A multiple regression analysis of hybrid vigour in single crosses ofDactylis glomerata L

Thirty-six crosses ofDactylis glomerata together with their parents were assessed for seasonal yield at twelve successive harvests during a 16 month period. The yields varied with the environment provided by the climatic seasons of the year. For some crosses, the hybrid approximated to its mid-parental value at one environment but exceeded both parents in another, showing hybrid vigour.The twelve yield values for a hybrid and for each of its parents were analysed as a multiple regression in the form -[Formula: see text] wherey ij,P i andp j are the yields of the hybrid and parents at any one harvest,b i andb j are regression coefficients pertaining to the respective parents and a is a constant. It was found that such a regression accounted for a great part of the seasonal yield variation of each cross, including the situation of a hybrid approximating to the mid-parental value or exceeding both parents.Theb value pertaining to an individual parent varied according to the parent with which it was crossed. In the discussion the values ofb anda were considered in relation to the incidence of hybrid vigour, and the use of a multiple regression is compared with other analyses of quantitative inheritance.