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Background: The French region of Brittany presents one of the highest cystic fibrosis (CF)-causing allele frequency in Europe. Here, we tested two hypotheses: i) CF-causing allele carriers arrived by sea in the middle of the 1st millennium AD, and ii) a selective advantage for healthy carriers explains this high rate., Methods: From the census of cystic fibrosis patients, frequency maps of the most widespread alleles were established. A mathematical model was developed, based on birth date and place of the ancestors of these patients over 5 centuries, to determine the distribution of local migrations and their parameters for inter-generational intervals of 32 years. This model was applied to simulate the spread of CF-causing variant carriers, according to different scenarios that corresponded to the immigration of a given number of variant carriers at different times (year) and places, and to compare their results to current frequency maps., Results: Migrants carrying a CFTR variant settled in several locations, around which they spread, notably in Central Brittany (F508del variant), Léon (G551D variant) and Cornouaille (1078delT variant). Until the end of the 18th century, the spreading of disease-causing allele carriers was relatively slow, and allele frequencies progressively increased. Then, the mean migration distances increased rapidly, leading to a decline in local frequencies., Conclusions: The main CFTR variants could only have reached their current frequencies through a selective advantage for healthy carriers of the order of 4-6 % at each generation. For the most widespread variant (F508del), the model supports the hypothesis that it appeared around 190 generations ago., Competing Interests: Declaration of Competing Interest The authors declare that there is no conflict of interest regarding the publication of this article., (Copyright © 2023 The Author(s). Published by Elsevier B.V. All rights reserved.)

The proper characterization of the size distribution and growth of firms represents an important issue in economics and business. We use the Maximum Entropy approach to assess the plausibility of the assumption that firm size follows Lognormal or Pareto distributions, which underlies most recent works on the subject. A comprehensive dataset covering the universe of French firms allows us to draw two major conclusions. First, the Pareto hypothesis for the whole distribution should be rejected. Second, by discriminating across firms based on the number of products sold and markets served, we find that, within the class of multi-product companies active in multiple markets, the distribution converges to a Zipf’s law. Conversely, Lognormal distribution is a good benchmark for small single-product firms. The size distribution of firms largely depends on firms’ diversification patterns. [ABSTRACT FROM AUTHOR]

Two fluted panels in Rouffignac Cave, France, appear highly ordered as opposed to other panels that appear haphazardly made. Is it possible to objectively establish that an intention to communicate thoughts and ideas lay behind the fluting of the two “ordered” panels? To help answer this, we apply a concept from communications theory called Zipf's Law, which can establish whether data represent “efficient communication” or are random. Applying the law to the two panels (using the number of fingers in each fluted hand as the variable) shows that the two panels may constitute efficient communication. We conclude by discussing related matters, including the idea of Paleolithic notational markings. [ABSTRACT FROM AUTHOR]