AUTHOR=Wu Jie , Liu Yangxiu , Zhao Yiqiang TITLE=Systematic Review on Local Ancestor Inference From a Mathematical and Algorithmic Perspective JOURNAL=Frontiers in Genetics VOLUME=Volume 12 - 2021 YEAR=2021 URL=https://www.frontiersin.org/journals/genetics/articles/10.3389/fgene.2021.639877 DOI=10.3389/fgene.2021.639877 ISSN=1664-8021 ABSTRACT=Genotypic data provide important perceptions into population and medical genetics. Local ancestry inference (LAI) (sometimes termed as ancestry deconvolution) which is based on genomic data is also developing rapidly, in which Hidden Markov model (HMM) serve as a major algorithm, combined with other statistical model and machine learning techniques. In this article, we surveyed the mathematical structure, application characteristics, historical development and benchmark analysis of LAI method in detail, which will help people better understand and further develop LAI methods. First and foremost, this review extensively explores mathematical structure of each model and their application characteristics. Next, we use bibliometrics to show a detailed model application fields and list articles to show important history development. Benchmark was provided to evaluate the model's efficiency, accuracy, and stability. We finally addressed the challenges and prospects in this field. This review may help the model developers to realize current challenges, develop more advanced models, and enable scholars to select appropriate models according to given populations and datasets.