Although Zipf’s law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf’s law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf’s law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.

No abstract

Up to November 2021, over 200 different SARS-CoV-2 lineages circulated in Mexico. To investigate lineage replacement dynamics, we applied a phylodynamic approach to explore the evolutionary trajectories of five dominant lineages that circulated during the first year of the local epidemic. For most lineages, peaks in sampling frequencies coincided with different epidemiological waves of infection in the country. Lineages B.1.1.222 and B.1.1.519 showed comparable dynamics, represented by clades likely originating in Mexico and persisting for over a year. Lineages B.1.1.7, P.1 and B.1.617.2 also displayed similar dynamics, characterized by multiple introduction events leading to a few successful extended local transmission chains that persisted for several months. We further explored viral movements across the country, applied within the largest clades identified (belonging to lineage B.1.617.2). Many clades were located within the south region of the country, suggesting that this area played a key role in the spread of SARS-CoV-2 in Mexico.

The sizes of paralogues—gene families produced by ancestral duplication—are known to follow a power-law distribution. We examine the size distribution of gene sets or gene families where genes are grouped by a similar function or share a common property. The size distribution of Human Gene Nomenclature Committee (HGNC) gene sets deviate from the power-law, and can be fitted much better by a beta rank function. We propose a simple mechanism to break a power-law size distribution by a combination of splitting and merging operations. The largest gene sets are split into two to account for the subfunctional categories, and a small proportion of other gene sets are merged into larger sets as new common themes might be realized. These operations are not uncommon for a curator of gene sets. A simulation shows that iteration of these operations changes the size distribution of Ensembl paralogues and could lead to a distribution fitted by a rank beta function. We further illustrate application of beta rank function by the example of distribution of transcription factors and drug target genes among HGNC gene families.

Over 200 different SARS-CoV-2 lineages have been observed in Mexico by November 2021. To investigate lineage replacement dynamics, we applied a phylodynamic approach and explored the evolutionary trajectories of five dominant lineages that circulated during the first year of local transmission. For most lineages, peaks in sampling frequencies coincided with different epidemiological waves of infection in Mexico. Lineages B.1.1.222 and B.1.1.519 exhibited similar dynamics, constituting clades that likely originated in Mexico and persisted for >12 months. Lineages B.1.1.7, P.1 and B.1.617.2 also displayed similar dynamics, characterized by multiple introduction events leading to a few successful extended local transmission chains that persisted for several months. For the largest B.1.617.2 clades, we further explored viral lineage movements across Mexico. Many clades were located within the south region of the country, suggesting that this area played a key role in the spread of SARS-CoV-2 in Mexico.

Human mobility networks are widely used for diverse studies in geography, sociology, and economics. In these networks, nodes usually represent places or regions and links refer to movement between them. They become essential when studying the spread of a virus, the planning of transit, or society’s local and global structures. Therefore, the construction and analysis of human mobility networks are crucial for a vast number of real-life applications. This work presents a collection of networks that describe the human travel patterns between municipalities in Mexico in the 2020–2021 period. Using anonymized mobile location data, we constructed directed, weighted networks representing the volume of travels between municipalities. We analysed changes in global, local, and mesoscale network features. We observe that changes in these features are associated with factors such as COVID-19 restrictions and population size. In general, the implementation of restrictions at the start of the COVID-19 pandemic in early 2020, induced more intense changes in network features than later events, which had a less notable impact in network features. These networks will result very useful for researchers and decision-makers in the areas of transportation, infrastructure planning, epidemic control and network science at large.

We present a collection of networks that describe the travel patterns between municipalities in Mexico between 2020 and 2021. Using anonymized mobile device geo-location data we constructed directed, weighted networks representing the (normalized) volume of travels between municipalities. We analysed changes in global (graph total weight sum), local (centrality measures), and mesoscale (community structure) network features. We observe that changes in these features are associated with factors such as Covid-19 restrictions and population size. In general, events in early 2020 (when initial Covid-19 restrictions were implemented) induced more intense changes in network features, whereas later events had a less notable impact in network features. We believe these networks will be useful for researchers and decision makers in the areas of transportation, infrastructure planning, epidemic control and network science at large.