The Enigma of Frequency-Dependent Selection [Revised and updated 16 June 1998]

Frequency-dependent selection is so fundamental to modern evolutionary thinking that everyone interested in evolutionary biology 'knows' the concept. It is even so fundamental that many authors of textbooks do not bother to define it. Yet it turns out that different authors (and sometimes even one and the same author) use the term to refer to different types of selection. In this paper we try to uncover the sources of this confusion. The concept is fairly well defined in the original concept of population genetical theory, which focuses on short-term evolutionary change, and basically ignores density-dependence. The problems start when the original concept is used in the context of long-term evolution, in which density-dependence is essential: without density dependence, lines of descent either die out or explode on the relevant time scales. With density-dependence, the definition of frequency-dependent selection, in the form in which it is usually given, becomes ambiguous. The concept of weak and strong frequency-dependence distinguish between two very different forms of frequency-dependent selection occurring in populations which experience density-dependent population regulation

Evolution of Mixed Maturation Strategies in Semelparous Life-histories: the Crucial Role of Dimensionality of Feedback Environment [Updated 18 August 1998]

We study the evolution of age-at-maturity in a semelparous life history with two age-classes. An individual may breed in the first year of its life and die, or delay breeding to the second year. In this setting a mixed strategy means that a fraction of the individual's offspring breed in the first possible breeding event, while the remaining fraction delay breeding. Current theory seems to imply that mixed strategies are not evolutionarily stable strategies (ESS) under a steady state population dynamical regime. We show that a two-dimensional feedback environment may allow the evolution of mixed age-at-maturity. Furthermore, different phenotypes need to perceive the environment differently. The biological reasoning behind these conditions is different resource usage or predation pressure between two age-classes. Thus, the conventional explanations for the occurrence of mixed strategies in natural populations, environmental stochasticity or complex dynamics, are not needed

Lorentz invariance relations and Wandzura-Wilczek approximation

A complete list of the so-called Lorentz invariance relations between parton distribution functions is given and some of their consequences are discussed, such as the Burkhardt-Cottingham sum rule. The violation of these relations is considered in a model independent way. It is shown that several Lorentz invariance relations are not violated in a generalized Wandzura-Wilczek approximation, indicating that numerically their violation may be small.Comment: 10 pages; Proceedings of the workshop "Recent Advances in Perturbative QCD and Hadronic Physics", July 20-24, 2009, at ECT*, Trento (Italy), in honor of Anatoli V. Efremov on the occasion of his 75th birthday; to appear in Mod. Phys. Lett.

Relations between generalized and transverse momentum dependent parton distributions

Recent work suggests non-trivial relations between generalized parton distributions on the one hand and (naive time-reversal odd) transverse momentum dependent distributions on the other. Here we review the present knowledge on such type of relations. Moreover, as far as spectator model calculations are concerned, the existing results are considerably extended. While various relations between the two types of parton distributions can be found in the framework of spectator models, so far no non-trivial model-independent relations have been established.Comment: 25 pages, 9 figures; Eq. (B17) and typos corrected, identical with journal versio

Generalized polarizabilities of the nucleon studied in the linear sigma model (II)

In a previous paper virtual Compton scattering off the nucleon has been investigated in the one-loop approximation of the linear sigma model in order to determine the 3 scalar generalized polarizabilities. We have now extended this work and calculated the 7 vector polarizabilities showing up in the spin-dependent amplitude of virtual Compton scattering. The results fulfill 3 model-independent constraints recently derived. Compared to the constituent quark model there exist enormous differences for some of the vector polarizabilities. At vanishing three-momentum of the virtual photon, the analytical results of the sigma model and of chiral perturbation theory can be related. The influence of the $\pi^{0}$ exchange in the $t$ channel has been discussed in some detail. Besides, the vector polarizabilities determine 2 linear combinations of the third order spin-polarizabilities appearing in real Compton scattering.Comment: 17 pages, 4 figures, latex2e (Revtex), submitted to Z. Phys.

Reactive transport modelling of the long-term interaction between carbon steel and MX-80 bentonite at 25 °C

The geological disposal in deep bedrock repositories is the preferred option for the management of high-level radioactive waste (HLW). In some of these concepts, carbon steel is considered as a potential canister material and bentonites are planned as backfill material to protect metallic waste containers. Therefore, a 1D radial reactive transport model has been developed in order to better understand the processes occurring during the long-term iron-bentonite interaction. The numerical model accounts for diffusion, aqueous complexation reactions, mineral dissolution/precipitation and cation exchange at a constant temperature of 25 °C under anoxic conditions. Our results suggest that Fe is sorbed at the montmorillonite surface via cation exchange in the short-term, and it is consumed by formation of the secondary phases in the long-term. The numerical model predicts precipitation of nontronite, magnetite and greenalite as corrosion products. Calcite precipitates due to cation exchange in the short-term and due to montmorillonite dissolution in the long-term. Results further reveal a significant increase in pH in the long-term, while dissolution/precipitation reactions result in limited variations of the porosity. A sensitivity analysis has also been performed to test the effect of selected parameters, such as corrosion rate, diffusion coefficient and composition of the bentonite porewater, on the corrosion processes. Overall, outcomes suggest that the predicted main corrosion products in the long-term are Fe-silicate minerals, such phases thus should deserve further attention as a chemical barrier in the diffusion of radionuclides to the repository far field

Sivers effect in Drell Yan at RHIC

On the basis of a fit to the Sivers effect in deep-inelastic scattering, we make predictions for single-spin asymmetries in the Drell-Yan process at RHIC.Comment: 10 pages, 7 figures, 1 table. v2: References and comments added, minor correction

Spectra of sparse non-Hermitian random matrices: an analytical solution

We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the Kesten-Mckay law as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs. In this context, we show analytically that the convergence rate of a transport process on a very sparse graph depends upon the degree of symmetry of the edges in a non-monotonous way.Comment: 5 pages, 5 figures, 12 pages supplemental materia

Are there approximate relations among transverse momentum dependent distribution functions?

Certain exact relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into approximate ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES we test the practical usefulness of one such ``Wandzura-Wilczek-type approximation'', namely of that connecting h_{1L}^{\perp(1)a}(x) to h_L^a(x), and discuss how it can be further tested by future CLAS and COMPASS data.Comment: 9 pages, 3 figure