Related papers: Bak--Sneppen type models and rank-driven processes
The reduced Markov branching process is a stochastic model for the genealogy of an unstructured biological population. Its limit behavior in the critical case is well studied for the Zolotarev-Slack regularity parameter $\alpha\in(0,1]$. We…
In this paper, we investigate the asymptotic behavior of individual-based models describing the evolution of a population structured by a real trait, subject to selection and mutation. We consider two different sets of assumptions: first,…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
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…
Nested structure, which is non-random, controls cooperation dynamics and biodiversity in plant-animal mutualistic networks. This structural pattern has been explained in a static (non-growth) network models. However, evolutionary processes…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
Large scale organization in ensembles of events of atmospheric convection can be generated by the combined effect of forcing and of the interaction between the raising plumes and the environment. Here the "large scale" refers to the space…
Non-Markovian stochastic processes are ubiquitous in biology. Nevertheless, we lack a general framework for quantifying historical dependencies. In this Letter, we propose an information-theoretic approach to decompose history dependence in…
We introduce a self-reinforced point processes on the unit interval that appears to exhibit self-organized criticality, somewhat reminiscent of the well-known Bak-Sneppen model. The process takes values in the finite subsets of the unit…
We are interested in the impact of natural selection in a prey-predator community. We introduce an individual-based model of the community that takes into account both prey and predator phenotypes. Our aim is to understand the phenotypic…
We consider a stochastic individual-based population model with competition, trait-structure affecting reproduction and survival, and changing environment. The changes of traits are described by jump processes, and the dynamics can be…
Group-based social dominance hierarchies are of essential interest in animal behavior research. Studies often record aggressive interactions observed over time, and models that can capture such dynamic hierarchy are therefore crucial.…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. A Spike-Timing Dependent Plasticity (STDP) rule is a…
Technical analysis (TA) has been used for a long time before the availability of more sophisticated instruments for financial forecasting in order to suggest decisions on the basis of the occurrence of data patterns. Many mathematical and…
In this article, a stochastic individual-based model describing Darwinian evolution of asexual, phenotypic trait-structured population, is studied. We consider a large population with constant population size characterised by a resampling…
This study introduces a novel theoretical framework, the Stacked Autoencoder Evolution Hypothesis, which proposes that biological evolutionary systems operate through multi-layered self-encoding and decoding processes, analogous to stacked…
A feature often observed in epidemiological networks is significant heterogeneity in degree. A popular modelling approach to this has been to consider large populations with highly heterogeneous discrete contact rates. This paper defines an…
We consider Markov jump processes describing structured populations with interactions via density dependance. We propose a Markov construction with a distinguished individual which allows to describe the random tree and random sample at a…
We propose a simple quantitative model of Schumpeterian economic dynamics. New goods and services are endogenously produced through combinations of existing goods. As soon as new goods enter the market they may compete against already…