Population genetics models of local ancestry

Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population structure and gene flow, and interpret genomes of individuals that have ancestry from multiple source populations as mosaics of segments originating from each population. We propose general and tractable models for describing the evolution of these patterns of local ancestry and their impact on genetic diversity. We focus on the length distribution of continuous ancestry tracts, and the variance in total ancestry proportions among individuals. The proposed models offer improved agreement with Wright-Fisher simulation data when compared to state-of-the art models, and can be used to infer various demographic parameters in gene flow models. Considering HapMap African-American (ASW) data, we find that a model with two distinct phases of `European' gene flow significantly improves the modeling of both tract lengths and ancestry variances.Comment: 25 pages with 7 figures; Genetics: Published online before print April 4, 201

Appraising Diversity with an Ordinal Notion of Similarity: An Axiomatic Approach

This paper provides an axiomatic characterization of two rules for comparing alternative sets of objects on the basis of the diversity that they offer. The framework considered assumes a finite universe of objects and an a priori given ordinal quadernary relation that compares alternative pairs of objects on the basis of their ordinal dissimilarity. Very few properties of this quadernary relation are assumed (beside completeness, transitivity and a very natural form of symmetry). The two rules that we characterize are the maxi-max criterion and the lexi-max criterion. The maxi-max criterion considers that a set is more diverse than another if and only if the two objects that are the most dissimilar in the former are weakly as dissimilar as the two most dissimilar objects in the later. The lexi-max criterion is defined as usual as the lexicographic extension of the maxi-max criterion. Some connections with the broader issue of measuring freedom of choice are also provided.Diversity, Measurement, Axioms, Freedom of choice

Utilitarianism or Welfarism: Does it Make a Difference?

We show that it is possible to reconcile the utilitarian and welfarist principles under the requirement of unanimity provided that the set of profiles over which the consensus is attained is rich enough. More precisely, we identify a closedness condition which, if satisfied by a class of n-tuples of utility functions, guarantees that the rankings of social states induced by utilitarian and welfarist unanimities over that class are identical. We illustrate the importance of the result for the measurement of unidimensional as well as multidimensional inequalities from a dominance point of view.Unanimity; Utilitarianism; Welfarism; Stochastic Dominance; Inequality

Real Options at Bell Canada

In this report, we first develop a simplified example that illustrates the importance of considering the option ``waiting to invest'' when valuing an investment. This is followed by a short description of other options that could be embedded in an investment opportunity. In order to stress the importance of the real option mind-set in strategic planning and competitive assessment, we present three examples of possible applications of real options for evaluating investments at Bell Canada. A brief discussion follows on the importance of a real options mind-set in the telecommunications regulation context. Finally we conclude by underlining the importance of an efficient information gathering and processing framework to implement a real options framework. Two technical appendices provide more details on both the modeling and the solving techniques that are commonly used to implement real options. The complete version of this publication is confidential. Nous débutons ce rapport en développant un exemple simplifié qui illustre l'importance de valoriser l'option de retarder un investissement. Une courte description des différentes options susceptibles d'être incorporées dans un projet d'investissement est ensuite donnée. Pour illustrer l'importance d'adopter un cadre d'analyse basé sur la méthodologie des options réelles pour la planification stratégique et l'analyse concurrentielle, nous présentons trois applications possibles d'options réelles dans l'évaluation d'investissements chez Bell Canada. La nécessité de l'adoption d'un tel cadre d'analyse dans le contexte de la réglementation des télécommunications fait ensuite l'objet d'une brève discussion. Nous terminons en soulignant que le succès de la mise en pratique d'un cadre «options réelles» dépend essentiellement d'un système efficace de collecte et de traitement de l'information. Deux appendices techniques fournissent plus de détails sur les techniques de modélisation et de solution qui sont couramment utilisées pour des problèmes d'options réelles. La version complète de cette publication est confidentielle.Real options, option value, volatility, risk, irreversibility, telecommunications, Options réelles, valeur d'option, volatilité, risque, irréversibilité, télécommunications