The quantitative analysis of chromosome pairing and chiasma formation based on the relative frequencies of M I configurations

Whilst reliable estimates of chiasma frequencies can usually not be obtained, the probability (b) of a chromosome arm to be bound by at least one chiasma can often be determined. In the absence of interference this probability equals (1−e−2μ), where 2μ is the average chiasma frequency of the chromosome arm and μ the average crossover frequency or map length. In the presence of interference μ is shown to retain its genetic meaning as an additive metric that may describe the chromosome arm or other distinctive chromosome segment in terms of genetic recombination. It is a form of potential map length, comparable to, but numerically different from the regular map length. It is termed provisionally “crossing-over potential”.A chromosome with armsm andn with “crossing-over potentials” μ and ν will form ring bivalents with a frequency (1−e−2μ).(1−e−2ν); open bivalents with a frequency (1−e−2μ).e−2ν+(1−e−2ν).e−2μ; univalent pairs with a frequencye−2μ.e−2ν. Estimates of these frequencies yield equations from which μ and ν may be solved. In rye (Secale cereale) their ratio (q) is approximately two and differs from the mitotic arm length ratio of 1.4, indicating localization of chiasmata in the long arms.Graphs are given to show how, with constantq, the relation between the probabilitiesbm andbn of the two arms being bound changes with changing averageb.Data are presented on chiasma frequencies in M I, and compared with the frequencies expected in the absence of interference to give an impression of the degree of interference. Apparent fusion of chiasmata simulates interference.