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We propose and study a model of traffic in communication networks. The underlying network has a structure that is tunable between a scale-free growing network with preferential attachments and a random growing network. To model realistic…
Evolutionary analyses of large populations commonly incorporate stochasticity through temporal variation in selection while treating genetic transmission as fixed. Much less attention has been given to stochasticity in transmission itself.…
A model of the urban agglomeration and segregation is formulated, in which two types of agents move around on the square-lattice aligned cells. The model is shown to exhibit, when the density of agents are varied as the control parameter,…
We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…
We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement…
In this work we characterize sudden increases in the land price of certain urban areas, a phenomenon causing gentrification, via an extended Schelling model. An initial price rise forces some of the disadvantaged inhabitants out of the…
Growth is a multi-layered phenomenon in human societies, composed of socioeconomic and demographic change at many different scales. Yet, standard macroeconomic indicators average over most of these processes, blurring the spatial and…
We introduce and study a metapopulation model of random walkers interacting at the nodes of a complex network. The model integrates random relocation moves over the links of the network with local interactions depending on the node…
Epidemiological dynamics are affected by the spatial and demographic structure of the host population. Households and neighbourhoods are known to be important groupings but little is known about the epidemiological interplay between them.…
In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the…
A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell…
A key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Population spatial structure can impact mutant fixation probabilities. We introduce a model for structured…
We consider a neutral haploid population whose generations are not overlapping and whose size is large and constantly of $N$ individuals. Any generation is replaced by a new one and any individual has a single parent. We do not choose the…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
There is now experimental evidence that nearest-neighbour interactions in flocks of birds are metric free, i.e. they have no characteristic interaction length scale. However, models that involve interactions between neighbours that are…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
Why are some neighborhoods strongly connected while others remain isolated? Although standard explanations focus on demographics, economics, and geography, movement across the city may also depend on cultural styles and amenity mix. This…
Recent advances in metagenomics have revealed macroecological patterns or "laws" describing robust statistical regularities across microbial communities. Stochastic logistic models (SLMs), which treat species as independent -- akin to ideal…
Urban segregation of different communities, like blacks and whites in the USA, has been simulated by Ising-like models since Schelling 1971. This research was accompanied by a scientific segregation, with sociologists and physicists…
We studied residential clustering and mobility of ethnic minorities using a theoretical framework based on null models of spatial distributions and movements of populations. Using microdata from population registers we compared the patterns…