Mapping human disease susceptibility genes can be the first in a series of steps leading to better diagnostic tests and ultimately strategies for combating or controlling the disease. The use of pairs or other small groups of relatives who share a trait as the basic unit for mapping genes has great advantages when the trait of interest is genetically complex or has low or age-dependent penetrance. The aim of the proposed research is to provide statistical methods to aid in the design and analysis of such gene mapping studies in human genetics and in experimental genetics, particularly when the whole genome or a portion thereof is scanned to search for the relevant genes. The problems emphasized in the proposal are motivated by the laboratory technique of Genomic Mismatch Scanning which is under development in the laboratory of Dr. Patrick O. Brown; but the proposed statistical ideas are relevant to the analysis of data obtained from any highly polymorphic, reasonably dense genetic map and can be applied to discrete or quantitative traits. Specific long term goals are the following: (1) Develop general methodology for searching the genome to identify regions of enriched identity by descent, hence likely to contain genes affecting the trait or traits of interest. (2) Develop general, flexible models of multigenic traits; develop statistical techniques appropriate for those models. Statistical models will be developed by mathematical analysis and computer simulation. The analysis of experimental data will serve to validate and refine the models. The distinguishing features of the proposal are: (1) systematic consideration of the effect of scanning markers distributed throughout the genome and (2) exploitation of the relation between the statistics of gene mapping problems and of "change-point problems," which have been thoroughly studied in recent statistical research.