Diffusion on a hypercubic lattice with pinning potential: exact results for the error-catastrophe problem in biological evolution

In the theoretical biology framework one fundamental problem is the so-called error catastrophe in Darwinian evolution models. We reexamine Eigen's fundamental equations by mapping them into a polymer depinning transition problem in a ``genotype'' space represented by a unitary hypercubic lattice. The exact solution of the model shows that error catastrophe arises as a direct consequence of the equations involved and confirms some previous qualitative results. The physically relevant consequence is that such equations are not adequate to properly describe evolution of complex life on the Earth.Comment: 10 pages in LaTeX. Figures are available from the authors. [email protected] (e-mail address

Molecular Evolution in Time Dependent Environments

The quasispecies theory is studied for dynamic replication landscapes. A meaningful asymptotic quasispecies is defined for periodic time dependencies. The quasispecies' composition is constantly changing over the oscillation period. The error threshold moves towards the position of the time averaged landscape for high oscillation frequencies and follows the landscape closely for low oscillation frequencies.Comment: 5 pages, 3 figures, Latex, uses Springer documentclass llncs.cl

Global Fits of the CKM Matrix

We report upon the present status of global fits to Cabibbo-Kobayashi-Maskawa matrix.Comment: 3 pages, 3 figures invited talk presented at EPS conference, Aachen July 17-2

Eigen model as a quantum spin chain: exact dynamics

We map Eigen model of biological evolution [Naturwissenschaften {\bf 58}, 465 (1971)] into a one-dimensional quantum spin model with non-Hermitean Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.Comment: 10 pages. Physical Revew E vol. 69, in press (2004

Error Thresholds on Dynamic Fittness-Landscapes

In this paper we investigate error-thresholds on dynamics fitness-landscapes. We show that there exists both lower and an upper threshold, representing limits to the copying fidelity of simple replicators. The lower bound can be expressed as a correction term to the error-threshold present on a static landscape. The upper error-threshold is a new limit that only exists on dynamic fitness-landscapes. We also show that for long genomes on highly dynamic fitness-landscapes there exists a lower bound on the selection pressure needed to enable effective selection of genomes with superior fitness independent of mutation rates, i.e., there are distinct limits to the evolutionary parameters in dynamic environments.Comment: 5 page

Group selection models in prebiotic evolution

The evolution of enzyme production is studied analytically using ideas of the group selection theory for the evolution of altruistic behavior. In particular, we argue that the mathematical formulation of Wilson's structured deme model ({\it The Evolution of Populations and Communities}, Benjamin/Cumings, Menlo Park, 1980) is a mean-field approach in which the actual environment that a particular individual experiences is replaced by an {\it average} environment. That formalism is further developed so as to avoid the mean-field approximation and then applied to the problem of enzyme production in the prebiotic context, where the enzyme producer molecules play the altruists role while the molecules that benefit from the catalyst without paying its production cost play the non-altruists role. The effects of synergism (i.e., division of labor) as well as of mutations are also considered and the results of the equilibrium analysis are summarized in phase diagrams showing the regions of the space of parameters where the altruistic, non-altruistic and the coexistence regimes are stable. In general, those regions are delimitated by discontinuous transition lines which end at critical points.Comment: 22 pages, 10 figure

Measurement of the B Semileptonic Branching Fraction with Lepton Tags

We have used the CLEO II detector and 2.06fb^(-1) of ϒ(4S) data to measure the B-meson semileptonic branching fraction. The B→Xeν momentum spectrum was obtained over nearly the full momentum range by using charge and kinematic correlations in events with a high-momentum lepton tag and an additional electron. We find B(B→Xeν) = (10.49±0.17±0.43)%, with overall systematic uncertainties less than those of untagged single-lepton measurements. We use this result to calculate the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element V_(cb) and to set an upper limit on the fraction of ϒ(4S) decays to final states other than BB̅