Turing Patterns and Biological Explanation

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Turing patterns are a class of minimal mathematical models that have been used to discover and conceptualize certain abstract features of early biological development. This paper examines a range of these minimal models in order to articulate and elaborate a philosophical analysis of their epistemic uses. It is argued that minimal mathematical models aid in structuring the epistemic practices of biology by providing precise descriptions of the quantitative relations between various features of the complex systems, generating novel predictions that can be compared with experimental data, promoting theory exploration, and acting as constitutive parts of empirically adequate explanations of naturally occurring phenomena, such as biological pattern formation. Focusing on the roles that minimal model explanations play in science motivates the adoption of a broader diachronic view of scientific explanation.

Amundson, Ron. 2005. The Changing Role of the Embryo in Evolutionary Thought: Roots of Evo-Devo. Cambridge MA: Cambridge University Press.

Baker, Alan. 2005. Are there genuine mathematical explanations of physical phenomena? Mind 114 (454): 223–38.

Baker, Alan. 2009. Mathematical explanation in science. British Journal for the Philosophy of Science 60 (3): 611–33.

Batterman, Robert. 2002. Asymptotics and the role of minimal models. British Journal for the Philosophy of Science 53 (1): 21–38.

Baron, Sam; and Colyvan, Mark. 2016. Time enough for explanation. Journal of Philosophy 113(2): 61–88.

Bechtel, William P.; and Abrahamsen, Adele. 2010. Dynamic mechanistic explanation: computational modeling of circadian rhythms as an exemplar for cognitive science. Studies in History and Philosophy of Science Part A 41(3): 321–33.

Bechtel, Wiliam P.; and Richardson, Robert C. 2010. Discovering Complexity Decomposition and Localization as Strategies in Scientific Research. 2nd edition. Cambridge MA: MIT Press.

Bechtel, William P. 2015. Can mechanistic explanation be reconciled with scale-free constitution and dynamics? Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 53: 84–93.

Bourgine, Paul; and Lesne, Annick. 2006. Morphogenesis: Origins of Patterns and Shapes. Berlin: Springer Verlag.

Brigandt, Ingo. 2010. Beyond reduction and pluralism: Toward an epistemology of explanatory integration in biology. Erkenntnis 73 (3):295-311.

Brigandt, Ingo. 2013. Systems biology and the integration of mechanistic explanation and mathematical explanation. Studies in History and Philosophy of Biological and Biomedical Sciences 44(4): 477–92.

Cooper, S. Barry; and Maini, Philip K. 2012. The mathematics of nature at the Alan Turing centenary. Interface Focus 2: 393–6.

Craver, Carl F.; and Darden, Lindley. 2013. In Search of Mechanisms: Discoveries across the life sciences. Chicago: University of Chicago Press.

Dilão, Rui. 2015. Mathematical models of morphogenesis. ITM Web of Conferences 4.

Dretske, Fred. 1988. Explaining Behavior: Reasons in a World of Causes. Cambridge MA: MIT Press.

Economou, Andrew et al. 2012. Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate Nature Genetics 44: 348–51.

Fox Keller, Evelyn. 2003. Making Sense of Life: Explaining Biological Development with Models, Metaphors, and Machines. Harvard University Press.

Horvath, Judit; Szalai, Istvan; and De Kepper, Patrick. 2009. An experimental design method leading to chemical Turing patterns. Science 324: 772–5.

Kondo, Shigeru; and Miura, Takashi. 2010. Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329(5999): 1616–20.

Lange, Marc. 2013. What makes a scientific explanation distinctively mathematical? British Journal for the Philosophy of Science 64 (3): 485–511.

Levy, Arnon. 2015. Modeling without models. Philosophical Studies 172 (3): 781–98.

Love, Alan. 2008. Explaining the ontogeny of form: philosophical issues. In A Companion to the Philosophy of Biology, ed. by Sarkar Sahorta and Anya Plutinski. Oxford: Wiley Press.

Love, Alan C.; and Lugar, Gary L. 2013. Dimensions of integration in interdisciplinary explanations of the origin of evolutionary novelty. Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 44(4): 537–50.

Love, Alan C.; and Nathan, Marco J. 2015. The idealization of causation in mechanistic explanation. Philosophy of Science 82(5): 761–74.

Madzvamuse, Anotida; Gaffney, Eamonn A.; and Maini, Philip K. 2010. Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains. Journal of mathematical biology 61(1): 133–64 PMID: 19727733.

Maini, Philip K.; Baker, Ruth E.; and Chuong, Cheng-Ming. 2006. The Turing model comes of molecular age. Science Developmental Biology 314: 1397–8.

Maini, Philip K. et al. 2012. Turing’s model for biological pattern formation and the robustness problem. Interface Focus 2: 483-496.

Maini, Philip K. 2012. Turing’s mathematical theory of morphogenesis. Asia Pacific Mathematics Newsletter 2(1): 7–8.

Meinhardt, Hans. 1982. Models of Biological Pattern Formation. London: Academic London.

Meinhardt, Hans et al. 2003. The Algorithmic Beauty of Sea Shells, 3rd edition. New York: Springer.

Murray, James D. 2003. Mathematical Biology II: Spatial Models and Biomedical Applications. Springer USA.

Murray, James D. 2012. Vignettes from the field of mathematical biology: the application of mathematics to biology and medicine. Interface Focus 2: 397–406.

Nathan, Marco J. 2012. The varieties of molecular explanation. Philosophy of Science 79(2): 233–54.

Othmer, Hans G.; Maini, Philip K.; and Murray, James D. 1993. Experimental and Theoretical Advances in Biological Pattern Formation. Springer USA.

Pincock, Christopher. 2007. Mathematical idealization. Philosophy of Science 74 (5): 957–967.

Pincock, Christopher. 2011. Mathematics and Scientific Representation. Cambridge MA: Oxford University Press.

Pincock, Christopher. 2012. Mathematical models of biological patterns: lessons from Hamilton’s selfish herd. Biology and Philosophy 27(4): 481–96.

Pincock, Christopher. 2015a. The unsolvability of the quintic: a case study in abstract mathematical explanation. Philosophers’ Imprint 15(3).

Pincock, Christopher. 2015b. Abstract explanations in science. British Journal for the Philosophy of Science 66 (4): 857–82.

Raz, Tim; and Sauer, Tilman. 2015. Outline of a dynamical inferential conception of the application of mathematics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 49: 57–72.

Tompkins, Nathan et al. 2014. Testing Turing’s theory of morphogenesis in chemical cells. PNAS 111(12): 4397–402.

Turing, Alan M. 1952. The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences DOI: 10.1098/rstb.1952.0012.

Weisberg, Michael. 2007. Three kinds of idealization. Journal of Philosophy 104 (12): 639–59.

Winther, Rasmus G. 2012. Mathematical modeling in biology: philosophy and pragmatics. Frontiers in Plant Evolution and Development 2012: 1–3.

Woody, Andrea. 2015. Re-orienting discussions of scientific explanation: a functional perspective. Studies in History and Philosophy of Science Part A 52: 79–87.

Yablo, Stephen. 2012. Explanation, extrapolation, and existence. Mind 121 (484): 1007–29.


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