Evolutionary dynamics, intrinsic noise and cycles of co-operation

We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of amplification of demographic noise can give rise to coherent oscillations in parameter regimes where deterministic descriptions converge to fixed points with complex eigenvalues. These quasi-cycles between co-operation and defection have previously been observed in computer simulations; here we provide a systematic and comprehensive analytical characterization of their properties. We are able to predict their power spectra as a function of the mutation rate and other model parameters, and to compare the relative magnitude of the cycles induced by different types of underlying microscopic dynamics. We also extend our analysis to the iterated prisoner's dilemma game with a win-stay lose-shift strategy, appropriate in situations where players are subject to errors of the trembling-hand type.Comment: 14 pages, 12 figures, accepted for publication by Phys. Rev.

Inertial effects in three dimensional spinodal decomposition of a symmetric binary fluid mixture: A lattice Boltzmann study

The late-stage demixing following spinodal decomposition of a three-dimensional symmetric binary fluid mixture is studied numerically, using a thermodynamicaly consistent lattice Boltzmann method. We combine results from simulations with different numerical parameters to obtain an unprecendented range of length and time scales when expressed in reduced physical units. Using eight large (256^3) runs, the resulting composite graph of reduced domain size l against reduced time t covers 1 < l < 10^5, 10 < t < 10^8. Our data is consistent with the dynamical scaling hypothesis, that l(t) is a universal scaling curve. We give the first detailed statistical analysis of fluid motion, rather than just domain evolution, in simulations of this kind, and introduce scaling plots for several quantities derived from the fluid velocity and velocity gradient fields.Comment: 49 pages, latex, J. Fluid Mech. style, 48 embedded eps figs plus 6 colour jpegs for Fig 10 on p.2

Carbon isotope discrimination and water stress in trembling aspen following variable retention harvesting

Variable retention harvesting (VRH) has been proposed as a silvicultural practice to maintain biodiversity and ecosystem integrity. No previous study has examined tree carbon isotope discrimination to provide insights into water stress that could lead to dieback and mortality of trees following VRH. We measured and compared the carbon isotope ratios (δ13C) in stem wood of trembling aspen (Populus tremuloides Michx.) before and after VRH. Eight trees were sampled from isolated residual, edge and control (interior of unharvested stand) positions from each of seven plots in three regions (Calling Lake and Drayton Valley, Alberta and Lac Duparquet, Qu

Theoretical calculations of solvent effects on the adsorption of linear molecules using the multilayer lattice model

Ash, Everett, and Findenegg's model for multilayer polymer adsorption was modified to handle solvent effects upon adsorption behavior. Some of the assumptions of the model are: (1) the segments of the polymer and the solvent monomer are approximately the same size, (2) the segments of the polymer and the solvent monomer occupy only the lattice points of a given geometrical array (close-packed hexagonal) ; (3) the energies of interaction between nonbonded segments are angularly independent, are additive in nature, and extend no further than the nearest neighbors; and (4) the surface has a homogeneous interaction energy for each segment type.The specific polymers examined were the asymmetric dimer (A-B) and the asymmetric tetramer (A-B-B-B) in a solvent (C).Parameters required for computer calculations were the nearest neighbor energies of interaction between all combinations of nonbonded segment pairs (A, A; B, B; C, C; A, B; A, C; and B, C) and interaction energies between the surface and each segment type in each layer near the surface. Analyses were made for the effects of each of these parameters on the surface excess, and on the energy, entropy, and number of each molecular configuration in each layer near the surface.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22027/1/0000444.pd

Tests of Dynamical Scaling in 3-D Spinodal Decomposition

We simulate late-stage coarsening of a 3-D symmetric binary fluid. With reduced units l,t (with scales set by viscosity, density and surface tension) our data extends two decades in t beyond earlier work. Across at least four decades, our own and others' individual datasets (< 1 decade each) show viscous hydrodynamic scaling (l ~ a + b t), but b is not constant between runs as this scaling demands. This betrays either the unexpected intrusion of a discretization (or molecular) lengthscale, or an exceptionally slow crossover between viscous and inertial regimes.Comment: Submitted to Phys. Rev.

3D Spinodal Decomposition in the Inertial Regime

We simulate late-stage coarsening of a 3D symmetric binary fluid using a lattice Boltzmann method. With reduced lengths and times l and t respectively (scales set by viscosity, density and surface tension) our data sets cover 1 < l 100 we find clear evidence of Furukawa's inertial scaling (l ~ t^{2/3}), although the crossover from the viscous regime (l ~ t) is very broad. Though it cannot be ruled out, we find no indication that Re is self-limiting (l ~ t^{1/2}) as proposed by M. Grant and K. R. Elder [Phys. Rev. Lett. 82, 14 (1999)].Comment: 4 pages, 3 eps figures, RevTex, minor changes to bring in line with published version. Mobility values added to Table

Notes on the behaviour, plumage and distribution of the White-tailed Swallow Hirundo megaensis

The White-tailed Swallow Hirundo megaensis is a threatened and poorly known bird endemic to southern Ethiopia, where it is restricted to a small area of Acacia savanna. Despite the paucity of previous nest records, we found 67 nests in the years 2010–14, commonly in village huts lived in by people, and report the first confirmation of nesting (two certain records) in termite mounds. Its nests are small mud cups lined with grass and animal hair, fixed to roof joists and similar to those of its sister species, the Pearl-breasted Swallow H. dimidiata of southern Africa, although it appears to lay larger clutches (3–4 pure white eggs) and breed less frequently, producing one brood in each of its two rain-driven breeding seasons (April–June and October–November). The same nests are reportedly used in these two seasons, presumably by the same pairs. Incubation lasts 16–17 days, with some broods showing clearly smaller chicks and hence presumably asynchronous hatching. Study of nestlings in the hand and museum skins confirmed that juveniles can be determined by their shorter tails, browner heads and frequently also wings, and reduced white in the tail. Although birds are typically seen singly or in pairs, flocks of up to 50, sometimes mixed with other hirundines, can occur. The breeding range appears to be almost identical to that of the Ethiopian Bush-crow Zavattariornis stresemanni but regular sightings of White-tailed Swallows since 2005 at the Liben Plain, 120 km to the east of the core area, suggest that the birds are frequent visitors there.We are grateful to the numerous funding bodies which have supported this research over several years: NERC, RSPB, British Birdfair, African Bird Club, British Ornithologists’ Union, Gesellschaft für Tropenornithologie, Tim Whitmore Zoology Fund, Magdalene College (Cambridge), Cambridge Philosophical Society, and BirdLife Preventing Extinctions Programme; and especially to Julian Francis. We also thank Robert Prys-Jones at the Natural History Museum (NHMUK) for access to specimens; Les Colley for his photograph used in Fig. 5; Stefanie Rick for her excellent drawings used in Fig. 9; Steve Rooke (Sunbird Tours), Bernard, Willem and Sjoerd Oosterbaan, Simon Busuttil, Merid Gabremichael and Claire Spottiswoode for providing additional information and sightings; Alazar Dakar, Abiy Dange, Birhan Dessalegn, Solomon Desta, Okotu Dida, Ali Guche, Sam Jones, Gufu Kashina, Stuart Marsden, Tesfaye Mekonnen, Samson Zelleke and many others including all the staff of Borana National Park for help with fieldwork; Angela Turner and John Atkins for their services as referees; and the Borana villagers who so kindly allowed us into their homes to study the White-tailed Swallow’s nests and without whose hospitality our knowledge of this species would be much poorer.This is the author accepted manuscript. The final version is available from African Bird Club

Entropy-induced smectic phases in rod-coil copolymers

We present a self-consistent field theory (SCFT) of semiflexible (wormlike) diblock copolymers, each consisting of a rigid and a flexible part. The segments of the polymers are otherwise identical, in particular with regard to their interactions, which are taken to be of an Onsager excluded-volume type. The theory is developed in a general three-dimensional form, as well as in a simpler one-dimensional version. Using the latter, we demonstrate that the theory predicts the formation of a partial-bilayer smectic-A phase in this system, as shown by profiles of the local density and orientational distribution functions. The phase diagram of the system, which includes the isotropic and nematic phases, is obtained in terms of the mean density and rigid-rod fraction of each molecule. The nematic-smectic transition is found to be second order. Since the smectic phase is induced solely by the difference in the rigidities, the onset of smectic ordering is shown to be an entropic effect and therefore does not have to rely on additional Flory-Huggins-type repulsive interactions between unlike chain segments. These findings are compared with other recent SCFT studies of similar copolymer models and with computer simulations of several molecular models.Comment: 13 pages, 8 figure