Estimates of gene frequencies in two heterotic maize populations

Summary The present study was undertaken to obtain information on average gene frequency in two heterotic populations of maize (Zea mays L.), Mezcla Amarillo Selection (MAS) and J607. Sixty-four male plants were taken in each of the populations and each of these were crossed to a different set of eight plants, four of which belonged to the same population and four to the other population. This resulted in two groups of intra-population (within MAS and within J607) and two groups of inter-population (MAS X J607 and J607 X MAS) progenies. Each group consisted of 256 full-sib progenies on the pattern of the North Carolina Design I mating system. The male plants were selfed to produce 64 S₁ prgenies in each population. The materials were evaluated at two diverse locations, Ludhiana and Gurdaspur, for grain yield, ear length, ear girth, number of kernel rows, plant height, ear height and days to silk. An incomplete block design with two replications were used. The plot consisted of a 5 m long row. Ratios of estimated genetic components of variance and covariance were compared with corresponding theoretical ratios computed for a single locus for various gene frequencies and levels of dominance, and approximate ranges of the gene frequencies and their relative magnitude were worked out in the two populations. The average frequency of favourable genes for plant height was estimated as 0.6 in MAS and 0.8 in J607. For grain yield the average gene frequency was 0.8 to 0.9 in MAS and 0.7 to 0.8 in J607 whereas for ear height it was 0.5 to 0.7 in MAS and 0.4 to 0.6 in J607. The gene frequency in the two populations seemed to be similar for days to silk, ear length, ear girth and kernel rows.     

Multivariate Polya and Inverse Polya Distributions of Order k

Multivariate Polya and inverse Polya distributions of order k are derived by means of generalized urn models and by compounding the type II multinomial and multivariate negative binomial distributions of order k of PHILIPPOU , ANTZOULAKOS and TRIPSIANNIS (1990, 1988), respectively, with the Dirichlet distribution. It is noted that the above two distributions include as special cases a multivariate hypergeometric distribution of order k, a negative one, an inverse one, a negative inverse one and a discrete uniform of the same order. The probability generating functions, means, variances and covariances of the new distributions are obtained and five asymptotic results are established relating them to the above-mentioned multinomial and multivariate negative binomial distributions of order k, and to the type II negative binomial and the type I multivariate Poisson distributions of order k of PHILIPPOU (1983), and PHILIPPOU , ANTZOULAKOS and TRIPSIAN-NIS (1988), respectively. Potential applications are also indicated. The present paper extends to the multivariate case the work of PHILIPPOU , TRIPSIANNIS and ANTZOULAKOS (1989) on Polya and inverse Polya distributions of order k..     

Individual and group selection with competition

Summary The response of a randomly mating population which is expected to follow selection of phenotypic units, comprising individuals or groups whose members have an arbitrary degree of relatedness, was formulated using a model which included additive and dominance competition effects. The derivation involved three steps. Twenty-two quadratic components were defined, six describing individual (direct) and neighbor (associate) effects, and 16 describing direct by associate interactions for different loci, for single loci with different alleles, and for identical alleles. Six covariances between pairs of individual phenotypes and three of individuals with their offspring were defined according to whether or not their direct or associate genotypes are common, and expressed in terms of the quadratic components. Finally, variances of selection units of different types and their covariance with their offspring were expressed as compounds of these individual covariances. Explicit formulations for mass, clonal and full-sib selection show that without constraints on the quadratic components, and hence on the magnitude and type of competition operative, no predictions as to the relative efficiencies of these three methods can be made.     

Covariances of relatives and selection response in generations of selfing from an outcrossed base population

Summary The covariances of relatives arising under selfing from a general outbred base population in linkage equilibrium and without epistasis given by Cockerham (1983) are expressed in an alternative form which is an extension of the treatment by Mather and Jinks (1982) of the more restricted population descended from a single F₁ family. Whereas no more than two quadratic components are required to describe any covariance in the case of F₁, descendants, this more general case calls for a total of four, three of which are needed for any particular covariance. The estimation of covariances and their use for the prediction of selection response is described for breeding programs initiated by one or more cycles of intermating among a number of parental lines, as advocated by Hansel (1964) and Jensen (1970). It is pointed out that the homozygous lines descended from such a population will have up to twice as much variance as those from an F₁ between a randomly chosen pair from the same population of parents. The selection method is especially recommended for undeveloped species in which the parental lines are not well characterized and large selection responses are needed.