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We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…
We introduce a mathematical model that combines the concepts of complex contagion with payoff-biased imitation, to describe how social behaviors spread through a population. Traditional models of social learning by imitation are based on…
We consider a class of nonlocal reaction-diffusion problems, referred to as replicator-mutator equations in evolutionary genetics. By using explicit changes of unknown function, we show that they are equivalent to the heat equation and,…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties and…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…
Food-web perturbations stemming from climate change, overexploitation, invasive species, and habitat degradation often cause an initial loss of species that results in a cascade of secondary extinctions, posing considerable challenges to…
A novel mathematical framework is proposed to describe the ecological and evolutionary consequences of consumer--resource interactions. Both the consumer and resource are assumed to consist of several (sub)species, which interact between…
Understanding the time evolution of fragmented animal populations and their habitats, connected by migration, is a problem of both theoretical and practical interest. This paper presents a method for calculating the time evolution of the…
We combine incentive, adaptive, and time-scale dynamics to study multipopulation dynamics on the simplex equipped with a large class of Riemmanian metrics, simultaneously generalizing and extending many dynamics commonly studied in dynamic…
The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events'). We study the large, internal changes produced in a…
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…
The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…
Our paper computationally explores the extinction dynamics of an animal species effected by a sudden spike in mortality due to an extreme event. In our study, the animal species has a 2-year life cycle and is endowed with a high survival…
Predicting the outcomes of species invasions is a central goal of ecology, a task made especially challenging due to ecological feedbacks. To address this, we develop a general theory of ecological invasions applicable to a wide variety of…
The functioning of animal as well as human societies fundamentally relies on cooperation. Yet, defection is often favorable for the selfish individual, and social dilemmas arise. Selection by individuals' fitness, usually the basic driving…
We introduce a simple computational model that, with a microscopic dynamics driven by natural selection and mutation alone, allows the description of true speciation events. A statistical analysis of the so generated evolutionary tree…