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The Hardy–Weinberg law is shown to be transitive in the sense that a multi-allelic polymorphism that is in equilibrium will retain its equilibrium status if any allele together with its corresponding genotypes is deleted from the population. Similarly, the transitivity principle also applies if alleles are joined, which leads to the summation of allele frequencies and their corresponding genotype frequencies. These basic polymorphism properties are intuitive, but they have apparently not been formalized or investigated. This article provides a straightforward proof of the transitivity principle, and its usefulness in genetic data analysis is explored, using high-quality autosomal microsatellite databases from the US National Institute of Standards and Technology. We address the reduction of multi-allelic polymorphisms to variants with fewer alleles, two in the limit. Equilibrium test results obtained with the original and reduced polymorphisms are generally observed to be coherent, in particular when results obtained with length-based and sequence-based microsatellites are compared. We exploit the transitivity principle in order to identify disequilibrium-related alleles, and show its usefulness for detecting population substructure and genotyping problems that relate to null alleles and allele imbalance., Peer Reviewed, Postprint (published version)

(Marta G. - 25/03/2022) enviem a Clara, Peer Reviewed, Postprint (author's final draft)

Este informe está alineado con la visión de sistema alimentario de Fundación Triptolemos, con la intención de contribuir, como miembro de la sociedad civil, al desarrollo de una política alimentaria integral en la UE siguiendo el dictamen del Comité Económico y Social Europeo. Cada uno de los 6 capítulos contiene al inicio una pequeña introducción. Habida cuenta de la complejidad de los temas tratados y del número de autores (30), puede suceder que un solo hecho influya en varios conceptos y pueda darse por ello, alguna repetición con enfoques diferentes., El Pacto Verde corre el riesgo de acabar siendo más un cambio de formas que de fondo del sector agroalimentario europeo, si solo se plantea un cambio de sistema productivo, sin que se lleven a cabo valoraciones respecto de lo que este puede representar en aspectos cuantitativos y cualitativos y, por ende, en los agricultores y sectores asociados, más teniendo en cuenta la enorme diferencia edafoclimática y cultural de los diferentes países y regiones de la UE. Europa aspira a convertirse en líder mundial en sostenibilidad y competitividad y para conseguirlo, el sector agroalimentario deberá jugar un papel crucial, pero la Comisión Europea parece excesivamente optimista en sus planteamientos., Objectius de Desenvolupament Sostenible::3 - Salut i Benestar, Objectius de Desenvolupament Sostenible::12 - Producció i Consum Responsables, Objectius de Desenvolupament Sostenible::1 - Fi de la Pobresa, Objectius de Desenvolupament Sostenible::13 - Acció per al Clima, Objectius de Desenvolupament Sostenible::2 - Fam zero, Preprint

The consequences of supplementing Lys, Met, and Thr in milk replacers (MR) for calves have been widely studied, but scarce information exists about potential roles of other AA (whether essential or not). The effects on growth performance of supplementation of 4 different AA combinations in a mixed ration (25.4% crude protein and 20.3% fat) based on skim milk powder and whey protein concentrate were evaluated in 76 Holstein male calves (3 ± 1.7 d old). The 4 MR were as follows: CTRL with no AA supplementation; PG, supplying additional 0.3% Pro and 0.1% Gly; FY, supplying additional 0.2% Phe and 0.2% Tyr; and KMT, providing additional 0.62% Lys, 0.22% Met, and 0.61% Thr. All calves were fed the same milk allowance program and were weaned at 56 d of study. Concentrate intake was limited to minimize interference of potential differences in solid feed intake among treatments. Animals were weighed weekly, intakes recorded daily, and blood samples obtained at 2, 5, and 7 wk of study to determine serum urea and plasma AA concentrations. Plasma AA concentrations were explored using compositional data analysis, and their isometric log-ratio transformations were used to analyze their potential influence on ADG and serum urea concentration using a linear mixed-effects model. We detected no differences in calf performance and feed intake. Plasma relative concentration of the AA supplemented in the KMT and PG treatments increased in their respective treatments, and, in PG calves, a slight increase in the proportion of plasma Gly, Glu, and branched-chain AA was also observed. The proportions of plasma branched-chain AA, His, and Gln increased, and those of Thr, Arg, Lys, and Glu decreased with calves' age. A specific log-contrast balance formed by Arg, Thr, and Lys was found to be the main driver for lowering serum urea concentrations and increasing calf growth. The use of compositional mixed-effects models identified a cluster formed by the combination of Arg, Thr, and Lys, as a, Peer Reviewed, Postprint (published version)

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Maritime Policy & Management on Published online: 12 Sep 2021, available online at: http://www.tandfonline.com/10.1080/03088839.2021.1972175., The Yangtze River Delta multi-port system (YMPS) receives increasing attention due to its relevance in world trade and excellent competitiveness in the container traffic market. To insight into the development pattern of YMPS, this paper proposes a method that combines the Hierarchical Clustering with compositional data (CoDa) exploratory tools (i.e., biplot and dendrogram) to explore the temporal and spatial evolution of the YMPS from 1992 to 2019. CoDa describes parts of some whole (i.e., frequency and percentage), conveying relative information in the ratios between its components. Container traffic share in a multi-port region is typical CoDa. Traditional statistical approaches to CoDa could lead to spurious correlations and erroneous conclusions. However, using suitable CoDa techniques, such as the centered log-ratio (clr) transformation, can effectively avoid these misinterpretations. The novel method can simultaneously find the temporal and spatial characteristics. The findings indicate that the development of the YMPS has gone through four stages and the evolution of the YMPS is characterized by a tendency towards a ‘multi-core development’ and faces a differentiated pattern of ‘peripheral port challenges’. The analysis further improves the port system’s evolutionary model and explains the underlying reason for the YMPS development. CoDa techniques also provide a new perspective for the temporal and spatial evolution of the transport discipline., This work was supported by the Ministerio de Ciencia, Innovación y Universidades under project Methods for Compositional analysis of Data (CODAMET) [grant number RTI2018-095518-B-C22, 2019-2021] and 111 Project [grant number D21013], Peer Reviewed, Postprint (author's final draft)

This is the peer reviewed version of the following article: Graffelman, J. Maximum-likelihood estimation of the geometric niche preemption model. "Ecosphere", Desembre 2021, vol. 12, núm. 12, p. e03834:1-e03834:12., which has been published in final form at https://esajournals.onlinelibrary.wiley.com/doi/10.1002/ecs2.3834. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving., The geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May’s equation. This article proposes a maximum-likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum-likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum-likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use., This work was partially supported by grantsRTI2018-095518-B-C22 of the Spanish Ministry ofScience, Innovation and Universities and the Euro-pean Regional Development Fund and by grant R01GM075091 from the United States National Institutesof Health. I thank two anonymous reviewers whosecomments on the manuscript have helped toimprove it. The author declares there are no conflictsof interest., Peer Reviewed, Postprint (author's final draft)

Genotype-phenotype association studies often combine phenotype data from multiple studies to increase statistical power. Harmonization of the data usually requires substantial effort due to heterogeneity in phenotype definitions, study design, data collection procedures, and data-set organization. Here we describe a centralized system for phenotype harmonization that includes input from phenotype domain and study experts, quality control, documentation, reproducible results, and data-sharing mechanisms. This system was developed for the National Heart, Lung, and Blood Institute’s Trans-Omics for Precision Medicine (TOPMed) program, which is generating genomic and other -omics data for more than 80 studies with extensive phenotype data. To date, 63 phenotypes have been harmonized across thousands of participants (recruited in 1948–2012) from up to 17 studies per phenotype. Here we discuss challenges in this undertaking and how they were addressed. The harmonized phenotype data and associated documentation have been submitted to National Institutes of Health data repositories for controlled access by the scientific community. We also provide materials to facilitate future harmonization efforts by the community, which include 1) the software code used to generate the 63 harmonized phenotypes, enabling others to reproduce, modify, or extend these harmonizations to additional studies, and 2) the results of labeling thousands of phenotype variables with controlled vocabulary terms., Peer Reviewed, Postprint (published version)

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Statistical methodology for testing the Hardy-Weinberg equilibrium at X chromosomal variants has recently experienced considerable development. Up to a few years ago, testing X chromosomal variants for equilibrium was basically done by applying autosomal test procedures to females only. At present, male alleles can be taken into account in asymptotic and exact test procedures for both the bi-and multiallelic case. However, current X chromosomal exact procedures for multiple alleles rely on a classical full enumeration algorithm and are computationally expensive, and in practice not feasible for more than three alleles. In this article, we extend the autosomal network algorithm for exact Hardy-Weinberg testing with multiple alleles to the X chromosome, achieving considerable reduction in computation times for multiallelic variants with up to five alleles. The performance of the X chromosomal network algorithm is assessed in a simulation study. Beyond four alleles, a permutation test is, in general, the more feasible approach. A detailed description of the algorithm is given, and examples of X chromosomal indels and microsatellites are discussed., This work was supported by grant RTI2018‐095518‐B‐C22 (MCIU/AEI/FEDER) of the Spanish Ministry of Science, Innovation and Universities and the European Regional Development Fund, and by grant R01 GM075091 from the United States National Institutes of Health. We thank three anonymous reviewers whose comments have helped us to improve the article., Peer Reviewed, Postprint (author's final draft)

The detection of family relationships in genetic databases is of interest in various scientific disciplines such as genetic epidemiology, population and conservation genetics, forensic science, and genealogical research. Nowadays, screening genetic databases for related individuals forms an important aspect of standard quality control procedures. Relatedness research is usually based on an allele sharing analysis of identity by state (IBS) or identity by descent (IBD) alleles. Existing IBS/IBD methods mainly aim to identify first-degree relationships (parent–offspring or full siblings) and second degree (half-siblings, avuncular, or grandparent–grandchild) pairs. Little attention has been paid to the detection of in-between first and second-degree relationships such as three-quarter siblings (3/4S) who share fewer alleles than first-degree relationships but more alleles than second-degree relationships. With the progressively increasing sample sizes used in genetic research, it becomes more likely that such relationships are present in the database under study. In this paper, we extend existing likelihood ratio (LR) methodology to accurately infer the existence of 3/4S, distinguishing them from full siblings and second-degree relatives. We use bootstrap confidence intervals to express uncertainty in the LRs. Our proposal accounts for linkage disequilibrium (LD) by using marker pruning, and we validate our methodology with a pedigree-based simulation study accounting for both LD and recombination. An empirical genome-wide array data set from the GCAT Genomes for Life cohort project is used to illustrate the method., This work was partially supported by grants RTI2018-095518-B-C22 (JG), RTI2018-095518-B-C21 (IGF and CBV), and ADE 10/00026 (RdC) (MCIU/AEI/FEDER) of the Spanish Ministry of Science, Innovation and Universities and the European Regional Development Fund, by grants SGR1269 and 2017 SGR529 (RdC) of the Generalitat de Catalunya, by grant R01 GM075091 (JG) from the United States National Institutes of Health, by the Ramon y Cajal action RYC-2011-07822 (RdC), by Agency for Management of University and Research Grants (AGAUR) of the Catalan Government grant 2017SGR723 (VM), and by the Spanish Association Against Cancer (AECC) Scientific Foundation, grant GCTRA18022MORE (VM)., Peer Reviewed, Postprint (published version)

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The main goal of this paper is to go some steps further to improve the understanding and manageability of air quality. Quality of atmospheric air in large cities is a matter of great importance because of its impact on the environment and on the health of the population. Recently, measures restricting access of private vehicles to the centre of large cities and other measures to prevent atmospheric air pollution are currently topical. The knowledge of air quality acquires special relevance to be able to evaluate the impact of those great social and economic measures. There are many indices to express air quality. In fact, quite every country has its own, depending on the main pollutants. In general, all indices ignore the compositional nature of the concentrations of air pollutants and do not apply methods of Compositional Data Analysis and have some other weak points such as leak of standardized scale. Therefore, the methodology used is founded on Compositional Data Analysis. The air quality index has an adequate correlation between input (concentrations) and output (air quality index), it distinguishes between air pollution and air quality and it has a 0-100 reference scale which makes easier interpretation and management of air quality expression. To illustrate the proposed method, an application is made to a series of air pollution data (Barcelona, 2001-2015). The results show the effectiveness of the 2008 European directive on ambient air quality, Peer Reviewed, Postprint (published version)

Storm surges are one of the main drivers for extreme flooding at the coastal areas. Such events can be characterized with the maximum level in an extreme storm surge event (surge peak), as well as the duration of the event. Surge projections come from a barotropic model for the 1950–2100 period, under a severe climate change scenario (RCP 8.5) at the northeastern Spanish coast. The relationship of extreme storm surges to three large-scale climate patterns was assessed: North Atlantic Oscillation (NAO), East Atlantic Pattern (EAWR), and Scandinavian Pattern (SC). The statistical model was built using two different strategies. In Strategy #1, the joint probability density was characterized by a moving-average series of stationary Archimedean copula, whereas in Strategy #2, the joint probability density was characterized by a non-stationary probit copula. The parameters of the marginal distribution and the copula were defined with generalized additive models. The analysis showed that the mean values of surge peak and event duration were constant and were independent of the proposed climate patterns. However, the values of NAO and SC influenced the threshold and the storminess of extreme events. According to Strategy #1, the variance of the surge peak and event duration increased with a fast shift of negative SC and a positive NAO, respectively. Alternatively, Strategy #2 showed that the variance of the surge peak increased with a positive EAWR. Both strategies coincided in that the joint dependence of the maximum surge level and the duration of extreme surges ranged from low to medium degree. Its mean value was stationary, and its variability was linked to the geographical location. Finally, Strategy #2 helped determine that this dependence increased with negative NAO., Peer Reviewed, Postprint (published version)

Trees provide a broad amount of ecosystem services in urban areas. Although it is well documented that trees are essential for the well-being and livability of cities, trees are often not evenly distributed. Studies have found that urban residents with a deprived socioeconomic status are associated with a lower coverage and access to urban trees in their communities, yet a fair distribution of trees contributes to the sustainability and resilience of cities. In this context, the environmental justice movement seeks to ensure equal distribution of green infrastructure and its benefits throughout a territory. The objective of this study is threefold: (i) to determine whether urban trees in Guadalajara, Mexico, are distributed equally; (ii) to assess the association between urban trees and socioeconomic status; and (iii) to introduce compositional data analysis to the existing literature. Due to the compositional nature of the data, compositional analysis techniques are applied. We believe this novel approach will help define the proper management of data used in the literature. The outcomes provide insights for urban planners working towards the Sustainable Development Goals to help eradicate the uneven distribution of urban trees in cities., Peer Reviewed, Postprint (published version)

This is the accepted version of the following article: Sanuy, M, Jiménez, JA, Ortego, MI, Toimil, A. Differences in assigning probabilities to coastal inundation hazard estimators: Event versus response approaches. J Flood Risk Management. 2020; 13 (Suppl. 1):e12557. https://doi.org/10.1111/jfr3.12557, which has been published in final form at https://onlinelibrary.wiley.com/doi/full/10.1111/jfr3.12557., Coastal flood risk assessment requires a reliable estimation of the frequency of inundation hazards, that is, characterising the hazard magnitude and assigning a probability of occurrence. In this work we analyse the uncertainty introduced in the assessment associated to the method to assign the probability of occurrence to coastal flood hazards. To this end we have compared the use of two general methods, the response and the event approaches. Different procedures are used to characterise coastal inundation hazards depending on the analysis scale and data availability. Thus, a range of possibilities has been analysed, from simple estimators such as run-up to modelled flood-prone areas. The analysis has been performed for all wave and water level conditions around the Spanish coast. The results show that the differences between the methods are location-dependent, and thus, determined by the exposure to wave and water level conditions. When using the event approach, the run-up or total water level (with good correlation between waves and surge) distributions reasonably approximate those of the response approach with low associated uncertainty. When the assessment aims to output overtopping discharges or inundation maps, observed differences suggest that the event approach would produce misleading conclusions in inundation-related coastal management and decision-making., Peer Reviewed, Postprint (author's final draft)

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Measurements in sequencing studies are mostly based on counts. There is a lack of theoretical developments for the analysis and modelling of this type of data. Some thoughts in this direction are presented, which might serve as a seed. The main issues addressed are the compositional character of multinomial probabilities and the corresponding representation in orthogonal (isometric) coordinates, and modelling distributions for sequencing data taking into account possible effects of amplification techniques., Peer Reviewed, Postprint (published version)

In this note, we give an explicit bound for the modules of the zeros of a polynomial that involves binomial coefficients and recursive numbers., Peer Reviewed, Postprint (author's final draft)

This article presents alternative solutions to some problems involving Lalescu’s sequence that have been published in problem magazines around the world., Peer Reviewed, Postprint (author's final draft)

In this short note Carleman's inequality is combined with convergent series to obtain new inequalities., Peer Reviewed, Postprint (author's final draft)

The location and context in which people live influences and conditions their opportunities in life. This becomes relevant in a world subject to rapid urban and demographic growth, in which different economic, social, and political forces generate and accentuate disparities in cities. The foregoing generates an unequal distribution of the different social groups in the territory known as socio-spatial segregation. The study of this phenomenon incorporates a large number of variables belonging to different dimensions. Nonetheless, few studies have addressed socio-spatial segregation with a multivariate analysis approach. In addition, the existing studies may have obtained misleading outcomes by not acknowledging the inherent compositional nature of their variables. The objective of the present study is twofold: (i) To assess whether the phenomenon of socio-spatial segregation in Guadalajara, Mexico exists; and (ii) to introduce and stress the use of compositional techniques for the study of socio-spatial segregation. The study applied principal component analysis and cluster analysis considering the compositional nature of census variables, particularly from economic and educative indicators. In addition, the study used geographical information tools to depict and interpret the results. The results are intended to serve in the fulfillment of the Sustainable Development Goals towards inclusive and sustainable cities., Peer Reviewed, Postprint (published version)

Monitoring energy indicators has acquired a renewed interest with the 2030 Agenda for Sustainable Development, and specifically with goal 7 (SDG7), which seeks to guarantee universal access to energy. The predominant criteria to monitor SDG7 are given in a set of individual indicators. Along this line, the UN indicators proposed in the 47th session of the UN Statistical commission are a practical starting point. A relevant characteristic of these indicators is that they can be expressed as proportions from a whole, i.e., they are compositions. Notably, directly implementing traditional multivariate models onto indicators that are proportions without an intermediate process can lead to spurious analysis. Here, we aim to assess the application of compositional data analysis(CoDa) to follow up on the temporal trend indicators of the energy sector in the context of SDG7, with a case study for the most affected areas addressing the problem of electricity access. Following CoDa methodology, we first use a log-ratio transformation to bring compositions to real space and then apply three multivariate methods: linear regression, generalized additive models and support vector machine. We also address other characteristic problems of the electricity access indicators, such as data quality, which was treated by considering models with interactions. In sum, CoDa facilitates a controlled management of the parts that make up population based indicators, suggesting that modelling evolution of compositions as individual components – even the standard splitting of country data into rural and urban “access to” indicator –should be avoided., This research has been partially funded by the Ministerio de Economía y Competitividad del Gobierno de España (MINECO/FEDER, Ref: MTM2015-65016-C2-2-R); and by the Agència de Gestió d′Ajuts Universitaris i de Recerca de la Generalitat de Catalunya (Ref. 2017 SGR 656 and 2017 SGR 1496)., Peer Reviewed, Postprint (author's final draft)

Urban green infrastructure such as parks, gardens and trees, provide several ecosystem services and benefits. Particularly trees provide a broad amount of services in urban areas, such as improving air quality, mitigating carbon pollution and heat-island effect, attenuating storm-water floods, reducing noise and serving as habitat for different species among others. Likewise, urban trees provide different social (i.e., social cohesion), economic (i.e., increase in property value), psychological (i.e., stress reduction) and medical (i.e., increase in longevity of life) benefits (Landry, 2009; Roy et al., 2012; Battisti et al., 2019). Although it is well documented that trees are essential for the well-being and health of urban areas and their inhabitants, trees are not evenly distributed in urban areas. Previous studies have found that urban residents with a deprived socioeconomic status are associated with low coverage of urban trees in their communities (Hernández and Villaseñor, 2017; Park and Kwan, 2017; Wang and Qiu, 2018). Therefore, environmental justice seeks to ensure that green infrastructure and its benefits are distributed equally throughout the territory (Anguelovski, 2013; Gould and Lewis, 2017). The objective of this study is to determine whether the distribution of urban trees in the city of Guadalajara, Mexico is distributed equally or not among its colonies and urban districts. The information is obtained from the first and only tree census conducted in the city on June 2018 and treated with geographic information systems (GIS). The attributes of the tree dataset include their location (urban blocks, streets, parks and gardens), heights and diameters of their canopy (Government of Guadalajara, 2019). For the analysis and due to the compositional nature of the data, compositional analysis techniques are applied (see Aitchison, 1986; Pawlowsky-Glahn, et al., 2015; Filzmoser et al., 2018). With this novel approach, we contribute to the existing literat, Peer Reviewed, Postprint (author's final draft)

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Analysis of RNA sequencing (RNA-seq) data from related individuals is widely used in clinical and molecular genetics studies. Prediction of kinship from RNA-seq data would be useful for confirming the expected relationships in family based studies and for highlighting samples from related individuals in case-control or population based studies. Currently, reconstruction of pedigrees is largely based on SNPs or microsatellites, obtained from genotyping arrays, whole genome sequencing and whole exome sequencing. Potential problems with using RNA-seq data for kinship detection are the low proportion of the genome that it covers, the highly skewed coverage of exons of different genes depending on expression level and allele-specific expression. In this study we assess the use of RNA-seq data to detect kinship between individuals, through pairwise identity by descent (IBD) estimates. First, we obtained high quality SNPs after successive filters to minimize the effects due to allelic imbalance as well as errors in sequencing, mapping and genotyping. Then, we used these SNPs to calculate pairwise IBD estimates. By analysing both real and simulated RNA-seq data we show that it is possible to identify up to second degree relationships using RNA-seq data of even low to moderate sequencing depth, Peer Reviewed, Postprint (published version)

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This is an Accepted Manuscript of an article published by Taylor &Francis in “ Journal of applied statistics” on 17 Dec 2019 ,available online: https://www.tandfonline.com/doi/abs/10.1080/02664763.2019.1702929?journalCode=cjas20, Metric multidimensional scaling (MDS) is a widely used multivariate method with applications in almost all scientific disciplines. Eigenvalues obtained in the analysis are usually reported in order to calculate the overall goodness-of-fit of the distance matrix. In this paper, we refine MDS goodness-of-fit calculations, proposing additional point and pairwise goodness-of-fit statistics that can be used to filter poorly represented observations in MDS maps. The proposed statistics are especially relevant for large data sets that contain outliers, with typically many poorly fitted observations, and are helpful for improving MDS output and emphasizing the most important features of the dataset. Several goodness-of-fit statistics are considered, and both Euclidean and non-Euclidean distance matrices are considered. Some examples with data from demographic, genetic and geographic studies are shown., Peer Reviewed, Postprint (author's final draft)

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Different authors have highlighted the internal existing social differences in cities as a consequence of different economic, social and political forces. The mercantile logic that affects urban spaces incentives the dichotomy winners-losers in the current urban landscape and leads to the differentiation and unequal distribution of certain social groups within the urban space. This clear differentiation in distribution of social groups in the urban space has been called socio-spatial segregation. This concept arises from the urban sociology, the first studies were focused on the differentiation of ethnicity and income level to identify the most vulnerable groups and of mitigate their current situation through different policies. A more significant number of variables belonging to different dimensions (social, economic, political and environmental) have been incorporated into the study of this phenomenon, traditionally addressed by different disciplines such as sociology, geography and anthropology. Nonetheless, few studies have addressed it from a multivariate analysis approach. Moreover, the few existing studies with a multivariate statistical analysis ignored or did not know the compositional nature of their data. The objective of the present study is to apply the compositional data analysis in urban studies to better understand socio-spatial segregation in the different urban contexts. Specifically, the analysis of social-spatial segregation considering the compositional nature of the data in the city of Guadalajara, Mexico, is carried out. Socio-economic and socio-educative variables from census data of approximately 13,520 urban blocks grouped in 395 colonias and seven urban districts are used to carry out this study through the most straightforward compositions of two parts. Additionally, Principal Component Analysis (PCA) and cluster analysis are performed to identify the socio-economic distribution within the territory. The analysis is complemented with the, Peer Reviewed, Postprint (published version)

Understanding diversity in complex urban systems is fundamental in facing current and future sustainability challenges. In this article, we apply an exploratory multivariate statistical analysis (i.e., Principal Component Analysis (PCA) and Multiple Factor Analysis (MFA)) to an urban system’s abstraction of the city’s functioning. Specifically, we relate the environmental, economical, and social characters of the city in a multivariate system of indicators by collecting measurements of those variables at the district scale. Statistical methods are applied to reduce the dimensionality of the multivariate dataset, such that, hidden relationships between the districts of the city are exposed. The methodology has been mainly designed to display diversity, being understood as differentiated attributes of the districts in their dimensionally-reduced description, and to measure it with Euclidean distances. Differentiated characters and distinctive functions of districts are identifiable in the exploratory analysis of a case study of Barcelona (Spain). The distances allow for the identification of clustered districts, as well as those that are separated, exemplifying dissimilarity. Moreover, the temporal dependency of the dataset reveals information about the district’s differentiation or homogenization trends between 2003 and 2015., Postprint (published version)

Standard statistical tests for Hardy-Weinberg equilibrium assume the equality of allele frequencies in the sexes, whereas tests for the equality of allele frequencies in the sexes assume Hardy–Weinberg equilibrium. This produces a circularity in the testing of genetic variants, which has recently been resolved with new frequentist likelihood and exact procedures. In this paper, we tackle the same problem by posing it as a Bayesian model comparison problem. We formulate an exhaustive set of ten alternative scenarios for biallelic genetic variants. Using Dirichlet and Beta priors for genotype and allele frequencies, we derive marginal likelihoods for all scenarios, and select the most likely scenario using the posterior probabilities that each of these scenarios is the one in place. Different from the usual frequentist testing approach, the Bayesian approach allows one to compare any number of models, and not just two at a time, and the models compared do not have to be nested. We illustrate our Bayesian approach with genetic data from the 1,000 genomes project and through a simulation study., Peer Reviewed, Postprint (published version)

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