RESUMEN

The shifted multiplicative model (SHMM) is used with a cluster method to identify subsets of sites in an international maize (Zea mays L.) trial without genotypic rank-change. For cluster analysis, distance between two sites is defined as the residual sum of squares after fitting SHMM with one multiplicative term (SHMM1) if SHMM1 does not show genotypic rank-change. However, if SHMM1 does show genotypic rank-change, the distance between two sites is defined as the smaller of the sums of squares owing to genotypes within each of the two sites. Calculation of distance between two sites is facilitated by using the site regression model with one multiplicative term (SREG1), which can be reparameterized as SHMM1 when only two sites are considered. The dichotomous splitting procedure, used on the dendrogram obtained from cluster analysis, will first perform SHMM analyses on each of the last two cluster groups to join (end of the dendrogram). If SHMM1 does not give an adequate fit, the next step is to move down the branches of the tree until groups of sites (clusters) are found to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign. Five final groups of sites to which SHMM1 provides an adequate fit and primary effects of sites are all of the same sign were obtained. The procedure appears to be useful in identifying subsets of sites in which genotypic rank-change interactions are negligible.

RESUMEN

The shifted multiplicative model (SHMM) is used in an exploratory step-down method for identifying subsets of environments in which genotypic effects are "separable" from environmental effects. Subsets of environments are chosen on the basis of a SHMM analysis of the entire data set. SHMM analyses of the subsets may indicate a need for further subdivision and/or suggest that a different subdivision at the previous stage should be tried. The process continues until SHMM analysis indicates that a SHMM with only one multiplicative term and its "point of concurrence" outside (left or right) of the cluster of data points adequately fits the data in all subsets. The method is first illustrated with a simple example using a small data set from the statistical literature. Then results obtained in an international maize (Zea mays L.) yield trial with 20 sites and nine cultivars is presented and discussed.

RESUMEN

Livestock grazing endophyte (Acremonium coenophialum)-infected tall fescue (Festuca arundinacea Schreb. cv. Kentucky 31) at high ambient temperatures may suffer from fescue toxicosis. Adult Angus cows (Bos taurus) were fed 0 to 1 kg/d of 70% infected tall fescue seed containing about 4.4 g of loline alkaloids in factorial combination with thiamin at 0 or 1 g/d. Cows assigned to the zero level of tall fescue seed received a supplement of equivalent energy and protein. Ingestive behavior was measured at 1330 to 1430 EDT during two 4-d periods in two consecutive weeks in August on alfalfa (Medicago sativa L.) pastures using a tethered grazing system. Alfalfa intake per measured grazing session of cows given tall fescue seed declined linearly (P less than .01) as air temperatures during grazing increased above 25 degrees C, largely because of shorter grazing meals. Thiamin increased alfalfa intake per measured grazing session by extending grazing time. Alkaloids in ingested endophyte-infected tall fescue induce thiamin deficiencies in cattle that result in symptoms of tall fescue toxicosis.

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Livestock grazing endophyte (Acremonium coenophialum Morgan-Jones and Gams)-infected tall fescue (Festuca arundinacea Schreb.) perform poorly due to tall fescue toxicosis, especially when animals are under heat stress. In order to determine whether thiamin promotes recovery from tall fescue toxicosis, 1 or 0 g of thiamin per day, as mononitrate, was fed orally to adult Angus (Bos taurus) cows (380 +/- 8 kg) grazing either tall fescue pasture with and without endophyte or alfalfa (Medicago sativa L.). A tethered grazing system employing a split-plot design was used to estimate intake and components of ingestive behavior. No significant differences attributable to thiamin supplements were seen in rates of intake and biting, grazing time and intake per bite when cows grazed endophyte-infected tall fescue during the first 4 d of exposure. When cows grazed endophyte-infected (greater than 95%) tall fescue with 2,091 micrograms/g loline alkaloids after 4 d of exposure, the untreated animals ingested herbage dry matter (DM) at 1.19 kg/h, whereas the cows receiving thiamin ate 1.57 kg/h (P less than .05). Cattle achieved these rates of DM intake by forming bites of 1.0 and 1.2 g DM at 24 and 26 bites/min when treated with 0 and 1 g of thiamin per day, respectively. Thiamin supplements had no effect on ingestive behavior of cows grazing endophyte-free tall fescue or alfalfa after exposure to these forages for 4 d. Responses to thiamin generally were greater when cattle grazing endophyte-infected tall fescue were exposed to heat stress. Oral thiamin supplementation may alleviate tall fescue toxicosis of beef cattle during warm weather.

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A generation matrix theory of full-sib mating is developed in which 13 mating "classes" are distinguished according to identity of genes in individuals mated and identity of genotypes as belonging to homozygous, parental, or offspring sets. The 13 times 13 matrix reveals some properties of the full-sib mating system not shown by previous work. The eigenvalues and a set of eigenvectors for the generation matrix, and the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab times cd, are given. The genotypic array of descendants in an arbitrary generation is also given. A new formula is derived for the coefficient of inbreeding in generation n + m in terms of coefficients of inbreeding in earlier generations. An algorithm is presented for calculating the probability of a given situation of identity of alleles carried by two individuals given only the indices of their own respective generations and the generation of their most recent common ancestor. The application of such probabilities to obtaining covariances between relatives in a full-sib mating system, under the assumptions of independence and non-interaction among loci, is illustrated. All results are shown to agree with previous work in special cases. All possible full sib, generation n - 1 parent-generation n + m offspring, and generation n uncle-generation n + m nephew covariances for 1 less than n + m less than or equal to 8 are obtained using the given algorithm.

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RESUMEN

A one-locus "operator" for a younger parent-offspring inbreeding system is obtained by a generation matrix method in which 14 "classes" of matings are defined. The eigenvalues and a set of eigenvectors for the generation matrix and, also, the general solution for the frequencies of mating classes among descendants of an original mating of genotypes ab x cd are given. The operator gives the genotypic array of descendants of a given mating an arbitrary number of generations later. Using this operator, an algorithm is developed for calculating identity coefficients between any two relatives in a possibly branching younger parent-off spring mating system. Application to obtaining covariances between relatives for a one-locus model is illustrated.