Index

active edge, 14, 154adaptation, 20

research program, 10adaptive dynamics, 21adaptive landscape, 109, 113

compound, 226flexible, 13rigid, 266

adaptive radiation, 260Lotka–Volterra example, 262predator–prey example, 266

adaptive speciation, 210advertising game, 11allometry, 98allopatric speciation, 251

Lotka–Volterra example, 258altruism, 14, 86anisogamy, 234archetype, 232, 237assortative mating, 129, 231, 252asymmetric matrix game, 66asymptotic stability

Leslie predator–prey continuous example,56

Leslie predator–prey discrete example, 54local, 58logistic equation example, 51

ball, 162bang-bang solution, 325battle of sexes, 66bauplan, 2, 22, 81

multistage, 106two or more, 99unique, 92, 93, 96, 103

Bergmann’s rule, 97, 141, 173, 212

bi-linear game, 69, 279bully function, 95

carrying capacity, 43chaotic attractor, 60chaotic motion, 60characteristics

that define a species, 232clump of strategies

distribution becomes bimodal, 249following a mean, 247

clumped strategies, 243clumping

of individuals, 231co-adaptation, 21coalition, 127coalition vector, 164

non-equilibrium, 191co-evolutionary stable strategy, 159competition coefficient, 43competitive speciation, 159, 252compound

adaptive landscape, 226fitness example, 189fitness function, 189fitness generating function, 225

consumer-resource models, 46continuous games, 70continuous strategy, 68convergent

stability, 148, 158stable, 152stable point, 165

converting density to frequency, 80corollary

sufficient condition for a matrix-ESS, 282

377

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378 Index

critical value, 108, 185gradient of, 144of the G-matrix, 222of H, 109

Darwin’s postulates, 5Darwinian dynamics, 22, 27, 112definitions

coalition vector – frequency, 181coalition vector – multistage, 186coalition vector for the scalar bauplan, 164critical value, 109dominant eigenvalue, 108ecological equilibrium, 162ecological equilibrium – multistage, 183ecological equilibrium for the resource

bauplan, 171ecologically stable equilibrium for the

resource bauplan, 171ESC, 189ESE – frequency, 180ESE – multiple, 175ESE for the scalar bauplan, 162ESS – frequency, 181ESS – multistage, 186ESS for the scalar bauplan, 164fitness for multistage G-functions, 109fitness generating function, 62, 77fitness matrix, 108G-function, 77G-function for multistage systems, 109G-function in terms of population

frequency, 105G-function with resources, 97G-function with scalar strategies, 93G-function with vector strategies, 94G-matrix, 109matrix ecological equilibrium, 280matrix ecologically stable equilibrium,

280matrix-ESS, 281multiple G-functions, 102single-mutant-ESS, 283species, 242

density-dependent selection, 79, 116difference equations, 34

solution by iteration, 35differential equations

solution by integration, 37differential games, 334domain of attraction, 52, 163dominant eigenvalue, 108

ecological cycle, 188, 225equilibrium requirement, 190

ecological equilibrium, 162multiple, 174

ecological theater, 15, 75, 304ecologically enlightened manager, 354ecologically keystone, 264ecologically stable, 152

cycle (ESC), 189, 225equilibrium (see also ESE), 162

eigenvaluedominant, 108

epistasis, 86equilibrium point, 50, 162

asymptotically stable, 51, 58globally asymptotically stable, 51stable, 50, 51, 58unstable, 58

ESC, 189ESE, 162, 163

global, 163, 175local, 163, 175multiple, 175

ESS, 18, 21, 22, 151, 164candidate, 197global, 164local, 164maximum principle, 197non-equilibrium, 191, 225optimal harvesting (ESOHS), 351

ESS maximum principle, 197evolutionarily enlightened manager, 354evolutionarily identical, 62

individuals, 17evolutionarily stable

minima, 159optimal harvesting strategy, 351strategy (see ESS)

evolutionarybranching, 159game, 16keystone, 264play, 15, 75, 304strategies, 61

evolutionary stabilityconvergence stability, 19resistant to invasion, 19

existencestruggle for, 62

expected payoff, 69, 279extinction

contexts for, 233

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Index 379

families, 82fast tracking, 196first-order approximation, 124Fisher’s theorem of natural selection,

125fit of form and function, 1fitness, 40

density dependent, 8density independent, 8frequency dependent, 8frequency independent, 8function, 40generating function, 22, 62, 77generating function (compound), 225landscape, 13, 113matrix, 108multistage G-functions, 109set, 154

fixed point, 50, 162forming a G-fuction, 89frequency, 27

of individuals, 104of phenotypes, 122space, 180, 277vector, 277

frequency-dependent selection, 79

G-function, 22G-functions, 77

categorizing, 92multiple, 24, 99multistage, 106in terms of population frequency,

103with resources, 96with scalar strategies, 92with vector strategies, 93, 106

G-matrix, 109game of chicken, 67games

ant wars, 71asymmetric matrix, 66battle of the sexes, 66bi-linear, 69cancer chemotherapy, 359continuous, 70ESS under hump-shaped harvest, 348ESS under linear harvest, 347ESS under no harvest, 347flowering time – cooperative solution,

328flowering time, N > 1, 327

flowering time, N = 1, 327game of chicken, 67, 290, 293gerbil-owl fear, 333kin selection, 294L–V big bully, 95, 139, 169L–V big bully – coalition of one, 206L–V big bully – coalition of two, 208L–V competition, 93, 127, 131, 166L–V competition – coalition of one, 200L–V competition – coalition of two, 201L–V competition in terms of frequency,

105, 143, 182, 220life cycle, 109, 144modified game of chicken, 295multistage tutorial, 187non-equilibrium L–V, 145, 192, 227non-equilibrium L–V dependent on x ,

229non-equilibrium with x dependence,

193offspring size vs. number, 64predator–prey coevolution, 102, 142, 177,

215predators seeking wary prey, 338prisoner’s dilemma, 66, 288reciprocal altruism, 294resource discovery, 308resource matching, 307resource renewal, 309rock–scissor–paper, 290root competition, 329root–shoot ratio, 311, 313root–shoot with an ESS coalition of two,

315Schaeffer model with no harvest, 357Schaeffer model with size-restricted harvest,

357symmetric competition, 89symmetric matrix, 66war of attrition, 71zero-sum, 63

genetic drift, 266genetic interactions

epistatic, 7pleiotropic, 7

geneticsepistasis, 86pleiotropy, 86population, 7quantitative, 7

group selection, 78group-optimal strategy, 70

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380 Index

habitat quality, 306habitat selection

density dependent, 305ideal free distribution, 305identity matrix, 32, 48

Hamilton’s rule, 294heritable variability, 13heritable variation, 62

invasion-driven, 117strategy-driven, 118

ideal free distribution, 305, 337identity matrix, 32, 48inclusive fitness, 14incumbent replacement, 272individual selection, 78inner game, 17, 75intrinsic growth rate, 43invariant set, 52isodar plot, 306

kin selection, 294

landscapeadaptive, 113fitness, 113rigid, 266

lemmasecologically stable cycle, 190ESC, 190ESE, 163ESE – frequency, 181ESE – multiple, 175ESE – multistage, 185ESE for the resource bauplan, 171multistage eigenvalues, 184

lifediversity, 1procession, 1

life cycle example, 223life-history stages, 106limit cycle

stable, 60linearization, 52logistic equation, 35

continuous, 38discrete, 35discrete exponential, 36

Lotka–Volterra predator–prey model,51

Lyapunov’s first method, 52

macroevolution, 9, 233, 269map, 35mating

assortative, 231matrix, 31

fitness, 48, 108identity, 32, 48population projection, 48square, 32transpose, 48

matrix gamesas an evoutionary game, 72bi-linear, 275, 279non-linear, 275symmetric, 66, 278

matrix-ESE, 280matrix-ESS, 281

sufficient condition, 282max-min strategy, 69microevolution, 9, 233, 268mixed strategy, 68, 292Modern Synthesis, 7monomorphic population, 276

Nashequilibrium, 18solution, 70

natural selection, 5density dependent, 7Fisher’s fundamental theorem, 13frequency dependent, 7

niche, 260construction, 30

no-regret strategy, 70nominal operating condition, 50non-equilibrium dynamics, 58non-negative orthant, 161notation example

fitness matrix, 48species, strategies, and resources, 30transpose, 48

optimization problem, 64organism

distribution and abundance, 2outer game, 17, 75

pangenesis, 4, 85Pareto-optimal

set, 154solution, 15

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Index 381

payoffbi-linear, 279expected, 69

periodic orbits, 59perturbation

equations, 147solutions, 52

phenotype, 121pleiotropy, 86polymorphic population, 276population dynamics, 93, 112population projection function, 40population projection matrix, 106positively invariant set, 52predator–prey coevolution, 102, 142prisoner’s dilemma, 66pristine environment, 344procession of life, 273punctuated equilibria, 274pure strategy, 69

quasi-periodic orbit, 60

rational reaction set, 157reciprocal altruism, 294reproduction

asexual, 117sexual, 117

resistance to invasion, 158resource dynamics, 96resources, 30rising number of species, 99root competition, 329

scalar, 28Schaeffer model, 355sector stability, 162selection

density-dependent, 116social systems

despotic, 73eusocial, 73

speciation, 128adaptive, 210adaptive radiation, 260allopatric, 251competitive, 159, 252sympatric, 251, 252

species, 1, 27, 121, 242archetype, 237biological species concept, 121, 234

ecologically keystone, 264evolutionarily keystone, 264morphological species concept, 121, 235phylogenetic species concept, 235strategy species concept, 121strategy-species definition, 28

species archetype, 237speed, 126stable equilibrium point, 50stability, 50

convergent, 148, 152ecological, 49, 152evolutionary, 49global, 53linear systems, 56local, 53Lotka–Volterra predator–prey example,

51periodic orbits, 59

state, 33perturbation equations, 52variables, 33

state-space notation, 33difference equations, 33differential equations, 34

stock recruitment, 355strategies, 27, 73

as heritable phenotypes, 8concatenation, 94continuous, 68evolutionarily stable, 151fixed, 73group-optimal, 70max-max, 70max-min, 69mean, 121mixed, 68, 276Nash solution, 70no-regret, 70pure, 69, 276scalar, 92, 106variable, 73vector, 93, 96, 99, 103

strategy dynamics, 21, 112, 114strategy species concept, 121, 236, 242struggle for existence, 62sustainable yield, 355symmetric competition game, 89symmetric matrix game, 66, 278sympatric speciation, 251, 252

gene flow example, 253

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382 Index

theoremsESS – frequency, 219ESS – multiple, 213ESS – multistage, 222ESS – resource, 211ESS – scalar, 198ESS – vector, 205game against relatives, 303matrix-ESS, 282matrix-ESS maximum principle, 281

time scale, 126ecological, 119evolutionary, 119

tragedy of the commons, 12, 96, 329

ecological, 350evolutionary, 350

transpose, 48, 108

variance, 125variance dynamics

in the L–V competition game, 244vector, 28

partitioning of, 94virtual strategy, 78

war of attrition, 71

zero-sum game, 63

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