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The Role of Mathematics in Evolutionary Theory
Published online by Cambridge University Press: 05 February 2020
Summary
The central role of mathematical modeling in modern evolutionary theory has raised a concern as to why and how abstract formulae can say anything about empirical phenomena of evolution. This Element introduces existing philosophical approaches to this problem and proposes a new account according to which evolutionary models are based on causal, and not just mathematical, assumptions. The novel account features causal models both as the Humean 'uniform nature' underlying evolutionary induction and as the organizing framework that integrates mathematical and empirical assumptions into a cohesive network of beliefs that functions together to achieve epistemic goals of evolutionary biology.
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- Online ISBN: 9781108672115Publisher: Cambridge University PressPrint publication: 17 October 2019
References
Baker, A. (2005). Are There Genuine Mathematical Explanations of Physical Phenomena? Mind, 114(454):223–238.CrossRefGoogle Scholar
Beatty, J. (1980). Optimal-Design Models and the Strategy of Model Building in Evolutionary Biology. 47(4):532–561.Google Scholar
Beatty, J. (1981). What’s Wrong with the Received View of Evolutionary Theory? PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1980, 2:397–426.Google Scholar
Beatty, J. (1995). The Evolutionary Contingency Thesis. In Wolters, G. and Lennox, J. G., editors, Concepts, Theories, and Rationality in the Biological Sciences, pp. 45–81. University of Pittsburgh Press.Google Scholar
Bouchard, F. and Rosenberg, A. (2005). Matthen and Ariew’s Obituary for Fitness: Reports of Its Death Have Been Greatly Exaggerated. Biology & Philosophy, 20(2–3):343–353.Google Scholar
Bourrat, P. and Qiaoying, L. (2017). Dissolving the Missing Heritability Problem. Philosophy of Science, (84):1055–1067.Google Scholar
Bowler, P. J. (1983). The Eclipse of Darwinism: Anti-Darwinian Evolution Theories in the Decades around 1900. John Hopkins University Press, Baltimore, MD.Google Scholar
Boyd, R. N. (1991). Realism, Anti-foundationalism and the Enthusiasm for Natural Kinds. Philosophical Studies, 61(1–2):127–148.Google Scholar
Brading, K. and Castellani, E. (2003). Symmetries in Physics: Philosophical Reflections. Cambridge University Press, Cambridge, UK.Google Scholar
Brandon, R. N. (1981). A Structural Description of Evolutionary Theory. In PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1980, pp. 427–439.Google Scholar
Brandon, R. N. and Beatty, J. (1984). The Propensity Interpretation of ‘Fitness’ – No Interpretation Is No Substitute. Philosophy of Science, 51(2):342–347.Google Scholar
Carnap, R. (1966). An Introduction to the Philosophy of Science. Dover Publications, Inc., Mineola, NY.Google Scholar
Darwin, C. (2003). On the Origin of Species: A Facsimile of the First Edition. Harvard University Press, Cambridge, MA.Google Scholar
Eichler, E. E., Flint, J., Gibson, G., Kong, A., Leal, S. M., Moore, J. H., and Nadeau, J. H. (2010). Missing Heritability and Strategies for Finding the Underlying Causes of Complex Disease. Nature Reviews Genetics, 11(6):446–450.CrossRefGoogle ScholarPubMed
Endler, J. A. (1986). Natural Selection in the Wild. Princeton University Press, Princeton, NJ.Google Scholar
Fisher, R. A. (1918). The Correlation between Relatives on the Supposition of Mendelian Inheritance. Transactions of the Royal Society of Edinburgh, 51:399–433.Google Scholar
Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Oxford University Press, Oxford.Google Scholar
Fodor, J. A. (1974). Special Sciences (or: The Disunity of Science as a Working Hypothesis). Synthese, 28(2):97–115.CrossRefGoogle Scholar
Frank, S. A. (1995). George Price’s Contributions to Evolutionary Genetics. Journal of Theoretical Biology, 175:373–388.Google Scholar
Frank, S. A. (1997). The Price Equation, Fisher’s Fundamental Theorem, Kin Selection, and Causal Analysis. Evolution, 51(6):1712–1729.Google Scholar
Frank, S. A. (2012). Natural Selection. IV. The Price Equation. Journal of Evolutionary Biology, 25(6):1002–1019.Google Scholar
Frank, S. A. (2015). D’Alembert’s Direct and Inertial Forces Acting on Populations: The Price Equation and the Fundamental Theorem of Natural Selection. Entropy, 17(10):7087–7100.CrossRefGoogle Scholar
Friedman, M. (1974). Explanation and Scientific Understanding. The Journal of Philosophy, 71(1):5–19.Google Scholar
Goodman, N. (1955). Fact, Fiction, and Forecast. Harvard University Press, Cambridge, MA.Google Scholar
Grafen, A. (2014). The Formal Darwinism Project in Outline. Biology & Philosophy, 29(2):155–174.CrossRefGoogle Scholar
Griesemer, J. R. (2012). Formalization and the Meaning of “Theory” in the Inexact Biological Sciences. Biological Theory, 7(4):298–310.Google Scholar
Hadfield, J. D. (2008). Estimating Evolutionary Parameters When Viability Selection Is Operating. Proceedings of the Royal Society B: Biological Sciences, 275(1635):723–734.CrossRefGoogle ScholarPubMed
Haldane, J. B. S. (1964). A Defense of Beanbag Genetics. Perspectives in Biology and Medicine, 7(3):434–359.CrossRefGoogle ScholarPubMed
Haldane, J. B. S. (1931). The Philosophical Basis of Biology. Hodder and Stoughton Limited, London, UK.Google Scholar
Houle, D., Hansen, T. F., Pélabon, C., and Wagner, G. P. (2011). Measurement and Meaning in Biology. The Quarterly Review of Biology, 86(1):3–34.Google Scholar
Hull, D. L. (1974). Philosophy of Biological Science. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Huttegger, S. M. and Mitteroecker, P. (2011). Invariance and Meaningfulness in Phenotype Spaces. Evolutionary Biology, 38(3):335–351.Google Scholar
Imbens, G. W. and Rubin, D. (2015). Causal Inference in Statistics, Social, and Biomedical Sciences. Cambridge University Press, New York, NY.CrossRefGoogle Scholar
Jantzen, B. C. (2015). Projection, Symmetry, and Natural Kinds. Synthese, 192(11):3617–3646.CrossRefGoogle Scholar
Jantzen, B. C. (2019). Kinds of Process and the Levels of Selection. Synthese, 196(6):2407–2433.Google Scholar
Kim, J. (1992). Multiple Realization and the Metaphysics of Reduction. Philosophy and Phenomenological Research, 52(1):1–26.Google Scholar
Lewontin, R. C. (1970). The Units of Selection. Annual Review of Ecology and Systematics, 1:1–18.Google Scholar
Lewontin, R. C. (1974). The Genetic Basis of Evolutionary Change. Columbia University Press, New York, NY.Google Scholar
Lloyd, E. A. (1988). The Structure and Confirmation of Evolutionary Theory. Princeton University Press, Princeton, NJ.Google Scholar
Luque, V. J. (2017). One Equation to Rule Them All: A Philosophical Analysis of the Price Equation. Biology & Philosophy, 32(1):97–125.Google Scholar
Machamer, P., Darden, L., and Craver, C. F. (2000). Thinking about Mechanisms. Philosophy of Science, 67(1):1–25.Google Scholar
Magalhães, J. C. M. and Krause, D. (2001). Suppes Predicate for Genetics and Natural Selection. Journal of Theoretical Biology, 209(2):141–153.Google Scholar
Manolio, T. A., Collins, F. S., Cox, N. J., Goldstein, D. B., Hindorff, L. A., Hunter, D. J., McCarthy, M. I., Ramos, E. M., Cardon, L. R., Chakravarti, A., Cho, J. H., Guttmacher, A. E., Kong, A., Kruglyak, L., Mardis, E., Rotimi, C. N., Slatkin, M., Valle, D., Whittemore, A. S., Boehnke, M., Clark, A. G., Eichler, E. E., Gibson, G., Haines, J. L., Mackay, T. F. C., McCarroll, S. A., and Visscher, P. M. (2009). Finding the Missing Heritability of Complex Diseases. Nature, 461(7265):747–753.Google Scholar
Matthen, M. (2009). Drift and “Statistically Abstractive Explanation.” Philosophy of Science, 76:464–487.Google Scholar
Matthen, M. and Ariew, A. (2002). Two Ways of Thinking about Fitness and Natural Selection. Journal of Philosophy, 99(2):55–83.Google Scholar
Matthen, M. and Ariew, A. (2005). How to Understand Casual Relations in Natural Selection: Reply to Rosenberg and Bouchard. Biology & Philosophy, 20(2–3):355–364.CrossRefGoogle Scholar
Matthen, M. and Ariew, A. (2009). Selection and Causation. Philosophy of Science, 76(2):201–224.CrossRefGoogle Scholar
Mayr, E. (1975). Evolution and the Diversity of Life: Selected Essays. Harvard University Press, Cambridge, MA.Google Scholar
Mayr, E. (1982). The Growth of Biological Thought. Diversity, Evolution, and Inheritance. The Belknap Press of Harvard University Press, Cambridge, MA.Google Scholar
Mckinsey, J. C. C., Suppes, P., and Sugar, A. C. (1953). Axiomatic Foundations of Classical Particle Mechanics. Journal of Rational Mechanics and Analysis, 2(2):253–272.Google Scholar
Mills, S. K. and Beatty, J. (1979). The Propensity Interpretation of Fitness. Philosophy of Science, 46:263–286.Google Scholar
Millstein, R. L. (2006). Natural Selection as a Population-Level Causal Process. The British Journal for the Philosophy of Science, 57(4):627–653.Google Scholar
Millstein, R. L., Skipper, R. A. J., and Dietrich, M. R. (2009). (Mis)interpreting Mathematical Models: Drift As a Physical Process. Philosophy, Theory, and Practice in Biology, 1:e002.Google Scholar
Morrison, M. (2000). Unifying Scientific Theories. Physical Concepts and Mathematical Structures. Cambridge University Press, Cambridge, UK.CrossRefGoogle Scholar
Morrissey, M. B., Kruuk, L. E. B., and Wilson, A. J. (2010). The Danger of Applying the Breeder’s Equation in Observational Studies of Natural Populations. Journal of Evolutionary Biology, 23(11):2277–2288.Google Scholar
Okasha, S. (2006). Evolution and the Levels of Selection. Oxford University Press, Oxford.Google Scholar
Otsuka, J. (2014). The Causal Structure of Evolutionary Theory. PhD diss., Indiana University.Google Scholar
Otsuka, J. (2016a). A Critical Review of the Statisticalist Debate. Biology & Philosophy, 31(4):459–482.Google Scholar
Otsuka, J. (2016b). Causal Foundations of Evolutionary Genetics. The British Journal for the Philosophy of Science, 67:247–269.CrossRefGoogle Scholar
Otsuka, J. (2016c). Discovering Phenotypic Causal Structure from Nonexperimental Data. Journal of Evolutionary Biology, 29(6):1268–1277.Google Scholar
Otsuka, J. (2017). The Causal Homology Concept. Philosophy of Science, 84(5):1128–1139.Google Scholar
Otsuka, J. (forthcoming a). Ontology, Causality, and Methodology of Evolutionary Research Programs. In Uller, T. and Laland, K. N., editors, Vienna Series in Theoretical Biology Evolutionary Causation. The Massachusetts Institute of Technology Press.Google Scholar
Pearl, J. (2000). Causality: Models, Reasoning, and Inference. Cambridge University Press, New York, NY.Google Scholar
Pence, C. H. and Ramsey, G. (2013). A New Foundation for the Propensity Interpretation of Fitness. The British Journal for the Philosophy of Science, 64(4):851–881.CrossRefGoogle Scholar
Pigliucci, M. and Kaplan, J. (2006). Making Sense of Evolution: The Conceptual Foundations of Evolutionary Biology. University of Chicago Press, Chicago, IL.CrossRefGoogle Scholar
Popper, K. R. (1974). Autobiography of Karl Popper. In Schlipp, P. A., editor, The Philosophy of Karl Popper. La Salle, IL.Google Scholar
Pothos, E. M. and Busemeyer, J. R. (2009). A Quantum Probability Explanation for Violations of ‘Rational’ Decision Theory. Proceedings of the Royal Society B: Biological Sciences, 276(1665):2171–2178.CrossRefGoogle ScholarPubMed
Provine, W. B. (2001). The Origins of Theoretical Population Genetics: With a New Afterword. University of Chicago Press, Chicago, IL.Google Scholar
Punnett, R. C. (1915). Mimicry in Butterflies. Cambridge University Press, Cambridge, UK.Google Scholar
Putnam, H. (1975). Philosophy and our Mental Life. In Mind, Language, and Reality, pp. 291–303. Cambridge University Press, Cambridge, UK.Google Scholar
Queller, D. C. (2017). Fundamental Theorems of Evolution. The American Naturalist, 189(4):345–353.Google Scholar
Quine, W. V. O. (1951). Two Dogmas of Empiricism. The Philosophical Review, 60(1):20–43.Google Scholar
Ramsey, G. (2013). Can Fitness Differences Be a Cause of Evolution? Philosophy, Theory, and Practice in Biology, 5:e401.Google Scholar
Ramsey, G. (2016). The Causal Structure of Evolutionary Theory. Australasian Journal of Philosophy, 94(3):421–434.Google Scholar
Ramsey, G. and Brandon, R. N. (2007). What’s Wrong with the Emergentist Statistical Interpretation of Natural Selection and Random Drift? In Hull, D. L. and Ruse, M., editors, The Cambridge Companion to the Philosophy of Biology, pp. 66–84. Cambridge University Press, Cambridge, UK.Google Scholar
Rausher, M. D. (1992). The Measurement of Selection on Quantitative Traits: Biases Due to Environmental Covariances between Traits and Fitness. Evolution, 46(3):616–626.CrossRefGoogle ScholarPubMed
Reisman, K. and Forber, P. (2004). Manipulation and the Causes of Evolution. 72:1113–1123.Google Scholar
Rice, S. H. (2004). Evolutionary Theory: Mathematical and Conceptual Foundations. Sinauer Associates, Sunderland, MA.Google Scholar
Robertson, A. (1966). A Mathematical Model of the Culling Process in Dairy Cattle. Animal Production, 8(1):95–108.Google Scholar
Rosenberg, A. (1982). On the Propensity Definition of Fitness. Philosophy of Science, 49:268–273.Google Scholar
Rosenberg, A. (1985). The Structure of Biological Science. Cambridge University Press, Cambridge.Google Scholar
Salmon, W. C. (1984). Scientific Explanation and the Causal Structure of the World. Princeton University Press, Princeton, NJ.Google Scholar
Servedio, M. R., Brandvain, Y., Dhole, S., Fitzpatrick, C. L., Goldberg, E. E., Stern, C. A., Van Cleve, J., and Yeh, D. J. (2014). Not Just a Theory – The Utility of Mathematical Models in Evolutionary Biology. PLoS Biology, 12(12):e1002017–5.Google Scholar
Shipley, B. (2000). Cause and Correlation in Biology: A User’s Guide to Path Analysis, Structural Equations and Causal Inference. Cambridge University Press, Cambridge, UK.Google Scholar
Smocovitis, V. B. (1996). Unifying Biology: The Evolutionary Synthesis and Evolutionary Biology. Princeton University Press, Princeton, NJ.Google Scholar
Sober, E. (1984). The Nature of Selection: Evolutionary Theory in Philosophical Focus. University of Chicago Press, Chicago, IL.Google Scholar
Sober, E. (1997). Two Outbreaks of Lawlessness in Recent Philosophy of Biology. Philosophy of Science, 64(Proceedings):S458–S467.Google Scholar
Spirtes, P., Glymour, C., and Scheines, R. (1993). Causation, Prediction, and Search. The Massachusetts Institute of Technology Press, Cambridge, MA.Google Scholar
Suppes, P. (1962). Models of data. In Logic, Methodology, and Philosophy of Science: Proceedings of the 1960 International Congress, pp. 252–261.Google Scholar
Suppes, P. (1967). What Is a Scientific Theory? In Philosophy of Science Today, pp. 55–67. Basic Books, Inc., New York, NY.Google Scholar
Suppes, P. (2002). Representation and Invariance of Scientific Structures. CSLI Publication, Stanford, CA.Google Scholar
Tabery, J. (2014). Beyond Versus: The Struggle to Understand the Interaction of Nature and Nurture. The Massachusetts Institute of Technology Press, Cambridge, MA.Google Scholar
Valente, B. D., Rosa, G. J. M., De los Campos, G., Gianola, D., and Silva, M. A. (2010). Searching for Recursive Causal Structures in Multivariate Quantitative Genetics Mixed Models. Genetics, 185(2):633–644.Google Scholar
van Veelen, M. (2005). On the Use of the Price Equation. Journal of Theoretical Biology, 237(4):412–426.Google Scholar
van Veelen, M., Garca, J., Sabelis, M. W., and Egas, M. (2012). Group Selection and Inclusive Fitness Are Not Equivalent; the Price Equation vs. Models and Statistics. Journal of Theoretical Biology, 299:64–80.CrossRefGoogle ScholarPubMed
Walsh, D. M., Ariew, A., and Matthen, M. (2017). Four Pillars of Statisticalism. Philosophy & Theory in Biology, 9(20171201).Google Scholar
Walsh, D. M., Lewins, T., and Ariew, A. (2002). The Trials of Life: Natural Selection and Random Drift. Philosophy of Science, 69(3):429–446.Google Scholar
Wigner, E. (1960). The Unreasonable Effectiveness of Mathematics in the Natural Sciences. Communications in Pure and Applied Mathematics, 13(1):1–14.Google Scholar
Williams, M. B. (1970). Deducing the Consequences of Evolution: A Mathematical Model. Journal of Theoretical Biology, 29:343–385.Google Scholar
Wright, S. (1934). The Method of Path Coefficients. The Annals of Mathematical Statistics, 5:161–215.Google Scholar
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