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Fitness and Prediction in Evolutionary Theory

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I argue that both careful conceptual analysis and recent results from mathematical biology cast doubt on the utility of predictive fitness. In most cases, there is simply no sense to be made of the claim that predictive fitness predicts the future evolutionary trajectory of traits, organisms, or populations. If the very reason that we have retained the concept of fitness in evolutionary theory is to enable these kinds of predictions, this is a serious problem, and one which points to a fundamental misunderstanding in our philosophical analyses of fitness. We have privileged a role for fitness that it in fact is unable to play. Whatever else fitness may be, it is not (or at least is not very) predictive.

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Fitness and Prediction in Evolutionary Theory

  1. 1. Fitness and Prediction in Evolutionary Theory London School of Economics, 25/1/2017 Charles H. Pence Department of Philosophy
  2. 2. Outline 1. Fundamentals of Selection 2. Two Roles for Fitness 3. The Claim 4. Predictive Fitness 4.1 From the PIF to Predictive Fitness 4.2 Ways Out? 5. The Moral The take-home: A common conceptual analysis of fitness in the philosophy of biology is mistaken. Charles H. Pence 2 / 53
  3. 3. Natural Selection Charles H. Pence Fundamentals of Selection 3 / 53
  4. 4. t = 0 Charles H. Pence Fundamentals of Selection 4 / 53
  5. 5. t = 0 t = 1 Charles H. Pence Fundamentals of Selection 4 / 53
  6. 6. t = 0 t = 1 t = 2 Charles H. Pence Fundamentals of Selection 4 / 53
  7. 7. Fitness Charles H. Pence Fundamentals of Selection 5 / 53
  8. 8. Charles H. Pence Fundamentals of Selection 6 / 53
  9. 9. Charles H. Pence Fundamentals of Selection 6 / 53
  10. 10. > Charles H. Pence Fundamentals of Selection 6 / 53
  11. 11. Blue organisms leave more offspring than red organisms. Charles H. Pence Fundamentals of Selection 7 / 53
  12. 12. Blue organisms leave more offspring than red organisms. A circle: the tautology problem Charles H. Pence Fundamentals of Selection 7 / 53
  13. 13. Blue organisms will probably (are disposed to) leave more offspring than red organisms. Charles H. Pence Fundamentals of Selection 8 / 53
  14. 14. The Propensity Interpretation of Fitness Charles H. Pence Fundamentals of Selection 9 / 53
  15. 15. Charles H. Pence Fundamentals of Selection 10 / 53
  16. 16. Two Notions of Fitness Charles H. Pence Two Roles for Fitness 11 / 53
  17. 17. Matthen and Ariew (2002) [F]or many this notion of an organism’s overall competitive advantage traceable to heritable traits is at the heart of the theory of natural selection. Recognizing this, we shall call this measure of an organism’s selective advantage its vernacular fitness. According to one standard way of understanding natural selection, vernacular fitness – or rather the variation thereof – is a cause of evolutionary change. (p. 56) Charles H. Pence Two Roles for Fitness 12 / 53
  18. 18. Matthen and Ariew (2002) Fitness occurs also in equations of population genetics which predict, with some level of probability, the frequency with which a gene occurs in a population in generation n + 1 given its frequency in generation n. In population genetics, predictive fitness (as we shall call it) is a statistical measure of evolutionary change, the expected rate of increase (normalized relative to others) of a gene ... in future generations.... (p. 56) Charles H. Pence Two Roles for Fitness 13 / 53
  19. 19. Causal (vernacular) fitness: general (causal) notion in natural selection Predictive (mathematical) fitness: predict future representation from central tendency/expected value Charles H. Pence Two Roles for Fitness 14 / 53
  20. 20. Matthen and Ariew (2002) [N]atural selection is not a process driven by various evolutionary factors taken as forces; rather, it is a statistical “trend” with these factors (vernacular fitness excluded) as predictors. These theses demand a radical revision of received conceptions of causal relations in evolution. (p. 57) Charles H. Pence Two Roles for Fitness 15 / 53
  21. 21. The Claim Charles H. Pence The Claim 16 / 53
  22. 22. Contra Matthen and Ariew, predictive fitness is not a fruitful way to understand fitness in biology. By extension, neither is the dichotomy between causal and predictive fitness. Charles H. Pence The Claim 17 / 53
  23. 23. It fails in a way that should lead us to question not only the predictive-causal dichotomy, but the relationship between short-term and long-term evolutionary processes. Charles H. Pence The Claim 18 / 53
  24. 24. Predictive Fitness Charles H. Pence Predictive Fitness 19 / 53
  25. 25. Standard view: predictive fitness tracks something like a central tendency extracted from the distribution of outcomes of interest Charles H. Pence Predictive Fitness 20 / 53
  26. 26. Matthen and Ariew (2002) The basic principle of statistical thermodynamics is that less probable thermodynamic states give way in time to more probable ones, simply by the underlying entities participating in fundamental processes. [...] The same is true of evolution. (p. 80) Charles H. Pence Predictive Fitness 21 / 53
  27. 27. Lewontin (1974) When we say that we have an evolutionary perspective on a system or that we are interested in the evolutionary dynamics of some phenomenon, we mean that we are interested in the change of state of some universe in time. [...] The sufficient set of state variables for describing an evolutionary process within a population must include some information about the statistical distribution of genotypic frequencies. (pp. 6, 16; orig. emph.) Charles H. Pence Predictive Fitness 22 / 53
  28. 28. Among other reasons, this is to be useful for grounding medium- to long-term predictions about evolutionary change in fitness comparisons. Charles H. Pence Predictive Fitness 23 / 53
  29. 29. Charles H. Pence Predictive Fitness 24 / 53
  30. 30. Charles H. Pence Predictive Fitness 24 / 53
  31. 31. Fitness Maximization Charles H. Pence Predictive Fitness 25 / 53
  32. 32. One way to get these predictions: Evolution as a process that maximizes fitness over time Charles H. Pence Predictive Fitness 26 / 53
  33. 33. Birch (2016) Neither [of the approaches surveyed] establishes a maximization principle with biological meaning, and I conclude that it may be a mistake to look for universal maximization principles justified by theory alone. (p. 714) Charles H. Pence Predictive Fitness 27 / 53
  34. 34. But this isn’t the only way to generate predictions. What about building predictions from the PIF itself? Charles H. Pence Predictive Fitness 28 / 53
  35. 35. From Causal to Predictive Charles H. Pence From the PIF to Predictive Fitness 29 / 53
  36. 36. How should defenders of the PIF respond to M&A’s emphasis on predictive fitness? Charles H. Pence From the PIF to Predictive Fitness 30 / 53
  37. 37. Millstein (2016) Fitness is an organism’s propensity to survive and reproduce (based on its heritable physical traits) in a particular environment and a particular population over a specified number of generations. That is what fitness is. [...] Expected reproductive success is not the propensity interpretation of fitness and it never was; it was just one way of trying to grapple with probability distributions and assign fitness values. (p. 615) Charles H. Pence From the PIF to Predictive Fitness 31 / 53
  38. 38. Charles H. Pence From the PIF to Predictive Fitness 32 / 53
  39. 39. The basic idea: Define the propensity interpretation in terms of facts about the possible lives an organism (with a given genotype, in a given environment) could have lived. Charles H. Pence From the PIF to Predictive Fitness 33 / 53
  40. 40. F(G, E) = exp(lim t→∞ 1 t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω) Having our cake and eating it, too: • Gives you a mathematical model... • ...that’s grounded in a specific dispositional property Charles H. Pence From the PIF to Predictive Fitness 34 / 53
  41. 41. Can we draw any conclusions about the quality of predictions from the Pence & Ramsey model? Charles H. Pence From the PIF to Predictive Fitness 35 / 53
  42. 42. F(G, E) = exp(lim t→∞ 1 t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω) A long-run limit: perfect for prediction! But it relies on an assumption: non-chaotic population dynamics Charles H. Pence From the PIF to Predictive Fitness 36 / 53
  43. 43. Question: How common is non-chaotic dynamics in evolving systems? My assumption: Won’t be able to answer this – model is far too general. Charles H. Pence From the PIF to Predictive Fitness 37 / 53
  44. 44. Approach of Doebeli & Ispolatov (2014): Investigate by simulating populations with two features: 1. Density-dependent selection pressures 2. High-dimensional phenotype space Charles H. Pence From the PIF to Predictive Fitness 38 / 53
  45. 45. Doebeli & Ispolatov (2014) Our main result is that the probability of chaos increases with the dimensionality d of the evolving system, approaching 1 for d ∼ 75. Moreover, our simulations indicate that already for d ≳ 15, the majority of chaotic trajectories essentially fill out the available phenotype space over evolutionary time.... (p. 1368) Charles H. Pence From the PIF to Predictive Fitness 39 / 53
  46. 46. -100 0 100 -100 0 100 x1 x2 Doebeli and Ispolatov (2014), fig. 5 Charles H. Pence From the PIF to Predictive Fitness 40 / 53
  47. 47. What’s the real-world timescale here? How does it relate to the rate of environmental change? Charles H. Pence From the PIF to Predictive Fitness 41 / 53
  48. 48. A surprising result at this level of generality. In cases where it holds, what kinds of fitness-based predictions would remain viable? Charles H. Pence From the PIF to Predictive Fitness 42 / 53
  49. 49. Charles H. Pence Ways Out? 43 / 53
  50. 50. Grant (1997) The invasion is exponential, but nonlinear dynamics of the resident type produce fluctuations around this trend. [Fitness] can therefore be most accurately estimated by the slope of the least squares regression of [daughter population size] on t. (p. 305) Charles H. Pence Ways Out? 44 / 53
  51. 51. Two major problems: • Loses sight of the dynamics • Offers poor predictions Charles H. Pence Ways Out? 45 / 53
  52. 52. Move the goalposts: • Abandon all but short-term predictions • Abandon predictive content; predict simply ‘chaos’ • Abandon prediction, focus on statistical retrodiction Charles H. Pence Ways Out? 46 / 53
  53. 53. • Resuscitate central tendencies: poor predictions that ignore (interesting) dynamics • Move the goalposts: loses the medium-to-long-term predictions cited above Charles H. Pence Ways Out? 47 / 53
  54. 54. The Moral Charles H. Pence The Moral 48 / 53
  55. 55. Many uses of fitness: • Mathematical parameter in models • Causal property • Proxies for strength of selection in populations • Statistical estimator for any of the above Charles H. Pence The Moral 49 / 53
  56. 56. Fitness concepts are far more complex than a dichotomy between two simple roles for fitness. Charles H. Pence The Moral 50 / 53
  57. 57. What’s the relationship between short-term and long-term evolutionary processes? Charles H. Pence The Moral 51 / 53
  58. 58. Complete continuity, all the way to the long run? Unlikely. Charles H. Pence The Moral 52 / 53
  59. 59. Complete continuity, all the way to the long run? Unlikely. Medium-term continuity? Threatened by these results! Charles H. Pence The Moral 52 / 53
  60. 60. Questions? charles@charlespence.net http://charlespence.net @pencechp
  61. 61. F(G, E) = exp( lim t→∞ 1 t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω) Charles H. Pence Bonus! 1 / 4
  62. 62. F(G, E) = exp( lim t→∞ 1 t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω) • Multi-generational life histories Charles H. Pence Bonus! 1 / 4
  63. 63. F(G, E) = exp( lim t→∞ 1 t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω) • Multi-generational life histories • Changing genotypes and environments over time Charles H. Pence Bonus! 1 / 4
  64. 64. F(G, E) = exp( lim t→∞ 1 t ∫ω∈Ω Pr(ω) ⋅ ln(ϕ(ω, t)) dω) • Multi-generational life histories • Changing genotypes and environments over time • Disposition (propensity) defined over modal facts about other possible lives of organisms Charles H. Pence Bonus! 1 / 4
  65. 65. State space of possible lives: Ω {f R → Rn} Cardinality, though, is too big! N(Ω) = 22ℵ0 Can still define a σ-algebra F and a probability measure Pr if we restrict our attention to: • continuous functions ω, • functions ω with only point discontinuities, or • functions ω with only jump discontinuities (Nelson 1959) Charles H. Pence Bonus! 2 / 4
  66. 66. With that state space defined, we need three simplifying assumptions: 1. Non-chaotic population dynamics 2. Probabilities generated by a stationary random process 3. Logarithmic moment of vital rates is bounded The last two are trivial in our context. Charles H. Pence Bonus! 3 / 4
  67. 67. Then the following limit exists: a = lim t→∞ 1 t Ew ln(ϕ(t)), with Ew an expectation value (Tuljapurkar 1989). Fitness is the exponential of this quantity a, and is equivalent (under further simplifying assumptions) to net reproductive rate and related to the Malthusian parameter. Charles H. Pence Bonus! 4 / 4

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