Reproductive Conflict and the Evolution of Menopause in Killer Whales.

Why females of some species cease ovulation prior to the end of their natural lifespan is a long-standing evolutionary puzzle [1-4]. The fitness benefits of post-reproductive helping could in principle select for menopause [1, 2, 5], but the magnitude of these benefits appears insufficient to explain the timing of menopause [6-8]. Recent theory suggests that the cost of inter-generational reproductive conflict between younger and older females of the same social unit is a critical missing term in classical inclusive fitness calculations (the "reproductive conflict hypothesis" [6, 9]). Using a unique long-term dataset on wild resident killer whales, where females can live decades after their final parturition, we provide the first test of this hypothesis in a non-human animal. First, we confirm previous theoretical predictions that local relatedness increases with female age up to the end of reproduction. Second, we construct a new evolutionary model and show that given these kinship dynamics, selection will favor younger females that invest more in competition, and thus have greater reproductive success, than older females (their mothers) when breeding at the same time. Third, we test this prediction using 43 years of individual-based demographic data in resident killer whales and show that when mothers and daughters co-breed, the mortality hazard of calves from older-generation females is 1.7 times that of calves from younger-generation females. Intergenerational conflict combined with the known benefits conveyed to kin by post-reproductive females can explain why killer whales have evolved the longest post-reproductive lifespan of all non-human animals

The model based approach to smoothing

Nonparametric regression methods are devised in order to obtain a smooth fit of a regression curve without having to specify a parametric model. This, in principle, provides a flexible approach to curve estimation. It is shown how splines are not such a flexible tool for smoothing. It is proposed to use the modern approach of state space modeling instead, to solve a variety of smoothing problems. This model based approach alleviates estimation and computational problems as well as provides insightful solutions to smoothing problems.Science, Faculty ofStatistics, Department ofGraduat

A new measure of quantitative robustness

The Gross-Error Sensitivity (GES) and the Breakdown Point (BP) are two measures of quantitative robustness which have played a key role in the development of the theory of robust-ness. Both can be derived from the maximum bias function B(€) and constitute a two-number summary of this function. The GES is the derivative of B(€) at the origin whereas the BP determines the asymptote of the curve (c, B(€)). Since GES€ ≈ B(€) for € near zero, the GES summarizes the behavior of B(€) near the origin. On the other hand, the BP does not provide an approximation for B(€) for c large and, consequently, estimates with strikingly different bias performance when c is large may have the same BP. A new robustness quantifier, the breakdown rate (BR), that summarizes the behavior of B(€)for € near BP will be introduced. The BR for several families of robust estimates of regression will be presented and the increased usefulness of the three-number summary (GES,BP,BR) for comparing robust estimates will be illustrated by several examples.Science, Faculty ofStatistics, Department ofGraduat

Modeling and Smoothing Unequally Spaced Sequence Data

Kalman filter, Splines, Smoothing, State space model,

Modeling and smoothing unequally spaced sequence data

The application of the continuous state space model to unequally spaced sequence data is discussed and illustrated. The continuous model implies a discrete model for the observed data. Practical expressions for relevant discrete model quantities are given. These quantites are required for the digital processing of the data and in particular for the application of the Kalman and smoothing filter and related calculations. Applications illustrate the procedures.19 page(s

A Commonwealth vulnerability index for developing countries: the position of small states

There is growing international recognition that high economic exposure, remoteness, isolation and proneness to natural disasters all have a debilitating effect on small economies, despite the fact that some of them exhibit relatively high per capita incomes. This paper presents a Commonwealth vulnerability index that is designed to quantify vulnerability, and hence provide a means to identify vulnerable states. This index can be used as an operational tool in determining whether small states should be accorded differential treatment by the international community. It is intended as an additional criterion to augment other factors, such as per capita income, which are taken into account in reaching decisions on the treatment of certain developing countries by international organisations

Coherent activity within and between hemispheres: cortico-cortical connectivity revealed by rTMS of the right posterior parietal cortex

IntroductionLow frequency (1 Hz) repetitive transcranial stimulation (rTMS) applied over right posterior parietal cortex (rPPC) has been shown to reduce cortical excitability both of the stimulated area and of the interconnected contralateral homologous areas. In the present study, we investigated the whole pattern of intra- and inter-hemispheric cortico-cortical connectivity changes induced by rTMS over rPPC.MethodsTo do so, 14 healthy participants underwent resting state EEG recording before and after 30 min of rTMS at 1 Hz or sham stimulation over the rPPC (electrode position P6). Real stimulation was applied at 90% of motor threshold. Coherence values were computed on the electrodes nearby the stimulated site (i.e., P4, P8, and CP6) considering all possible inter- and intra-hemispheric combinations for the following frequency bands: delta (0.5–4 Hz), theta (4–8 Hz), alpha (8–12Hz), low beta (12–20 Hz), high beta (20–30 Hz), and gamma (30–50 Hz).Results and discussionResults revealed a significant increase in coherence in delta, theta, alpha and beta frequency bands between rPPC and the contralateral homologous sites. Moreover, an increase in coherence in theta, alpha, beta and gamma frequency bands was found between rPPC and right frontal sites, reflecting the activation of the fronto-parietal network within the right hemisphere. Summarizing, subthreshold rTMS over rPPC revealed cortico-cortical inter- and intra-hemispheric connectivity as measured by the increase in coherence among these areas. Moreover, the present results further confirm previous evidence indicating that the increase of coherence values is related to intra- and inter-hemispheric inhibitory effects of rTMS. These results can have implications for devising evidence-based rehabilitation protocols after stroke