# From adaptive dynamics to adaptive walks.

@article{Kraut2019FromAD, title={From adaptive dynamics to adaptive walks.}, author={Ann Kraut and Anton Bovier}, journal={Journal of mathematical biology}, year={2019} }

We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this population can be modelled as a measure-valued Markov process. Multiple variations of this system have been studied in the simultaneous limit of large populations and rare mutations, where the regime is chosen such that mutations are separated. We consider…

## 11 Citations

A general multi-scale description of metastable adaptive motion across fitness valleys

- Mathematics
- 2021

This work develops the framework of a meta graph that is constituted of ESCs and possible metastable transitions between those, and proves the convergence of the population process to a Markov jump process visiting only ESCs of sufficiently high stability.

Stochastic analysis of emergence of evolutionary cyclic behavior in population dynamics with transfer

- BiologyThe Annals of Applied Probability
- 2021

The goal is to analyze the trade-off between natural evolution to higher birth rates and transfer, which drives the population towards lower birth rates, and implies that negligible sub-populations may have a strong contribution to evolution.

Stochastic models for adaptive dynamics: Scaling limits and diversity

- BiologyProbabilistic Structures in Evolution
- 2019

I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation…

Punctuated equilibrium as the default mode of evolution of large populations on fitness landscapes dominated by saddle points in the weak-mutation limit

- BiologybioRxiv
- 2020

A mathematical model of population evolution on fitness landscapes is analyzed and it is shown that, for a large population in the weak-mutation limit, the process of adaptive evolution consists of extended periods of stasis, which the population spends around saddle points on the landscape, interrupted by rapid transitions to new saddle points when a beneficial mutation is fixed.

Evolution in the weak-mutation limit: Stasis periods punctuated by fast transitions between saddle points on the fitness landscape

- BiologyProceedings of the National Academy of Sciences
- 2021

A mathematical analysis of the evolution of a large population under the weak-mutation limit shows that such a population would spend most of the time in stasis in the vicinity of saddle points on the fitness landscape, interrupted by rapid transitions to new saddle points when a beneficial mutation is fixed.

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

- Biology
- 2021

It is shown that long term dynamics of viral mutants evolving resistance at distinct epitopes (viral proteins targeted by immune responses) are governed by epistasis in the virus fitness landscape, and how pairwise or multiplicative epistatic interactions shape viral evolution against concurrent immune responses and convergence to the multi-variant steady state predicted by theoretical results.

Deterministic approaches for head lice infestations and treatments

- Computer ScienceInfectious Disease Modelling
- 2020

A mathematical view on head lice infestations

- Computer Science
- 2019

A mathematical model for head lice population dynamics in hosts who could be or not quarantined and treated as a system of hyperbolic PDEs is proposed, which shows the existence of (in certain cases multiple) equilibria at which the infestation persists on the host's head.

Principles of seed banks and the emergence of complexity from dormancy

- Computer ScienceNature communications
- 2021

The fundamental attributes and emergent phenomena associated with dormancy and seed banks are outlined, with the vision for a unifying and mathematically based framework that can address problems in the life sciences, ranging from global change to cancer biology.

Principles of seed banks: complexity emerging from dormancy.

- Computer Science
- 2020

The fundamental attributes and emergent phenomena associated with dormancy and seed banks are outlined, with the goal of developing a unifying framework that can address problems in the life sciences, ranging from global change to cancer biology.

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