Journal of Statistical Physics

, Volume 172, Issue 1, pp 74–104 | Cite as

Innovation Rather than Improvement: A Solvable High-Dimensional Model Highlights the Limitations of Scalar Fitness

  • Mikhail Tikhonov
  • Remi Monasson


Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining “fitness”. It is not always clear to what extent the intuition derived from low-dimensional models applies to the complex, high-dimensional reality. For instance, most naturally occurring microbial communities are strikingly diverse, harboring a large number of coexisting species, each of which contributes to shaping the environment of others. Understanding the eco-evolutionary interplay in these systems is an important challenge, and an exciting new domain for statistical physics. Recent work identified a promising new platform for investigating highly diverse ecosystems, based on the classic resource competition model of MacArthur. Here, we describe how the same analytical framework can be used to study evolutionary questions. Our analysis illustrates how, at high dimension, the intuition promoted by a one-dimensional (scalar) notion of fitness can become misleading. Specifically, while the low-dimensional picture emphasizes organism cost or efficiency, we exhibit a regime where cost becomes irrelevant for survival, and link this observation to generic properties of high-dimensional geometry.


Ecology Evolution High diversity Replica theory 



We thank Michael P. Brenner, Andreas Engel, Daniel S. Fisher, Carl P. Goodrich, Alpha Lee, David Zwicker, Harvard Center of Mathematical Sciences and Applications, IESC Cargese and the Simons Foundation. MT was supported in part by National Science Foundation Grant DMS-1411694.

Supplementary material

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Supplementary material 1 (7z 410 KB)


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Authors and Affiliations

  1. 1.School of Engineering and Applied Sciences, Kavli Institute for Bionano Science and TechnologyHarvard UniversityCambridgeUSA
  2. 2.Department of Applied PhysicsStanford UniversityStanfordUSA
  3. 3.Laboratoire de Physique Théorique de l’École Normale Supérieure – UMR 8549, CNRS and PSL ResearchSorbonne Université UPMCParisFrance

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