arXiv subjects

Guillaume Achaz

Publications and source records attributed to Guillaume Achaz.

9 recordsLinked to original sources

arXiv2026

Epistatic strength, modularity, and locus heterogeneity shape the number of local optima in fitness landscapes

Fitness landscapes provide a quantitative framework for understanding how natural selection shapes evolutionary trajectories. A central feature of these landscapes is their number of local optima, which determines whether fitness-increasing evolution can proceed towards a global optimum or become trapped on suboptimal peaks. Although multiple peaks are known to require reciprocal sign epistasis, the quantitative relationship between epistasis and number of peaks remains incompletely understood. Here, we show that for a broad class of unstructured fitness landscapes, i.e. isotropic Gaussian random fields, the expected number of local optima is determined by a single local measure of epistasis: the correlation of fitness effects. This provides a baseline prediction for the number of peaks in typical unstructured landscapes and links peak density directly to the amount of reciprocal sign epistasis. This baseline changes when epistatic interactions are structured. We show that clustering interactions within blocks of loci slightly increases the number of local optima. In contrast, strong heterogeneity between loci, where only a small subset of loci participate in epistatic interactions, causes the number of peaks to collapse. These results show that the number of local optima is governed not only by the overall strength of epistasis, but also by how epistatic interactions are distributed across the genotype space. Our framework therefore reconciles the central role of reciprocal sign epistasis with the observation that landscapes with similar amounts of epistasis can differ substantially in ruggedness, and provides a guide to the range of peak numbers expected in typical landscapes.

q-bio.PE↗

arXiv2026

Simple sign epistasis and evolutionary detours in fitness landscapes

In epistatic fitness landscapes, the fitness effect of a mutation depends on the genetic background and may even switch between deleterious and beneficial depending on the presence of another mutation. Epistatic interactions may cause both mutations to change the sign of each other's fitness effects (reciprocal sign epistasis) or only one mutation to do so (simple sign epistasis). Both these forms of epistasis influence evolutionary trajectories. While reciprocal sign epistasis has been associated with multi-peaked landscapes and their ruggedness, the role and relative frequency of simple sign epistasis in fitness landscapes have not been systematically investigated. Here, we prove that the presence of simple sign epistasis is associated with evolutionary detours, i.e., indirect, longer fitness-increasing paths to fitness peaks that include back-mutations. We also show that in experimentally resolved, weakly epistatic landscapes, simple sign epistasis occurs much more frequently than reciprocal sign epistasis. This result is consistent with the theoretical predictions we derive for most landscape models, with the exception of the block model and of landscapes dominated by pairwise allelic incompatibilities, such as RNA stability landscapes. Our results suggest that detours represent a general feature of evolutionary trajectories in weakly epistatic landscapes.

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arXiv2021

An appeal for an open scientific debate about the proximal origin of SARS-CoV-2

One year after the onset of the COVID-19 pandemic, the origin of SARS-CoV-2 still eludes humanity. Early publications firmly stated that the virus was of natural origin, and the possibility that the virus might have escaped from a lab was discarded in most subsequent publications. However, based on a re-analysis of the initial arguments, highlighted by the current knowledge about the virus, we show that the natural origin is not supported by conclusive arguments, and that a lab origin cannot be formally discarded. We call for an opening of peer-reviewed journals to a rational, evidence-based and prejudice-free evaluation of all the reasonable hypotheses about the virus' origin. We advocate that this debate should take place in the columns of renowned scientific journals, rather than being left to social media and newspapers.

q-bio.OT↗

arXiv2021

Correlated evolution: models and methods

In this article, we review the different models and methods to understand and estimate correlated evolution within the same genome, individual or species. We describe correlated evolution among traits, among genetic components and finally between traits and genetics.

q-bio.PE↗

arXiv2018

The sequential loss of allelic diversity

This paper gives a new flavor of what Peter Jagers and his co-authors call `the path to extinction'. In a neutral population with constant size $N$, we assume that each individual at time $0$ carries a distinct type, or allele. We consider the joint dynamics of these $N$ alleles, for example the dynamics of their respective frequencies and more plainly the nonincreasing process counting the number of alleles remaining by time $t$. We call this process the extinction process. We show that in the Moran model, the extinction process is distributed as the process counting (in backward time) the number of common ancestors to the whole population, also known as the block counting process of the $N$-Kingman coalescent. Stimulated by this result, we investigate: (1) whether it extends to an identity between the frequencies of blocks in the Kingman coalescent and the frequencies of alleles in the extinction process, both evaluated at jump times; (2) whether it extends to the general case of $Λ$-Fleming-Viot processes.

math.PR↗

arXiv2017

Decomposing the site frequency spectrum: the impact of tree topology on neutrality tests

We investigate the dependence of the site frequency spectrum (SFS) on the topological structure of genealogical trees. We show that basic population genetic statistics - for instance estimators of $θ$ or neutrality tests such as Tajima's $D$ - can be decomposed into components of waiting times between coalescent events and of tree topology. Our results clarify the relative impact of the two components on these statistics. We provide a rigorous interpretation of positive or negative values of an important class of neutrality tests in terms of the underlying tree shape. In particular, we show that values of Tajima's $D$ and Fay and Wu's $H$ depend in a direct way on a peculiar measure of tree balance which is mostly determined by the root balance of the tree. We present a new test for selection in the same class as Fay and Wu's $H$ and discuss its interpretation and power. Finally, we determine the trees corresponding to extreme expected values of these neutrality tests and present formulae for these extreme values as a function of sample size and number of segregating sites.

q-bio.PE↗

arXiv2017

The expected neutral frequency spectrum of linked sites

We present an exact, closed expression for the expected neutral Site Frequency Spectrum for two neutral sites, 2-SFS, without recombination. This spectrum is the immediate extension of the well known single site $θ/f$ neutral SFS. Similar formulae are also provided for the case of the expected SFS of sites that are linked to a focal neutral mutation of known frequency. Formulae for finite samples are obtained by coalescent methods and remarkably simple expressions are derived for the SFS of a large population, which are also solutions of the multi-allelic Kolmogorov equations. Besides the general interest of these new spectra, they relate to interesting biological cases such as structural variants and introgressions. As an example, we present the expected neutral frequency spectrum of regions with a chromosomal inversion.

q-bio.PE↗

arXiv2015

Epistasis and constraints in fitness landscapes

Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness landscapes are high-dimensional, their characterization relies on simple measures of their structure, which can be used as statistics in empirical applications. Here we propose two new sets of measures that explicitly capture two relevant features of fitness landscapes: epistasis and constraints. The first set contains new measures for epistasis based on the correlation of fitness effects of mutations. They have a natural interpretation, capture well the interaction between mutations, can be obtained analytically for most landscape models and can therefore be used to discriminate between different models. The second set contains measures of evolutionary constraints based on "chains" of forced mutations along fitness-increasing paths. Some of these measures are non-monotonic in the amount of epistatic interactions, but have instead a maximum for intermediate values. We further characterize the relationships of these measures to the ones that were previous proposed (e.g. number of peaks, roughness/slope, fraction of non-additive components, etc). Finally, we show how these measures can help uncovering the amount and the nature of epistatic interactions in two experimental landscapes.

q-bio.PE↗

arXiv2014

Properties of selected mutations and genotypic landscapes under Fisher's Geometric Model

The fitness landscape - the mapping between genotypes and fitness - determines properties of the process of adaptation. Several small genetic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here we generate several testable predictions for the properties of these landscapes under Fisher's geometric model of adaptation (FGMA). When far from the fitness optimum, we analytically compute the fitness effect of beneficial mutations and their epistatic interactions. We show that epistasis may be negative or positive on average depending on the distance of the ancestral genotype to the optimum and whether mutations were independently selected or co-selected in an adaptive walk. Using simulations, we show that genetic landscapes built from FGMA are very close to an additive landscape when the ancestral strain is far from the optimum. However, when close to the optimum, a large diversity of landscape with substantial ruggedness and sign epistasis emerged. Strikingly, landscapes built from different realizations of stochastic adaptive walks in the same exact conditions were highly variable, suggesting that several realizations of small genetic landscapes are needed to gain information about the underlying architecture of the global adaptive landscape.

q-bio.PE↗