Wheat bunt field trials

A mathematical model of wheat bunt field trials has been constructed which seems to be adequate. The mean and spread of the heterozygous plants cannot be observed, but these can be calculated because the means and variances of the percentages for the homozygous and segregating rows can be observed and it can be assumed that the probabilities of infection for different types of plants are perfectly correlated as between rows. The variance of the percentages for the segregating rows results from the probabilities of infection for the various genotypes present. For the data presented the variance for the segregating rows was very close to the binomial variance, although the variances for the homozygous rows are considerably greater. This apparent inconsistency did not result from different a values for the genotypes of plants present. It was shown that by using a value of 1.6 for a1 and a2 the calculated errors resulting did not differ significantly from those observed. It was assumed that the spreading effects noted in this experiment were due to environmental influences. Modifying factors would have a similar effect and probably the two could not be distinguished unless the modifiers affected only some genotypes. This model should be of aid in interpreting complex hybrids in that the nature of the variances will be understood better. This is particularly true where a row or family is heterozygous or made up of plants of different genotypes which have different probabilities of infection. It also indicates that the spread of the percentages depends on the length of rows, the spread of infectivity levels, and the general level of infection. The considerations involved in developing this model apply to developing models for any similar experiments. The results of the mathematical model have been applied in detail to extensive genetic data from a cross between Banner Berkeley and Baart wheats. The results are consistent with the assumption that the spreading effect as measured by a is independent of genotype and length of row. This assumption is probably only true for certain ranges of genotypes and lengths of row.