Mathematical bounds on Shannon entropy given the abundance of the ith most abundant taxon.

The measurement of diversity is a central component of studies in ecology and evolution, with broad uses spanning multiple biological scales. Studies of diversity conducted in population genetics and ecology make use of analogous concepts and even employ equivalent mathematical formulas. For the Shannon entropy statistic, recent developments in the mathematics of diversity in population genetics have produced mathematical constraints on the statistic in relation to the frequency of the most frequent allele. These results have characterized the ways in which standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we extend mathematical constraints on the Shannon entropy in relation to entries in specific positions in a vector of species abundances, listed in decreasing order. We illustrate the new mathematical results using abundance data from examples involving coral reefs and sponge microbiomes. The new results update the understanding of the relationship of a standard measure to the abundance vectors from which it is calculated, potentially contributing to improved interpretation of numerical measurements of biodiversity.

Conscientious vaccination exemptions in kindergarten to eighth-grade children across Texas schools from 2012 to 2018: A regression analysis.

BACKGROUND: As conscientious vaccination exemption (CVE) percentages rise across the United States, so does the risk and occurrence of outbreaks of vaccine-preventable diseases such as measles. In the state of Texas, the median CVE percentage across school systems more than doubled between 2012 and 2018. During this period, the proportion of schools surpassing a CVE percentage of 3% rose from 2% to 6% for public schools, 20% to 26% for private schools, and 17% to 22% for charter schools. The aim of this study was to investigate this phenomenon at a fine scale. METHODS AND FINDINGS: Here, we use beta regression models to study the socioeconomic and geographic drivers of CVE trends in Texas. Using annual counts of CVEs at the school system level from the 2012-2013 to the 2017-2018 school year, we identified county-level predictors of median CVE percentage among public, private, and charter schools, the proportion of schools below a high-risk threshold for vaccination coverage, and five-year trends in CVEs. Since the 2012-2013 school year, CVE percentages have increased in 41 out of 46 counties in the top 10 metropolitan areas of Texas. We find that 77.6% of the variation in CVE percentages across metropolitan counties is explained by median income, the proportion of the population that holds a bachelor's degree, the proportion of the population that self-reports as ethnically white, the proportion of the population that is English speaking, and the proportion of the population that is under the age of five years old. Across the 10 top metropolitan areas in Texas, counties vary considerably in the proportion of school systems reporting CVE percentages above 3%. Sixty-six percent of that variation is explained by the proportion of the population that holds a bachelor's degree and the proportion of the population affiliated with a religious congregation. Three of the largest metropolitan areas-Austin, Dallas-Fort Worth, and Houston-are potential vaccination exemption "hotspots," with over 13% of local school systems above this risk threshold. The major limitations of this study are inconsistent school-system-level CVE reporting during the study period and a lack of geographic and socioeconomic data for individual private schools. CONCLUSIONS: In this study, we have identified high-risk communities that are typically obscured in county-level risk assessments and found that public schools, like private schools, are exhibiting predictable increases in vaccination exemption percentages. As public health agencies confront the reemerging threat of measles and other vaccine-preventable diseases, findings such as ours can guide targeted interventions and surveillance within schools, cities, counties, and sociodemographic subgroups.

Quantifying compositional variability in microbial communities with FAVA.

Microbial communities vary across space, time, and individual hosts, presenting new challenges for the development of statistics measuring the variability of community composition. To understand differences across microbiome samples from different host individuals, sampling times, spatial locations, or experimental replicates, we present FAVA, a new normalized measure for characterizing compositional variability across multiple microbiome samples. FAVA quantifies variability across many samples of taxonomic or functional relative abundances in a single index ranging between 0 and 1, equaling 0 when all samples are identical and equaling 1 when each sample is entirely comprised of a single taxon. Its definition relies on the population-genetic statistic F S T , with samples playing the role of "populations" and taxa playing the role of "alleles." Its convenient mathematical properties allow users to compare disparate data sets. For example, FAVA values are commensurable across different numbers of taxonomic categories and different numbers of samples considered. We introduce extensions that incorporate phylogenetic similarity among taxa and spatial or temporal distances between samples. We illustrate how FAVA can be used to describe across-individual taxonomic variability in ruminant microbiomes at different regions along the gastrointestinal tract. In a second example, a longitudinal analysis of gut microbiomes of healthy human adults taking an antibiotic, we use FAVA to quantify the increase in temporal variability of microbiomes following the antibiotic course and to measure the duration of the antibiotic's influence on microbial variability. We have implemented this tool in an R package, FAVA, which can fit easily into existing pipelines for the analysis of microbial relative abundances.

Prolonged delays in human microbiota transmission after a controlled antibiotic perturbation.

Humans constantly encounter new microbes, but few become long-term residents of the adult gut microbiome. Classical theories predict that colonization is determined by the availability of open niches, but it remains unclear whether other ecological barriers limit commensal colonization in natural settings. To disentangle these effects, we used a controlled perturbation with the antibiotic ciprofloxacin to investigate the dynamics of gut microbiome transmission in 22 households of healthy, cohabiting adults. Colonization was rare in three-quarters of antibiotic-taking subjects, whose resident strains rapidly recovered in the week after antibiotics ended. In contrast, the remaining antibiotic-taking subjects exhibited lasting responses, with extensive species losses and transient expansions of potential opportunistic pathogens. These subjects experienced elevated rates of commensal colonization, but only after long delays: many new colonizers underwent sudden, correlated expansions months after the antibiotic perturbation. Furthermore, strains that had previously transmitted between cohabiting partners rarely recolonized after antibiotic disruptions, showing that colonization displays substantial historical contingency. This work demonstrates that there remain substantial ecological barriers to colonization even after major microbiome disruptions, suggesting that dispersal interactions and priority effects limit the pace of community change.

FSTruct: An FST -based tool for measuring ancestry variation in inference of population structure.

In model-based inference of population structure from individual-level genetic data, individuals are assigned membership coefficients in a series of statistical clusters generated by clustering algorithms. Distinct patterns of variability in membership coefficients can be produced for different groups of individuals, for example, representing different predefined populations, sampling sites or time periods. Such variability can be difficult to capture in a single numerical value; membership coefficient vectors are multivariate and potentially incommensurable across predefined groups, as the number of clusters over which individuals are distributed can vary among groups of interest. Further, two groups might share few clusters in common, so that membership coefficient vectors are concentrated on different clusters. We introduce a method for measuring the variability of membership coefficients of individuals in a predefined group, making use of an analogy between variability across individuals in membership coefficient vectors and variation across populations in allele frequency vectors. We show that in a model in which membership coefficient vectors in a population follow a Dirichlet distribution, the measure increases linearly with a parameter describing the variance of a specified component of the membership vector and does not depend on its mean. We apply the approach, which makes use of a normalized FST statistic, to data on inferred population structure in three example scenarios. We also introduce a bootstrap test for equivalence of two or more predefined groups in their level of membership coefficient variability. Our methods are implemented in the r package FSTruct.

Projecting COVID-19 isolation bed requirements for people experiencing homelessness.

As COVID-19 spreads across the United States, people experiencing homelessness (PEH) are among the most vulnerable to the virus. To mitigate transmission, municipal governments are procuring isolation facilities for PEH to utilize following possible exposure to the virus. Here we describe the framework for anticipating isolation bed demand in PEH communities that we developed to support public health planning in Austin, Texas during March 2020. Using a mathematical model of COVID-19 transmission, we projected that, under no social distancing orders, a maximum of 299 (95% Confidence Interval: 223, 321) PEH may require isolation rooms in the same week. Based on these analyses, Austin Public Health finalized a lease agreement for 205 isolation rooms on March 27th 2020. As of October 7th 2020, a maximum of 130 rooms have been used on a single day, and a total of 602 PEH have used the facility. As a general rule of thumb, we expect the peak proportion of the PEH population that will require isolation to be roughly triple the projected peak daily incidence in the city. This framework can guide the provisioning of COVID-19 isolation and post-acute care facilities for high risk communities throughout the United States.

The landscape of host genetic factors involved in immune response to common viral infections.

BACKGROUND: Humans and viruses have co-evolved for millennia resulting in a complex host genetic architecture. Understanding the genetic mechanisms of immune response to viral infection provides insight into disease etiology and therapeutic opportunities. METHODS: We conducted a comprehensive study including genome-wide and transcriptome-wide association analyses to identify genetic loci associated with immunoglobulin G antibody response to 28 antigens for 16 viruses using serological data from 7924 European ancestry participants in the UK Biobank cohort. RESULTS: Signals in human leukocyte antigen (HLA) class II region dominated the landscape of viral antibody response, with 40 independent loci and 14 independent classical alleles, 7 of which exhibited pleiotropic effects across viral families. We identified specific amino acid (AA) residues that are associated with seroreactivity, the strongest associations presented in a range of AA positions within DRß1 at positions 11, 13, 71, and 74 for Epstein-Barr virus (EBV), Varicella zoster virus (VZV), human herpesvirus 7, (HHV7), and Merkel cell polyomavirus (MCV). Genome-wide association analyses discovered 7 novel genetic loci outside the HLA associated with viral antibody response (P < 5.0 × 10-8), including FUT2 (19q13.33) for human polyomavirus BK (BKV), STING1 (5q31.2) for MCV, and CXCR5 (11q23.3) and TBKBP1 (17q21.32) for HHV7. Transcriptome-wide association analyses identified 114 genes associated with response to viral infection, 12 outside of the HLA region, including ECSCR: P = 5.0 × 10-15 (MCV), NTN5: P = 1.1 × 10-9 (BKV), and P2RY13: P = 1.1 × 10-8 EBV nuclear antigen. We also demonstrated pleiotropy between viral response genes and complex diseases, from autoimmune disorders to cancer to neurodegenerative and psychiatric conditions. CONCLUSIONS: Our study confirms the importance of the HLA region in host response to viral infection and elucidates novel genetic determinants beyond the HLA that contribute to host-virus interaction.

The landscape of host genetic factors involved in immune response to common viral infections.

INTRODUCTION: Humans and viruses have co-evolved for millennia resulting in a complex host genetic architecture. Understanding the genetic mechanisms of immune response to viral infection provides insight into disease etiology and therapeutic opportunities. METHODS: We conducted a comprehensive study including genome-wide and transcriptome-wide association analyses to identify genetic loci associated with immunoglobulin G antibody response to 28 antigens for 16 viruses using serological data from 7924 European ancestry participants in the UK Biobank cohort. RESULTS: Signals in human leukocyte antigen (HLA) class II region dominated the landscape of viral antibody response, with 40 independent loci and 14 independent classical alleles, 7 of which exhibited pleiotropic effects across viral families. We identified specific amino acid (AA) residues that are associated with seroreactivity, the strongest associations presented in a range of AA positions within DRß1 at positions 11, 13, 71, and 74 for Epstein-Barr Virus (EBV), Varicella Zoster Virus (VZV), Human Herpes virus 7, (HHV7) and Merkel cell polyomavirus (MCV). Genome-wide association analyses discovered 7 novel genetic loci outside the HLA associated with viral antibody response (P<5.×10-8), including FUT2 (19q13.33) for human polyomavirus BK (BKV), STING1 (5q31.2) for MCV, as well as CXCR5 (11q23.3) and TBKBP1 (17q21.32) for HHV7. Transcriptome-wide association analyses identified 114 genes associated with response to viral infection, 12 outside of the HLA region, including ECSCR: P=5.0×10-15 (MCV), NTN5: P=1.1×10-9 (BKV), and P2RY13: P=1.1×10-8 EBV nuclear antigen. We also demonstrated pleiotropy between viral response genes and complex diseases; from autoimmune disorders to cancer to neurodegenerative and psychiatric conditions. CONCLUSIONS: Our study confirms the importance of the HLA region in host response to viral infection and elucidates novel genetic determinants beyond the HLA that contribute to host-virus interaction.