Computer modeling is now an integral part of research in evolutionary biology. The advent of increased processing power in the personal computer, coupled with the availability of languages such as R, SPLUS, Mathematica, Maple, Mathcad, and MATLAB, has ensured that the development and analysis of computer models of evolution is now within the capabilities of most graduate students. However, there are two hurdles that tend to discourage students from making full use of the power of computer modeling. The first is the general problem of formulating the question and the second is its implementation using an appropriate computer language. Modelling Evolution outlines how evolutionary questions are formulated and how, in practice, they can be resolved by analytical and numerical methods (with the emphasis being on the latter). Following a general introduction to computer modeling, successive chapters describe "Fisherian" optimality models, invasibility analysis, genetic models, game theoretic models, and dynamic programming. A common chapter plan facilitates tuition and comprises an introduction (in which the general approach and methods are described) followed by a series of carefully structured scenarios that have been selected to highlight particular aspects of evolutionary modeling. Coding for each example is provided in either R or MATLAB since both of these programs are readily available and extensively used. This coding is available on the author's web site allowing easy implementation and study of the programs. Each chapter concludes with a list of exemplary papers which have been chosen on the basis of how well they explain and illustrate the techniques discussed in the chapter.
Author(s): Derek A. Roff
Publisher: Oxford University Press, USA
Year: 2010
Language: English
Pages: 464
Contents......Page 6
1.1.1 The aim of this book......Page 14
1.1.2 Why R and MATLAB?......Page 15
1.2 Operational definitions of fitness......Page 16
1.2.2 Demographic stochasticity......Page 18
1.2.4 Constant environment, density-dependence with a stable equilibrium......Page 20
1.2.5 Constant environment, variable population dynamics......Page 22
1.2.6 Temporally stochastic environments......Page 23
1.2.7 Temporally variable, density-dependent environments......Page 25
1.2.8 Spatially variable environments......Page 26
1.2.9 Social environment......Page 27
1.2.10 Frequency-dependence......Page 28
1.3 Some general principles of model building......Page 29
1.4.1 General assumptions......Page 30
1.4.2 Mathematical assumptions of model 1......Page 31
1.4.3 Mathematical assumptions of model 2......Page 38
1.4.4 Mathematical assumptions of model 3......Page 53
1.4.5 Mathematical assumptions of model 4......Page 56
1.4.6 Mathematical assumptions of model 5......Page 58
1.4.7 Mathematical assumptions of model 6......Page 64
1.5.1 Fisherian optimality analysis (Chapter 2)......Page 68
1.5.3 Genetic models (Chapter 4)......Page 69
1.5.5 Dynamic programming (Chapter 6)......Page 70
2.1.1 Fitness measures......Page 72
2.1.2 Methods of analysis: introduction......Page 74
2.1.3 Methods of analysis: W = f(θ[sub(1)], θ[sub(2}],...,θ[sub(k)], x[sub(1)], x[sub(2)],...,x[sub(n)]) and well-behaved......Page 75
2.1.4 Methods of analysis: W = f(θ[sub(1)],θ[sub(2)],...,θ[sub(k)],x[sub(1)],x[sub(2)],...,x[sub(n)]) and not well-behaved......Page 78
2.1.5 Methods of analysis: g(w) = f(θ[sub(1)],θ[sub(2)],...,θ[sub(k)],x[sub(1)],x[sub(2)],...,x[sub(n)],W)......Page 80
2.2 Summary of scenarios (Table 2.1)......Page 82
2.3.1 General assumptions......Page 84
2.3.3 Plotting the fitness function......Page 85
2.3.4 Finding the maximum using the calculus......Page 86
2.4.2 Mathematical assumptions......Page 88
2.5.2 Mathematical assumptions......Page 89
2.5.3 Plotting the fitness function......Page 90
2.5.4 Finding the maximum using the calculus......Page 92
2.6.1 General assumptions......Page 94
2.6.3 Plotting the fitness function......Page 95
2.6.4 Finding the maximum using the calculus......Page 97
2.6.5 Finding the maximum using a numerical approach......Page 98
2.7 Scenario 5: Maximizing the Malthusian parameter, r, rather than expected lifetime reproductive success, R[sub(o)]......Page 99
2.7.2 Mathematical assumptions......Page 100
2.7.3 Plotting the fitness function......Page 101
2.7.4 Finding the maximum using the calculus......Page 102
2.7.5 Finding the maximum using a numerical approach......Page 105
2.8 Scenario 6: Stochastic variation in parameters......Page 106
2.8.2 Mathematical assumptions......Page 107
2.8.3 Plotting the fitness function......Page 108
2.8.4 Finding the maximum using the calculus......Page 110
2.8.5 Finding the maximum using a numerical approach......Page 112
2.9.2 Mathematical assumptions......Page 113
2.9.3 Plotting the fitness function......Page 114
2.9.4 Finding the maximum using the calculus......Page 115
2.9.5 Finding the maximum using numerical methods......Page 117
2.10.2 Mathematical assumptions......Page 118
2.10.3 Plotting the fitness function......Page 119
2.10.4 Finding the maximum using a numerical approach......Page 120
2.11.1 General assumptions......Page 121
2.11.2 Mathematical assumptions......Page 122
2.11.3 Plotting the fitness function......Page 123
2.11.5 Finding the maximum using a numerical approach......Page 125
2.12.2 Mathematical assumptions......Page 126
2.13 Scenario 11: Two traits may be resolved into a single trait......Page 127
2.13.2 Mathematical assumptions......Page 128
2.13.3 Plotting the fitness function......Page 129
2.13.4 Finding the optimum using the calculus......Page 130
2.14.1 General assumptions......Page 132
2.14.3 Plotting the fitness function......Page 133
2.14.4 Finding the maximum using the calculus......Page 136
2.14.5 Finding the maximum using a numerical approach......Page 141
2.15.1 General assumptions......Page 143
2.15.2 Mathematical assumptions......Page 144
2.15.3 Plotting the fitness function......Page 145
2.15.5 Finding the maximum using a numerical approach......Page 147
2.16 Scenario 14: Adding a third variable and more......Page 148
2.16.2 Mathematical assumptions......Page 149
2.16.5 Finding the maximum using a numerical approach......Page 150
2.17 Some exemplary papers......Page 152
2.18.2 Scenario 1: Finding the maximum using the calculus......Page 153
2.18.4 Scenario 3: Plotting the fitness function......Page 154
2.18.7 Scenario 4: Plotting the fitness function......Page 155
2.18.8 Scenario 4: Finding the maximum using the calculus......Page 156
2.18.10 Scenario 5: Plotting the fitness function......Page 157
2.18.12 Scenario 5: Finding the maximum using a numerical approach......Page 158
2.18.13 Scenario 6: Plotting the fitness function......Page 159
2.18.15 Scenario 6: Finding the maximum using a numerical approach......Page 160
2.18.16 Scenario 7: Plotting the fitness function......Page 161
2.18.17 Scenario 7: Finding the maximum using the calculus......Page 162
2.18.19 Scenario 8: Plotting the fitness function......Page 163
2.18.22 Scenario 9: Plotting the fitness function......Page 164
2.18.24 Scenario 9: Finding the maximum using a numerical approach......Page 165
2.18.26 Scenario 11: Finding the optimum using the calculus......Page 166
2.18.28 Scenario 12: Plotting the fitness function......Page 167
2.18.29 Scenario 12: Finding the maximum using the calculus......Page 168
2.18.30 Scenario 12: Finding the maximum using a numerical approach......Page 171
2.18.31 Scenario 13: Plotting the fitness function......Page 173
2.18.32 Scenario 13: Finding the maximum using a numerical approach......Page 175
2.18.33 Scenario 14: Finding the maximum using a numerical approach......Page 176
3.1.1 Age-or stage-structured models......Page 178
3.1.2 Modeling evolution using the Leslie matrix......Page 182
3.1.4 Adding density-dependence......Page 183
3.1.5 Estimating fitness......Page 186
3.1.6 Pairwise invasibility analysis......Page 187
3.1.7 Elasticity analysis......Page 193
3.1.8 Multiple invasibility analysis......Page 194
3.3.2 Mathematical assumptions......Page 197
3.3.3 Solving using the methods of Chapter 2......Page 198
3.3.4 Solving using the eigenvalue of the Leslie matrix......Page 199
3.4.1 General assumptions......Page 201
3.4.4 Pairwise invasibility analysis......Page 202
3.4.5 Elasticity analysis......Page 206
3.5 Scenario 3: Functional dependence in the Ricker model......Page 207
3.5.3 Pairwise invasibility analysis......Page 208
3.5.4 Elasticity analysis......Page 211
3.5.5 Multiple invasibility analysis......Page 214
3.6.2 Mathematical assumptions......Page 216
3.6.3 Pairwise invasibility analysis......Page 217
3.6.4 Elasticity analysis......Page 219
3.7.2 Mathematical assumptions......Page 221
3.7.3 Elasticity analysis......Page 223
3.7.4 Pairwise invasibility analysis......Page 224
3.8.3 Pairwise invasibility analysis......Page 226
3.8.4 Elasticity analysis......Page 228
3.8.5 Multiple invasibility analysis......Page 232
3.9 Some exemplary papers......Page 234
4.1.1 Population variance components (PVC) models......Page 236
4.1.2 Individual variance components (IVC) models......Page 241
4.1.3 Individual locus (IL) models......Page 246
4.3 Scenario 1: Stabilizing selection on two traits using a PVC model......Page 256
4.3.3 Analysis......Page 257
4.4 Scenario 2: Stabilizing selection using an IVC model......Page 258
4.4.3 Analysis......Page 259
4.5 Scenario 3: Directional selection using an IVC model......Page 261
4.5.3 Analysis......Page 262
4.6.1 General assumptions......Page 264
4.6.3 Analysis......Page 265
4.7.1 General assumptions......Page 268
4.7.2 Mathematical assumptions......Page 269
4.7.3 Analysis......Page 270
4.8 Scenario 6: Evolution of two traits using an IVC model......Page 271
4.8.3 Analysis......Page 272
4.9.2 Mathematical assumptions......Page 275
4.9.3 Analysis......Page 276
4.10 Some exemplary papers......Page 281
5.1.1 Frequency-independent models......Page 284
5.1.2 Frequency-dependent models......Page 286
5.1.4 The mode of inheritance in two-strategy games......Page 287
5.2 Summary of scenarios......Page 289
5.3.2 Mathematical assumptions......Page 290
5.3.3 Plotting the fitness curves......Page 291
5.3.4 Finding the ESS using the calculus......Page 293
5.4.1 General assumptions......Page 295
5.4.3 Finding the ESS using a numerical approach......Page 296
5.5.3 A graphical analysis......Page 300
5.5.4 Finding the ESS using a numerical approach......Page 304
5.6.2 Mathematical assumptions......Page 307
5.6.3 A graphical analysis......Page 308
5.6.4 Finding the ESS using a numerical approach......Page 312
5.7.1 General assumptions......Page 314
5.7.3 Finding the ESS using a numerical approach......Page 315
5.8.2 Mathematical assumptions......Page 319
5.8.3 A graphical analysis......Page 320
5.8.4 Finding the ESS using a numerical approach......Page 326
5.9 Scenario 7: Rock-Paper-Scissors: a quantitative genetics model......Page 328
5.9.3 A graphical analysis......Page 329
5.9.4 Finding the ESS using a numerical approach......Page 330
5.10.2 Mathematical assumptions......Page 335
5.10.3 Finding the ESS analytically......Page 336
5.10.4 Finding the ESS using a numerical approach......Page 341
5.11.2 Mathematical assumptions......Page 344
5.11.3 Finding the ESS using a numerical approach......Page 345
5.12 Some exemplary papers......Page 350
6.1.1 General assumptions in the patch-foraging model......Page 354
6.1.3 A first look at the model......Page 355
6.1.4 An algorithm for constructing the decision matrix......Page 357
6.1.5 Using the decision matrix: individual prediction......Page 364
6.1.6 Using the decision matrix: expected state......Page 367
6.1.7 Using the decision and transition density matrices to get expected choices......Page 369
6.1.9 Linear interpolation to adjust for non-integer state variables......Page 370
6.3.1 General assumptions......Page 373
6.4.1 General assumptions......Page 374
6.4.2 Mathematical assumptions......Page 375
6.4.4 Calculating the decision matrix......Page 376
6.5.2 Mathematical assumptions......Page 380
6.5.3 Outcome chart and expected lifetime fitness function......Page 381
6.5.4 Calculating the decision matrix......Page 383
6.6.2 Mathematical assumptions......Page 388
6.6.3 Outcome chart and expected lifetime fitness function......Page 391
6.6.4 Calculating the decision matrix......Page 392
6.6.5 Using the decision matrix: individual prediction......Page 398
6.7.1 General assumptions......Page 402
6.7.3 Outcome chart and expected lifetime fitness function......Page 404
6.7.4 Calculating the decision matrix......Page 406
6.8 Some exemplary papers......Page 412
6.9.1 An algorithm for constructing the decision matrix......Page 415
6.9.2 Using the decision matrix: individual prediction......Page 417
6.9.3 Using the decision matrix: expected state......Page 419
6.9.4 Scenario 2: Calculating the decision matrix......Page 420
6.9.5 Scenario 3: Calculating the decision matrix......Page 422
6.9.6 Scenario 4: Calculating the decision matrix......Page 426
6.9.7 Scenario 4: Using the decision matrix: individual prediction......Page 429
6.9.8 Scenario 5: Calculating the decision matrix......Page 430
Appendix 1......Page 436
Appendix 2......Page 441
References......Page 448
F......Page 456
M......Page 457
V......Page 458
Z......Page 459
E......Page 460
O......Page 461
Z......Page 462
W......Page 463
