Biology & Philosophy

, 34:21 | Cite as

Locating uncertainty in stochastic evolutionary models: divergence time estimation

  • Charles H. PenceEmail author


Philosophers of biology have worked extensively on how we ought best to interpret the probabilities which arise throughout evolutionary theory. In spite of this substantial work, however, much of the debate has remained persistently intractable. I offer the example of Bayesian models of divergence time estimation (the determination of when two evolutionary lineages split) as a case study in how we might bring further resources from the biological literature to bear on these debates. These models offer us an example in which a number of different sources of uncertainty are combined to produce an estimate for a complex, unobservable quantity. These models have been carefully analyzed in recent biological work, which has determined the relationship between these sources of uncertainty (their relative importance and their disappearance in the limit of increasing data), both quantitatively and qualitatively. I suggest here that this case shows us the limitations of univocal analyses of probability in evolution, as well as the simple dichotomy between “subjective” and “objective” probabilities, and I conclude by gesturing toward ways in which we might introduce more sophisticated interpretive taxonomies of probability (modeled on some recent work in the philosophy of physics) as a path toward advancing debates on probability in the life sciences.


Probability Uncertainty Evolutionary theory Divergence time Scientific modeling Stochastic models Bayesian models 



My sincere thanks to two anonymous reviewers for this journal, who very dramatically improved this paper (and caught a few serious errors!). For comments on a very early version of this project, thanks to an audience at the Models and Simulations 6 conference, at the University of Notre Dame. Many thanks also to Mario dos Reis for the initial inspiration behind the project, which was born at NESCent—still inspiring interdisciplinary work years after its unfortunate closure.


  1. Abrams M (2009) What determines biological fitness? The problem of the reference environment. Synthese 166(1):21–40Google Scholar
  2. Abrams M (2012a) Measured, modeled, and causal conceptions of fitness. Front Genet 3:196Google Scholar
  3. Abrams M (2012b) Mechanistic probability. Synthese 187(2):343–375Google Scholar
  4. Abrams M (2015) Probability and manipulation: evolution and simulation in applied population genetics. Erkenntnis 80(S3):519–549Google Scholar
  5. Ariew A, Lewontin RC (2004) The confusions of fitness. Br J Philos Sci 55(2):347–363Google Scholar
  6. Baker A (2017) Mathematical spandrels. Australas J Philos 95(4):779–793Google Scholar
  7. Beatty JH, Desjardins EC (2009) Natural selection and history. Biol Philos 24(2):231–246Google Scholar
  8. Benton MJ, Donoghue PCJ, Asher RJ (2009) Calibrating and constraining molecular clocks. In: Hedges SB, Kumar S (eds) The timetree of life. Oxford University Press, Oxford, pp 35–86Google Scholar
  9. Brandon RN (1990) Adaptation and environment. Princeton University Press, PrincetonGoogle Scholar
  10. Brandon RN, Ramsey G (2007) What’s wrong with the emergentist statistical interpretation of natural selection and random drift? In: Hull DL, Ruse M (eds) The Cambridge companion to the philosophy of biology. Cambridge University Press, Cambridge, pp 66–84Google Scholar
  11. Desjardins E (2011) Reflections on path dependence and irreversibility: Lessons from evolutionary biology. Philosophy of Science 78(5):724–738Google Scholar
  12. Desjardins E (2016) Contingent evolution: not by chance alone. In: Ramsey G, Pence CH (eds) Chance in evolution. University of Chicago Press, Chicago, pp 223–243Google Scholar
  13. dos Reis M, Yang Z (2013) The unbearable uncertainty of Bayesian divergence time estimation. J Syst Evol 51(1):30–43Google Scholar
  14. Drouet I, Merlin F (2013) The propensity interpretation of fitness and the propensity interpretation of probability. Erkenntnis 80(S3):457–468Google Scholar
  15. Drummond AJ, Ho SYW, Phillips MJ, Rambaut A (2006) Relaxed phylogenetics and dating with confidence. PLoS Biol 4(5):e88Google Scholar
  16. Earman J (2007) Aspects of determinism in modern physics. In: Butterfield J, Earman J (eds) Handbook of the philosophy of science: philosophy of physics. North-Holland, Amsterdam, pp 1369–1434Google Scholar
  17. Endler JA (1986) Natural selection in the wild. Princeton University Press, PrincetonGoogle Scholar
  18. Felsenstein J (2004) Inferring phylogenies. Sinauer Associates, SunderlandGoogle Scholar
  19. Foley A (2010) Uncertainty in regional climate modelling: a review. Prog Phys Geogr 34(5):647–670Google Scholar
  20. Gillespie JH (1984) Molecular evolution over the mutational landscape. Evolution 38(5):1116–1129Google Scholar
  21. Gillespie JH (1991) The causes of molecular evolution. Oxford University Press, OxfordGoogle Scholar
  22. Graur D, Martin W (2004) Reading the entrails of chickens: molecular timescales of evolution and the illusion of precision. Trends Genet 20(2):80–86Google Scholar
  23. Graves L, Horan BL, Rosenberg A (1999) Is indeterminism the source of the statistical character of evolutionary theory? Philos Sci 66(1):140–157Google Scholar
  24. Halpern AL, Bruno WJ (1998) Evolutionary distances for protein-coding sequences: modeling site- specific residue frequencies. Mol Biol Evol 15(7):910–917Google Scholar
  25. Hasegawa M, Kishino H, Yano T (1985) Dating of the human-ape splitting by a molecular clock of mitochondrial DNA. J Mol Evol 22(2):160–174Google Scholar
  26. Jukes TH, Cantor CR (1969) Evolution of protein molecules. In: Munro HN (ed) Mammalian protein metabolism, vol 3. Academic Press, New York, pp 21–132Google Scholar
  27. Lenormand T, Roze D, Rousset F (2009) Stochasticity in evolution. Trends Ecol Evol 24(3):157–165Google Scholar
  28. Lepage T, Bryant D, Philippe H, Lartillot N (2007) A general comparison of relaxed molecular clock models. Mol Biol Evol 24(12):2669–2680Google Scholar
  29. Linder M, Britton T, Sennblad B (2011) Evaluation of Bayesian models of substitution rate evolution—parental guidance versus mutual independence. Syst Biol 60(3):329–342Google Scholar
  30. Matthen M (2009) Drift and “statistically abstractive explanation”. Philos Sci 76(4):464–487Google Scholar
  31. Matthen M, Ariew A (2002) Two ways of thinking about fitness and natural selection. J Philos 99(2):55–83Google Scholar
  32. Merlin F (2010) Evolutionary chance mutation: a defense of the modern synthesis’ consensus view. Philos Theory Biol 2:e103Google Scholar
  33. Merlin F (2016) Weak randomness at the origin of biological variation: the case of genetic mutations. In: Ramsey G, Pence CH (eds) Chance in evolution. University of Chicago Press, Chicago, pp 176–195Google Scholar
  34. Millstein RL (2003) Interpretations of probability in evolutionary theory. Philos Sci 70:1317–1328Google Scholar
  35. Millstein RL (2006) Natural selection as a population-level causal process. Br J Philos Sci 57(4):627–653Google Scholar
  36. Millstein RL (2008) Distinguishing drift and selection empirically: “The Great Snail Debate” of the 1950s. J History Biol 41(2):339–367Google Scholar
  37. Millstein RL (2011) Chances and causes in evolutionary biology: how many chances become one chance. In: Illari PM, Russo F, Williamson J (eds) Causality in the sciences. Oxford University Press, Oxford, pp 425–444Google Scholar
  38. Millstein RL (2016) Probability in biology: the case of fitness. In: Hájek A, Hitchcock C (eds) The Oxford handbook of probability and philosophy. Oxford University Press, Oxford, pp 601–622Google Scholar
  39. Mulcahy DG, Noonan BP, Moss T, Townsend TM, Reeder TW, Sites JW, Wiens JJ (2012) Estimating divergence dates and evaluating dating methods using phylogenomic and mitochondrial data in squamate reptiles. Mol Phylogenetics Evol 65(3):974–991Google Scholar
  40. Nascimento FF, dos Reis M, Yang Z (2017) A biologist’s guide to Bayesian phylogenetic analysis. Nat Ecol Evol 1(10):1446–1454Google Scholar
  41. Otsuka J (2016) A critical review of the statisticalist debate. Biol Philos 31(4):459–482Google Scholar
  42. Pence CH (2017) Is genetic drift a force? Synthese 194(6):1967–1988Google Scholar
  43. Pence CH, Ramsey G (2013) A new foundation for the propensity interpretation of fitness. Br J Philos Sci 64(4):851–881Google Scholar
  44. Rannala B, Yang Z (2007) Inferring speciation times under an episodic molecular clock. Syst Biol 56(3):453–466Google Scholar
  45. Ronquist F, Klopfstein S, Vilhelmsen L, Schulmeister S, Murray DL, Rasnitsyn AP (2012) A total-evidence approach to dating with fossils, applied to the early radiation of the Hymenoptera. Syst Biol 61(6):973–999Google Scholar
  46. Rosenberg A (1994) Instrumental biology, or the disunity of science. University of Chicago Press, ChicagoGoogle Scholar
  47. Sanderson MJ (1997) A nonparametric approach to estimating divergence times in the absence of rate constancy. Mol Biol Evol 14(12):1218–1231Google Scholar
  48. Schwartz JH, Maresca B (2006) Do molecular clocks run at all? A critique of molecular systematics. Biol Theory 1(4):357–371Google Scholar
  49. Sober E (2011) A priori causal models of natural selection. Australas J Philos 89(4):571–589Google Scholar
  50. Stamos DN (2001) Quantum indeterminism and evolutionary biology. Philos Sci 68(2):164–184Google Scholar
  51. Strevens M (2011) Probability out of determinism. In: Beisbart C, Hartmann S (eds) Probabilities in physics. Oxford University Press, Oxford, pp 339–364Google Scholar
  52. Strevens M (2013) Tychomancy: inferring probability from causal structure. Harvard University Press, CambridgeGoogle Scholar
  53. Strevens M (2016) The reference class problem in evolutionary biology: distinguishing selection from drift. In: Ramsey G, Pence CH (eds) Chance in evolution. University of Chicago Press, Chicago, pp 145–175Google Scholar
  54. Thorne JL, Kishino H (2002) Divergence time and evolutionary rate estimation with multilocus data. Syst Biol 51(5):689–702Google Scholar
  55. Thorne JL, Kishino H, Painter IS (1998) Estimating the rate of evolution of the rate of molecular evolution. Mol Biol Evol 15(12):1647–1657Google Scholar
  56. Turner D (2005) Local underdetermination in historical science. Philos Sci 72(1):209–230Google Scholar
  57. Walsh DM (2007) The pomp of superfluous causes: the interpretation of evolutionary theory. Philos Sci 74(3):281–303Google Scholar
  58. Walsh DM, Lewens T, Ariew A (2002) The trials of life: natural selection and random drift. Philos Sci 69(3):429–446Google Scholar
  59. Walsh DM, Ariew A, Matthen M (2017) Four pillars of statisticalism. Philos Theory Pract Biol 9:1Google Scholar
  60. Weisberg M (2014) Understanding the emergence of population behavior in individual-based models. Philos Sci 81(5):785–797Google Scholar
  61. Werndl C (2013) On choosing between deterministic and indeterministic models: underdetermination and indirect evidence. Synthese 190(12):2243–2265Google Scholar
  62. Wilkinson RD, Steiper ME, Soligo C, Martin RD, Yang Z, Tavaré S (2011) Dating primate divergences through an integrated analysis of palaeontological and molecular data. Syst Biol 60(1):16–31Google Scholar
  63. Yang Z, Rannala B (2006) Bayesian estimation of species divergence times under a molecular clock using multiple fossil calibrations with soft bounds. Mol Biol Evol 23(1):212–226Google Scholar
  64. Zuckerkandl E, Pauling L (1965) Molecules as documents of evolutionary history. J Theor Biol 8(2):357–366Google Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institut supérieur de philosophieUniversité catholique de LouvainLouvain-la-NeuveBelgium

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