arXiv subjects

Joachim Hermisson

Publications and source records attributed to Joachim Hermisson.

11 recordsLinked to original sources

arXiv2021

Disease Momentum: Estimating the Reproduction Number in the Presence of Superspreading

A primary quantity of interest in the study of infectious diseases is the average number of new infections that an infected person produces. This so-called reproduction number has significant implications for the disease progression. There has been increasing literature suggesting that superspreading, the significant variability in number of new infections caused by individuals, plays an important role in the spread of SARS-CoV-2. In this paper, we consider the effect that such superspreading has on the estimation of the reproduction number and subsequent estimates of future cases. Accordingly, we employ a simple extension to models currently used in the literature to estimate the reproduction number and present a case-study of the progression of COVID-19 in Austria. Our models demonstrate that the estimation uncertainty of the reproduction number increases with superspreading and that this improves the performance of prediction intervals. Of independent interest is the derivation of a transparent formula that connects the extent of superspreading to the width of credible intervals for the reproduction number. This serves as a valuable heuristic for understanding the uncertainty surrounding diseases with superspreading.

q-bio.PE↗

arXiv2014

A general condition for adaptive genetic polymorphism in temporally and spatially heterogeneous environments

Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that fluctuates in space and time, and derive an analytical condition for when these fluctuations promote genetic diversification. As ecological scenario we use a generalized island model with soft selection within patches in which we incorporate generation overlap. We allow for arbitrary fluctuations in the environment including spatio-temporal correlations and any functional form of selection on the trait. Using the concepts of invasion fitness and evolutionary branching, we derive a simple and transparent condition for the adaptive evolution and maintenance of genetic diversity. This condition relates the strength of selection within patches to expectations and variances in the environmental conditions across space and time. Our results unify, clarify, and extend a number of previous results on the evolution and maintenance of genetic variation under fluctuating selection. Individual-based simulations show that our results are independent of the details of the genetic architecture and on whether reproduction is clonal or sexual. The onset of increased genetic variance is predicted accurately also in small populations in which alleles can go extinct due to environmental stochasticity.

q-bio.PE↗

arXiv2010

Selective sweeps for recessive alleles and for other modes of dominance

A selective sweep describes the reduction of linked genetic variation due to strong positive selection. If s is the fitness advantage of a homozygote for the beneficial allele and h its dominance coefficient, it is usually assumed that h=1/2, i.e. the beneficial allele is co-dominant. We complement existing theory for selective sweeps by assuming that h is any value in [0,1]. We show that genetic diversity patters under selective sweeps with strength s and dominance 0<h<1 are similar to co-dominant sweeps with selection strength 2hs. Moreover, we focus on the case h=0 of a completely recessive beneficial allele. We find that the length of the sweep, i.e. the time from occurrence until fixation of the beneficial allele, is of the order of sqrt(N/s) generations, if N is the population size. Simulations as well as our results show that genetic diversity patterns in the recessive case h=0 greatly differ from all other cases.

q-bio.PE↗

arXiv2008

The pattern of genetic hitchhiking under recurrent mutation

Genetic hitchhiking describes evolution at a neutral locus that is linked to a selected locus. If a beneficial allele rises to fixation at the selected locus, a characteristic polymorphism pattern (so-called selective sweep) emerges at the neutral locus. The classical model assumes that fixation of the beneficial allele occurs from a single copy of this allele that arises by mutation. However, recent theory (Pennings and Hermisson, 2006a; Pennings and Hermisson, 2006b) has shown that recurrent beneficial mutation at biologically realistic rates can lead to markedly different polymorphism patterns, so called soft selective sweeps. We extend an approach that has recently been developed for the classical hitchhiking model (Schweinsbergand Durrett, 2005; Etheridge, Pfaffelhuber, Wakolbinger, 2006) to study the recurrent mutation scenario. We show that the genealogy at the neutral locus can be approximated (to leading orders in the selection strength) by a marked Yule process with immigration. Using this formalism, we derive an improved analytical approximation for the expected heterozygosity at the neutral locus at the time of fixation of the beneficial allele.

math.PR↗

arXiv2002

Mutation-Selection Balance: Ancestry, Load, and Maximum Principle

We show how concepts from statistical physics, such as order parameter, thermodynamic limit, and quantum phase transition, translate into biological concepts in mutation-selection models for sequence evolution and can be used there. The article takes a biological point of view within a population genetics framework, but contains an appendix for physicists, which makes this correspondence clear. We analyze the equilibrium behavior of deterministic haploid mutation-selection models. Both the forward and the time-reversed evolution processes are considered. The stationary state of the latter is called the ancestral distribution, which turns out as a key for the study of mutation-selection balance. We find that it determines the sensitivity of the equilibrium mean fitness to changes in the fitness values and discuss implications for the evolution of mutational robustness. We further show that the difference between the ancestral and the population mean fitness, termed mutational loss, provides a measure for the sensitivity of the equilibrium mean fitness to changes in the mutation rate. For a class of models in which the number of mutations in an individual is taken as the trait value, and fitness is a function of the trait, we use the ancestor formulation to derive a simple maximum principle, from which the mean and variance of fitness and the trait may be derived; the results are exact for a number of limiting cases, and otherwise yield approximations which are accurate for a wide range of parameters. These results are applied to (error) threshold phenomena caused by the interplay of selection and mutation. They lead to a clarification of concepts, as well as criteria for the existence of thresholds.

cond-mat.stat-mech↗

arXiv2002

The control of phenotype: connecting enzyme variation to physiology

Metabolic control analysis (Kacser & Burns (1973). Symp. Soc. Exp. Biol. 27, 65-104; Heinrich & Rapoport (1974). Eur. J. Biochem. 42, 89-95) was developed for the understanding of multi-enzyme networks. At the core of this approach is the flux summation theorem. This theorem implies that there is an invariant relationship between the control coefficients of enzymes in a pathway. One of the main conclusions that has been derived from the summation theorem is that phenotypic robustness to mutation (e.g. dominance) is an inherent property of metabolic systems and hence does not require an evolutionary explanation (Kacser & Burns (1981). Genetics. 97, 639-666; Porteous (1996). J. theor. Biol. 182, 223-232). Here we show that for mutations involving discrete changes (of any magnitude) in enzyme concentration the flux summation theorem does not hold. The scenarios we examine are two-enzyme pathways with a diffusion barrier, two enzyme pathways that allow for enzyme saturation and two enzyme pathways that have both saturable enzymes and a diffusion barrier. Our results are extendable to sequential pathways with any number of enzymes. The fact that the flux summation theorem cannot hold in sequential pathways casts serious doubts on the claim that robustness with respect to mutations is an inherent property of metabolic systems.

physics.bio-ph↗

arXiv2000

Four-state quantum chain as a model of sequence evolution

A variety of selection-mutation models for DNA (or RNA) sequences, well known in molecular evolution, can be translated into a model of coupled Ising quantum chains. This correspondence is used to investigate the genetic variability and error threshold behaviour in dependence of possible fitness landscapes. In contrast to the two-state models treated hitherto, the model explicitly takes the four-state nature of the nucleotide alphabet into account and allowes for the distinction of mutation rates for the different base substitutions, as given by standard mutation schemes of molecular phylogeny. As a consequence of this refined treatment, new phase diagrams for the error threshold behaviour are obtained, with appearance of a novel phase in which the nucleotide ordering of the wildtype sequence is only partially conserved. Explicit analytic and numeric results are presented for evolution dynamics and equilibrium behaviour in a number of accessible situations, such as quadratic fitness landscapes and the Kimura 2 parameter mutation scheme.

cond-mat.stat-mech↗

arXiv1998

Aperiodic and correlated disorder in XY-chains: exact results

We study thermodynamic properties, specific heat and susceptibility, of XY quantum chains with coupling constants following arbitrary substitution rules. Generalizing an exact renormalization group transformation, originally formulated for Ising quantum chains, we obtain exact relevance criteria of Harris-Luck type for this class of models. For two-letter substitution rules, a detailed classification is given of sequences leading to irrelevant, marginal or relevant aperiodic modulations. We find that the relevance of the same aperiodic sequence of couplings in general will be different for XY and Ising quantum chains. By our method, continuously varying critical exponents may be calculated exactly for arbitrary (two-letter) substitution rules with marginal aperiodicity. A number of examples are given, including the period-doubling, three-folding and precious mean chains. We also discuss extensions of the renormalization approach to a special class of long-range correlated random chains, generated by random substitutions.

cond-mat.stat-mech↗

arXiv1998

Random Tilings: Concepts and Examples

We introduce a concept for random tilings which, comprising the conventional one, is also applicable to tiling ensembles without height representation. In particular, we focus on the random tiling entropy as a function of the tile densities. In this context, and under rather mild assumptions, we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble. Explicit examples are obtained through the re-interpretation of several exactly solvable models. This also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum.

cond-mat.stat-mech↗

arXiv1997

Aperiodic Ising Quantum Chains

Some years ago, Luck proposed a relevance criterion for the effect of aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In this article, we show how Luck's criterion can be derived within an exact renormalisation scheme for Ising quantum chains with coupling constants modulated according to substitution rules. Luck's conjectures for this case are confirmed and refined. Among other outcomes, we give an exact formula for the correlation length critical exponent for arbitrary two-letter substitution sequences with marginal fluctuations of the coupling constants.

cond-mat.stat-mech↗

arXiv1995

Bosonization of interacting fermions in arbitrary dimension beyond the Gaussian approximation

We use our recently developed functional bosonization approach to bosonize interacting fermions in arbitrary dimension $d$ beyond the Gaussian approximation. Even in $d=1$ the finite curvature of the energy dispersion at the Fermi surface gives rise to interactions between the bosons. In higher dimensions scattering processes describing momentum transfer between different patches on the Fermi surface (around-the-corner processes) are an additional source for corrections to the Gaussian approximation. We derive an explicit expression for the leading correction to the bosonized Hamiltonian and the irreducible self-energy of the bosonic propagator that takes the finite curvature as well as around-the-corner processes into account. In the special case that around-the-corner scattering is negligible, we show that the self-energy correction to the Gaussian propagator is negligible if the dimensionless quantities $ ( \frac{q_{c} }{ k_{F}} )^d F_{0} [ 1 + F_{0} ]^{-1} \fracμ{ν^α} | \frac{ \partial ν^α }{ \partial μ} |$ are small compared with unity for all patches $α$. Here $q_{c}$ is the cutoff of the interaction in wave-vector space, $k_{F}$ is the Fermi wave-vector, $μ$ is the chemical potential, $F_{0}$ is the usual dimensionless Landau interaction-parameter, and $ν^α $ is the {\it{local}} density of states associated with patch $α$. We also show that the well known cancellation between vertex- and self-energy corrections in one-dimensional systems, which is responsible for the fact that the random-phase approximation for the density-density correlation function is exact in $d=1$, exists also in $d> 1$, provided (1) the interaction cutoff $q_{c}$ is small compared with $k_{F}$, and (2) the energy dispersion is locally linearized at the Fermi the Fermi surface. Finally, we suggest a new systematic method to calculate corrections to the RPA, which is based on the perturbative calculation of the irreducible bosonic self-energy arising from the non-Gaussian terms of the bosonized Hamiltonian.

cond-mat↗