A statistical mixture model for estimating the proportion of unreduced pollen grains in perennial ryegrass (Lolium perenne L.) via the size of pollen grains

The size of pollen grains is commonly used to indicate the ploidy level of pollen grains. In this paper observations of the diameter of pollen grains are evaluated from one diploid accession of perennial ryegrass (Lolium perenne L.), which was expected to produce diploid (unreduced) pollen grains in addition to haploid pollen grains. The considerable overlap of the diameter distributions of haploid and diploid pollen grains severely hampers the accurate estimation of the proportion of diploid pollen grains. To overcome this problem we develop in this paper a statistical normal mixture model and we describe a method to test for the production of diploid pollen grains from a diploid parent, and to estimate the proportion of diploid pollen grains.