An exactly solvable coarse-grained model for species diversity

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results of ecological neutral theory and empirical evidence on species diversity preservation. Neutral model of biodiversity deals with ecosystems in the same trophic level where per-capita vital rates are assumed to be species-independent. Close-form analytical solutions for neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain: the probability distribution function of the number of species in the ecosystem both in transient and stationary states; the n-points connected time correlation function; and the survival probability, definned as the distribution of time-spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from a estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications on biodiversity and conservation biology.Comment: 20 pages, 4 figures. To appear in Journal of Statistichal Mechanic

Magnetization and Magnetotransport of LnBaCo2O5.5 (Ln=Gd, Eu) Single Crystals

The magnetization, resistivity and magnetoresistance (MR) of single crystals of GdBaCo2O5.5 and EuBaCo2O5.5 are measured over a wide range of dc magnetic fields (up to 30 T) and temperature. In LnBaCo2O5.5 (Ln=Gd, Eu), the Co-ions are trivalent and can exist in three spin states, namely, the S=0 low spin state (LS), the S= 1 intermediate spin state (IS) and the S=2 high spin state (HS). We confirm that GdBaCo2O5.5 and EuBaCo2O5.5 have a metal-insulator transition accompanied by a spin-state transition at TMI >> 365 and 335 K, respectively. The data suggest an equal ratio of LS (S=0) and IS (S=1) Co3+ ions below TMI, with no indication of additional spin state transitions. The low field magnetization shows a transition to a highly anisotropic ferromagnetic phase at 270 K, followed by another magnetic transition to an antiferromagnetic phase at a slightly lower temperature. The magnetization data are suggestive of weak correlations between the Gd-spins but no clear signature of ordering is seen for T > 2 K. Significant anisotropy between the a-b plane and c axis was observed in magnetic and magnetotransport properties for both compounds. For GdBaCo2O5.5, the resistivity and MR data imply a strong correlation between the spin-order and charge carriers. For EuBaCo2O5.5, the magnetic phase diagram is very similar to its Gd counterpart, but the low-T MR with current flow in the ab plane is positive rather than negative as for Gd. The magnitude and the hysteresis of the MR for EuBaCo2O5.5 decrease with increasing temperature, and at higher T the MR changes sign and becomes negative. The difference in the behavior of both compounds may arise from a small valence admixture in the nonmagnetic Eu ions, i.e. a valence slightly less than 3+.Comment: Accepted for publication in PR

Random copying in space

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.Comment: 26 pages, 11 figures. Based on invited talk at AHRC CECD Conference on "Cultural Evolution in Spatially Structured Populations" at UCL, September 2010. To appear in ACS - Advances in Complex System

Feminism, Abortion and Disability: irreconcilable differences?

There has been considerable discussion of the political allegiance between the feminist and disability movements, but the question of abortion remains a thorny one. Disability rights advocates have been keen to demonstrate that it is possible to believe in a woman's right to sovereignty over the body and, yet, be opposed to the selective abortion of an impaired foetus – describing the latter as a form of 'weak' eugenics. The aim of this paper is to show that whilst there may be some points of agreement between the feminist and disability movements on the question of abortion, there exist fundamental and irreconcilable differences

Voter Model with Time dependent Flip-rates

We introduce time variation in the flip-rates of the Voter Model. This type of generalisation is relevant to models of ageing in language change, allowing the representation of changes in speakers' learning rates over their lifetime and may be applied to any other similar model in which interaction rates at the microscopic level change with time. The mean time taken to reach consensus varies in a nontrivial way with the rate of change of the flip-rates, varying between bounds given by the mean consensus times for static homogeneous (the original Voter Model) and static heterogeneous flip-rates. By considering the mean time between interactions for each agent, we derive excellent estimates of the mean consensus times and exit probabilities for any time scale of flip-rate variation. The scaling of consensus times with population size on complex networks is correctly predicted, and is as would be expected for the ordinary voter model. Heterogeneity in the initial distribution of opinions has a strong effect, considerably reducing the mean time to consensus, while increasing the probability of survival of the opinion which initially occupies the most slowly changing agents. The mean times to reach consensus for different states are very different. An opinion originally held by the fastest changing agents has a smaller chance to succeed, and takes much longer to do so than an evenly distributed opinion.Comment: 16 pages, 6 figure

Exact Solution for the Time Evolution of Network Rewiring Models

We consider the rewiring of a bipartite graph using a mixture of random and preferential attachment. The full mean field equations for the degree distribution and its generating function are given. The exact solution of these equations for all finite parameter values at any time is found in terms of standard functions. It is demonstrated that these solutions are an excellent fit to numerical simulations of the model. We discuss the relationship between our model and several others in the literature including examples of Urn, Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem and some models of zero range processes. Our model is also equivalent to those used in various applications including cultural transmission, family name and gene frequencies, glasses, and wealth distributions. Finally some Voter models and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E versio

Fixation and consensus times on a network: a unified approach

We investigate a set of stochastic models of biodiversity, population genetics, language evolution and opinion dynamics on a network within a common framework. Each node has a state, 0 < x_i < 1, with interactions specified by strengths m_{ij}. For any set of m_{ij} we derive an approximate expression for the mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in a case relevant to language change this time is independent of the network structure.Comment: 4+epsilon pages, two-column, RevTeX4, 3 eps figures; version accepted by Phys. Rev. Let

Adaptive evolution of molecular phenotypes

Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a quantitative trait under time-dependent selection, which arises from environmental changes or through fitness interactions with other co-evolving phenotypes. We analyze a model of trait evolution under mutations and genetic drift in a single-peak fitness seascape. The fitness peak performs a constrained random walk in the trait amplitude, which determines the time-dependent trait optimum in a given population. We derive analytical expressions for the distribution of the time-dependent trait divergence between populations and of the trait diversity within populations. Based on this solution, we develop a method to infer adaptive evolution of quantitative traits. Specifically, we show that the ratio of the average trait divergence and the diversity is a universal function of evolutionary time, which predicts the stabilizing strength and the driving rate of the fitness seascape. From an information-theoretic point of view, this function measures the macro-evolutionary entropy in a population ensemble, which determines the predictability of the evolutionary process. Our solution also quantifies two key characteristics of adapting populations: the cumulative fitness flux, which measures the total amount of adaptation, and the adaptive load, which is the fitness cost due to a population's lag behind the fitness peak.Comment: Figures are not optimally displayed in Firefo

Comprehensive Analysis of Coronal Mass Ejection Mass and Energy Properties Over a Full Solar Cycle

The LASCO coronagraphs, in continuous operation since 1995, have observed the evolution of the solar corona and coronal mass ejections (CMEs) over a full solar cycle with high quality images and regular cadence. This is the first time that such a dataset becomes available and constitutes a unique resource for the study of CMEs. In this paper, we present a comprehensive investigation of the solar cycle dependence on the CME mass and energy over a full solar cycle (1996-2009) including the first in-depth discussion of the mass and energy analysis methods and their associated errors. Our analysis provides several results worthy of further studies. It demonstrates the possible existence of two event classes; 'normal' CMEs reaching constant mass for $>10$ R_{\sun} and 'pseudo' CMEs which disappear in the C3 FOV. It shows that the mass and energy properties of CME reach constant levels, and therefore should be measured, only above \sim 10 R_\sun. The mass density (g/R_\sun^2) of CMEs varies relatively little ($<$ order of magnitude) suggesting that the majority of the mass originates from a small range in coronal heights. We find a sudden reduction in the CME mass in mid-2003 which may be related to a change in the electron content of the large scale corona and we uncover the presence of a six-month periodicity in the ejected mass from 2003 onwards.Comment: 42 pages, 16 figures, To appear in Astrophysical Journa

Renewing Teaching Practices: Differentiated Instruction in the College Classroom

At a time of high college student attrition rates, faculty who work in higher education settings are being challenged more than ever before with accountability for student learning. The purpose of this article is to share insights relative to a multi-year professional development initiative that provided college faculty with an opportunity to explore changes in their teaching. Over the course of three years, faculty members honed their knowledge, skills, and dispositions relative to a specific instructional strategy for their own classrooms: differentiated instruction. An experiential approach to the initiative was used, and the degree to which participants committed to change their own instructional practices was evaluated. Results indicated an encouraging degree of success, especially in technology integration, providing clear objectives and feedback to students, and enhanced student engagement