Foreword ...................................................... VII
1. Introduction ................................................. 1
1.1. Synopsis ................................................ 1
1.2. Background .............................................. 3
1.2.1. Senescence - Paradox? - Inevitable? .............. 3
1.2.2. Evolutionary Theories of Senescence .............. 4
1.2.3. Measuring Senescence ............................. 5
1.2.4. Measuring Fitness ................................ 9
1.2.5. Optimal Life History ............................ 10
1.2.6. Interesting Recent Developments ................. 13
1.3. Orientation ............................................ 15
Part I Hamilton
2. Hamilton's Indicators of the Force of Selection ............. 19
2.1. Introduction ........................................... 19
2.2. Hamilton's Derivations ................................. 20
2.2.1. The Framework ................................... 20
2.2.2. Hamilton's Indicator of Survival ................ 21
2.3. Alternative Indicators ................................. 22
2.3.1. Different Parametrization ....................... 22
2.3.2. When Selection Pressure Increases ............... 22
2.3.3. Fertility Indicators ............................ 23
2.3.4. Are Some Indicators Better? ..................... 24
2.3.5. Optimization vs. Mutational Burden .............. 26
2.4. Mutation-Selection Balance ............................. 26
2.4.1. Additive vs. Proportional Parametrization ....... 27
2.4.2. A Simple Box Model .............................. 28
2.5. The Importance of Mutation Accumulation ................ 32
2.6. Conclusion ............................................. 33
3. Further Challenges .......................................... 35
3.1. General Problem with All Indicators .................... 35
3.2. Theoretical Arguments .................................. 38
3.2.1. Mutation-Selection Balance ...................... 38
3.2.2. Unraveling ...................................... 38
3.2.3. Variable Environments ........................... 40
3.2.4. Other Mechanisms ................................ 41
3.3. Empirical Evidence ..................................... 41
3.3.1. Testing Preconditions for Mutation
Accumulation .................................... 41
3.3.2. Checking Predictions from Mutation
Accumulation .................................... 42
3.3.3. Empirical Evidence for Non-senescence ........... 44
3.4. Conclusion ............................................. 45
Part II Optimization Models
4. Optimization Models Based on Size ........................... 49
4.1. Size Matters ........................................... 49
4.2. A Size-Based Life-History Model ........................ 51
4.2.1. The General Optimization Problem ................ 53
4.2.2. The Specific Optimization Problem ............... 54
4.3. An Optimization Model that Leads to Non-senescence ..... 57
4.3.1. The State Ratchet ............................... 58
4.3.2. The Maximum Principle ........................... 59
4.3.3. An Alternative Derivation ....................... 63
4.3.4. The Simplest Model Leads to Sustenance .......... 65
4.3.5. Introducing Nonlinearity Can Lead to
Enhancement ..................................... 67
4.4. An Optimization Model that Leads to Senescence ......... 68
4.5. Discussion ............................................. 71
4.6. Next Steps ............................................. 73
5. An Optimization Model Based on Vitality ..................... 75
5.1. The Vitality Model ..................................... 76
5.1.1. The Parameters .................................. 81
5.2. The Vitality Model as a Control Problem ................ 83
5.2.1. Problem Formulation ............................. 83
5.2.2. Solution ........................................ 85
5.2.3. The Role of the Second State Variable ........... 87
5.2.4. Hamilton and Reproductive Value - Revisited ..... 88
5.3. The Constrained Vitality Model ......................... 90
5.3.1. Expected Solutions .............................. 94
5.4. Numerical Results ...................................... 98
5.4.1. The Five Varieties of Life History Strategies ... 98
5.4.2. When Senescence Is Optimal and when It Is
Not ............................................ 108
5.5. Discussion ............................................ 116
5.5.1. Senescence vs. Non-senescence .................. 116
5.5.2. The η Parameters in Nature ..................... 117
5.5.3. The Mortality Paradox .......................... 119
5.5.4. Plateaus ....................................... 121
5.6. Summary ............................................... 121
6. Directions for Research .................................... 123
6.1. Orientation ........................................... 123
6.2. Direct Extensions of my Models ........................ 123
6.2.1. Linking Burden & Optimization .................. 123
6.2.2. Measurable Quantities and Testable
Hypotheses ..................................... 124
6.2.3. The Diversity of Aging ......................... 125
6.2.4. The Characteristics of Senescent vs. Non-
senescent Species .............................. 125
6.2.5. Alternative Applications ....................... 127
6.3. Other Modeling Extensions ............................. 127
6.3.1. Density Effects ................................ 127
6.3.2. Intergenerational Transfers .................... 128
6.3.3. Environmental Fluctuations ..................... 129
6.3.4. Population Dynamics ............................ 130
6.3.5. Summary ........................................ 130
6.4. Prospects for Evolutionary Demography ................. 131
6.4.1. Moving Beyond the Burden of "Deleterious
Fixations" ..................................... 131
6.4.2. The Need for Data, Methods, and Measures ....... 133
6.4.3. A New Burning Question ......................... 135
6.5. Conclusion ............................................ 138
Vitality Model - Appendix ..................................... 141
A.l. Solving Differential Equations ........................ 141
A.2. Proof of Non-Existence of an Optimal Solution for a
Special Case .......................................... 143
A.3. The Algorithm ......................................... 144
References .................................................... 149
Index ......................................................... 167
List of Figures
2.1. Example of survival and maternity functions lα and
mα ..................................................... 23
2.2. Comparison of H1 — dr / d ln pα with dr / d ln μα ..... 24
2.3. Equilibrium number of mutations: additive vs.
proportional; theoretical example ...................... 30
2.4. Equilibrium number of mutations: additive vs.
proportional; example Swedish females 1778-82 .......... 31
2.5. Mortality trajectories resulting from mutation
accumulation; example Swedish females 1778-82 .......... 31
2.6. Proportion of mortality explained by mutation
accumulation: additive vs. proportional ................ 33
3.1. The relation between Hamilton's declining indicator
of selection pressure and three possible age-
patterns of mortality .................................. 37
3.2. Different hypothetical mortality trajectories .......... 46
4.1. Size ε(α) as a function of age α ....................... 55
4.2. Determinate growth with Sustenance - optimal size
at maturity ............................................ 65
4.3. Indeterminate growth with Enhancement - optimal
trajectories for model variant with nonlinear
fertility function ..................................... 68
4.4. Determinate growth with Senescence - optimal
trajectories for model variant with nonlinear
fertility function and two state variables ............. 70
5.1. Influence of parameter ηg via investment -π on
the change in vitality ................................. 80
5.2. Energy trajectories .................................... 82
5.3. Example Enhancementηr = 0.5 and ηg = 0.5 ............... 99
5.4. Example Enhancement: ηr = 1 and ηg = 0.5 .............. 100
5.5. Example Enhancement: ηr = 0.5 and ηg = 1 .............. 100
5.6. Example Sustenance: ηr — 1 and ηg = 1 ................. 101
5.7. Example Senescence: ηr = 1 ηg ~ 1.5 ................... 102
5.8. Example Senescenceηr = 3 ηg — 1.5 ..................... 102
5.9. Example Senescence (humanesque case): ηr — 3 ηg = 3 ... 103
5.10. Example Ensenescence: ηr = 0.5 ηr = 1.5 .............. 104
5.11. Example Ensenescence: ηr = 0.5 ηg = 3 ................ 105
5.12. Example Enhancement: ηr = 1.5 ηg = 0.5 ............... 105
5.13. Example Subsenescence: ηr = 3 ηg = 0.5 ............... 106
5.14. Overview of optimal investment strategies across η
parameters ............................................ 107
5.15. Degree of senescence S, in %, across η and
mortality parameters ................................. 109
5.16. Vitality at maturity across η and mortality
parameters ........................................... 1ll
5.17. Vitality at maturity across η parameters ............. 114
5.18. Vitality at maintenance across η parameters .......... 114
5.19. Vitality at maturity and vitality at maintenance
across η parameters .................................. 115
5.20. Vitality at maturity and vitality at maintenance
across extrinsic mortality с for different values
of intrinsic mortality b ............................. 116
List of Tables
1.1. Senescence or not ....................................... 8
2.1. Various indicators of the force of selection in
Hamilton's framework ................................... 25
4.1. Determinate growth with Sustenance - optimal size
and age at the start of reproduction for size-
dependent mortality .................................... 66
|
