Amy Willis

Estimating diversity via frequency ratios

We wish to estimate the total number of classes in a population based on sample counts, especially in the presence of high latent diversity. Drawing on probability theory that characterizes distributions on the integers by ratios of consecutive probabilities, we construct a nonlinear regression model for the ratios of consecutive frequency counts. This allows us to predict the unobserved count and hence estimate the total diversity. We believe that this is the first approach to depart from the classical mixed Poisson model in this problem. Our method is geometrically intuitive and yields good fits to data with reasonable standard errors. It is especially well-suited to analyzing high diversity datasets derived from next-generation sequencing in microbial ecology. We demonstrate the methods performance in this context and via simulation, and we present a dataset for which our method outperforms all competitors.

Follicle number, not assessments of the ovarian stroma, represents the best ultrasonographic marker of polycystic ovary syndrome

OBJECTIVE To compare the diagnostic potential of ultrasonographic markers of ovarian morphology, used alone or in combination, to predict polycystic ovary syndrome (PCOS). DESIGN A diagnostic test study using cross-sectional data collected from 2006-2011. SETTING Academic hospital and clinical research unit. PATIENT(S) Eighty-two women with PCOS and 60 healthy female volunteers. INTERVENTION(S) None. MAIN OUTCOME MEASURE(S) Follicle number per ovary (FNPO), ovarian volume (OV), follicle number per single cross-section (FNPS), follicle distribution pattern, stromal area, ovarian area, stromal-to-ovarian area ratio (S:A), and stromal index (SI). RESULT(S) Follicle number per ovary best predicted PCOS (R(2) = 67%) with 85% sensitivity and 98% specificity, followed by OV (R(2) = 44%), and FNPS (R(2) = 36%). Neither S:A nor SI had predictive power for PCOS. In combination, FNPO+S:A and FNPO+SI most significantly predicted PCOS (R(2) = 74% vs. 73%, respectively). The diagnostic potentials of OV and FNPS were substantially improved when used in combination (OV+FNPO, R(2) = 55%). CONCLUSION(S) As a single metric, FNPO best predicted PCOS. Although the addition of S:A or SI improved the predictive power of FNPO, gains were marginal, suggesting limited use in clinical practice. When image quality precludes a reliable estimation of FNPO, measurements of OV+FNPS provide the next closest level of diagnostic potential.

Nonstandard regular variation of in-degree and out-degree in the preferential attachment model

The research of the authors was supported by MURI ARO Grant W911NF-12-10385 to Cornell University

Influencing the Tumor Microenvironment: A Phase II Study of Copper Depletion Using Tetrathiomolybdate in Patients with Breast Cancer at High Risk for Recurrence and in Preclinical Models of Lung Metastases

Purpose: Bone marrow–derived progenitor cells, including VEGFR2+ endothelial progenitor cells (EPCs) and copper-dependent pathways, model the tumor microenvironment. We hypothesized that copper depletion using tetrathiomolybdate would reduce EPCs in high risk for patients with breast cancer who have relapsed. We investigated the effect of tetrathiomolybdate on the tumor microenvironment in preclinical models. Experimental Design: Patients with stage II triple-negative breast cancer (TNBC), stage III and stage IV without any evidence of disease (NED), received oral tetrathiomolybdate to maintain ceruloplasmin (Cp) between 8 and 17 mg/dL for 2 years or until relapse. Endpoints were effect on EPCs and other biomarkers, safety, event-free (EFS), and overall survival (OS). For laboratory studies, MDA-LM2-luciferase cells were implanted into CB17-SCID mice and treated with tetrathiomolybdate or water. Tumor progression was quantified by bioluminescence imaging (BLI), copper depletion status by Cp oxidase levels, lysyl oxidase (LOX) activity by ELISA, and collagen deposition. Results: Seventy-five patients enrolled; 51 patients completed 2 years (1,396 cycles). Most common grade 3/4 toxicity was neutropenia (3.7%). Lower Cp levels correlated with reduced EPCs (P = 0.002) and LOXL-2 (P < 0.001). Two-year EFS for patients with stage II–III and stage IV NED was 91% and 67%, respectively. For patients with TNBC, EFS was 90% (adjuvant patients) and 50% (stage IV NED patients) at a median follow-up of 6.3 years, respectively. In preclinical models, tetrathiomolybdate decreased metastases to lungs (P = 0.04), LOX activity (P = 0.03), and collagen crosslinking (P = 0.012). Conclusions: Tetrathiomolybdate is safe, well tolerated, and affects copper-dependent components of the tumor microenvironment. Biomarker-driven clinical trials in high risk for patients with recurrent breast cancer are warranted. Clin Cancer Res; 23(3); 666–76. ©2016 AACR.

Continental igneous rock composition: A major control of past global chemical weathering

Changes in the isotopic composition of the continental crust control the strontium isotope ratio in seawater. The composition of igneous rocks in the continental crust has changed throughout Earth’s history. However, the impact of these compositional variations on chemical weathering, and by extension on seawater and atmosphere evolution, is largely unknown. We use the strontium isotope ratio in seawater [(87Sr/86Sr)seawater] as a proxy for chemical weathering, and we test the sensitivity of (87Sr/86Sr)seawater variations to the strontium isotopic composition (87Sr/86Sr) in igneous rocks generated through time. We demonstrate that the 87Sr/86Sr ratio in igneous rocks is correlated to the epsilon hafnium (εHf) of their hosted zircon grains, and we use the detrital zircon record to reconstruct the evolution of the 87Sr/86Sr ratio in zircon-bearing igneous rocks. The reconstructed 87Sr/86Sr variations in igneous rocks are strongly correlated with the (87Sr/86Sr)seawater variations over the last 1000 million years, suggesting a direct control of the isotopic composition of silicic magmatism on (87Sr/86Sr)seawater variations. The correlation decreases during several time periods, likely reflecting changes in the chemical weathering rate associated with paleogeographic, climatic, or tectonic events. We argue that for most of the last 1000 million years, the (87Sr/86Sr)seawater variations are responding to changes in the isotopic composition of silicic magmatism rather than to changes in the global chemical weathering rate. We conclude that the (87Sr/86Sr)seawater variations are of limited utility to reconstruct changes in the global chemical weathering rate in deep times.

Extrapolating abundance curves has no predictive power for estimating microbial biodiversity

Locey and Lennon (1) recently conducted an analysis of microbial and macrobial communities to investigate the effect of sample size (N, number of individuals or reads observed) on community species richness (S), species evenness (Simpson), frequency distribution skew, and frequency count of most abundant taxa. They argue that log–log linear models fit these relationships, specifically claiming that the index of the power law between sample size and species richness is consistent across macro- and microorganisms. Furthermore, they use the “lognormal model of biodiversity” to estimate global microbial biodiversity around 1011 to 1012 taxa. Although their claims are appealing and elegant, I argue (from a statistical perspective) …

Confidence Sets for Phylogenetic Trees

ABSTRACT Inferring evolutionary histories (phylogenetic trees) has important applications in biology, criminology, and public health. However, phylogenetic trees are complex mathematical objects that reside in a non-Euclidean space, which complicates their analysis. While our mathematical, algorithmic, and probabilistic understanding of phylogenies in their metric space is mature, rigorous inferential infrastructure is as yet undeveloped. In this manuscript, we unify recent computational and probabilistic advances to construct tree–valued confidence sets. The procedure accounts for both center and multiple directions of tree–valued variability. We draw on block replicates to improve testing, identifying the best supported most recent ancestor of the Zika virus, and formally testing the hypothesis that a Floridian dentist with AIDS infected two of his patients with HIV. The method illustrates connections between variability in Euclidean and tree space, opening phylogenetic tree analysis to techniques available in the multivariate Euclidean setting. Supplementary materials for this article are available online.

DivNet: Estimating diversity in networked communities

Diversity is a marker of ecosystem health in ecology, microbiology and immunology, with implications for disease diagnosis and infection resistance. However, accurately comparing diversity across environmental gradients is challenging, especially when number of different taxonomic groups in the community is large. Furthermore, existing approaches to estimating diversity do not perform well when the taxonomic groups in the community interact via an ecological network, such as by competing within their niche, or with mutualistic relationships. To address this, we propose DivNet, a method for estimating within- and between-community diversity in ecosystems where taxa interact via an ecological network. In particular, accounting for network structure permits more accurate estimates of alpha- and beta-diversity, even in settings with a large number of taxa and a small number of samples. DivNet is fast, accurate, precise, performs well with large numbers of taxa, and is robust to both weakly and strongly networked communities. We show that the advantages of incorporating taxon interactions into diversity estimation are especially clear in analyzing microbiomes and other high-diversity, strongly networked ecosystems. Therefore, to illustrate the method, we analyze the microbiome of seafloor basalts based on a 16S amplicon sequencing dataset with 1490 taxa and 13 samples.

Uncertainty in Phylogenetic Tree Estimates

ABSTRACT Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy, and medicine. Although trees are estimated, their uncertainties are generally discarded in statistical models for tree-valued data. Here, we explicitly model the multivariate uncertainty of tree estimates. We consider both the cases where uncertainty information arises extrinsically (through covariate information) and intrinsically (through the tree estimates themselves). The latter case is applicable to any procedure for tree estimation, and thus has broad relevance to the entire field of phylogenetics. The importance of accounting for tree uncertainty in tree space is demonstrated in two case studies. In the first instance, differences between gene trees are small relative to their uncertainties, while in the second, the differences are relatively large. Our main goal is visualization of tree uncertainty, and we demonstrate advantages of our method with respect to reproducibility, speed, and preservation of topological differences compared to visualization based on multidimensional scaling. The proposal highlights that phylogenetic trees are estimated in an extremely high-dimensional space, resulting in uncertainty information that cannot be discarded. Most importantly, it is a method that allows biologists to diagnose whether differences between gene trees are biologically meaningful or due to uncertainty in estimation.

Niche Separation Increases With Genetic Distance Among Bloom-Forming Cyanobacteria

Bacterial communities are composed of distinct groups of potentially interacting lineages, each thought to occupy a distinct ecological niche. It remains unclear, however, how quickly niche preference evolves and whether more closely related lineages are more likely to share ecological niches. We addressed these questions by following the dynamics of two bloom-forming cyanobacterial genera over an 8-year time-course in Lake Champlain, Canada, using 16S amplicon sequencing and measurements of several environmental parameters. The two genera, Microcystis (M) and Dolichospermum (D), are frequently observed simultaneously during bloom events and thus have partially overlapping niches. However, the extent of their niche overlap is debated, and it is also unclear to what extent niche partitioning occurs among strains within each genus. To identify strains within each genus, we applied minimum entropy decomposition (MED) to 16S rRNA gene sequences. We confirmed that at a genus level, M and D have different preferences for nitrogen and phosphorus concentrations. Within each genus, we also identified strains differentially associated with temperature, precipitation, and concentrations of nutrients and toxins. In general, niche similarity between strains (as measured by co-occurrence over time) declined with genetic distance. This pattern is consistent with habitat filtering – in which closely related taxa are ecologically similar, and therefore tend to co-occur under similar environmental conditions. In contrast with this general pattern, similarity in certain niche dimensions (notably particulate nitrogen and phosphorus) did not decline linearly with genetic distance, and instead showed a complex polynomial relationship. This observation suggests the importance of processes other than habitat filtering – such as competition between closely related taxa, or convergent trait evolution in distantly related taxa – in shaping particular traits in microbial communities.