Theoretical Population Biology 56, 110 (1999) MINIREVIEW Coalescing into the 21st Century: An Overview and Prospects of Coalescent Theory Yun-Xun Fu Human Genetics Center, SPH, University of Texas, P.O. Box 20334, Houston, Texas 77225 and Wen-Hsiung Li Ecology and Evolution, University of Chicago, 1101 East 57th Street, Chicago, Illinois 60637 Received July 16, 1998 Coalescent theory represents the most significant progress in theoretical population genetics in the past two decades of this century. It is now widely recognized as a cornerstone for rigorous statistical analyses of molecular data from populations. In the future, challenges from the rapidly expanding body of molecular data will continue to inject fresh blood into the develop- ment of coalescent theory. As the 21st century looms, we review recent progress in coalescent theory and discuss some prospects for future developments, particularly with regard to human population genetics.  1999 Academic Press 1. INTRODUCTION A central theme in population genetics is understand- ing how a population evolves under a given set of condi- tions. Evolution is a forward process in the sense that a population changes its characteristics with time. Conse- quently, prospective approaches in population genetics dominated the field in the past. The focus of a prospec- tive approach is usually a certain characteristic or quan- tity, such as the frequency of a mutant gene in the pop- ulation. However, empirically the characteristics of a natural population are usually examined by taking sam- ples from the population. Interesting biological ques- tions that arise from a sample are mostly retrospective, such as the history of the population that gave rise to the sample, or the evolutionary mechanisms responsible for the characteristics observed. The rapid accumulation of DNA sequence data since the 1980s has transformed the mainstream of population genetics research from prospective to retrospective, from demonstration of prin- ciples to inference of events that happened in the past. To infer the past from a sample taken from a present population, a new approach is required. Coalescent theory arose from this necessity. The essence of coales- cent theory is to start with a sample, and trace backward in time to identify events that occurred in the past since the most recent common ancestor of the sample. Since the seminal work of Kingman (1982a, b), coalescent theory has been the most active topic in theoretical population genetics, and it is now widely recognized as the corner- stone for various statistical analyses of molecular popula- tion samples. The usefulness of the theory comes mainly from three features. First, it is a sample-based theory. Since the study of a population usually relies on a sample of individuals from that population, a theory that describes the properties of a sample is more relevant than the classical population genetics theory that describes the properties of the entire population. Second, it is a highly efficient approach. An important by-product of coalescent theory is the development of highly efficient algorithms for simulating population samples under various population genetics models, allowing various aspects of a model to be examined numerically. Third, coalescent theory is par- ticularly suitable for molecular data, such as DNA sequence samples, which contain rich information about the ancestral relationships among the individuals sampled. Various aspects of coalescent theory have been reviewed previously (Tavare , 1984; Takahata, 1991; Article ID tpbi.1999.1421, available online at http:www.idealibrary.com on 1 0040-580999 K30.00 Copyright ] 1999 by Academic Press All rights of reproduction in any form reserved.