On the susceptibility function of piecewise expanding interval maps

We study the susceptibility function Psi(z) associated to the perturbation f_t=f+tX of a piecewise expanding interval map f. The analysis is based on a spectral description of transfer operators. It gives in particular sufficient conditions which guarantee that Psi(z) is holomorphic in a disc of larger than one. Although Psi(1) is the formal derivative of the SRB measure of f_t with respect to t, we present examples satisfying our conditions so that the SRB measure is not Lipschitz.*We propose a new version of Ruelle's conjectures.* In v2, we corrected a few minor mistakes and added Conjectures A-B and Remark 4.5. In v3, we corrected the perturbation (X(f(x)) instead of X(x)), in particular in the examples from Section 6. As a consequence, Psi(z) has a pole at z=1 for these examples.Comment: To appear Comm. Math. Phy

Statistical severe storm nowcasting comparison of VAS and Rawinsonde soundings

The statistical severe storm nowcasting technique using upper air soundings (VAS or radiosonde) is translated to the IBM McIDAS system. The severe storm information content of Visible infrared spin scan radiometer Atmospheric Sounder (VAS) and rawinsonde sounding data is compared. The contours of the likelihood of severe storms based only upon upper air VAS and rawinsonde data are shown, as well as the outlook based upon surface data, radar, operational computer models, and other data sources

Resource supplements cause a change in colony sex-ratio specialization in the mound-building ant, Formica exsecta

We examine the role of food resources on split sex ratios in Formica exsecta. Models of resource-based sex allocation predict that greater resources will cause an increase in the production of reproductive females (gynes) and an increase in overall size of offspring. We experimentally increased food resources for a subset of colonies in a polygynous population with a very male-biased sex ratio. This increase in food availability caused colonies that were male specialists the prior year to switch to female production. Overall, a significantly greater proportion of food-supplemented colonies produced gynes, compared to control colonies. Moreover, food-supplemented colonies produced significantly larger workers and males (but not gynes), compared to those produced by control colonies. There was, however, no significant difference in the numerical productivity of food-supplemented and control colonies. We also measured the natural association between colony sex specialization and proximity to conifers, which typically harbor honeydew-bearing aphids (an important natural food source). In line with the view that resources play an important role for determining sex ratios in social insects, we found that female-producing colonies were significantly closer to conifers than were male-producing colonies

Near-Infrared, Adaptive Optics Observations of the T Tauri Multiple-Star System

With high-angular-resolution, near-infrared observations of the young stellar object T Tauri at the end of 2002, we show that, contrary to previous reports, none of the three infrared components of T Tau coincide with the compact radio source that has apparently been ejected recently from the system (Loinard, Rodriguez, and Rodriguez 2003). The compact radio source and one of the three infrared objects, T Tau Sb, have distinct paths that depart from orbital or uniform motion between 1997 and 2000, perhaps indicating that their interaction led to the ejection of the radio source. The path that T Tau Sb took between 1997 and 2003 may indicate that this star is still bound to the presumably more massive southern component, T Tau Sa. The radio source is absent from our near-infrared images and must therefore be fainter than K = 10.2 (if located within 100 mas of T Tau Sb, as the radio data would imply), still consistent with an identity as a low-mass star or substellar object.Comment: 11 pages, 3 figures, submitted to ApJ

Sex allocation in mound-building ants: The roles of resources and queen replenishment

Social Hymenoptera have become key organisms for tests of sex-ratio theory. We assess the role of resources for explaining sex-ratio variation in a highly male-biased population of the ant Formica exsecta. Key predictions of two of the three leading hypotheses invoking an effect of resource availability on sex ratios in social insects are not upheld. One prediction of the multifaceted parental-investment hypothesis is that colonies with greater brood production will rear a greater proportion of their diploid offspring as reproductive females (gynes), rather than workers, This study shows the positive correlation between female-biased sex ratio and the production of brood by female-producing colonies was not the outcome of a trade-off in the production of workers vs. gynes. The main prediction of the constant-female hypothesis is that investment in gynes should be constant. We found extreme variation among colonies in the number of gynes produced. By contrast, all the predictions of the queen-replenishment hypothesis were supported. The queen-replenishment hypothesis predicts that colonies produce gynes only when queen number is so low that colony production of brood is reduced, or colony survival threatened. We found that, as predicted by this hypothesis, female-producing colonies had fewer queens and produced a lower biomass of brood than male-producing colonies. In contrast, male-producing colonies had lower production per queen, and were more likely to be limited by external resources. This suggests that queen number limits production in female-producing colonies. These data provide evidence of adaptive adjustment of resources to worker, gyne, and male brood

Selection methods regulate evolution of cooperation in digital evolution.

A key, yet often neglected, component of digital evolution and evolutionary models is the 'selection method' which assigns fitness (number of offspring) to individuals based on their performance scores (efficiency in performing tasks). Here, we study with formal analysis and numerical experiments the evolution of cooperation under the five most common selection methods (proportionate, rank, truncation-proportionate, truncation-uniform and tournament). We consider related individuals engaging in a Prisoner's Dilemma game where individuals can either cooperate or defect. A cooperator pays a cost, whereas its partner receives a benefit, which affect their performance scores. These performance scores are translated into fitness by one of the five selection methods. We show that cooperation is positively associated with the relatedness between individuals under all selection methods. By contrast, the change in the performance benefit of cooperation affects the populations' average level of cooperation only under the proportionate methods. We also demonstrate that the truncation and tournament methods may introduce negative frequency-dependence and lead to the evolution of polymorphic populations. Using the example of the evolution of cooperation, we show that the choice of selection method, though it is often marginalized, can considerably affect the evolutionary dynamics