Structure of Evolution

Smerlak group at the Max Planck Institute for Mathematics in the Sciences, Leipzig

We are an interdisciplinary research group working on basic questions in evolutionary theory:

What determines the mode and tempo of evolution?Can evolution be predicted?What kind of growth processes enable evolution?What statistical patterns emerge in evolution?
We focus on those scales at which these questions can be posed meaningfully: the smallest scale (micro-evolution of biomolecules, viruses, etc., where fitness landscapes can be measured and analyzed) and the largest scale (macro-ecology, where universal patterns emerge).

We address these questions using conceptual tools from quantum/statistical physics and non-linear dynamics, and rely on data gathered from ecological meta-analyses, computer simulations, and, moving forward, online experiments.

The group is generously funded by a Sofja Kovalevskaja Award from the Alexander von Humboldt Foundation and a Young Investigator Award from the Human Frontier Science Program.


  • Dec 2021: Alvaro Diaz-Ruelas joins the group as postdoc

  • Dec 2020: Welcome to Onofrio Mazzari and Vaitea Opuu, two new postdocs

  • Jan 2020: Ian Hatton and Mohammad Salahshour join as postdocs

  • Dec 2019: New preprint on the analysis of fitness landscapes

  • Sept 2019: Anton Zadorin joins the group from Collège de France as postdoc

  • May 2019: Matteo wins an HFSP Young Investigator Grant to work with P. Nghe, E. Hayden and A. Ramesh on RNA self-replicators


Max Planck Institute for Mathematics in the Sciences
Inselstraße 22, D-04103 Leipzig, Germany
Office A3 12
+49 (0) 341 - 9959 - 546

Job openings

Postdoc: From self-reproduction to evolution in the RNA world

How probable is the emergence of self-reproduction in the prebiotic world? Recent work has demonstrated that RNA catalysts (ribozymes) can build copies of themselves by the recombination of smaller RNA fragments. A well-studied system has been engineered from a specific ribozyme (a group I intron). Traditional low-throughput engineering approaches have prevented a thorough investigation of the probability of this type of reproduction contributing to life’s origins. In collaboration with the groups of P. Nghe (ESPCI, France), E. Hayden (Boise State University, USA) and A. Ramesh (National Center for Biological Systems, India), this project aims to develop high-throughput engineering approaches to fill this knowledge gap.

We are seeking an RNA bioinformatician to join the team. The project is funded by the Human Frontier Science Project and involves labs with complementary expertise, located in four countries (USA, Germany, India and France). Funding is available for up to 3 years pending satisfactory progress. Sufficient travel funds are also available to facilitate international collaboration and training. Starting date as soon as possible given the current international situation.

Selection of publications from the teams:
Arsène, S., Ameta, S., Lehman, N., Griffiths, A. D., & Nghe, P. (2018). Coupled catabolism and anabolism in autocatalytic RNA sets. Nucleic acids research, 46(18), 9660-9666.Matsumura, S., Kun, Á., Ryckelynck, M., Coldren, F., Szilágyi, A., Jossinet, F., Nghe P., Szathmary E, Griffiths, A. D. (2016). Transient compartmentalization of RNA replicators prevents extinction due to parasites. Science, 354(6317), 1293-1296.Bendixsen, D.P., Collet, J., Østman, B., and Hayden, E.J. (2019). Genotype network intersections promote evolutionary innovation. PLoS Biol. 17, e3000300.Smerlak M. 2020. Localization of neutral evolution: selection for mutational robustness and the maximal entropy random walk, bioRxiv: 10.1101/2020.01.28.922831

Research assistant: online experiments on the evolution of cooperation

We seek a research assistant to help with behavioral experiments exploring the evolution of cooperation in multi-player economic games.

Joining a young and dynamic group of evolutionary theorists, the research assistant will participate in setting up the online platform, recruiting participants, monitoring results and analyzing data.

The successful candidate will either have:
a Bachelor’s degree in social science and a strong command of statistics and programming (particularly python)or a Bachelor’s degree in computer science and a strong interest in statistics, behavioural science and/or evolutionary theory
The contract is for one year (with a possible extension based on performance).

Contact Matteo to apply

Research directions

Analysis of fitness landscapes

The course of evolution is determined by the relationship between heritable types and their adaptive values, the fitness landscape. Thanks to the explosive development of sequencing technologies, fitness landscapes have now been measured in a diversity of systems from molecules to micro-organisms. How can we turn these data into evolutionary predictions?

  • Smerlak M. 2019. Effective potential reveals evolutionary trajectories in complex fitness landscapes, submitted to PNAS.

Statistical dynamics of selection

Natural selection acts on heritable fitness differences, and therefore amounts to a flow in the space of fitness distributions. This project investigates the nature of this flow from the perspective of probability limit theorems.

  • Smerlak M. 2017. Natural Selection as Coarsening. J. Stat. Phys. 83: 1–9.

  • Smerlak M. & Youssef A. 2017. Universal statistics of selected values. EPL. 117: 50003.

  • Smerlak M. & Youssef A. 2017. Limiting fitness distributions in evolutionary dynamics. J. Theor. Biol. 416: 68–80.

Growth laws across levels of biological organization

Deep down, evolution is powered by growth—the generation of new biomass through reproduction and ontogeny. One approach to quantifying growth across systems is through macro-ecological scaling laws. Can we explain the origin of these scaling laws, and what consequences do they have for evolution?

  • Hatton I.A. et al. 2015. The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes. Science. 349: aac6284–aac6284.

Inverse RNA folding

The function of cellular RNAs is largely determined by their secondary and tertiary structure, i.e. how their fold in space. We use evolutionary optimization to explore the inverse folding problem: given a structure of interest, how can we find a RNA sequence which folds into this structure?

Searching for RNA self-replicators (HFSP collaboration with P. Nghe, E. Hayden & A. Ramesh)

The RNA world hypothesis posits that an early stage of life involved RNA acting as both information carrier and catalyst. Extant self-splicing introns (such as the Azoarcus ribozyme, which can catalyze its own self-assembly from ~50nt-long fragments) may provide a window into this ancient world. The project aims to combine computational and experimental techniques to design new RNA self-replicators from group I introns and test whether they can evolve in vitro.


See our group page at MPI MiS for a complete list of our publications


Group leader

Matteo Smerlak is a theoretical physicist. He did his PhD work in quantum gravity under the co-supervision of Carlo Rovelli and Vincent Rivasseau. In 2013 he attended the Santa Fe Institute's complex systems summer school, at which point his research trajectory turned stochastic.

Supported by a Sofja Kovalevskaja Award and a HFSP Young Investigator Grant, he now leads the Structure of Evolution group at MPI MiS.

Matteo's current research interests include the structure and dynamics of fitness distributions, the analysis of fitness landscapes, the issues of directionality and predictability in evolution, and the link between growth laws and evolutionary stability.

Feel free to consult Matteo's CV, list of publications or popular science page.


Anton Zadorin graduated from the Moscow Institute of Physics and Technology in Applied Mathematics and Physics. He then obtained his PhD in Molecular Biology from the University of Strasbourg. Since then he combined wet lab experimental research with theoretical work in the fields of nonlinear biochemistry, pattern formation, and molecular evolution. His current theoretical interests include theory of evolution in large: the interplay between evolution and ontogenesis, and between evolution and ecology. In both cases he tries to find minimal toy models of such extended evolving systems with the emphasis on their geometric aspects. Anton is interested in elucidating generic properties of these models using tools from differential geometry and bifurcation theory.

Ian Hatton has a background in biology. He previously studied and worked at McGill University, Canada, the National Institutue for Mathematical Sciences, South Korea, Princeton University, USA, and the Institut de Ciència i Tecnologia Ambientals in Barcelona, Spain. He is currently a Humboldt Research Fellow.

As a physics PhD student, Onofrio Mazzarisi studied metastability in the Potts spin model. As postdoc in our group, he now studies ecological dynamics, both theoretically and through agent-based simulations. Onofrio is also interested multiplicative stochastic processes in relation to the evolution of cooperation.

Vaitea Opuu is a bioinformatician. In collaboration with Nono Saha, Vincent Messow and Frederik Koch, Vaitea studies RNA design, focusing on applications in to the problem of the origin of life.

Alvaro Diaz-Ruelas has a background in nonlinear dynamics and an interest in statistical and bio-physics.


Nono Saha Cyrille Merleau was a student at AIMS-Ghana where he completed a one year Master degree in Mathematics. He has also a Master in Computer Science from the University of Ngaoundere in Cameroon. He enjoys programming in Java, python and bash. Before joining the group as a PhD student he spent the last 3 years working as a freelancer in software engineering. Nono's current research interests include discrete optimization, evolutionary algorithms and their application to real life problems, RNA folding and inverse folding, fitness landscape analysis.

Vincent Messow is a bioinformatics student at the University of Leipzig. He joined the group to work on his Master's thesis as part of an researching self-reproduction capabilities of RNA molecules. Specifically, he is designing synthetic RNA sequences that fold into (pseudoknotted) secondary structures similar to those of naturally occuring ribozymes known to be capable of self-assembly from smaller fragments.
Although from a biological background, he has been interested in xombinatorics, graph theory, and other abstract nonsense, as well as their application to biological problems.

Frederik Koch is a physics student at the University of Leipzig. For his bachelor's thesis, Frederik works with Vaitea Opuu on RNA design, focusing on the interplay between thermodynamical and evolutionary constraints in shaping RNA diversity.


Mohammad Salahshour. From multicellular organisms to complex social structures, a high level of organization is produced in the course of evolution. For this to occur, biological populations had to address different challenges, e.g. find efficient ways to suppress selfishness, solve collective action problems, efficiently divide labor and solve coordination tasks. They also often need to collectively acquire and process a vast amount of information. Using ideas and methods from evolutionary game theory, statistical physics, and information theory, I try to understand how biological populations successfully perform these tasks, and how order and organization are produced in the course of evolution.

Aleksander Klimek is a mathematician. He has completed his PhD under the supervision of Alison Etheridge. Aleksander's main scientific interests lie in the intersection of Probability, Stochastic Analysis and Analysis of Partial Differential Equations. Most of his work is motivated by Mathematical Population Genetics. He is especially interested in spatial models in random environments, particle representations of population models and long time behaviour of scholastically perturbed systems.

Maseim Kenmoe worked as Teaching Assistant at AIMS-Ghana for four years after completing his Ph.D in Theoretical Condensed Matter Physics at the University of Dschang under the co-supervision of Prof. Lukong Cornelius Fai and Prof. Mikhail N. Kiselev. Maseim is interested in deciphering the complexity of living/biological systems from the viewpoint of physics. Maseim’s current researches focus on the interplay between mutation and selection using tools from quantum mechanics and statistical physics.

Camila Bräutigam is a physics student at the University of Leipzig. She joined the group for her Master's thesis. She has been interested in learning about parallels but also differences between physical and biological systems and approaches. She has been looking into stochastic models of the dynamics of gene frequencies in evolutionary systems. More recently she has worked on an application of an evolutionary stochastic process to a specific setting called Muller's ratchet in biology.

Matteo's popular science


A short book on the physics of black holes for the general public, in French. I spoke about it on the Canadian radio, here.

Book translation

I translated from Italian to French this book on the history and philosophy of science by Carlo Rovelli. Worth reading!

Book chapters

Thoughts on the philosophy of physics, and a weird poem.

Magazine articles