Marker-assisted selection efficiency in populations of finite size

The efficiency of marker-assisted selection (MAS) based on an index incorporating both phenotypic and molecular information is evaluated with an analytical approach that takes into account the size of the experiment. We consider the case of a population derived from a cross between two homozygous lines, which is commonly used in plant breeding, and we study the relative efficiency of MAS compared with selection based only on phenotype in the first cycle of selection. It is shown that the selection of the markers included in the index leads to an overestimation of the effects associated with these markers. Taking this bias into account, we study the influence of several parameters, including experiment size and heritability, on MAS efficiency. Even if MAS appears to be most interesting for low heritabilities, we point out the existence of an optimal heritability (similar to 0.2) below which the low power of quantilative trait loci detection and the bias caused by the selection of markers reduce the efficiency. In this situation, increasing the power of detection by using a higher probability of type I error can improve MAS efficiency. This approach, validated by simulations, gives results that are generally consistent with those previously obtained by simulations using a more sophisticated biological model than ours. Thus, though developed from a simple genetic model, our approach may be a useful tool to optimize the experimental means for more complex genetic situations.