TY - JOUR

T1 - Non-homogeneous infinite sites model under demographic change

T2 - Mathematical description and asymptotic behavior of pairwise distributions

AU - Bobrowski, Adam

AU - Wang, Ning

AU - Chakraborty, Ranajit

AU - Kimmel, Marek

N1 - Funding Information:
We thank Drs. B. Budowle and K. Miller of the FBI Academy FSRTC for kindly providing the mtDNA sequence data. This work was supported by US Public Health Service research grants GM 41399 and GM 45861 (to R.C.), CA 75432 (to M.K.) and GM 58545 (to R.C. and M.K.) and by the Keck's Center for Computational Biology at Rice University (M.K.). An anonymous referee contributed several important and helpful remarks. A.B. is on leave from the Department of Mathematics at the Lublin Technical University, Poland. M.K. did part of his research when he was a sabbatical visitor at the Human Genetics Center at the School of Public Health of the University of Texas in Houston.

PY - 2002

Y1 - 2002

N2 - We developed a mathematical model, which makes possible to predict joint distributions of numbers of mismatches in two or more linked regions of the genome, based on the Infinite Sites Models, under mutation-drift equilibrium as well as under various patterns of population growth. With mutation rates varying in the region, one of the predictions is different correlation between numbers of mismatches in the two regions, depending on the pattern of the past population growth (constant, slowly growing, or rapidly growing). Also, for slower growth patterns of population sizes, the coalescence tree is not necessarily 'starlike'. Thus, the joint distribution of mismatches, predicted by the model, provides additional insights into the demographic history of the populations. We also developed expectations and variances of sample statistics under different growth scenarios. As an application we used a sample of mitochondrial sequences from hypervariable regions 1 and 2 (HV1 and HV2), representing major world populations (Europeans, Asians and Africans). The patterns of joint distributions of numbers of mismatches differ markedly from one population to another. In addition, there is a considerable variability in the proportion of numbers of mismatches between HV1 and HV2 sequences. The patterns of bivariate distributions from the HV1 and HV2 data in these data are consistent with those generated by the model involving a stepwise change in population size.

AB - We developed a mathematical model, which makes possible to predict joint distributions of numbers of mismatches in two or more linked regions of the genome, based on the Infinite Sites Models, under mutation-drift equilibrium as well as under various patterns of population growth. With mutation rates varying in the region, one of the predictions is different correlation between numbers of mismatches in the two regions, depending on the pattern of the past population growth (constant, slowly growing, or rapidly growing). Also, for slower growth patterns of population sizes, the coalescence tree is not necessarily 'starlike'. Thus, the joint distribution of mismatches, predicted by the model, provides additional insights into the demographic history of the populations. We also developed expectations and variances of sample statistics under different growth scenarios. As an application we used a sample of mitochondrial sequences from hypervariable regions 1 and 2 (HV1 and HV2), representing major world populations (Europeans, Asians and Africans). The patterns of joint distributions of numbers of mismatches differ markedly from one population to another. In addition, there is a considerable variability in the proportion of numbers of mismatches between HV1 and HV2 sequences. The patterns of bivariate distributions from the HV1 and HV2 data in these data are consistent with those generated by the model involving a stepwise change in population size.

KW - Asymptotics

KW - Coalescence

KW - Fisher-Wright-Moran model

KW - Mitochondrial DNA

KW - Point processes

KW - Population genetics

UR - http://www.scopus.com/inward/record.url?scp=0036180540&partnerID=8YFLogxK

U2 - 10.1016/S0025-5564(01)00090-6

DO - 10.1016/S0025-5564(01)00090-6

M3 - Article

C2 - 11825592

AN - SCOPUS:0036180540

SN - 0025-5564

VL - 175

SP - 83

EP - 115

JO - Mathematical Biosciences

JF - Mathematical Biosciences

IS - 2

ER -