Related papers: Quantum mechanical formalism for biological evolut…
The present view of biological phenomena is based on a biochemical paradigm that development of living organisms is defined by information stored in a molecular form as some genetic code. However, new discoveries indicate that biological…
The problem of the rate and mechanisms of biological evolution was considered. It was shown that species could not be formed due to undirected mutations in characteristic times of about one million years. A mechanism of deterministic…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
We establish an analogy between the Fokker-Planck equation describing evolutionary landscape dynamics and the Schr\"{o}dinger equation which characterizes quantum mechanical particles, showing how a population with multiple genetic traits…
Each scheme of state reconstruction comes down to parametrize the state of a quantum system by expectation values or probabilities directly measurable in an experiment. It is argued that the time evolution of these quantities provides an…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We show that simple stochastic models of genome evolution lead to power law asymptotics of protein domain family size distribution. These models, called Birth, Death and Innovation Models (BDIM), represent a special class of balanced…
Stochastic models, based on random processes, may lead to power law distributions, which provide long range correlations. The observation of power law behavior and the presence of long range correlations in biological systems has been…
We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…
Quantum dynamics of the density operator in the framework of a single probability vector is analyzed. In this framework quantum states define a proper convex quantum subset in an appropriate simplex. It is showed that the corresponding…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
We review the statistical properties of the genealogies of a few models of evolution. In the asexual case, selection leads to coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
This paper considers a two-dimensional logistic model to study populations with two genders. The growth behavior of a population is guided by two coupled ordinary differential equations given by a non-differentiable vector field whose…
For the first time in history, humankind might conceivably begin to imagine itself as a multi-planetary species. This goal will entail technical innovation in a number of contexts, including that of healthcare. All life on Earth shares an…
By means of the examples of classical and Bohmian quantum mechanics, we illustrate the well-known ideas of Boltzmann as to how one gets from laws defined for the universe as a whole to dynamical relations describing the evolution of…