occur at two different equilibrium points. For a two-locus polymorphism to be stable, it is necessary that the viability locus be overdominant but not necessary that the fertility locus, considered separately, be able to support a stable polymorphism. The overlaps in stability are not as complex as under two locus symmetric fertilities, but considerably more complex than with symmetric viabilities. Extensions of the analysis for the central linkage equilibrium point with multiple viability and fertility loci are indicated.

Fertility↗
PubMed1984

On chiasma formation point processes having the count location property.

The count-location (C-L) chiasma formation schemes introduced by Karlin and Liberman (1979b) encompass a broad class of map functions involving positive, negative or no chiasma interference. The C-L schemes do not explicitly assume a specific mechanism of crossover formation, but rather a statistical property of the process. If viewed as a stochastic point process along the chromosome, it is shown that a crossing over mechanism having the C-L property is actually a rescaled mixture of Poisson processes. Surprisingly it turns out that these C-L point processes involve negative interference throughout the entire genome.

Crossing Over, Genetic↗
PubMed1979

Representation of Nonepistatic selection models and analysis of multilocus Hardy-Weinberg Equilibrium configurations.

The paper develops conditions for the existence and the stability of central equilibria emanating from selection recombination interaction with generalized nonepistatic selection forms operating in multilocus multiallele systems. The selection structure admits a natural representation as simple sums of Kronecker products based on a common set of marginal selection components. A flexible parametrization of the recombination process is introduced leading to a canonical derivation of the transformation equations connecting gamete frequency states over successive generations. Conditions for the existence and stability of multilocus Hardy-Weinberg (H.W.) type equilibria are elaborated for the classical nonepistatic models (multiplicative and additive viability effects across loci) as well as for generalized nonepistatic selection expressions. It is established that the range of recombination distributions maintaining a stable H.W. polymorphic equilibrium is confined to loose linkage in the pure multiplicative case, but is not restricted in the additive model. In the bisexual case we ascertain for the generalized nonepistatic model the stability conditions of a common H.W polymorphism.

Alleles↗
PubMed1978

Classifications and comparisons of multilocus recombination distributions.

Various classifications and representations of multilocus recombination structures are delineated based on generalized notions of linkage values and recombination rates. An important class of recombination distributions (called the count-location chiasma process) is parameterized by a distribution of the number of crossover events and, for each such crossover count, by a conditional distribution of crossover locations. A number of properties of this recombination structure are developed. A multilocus definition of a "natural" recombination range is set forth. Orderings among recombination distributions in the multilocus setting are also discussed. Comparisons are made in terms of complete linkage, free assortment and noninterference schemes serving as standards.

Journal Article↗