Related papers: The geometry of the Fisher selection dynamics
In biology, information flows from the environment to the genome by the process of natural selection. But it has not been clear precisely what sort of information metric properly describes natural selection. Here, I show that Fisher…
Fisher developed his geometric model to support the micro-mutationalism hypothesis which claims that small mutations are more likely to be beneficial and therefore to contribute to evolution and adaptation. While others have provided a…
Fisher's geometric model was originally introduced to argue that complex adaptations must occur in small steps because of pleiotropic constraints. When supplemented with the assumption of additivity of mutational effects on phenotypic…
Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
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…
Consider a mathematical model of evolutionary adaptation of fitness landscape and mutation matrix as a reaction to population changes. As a basis, we use an open quasispecies model, which is modified to include explicit death flow. We…
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and…
The fitness landscape defines the relationship between genotypes and fitness in a given environment, and underlies fundamental quantities such as the distribution of selection coefficient, or the magnitude and type of epistasis. A better…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
As artificial intelligence systems (AIs) become increasingly produced by recursive self-improvement, a form of evolution may emerge, with the traits of AI systems shaped by the success of earlier AIs in designing and propagating their…
Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…
Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a…
Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types, that elaborates this complexity, result from the activity of gene networks and…
Traditionally evolution is seen as a process where from a pool of possible variations of a population (e.g. biological species or industrial goods) a few variations get selected which survive and proliferate, whereas the others vanish.…
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This…
Geometric matching is a key step in computer vision tasks. Previous learning-based methods for geometric matching concentrate more on improving alignment quality, while we argue the importance of naturalness issue simultaneously. To deal…
We study competition between two biological species advected by a compressible velocity field. Individuals are treated as discrete Lagrangian particles that reproduce or die in a density-dependent fashion. In the absence of a velocity field…
Fisher's geometric model describes biological fitness landscapes by combining a linear map from the discrete space of genotypes to an $n$-dimensional Euclidean phenotype space with a nonlinear, single-peaked phenotype-fitness map. Genotypes…
We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…