# School of Mathematics

## Dr Mauro Mobilia

Associate Professor

Applied Mathematics

### Contact details

Room: Satellite 10.13

Tel: +44 (0)113 3431591

Email: M.Mobilia @ leeds.ac.uk

### Keywords

Statistical Mechanics

Evolutionary & Nonlinear Dynamics

Complex Systems

Individual-based Models

Mathematical Biology

Evolutionary Game Theory

Opinion Dynamics

Interacting Particle Systems & Stochastic Processes

## Research interests

My current research is chiefly concerned with multidisciplinary applications of nonequilibrium statistical mechanics to problems of evolutionary dynamics and to complex systems in the life and behavioural sciences. Some of the major challenges in these areas concern the emergence of cooperative behaviour, the maintenance of biodiversity, the dynamics of cultural changes, and the self-organisation of mobile populations. In my research, the mathematical formulation of the corresponding models is at the individual-based level and therefore naturally accounts for intrinsic fluctuations and spatial structure. This leads to deal with stochastic many-body problems that are studied using a combination of methods drawn from statistical physics, nonlinear dynamics and evolutionary game theory.

As examples of recent research outcomes, one can mention a series of works on "rock-paper-scissors" games to study the self-organisation and biodiversity in cyclically competing populations; another series of papers on the effects of heterogeneities ("zealots") in models of opinion dynamics; and some works on metastability and large fluctuations in social dilemmas and in models of population dynamics (including population genetics).

More details and links to all my research papers, as well as some movies, can be found on my personal web-page (see below).

### Useful links

Personal web-page

Research web-page (with link to my list of publications)

List of publications and preprints on the arXiv

Teaching web-page

## Current postgraduate students

Giacomo Baldo (2016)

Maria Nowicka (2012)

Fabio Peruzzo (2015)

Robert West (2016)

## Publications

**Sabsovich D, Mobilia M, Assaf M** Large fluctuations in anti-coordination games on scale-free graphs *Journal of Statistical Mechanics: Theory and Experiment*, **2017**

DOI:10.1088/1742-5468/aa6a21

View abstract

**Mellor A, Mobilia M, Zia RKP** Heterogeneous out-of-equilibrium nonlinear q -voter model with zealotry *Physical Review E*, **95**, 2017

DOI:10.1103/PhysRevE.95.012104

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**Widder S, Allen RJ, Pfeiffer T, Curtis TP, Wiuf C, Sloan WT, Cordero OX, Brown SP, Momeni B, Shou W, Kettle H, Flint HJ, Haas AF, Laroche B, Kreft J-U, Rainey PB, Freilich S, Schuster S, Milferstedt K, van der Meer JR, Groβkopf T, Huisman J, Free A, Picioreanu C, Quince C, Klapper I, Labarthe S, Smets BF, Wang H, Isaac Newton Institute Fellows, Soyer OS** Challenges in microbial ecology: building predictive understanding of community function and dynamics. *ISME J*, **10**, 2557-2568, 2016

DOI:10.1038/ismej.2016.45

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**Mobilia M, Rucklidge AM, Szczesny B** The influence of mobility rate on spiralwaves in spatial rock-paper-scissors games *Games*, **7**, 2016

DOI:10.3390/g7030024

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**Mellor A, Mobilia M, Zia RKP** Characterization of the nonequilibrium steady state of a heterogeneous nonlinear q-voter model with zealotry *EPL*, **113**, 2016

DOI:10.1209/0295-5075/113/48001

View abstract

**Mobilia M** Re-parametrizing the dilemmas: Comment on "Universal scaling for the dilemma strength in evolutionary games", by Z. Wang et al *Physics of life reviews*, **14**, 47-48, 2015

DOI:10.1016/j.plrev.2015.06.008

**Mellor A, Mobilia M, Redner S, Rucklidge AM, Ward JA** Influence of Luddism on innovation diffusion *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **92**, 2015

DOI:10.1103/PhysRevE.92.012806

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**Mobilia M** Nonlinear q-voter model with inflexible zealots *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, **92**, 2015

DOI:10.1103/PhysRevE.92.012803

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**Califano F; Mobilia M; Longobardi A ** *Heavy rainfall temporal characterization in the peri-urban Solofrana river basin, Southern Italy*Procedia Engineering, 1129-1138 2015

DOI:10.1016/j.proeng.2015.08.957

View abstract

**Szolnoki A, Mobilia M, Jiang LL, Szczesny B, Rucklidge AM, Perc M** Cyclic dominance in evolutionary games: A review *Journal of the Royal Society Interface*, **11**, 2014

DOI:10.1098/rsif.2014.0735

View abstract

**Szczesny B, Mobilia M, Rucklidge AM** Characterization of spiraling patterns in spatial rock-paper-scissors games *Physical Review E: Statistical, Nonlinear, and Soft Matter Physics*, **90**, 2014

DOI:10.1103/PhysRevE.90.032704

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**Szolnoki A, Perc M, Mobilia M** Facilitators on networks reveal optimal interplay between information exchange and reciprocity *Physical Review E*, **89**, 2014

DOI:10.1103/PhysRevE.89.042802

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**Mobilia M** Evolutionary games with facilitators: When does selection favor cooperation? *Chaos, Solitons and Fractals*, **56**, 113-123, 2013

DOI:10.1016/j.chaos.2013.07.011

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**Mobilia M** Reply to "comment on 'Stochastic dynamics of the prisoner's dilemma with cooperation facilitators' " *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **88**, 2013

DOI:10.1103/PhysRevE.88.046102

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**Mobilia M** Reply to "Comment on 'Stochastic dynamics of the prisoner's dilemma with cooperation facilitators' ". *Phys Rev E Stat Nonlin Soft Matter Phys*, **88**, 046102, 2013

DOI:10.1103/PhysRevE.88.046102

View abstract

**Assaf M; Mobilia M ** *Anomalous Metastability and Fixation Properties of Evolutionary Games on Scale-Free Graphs*Proceedings of the European Conference on Complex Systems 2012, 713-721 2013

DOI:10.1007/978-3-319-00395-5_88

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**Mobilia M** Commitment Versus Persuasion in the Three-Party Constrained Voter Model *Journal of Statistical Physics*, **151**, 69-91, 2013

DOI:10.1007/s10955-012-0656-x

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**Assaf, M, Mobilia M, Roberts E** Cooperation dilemma in finite populations under fluctuating environments *Physical Review Letters*, **111**, 1-5, 2013

DOI:10.1103/PhysRevLett.111.238101

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**Szczesny B, Mobilia M, Rucklidge AM** When does cyclic dominance lead to stable spiral waves? *EPL (Europhysics Letters) Vol. 102, 28012 (2013)*, 2012

DOI:10.1209/0295-5075/102/28012

View abstract

**Assaf M, Mobilia M** Metastability and anomalous fixation in evolutionary games on scale-free networks *Physical Review Letters*, **109**, 2012

DOI:10.1103/PhysRevLett.109.188701

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**Mobilia M** Stochastic dynamics of the prisoner's dilemma with cooperation facilitators. *Physical Review E*, **86**, 1-9, 2012

DOI:10.1103/PhysRevE.86.011134

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**Mobilia M** Fixation and polarization in a three-species opinion dynamics model *EPL-EUROPHYS LETT*, **95**, 2011

DOI:10.1209/0295-5075/95/50002

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**He Q, Mobilia M, Tauber UC** Coexistence in the two-dimensional May-Leonard model with random rates *EUR PHYS J B*, **82**, 97-105, 2011

DOI:10.1140/epjb/e2011-20259-x

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**Assaf M, Mobilia M** Fixation of a deleterious allele under mutation pressure and finite selection intensity. *Journal of Theoretical Biology*, **275**, 93-103, 2011

DOI:10.1016/j.jtbi.2011.01.025

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**He QA, Mobilia M, Tauber UC** Spatial rock-paper-scissors models with inhomogeneous reaction rates *PHYS REV E*, **82**, 1-11, 2010

DOI:10.1103/PhysRevE.82.051909

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**Assaf M, Mobilia M** Large fluctuations and fixation in evolutionary games *Journal of Statistical Mechanics: Theory and Experiment*, **2010**

DOI:10.1088/1742-5468/2010/09/P09009

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**Assaf M, Mobilia M** Large fluctuations and fixation in evolutionary games *J STAT MECH-THEORY AND EXPERIMENT*, 1-24, 2010

DOI:10.1088/1742-5468/2010/09/P09009

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**Mobilia M, Assaf M** Fixation in evolutionary games under non-vanishing selection *EPL-EUROPHYS LETT*, **91**, 1-6, 2010

DOI:10.1209/0295-5075/91/10002

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**Mobilia M** Oscillatory dynamics in rock-paper-scissors games with mutations. *J Theor Biol*, **264**, 1-10, 2010

DOI:10.1016/j.jtbi.2010.01.008

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**Volovik D, Mobilia M, Redner S** Dynamics of Strategic Three-Choice Voting *EPL*, **85**, 48003-p1-48003-p6, 2009

DOI:10.1209/0295-5075/85/48003

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**Reichenbach T, Mobilia M, Frey E** Self-organization of mobile populations in cyclic competition *J THEOR BIOL*, **254**, 368-383, 2008

DOI:10.1016/j.jtbi.2008.05.014

**Reichenbach T; Mobilia M; Frey E ** *Stochastic effects on biodiversity in cyclic coevolutionary dynamics*Banach Center Publications, 259-264 2008

DOI:10.4064/bc80

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**Mobilia M; Reichenbach T; Hinsch H; Franosch T; Frey E ** *Generic principles of active transport*Banach Center Publications, 101-120 2008

DOI:10.4064/bc80

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**Mobilia M; Georgiev IT; Tauber UC ** *Spatial stochastic predator-prey models*Banach Center Publications, 253-257 2008

DOI:10.4064/bc80

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**Reichenbach T; Mobilia M; Frey E ** *Stochastic effects on biodiversity in cyclic coevolutionary dynamics*Banach Center Publications, 259-264 2008

DOI:10.4064/bc80

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**Reichenbach T, Mobilia M, Frey E** Noise and correlations in a spatial population model with cyclic competition *PHYS REV LETT*, **99**, 2007

DOI:10.1103/PhysRevLett.99.238105

**Reichenbach T, Mobilia M, Frey E** Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games *NATURE*, **448**, 1046-1049, 2007

DOI:10.1038/nature06095

**Mobilia M, Petersen A, Redner S** On the role of zealotry in the voter model *J STAT MECH-THEORY E*, 2007

DOI:10.1088/1742-5468/2007/08/P08029

**Mobilia M, Georgiev IT, Tauber UC** Phase transitions and spatio-temporal fluctuations in stochastic lattice Lotka-Volterra models *JOURNAL OF STATISTICAL PHYSICS*, **128**, 447-483, 2007

DOI:10.1007/s10955-006-9146-3

**Washenberger MJ, Mobilia M, Tauber UC** Influence of local carrying capacity restrictions on stochastic predator-prey models *J PHYS-CONDENS MAT*, **19**, 2007

DOI:10.1088/0953-8984/19/6/065139

**Reichenbach T, Mobilia M, Frey E** Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model *PHYS REV E*, **74**, 2006

DOI:10.1103/PhysRevE.74.051907

**Reichenbach T, Mobilia M, Frey E** Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model. *Physical review. E, Statistical, nonlinear, and soft matter physics*, **74**, 051907, 2006

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**Pierobon P, Mobilia M, Kouyos R, Frey E** Bottleneck-induced transitions in a minimal model for intracellular transport. *Physical review. E, Statistical, nonlinear, and soft matter physics*, **74**, 031906, 2006

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**Pierobon P, Mobilia M, Kouyos R, Frey E** Bottleneck-induced transitions in a minimal model for intracellular transport *PHYS REV E*, **74**, 2006

DOI:10.1103/PhysRevE.74.031906

**Mobilia M, Georgiev IT, Tauber UC** Fluctuations and correlations in lattice models for predator-prey interaction *PHYS REV E*, **73**, 2006

DOI:10.1103/PhysRevE.73.040903

**Mobilia M, Schmittmann B, Zia RKP** Exact dynamics of a reaction-diffusion model with spatially alternating rates *PHYS REV E*, **71**, 2005

DOI:10.1103/PhysRevE.71.056129

**Mobilia M, Georgiev IT** Voting and catalytic processes with inhomogeneities *PHYS REV E*, **71**, 2005

DOI:10.1103/PhysRevE.71.046102

**Mobilia M** Competition between homogeneous and local processes in a diffusive many-body system *J STAT MECH-THEORY E*, 2005

DOI:10.1088/1742-5468/2005/04/P04003

**Mobilia M, Zia RKP, Schmittmann B** Complete solution of the kinetics in a far-from-equilibrium Ising chain *J PHYS A-MATH GEN*, **37**, L407-L413, 2004

DOI:10.1088/0305-4470/37/32/L03

**Mobilia M, Redner S** Majority versus minority dynamics: Phase transition in an interacting two-state spin system *PHYS REV E*, **68**, 2003

DOI:10.1103/PhysRevE.68.046106

**Mobilia M, Redner S** Majority versus minority dynamics: Phase transition in an interacting two-state spin system *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **68**, 461061-4610611, 2003

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**Mobilia M** Does a single zealot affect an infinite group of voters? *PHYS REV LETT*, **91**, 2003

DOI:10.1103/PhysRevLett.91.028701

**Mobilia M, Krapivsky PL, Redner S** Kinetic anomalies in addition-aggregation processes *J PHYS A-MATH GEN*, **36**, 4533-4542, 2003

**Mobilia M** Exact multipoint and multitime correlation functions of a one-dimensional model of adsorption and evaporation of dimers *PHYS REV E*, **65**, 2002

DOI:10.1103/PhysRevE.65.046127

**Mobilia M, Bares PA** Two-species d-dimensional diffusive model and its mapping onto a growth model *PHYS REV E*, **65**, 2002

DOI:10.1103/PhysRevE.65.016117

**Mobilia M, Bares PA** Generalized empty-interval method applied to a class of one-dimensional stochastic models *PHYS REV E*, **64**, 2001

DOI:10.1106/PhysRevE.64.066123

**Mobilia M, Bares PA** Generalized empty-interval method applied to a class of one-dimensional stochastic models *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **64**, 2001

View abstract

**Mobilia M, Bares PA** Solution of a one-dimensional stochastic model with branching and coagulation reactions *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **64**, 451011-451014, 2001

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**Mobilia M, Bares PA** Solution of a one-dimensional stochastic model with branching and coagulation reactions *PHYS REV E*, **6404**, 2001

**Mobilia M, Bares PA** Solution of a class of one-dimensional reaction-diffusion models in disordered media *PHYS REV B*, **6406**, 2001

**Mobilia M, Bares PA** Exact solution of a class of one-dimensional nonequilibrium stochastic models *PHYS REV E*, **6305**, 2001

**Mobilia M, Bares PA** Exact solution of a class of one-dimensional nonequilibrium stochastic models *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **63**, 561121-5611212, 2001

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**Mobilia M, Bares PA** Soluble two-species diffusion-limited models in arbitrary dimensions *PHYS REV E*, **6303**, 2001

**Mobilia M, Bares PA** Soluble two-species diffusion-limited models in arbitrary dimensions *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, **63**, 361211-361225, 2001

DOI:10.1103/PhysRevE.63.036121

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**Bares P, Mobilia M** Bares and mobilia reply: *Phys Rev Lett*, **85**, 893, 2000

DOI:10.1103/PhysRevLett.85.893

**Bares PA, Mobilia M** Comment on "Solution of classical stochastic one-dimensional many-body systems" - Bares and Mobilia reply *PHYS REV LETT*, **85**, 893-893, 2000

**Bares PA, Mobilia M** Solution of classical stochastic one-dimensional many-body systems *PHYS REV LETT*, **83**, 5214-5217, 1999

**Bares PA, Mobilia M** Diffusion-limited reactions of hard-core particles in one dimension *PHYS REV E*, **59**, 1996-2009, 1999

**Wienand K, Frey E, Mobilia M** Evolution of a fluctuating population in randomly switching environment *Physical Review Letters*

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