Research highlights

My current research is chiefly concerned with multidisciplinary applications of non-equilibrium statistical physics to problems of evolutionary dynamics and to complex systems in the life and behavioural sciences. Some important challenges in these areas concern the evolution of cooperative behaviour, the maintenance of biodiversity, the dynamics of cultural changes, and the self-organisation of mobile populations. In my research, mathematical modelling is usually at the individual-based level and leads to stochastic many-body problems. These are tackled by using a combination of methods drawn from statistical physics, nonlinear dynamics and evolutionary game theory.

We are happy to announce the L24EEDs workshop on “Mathematical modelling of microbial communities: cooperation, dynamics, and resistance” to be held in Leeds, 9-12 July 2024, see the poster. Registration and abstract submission are now open. All relevant info on the website: https://eedfp.com/l24eeds-workshop/

Publication List

Eco-evolutionary dynamics of cooperative antimicrobial resistance in a population of fluctuating volume and size

Submitted. E-print. Paper featured in the AMR@Leeds February 2024 Newsletter.

Coexistence of Competing Microbial Strains under Twofold Environmental Variability and Demographic Fluctuations

New J. Phys 25, 123010:1-18 (2023). Published paper. Supplementary Material. E-print  (main text + supplementary material). Figshare resources. (Mentioned in the AMR@Leeds February 2024 Newsletter.)

Coupled environmental and demographic fluctuations shape the evolution of cooperative antimicrobial resistance

J. R. Soc. Interface 20, 20230393:1-13 (2023). Published paper. Supplemental Material. E-print on biorXiv  (main text). E-print on arXiv (main text+ SM). Lay summary. Paper featured in the AMR@Leeds February 2024 Newsletter.

Polarization and Consensus in a Voter Model under Time-Fluctuating Influences

Physics 5, 517-536 (2023). Published paper. E-print.

Evolutionary Dynamics in a Varying Environment: Continuous versus Discrete Noise

Phys. Rev. Research 5, L022004:1-7 (2023). Published paper. Supplemental Material. Resources on Figshare. E-print. PRR's tweet.

Effect of mobility in the rock-paper-scissor dynamics with high mortality

Phys. Rev. E 105, 014215 (2022). E-print.

Effects of homophily and heterophily on preferred-degree networks: mean-field analysis  and overwhelming transition

J. Stat. Mech. 013402:1-28 (2022). Published paper. Supplementary Material. E-print.

How does homophily shape the topology of a dynamic network?

Phys. Rev. E 104, 044311:1-11 (2021). E-print.

Exclusion of the fittest predicts microbial community diversity in fluctuating environments

J. R. Soc. Interface 18, 20210613:1-13 (2021). Published paper. Supplementary Material. E-print.

Population Dynamics in a Changing Environment: Random versus Periodic Switching

Phys. Rev. Lett. 125, 048105:1-6 (2020). Supplementary Information. E-print.

Spatial patterns emerging from a stochastic process near criticality

Phys. Rev. X 10, 011032:1-21 (2020). Published paper. E-print.

Fixation properties of rock-paper-scissors games in fluctuating populations

J. Theor. Biol. 491, 110135:1-14 (2020). Supplementary Information. E-print.

Eco-Evolutionary Dynamics of a Population with Randomly Switching Carrying Capacity

J. R. Soc. Interface 15, 20180343:1-12 (2018). Published paper. Supplementary Information. E-print.

Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate

Phys. Rev. E 97, 022406:1-14 (2018). E-print.

Stochastic population dynamics in spatially extended predator-prey systems

J. Phys. A: Math. Theor. 51, 1-47 (2018). E-print. (Topical Review). 

Evolution of a Fluctuating Population in a Randomly Switching Environment

Phys. Rev. Lett. 119, 158301:1-6 (2017). Supplementary Information & Videos. E-print. Lay summary.

Large Fluctuations in Anti-Coordination Games on Scale-Free Graphs

J. Stat. Mech. 053405:1-23 (2017). E-print.

Heterogeneous Out-of-Equilibrium Nonlinear q-Voter Model with Zealotry

Phys. Rev. E 95, 012104:1-15 (2017). E-print.

The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games

Games 7, 1-12 (2016). Published paper. E-print.

Characterization of the Nonequilibrium Steady State of a Heteogeneous Nonlinear q-Voter Model with Zealotry

EPL (Europhysics Letters) 113, 48001:p1-p6 (2016). Supplementary Material. E-print.

Challenges in microbial ecology: building predictive understanding of community function and dynamics

The ISME Journal 10, 2557-2568 (2016). Published paper. Advanced on-line version.

Re-Parametrizing the Dilemmas: Comment on Universal scaling for the dilemma strength in evolutionary games

Physics of Life Reviews 14, 47-48 (2015).

Nonlinear q-voter model with inflexible zealots

Phys. Rev. E 92, 012806:1-10 (2015). E-print.

Influence of Luddism on Innovation Diffusion

Phys. Rev. E 92, 012803:1-11 (2015). E-print.

Characterization of spiraling patterns in spatial rock-paper-scissors games

Phys. Rev. E 90, 032704:1-14 (2014). E-print.

Cyclic dominance in evolutionary games: A review

J. R. Soc. Interface 11, 20140735:1-20 (2014). Published paper. E-print.

Facilitators reveal the optimal interplay between information exchange and reciprocity

Phys. Rev. E 89, 042802:1-8 (2014). E-print.

Cooperation dilemma in finite populations under fluctuating environments

Phys. Rev. Lett. 111, 238101 (2013). E-print.

Evolutionary games with facilitators: When does selection favor cooperation?

Chaos, Solitons & Fractals 56, 113 - 123 (2013). E-print.

When does cyclic dominance lead to spiral waves?

EPL (Europhysics Letters) 102, 28012:p1-p6 (2013). E-print. Movies and Supplementary Material.

Reply to “Comment on Stochastic dynamics of the prisoner’s dilemma with cooperation facilitators”

Phys. Rev. E 88, 046102:1-3 (2013). 

Commitment versus persuasion in the three-party constrained voter model

J. Stat. Phys. 151, 69-91 (2013). E-print.

Anomalous metastability and fixation properties of evolutionary games on scale-free graphs

In the Proceedings of the European Conference on Complex Systems 2012 (Chapter 88, pages 713-722). Published version.

Stochastic dynamics of the prisoner’s dilemma with cooperation facilitators

Phys. Rev. E 86, 011134:1-9 (2012). E-print.

Metastability and anomalous fixation in evolutionary games on scale-free networks

Phys. Rev. Lett. 109, 188701:1-5 (2012). E-print.

Fixation and Polarization in a Three-Species Opinion Dynamics Model

EPL (Europhysics Letters) 95, 50002:p1-p6 (2011). E-print.

Coexistence in the Two-Dimensional May-Leonard Model with Random Rates

Eur. Phys. J. B 82, 97-105 (2011). E-print.

Fixation of a Deleterious Allele under Mutation Pressure and Finite Selection Intensity

J. Theor. Biol. 275, 93-103 (2011). E-print.

Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates 

Phys. Rev. E 82, 051909:1-10 (2010). E-print.

Large Fluctuations and Fixation in Evolutionary Games

J. Stat. Mech. P09009:1-23 (2010). E-print.

Fixation in Evolutionary Games under Non-Vanishing Selection

EPL (Europhysics Letters) 91, 10002:p1-p6 (2010). E-print.

Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations

J. Theor. Biol. 264, 1-10 (2010). E-print.

Dynamics of Strategic Three-Choice Voting

EPL (Europhysics Letters) 85, 48003:p1-p6 (2009). E-print.

Self-Organization of Mobile Populations in Cyclic Competition

J. Theor. Biol. 254, 368-383 (2008). E-print.

Generic principles of active transport in cellular systems

Banach Center Publications 80, 101-120 (2008). E-print.

Stochastic effects on biodiversity in cyclic coevolutionary dynamics

Banach Center Publications 80, 259-264 (2008). E-print.

Spatial stochastic predator-prey models 

Banach Center Publications 80, 253-257 (2008). E-print.

Noise and correlations in a spatial population model with cyclic competition

Phys. Rev. Lett. 99, 238105:1-4 (2007). E-print.

On the role of zealotry in the voter model

J. Stat. Mech. P08029:1-17 (2007). E-print.

Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games

Nature 448, 1046-1049 (2007). E-print. 

(In the top 5% of all research outputs scored by Altmetric, and in the 94th percentile of tracked articles of a similar age) 

Phase transitions and spatio-temporal fluctuations in stochastic lattice Lotka-Volterra models

J. Stat. Phys. 128, 447-483 (2007). E-print.

Influence of local carrying capacity restrictions on stochastic predator-prey models

J. Phys.: Condens. Matter 19, 065139:1-14 (2007). E-print.

Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model

Phys. Rev. E 74 051907:1-11 (2006). E-print.

Bottleneck-induced transitions in a minimal model for intracellular transport

Phys. Rev. E 74, 031906:1-13 (2006). E-print.

Fluctuations and correlations in lattice models for predator-prey interaction

Phys. Rev. E 73, 040903(R):1-4 (2006). E-print.

Exact dynamics of a reaction-diffusion model with spatially alternating rates

Phys. Rev. E 71, 056129:1-12 (2005). E-print.

Voting and catalytic processes with inhomogeneities

Phys. Rev. E 71, 046102:1-17 (2005). E-print.

Competition between homogeneous and local processes in a diffusive many-body system

J. Stat. Mech. P04003:1-22 (2005). E-print.

Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain

J. Phys. A: Math. Gen. 37, L407-L413 (2004). E-print.

Majority versus minority dynamics: Phase transition in an interacting two-state spin system

Phys. Rev. E 68, 046106:1-11 (2003). E-print.

Does a Single Zealot Affect an Infinite Group of Voters?

Phys. Rev. Lett. 91, 28701:1-4 (2003). E-print.

Kinetic anomalies in addition-aggregation processes

J. Phys. A: Math. and Gen. 36, 4533-4542 (2003). E-print.

Exact multipoint and multitime correlation functions of a one-dimensional model of adsorption and evaporation of dimers

Phys. Rev. E 65, 046127:1-6 (2002). E-print.

Two-species d-dimensional diffusive model and its mapping onto a growth model

Phys. Rev. E 65, 016117:1-11 (2001). E-print.

Generalized empty-interval method applied to a class of one-dimensional stochastic models

Phys.Rev.E 64, 066123:1-18 (2001). E-print.

Solution of a one-dimensional stochastic model with branching and coagulation reactions

Phys. Rev. E 64, 045101(R):1-4 (2001). E-print.

Solution of a class of one-dimensional reaction-diffusion models in disordered media

Phys. Rev. B 64, 064203:1-10 (2001). E-print.

Exact solution of a class of one-dimensional nonequilibrium stochastic models

Phys. Rev. E 63, 056112:1-12 (2001). E-print.

Soluble two-species diffusion-limited models in arbitrary dimensions

Phys. Rev. E 63, 036121:1-25 (2001). E-print.

On the Solution of Classical Stochastic One-Dimensional Many-Body Systems: Reply

Phys. Rev. Lett. 85, 893 (2000). E-print.

Solution of Classical Stochastic One-Dimensional Many-Body Systems

Phys. Rev. Lett. 83, 5214-5217 (1999). E-print.

Diffusion-limited reactions of hard-core particles in one dimension

Phys. Rev. E 59, 1996-2009 (1999). E-print.


Theses (refereed)

Doctoral thesis N. 2552 of the Swiss Federal Institute of Technology, Lausanne (EPFL). (Lausanne, Switzerland, 2002). DOI:10.5075/epfl-thesis-2552.

Master’s thesis of the Swiss Federal Institute of Technology, Lausanne (EPFL). (Lausanne, Switzerland, 1998).

We are happy to advertise the L24EEDs workshop to be held in Leeds, 9-12 July 2024 on the “Mathematical modelling of microbial communities: cooperation, dynamics, and resistance”. All relevant info can be found on the website: https://eedfp.com/l24eeds-workshop/

Some research highlights

Eco-evolutionary dynamics and environmental variability

Environmental variability greatly influences how the size and composition of a population evolve. In microbial communities, variations of the composition and size of the population, i.e. their eco-evolutionary dynamics, are key to understand the mechanisms of antimicrobial resistance, and may lead to population bottlenecks, where new colonies consisting of few individuals are prone to fluctuations. How the composition and size of these communities evolve is often interdependent, and demographic fluctuations is generally coupled to the environmental variability. 

We have studied the evolution of populations of fluctuating size whose growth is limited by a binary carrying capacity that endlessly randomly switches between two very different values under various scenarios. This allowed us to model the evolution in a volatile environment where the available resources (nutrients) vary back and forth between abundance and scarcity. The content of the accompanying video is explained here along with a simple summary of the work that it illustrates.  We have also considered the case of periodic switching, different forms of environmental noise.

In an ongoing "EPSRC-NSF project", we generalize these ideas and investigate the eco-evolutionary dynamics of antimicrobial resistance as a cooperative behaviour and under the time variation of toxins and nutrients. 

ssa__L128_N64__b1.0_s1.0_z1.8_1.2_0.6_0.0_m0.02__d1.0_e1.0_.mp4

Bacterial rock-papers-scissors games

In Nature, organisms move and interact within their neighbourhood. In doing so, populations often self-organise by forming spatial patterns whose origin is an intense subject of research. Recently, there has been an increasing interest in how fluctuations and nonlinearity influence biological patterns. Remarkably, both questions can be tackled with the paradigmatic rock-paper-scissors (RPS) game: in some microbial communities, it has indeed been found that antibiotic producers inhibit sensitive species more than resistant ones which, along with costs for production and resistance, can lead to intransitive relationships of cyclic dominance among species.

In a series of papers, we have shown that there is a subtle interplay between individuals’ mobility and local interactions in spatial RPS systems. This leads to the loss of biodiversity above a certain mobility threshold, and, in two dimensions, the formation of spiralling patterns below the critical mobility rate. By adopting a metapopulation formulation, we have shown that the RPS dynamics can be faithfully described in terms of the system’s complex Ginzburg-Landau equation derived from a multi-scale expansion. This allowed us to derive the system’s phase diagram and to comprehensively characterise the spatio-temporal properties of the spiralling patterns, and discuss their stability. The content of the accompanying video is explained here (Mov. 1, top), alongside other movies illustrating our research. 

Sociophysics and opinion dynamics

Sociophysics aims at describing social phenomena, like the spead of opinions or the dynamics of cultural diversity, by means of models similar to those used in statistical physics, like the "voter model". To gain insight into social dynamics, “zealotry” was introduced in various forms to endow voters with different levels and forms of self-confidence. 

Moreover, group-size influence is captured in the nonlinear q-voter model and its many variants, at equilibrium and out-of-equilibrium. It has also been noted that social interactions often occur only among agents whose opinions are not too distant, a phenomenon that can lead to the polarization. Recently, we have studied how homophily or heterophily, the tendency for agents to establish ties with those having similar or dissimilar attributes to theirs, shapes the topology of the dynamic social network and can even lead to an "overwhelming transition". We have also investigated in an idealized three-party society how the formation of polarization and consensus is affected by time-varying influences, stemming, e.g., from news or social media.