Regional scores for localizing genes

This dissertation develops a regional score method to help find the location of a gene contributing to a specific trait. We adapt a technique from signal processing using weighted moving average to smooth the Identity By Descent (IBD) scores and the Identity by State (IBS) scores to localize contributing genes. To accomplish this, the IBD and the IBS processes are defined and their properties are derived for different cases. In addition, the Identity By Descent Proportion (IBDP), Identity By State Proportion (IBSP), the Normalized Identity By Descent (ZIBDP) and the Normalized Identity By State (ZIBSP) are defined and their properties derived. The regional scores method smooths the IBDP/IBSP by summing them over all of the markers on the chromosome with markers close to the location of interest weighted more heavily. The regional scores can be found at any location on the chromosome. It also allows for unevenly spaced markers and adjusts for the spacing. Here we implement the regional score method with the Haldane, no interference model for recombination. Simulations of a whole genome that consists of 20 chromosomes each of length 100 with markers every 10 cM have been made for different contributing gene cases and for different number of sib pairs. Critical values are determined for both the regional scores and ZIBDP/ZIBSP scores based on results from simulating the genome under the null hypothesis of no contributing gene. Then the regional scores and the ZIBDP/ZIBSP from the above simulations were compared to their corresponding threshold. The results indicated that in general the number of times each method detected a contributing gene is higher with the regional score method with higher true positives and similar false positive compared to the ZIBDP/ZIBSP methods. We also provide a computer program (SIGLEVEL) to calculate the significance level and the thresholds for genetic linkage.