The pace of evolution across fitness valleys

How fast does a population evolve from one fitness peak to another? We study the dynamics of evolving, asexually reproducing populations in which a certain number of mutations jointly confer a fitness advantage. We consider the time until a population has evolved from one fitness peak to another one with a higher fitness. The order of mutations can either be fixed or random. If the order of mutations is fixed, then the population follows a metaphorical ridge, a single path. If the order of mutations is arbitrary, then there are many ways to evolve to the higher fitness state. We address the time required for fixation in such scenarios and study how it is affected by the order of mutations, the population size, the fitness values and the mutation rate

Diffraction from Ordered States of Higher Multipoles

Possible ways of identification are discussed of an electronic order of higher multipoles such as octupoles and hexadecapoles. A particularly powerful method is resonant X-ray scattering (RXS) using quadrupolar resonance processes called E2.The characteristic azimuthal angle dependence of Ce$_{0.7}$La$_{0.3}$B$_6$ is interpreted as evidence of antiferro-octupole order. For PrRu$_4$P$_{12}$, eightfold pattern against azimuthal angle is predicted if its metal-insulator transition is a consequence of a hexadecapole order. In non-resonant superlattice Bragg scattering, hexadecapole contribution may also be identified because of absence of quadrupole component.Comment: Invited paper to be published in Proc. Hiroshima Workshop on Novel Functional Materials with Multinary Freedoms (Physica B, 2006

Electronic Orders Induced by Kondo Effect in Non-Kramers f-Electron Systems

This paper clarifies the microscopic nature of the staggered scalar order, which is specific to even number of f electrons per site. In such systems, crystalline electric field (CEF) can make a singlet ground state. As exchange interaction with conduction electrons increases, the CEF singlet at each site gives way to Kondo singlets. The collective Kondo singlets are identified with itinerant states that form energy bands. Near the boundary of itinerant and localized states, a new type of electronic order appears with staggered Kondo and CEF singlets. We present a phenomenological three-state model that qualitatively reproduces the characteristic phase diagram, which have been obtained numerically with use of the continuous-time quantum Monte Carlo combined with the dynamical mean-field theory. The scalar order observed in PrFe_4P_{12} is ascribed to this staggered order accompanying charge density wave (CDW) of conduction electrons. Accurate photoemission and tunneling spectroscopy should be able to probe sharp peaks below and above the Fermi level in the ordered phase.Comment: 7 pages, 8 figure

SIGNALING EFFICACY DRIVES THE EVOLUTION OF LARGER SEXUAL ORNAMENTS BY SEXUAL SELECTION.

Why are there so few small secondary sexual characters? Theoretical models predict that sexual selection should lead to reduction as often as exaggeration, and yet we mainly associate secondary sexual ornaments with exaggerated features such as the peacock's tail. We review the literature on mate choice experiments for evidence of reduced sexual traits. This shows that reduced ornamentation is effectively impossible in certain types of ornamental traits (behavioral, pheromonal, or color-based traits, and morphological ornaments for which the natural selection optimum is no trait), but that there are many examples of morphological traits that would permit reduction. Yet small sexual traits are very rarely seen. We analyze a simple mathematical model of Fisher's runaway process (the null model for sexual selection). Our analysis shows that the imbalance cannot be wholly explained by larger ornaments being less costly than smaller ornaments, nor by preferences for larger ornaments being less costly than preferences for smaller ornaments. Instead, we suggest that asymmetry in signaling efficacy limits runaway to trait exaggeration

Cell-cell signalling in sexual chemotaxis: a basis for gametic differentiation, mating types and sexes

While sex requires two parents, there is no obvious need for them to be differentiated into distinct mating types or sexes. Yet this is the predominate state of nature. Here, we argue that mating types could play a decisive role because they prevent the apparent inevitability of self-stimulation during sexual signalling. We rigorously assess this hypothesis by developing a model for signaller-detector dynamics based on chemical diffusion, chemotaxis and cell movement. Our model examines the conditions under which chemotaxis improves partner finding. Varying parameter values within ranges typical of protists and their environments, we show that simultaneous secretion and detection of a single chemoattractant can cause a multifold movement impediment and severely hinder mate finding. Mutually exclusive roles result in faster pair formation, even when cells conferring the same roles cannot pair up. This arrangement also allows the separate mating types to optimize their signalling or detecting roles, which is effectively impossible for cells that are both secretors and detectors. Our findings suggest that asymmetric roles in sexual chemotaxis (and possibly other forms of sexual signalling) are crucial, even without morphological differences, and may underlie the evolution of gametic differentiation among both mating types and sexes

The Fastest Evolutionary Trajectory

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.MathematicsOrganismic and Evolutionary Biolog

Normal zone in YBa2Cu3O6+xYBa_2Cu_3O_{6+x}-coated conductors

We consider the distribution of an electric field in YBCO-coated conductors for a situation in which the DC transport current is forced into the copper stabilizer due to a weak link -- a section of the superconducting film with a critical current less than the transport current. The electric field in the metal substrate is also discussed. The results are compared with recent experiments on normal zone propagation in coated conductors for which the substrate and stabilizer are insulated from each other. The potential difference between the substrate and stabilizer, and the electric field in the substrate outside the normal zone can be accounted for by a large screening length in the substrate, comparable to the length of the sample. During a quench, the electric field inside the interface between YBCO and stabilizer, as well as in the buffer layer, can be several orders of magnitude greater than the longitudinal macroscopic electric field inside the normal zone. We speculate on the possibility of using possible microscopic electric discharges caused by this large ($\sim$kV/cm) electric field as a means to detect a quench.Comment: 8 pages, 4 figure

Solution of reduced equations derived with singular perturbation methods

For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the normal form method, center manifold theory, the renormalization group method are well known. In this paper, it is shown that all of the solutions of the reduced equations constructed with those methods are exactly equal to sum of the most divergent secular terms appearing in the naive expansion. For the proof, a method to construct a perturbation solution which differs from the conventional one is presented, where we make use of the theory of Lie symmetry group.Comment: To be published in Phys. Rev.