# Mauro MobiliaUniversity of Leeds · Department of Applied Mathematics

Mauro Mobilia

PhD, MSc, FHEA

## About

108

Publications

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Introduction

I am currently a Full Professor of Applied Mathematics (Chair) at the University of Leeds, UK. I earned my PhD from the Swiss Institute of Technology in Lausanne (EPFL), and then held research fellowships at Boston University and Virginia Tech in the USA, the University of Munich (LMU, DE) and University of Warwick (UK). My research focuses on the applications of statistical physics and applied mathematics to model the evolutionary dynamics of complex systems in the life and behavioral sciences.

Additional affiliations

January 2009 - present

Education

June 1998 - February 2002

October 1993 - March 1998

## Publications

Publications (108)

The spatio-temporal arrangement of interacting populations often influences
the maintenance of species diversity and is a subject of intense research.
Here, we study the spatio-temporal patterns arising from the cyclic competition
between three species in two dimensions. Inspired by recent experiments, we
consider a generic metapopulation model com...

Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an environment that randomly switches between states of abundance and scarcity. Assuming that one strain grows slig...

Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity changing continuously in time according to either binary random switches, or by being driven by a noise of continu...

There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behavior leading to the coexistence of resistant and sensitive cells in larg...

Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability thus shapes the population long-time dynamics, notably by influencing the ability of different strains of microorganisms to...

Waiting times between successive events play an important role in population dynamics and can vary widely, notably due to environmental conditions. In this work, we focus on the zero-sum rock-paper-scissors (zRPS) model, broadly used to describe cyclic dominance in ecology and biology, with non-Markovian dynamics and study how its survival and fixa...

Antimicrobial resistance to drugs (AMR), a global threat to human and animal health, is often regarded as resulting from cooperative behaviour. Moreover, microbes generally evolve in volatile environments that, together with demographic fluctuations (birth and death events), drastically alter population size and strain survival. Motivated by the ne...

Antimicrobial resistance to drugs (AMR), a global threat to human and animal health, is often regarded as resulting from a cooperative behaviour, leading to the coexistence of drug-resistant and drug-sensitive cells in large communities and static environments. However, microbial populations generally evolve in volatile environments, yielding sudde...

Microbial populations generally evolve in volatile environments, under conditions fluctuating between harsh and mild, e.g. as the result of sudden changes in toxin concentration or nutrient abundance. Environmental variability thus shapes the long-time population dynamics, notably by influencing the ability of different strains of microorganisms to...

There is a pressing need to better understand how microbial populations respond to antimicrobial drugs, and to find mechanisms to possibly eradicate antimicrobial-resistant cells. The inactivation of antimicrobials by resistant microbes can often be viewed as a cooperative behaviour leading to the coexistence of resistant and sensitive cells in lar...

We study the effect of time-fluctuating social influences on the formation of polarization and consensus in a three-party community consisting of two types of voters (“leftists” and “rightists”) holding extreme opinions, and moderate agents acting as “centrists”. The former are incompatible and do not interact, while centrists hold an intermediate...

We study the effect of time-fluctuating social influences on the formation of polarization and consensus in a three-party community consisting of two types of voters ("leftists" and "rightists") holding extreme opinions, and moderate agents acting as "centrists". The former are incompatible and do not interact, while centrists hold an intermediate...

Supplemental Material to Phys. Rev. Research 5, L022004 (2023) at https://journals.aps.org/prresearch/supplemental/10.1103/PhysRevResearch.5.L022004

Supplemental Material on Figshare: https://doi.org/10.6084/m9.figshare.21763142.v1

Figshare resources for data and codes: https://doi.org/10.6084/m9.figshare.21603480.v1
Supplemental Material on Figshare: https://doi.org/10.6084/m9.figshare.21763142.v1

Environmental variations can significantly influence how populations compete for resources, and hence shape their evolution. Here, we study population dynamics subject to a fluctuating environment modeled by a varying carrying capacity changing continuously in time according to either binary random switches, or by being driven by a noise of continu...

In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mort...

In this Supplementary Material, we provide some further technical details and supplementary information in support of the results discussed in the main text of the paper "Effects of homophily and heterophily on preferred-degree networks: mean-field
analysis and overwhelming transition" (https://doi.org/10.1088/1742-5468/ac410f)

We investigate the long-time properties of a dynamic, out-of-equilibrium network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents’ opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped b...

In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mort...

We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by homophily, a form of social interaction. Characterized by the parameter J∈[−1,1], the latter plays a role simi...

Microorganisms live in environments that inevitably fluctuate between mild and harsh conditions. As harsh conditions may cause extinctions, the rate at which fluctuations occur can shape microbial communities and their diversity, but we still lack an intuition on how. Here, we build a mathematical model describing two microbial species living in an...

We investigate the long-time properties of a dynamic, out-of-equilibrium, network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents' opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped...

We consider a dynamic network of individuals that may hold one of two different opinions in a two-party society. As a dynamical model, agents can endlessly create and delete links to satisfy a preferred degree, and the network is shaped by homophily, a form of social interaction. Characterized by the parameter $J \in [-1,1]$, the latter plays a rol...

Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity switching either randomly or periodically between states of abundance and scarcity....

Microorganisms often live in environments that fluctuate between mild and harsh conditions. Although such fluctuations are bound to cause local extinctions and affect species diversity, it is unknown how diversity changes at different fluctuation rates and how this relates to changes in species interactions. Here, we use a mathematical model descri...

Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment modeled by a carrying capacity that switches either randomly or periodically between states of abundance and scarci...

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration, and local jumps on a regular lattice. We study...

Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different “laws” in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carryi...

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration and local jumps on a regular lattice. We study...

There is mounting empirical evidence that many communities of living organisms display key features which closely resemble those of physical systems at criticality. We here introduce a minimal model framework for the dynamics of a community of individuals which undergoes local birth-death, immigration and local jumps on a regular lattice. We study...

Rock-paper-scissors games metaphorically model cyclic dominance in ecology and microbiology. In a static environment, these models are characterized by fixation probabilities obeying two different "laws" in large and small well-mixed populations. Here, we investigate the evolution of these three-species models subject to a randomly switching carryi...

Environmental variability greatly influences the eco-evolutionary dynamics of a population, i.e. it affects how its size and composition evolve. Here, we study a well-mixed population of finite and fluctuating size whose growth is limited by a randomly switching carrying capacity. This models the environmental fluctuations between states of resourc...

Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey competition invalidates the deterministic Lotka-Volterra picture of neutral population cycles. Stochastic models y...

Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey competition invalidates the deterministic Lotka-Volterra picture of neutral population cycles. Stochastic models y...

We study the influence of a randomly switching reproduction-predation rate on the survival behavior of the non-spatial cyclic Lotka-Volterra model, also known as the zero-sum rock-paper-scissors game, used to metaphorically describe the cyclic competition between three species. In large and finite populations, demographic fluctuations (internal noi...

We study the influence of the complex topology of scale-free graphs on the dynamics of anti-coordination games (snowdrift games). These reference models are characterized by the coexistence (evolutionary stable mixed strategy) of two competing species, say "cooperators" and "defectors", and, in finite systems, by metastability and by large-fluctuat...

We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type $q_1$ or $q_2$, or is an inflexible zealot. At each time step, a $q_i$-susceptible voter...

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance (dominance-removal and dominance-replacement), mutations, an...

We introduce a heterogeneous nonlinear q-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type q
1 or q
2. While here zealots neve...

The importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth’s soil, oceans, and the atmosphere, and perform ecosystem functions that impact plants, animals, and humans. Yet our ability to predict and manage the function of these highly complex dynamically changing communities is limited. B...

Full supplementary Material for "Characterization of the Nonequilibrium Steady State of a Heteogeneous Nonlinear q-Voter Model with Zealotry'' (supplemntary text, figure and movie) is available here: https://dx.doi.org/10.6084/m9.figshare.2060595.v2

We generalize the classical Bass model of innovation diffusion to include a new class of agents - Luddites - that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously ado...

We study the dynamics of the nonlinear $q$-voter model with inflexible
zealots in a finite well-mixed population. In this system, each individual
supports one of two parties and is either a susceptible voter or an inflexible
zealot. At each time step, a susceptible adopts the opinion of a neighbor if
this belongs to a group of $q\geq 2$ neighbors a...

We generalize the classical Bass model of innovation diffusion to include a
new class of agents --- Luddites --- that oppose the spread of innovation. Our
model also incorporates ignorants, susceptibles, and adopters. When an ignorant
and a susceptible meet, the former is converted to a susceptible at a given
rate, while a susceptible spontaneously...

Rock is wrapped by paper, paper is cut by scissors, and scissors are crushed
by rock. This simple game is popular among children and adults to decide on
trivial disputes that have no obvious winner, but cyclic dominance is also at
the heart of predator-prey interactions, the mating strategy of side-blotched
lizards, the overgrowth of marine sessile...

Reciprocity is firmly established as an important mechanism that promotes cooperation. An efficient information exchange is likewise important, especially on structured populations, where interactions between players are limited. Motivated by these two facts, we explore the role of facilitators in social dilemmas on networks. Facilitators are here...

Supplementary material to the paper: "When does cyclic dominance lead to stable spiral waves?"

Movie illustrating some factors that influence the stability of spiral waves in populations evolving in cyclic competition:
http://www1.maths.leeds.ac.uk/~amtmmo/figshare_96949/ssa__L128_N64__b1.0_s1.0_z1.8_1.2_0.6_0.0_m0.02__d1.0_e1.0_.ogv

We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-) steady state in two-dimensional stochastic May-Leonard models
of mobile individuals, allowing for particle exchanges with...

We present a novel approach allowing the study of rare events like fixation
under fluctuating environments, modeled as extrinsic noise, in evolutionary
processes characterized by the dominance of one species. Our treatment consists
of mapping the system onto an auxiliary model, exhibiting metastable species
coexistence, that can be analyzed semicla...

The fixation properties of a simple prisoner's dilemma game in the presence of "cooperation facilitators" have recently been investigated in finite and well-mixed populations for various dynamics [Mobilia, Phys. Rev. E 86, 011134 (2012)]. In a Comment, Miękisz claims that, for cooperation to be favored by selection in the standard prisoner's dilemm...

This contribution concerns the influence of scale-free graphs on the metastability and fixation properties of a set of evolutionary pro-cesses. In the framework of evolutionary game theory, where the fitness and selection are frequency-dependent and vary with the population com-position, we analyze the dynamics of snowdrift games (characterized by...

Species diversity in ecosystems is often accompanied by the self-organisation
of the population into fascinating spatio-temporal patterns. Here, we consider
a two-dimensional three-species population model and study the spiralling
patterns arising from the combined effects of generic cyclic dominance,
mutation, pair-exchange and hopping of the indi...

We study the influence of complex graphs on the metastability and fixation properties of a set of evolutionary processes. In the framework of evolutionary game theory, where the fitness and selection are frequency dependent and vary with the population composition, we analyze the dynamics of snowdrift games (characterized by a metastable coexistenc...

In the framework of the three-party constrained voter model, where voters of
two radical parties (A and B) interact with "centrists" (C and Cz), we study
the competition between a persuasive majority and a committed minority. In this
model, A's and B's are incompatible voters that can convince centrists or be
swayed by them. Here, radical voters ar...

In the framework of the paradigmatic prisoner's dilemma, we investigate the
evolutionary dynamics of social dilemmas in the presence of "cooperation
facilitators". In our model, cooperators and defectors interact as in the
classical prisoner's dilemma game, where selection favors defection. However,
here the presence of a small number of cooperatio...

Motivated by the dynamics of cultural change and diversity, we generalize the
three-species constrained voter model on a complete graph introduced in [J.
Phys. A 37, 8479 (2004)]. In this opinion dynamics model, a population of size
N is composed of "leftists" and "rightists" that interact with "centrists": a
leftist and centrist can both become le...

The mean fixation time of a deleterious mutant allele is studied beyond the diffusion approximation. As in Kimura's classical work [M. Kimura, Proc. Natl. Acad. Sci. USA. 77, 522 (1980)], that was motivated by the problem of fixation in the presence of amorphic or hypermorphic mutations, we consider a diallelic model at a single locus comprising a...

We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices. Specifically, we investigate the influence of spatial variability of the reaction rates and site...

We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two absorbing states. We are particularly interested in the problem of fixation that refers to the possibility that a few...

We study the oscillatory dynamics in the generic three-species rock-paper-scissors games with mutations. In the mean-field limit, different behaviors are found: (a) for high mutation rate, there is a stable interior fixed point with coexistence of all species; (b) for low mutation rates, there is a region of the parameter space characterized by a l...

One of the most striking effect of fluctuations in evolutionary game theory is the possibility for mutants to fixate (take over) an entire population. Here, we generalize a recent WKB-based theory to study fixation in evolutionary games under non-vanishing selection, and investigate the relation between selection intensity w and demographic (random...

In certain parliamentary democracies, there are two major parties that move in and out of power every few elections, and a third minority party that essentially never governs. We present a simple model to account for this phenomenon, in which minority party supporters sometimes vote ideologically (for their party) and sometimes strategically (again...