Estimating parameters of the family-size distribution in ascertainment sampling schemes: numerical results

It is argued that, in any ascertainment sampling scheme using data from families of various sizes, there is never any need to assume a particular form for the (unknown) family-size distribution. There exists a simple conditional method, making no assumptions about the family-size distribution, that is always preferable to the assumption of any particular distributional form. Furthermore, the simplicity of the conditional method gives insights into properties of estimates of genetic and ascertainment parameters, which are not available when a particular form for the family-size distribution is assumed.     

Inequality constrained estimation of genetic parameters

Summary A method is presented for computing estimates of genetic parameters under linear inequality constraints such that solutions are within theoretical limits. The method produces biased estimators, yet a small scale numerical study, also presented, shows that the inequality constrained estimators have a small mean squared error of prediction than the best of unbiased estimators. The increase in efficiency of estimation is particularly useful for traits where heritability is near the boundary values of zero or one.     

Modified full-sib selection and estimation of genetic parameters

Summary A cycle of full-sib selection is completed in three seasons while that of a modified method is completed in two seasons. In modified full-sib selection, selected families can be recombined and new families generated following a partial-diallel cross. The components of genetic variance can be estimated from the partial-diallel analysis of such families. Thus, in addition to performing selection, genetic parameters can be estimated.     

Efficient experimental designs for the estimation of genetic parameters in plant populations.

Procedures for estimating the genetic parameters of plant populations frequently employ progeny testing to ascertain the genotype of maternal plants. However, when experimental resources are limited (e.g., electrophoretic markers), the large progeny sizes required for accurate typing severely restricts the numbers of families which can be tested. In this paper, four experimental designs with partial progeny testing are compared with the standard procedure of complete testing for their statistical efficiency in estimating the gene frequency, fixation index, and outcrossing rate at a single diallelic locus. It is shown that substantial increases in efficiency can be obtained (especially in inbred populations) if one or two individuals per family are assayed, and then further progeny testing is confined to those families which give rise to a heterozygote in this initial screening. Sample size for various purposes are computed and factors affecting the applicability of such "censored" designs are discussed.     

The effects of demography and linkage on the estimation of selection and mutation parameters

We explore the effects of demography and linkage on a maximum-likelihood (ML) method for estimating selection and mutation parameters in a reversible mutation model. This method assumes free recombination between sites and a randomly mating population of constant size and uses information from both polymorphic and monomorphic sites in the sample. Two likelihood-ratio test statistics were constructed under this ML framework: LRTγ for detecting selection and LRTκ for detecting mutational bias. By carrying out extensive simulations, we obtain the following results. When mutations are neutral and population size is constant, LRTγ and LRTκ follow a chi-square distribution with 1 d.f. regardless of the level of linkage, as long as the mutation rate is not very high. In addition, LRTγ and LRTκ are relatively insensitive to demographic effects and selection at linked sites. We find that the ML estimators of the selection and mutation parameters are usually approximately unbiased and that LRTκ usually has good power to detect mutational bias. Finally, with a recombination rate that is typical for Drosophila, LRTγ has good power to detect weak selection acting on synonymous sites. These results suggest that the method should be useful under many different circumstances.     

Upward bias in estimation of genetic effects

Because of the large number of tests for linkage that are performed in genome scans, the naive estimator of the size of a genetic effect in cases of borderline significance can be inflated and lead to unrealistic expectations for successful replication. As a remedy, this report proposes lower confidence limits that account for the multiple comparisons of the genome scan.     

Epistasis interaction of QTL effects as a genetic parameter influencing estimation of the genetic additive effect

Epistasis, an additive-by-additive interaction between quantitative trait loci, has been defined as a deviation from the sum of independent effects of individual genes. Epistasis between QTLs assayed in populations segregating for an entire genome has been found at a frequency close to that expected by chance alone. Recently, epistatic effects have been considered by many researchers as important for complex traits. In order to understand the genetic control of complex traits, it is necessary to clarify additive-by-additive interactions among genes. Herein we compare estimates of a parameter connected with the additive gene action calculated on the basis of two models: a model excluding epistasis and a model with additive-by-additive interaction effects. In this paper two data sets were analysed: 1) 150 barley doubled haploid lines derived from the Steptoe × Morex cross, and 2) 145 DH lines of barley obtained from the Harrington × TR306 cross. The results showed that in cases when the effect of epistasis was different from zero, the coefficient of determination was larger for the model with epistasis than for the one excluding epistasis. These results indicate that epistatic interaction plays an important role in controlling the expression of complex traits.     

The estimation of genetic divergence

Summary We have independently repeated the computer simulations on which Nei and Tateno (1978) base their criticism of REH theory and have extended the analysis to include mRNAs as well as proteins. The simulation data confirm the correctness of the REH method. The high average value of the fixation intensity ₂ found by Nei and Tateno is due to two factors: 1) they reported only the five replications in which ₂ was high, excluding the forty-five replications containing the more representative data;and 2) the lack of information, inherent to protein sequence data, about fixed mutations at the third nucleotide position within codons, as the values are lower when the estimate is made from the mRNAs that code for the proteins. REH values calculated from protein or nucleic acid data on the basis of the equiprobability of genetic events underestimate, not overestimate, the total fixed mutations. In REH theory the experimental data determine the estimate T₂ of the time average number of codons that have been free to fix mutations during a given period of divergence. In the method of Nei and Tateno it is assumed, despite evidence to the contrary, that every amino acid position may fix a mutation. Under the latter assumption, the measure X₂ of genetic divergence suggested by Nei and Tateno is not tenable: values of X₂ for the hemoglobin divergences are less than the minimum number of fixed substitutions known to have occurred.Within the context of REH theory, a paradox, first posed by Zuckerkandl, with respect to the high rate of covarion turnover and the nature of general function sites in proteins is resolved.     

Simultaneous estimation of all the parameters of a stepwise mutation model.

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (Jeffreys 1985; Litt and Luty 1989; Weber and May 1989), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (Tautz 1993). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.