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CROP BREEDING & GENETICS

Pollen Dispersion within a Population, Nonrandom Mating Theory, and Number of Replications in Polycross Nurseries

Dep. of Agronomy, Purdue Univ., 915 West State St., West Lafayette, IN 47907-2054

^* Corresponding author (wnyquist{at}purdue.edu).

A breeder is uncertain how many replications to include in a polycross. Our objective was to develop a method to answer the question. Four isolated, space-planted nurseries on a 0.91-m grid of 29 rows by 35 plants were established of ryegrass (Lolium perenne L.), a wind-pollinated species, with rows in each nursery oriented differently with respect to the compass. The middle row was homozygous for the dominant fluorescent marker gene. Seeds from the seven middle plants in the seven rows closest to the middle row on both sides were observed for the frequency of the dominant gene. From these observations a two-parameter exponential pollen dispersal function was fitted for the mean of all eight directions combined. The variance among the cross-pollination frequencies q_jk was calculated under two pollination assumptions: (i) pollination confined within each replication and (ii) pollination across all replications. After bulking equal quantities of seed from all replications we have the variance ² of the mean cross frequencies _jk. The square root of this variance, , was used as a measure of the closeness to random mating. The required number of replications to achieve specific levels of closeness to random mating is given for 3 to 100 clones for Assumption 1. The measure of closeness to random mating is given for 3 to 100 clones and up to 30 replications for Assumption 2. When pollination is assumed to occur across replications, a 70% reduction in the variance of is obtained compared to pollination within replications. Hence, fewer replications are required in this case.

Abbreviations: DST, daylight savings time.