The broad goals are 1. to provide robust, computationally feasible statistical methods for analysis of genetic linkage data, and 2. to analyze the strengths and faults of, improve, and extend existing methods. These should further the goals of locating genetic loci involved in various human traits and diseases, and determine their effects and modes of inheritance. Specific aims are as follows: A. To develop methods for mapping complex traits by allele-sharing in large pedigrees. Consider selection of most powerful sharing statistics. For multipoint identity-by-descent sharing, make specific proposals regarding properties of such sharing statistics and most powerful statistics under certain assumptions. Develop strategies for fine mapping of complex trait genes in those small isolated founder populations with nearly complete genealogical information, but that are too large for feasible full multipoint analysis. Consider identity-by-state and population association methods and propose strategy to determine most powerful methods under a variety of scenarios. B. To improve assessment of uncertainty in ordering of genetic markers using a robust yet efficient method that does not rely on strong assumptions about interference. Use with Bayesian methods to assess uncertainty, combine data from different studies, integrate maps. C. To develop methods and software for analysis of human sperm data. Implement and improve programs for detecting segregation distortion, modeling interference, and for robust marker ordering with sperm data. Use these implementations to study heterogeneity of genetic parameters in human males. D. To investigate robustness of linkage procedures to problems such as misspecified allele frequencies, genotyping errors, and interference. Study role of incomplete data in exacerbating misspecification problems. Pinpoint areas of greatest concern, develop diagnostics and remedies.