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Boris I. Shraiman

Publications and source records attributed to Boris I. Shraiman.

29 records · Page 2Linked to original sources
arXiv2011

Rate of Adaptation in Large Sexual Populations

Adaptation often involves the acquisition of a large number of genomic changes which arise as mutations in single individuals. In asexual populations, combinations of mutations can fix only when they arise in the same lineage, but for populations in which genetic information is exchanged, beneficial mutations can arise in different individuals and be combined later. In large populations, when the product of the population size N and the total beneficial mutation rate U_b is large, many new beneficial alleles can be segregating in the population simultaneously. We calculate the rate of adaptation, v, in several models of such sexual populations and show that v is linear in NU_b only in sufficiently small populations. In large populations, v increases much more slowly as log NU_b. The prefactor of this logarithm, however, increases as the square of the recombination rate. This acceleration of adaptation by recombination implies a strong evolutionary advantage of sex.

q-bio.PE↗
arXiv2011

Genetic Draft and Quasi-Neutrality in Large Facultatively Sexual Populations

Large populations may contain numerous simultaneously segregating polymorphisms subject to natural selection. Since selection acts on individuals whose fitness depends on many loci, different loci affect each other's dynamics. This leads to stochastic fluctuations of allele frequencies above and beyond genetic drift - an effect known as genetic draft. Since recombination disrupts associations between alleles, draft is strong when recombination is rare. Here, we study a facultatively outcrossing population in a regime where the frequency of out-crossing and recombination, r, is small compared to the characteristic scale of fitness differences σ. In this regime, fit genotypes expand clonally, leading to large fluctuations in the number of recombinant offspring genotypes. The power law tail in the distribution of the latter makes it impossible to capture the dynamics of draft by an effective neutral model. Instead, we find that the fixation time of a neutral allele increases only slowly with the population size but depends sensitively on the ratio r/σ. The efficacy of selection is reduced dramatically and alleles behave "quasi-neutrally" even for Ns>> 1, provided that |s|< s_c, where s_c depends strongly on r/σ, but only weakly on population size N. In addition, the anomalous fluctuations due to draft change the spectrum of (quasi)-neutral alleles from f(ν)\sim 1/ν, corresponding to drift, to \sim1/ν^2. Finally, draft accelerates the rate of two step adaptations through deleterious intermediates.

q-bio.PE↗
arXiv2011

Statistical Genetics and Evolution of Quantitative Traits

The distribution and heritability of many traits depends on numerous loci in the genome. In general, the astronomical number of possible genotypes makes the system with large numbers of loci difficult to describe. Multilocus evolution, however, greatly simplifies in the limit of weak selection and frequent recombination. In this limit, populations rapidly reach Quasi-Linkage Equilibrium (QLE) in which the dynamics of the full genotype distribution, including correlations between alleles at different loci, can be parameterized by the allele frequencies. This review provides a simplified exposition of the concept and mathematics of QLE which is central to the statistical description of genotypes in sexual populations. We show how key results of Quantitative Genetics such as the generalized Fisher's "Fundamental Theorem", along with Wright's Adaptive Landscape, emerge within QLE from the dynamics of the genotype distribution. We then discuss under what circumstances QLE is applicable, and what the breakdown of QLE implies for the population structure and the dynamics of selection. Understanding of the fundamental aspects of multilocus evolution obtained through simplified models may be helpful in providing conceptual and computational tools to address the challenges arising in the studies of complex quantitative phenotypes of practical interest.

q-bio.PE↗
arXiv2009

Competition between recombination and epistasis can cause a transition from allele to genotype selection

Biochemical and regulatory interactions central to biological networks are expected to cause extensive genetic interactions or epistasis affecting the heritability of complex traits and the distribution of genotypes in populations. However, the inference of epistasis from the observed phenotype-genotype correlation is impeded by statistical difficulties, while the theoretical understanding of the effects of epistasis remains limited, in turn limiting our ability to interpret data. Of particular interest is the biologically relevant situation of numerous interacting genetic loci with small individual contributions to fitness. Here, we present a computational model of selection dynamics involving many epistatic loci in a recombining population. We demonstrate that a large number of polymorphic interacting loci can, despite frequent recombination, exhibit cooperative behavior that locks alleles into favorable genotypes leading to a population consisting of a set of competing clones. When the recombination rate exceeds a certain critical value that depends on the strength of epistasis, this "genotype selection" regime disappears in an abrupt transition, giving way to "allele selection"-the regime where different loci are only weakly correlated as expected in sexually reproducing populations. We show that large populations attain highest fitness at a recombination rate just below critical. Clustering of interacting sets of genes on a chromosome leads to the emergence of an intermediate regime, where blocks of cooperating alleles lock into genetic modules. These haplotype blocks disappear in a second transition to pure allele selection. Our results demonstrate that the collective effect of many weak epistatic interactions can have dramatic effects on the population structure.

q-bio.PE↗
arXiv2001

Olfactory search at high Reynolds number

Locating the source of odor in a turbulent environment - a common behavior for living organisms - is non-trivial because of the random nature of mixing. Here we analyze the statistical physics aspects of the problem and propose an efficient strategy for olfactory search which can work in turbulent plumes. The algorithm combines the maximum likelihood inference of the source position with an active search. Our approach provides the theoretical basis for the design of olfactory robots and the quantitative tools for the analysis of the observed olfactory search behavior of living creatures (e.g. odor modulated optomotor anemotaxis of moth)

nlin.CD↗
arXiv1999

Lagrangian Tetrad Dynamics and the Phenomenology of Turbulence

A new phenomenological model of turbulent fluctuations is constructed by considering the Lagrangian dynamics of 4 points (the tetrad). The closure of the equations of motion is achieved by postulating an anisotropic, i.e. tetrad shape dependent, relation of the local pressure and the velocity gradient defined on the tetrad. The non-local contribution to the pressure and the incoherent small scale fluctuations are modeled as Gaussian white "noise". The resulting stochastic model for the coarse-grained velocity gradient is analyzed approximately, yielding predictions for the probability distribution functions of different 2nd and 3d order invariants. The results are compared with the direct numerical simulation of the Navier-Stokes. The model provides a reasonable representation of the non-linear dynamics involved in energy transfer and vortex stretching and allows to study interesting aspects of the statistical geometry of turbulence, e.g. vorticity/strain alignment. In a state with a constant energy flux (and K41 power spectrum) it exhibits the anomalous scaling of high moments associated with formation of high gradient sheets - events associated with large energy transfer. An approach to the more complete analysis of the stochastic model, properly including the effect of fluctuations, is outlined and will enable further quantitative juxtaposition of the model with the results of the DNS.

chao-dyn↗
arXiv1998

Anomalous Hall Effect in Double Exchange Magnets

We investigate the possible origin of anomalous Hall effect in the CMR (colossal magnetoresistance) materials - the doped rare earth manganites - observed recently by Matl et al. It is demonstrated that the spin-orbit interaction in the double exchange model couples magnetization to the Berry phase associated with three dimensional spin textures and induces a non-zero average topological flux which in turn generates an anomalous contribution to transverse resistivity. The same effect, but involving the orbital Berry phase, occurs in the model with orbital degeneracy and Coulomb repulsion.

cond-mat.str-el↗
arXiv1996

On the Kraichnan Model of Passive Scalar Advection Near the Batchelor limit

The third order correlation function of the scalar field advected by a Gaussian random velocity, with a spatial scaling exponent $2 - ε$, and in the presence of a mean gradient, is calculated perturbatively in $ε<< 1$. This expansion corresponds to the regime close to Batchelor's advection by linear diffeomorphisms. The scaling exponent is found to be equal to 1 in dimensions 2 and 3, up to corrections smaller than $ { \cal O } ( ε) $, implying an anomalous scaling of the third order correlation function and the persistence of small scale anisotropy.

cond-mat↗
arXiv1996

On the Fermi Liquid to Polaron Crossover II: Double Exchange and the Physics of "Colossal" Magnetoresistance

We use the dynamical mean field method to study a model of electrons Jahn-Teller coupled to localized classical oscillators and ferromagnetically coupled to ``core spins'', which, we argue, contains the essential physics of the ``colossal magnetoresistance'' manganites $Re_{1-x} A_x MnO_3$. We determine the different regimes of the model and present results for the temperature and frequency dependence of the conductivity, the electron spectral function and the root mean square lattice parameter fluctuations. We compare our results to data, and give a qualitative discussion of important physics not included in the calculation. Extensive use is made of results from a companion paper titled: ``On the Fermi Liquid to Polaron Crossover I: General Results''.

cond-mat↗
arXiv1995

Dynamic Jahn-Teller Effect and Colossal Magnetoresistance in $La_{1-x}A_xMnO_3$

A model for $La_{1-x}Sr_xMnO_3$ which incorporates the physics of dynamic Jahn-Teller and double-exchange effects is presented and solved via a dynamical mean field approximation. In an intermediate coupling regime the interplay of these two effects is found to reproduce the behavior of the resistivity and magnetic transition temperature observed in $La_{1-x} Sr_x MnO_3$.

cond-mat↗