Theoretical Population GeneticsSpringer Science & Business Media, 30. apr 1990 - 417 pages The rise of the neutral theory of molecular evolution seems to have aroused a renewed interest in mathematical population genetics among biologists, who are primarily experimenters rather than theoreticians. This has encouraged me to set out the mathematics of the evolutionary process in a manner that, I hope, will be comprehensible to those with only a basic knowledge of calculus and matrix algebra. I must acknowledge from the start my great debt to my students. Equipped initially with rather limited mathematics, they have pursued the subject with much enthusiasm and success. This has enabled me to try a number of different approaches over the years. I was particularly grateful to Dr L. J. Eaves and Professor W. E. Nance for the opportunity to give a one-semester course at the Medical College of Virginia, and I would like to thank them, their colleagues and their students for the many kindnesses shown to me during my visit. I have concentrated almost entirely on stochastic topics, since these cause the greatest problems for non-mathematicians. The latter are particularly concerned with the range of validity of formulae. A sense of confidence in applying these formulae is, almost certainly, best gained by following their derivation. I have set out proofs in fair detail, since, in my experience, minor points of algebraic manipulation occasionally cause problems. To avoid loss of continuity, I have sometimes put material in notes at the end of chapters. |
Contents
II | 3 |
III | 11 |
IV | 12 |
VI | 13 |
VII | 14 |
IX | 16 |
X | 17 |
XI | 20 |
LXXIX | 205 |
LXXX | 208 |
LXXXI | 213 |
LXXXIII | 215 |
LXXXIV | 217 |
LXXXV | 219 |
LXXXVI | 222 |
LXXXVII | 225 |
XII | 22 |
XIII | 31 |
XIV | 36 |
XV | 39 |
XVI | 42 |
XVII | 43 |
XVIII | 44 |
XIX | 46 |
XX | 49 |
XXI | 56 |
XXIII | 59 |
XXIV | 67 |
XXV | 69 |
XXVI | 71 |
XXVII | 75 |
XXVIII | 78 |
XXIX | 82 |
XXX | 84 |
XXXI | 86 |
XXXII | 89 |
XXXIV | 90 |
XXXV | 91 |
XXXVI | 106 |
XXXVII | 107 |
XXXIX | 108 |
XL | 110 |
XLI | 111 |
XLII | 113 |
XLIII | 114 |
XLIV | 115 |
XLV | 117 |
XLVI | 119 |
XLVII | 123 |
XLVIII | 124 |
XLIX | 126 |
LI | 127 |
LII | 130 |
LIII | 131 |
LIV | 137 |
LV | 138 |
LVI | 141 |
LVII | 143 |
LVIII | 144 |
LIX | 152 |
LXI | 153 |
LXII | 155 |
LXIII | 159 |
LXIV | 165 |
LXV | 167 |
LXVI | 170 |
LXVII | 172 |
LXVIII | 180 |
LXIX | 182 |
LXX | 183 |
LXXI | 189 |
LXXII | 194 |
LXXIV | 195 |
LXXV | 200 |
LXXVI | 203 |
LXXVIII | 204 |
LXXXVIII | 227 |
LXXXIX | 235 |
XC | 237 |
XCI | 243 |
XCII | 249 |
XCIII | 251 |
XCIV | 252 |
XCV | 253 |
XCVI | 257 |
XCVII | 258 |
XCVIII | 261 |
XCIX | 263 |
C | 265 |
CI | 267 |
CII | 269 |
CIII | 277 |
CIV | 279 |
CV | 281 |
CVI | 284 |
CVII | 286 |
CVIII | 290 |
CIX | 292 |
CX | 296 |
CXI | 297 |
CXII | 300 |
CXIII | 301 |
CXIV | 303 |
CXVI | 306 |
CXVII | 307 |
CXVIII | 310 |
CXIX | 313 |
CXX | 316 |
CXXI | 320 |
CXXII | 322 |
CXXIII | 324 |
CXXIV | 325 |
CXXV | 329 |
CXXVI | 331 |
CXXVII | 334 |
CXXVIII | 336 |
CXXX | 340 |
CXXXI | 344 |
CXXXII | 347 |
CXXXIII | 348 |
CXXXIV | 350 |
CXXXV | 353 |
CXXXVI | 355 |
CXXXVII | 357 |
CXXXVIII | 359 |
CXXXIX | 370 |
CXL | 374 |
CXLI | 375 |
CXLII | 379 |
CXLIII | 383 |
CXLIV | 387 |
CXLVI | 397 |
CXLVII | 399 |
CXLVIII | 403 |
411 | |
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Common terms and phrases
advantageous allele allele frequency approach argument backward equation boundary conditions branching process calculated change in allele Chapter close approximation conditional distribution consider constant continuous approximation corresponding derived deterministic diffusion methods diploid discussion drift earlier effective population size equals Ewens example finite Fisher flux forward mutation frequency i/(2N function genic selection give h₁ haploid Hence heterozygotes integral Kimura latent roots Maruyama mathematical mean absorption mean fixation mean number mean sojourn modified process monomorphism Moran's model mutation rate natural selection neutral allele neutral theory number of alleles obtain Poisson Poisson distribution population genetics probability density function probability distribution probability of fixation probability of ultimate problem random range selective advantage solution stationary distribution subpopulation Suppose u(po u₁ ultimate fixation usual variance viability Wright Wright-Fisher model write x₁ zero