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A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
The emergence and maintenance of cooperation has attracted intensive scholarly interest and has been analysed within the framework of evolutionary game theory. The role of innovation, which introduces novel strategies into the population,…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
Why do human languages change at some times, and not others? We address this longstanding question from a computational perspective, focusing on the case of sound change. Sound change arises from the pronunciation variability ubiquitous in…
We study the evolution of the network properties of a populated network embedded in a genotype space characterised by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution…
We give a closed form of the discrete-time evolution of a recombination transformation in population genetics. This decomposition allows to define a Markov chain in a natural way. We describe the geometric decay rate to the limit…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
This paper aims to shed light on the evolutionary dynamics of diverse and social populations by introducing the rich expressiveness of generative models into the trait expression of social agent-based evolutionary models. Specifically, we…
A fundamental problem in the fields of population genetics, evolution, and community ecology, is the fate of a single mutant, or invader, introduced in a finite population of wild types. For a fixed-size community of $N$ individuals, with…
Mutations in a microbial population can increase the frequency of a genotype not only by increasing its exponential growth rate, but also by decreasing its lag time or adjusting the yield (resource efficiency). The contribution of multiple…
Societies experience politically stable and unstable phases along history, whereas political power is usually passed to new elite groups by these changes. Structural dynamics of the elites in a society have been proposed to be one of the…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
In this paper we study networks of nodes characterised by binary traits that change both endogenously and through nearest-neighbour interaction. Our analytical results show that those traits can be ranked according to the noisiness of their…
Many real world, complex phenomena have underlying structures of evolving networks where nodes and links are added and removed over time. A central scientific challenge is the description and explanation of network dynamics, with a key test…
The outbreak of mutant strains and vaccination behaviors have been the focus of recent epidemiological research, but most existing epidemic models failed to simultaneously capture viral mutation and consider the complexity and behavioral…
We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represended by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows…
Decision-making by imitating the highest earners has been observed in experimental studies. In two-strategy decision-making problems, this behavior may result in perpetual fluctuations in the population proportions of the two strategies.…