Role of finite populations in determining evolutionary dynamics

Ray, Tania; Payne, Karl; Moseley, L. L.

doi:10.1103/physreve.77.021909

Cited by 2 publications

(1 citation statement)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Several researchers have studied stochastic versions of Eigen's deterministic evolution equations [1,3,10,[12][13][14][15][16]19]. One such stochastic version, motivated by the WrightFisher model in population genetics, was studied by Dixit et al [4].…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Dynamics in Finite Populations Mix Rapidly

Panageas¹,

Srivastava²,

Vishnoi³

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

In this paper we prove that the mixing time of a broad class of evolutionary dynamics in finite, unstructured populations is roughly logarithmic in the size of the state space. An important special case of such a stochastic process is the Wright-Fisher model from evolutionary biology (with selection and mutation) on a population of size N over m genotypes. Our main result implies that the mixing time of this process is O(log N ) for all mutation rates and fitness landscapes, and solves the main open problem from [4]. In particular, it significantly extends the main result in [18] who proved this for m = 2. Biologically, such models have been used to study the evolution of viral populations with applications to drug design strategies countering them. Here the time it takes for the population to reach a steady state is important both for the estimation of the steady-state structure of the population as well in the modeling of the treatment strength and duration. Our result, that such populations exhibit rapid mixing, makes both of these approaches sound.Technically, we make a novel connection between Markov chains arising in evolutionary dynamics and dynamical systems on the probability simplex. This allows us to use the local and global stability properties of the fixed points of such dynamical systems to construct a contractive coupling in a fairly general setting. We expect that our mixing time result would be useful beyond the evolutionary biology setting, and the techniques used here would find applications in bounding the mixing times of Markov chains which have a natural underlying dynamical system.

show abstract

Section: Introductionmentioning

confidence: 99%

Evolutionary Dynamics in Finite Populations Mix Rapidly

Panageas¹,

Srivastava²,

Vishnoi³

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

show abstract

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

et al. 2012

View full text Add to dashboard Cite

The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, , however, is not known. Application of the quasispecies theory to determine poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and . We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated to be substitutions/site/replication, ∼2–6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.

show abstract

Role of finite populations in determining evolutionary dynamics

Cited by 2 publications

References 21 publications

Evolutionary Dynamics in Finite Populations Mix Rapidly

Evolutionary Dynamics in Finite Populations Mix Rapidly

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

Contact Info

Product

Resources

About