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.

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.

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.