Matematicas De La Evolucion

Physics of Life Reviews 8 (2011) 1–18
www.elsevier.com/locate/plrev

Review

Toward a mathematical theory of living systems focusing on
developmental biology and evolution: A review and perspectives ✩
N. Bellomo a,∗ , B. Carbonaro b
a Department of Mathematics, Politecnico di Torino, Italy
b Department of Mathematics, University of Napoli, Italy

Received 15 November 2010; received inrevised form 25 December 2010; accepted 25 December 2010
Available online 31 December 2010
Communicated by J. Fontanari

Abstract
This review paper is devoted to present a personal perspective, based on a critical analysis of the existing literature, about
the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter focusing on thechallenging goal of developing a mathematical theory for living systems. The authors propose a personal path, starting from the
identification of a number of common features of living systems that can be viewed as sources of complexity, firstly in general,
and subsequently focusing specifically on evolution problems. Further, three key questions are posed addressing to a mathematical
theory. Finally, thetools of the kinetic theory of active particles are critically analyzed to understand how far this approach still is
from the achievement of the afore said ambitious objective.
© 2010 Elsevier B.V. All rights reserved.
Keywords: Living matters; Evolution; Mutations; Nonlinear interactions; Stochastic games; Genes and genome

Contents
1. On the difficult interaction between mathematics and lifesciences . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2. From five common complexity features of living systems to four key questions . . . . . . . . . . . . . . . . . . . .
3. From three common evolutionary features of living systems to a re-interpretation of the above key questions
4. Scaling, size, and functional subsystems to reduce complexity . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . .
5. Mathematical tools of the kinetic theory of active particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6. Conceptual lines toward a mathematical theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Appendix A. Mathematical equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Partially supported by the European Union FP7 Health Research Grant number FP7-HEALTH-F4-2008-202047, Termination of developmental
processes and their reactivation in adult life.
* Corresponding author.
E-mail addresses: nicola.bellomo@polito.it (N. Bellomo), bruno.carbonaro@unina2.it (B. Carbonaro).
1571-0645/$ – see front matter © 2010 Elsevier B.V. All rightsreserved.
doi:10.1016/j.plrev.2010.12.001

2

N. Bellomo, B. Carbonaro / Physics of Life Reviews 8 (2011) 1–18

1. On the difficult interaction between mathematics and life sciences
This review paper proposes a personal viewpoint, based on a critical analysis of the existing literature, about the
conceptual difficulties that mathematics meets when attempting to describe the complexity ofliving matter. Subsequently, we offer some speculations on the role of mathematics in the ambitious project of building a comprehensive
theory of developmental biology and evolution. The conceptual difficulties arising from dealing with living system
are well documented in the books by Mayr [61,62] (see also [63,64]); biologists [47], and applied physicists or mathematicians [50,60,69] present...