Many-body perturbation theory and fluctuation relations for interacting population dynamics

Information geometric bound on general chemical reaction networks

We investigate the convergence of chemical reaction networks (CRNs), aiming to establish an upper bound on their reaction rates. The nonlinear characteristics and discrete composition of CRNs pose significant challenges in this endeavor. To circumvent these complexities, we adopt an information geometric perspective, utilizing the natural gradient to formulate a nonlinear system. This system effectively determines an upper bound for the dynamics of CRNs. We corroborate our methodology through numerical simulations, which reveal that our constructed system converges more rapidly than CRNs within a particular class of reactions. This class is defined by the count of chemicals, the highest stoichiometric coefficients in the reactions, and the total number of reactions involved. Further, we juxtapose our approach with traditional methods, illustrating that the latter falls short in providing an upper bound for CRN reaction rates. Although our investigation centers on CRNs, the widespread presence of hypergraphs across various disciplines, ranging from natural sciences to engineering, indicates potential wider applications of our method, including in the realm of information science.

Sex as information processing: Optimality and evolution

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.