PubMed · 3374568
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A W Edwards. 1988-05-26. Lod score or log-likelihood?. https://doi.org/10.1038/333308b0
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In the Admixture Model, the probability that an individual carries a certain allele at a specific marker depends on the allele frequencies in K ancestral populations and the proportion of the individual's genome originating from these populations. The markers are assumed to be independent. The Linkage Model is a Hidden Markov Model that extends the Admixture Model by incorporating linkage between neighboring loci. We prove consistency and asymptotic normality of maximum likelihood estimators for the ancestry of individuals in the Linkage Model, complementing earlier results by (Pfaff et al., 2004; Pfaffelhuber and Rohde, 2022; Heinzel, 2025) for the Admixture Model. These results are used to prove that a statistical test that allows for model selection between the Admixture Model and the Linkage Model is an asymptotic level-α-test. Finally, we demonstrate the practical relevance of our results by applying the test to real-world data from The 1000 Genomes Project Consortium (2015).
To identify the genetic etiology of a disease of interest, disease-related characteristics (phenotypes) are often tested for association with genetic variants (genotypes). Although genetic association studies of single genetic variants have been widely performed, there has been increasing interest in studies of multiple adjacent genetic variants on one chromosome, known as a haplotype. In this review, we will provide background about the origin of haplotypes and why they can be useful in genetic studies; we will discuss approaches to determining haplotypes and performing haplotype-based genetic association studies; and we will compare single variant and haplotype-based approaches.
Association between markers and sugarcane diseases were investigated in a collection of 154 sugarcane clones, consisting of important ancestors or parents, and cultivars. 1,068 polymorphic AFLP and 141 SRR markers were scored across all clones. Data on the four most important diseases in the Australian sugarcane industry were obtained; these diseases being pachymetra root rot (Pachymetra chaunorhiza B.J. Croft & M.W. Dick), leaf scald (Xanthomonas albilineans Dowson), Fiji leaf gall (Fiji disease virus), and smut (Ustilago scitaminea H. & P. Sydow). By a simple regression analysis, association between markers and diseases could be readily detected. However, many of these associations were due to the effects of embedded population structure and random effects. After taking population structure into account, we found that 59% of the phenotypic variation in smut resistance ratings could be accounted for by 11 markers, 32% of variation for leaf scald and pachymetra root rot rating by 4 markers, and 26% of Fiji leaf gall by 5 markers. The results suggest that marker-trait associations can be readily detected in populations generated from modern sugarcane breeding programs. This may be due to special features of past sugarcane breeding programs leading to persistent linkage disequilibrium in modern parental populations.