Statistical Issues in Modelling the Ancestry from Y-Chromosome and Surname Data

278 Pages·2012·4.52 MB·English

Sharif, Maarya (2012) Statistical issues in modelling the ancestry from Y-
chromosome and surname data. PhD thesis.

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Statistical Issues in Modelling the
Ancestry from Y-Chromosome and
Surname Data
by
Maarya Sharif M.Sc., B.Sc. (Hons)
A thesis submitted in fulfillment for the
degree of Doctor of Philosophy
in the
College of Science and Engineering
School of Mathematics and Statistics
University of Glasgow
May 2012
c Maarya Sharif, May 2012
(cid:13)

Abstract
A considerable industry has grown-up around genealogical inference from genetic
testing, supplementing more traditional genealogical techniques but with very
limited quantification of uncertainty. In many societies Y-chromosomes are co-
inherited with surnames and as such passed down from father to son. This thesis
seeks to explore what the correlation can say about ancestry. In particular it is
concerned with estimation of the time to the most recent common paternal an-
cestor (TMRCA) for pairs of males who are not known to be directly related but
share the same surname, based on the repeat number at short tandem repeat
(STR) markers on their Y-chromosomes.
We develop a model of TMRCA estimation based on the difference in repeat num-
bers in pairs of male haplotypes using a Bayesian framework and Markov-Chain
Monte-Carlo techniques, such as adaptive Metropolis-Hastings algorithm. The
model incorporates the process of STR discovery and the calibration of mutation
rates, which can differ across STRs. In simulation studies, we find that the esti-
mates of TMRCA are rather robust to the ascertainment process and the way in
which it is modelled. However, they are affected by the site-specific mutation rates
at the typed STRs. Indeed sequencing the fastest mutating STRs yields a lower
error in the estimated TMRCA than random STRs. In the British context, we
extend our model to include additional information such as the haplogroup status
(as determined from single nucleotide polymorphisms, SNPs) of the pair of males,
as well as the frequency and origin of the surname. In general, the effect of this
is to reduce estimates of the TMRCA for pairs of males with an older TMRCA,
typically outwith the period of surname establishment (about 500-700 years ago).
Inthegenealogicalcontext, incorporatingsurname frequency (within theprior dis-
tribution) results in lower estimates of TMRCA for pairs of males who appear to
have diverged froma common male ancestor since the periodof surname establish-
ment. In addition, we include uncertainty in the years per generation conversion
factor in our model.
Keywords: Y-chromosome, surname, most recent common ancestor, haplotype,
haplogroup, British, genealogy, short tandem repeat, generation.
Acknowledgements
Praise and thanks be to Allah, Lord of the Worlds, with a praise that is adequate
to His favours and equal to His increase. Any mistakes that follow are mine and
the praise for the merits of this thesis belongs to Allah.
TherearemanypeoplewhomIwishtothankfortheirsupportofmy‘uniwork’. To
my supervisor, Dr Vincent Macaulay, who sat through my ramblings (often times
accompanied by general hand-waving), patiently taught me the art of debugging
code and was always kind in his supervision: you have enriched my research ex-
perience and have set the foundations for what I hope will be a fulfilling career
in academia. For the DTA Ph.D. studentship, I am indebted to the Engineering
and Physical Sciences Research Council. I am grateful for the support from the
School of Mathematics and Statistics and all its staff. It has been a pleasure to
study in such a friendly and understanding environment. A particular thank you
also to Dr Agostino Nobile and Beverley Dixon for their assistance over the years.
To the postgrads: I take it back, childbirth is far more painful! And to Joanna:
the notepad proved invaluable.
To all my family, may Allah reward you for all your prayers and encouragement.
For the free child care, my sincere gratitude to my Mum, Auntie Sharifa, Taee-
Amma andthenumerous others. To mybeloved children, NoorandZayn, Imissed
you too because I didn’t see you for a long time. Finally to Fahad, thank you for
helping with the laundry, wiping away my tears and believing in me. I couldn’t
have done it without you.
Contents
Abstract iii
Acknowledgements iv
List of Tables ix
List of Figures xi
Statistical Distributions xvii
Abbreviations xix
1 Introduction 1
1.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Genetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Genetic typing of STRs . . . . . . . . . . . . . . . . . . . . . 5
1.1.3 Genealogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.4 Surnames . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.1.5 Surname-based Genetic Genealogy . . . . . . . . . . . . . . 15
1.2 Y-Chromosome Databases . . . . . . . . . . . . . . . . . . . . . . . 20
1.3 Bayesian Inference . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2 Background 25
2.1 Estimate of Time to the Most Recent Common Ancestor . . . . . . 25
2.2 Y-chromosome and Surnames . . . . . . . . . . . . . . . . . . . . . 37
2.3 Estimation of STR Mutation Rates . . . . . . . . . . . . . . . . . . 47
2.3.1 Initial Mutation Rate Estimates . . . . . . . . . . . . . . . . 49
2.3.2 Intermediary Mutation Rate Estimates . . . . . . . . . . . . 50
2.3.3 Final Mutation Rate Estimates . . . . . . . . . . . . . . . . 51
3 Maximum Likelihood Estimation of TMRCA 61
3.1 Preliminary Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1.1 Materials and Methods . . . . . . . . . . . . . . . . . . . . . 61
v
Contents vi
3.1.2 Preliminary Results . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.3 Preliminary Conclusions . . . . . . . . . . . . . . . . . . . . 70
3.2 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.1 Stepwise Mutational Model . . . . . . . . . . . . . . . . . . 71
3.3.2 Infinite Sites Model . . . . . . . . . . . . . . . . . . . . . . . 71
3.3.3 Data Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.4.1 Mutation Rate Distribution 1 . . . . . . . . . . . . . . . . . 75
3.4.1.1 Stepwise Mutation Model Analysis 1 . . . . . . . . 75
3.4.1.2 Infinite Sites Model Analysis 1 . . . . . . . . . . . 79
3.4.2 Mutation Rate Distribution 2 . . . . . . . . . . . . . . . . . 80
3.4.2.1 Stepwise Mutation Model Analysis 2 . . . . . . . . 80
3.4.2.2 Infinite Sites Model Analysis 2 . . . . . . . . . . . 84
3.4.3 Mutation Rate Distribution 3 . . . . . . . . . . . . . . . . . 85
3.4.3.1 Stepwise Mutation Model Analysis 3 . . . . . . . . 87
3.4.3.2 Infinite Sites Model Analysis 3 . . . . . . . . . . . 89
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4 Modelling Mutational Mechanisms 99
4.1 Preliminary Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.1.1 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.1.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.3 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.3.1 Data Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.3.2 Bayesian Modelling . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.3 Markov-Chain Monte-Carlo Sampling . . . . . . . . . . . . . 110
4.3.3.1 Metropolis-Hastings Algorithm . . . . . . . . . . . 111
4.3.3.2 Adaptive MCMC . . . . . . . . . . . . . . . . . . . 113
4.3.3.3 Implementation: Modelling Mutational Mechanisms114
4.3.4 Data Simulation and Analysis Program . . . . . . . . . . . . 116
4.3.5 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.6 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4.1 Real Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4.2 Simulated Data Analysis . . . . . . . . . . . . . . . . . . . . 128
4.4.2.1 Varying the Information . . . . . . . . . . . . . . . 130
4.4.2.2 Misspecification . . . . . . . . . . . . . . . . . . . . 130
4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5 Modelling TMRCA 141
Contents vii
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.2.1 Simulation Study . . . . . . . . . . . . . . . . . . . . . . . . 142
5.2.2 Bayesian Modelling . . . . . . . . . . . . . . . . . . . . . . . 144
5.2.3 Markov-Chain Monte-Carlo Sampling . . . . . . . . . . . . . 146
5.2.3.1 Implementation: TMRCA Model . . . . . . . . . . 147
5.2.4 Data Simulation and Analysis Program . . . . . . . . . . . 149
5.2.5 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.2.6 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
5.3.1 Varying the Proportion of Typed STRs . . . . . . . . . . . . 153
5.3.2 Use of Fast Mutating STRs . . . . . . . . . . . . . . . . . . 161
5.3.3 Misspecification of the Proportion of Non-Ascertained Loci . 162
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6 TMRCA Estimation: Real Data Applications 173
6.1 Haplogroup- and Surname-Based Priors . . . . . . . . . . . . . . . . 173
6.1.1 Materials and Methods . . . . . . . . . . . . . . . . . . . . . 173
6.1.2 Same haplogroup . . . . . . . . . . . . . . . . . . . . . . . . 178
6.1.2.1 Surname Origins and Frequency . . . . . . . . . . . 178
6.1.2.2 Surname Frequency . . . . . . . . . . . . . . . . . 183
6.1.2.3 Surname Origins . . . . . . . . . . . . . . . . . . . 184
6.1.2.4 No Frequency or Surname Origin . . . . . . . . . . 187
6.1.3 Random/No Haplogroup . . . . . . . . . . . . . . . . . . . . 189
6.1.3.1 Surname Origin and Frequency . . . . . . . . . . . 189
6.1.3.2 Surname Frequency . . . . . . . . . . . . . . . . . 191
6.1.3.3 Surname Origins . . . . . . . . . . . . . . . . . . . 193
6.1.3.4 No Frequency or Surname Origin . . . . . . . . . . 195
6.1.4 Different Haplogroup . . . . . . . . . . . . . . . . . . . . . . 197
6.1.4.1 Surname Origin and Frequency . . . . . . . . . . . 197
6.1.4.2 Surname Origin . . . . . . . . . . . . . . . . . . . . 197
6.1.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.2 Additional Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
6.2.1 Absence of Surname and Haplogroup Information . . . . . . 207
6.2.2 Generation Time in Years . . . . . . . . . . . . . . . . . . . 207
6.3 Assessment of Priors on TMRCA . . . . . . . . . . . . . . . . . . . 209
6.3.1 Materials and Methods . . . . . . . . . . . . . . . . . . . . . 209
6.3.2 Same haplogroup . . . . . . . . . . . . . . . . . . . . . . . . 212
6.3.3 Random Haplogroup . . . . . . . . . . . . . . . . . . . . . . 213
6.3.4 Different Haplogroup . . . . . . . . . . . . . . . . . . . . . . 214
6.3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Contents viii
7 Discussion 219
8 Conclusions 231
A The Delta Method 235
Bibliography 237
List of Tables
1.1 STR data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.2 Y-chromosome testing companies . . . . . . . . . . . . . . . . . . . 19
1.3 Y-DNA databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1 Sources for initial mutation rate review . . . . . . . . . . . . . . . . 50
2.2 Initial mutation rate estimates . . . . . . . . . . . . . . . . . . . . . 50
2.3 Sources for intermediary mutation rate review . . . . . . . . . . . . 51
2.4 Additional sources for final mutation rate review . . . . . . . . . . . 51
2.5 Final mutation rate estimates . . . . . . . . . . . . . . . . . . . . . 53
2.6 STR markers one proportion test results . . . . . . . . . . . . . . . 54
2.7 Summary of STR markers properties . . . . . . . . . . . . . . . . . 56
2.8 Multi-step mutations . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.1 Mutationrate distribution 1: ISM FSE < SMM FSE using true and
empirical site-specific mutation rates . . . . . . . . . . . . . . . . . 93
3.2 Mutationrate distribution 2: ISM FSE < SMM FSE using true and
empirical site-specific mutation rates . . . . . . . . . . . . . . . . . 94
3.3 Mutationrate distribution 3: ISM FSE < SMM FSE using true and
empirical site-specific mutation rates . . . . . . . . . . . . . . . . . 94
4.1 Empirical and Bayesian mutation rate estimates . . . . . . . . . . . 123
4.2 Real data Bayesian parameter estimates . . . . . . . . . . . . . . . 124
4.3 Regression of posterior mean against percentage of non-ascertained
loci . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.1 Model for validating ANCOVA permutation test . . . . . . . . . . . 177
6.2 Simulated data error rates . . . . . . . . . . . . . . . . . . . . . . . 177
6.3 Same haplogroup: surname origin and frequency fitted model pa-
rameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
6.4 Same haplogroup: surname origin and frequency permutation test
p-values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.5 Same haplogroup: significant Tukey multiple comparisons between
surname origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6.6 Same haplogroup: exponential surname origin fitted model param-
eters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.7 Same haplogroup: gamma surname origin fitted model parameters . 186
ix