Anton S. Zadorin’s research while affiliated with ESPCI Paris and other places

Phenotypes are partly shaped by the environment, which can impact both short-term adaptation and long-term evolution. In dioecious species, the two sexes may exhibit different degrees of phenotypic plasticity and theoretical models indicate that such differences may confer an adaptive advantage when the population is subject to directional selection, either because of a systematically varying environment or a load of deleterious mutations. The effect stems from the fundamental asymmetry between the two sexes: female fertility is more limited than male fertility. Whether this asymmetry is sufficient for sexual dimorphism in phenotypic plasticity to evolve is, however, not obvious. Here, we show that even in conditions where it provides an adaptive advantage, dimorphic phenotypic plasticity may be evolutionarily unstable due to sexual selection. This is the case, in particular, for panmictic populations where mating partnerships are formed at random. However, we show that the effects of sexual selection can be counteracted when mating occurs within groups of related individuals. Under this condition, sexual dimorphism in phenotypic plasticity can not only evolve but offset the twofold cost of males. We demonstrate these points with a simple mathematical model through a combination of analytical and numerical results.

Phenotypes are partly shaped by the environment, which can impact both short- term adaptation and long-term evolution. In dioecious species, the two sexes may exhibit different degrees of phenotypic plasticity and theoretical models indicate that such differences may confer an adaptive advantage when the population is subject to directional selection, either because of a systematically varying environment or of a load of deleterious mutations. The effect stems from the fundamental asymmetry between the two sexes: female fertility is more limited than male fertility. Whether this asymmetry is sufficient for sexual dimorphism in phenotypic plasticity to evolve is, however, not obvious. Here, we show that even in conditions where it provides an adaptive advantage, dimorphic phenotypic plasticity may be evolutionarily unstable due to sexual selection. This is the case, in particular, for panmictic populations where mating partners are formed at random. However, we show that the effects of sexual selection can be counteracted when mating occurs within groups of related individuals. Under this condition, sexual dimorphism in phenotypic plasticity can not only evolve but offset the twofold cost of males. We demonstrate these points with a simple mathematical model through a combination of analytical and numerical results.

A generalisation of reaction diffusion systems and their travelling solutions to cases when the productive part of the reaction happens only on a surface in space or on a line on plane but the degradation and the diffusion happen in bulk are important for modelling various biological processes. These include problems of invasive species propagation along boundaries of ecozones, problems of gene spread in such situations, morphogenesis in cavities, intracellular reaction etc. Piecewise linear approximations of reaction terms in reaction-diffusion systems often result in exact solutions of propagation front problems. This article presents an exact travelling solution for a reaction-diffusion system with a piecewise constant production restricted to a codimension-1 subset. The solution is monotone, propagates with the unique constant velocity, and connects the trivial solution to a nontrivial nonhomogeneous stationary solution of the problem. The properties of the solution closely parallel the properties of monotone travelling solutions in classical bistable reaction-diffusion systems.

The long-term growth rate of populations in varying environments quantifies the evolutionary value of processing the information that biological individuals inherit from their ancestors and acquire from their environment. Previous models were limited to asexual reproduction with inherited information coming from a single parent with no recombination. We present a general extension to sexual reproduction and an analytical solution for a particular but important case, the infinitesimal model of quantitative genetics which assumes traits to be normally distributed. We study with this model the conditions under which sexual reproduction is advantageous and can evolve in the context of autocorrelated or directionally varying environments, mutational biases, spatial heterogeneities, and phenotypic plasticity. Our results generalize and unify previous analyses. We also examine the proposal made by Geodakyan that the presence of two phenotypically distinct sexes permits an optimal adaptation to varying environments. We verify that conditions exists where sexual dimorphism is adaptive but find that its evolutionary value does not generally compensate for the twofold cost of males.

Models of asexually reproducing populations in varying environments have provided insights into the diversity of adaptive strategies, revealed deep analogies with information theory and stochastic thermodynamics, and inspired quantitative methods to analyze single-cell experiments. Here we show how these models can be generalized to sexually reproducing populations. The resulting framework is applied to two fundamental questions. First, what are the conditions under which sexual reproduction is advantageous over asexual reproduction? Second, what are the conditions under which sexual dimorphism, the presence of two phenotypically distinct sexes, is advantageous? We study these questions from the two standpoints of optimal information processing and evolvability. Our analysis provides a new perspective on long-standing problems as well as fresh insights into unexamined questions. More generally, it opens the door to novel interdisciplinary approaches to a central problem of evolutionary biology, the role of sex in adaptation.

We introduce a novel iterative eigenvalue algorithm for near-diagonal matrices termed \textit{iterative perturbative theory} (IPT). Built upon a "perturbative" partitioning of the matrix into diagonal and off-diagonal parts, IPT has the complexity of one matrix-vector (when one eigenpair is requested) or one matrix-matrix multiplication (when all eigenpairs are requested) per iteration. Thanks to the high parallelism of these basic linear algebra operations, we obtain excellent performance on multi-core processors and GPUs, with large speed-ups over standard methods (up to $\sim50$x with respect to LAPACK and ARPACK, $\sim5$x with respect to Davidson). When off-diagonal elements are comparable to eigengaps, IPT diverges like the quadratic map outside the Mandelbrot set; for such general matrices IPT can nevertheless be used to refine low-precision eigenvectors obtained by other methods. We give sufficient conditions for linear convergence and demonstrate performance on dense and sparse test matrices.

Many problems in physics, chemistry and other fields are perturbative in nature, i.e. differ only slightly from related problems with known solutions. Prominent among these is the eigenvalue perturbation problem, wherein one seeks the eigenvectors and eigenvalues of a matrix with small off-diagonal elements. Here we introduce a novel iterative algorithm to compute these eigenpairs based on a reformulation of the eigenvalue problem as an algebraic equation in complex projective space. We show from explicit and numerical examples that our algorithm outperforms the usual Rayleigh-Schr\"odinger expansion on three counts. First, since it is not defined as a power series, its domain of convergence is not a priori confined to a disk in the complex plane; we find that it indeed usually extends beyond the standard perturbative radius of convergence. Second, it converges at a faster slower rate than the Rayleigh-Schr\"odinger expansion, i.e. fewer iterations are required to reach a given precision. Third, the (time- and space-) algorithmic complexity of each iteration does not increase with the order of the approximation, allowing for higher precision computations. Because this complexity is merely that of matrix multiplication, our dynamical scheme also scales better with the size of the matrix than general-purpose eigenvalue routines such as the shifted QR or divide-and-conquer algorithms. Whether they are dense, sparse, symmetric or unsymmetric, we confirm that dynamical diagonalization quickly outpaces LAPACK drivers as the size of matrices grows; for the computation of just the dominant eigenvector, our method converges order of magnitudes faster than the Arnoldi algorithm implemented in ARPACK.

High-throughput, in vitro approaches for the evolution of enzymes rely on a random micro-encapsulation to link phenotypes to genotypes, followed by screening or selection steps. In order to optimise these approaches, or compare one to another, one needs a measure of their performance at extracting the best variants of a library. Here, we introduce a new metric, the Selection Quality Index (SQI), which can be computed from a simple mock experiment, performed with a known initial fraction of active variants. In contrast to previous approaches, our index integrates the effect of random co-encapsulation, and comes with a straightforward experimental interpretation. We further show how this new metric can be used to extract general protocol efficiency trends or reveal hidden selection mechanisms such as a counterintuitive form of beneficial poisoning in the compartmentalized self-replication protocol.

The emerging field of compartmentalized in vitro evolution, where selection is carried out by differential reproduction in each compartment, is a promising new approach to protein engineering. From practical point of view, it is important to know the effect of the increase in the average number of genotype bearing agents per compartment. This effect is also interesting on its own in the context of primordial evolution in the hypothetical RNA world. The question is important as genotypes with different phenotypes in the same compartment share their fitness (the number of produced copies) rendering the selection frequency-dependent. We carried out a theoretical investigation of this problem in the context of selection dynamics for a simple model with an infinite population that is periodically redistributed among infinite number of identical compartments, inside which all molecules are copied without distinction with the success rate as a function of the total genomic composition in the compartment. Using the obtained update equation, we demonstrated that, for the linear additive fitness function, the best genotype is still selected regardless of the average number of individuals per compartment. Furthermore, the selection process is slowed down approximately inversely proportional to this number. We also derived more general expressions that cover nonadditive fitness and non-Poissonian distribution among compartments.