Abstract
In 1966 Richard Levins argued that applications of mathematics to population biology faced various constraints which forced mathematical modelers to trade-off at least one of realism, precision, or generality in their approach. Much traditional mathematical modeling in biology has prioritized generality and precision in the place of realism through strategies of idealization and simplification. This has at times created tensions with experimental biologists. The past 20 years however has seen an explosion in mathematical modeling of biological systems with the rise of modern computational systems biology and many new collaborations between modelers and experimenters. In this paper I argue that many of these collaborations revolve around detail-driven modeling practices which in Levins’ terms trade-off generality for realism and precision. These practices apply mathematics by working from detailed accounts of biological systems, rather than from initially idealized or simplified representations. This is possible by virtue of modern computation. The form these practices take today suggest however Levins’ constraints on mathematical application no longer apply, transforming our understanding of what is possible with mathematics in biology. Further the engagement with realism and the ability to push realistic models in new directions aligns well with the epistemological and methodological views of experimenters, which helps explain their increased enthusiasm for biological modeling.
Highlights
In a paper titled ‘‘The Strategy of Model Building in Population Biology’’ Levins (1966) famously characterized mathematical applications to mathematical ecology and population biology as bound by several unavoidable constraints given biological complexity
Modern systems biology is remarkably eclectic trying to marry under the common label of “systems biologist” theoretical biologists, committed to more traditional theoretical positions on the purpose and need for a well-developed biological theory, with technology-driven computer scientists and engineers who see an opportunity to enter biology and make substantial new discoveries using new data sources
Once fit the model should be in theory capable of replicating the operations of its target biological networks, in response to perturbations. With such a model in hand calculations can be made on how to best harness or control that network towards given ends. Whereas mathematicians such as Rashevsky others might have been comfortable drawing on theoretical perspectives and mathematical hypotheses to limit the level of biological detail required upfront, the modelers we studied operate with large degrees of biological information and base their confidence as much as possible on the completeness of that information
Summary
In a paper titled ‘‘The Strategy of Model Building in Population Biology’’ Levins (1966) famously characterized mathematical applications to mathematical ecology and population biology as bound by several unavoidable constraints given biological complexity. Generality, precision and realism can be obtainable conjointly with respect to particular generalizations, and preferably so These detail-driven practices align better with the methodological and epistemological preferences of experimenters and what experimenters generally consider useful and viable goals for modeling. This helps explain to some extent their relative engagement of experimenters with these practices, compared to those of systems biologists working with a more traditional approach. This ethnographic study of two labs, provided us a first-hand insight into the nature of these practices and how participants in the modeling process rationalize their activity and their involvement
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