Related papers: A stochastic evolutionary model for capturing huma…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
Ecosystems dynamics is often considered as driven by a coupling of species' resource consumption and its population size dynamics. Such resource-population dynamics is captured by MacArthur-type models. One biologically relevant feature…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
Stochastic reaction networks are mathematical models with a wide range of applications in biochemistry, ecology, and epidemiology, and are often complex to analyze. Except for some special cases, it is generally difficult to predict how the…
We are interested in modeling some two-level population dynamics, resulting from the interplay of ecological interactions and phenotypic variation of individuals (or hosts) and the evolution of cells (or parasites) of two types living in…
We investigate a selection-mutation model for the dynamics of technological innovation,a special case of reaction-diffusion equations. Although mutations are assumed to increase the variety of technologies, not their average success…
The population is composed of individuals characterised by their genetic strings, phenotypes and ages. We discuss the influence of probabilities of survival of the individuals on the dynamics and phenotypic variability of the population. We…
Computer modelling for evolutionary systems consists in: 1) to store in the memory the individual features of each member of a large population; and 2) to update the whole system repeatedly, as time goes by, according to some prescribed…
In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of…
Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear…
Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
Epochal dynamics, in which long periods of stasis in an evolving population are punctuated by a sudden burst of change, is a common behavior in both natural and artificial evolutionary processes. We analyze the population dynamics for a…
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…