A New Mechanism for Recurrent Adaptive Radiations

Models of adaptive radiation through intraspecific competition have attracted mounting attention. Here we show how extending such models in a simple manner, by including a quantitative trait under weak directional selection, naturally leads to rich macroevolutionary patterns involving recurrent adaptive radiations and extinctions. Extensive tests demonstrate the robustness of this finding to a wide range of variations in model assumptions. In particular, recurrent adaptive radiations and extinctions readily unfold both for asexual and for sexual populations. Since the mechanisms driving the investigated processes of endogenous diversification result from generic geometric features of the underlying fitness landscapes - frequency-dependent disruptive selection in one trait and weak directional selection in another - the reported phenomena can be expected to occur in a wide variety of eco-evolutionary settings

Evolutionary-branching lines and areas in bivariate trait spaces

Aims: Evolutionary branching is a process of evolutionary diversification induced by frequency-dependent ecological interaction. Here we show how to predict the occurrence of evolutionary branching in bivariate traits when populations are evolving directionally. Methods: Following adaptive dynamics theory, we assume low mutation rates and small mutational step sizes. On this basis, we generalize conditions for evolutionary-branching points to conditions for evolutionary-branching lines and areas, which delineate regions of trait space in which evolutionary branching can be expected despite populations still evolving directionally along these lines and within these areas. To assess the quality of predictions provided by our new conditions for evolutionary branching lines and areas, we analyse three eco-evolutionary models with bivariate trait spaces, comparing the predicted evolutionary- branching lines and areas with actual occurrences of evolutionary branching in numerically calculated evolutionry dynamics. In the three examples, a phenotype's fitness is affected by frequency-dependent resource competition and/or predator-prey interaction. Conclusions: In the limit of infinitesimal mutational step sizes, evolutionary branching in bivariate trait spaces can occur only at evolutionary-branching points, i.e., where the evolving population experiences disruptive selection in the absence of any directional selection. In contrast, when mutational step sizes are finite, evolutionary branching can occur also along evolutioary-branching lines, i.e., where disruptive selection orthogonal to these lines is sufficiently strong relative to directional selection along them. Moreover, such evolutionary- branching lines are embedded in evolutionary-branching areas, which delineate all bivariate trait combinations for which evolutionary branching can occur when mutation rates are low, while mutational step sizes are finite. Our analyses show that evolutionary-branching lines and areas are good indicators of evolutionary branching in directionally evolving populations. We also demonstrate that not all evolutionary-branching lines and areas contain evolutionary- branching points, so evolutionary branching is possible even in trait spaces that contain no evolutionary-branching point at all

Evolutionary branching in distorted trait spaces

Biological communities are thought to have been evolving in trait spaces that are not only multi-dimensional, but also distorted in a sense that mutational covariance matrices among traits depend on the parental phenotypes of mutants. Such a distortion may affect diversifying evolution as well as directional evolution. In adaptive dynamics theory, diversifying evolution through ecological interaction is called evolutionary branching. This study analytically develops conditions for evolutionary branching in distorted trait spaces of arbitrary dimensions, by a local nonlinear coordinate transformation so that the mutational covariance matrix becomes locally constant in the neighborhood of a focal point. The developed evolutionary branching conditions can be affected by the distortion when mutational step sizes have significant magnitude difference among directions, i.e., the eigenvalues of the mutational covariance matrix have significant magnitude difference

Lotka–Volterra approximations for evolutionary trait-substitution processes

A set of axioms is formulated characterizing ecologically plausible community dynamics. Using these axioms, it is proved that the transients following an invasion into a sufficiently stable equilibrium community by a mutant phenotype similar to one of the community's finitely many resident phenotypes can always be approximated by means of an appropriately chosen Lotka-Volterra model. To this end, the assumption is made that similar phenotypes in the community form clusters that are well-separated from each other, as is expected to be generally the case when evolution proceeds through small mutational steps. Each phenotypic cluster is represented by a single phenotype, which we call an approximate phenotype and assign the cluster's total population density. We present our results in three steps. First, for a set of approximate phenotypes with arbitrary equilibrium population densities before the invasion, the Lotka-Volterra approximation is proved to apply if the changes of the population densities of these phenotypes are sufficiently small during the transient following the invasion. Second, quantitative conditions for such small changes of population densities are derived as a relationship between within-cluster differences and the leading eigenvalue of the community's Jacobian matrix evaluated at the equilibrium population densities before the invasion. Third, to demonstrate the utility of our results, the 'invasion implies substitution' result for monomorphic populations is extended to arbitrarily polymorphic populations consisting of well-recognizable and -separated clusters

Evolutionary branching under slow directional evolution

Evolutionary branching is the process by which ecological interactions induce evolutionary diversification. In asexual populations with sufficiently rare mutations, evolutionary branching occurs through trait-substitution sequences caused by the sequential invasion of successful mutants. A necessary and sufficient condition for evolutionary branching of univariate traits is the existence of a convergence stable trait value at which selection is locally disruptive. Real populations, however, undergo simultaneous evolution in multiple traits. Here we extend conditions for evolutionary branching to bivariate trait spaces in which the response to disruptive selection on one trait can be suppressed by directional selection on another trait. To obtain analytical results, we study trait-substitution sequences formed by invasions that possess maximum likelihood. By deriving a sufficient condition for evolutionary branching of bivariate traits along such maximum-likelihood-invasion paths (MLIPs), we demonstrate the existence of a threshold ratio specifying how much disruptive selection in one trait direction is needed to overcome the obstruction of evolutionary branching caused by directional selection in the other trait direction. Generalizing this finding, we show that evolutionary branching of bivariate traits can occur along evolutionary-branching lines on which residual directional selection is sufficiently weak. We then present numerical analyses showing that our generalized condition for evolutionary branching is a good indicator of branching likelihood even when trait-substitution sequences do not follow MLIPs and when mutations are not rare. Finally, we extend the derived conditions for evolutionary branching to multivariate trait spaces

Separable potential model for K−NK^{-}N interactions at low energies

The effective separable meson-baryon potentials are constructed to match the equivalent chiral amplitudes up to the second order in external meson momenta. We fit the model parameters (low energy constants) to the threshold and low energy $K^{-}p$ data. In the process, the $K^{-}$-proton bound state problem is solved exactly in the momentum space and the 1s level characteristics of the kaonic hydrogen are computed simultaneously with the available low energy $K^{-}p$ cross sections. The model is also used to describe the $\pi \Sigma$ mass spectrum and the energy dependence of the $K^{-}n$ amplitude.Comment: 31 pages, v2 - added corrections to make it compatible with the published versio

Scintillation Counters for the D0 Muon Upgrade

We present the results of an upgrade to the D0 muon system. Scintillating counters have been added to the existing central D0 muon system to provide rejection for cosmic ray muons and out-of-time background, and to provide additional fast timing information for muons in an upgraded Tevatron. Performance and results from the 1994-1996 Tevatron run are presented.Comment: 30 pages, 25 postscript figure

Holographic dark energy with time varying c2c^2 parameter

We consider the holographic dark energy model in which the model parameter $c^2$ evolves slowly with time. First we calculate the evolution of EoS parameter as well as the deceleration parameter in this generalized version of holographic dark energy (GHDE). Depending on the parameter $c^2$, the phantom regime can be achieved earlier or later compare with original version of holographic dark energy. The evolution of energy density of GHDE model is investigated in terms of parameter $c^2$. We also show that the time-dependency of $c^2$ can effect on the transition epoch from decelerated phase to accelerated expansion. Finally, we perform the statefinder diagnostic for GHDE model and show that the evolutionary trajectories of the model in $s-r$ plane are strongly depend on the parameter $c^2$.Comment: 16 pages, 4 figures, accepted by Astrophys Space Sc

Statefinder diagnostic and stability of modified gravity consistent with holographic and new agegraphic dark energy

Recently one of us derived the action of modified gravity consistent with the holographic and new-agegraphic dark energy. In this paper, we investigate the stability of the Lagrangians of the modified gravity as discussed in [M. R. Setare, Int. J. Mod. Phys. D 17 (2008) 2219; M. R. Setare, Astrophys. Space Sci. 326 (2010) 27]. We also calculate the statefinder parameters which classify our dark energy model.Comment: 12 pages, 2 figures, accepted by Gen. Relativ. Gravi