Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

IMPACTO DO CÂNCER NA ATIVIDADE CEREBRAL

in Portuguese Agradecimentos A realização do trabalho foi possível devido ao auxílio financeiro das seguintes agências: Fundação Araucária, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior e Conselho Nacional de Desenvolvimento Científico e Tecnológico – Programa Ciência sem Fronteiras, processos número : 245377/2012-3 e 17656125.

Suppression of neuronal phase synchronisation in cat cerebral cortex

We wish to acknowledge the support of the Brazilian agencies: CNPq, CAPES, and FAPESP (2015/07311-7 and 2011/19296-1).

Quantifying topological invariants of neuronal morphologies

10 pages, 5 figures, conference or other essential info Acknowledgments LK and JCS were supported by Blue Brain Project. P.D. and R.L. were supported in part by the Blue Brain Project and by the start-up grant of KH. Partial support for P.D. has been provided by the Advanced Grant of the European Research Council GUDHI (Geometric Understanding in Higher Dimensions). MS was supported by the SNF NCCR ”Synapsy”.

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire

Acknowledgements This study was possible by partial financial support from the following Brazilian government agencies: CNPq, CAPES, and FAPESP (2011/19296-1 and 2015/07311-7). We also wish thank Newton Fund and COFAP.

Suppression of phase synchronisation in network based on cat’s brain

We wish to acknowledge the support of the Brazilian agencies: CNPq, CAPES, and FAPESP (2015/07311-7 and 2011/19296-1).

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