Related papers: Phenotypic Equilibrium as Probabilistic Convergenc…
A class of models of biological population and communities with a singular equilibrium at the origin is analyzed; it is shown that these models can possess a dynamical regime of deterministic extinction, which is crucially important from…
Some deterministic cellular automata have been observed to follow the pattern of the second law of thermodynamics: starting from a partially disordered state, the system evolves towards a state of equilibrium characterized by maximal…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…
We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are…
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…
All possible phenotypes are not equally accessible to evolving populations. In fact, only phenotypes of large size, i.e. those resulting from many different genotypes, are found in populations of sequences, presumably because they are…
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…
Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localised clusters, suggesting a simple mechanism…
Genetically identical cells in the same population can take on phenotypically variable states, leading to differentiated responses to external signals, such as nutrients and drug-induced stress. Many models and experiments have focused on a…
Certain Markov processes, or deterministic evolution equations, have the property that they are dual to a stochastic process that exhibits extinction versus unbounded growth, i.e., the total mass in such a process either becomes zero, or…
We use a classical combinatorial inequality to establish a Markov inequality for multivariate binary Markov processes on trees. We then apply this result, alongside with the FKG inequality, to compare the expected loss of biodiversity under…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
Age-structured models capture the dynamic behavior of populations over time and result in nonlinear integro-partial differential equations (IPDEs). These processes arise in various fields such as biotechnology, economics, or demography.…
Phylogenetic comparative analysis is an approach to inferring evolutionary process from a combination of phylogenetic and phenotypic data. The last few years have seen increasingly sophisticated models employed in the evaluation of more and…
Many biological processes exhibit oscillatory behavior. Among these, glycolytic oscillations have been extensively studied due to their well-characterized biochemical reaction networks. However, the complexity of these networks necessitates…
Phenotype variations define heterogeneity of biological and molecular systems, which play a crucial role in several mechanisms. Heterogeneity has been demonstrated in tumor cells. Here, samples from blood of patients affected from colon…
We study a stochastic branching model for a population structured by a quantitative phenotypic trait and subject to births, deaths, and mutations. In a regime of large population and small mutations, and in logarithmic scales of size and…
Evolutionary and ecosystem dynamics are often treated as different processes --operating at separate timescales-- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field…
Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely…
Many types of bacteria can survive under stress by switching stochastically between two different phenotypes: the "normals" who multiply fast, but are vulnerable to stress, and the "persisters" who hardly multiply, but are resilient to…