## Mathematical and Statistical Methods for Genetic AnalysisDuring the past decade, geneticists have cloned scores of Mendelian disease genes and constructed a rough draft of the entire human genome. The unprecedented insights into human disease and evolution offered by mapping, cloning, and sequencing will transform medicine and agriculture. This revolution depends vitally on the contributions of applied mathematicians, statisticians, and computer scientists. Mathematical and Statistical Methods for Genetic Analysis is written to equip students in the mathematical sciences to understand and model the epidemiological and experimental data encountered in genetics research. Mathematical, statistical, and computational principles relevant to this task are developed hand in hand with applications to population genetics, gene mapping, risk prediction, testing of epidemiological hypotheses, molecular evolution, and DNA sequence analysis. Many specialized topics are covered that are currently accessible only in journal articles. This second edition expands the original edition by over 100 pages and includes new material on DNA sequence analysis, diffusion processes, binding domain identification, Bayesian estimation of haplotype frequencies, case-control association studies, the gamete competition model, QTL mapping and factor analysis, the Lander-Green-Kruglyak algorithm of pedigree analysis, and codon and rate variation models in molecular phylogeny. Sprinkled throughout the chapters are many new problems. Kenneth Lange is Professor of Biomathematics and Human Genetics at the UCLA School of Medicine. At various times during his career, he has held appointments at the University of New Hampshire, MIT, Harvard, and the University of Michigan. While at the University of Michigan, he was the Pharmacia & Upjohn Foundation Professor of Biostatistics. His research interests include human genetics, population modeling, biomedical imaging, computational statistics, and applied stochastic processes. Springer-Verlag published his book Numerical Analysis for Statisticians in 1999. |

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### Contents

IV | 1 |

V | 4 |

VI | 8 |

VII | 9 |

VIII | 12 |

IX | 13 |

X | 19 |

XI | 21 |

LXXXI | 188 |

LXXXII | 191 |

LXXXIII | 192 |

LXXXIV | 195 |

LXXXV | 199 |

LXXXVI | 203 |

LXXXVII | 205 |

LXXXVIII | 209 |

XII | 23 |

XIII | 24 |

XIV | 26 |

XV | 27 |

XVI | 31 |

XVII | 32 |

XVIII | 37 |

XIX | 39 |

XX | 40 |

XXI | 43 |

XXII | 45 |

XXIII | 47 |

XXIV | 48 |

XXV | 51 |

XXVI | 52 |

XXVII | 57 |

XXVIII | 59 |

XXIX | 62 |

XXX | 63 |

XXXI | 65 |

XXXII | 67 |

XXXIII | 69 |

XXXIV | 70 |

XXXV | 73 |

XXXVI | 76 |

XXXVII | 81 |

XXXVIII | 84 |

XXXIX | 86 |

XLI | 88 |

XLII | 91 |

XLIII | 94 |

XLIV | 97 |

XLV | 99 |

XLVI | 102 |

XLVII | 106 |

XLVIII | 109 |

XLIX | 113 |

L | 115 |

LI | 118 |

LII | 120 |

LIII | 122 |

LIV | 124 |

LV | 133 |

LVI | 137 |

LVII | 141 |

LIX | 142 |

LX | 146 |

LXI | 147 |

LXII | 149 |

LXIII | 150 |

LXIV | 151 |

LXV | 152 |

LXVI | 154 |

LXVII | 157 |

LXVIII | 158 |

LXIX | 165 |

LXX | 169 |

LXXII | 170 |

LXXIII | 173 |

LXXIV | 175 |

LXXV | 177 |

LXXVI | 181 |

LXXVII | 184 |

LXXVIII | 185 |

LXXIX | 186 |

LXXX | 187 |

LXXXIX | 211 |

XC | 214 |

XCI | 215 |

XCII | 218 |

XCIII | 219 |

XCIV | 221 |

XCV | 223 |

XCVI | 228 |

XCVII | 231 |

XCVIII | 232 |

XCIX | 233 |

C | 236 |

CI | 238 |

CII | 239 |

CIII | 240 |

CIV | 244 |

CV | 245 |

CVI | 248 |

CVII | 250 |

CVIII | 253 |

CIX | 257 |

CX | 258 |

CXI | 260 |

CXII | 261 |

CXIII | 264 |

CXIV | 270 |

CXV | 273 |

CXVI | 274 |

CXVII | 278 |

CXVIII | 281 |

CXIX | 283 |

CXX | 285 |

CXXI | 289 |

CXXII | 290 |

CXXIII | 291 |

CXXIV | 292 |

CXXV | 296 |

CXXVI | 299 |

CXXVII | 300 |

CXXIX | 301 |

CXXX | 304 |

CXXXI | 306 |

CXXXII | 308 |

CXXXIII | 311 |

CXXXIV | 315 |

CXXXV | 317 |

CXXXVI | 321 |

CXXXVII | 322 |

CXXXVIII | 325 |

CXXXIX | 326 |

CXL | 328 |

CXLI | 332 |

CXLII | 333 |

CXLIII | 336 |

CXLIV | 338 |

CXLV | 341 |

CXLVI | 343 |

CXLVII | 345 |

CXLVIII | 346 |

348 | |

CL | 351 |

CLI | 352 |

CLII | 354 |

355 | |

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### Common terms and phrases

algorithm alignment allele frequencies Amer J Hum approximation autosomal base binomial calculation cell Chapter Chen-Stein chiasma chromosome clone codon column components compute condensed identity conditional Consider corresponding counts covariance define denote density descent graph descent tree detailed balance distance entries equilibrium distribution expected number exponential Figure formula founder gene gamete geneticists genotype given haplotype Hardy-Weinberg equilibrium Hint Hum Genet human identity coefficients independent inequality interval kinship coefficients Lange linkage equilibrium location scores loci locus loglikelihood marker locus Markov chain mating matrix maximum likelihood estimates maximum parsimony method nodes obligate breaks observed p-value pairs parameters parents pattern pedigree phenotypes Poisson Poisson process polygenic population positive posterior Pr(X probability problem protein radiation hybrid random variable randomly ratio recessive disease recombination fraction recurrence rooted tree sample sequence statistic Suppose Table tion trait transition typed update Var(X variance vector Zmax