Linkage between markers and genes that affect a phenotype of interest may be determined by examining differences in marker allele frequency in the extreme progeny of a cross between two inbred lines. This strategy is usually employed when pooling is used to reduce genotyping costs. When the cross progeny are asexual the extreme progeny may be selected by multiple generations of asexual reproduction and selection. In this thesis I will analyse this method of measuring phenotype in asexual cross progeny. The aim is to examine the behaviour of marker allele frequency due to selection over many generations, and also to identify statistically significant changes in frequency in the selected population. I will show that stochasticity in marker frequency in the selected population arises due the finite initial population size. For Mendelian traits, the initial population size should be at least in the low to mid hundreds to avoid spurious changes in marker frequency in the selected population. For quantitative traits the length of time selection is applied for, as well as the initial population size, will affect the stochasticity in marker frequency. The longer selection is applied for, the more chance of spurious changes in marker frequency. Also for quantitative traits, I will show that the presence of epistasis can hinder changes in marker frequency at selected loci, and consequently make identification of selected loci more difficult. I also show that it is possible to detect epistasis from the marker frequency by identifying reversals in the direction of marker frequency change. Finally, I develop a maximum likelihood based statistical model that aims to identify significant changes in marker frequency in the selected population. I will show that the power of this statistical model is high for detecting large changes in marker frequency, but very low for detecting small changes in frequency.