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Biomedical subjects

C C Cockerham

Publications and source records attributed to C C Cockerham.

At least 37 records · Page 2Linked to original sources
PubMed1986

Linkage disequilibria in finite populations.

Four-locus recombination frequencies are summarized into two-locus pair frequencies and three-locus frequencies, and further, into two-locus frequencies such that higher-order frequencies are linear functions of lower-order frequencies. Frequencies of gene combinations are defined according to their position on the same or distinct gametes, and linear functions of these provide the measures of linkage disequilibria. These concepts are utilized to derive the transitional behavior of the gene combinations frequencies and the linkage disequilibria in a finite monoecious population with random union of gametes for up to four loci. The transitions of lower-order disequilibria in a higher-order (more loci) setting involve the higher-order disequilibria which must be taken into account in arriving at the final (fixation) frequencies. The methods allow different initial conditions. Since corresponding data functions of the gene combination frequencies provide unbiased estimates of the parameters, estimators follow naturally.

Gene Frequency↗
PubMed1986

Modifications in estimating the number of genes for a quantitative character.

In estimating the minimum number of genes contributing to a quantitative character, it is suggested that the squared difference between the means of the two parents be corrected for experimental variance and that the genetic variance stemming from differences in gene frequencies of the parents be estimated by least squares utilizing information on all entries.

Analysis of Variance↗
PubMed1986

Estimation of inbreeding parameters in stratified populations.

A clarification is given of the differences in approaches to the estimation of F-statistics of Nei & Chesser [Ann. Hum. Genet. (1983) 47, 253-259] and Cockerham [Genetics (1973) 74, 679-700]. The principal difference is that Nei & Chesser define quantities with respect to fixed extant populations, while Cockerham allows for evolutionary variation between populations. Weighted and unweighted analyses are compared, and a numerical example given.

Alleles↗
PubMed1985

Selection with partial selfing. I. Mass selection.

The expected responses to mass selection carried out before or after reproduction in a population whose members all have a fixed probability of self pollination (s) are formulated using covariances of relatives and their component quadratic functions for a model with arbitrary additive and dominance effects. The response measured in the first generation offspring after selection (immediate gain) can differ from that retained when the population has regained equilibrium (permanent gain). The population mean behaves in a predictable manner during the return to equilibrium, and its value at any time can be predicted from earlier generations. The permanent gain from selection after reproduction is always (1 + s)/2 times as large as that from selection before reproduction, but the relationship of the immediate gains depends on the genetic model assumed. Numerical analysis applied to a model with two alleles per locus and varying allele frequencies, dominance ratios and numbers of loci showed that the proportion of the immediate gain retained at equilibrium was reduced with the large inbreeding depression associated with increasing dominance levels and numbers of loci and was generally lower for selection after reproduction than before. In the absence of information as to the magnitude of genetic variances and inbreeding depression in species reproducing by partial selfing, the importance of this phenomenon is unknown.

Genetic Variation↗
PubMed1984

Drift and mutation with a finite number of allelic states.

The frequencies with which alleles are alike within (Q) and between (q) populations are formulated for monoecious populations undergoing drift and mutation with unequal mutation rates among alleles for a finite number (k) of allelic states. The effective number of alleles and an application to Nei's measure of genetic distance [Nei, M. (1972) Am. Nat. 106, 283-292] are also considered for this model. The equilibrium values of Q and q increase as k decreases. Unequal mutation rates further increase the equilibrium values and reduce the rates of approach of Q and q to these values. The transitional values of Q and q are very dependent on the initial population frequency composition when mutation rates are unequal. Reducing k, of course, reduces the effective number of alleles, which is further reduced by unequal mutation rates. Complications introduced by initial population composition, unequal mutation rates, and number of allelic states, coupled with data limitations for long-term measures of genetic distance or population differentiation, with mutation as the main driving force, are discussed.

Journal Article↗
PubMed1984

Additive by additive variance with inbreeding and linkage.

Two-locus coancestries, which provide the coefficients of the additive by additive component in the variance and covariance of relatives for a quantitative trait, were formulated generally in terms of two-locus probabilities of identity by descent for combinations of parental and recombinant gametes. Explicit expressions, with linkage, were developed for all relatives of self-fertilization, for selfed and outbred relatives and for full and half sibs from unrelated inbred parents. The relative effect of linkage on the two-locus coancestry decreases rapidly as inbreeding and relatedness of the relatives increase. It was concluded that the error caused by ignoring linkage would probably be small in the estimation of genetic variances or in the projection of selection response with self-fertilization.

Epistasis, Genetic↗
PubMed1984

Covariances of relatives stemming from a population undergoing mixed self and random mating.

We consider covariances of all parent and first-generation relatives from outcrossing or self-fertilization in a parent population that is in equilibrium with respect to these processes. The results, which are for any number of alleles and loci with additive and dominance effects, are phrased in terms of six quadratic genetic components whose coefficients are given by descent measures for equilibrium populations. Because of the variation in the inbreeding coefficients for this system of mating, the expressions include joint contributions of loci to the variances and covariances of relatives. By inclusion of the full complement of relatives, all quadratic components can be estimated. The findings of Ghai (1982, Biometrics 38, 87-92) for compound functions of the covariances with two alleles at a single locus are analyzed in terms of the more general model.

Alleles↗
PubMed1983

Variance of actual inbreeding.

The variances of actual inbreeding and coancestry in terms of their corresponding identities by descent were studied for finite populations. For inbreeding at a single locus, the total variance sigma 2 equal F(1-F) (F is the inbreeding coefficient) is comprised of a component sigma 2w within populations and a component sigma 2b between replicate populations. These variances increase in time to a maximum at about 1.1Ne generations for sigma 2w, about 2.3Ne generations for sigma 2b, and about 1.4 NE generations for sigma 2, and decrease thereafter (Ne is effective population size). The ratio sigma 2b/sigma 2 is ever increasing to an asymptote in the range 0.4-0.5 depending on Ne and the mating system. For finite populations with variation in pedigree F's, there are contributions sigma 2wF within and sigma 2bF between populations. The component sigma 2bF is insignificant except for very small populations, and sigma 2wF is largest in the early generations and then decreases roughly as (1-F)2/KNe where K is formulated in terms of the mating strategy and the degree of avoidance of mating relatives. An additional degree of avoidance increases K by a factor of 4. In a large population at equilibrium with respect to mixed self and random mating, sigma 2wF accounts for one-half to two-thirds of sigma 2w. Bringing in more loci leads to decomposition of the total variance into four components whose values are affected by linkages among the loci. The relationships between these components and sigma 2w, sigma 2wF, and sigma 2bF are elaborated in terms of tight and loose linkage. The exact computations of sigma 2wF and sigma 2bF require the use of two locus descent measures without linkage. The variances of various averages of actual identities by descent, such as the proportions for individuals or populations, are formulated for a sample of individuals.

Analysis of Variance↗
PubMed1983

Linkage between a marker locus and a quantitative trait of sibs.

Several variations of a method for detecting linkage between a marker locus and a quantitative trait in full sib families are presented along with computational details. All variations are based on contrasts within qualifying families of three or more sibs. The empirical powers of the various test statistics, evaluated by simulation, were very similar, and also similar to that of Smith. These single-generation tests are likely to be successful only for many families and relatively tight linkage.

Alleles↗
PubMed1980

Selection limits and strategies.

Strategies are analyzed for maximizing the ultimate limit to truncation selection for a quantitative trait in finite populations. By using a formulation of Kimura and Crow [Kimura, M. & Crow, J. F. (1978) Proc. Natl. Acad. Sci. USA 75, 6168-6171], it is shown that the limit is maximized by truncating at the mode with the highest ordinate of the phenotypic distribution. This implies 50% selection for the normal or any unimodal symmetric distribution and, for skewed distributions, selection of more than one-half if desired phenotypes are in the long tail of the distribution, less than one-half if in the short tail. For dioecious populations, the optimal procedure requires, in addition, equal numbers recorded and selected of each sex. For monoecious populations the limit can be improved by using the best individuals mated to the next-best individuals. Limitations of the results are discussed.

Journal Article↗
PubMed1977

Spontaneous mutation rates at enzyme loci in Drosophila melanogaster.

In a marked-inversion-balanced lethal system mutations were accumulated at a minimum pressure of natural selection on 2000 second chromosomes of Drosophila melanogaster that originated from 4 stem chromosomes. Five enzyme loci were tested: alpha-glycerol-3-phosphate dehydrogenase (EC 1.1.1.8), malate dehydrogenase (Mdh, EC 1.1.1.37), alcohol dehydrogenase (EC 1.1.1.1), hexokinase-C (Hex-C tentative name), and alpha-amylase (Amy, EC 3.2.1.1). Three band-morph mutants, one at the Mdh locus, one at the Hex-C locus, and one at the Amy locus, were detected out of 1,658,308 allele replications. In addition, 17 null mutants were found. Accepting that the number of structural genes is the same as that of bands in the salivary gland chromosomes, the total mutation rate per generation for all the structural genes in the second chromosomes is estimated to be 0.008-0.040, which is much smaller than that estimated for viability polygenes (0.12-0.17). Thus, it is speculated that most viability and other fitness polygenes are located in controlling regions outside the structural genes.

Alcohol Oxidoreductases↗
PubMed1977

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.

Crosses, Genetic↗