Related papers: Analysis of evolution through competitive selectio…
While Neutral Theory famously describes the number of discrete genetic differences in populations, we consider the number of genetic backgrounds under which such differences are observed - setting limits to the generalizability of their…
In a convergence of machine learning and biology, we reveal that diffusion models are evolutionary algorithms. By considering evolution as a denoising process and reversed evolution as diffusion, we mathematically demonstrate that diffusion…
We study the theory of systems with constraints from the point of view of the formal theory of partial differential equations. For finite-dimensional systems we show that the Dirac algorithm completes the equations of motion to an…
In this review some simple models of asexual populations evolving on smooth landscapes are studied. The basic model is based on a cellular automaton, which is analyzed here in the spatial mean-field limit. Firstly, the evolution on a fixed…
The evolution model with parallel mutation-selection scheme is solved for the case when selection is accompanied by base substitutions, insertions, and deletions. The fitness is assumed to be either a single-peak function (i.e., having one…
We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation…
This paper presents a general theory that aims at explaining timescales observed empirically in technology transitions and predicting those of future transitions. This framework is used further to derive a theory for exploring the dynamics…
The adaptive evolution of large asexual populations is generally characterized by competition between clones carrying different beneficial mutations. This interference phenomenon slows down the adaptation speed and makes the theoretical…
We consider a mutation-selection model of a population structured by the spatial variables and a trait variable which is the diffusion rate. Competition for resource is local in spatial variables, but nonlocal in the trait variable. We…
Possibility to establish macroscopic phenomenological theory for biological systems, akin to the akin to the well-established framework of thermodynamics, is briefly reviewed. We introduce the concept of an evolutionary fluctuation-response…
We considered a {multi-block} molecular model of biological evolution, in which fitness is a function of the mean types of alleles located at different parts (blocks) of the genome. We formulated an infinite population model with selection…
The modeling of time series is becoming increasingly critical in a wide variety of applications. Overall, data evolves by following different patterns, which are generally caused by different user behaviors. Given a time series, we define…
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:…
We apply the theory of learning to physically renormalizable systems in an attempt to develop a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution…
This brief discusses evolutionary game theory as a powerful and unified mathematical tool to study evolution of collective behaviours. It summarises some of my recent research directions using evolutionary game theory methods, which include…
We simulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves 1) the structure of the ground state, 2) its thermodynamic stability and 3) its kinetic accessibility. All other…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
This paper focuses on the maximum speed at which biological evolution can occur. I derive inequalities that limit the rate of evolutionary processes driven by natural selection, mutations, or genetic drift. These \emph{rate limits} link the…
All famous machine learning algorithms that comprise both supervised and semi-supervised learning work well only under a common assumption: the training and test data follow the same distribution. When the distribution changes, most…
Speciation is of fundamental importance to understanding the huge diversity of life on Earth. In contrast to current phenomenological models, we develop a biophysically motivated approach to study speciation involving the co-evolution of…