Estimating the distribution of heterogeneous treatment effects from treatment responses and from a predictive biomarker in a parallel-group RCT: A structural model approach

When the objective is to administer the best of two treatments to an individual, it is necessary to know his or her individual treatment effects (ITEs) and the correlation between the potential responses (PRs) and under treatments 1 and 0. Data that are generated in a parallel-group design RCT does not allow the ITE to be determined because only two samples from the marginal distributions of these PRs are observed and not the corresponding joint distribution. This is due to the “fundamental problem of causal inference.” Here, we present a counterfactual approach for estimating the joint distribution of two normally distributed responses to two treatments. This joint distribution of the PRs and can be estimated by assuming a bivariate normal distribution for the PRs and by using a normally distributed baseline biomarker functionally related to the sum . Such a functional relationship is plausible since a biomarker and the sum encode for the same information in an RCT, namely the variation between subjects. The estimation of the joint trivariate distribution is subjected to some constraints. These constraints can be framed in the context of linear regressions with regard to the proportions of variances in the responses explained and with regard to the residual variation. This presents new insights on the presence of treatment–biomarker interactions. We applied our approach to example data on exercise and heart rate and extended the approach to survival data.     

Intuitive and broadly applicable definitions of niche and fitness differences

Explaining nature’s biodiversity is a key challenge for science. To persist, populations must be able to grow faster when rare, a feature called negative frequency dependence and quantified as ‘niche differences’ () in modern coexistence theory. Here, we first show that available definitions of differ in how link to species interactions, are difficult to interpret and often apply to specific community types only. We then present a new definition of that is intuitive and applicable to a broader set of (modelled and empirical) communities than is currently the case, filling a main gap in the literature. Given , we also redefine fitness differences () and illustrate how and determine coexistence. Finally, we demonstrate how to apply our definitions to theoretical models and experimental data, and provide ideas on how they can facilitate comparison and synthesis in community ecology.     

Temperature response of denitrification rate and greenhouse gas production in agricultural river marginal wetland soils

Soils are predicted to exhibit significant feedback to global warming via the temperature response of greenhouse gas (GHG) production. However, the temperature response of hydromorphic wetland soils is complicated by confounding factors such as oxygen (O₂), nitrate () and soil carbon (C). We examined the effect of a temperature gradient (2–25 °C) on denitrification rates and net nitrous oxide (N₂O), methane (CH₄) production and heterotrophic respiration in mineral (Eutric cambisol and Fluvisol) and organic (Histosol) soil types in a river marginal landscape of the Tamar catchment, Devon, UK, under non‐flooded and flooded with enriched conditions. It was hypothesized that the temperature response is dependent on interactions with ‐enriched flooding, and the physicochemical conditions of these soil types. Denitrification rate (mean, 746 ± 97.3 μg m^?2 h^?1), net N₂O production (mean, 180 ± 26.6 μg m^?2 h^?1) and net CH₄ production (mean, 1065 ± 183 μg m^?2 h^?1) were highest in the organic Histosol, with higher organic matter, ammonium and moisture, and lower concentrations. Heterotrophic respiration (mean, 127 ± 4.6 mg m^?2 h^?1) was not significantly different between soil types and dominated total GHG (CO₂eq) production in all soil types. Generally, the temperature responses of denitrification rate and net N₂O production were exponential, whilst net CH₄ production was unresponsive, possibly due to substrate limitation, and heterotrophic respiration was exponential but limited in summer at higher temperatures. Flooding with increased denitrification rate, net N₂O production and heterotrophic respiration, but a reduction in net CH₄ production suggests inhibition of methanogenesis by or N₂O produced from denitrification. Implications for management and policy are that warming and flood events may promote microbial interactions in soil between distinct microbial communities and increase denitrification of excess with N₂O production contributing to no more than 50% of increases in total GHG production.     

Inverse problem approach to regularized regression models with application to predicting recovery after stroke

Regression modelling is a powerful statistical tool often used in biomedical and clinical research. It could be formulated as an inverse problem that measures the discrepancy between the target outcome and the data produced by representation of the modelled predictors. This approach could simultaneously perform variable selection and coefficient estimation. We focus particularly on a linear regression issue, , where is the parameter of interest and its components are the regression coefficients. The inverse problem finds an estimate for the parameter , which is mapped by the linear operator to the observed outcome data . This problem could be conveyed by finding a solution in the affine subspace . However, in the presence of collinearity, high-dimensional data and high conditioning number of the related covariance matrix, the solution may not be unique, so the introduction of prior information to reduce the subset and regularize the inverse problem is needed. Informed by Huber's robust statistics framework, we propose an optimal regularizer to the regression problem. We compare results of the proposed method and other penalized regression regularization methods: ridge, lasso, adaptive-lasso and elastic-net under different strong hypothesis such as high conditioning number of the covariance matrix and high error amplitude, on both simulated and real data from the South London Stroke Register. The proposed approach can be extended to mixed regression models. Our inverse problem framework coupled with robust statistics methodology offer new insights in statistical regression and learning. It could open a new research development for model fitting and learning.     

Estimating the decision curve and its precision from three study designs

The decision curve plots the net benefit of a risk model for making decisions over a range of risk thresholds, corresponding to different ratios of misclassification costs. We discuss three methods to estimate the decision curve, together with corresponding methods of inference and methods to compare two risk models at a given risk threshold. One method uses risks (R) and a binary event indicator (Y) on the entire validation cohort. This method makes no assumptions on how well-calibrated the risk model is nor on the incidence of disease in the population and is comparatively robust to model miscalibration. If one assumes that the model is well-calibrated, one can compute a much more precise estimate of based on risks R alone. However, if the risk model is miscalibrated, serious bias can result. Case–control data can also be used to estimate if the incidence (or prevalence) of the event () is known. This strategy has comparable efficiency to using the full data, and its efficiency is only modestly less than that for the full data if the incidence is estimated from the mean of Y. We estimate variances using influence functions and propose a bootstrap procedure to obtain simultaneous confidence bands around the decision curve for a range of thresholds. The influence function approach to estimate variances can also be applied to cohorts derived from complex survey samples instead of simple random samples.     

Chemodenitrification in the cryoecosystem of Lake Vida,Victoria Valley,Antarctica

Lake Vida, in the Victoria Valley of East Antarctica, is frozen, yet harbors liquid brine (~20% salt, >6 times seawater) intercalated in the ice below 16 m. The brine has been isolated from the surface for several thousand years. The brine conditions (permanently dark, ?13.4 °C, lack of O₂, and pH of 6.2) and geochemistry are highly unusual. For example, nitrous oxide (N₂O) is present at a concentration among the highest reported for an aquatic environment. Only a minor ¹⁷O anomaly was observed in N₂O, indicating that this gas was predominantly formed in the lake. In contrast, the ¹⁷O anomaly in nitrate () in Lake Vida brine indicates that approximately half or more of the present is derived from atmospheric deposition. Lake Vida brine was incubated in the presence of ¹⁵N‐enriched substrates for 40 days. We did not detect microbial nitrification, dissimilatory reduction of to ammonium (), anaerobic ammonium oxidation, or denitrification of N₂O under the conditions tested. In the presence of ¹⁵N‐enriched nitrite (), both N₂ and N₂O exhibited substantial ¹⁵N enrichments; however, isotopic enrichment declined with time, which is unexpected. Additions of ¹⁵N– alone and in the presence of HgCl₂ and ZnCl₂ to aged brine at ?13 °C resulted in linear increases in the δ¹⁵N of N₂O with time. As HgCl₂ and ZnCl₂ are effective biocides, we interpret N₂O production in the aged brine to be the result of chemodenitrification. With this understanding, we interpret our results from the field incubations as the result of chemodenitrification stimulated by the addition of ¹⁵N‐enriched and ZnCl₂ and determined rates of N₂O and N₂ production of 4.11–41.18 and 0.55–1.75 nmol L^?1 day^?1, respectively. If these rates are representative of natural production, the current concentration of N₂O in Lake Vida could have been reached between 6 and 465 years. Thus, chemodenitrification alone is sufficient to explain the high levels of N₂O present in Lake Vida.     

Mean growth rate when rare is not a reliable metric for persistence of species

The coexistence of many species within ecological communities poses a long‐standing theoretical puzzle. Modern coexistence theory (MCT) and related techniques explore this phenomenon by examining the chance of a species population growing from rarity in the presence of all other species. The mean growth rate when rare, , is used in MCT as a metric that measures persistence properties (like invasibility or time to extinction) of a population. Here we critique this reliance on and show that it fails to capture the effect of temporal random abundance variations on persistence properties. The problem becomes particularly severe when an increase in the amplitude of stochastic temporal environmental variations leads to an increase in , since at the same time it enhances random abundance fluctuations and the two effects are inherently intertwined. In this case, the chance of invasion and the mean extinction time of a population may even go down as increases.     

The effects of hurricanes on the stochastic population growth of the endemic epiphytic orchid Broughtonia cubensis living in Cuba

We carried out a posthurricane evaluation of Broughtonia cubensis (Lindl.) Cogn., an endemic Cuban epiphytic orchid, after Hurricane Ivan (2004). We studied the transient responses in the stochastic dynamics of the species at three different sites over 13 successive years (2006–2019), monitored plot inventories (464 individuals in 10 transects) and built stochastic population models. The deterministic stochastic growth rate values () did not significantly differ (F = 2.76; p > 0.076) among the three sites over the 2006–2019 period. The long-term stochastic growth rate was 0.973 [0.932, 1.034]. The matrix elements that had the largest effect on were the transition to and stasis within the largest size class. Transient responses explained an average of 86% of the variation in the observed population growth rates , compared to 4% of the variation in the vital rates . Because transient dynamics are dependent on the population size composition, we ran extinction risk analyses under two scenarios: a population composed mainly of juveniles and another composed mainly of adults. There was little risk of falling below the quasi-extinction threshold before 25 year for both juveniles and adults. However, the risk of quasi-extinction was almost certain for both size classes by 80 year. We also simulated the effect of increasing the hurricane occurrence probability over 80 year on the population. There was little risk of extinction before 20 year in the baseline model, but there was a significant risk of extinction within 5 year when 90% of the individuals were affected by a new hurricane event.     

Evidence for Depressed Reproduction of Golden Eagles in Washington

Beginning in 1977 the Washington Department of Fish and Wildlife conducted annual surveys to determine statewide golden eagle (Aquila chrysaetos) occupancy and productivity. Current interest in the regional and national status of the species prompted our investigation to determine utility of historical data in assessing trends in reproduction, and to test efficacy of a sampling protocol that surveyed randomly selected territories and also accounted for detection probability. We found evidence indicating poor reproduction from 38 annual surveys conducted at 301 known territories statewide between 1977 and 2014. At 256 territories in eastern Washington, USA, apparent occupancy was low ( = 50.9%) and nesting success declined by 22%. All reproductive parameters were higher than at 45 territories in western Washington. We tested efficacy of a sampling protocol in 2013 and 2014 by surveying 108 randomly selected eastern territories. Probability of detecting eagles for these years from ground (= 89%) was greater than from air (= 66%). Our estimate of territory occupancy, corrected by probability of detection, was lower in 2013 (= 56.7%, 95% CI = 46.3–66.7%) than in 2014 (= 73.7%, 95% CI = 64.8–81.7%), as was the estimated number of breeding pairs (2013: = 158, 95% CI = 151–164; 2014: = 187, 95% CI = 182–192). Higher productivity (young/occupied territory) in 2013 (= 0.59, 95% CI = 0.40–0.82) than in 2014 (= 0.41, 95% CI = 0.27–0.59) and lower proportions of ≥1 immature eagle among nesting pairs in 2013 (16%) than in 2014 (31%), suggested higher immature pairing among sampled pairs contributed to inter-year differences in these reproductive parameters. Current and historical evidence for depressed golden eagle nesting in Washington is consistent with documented effects from habitat conversion, prey declines, lead contamination, and wind power development. We recommend future surveys in eastern Washington adhere to the random sampling protocol and conduct surveys at regular intervals to allow for trend analysis of reproductive parameters to better monitor golden eagle status. Surveys in western Washington, conducted exclusively from ground at all nests, will improve detection and cost efficiency. © 2020 The Wildlife Society.     

Important role of genetic drift in rapid polygenic adaptation

We analyzed a model to determine the factors that facilitate or limit rapid polygenic adaptation. This model includes population genetic terms of mutation and both directional and stabilizing selection on a highly polygenic trait in a diploid population of finite size. First, we derived the equilibrium distribution of the allele frequencies of the multilocus model by diffusion approximation. This formula describing the equilibrium allele frequencies as a mutation‐selection‐drift balance was examined by computer simulation using parameter values inferred for human height, a well‐studied polygenic trait. Second, assuming that a sudden environmental shift of the fitness optimum occurs while the population is in equilibrium, we analyzed the adaptation of the trait to the new optimum. The speed at which the trait mean approaches the new optimum increases with the equilibrium genetic variance. Thus, large population size and/or large mutation rate may facilitate rapid adaptation. Third, the contribution of an individual locus i to polygenic adaptation depends on the compound parameter , where is the effect size, the equilibrium frequency of the trait‐increasing allele of this locus, and . Thus, only loci with large values of this parameter contribute coherently to polygenic adaptation. Given that mutation rates are relatively small, this is more likely in large populations, in which the effects of drift are limited.     

Anthropogenic Disturbance and Population Viability of Woodland Caribou in Ontario

One of the most challenging tasks in wildlife conservation and management is to clarify how spatial variation in land cover due to anthropogenic disturbance influences wildlife demography and long-term viability. To evaluate this, we compared rates of survival and population growth by woodland caribou (Rangifer tarandus caribou) from 2 study sites in northern Ontario, Canada that differed in the degree of anthropogenic disturbance because of commercial logging and road development, resulting in differences in predation risk due to gray wolves (Canis lupus). We used an individual-based model for population viability analysis (PVA) that incorporated adaptive patterns of caribou movement in relation to predation risk and food availability to predict stochastic variation in rates of caribou survival. Field estimates of annual survival rates for adult female caribou in the unlogged ( 0.90) and logged ( 0.76) study sites recorded during 2010–2014 did not differ significantly (P > 0.05) from values predicted by the individual-based PVA model (unlogged: = 0.87; logged: 0.79). Outcomes from the individual-based PVA model and a simpler stage-structured matrix model suggest that substantial differences in adult survival largely due to wolf predation are likely to lead to long-term decline of woodland caribou in the commercially logged landscape, whereas the unlogged landscape should be considerably more capable of sustaining caribou. Estimates of population growth rates (λ) for the 2010–2014 period differed little between the matrix model and the individual-based PVA model for the unlogged (matrix model = 1.01; individual-based model = 0.98) and logged landscape (matrix model = 0.88; individual-based model = 0.89). We applied the spatially explicit PVA model to assess the viability of woodland caribou across 14 woodland caribou ranges in Ontario. Outcomes of these simulations suggest that woodland caribou ranges that have experienced significant levels of commercial forestry activities in the past had annual growth rates <0.89, whereas caribou ranges that had not experienced commercial forestry operations had population growth rates >0.96. These differences were strongly related to regional variation in wolf densities. Our results suggest that increased wolf predation risk due to anthropogenic disturbance is of sufficient magnitude to cause appreciable risk of population decline in woodland caribou in Ontario. © 2020 The Authors. The Journal of Wildlife Management published by Wiley Periodicals, Inc. on behalf of The Wildlife Society.     

Optimal rotation of insecticides to prevent the evolution of resistance in a structured environment

Several strategies have been used in insecticide resistance management to prevent the evolution of resistance, but the spatial aspects of insecticide application are crucially important among these strategies. Here, we consider a structured environment that consists of on-farm and off-farm fields where crops are planted periodically in on-farm fields during cultivation periods. We define the basic reproduction rate () of resistance as the expected number of offspring of a resistant individual divided by that of a susceptible individual under the condition that the proportion of resistance is extremely small; it is measured as the quantity per cycle of the cultivation period. We calculate using realistic dose-survival curves under a given fitness cost of resistance genes. The evolution of resistance occurs if and only if the value is larger than 0. Then, we propose a procedure for calculating the optimal design of rotational spraying that prevents the evolution of resistance, that is, the evolutionary stable strategy (ESS) for farmers, satisfying the mortality required for managing the abundance of insects. We consider the following controllable factors in calculating the optimal design: the dose of insecticide, the number of sprays, the number of different types of insecticides and potentially, the size of on-farm fields.     

Optimal Strategies for Managing Wildlife Harvest Under System Change

Wildlife populations are experiencing shifting dynamics due to climate and landscape change. Management policies that fail to account for non-stationary dynamics may fail to achieve management objectives. We establish a framework for understanding optimal strategies for managing a theoretical harvested population under non-stationarity. Building from harvest theory, we develop scenarios representing changes in population growth rate () or carrying capacity () and derive time-dependent optimal harvest policies using stochastic dynamic programming. We then evaluate the cost of falsely assuming stationarity by comparing the outcomes of forward projections in which either the optimal policy or a stationary policy is applied. When declines over time, the stationary policy leads to an underharvest of the population, resulting in less harvest over the short term but leaving the population in a higher-value state. When declines over time, the stationary policy leads to overharvest, resulting in greater harvest returns in the short term but leaving the population in a lower and potentially more vulnerable state. This work demonstrates the basic properties of time-dependent harvest management and provides a framework for evaluating the many outstanding questions about optimal management strategies under climate change. Published 2021. This article is a U.S. Government work and is in the public domain in the USA.     

Dual‐ and single‐shot susceptibility ratio measurements with circular polarizations in second‐harmonic generation microscopy

Polarization‐resolved second‐harmonic generation (P‐SHG) microscopy is a technique capable of characterizing nonlinear optical properties of noncentrosymmetric biomaterials by extracting the nonlinear susceptibility tensor components ratio , with z‐axis parallel and x‐axis perpendicular to the C₆ symmetry axis of molecular fiber, such as a myofibril or a collagen fiber. In this paper, we present two P‐SHG techniques based on incoming and outgoing circular polarization states for a fast extraction of : A dual‐shot configuration where the SHG circular anisotropy generated using incident right‐ and left‐handed circularly‐polarized light is measured; and a single‐shot configuration for which the SHG circular anisotropy is measured using only one incident circular polarization state. These techniques are used to extract the of myosin fibrils in the body wall muscles of Drosophila melanogaster larva. The results are in good agreement with values obtained from the double Stokes‐Mueller polarimetry. The dual‐ and single‐shot circular anisotropy measurements can be used for fast imaging that is independent of the in‐plane orientation of the sample. They can be used for imaging of contracting muscles, or for high throughput imaging of large sample areas.     

An estimator of the Opportunity for Selection that is independent of mean fitness

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crow's Opportunity for Selection (I), which is the variance in relative fitness (I = σ²_k/(u_k)²). Crow's I has been widely used but remains controversial because it depends on mean offspring number in a sample (). Here, I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crow's I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance (s²_k) to its expected value at a fixed removes dependence of I on mean offspring number, but the result still depends on choice of . A new index is introduced, Δ_I = Π– E(Î_drift) = Π– 1/, which makes Î independent of sample without the need for variance rescaling. Δ_I has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. Δ_I can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.     

The design heatmap: A simple visualization of -optimality design problems

Optimal experimental designs are often formal and specific, and not intuitively plausible to practical experimenters. However, even in theory, there often are many different possible design points providing identical or nearly identical information compared to the design points of a strictly optimal design. In practical applications, this can be used to find designs that are a compromise between mathematical optimality and practical requirements, including preferences of experimenters. For this purpose, we propose a derivative-based two-dimensional graphical representation of the design space that, given any optimal design is already known, will show which areas of the design space are relevant for good designs and how these areas relate to each other. While existing equivalence theorems already allow such an illustration in regard to the relevance of design points only, our approach also shows whether different design points contribute the same kind of information, and thus allows tweaking of designs for practical applications, especially in regard to the splitting and combining of design points. We demonstrate the approach on a toxicological trial where a -optimal design for a dose–response experiment modeled by a four-parameter log-logistic function was requested. As these designs require a prior estimate of the relevant parameters, which is difficult to obtain in a practical situation, we also discuss an adaption of our representations to the criterion of Bayesian -optimality. While we focus on -optimality, the approach is in principle applicable to different optimality criteria as well. However, much of the computational and graphical simplicity will be lost.     

Rates and pathways of CH4 oxidation in ferruginous Lake Matano,Indonesia

This study evaluates rates and pathways of methane (CH₄) oxidation and uptake using ¹⁴C‐based tracer experiments throughout the oxic and anoxic waters of ferruginous Lake Matano. Methane oxidation rates in Lake Matano are moderate (0.36 nmol L^?1 day^?1 to 117 μmol L^?1 day^?1) compared to other lakes, but are sufficiently high to preclude strong CH₄ fluxes to the atmosphere. In addition to aerobic CH₄ oxidation, which takes place in Lake Matano's oxic mixolimnion, we also detected CH₄ oxidation in Lake Matano's anoxic ferruginous waters. Here, CH₄ oxidation proceeds in the apparent absence of oxygen (O₂) and instead appears to be coupled to some as yet uncertain combination of nitrate (), nitrite (), iron (Fe) or manganese (Mn), or sulfate () reduction. Throughout the lake, the fraction of CH₄ carbon that is assimilated vs. oxidized to carbon dioxide (CO₂) is high (up to 93%), indicating extensive CH₄ conversion to biomass and underscoring the importance of CH₄ as a carbon and energy source in Lake Matano and potentially other ferruginous or low productivity environments.     

Physiological and pathophysiological role of ion channels and transporters in the colorectum and colorectal cancer

The incidence of colorectal cancer has increased annually, and the pathogenesis of this disease requires further investigation. In normal colorectal tissues, ion channels and transporters maintain the water‐electrolyte balance and acid/base homeostasis. However, dysfunction of these ion channels and transporters leads to the development and progression of colorectal cancer. Therefore, this review focuses on the progress in understanding the roles of ion channels and transporters in the colorectum and in colorectal cancer, including aquaporins (AQPs), Cl^? channels, Cl^?/ exchangers, Na⁺/ transporters and Na⁺/H⁺ exchangers. The goal of this review is to promote the identification of new targets for the treatment and prognosis of colorectal cancer.     

Another chemolithotrophic metabolism missing in nature: sulfur comproportionation

Chemotrophic microorganisms gain energy for cellular functions by catalyzing oxidation–reduction (redox) reactions that are out of equilibrium. Calculations of the Gibbs energy ( ΔG _r ) can identify whether a reaction is thermodynamically favourable and quantify the accompanying energy yield at the temperature, pressure and chemical composition in the system of interest. Based on carefully calculated values of ΔG _r , we predict a novel microbial metabolism – sulfur comproportionation (3H₂S + + 2H⁺ ⇌ 4S⁰ + 4H₂O). We show that at elevated concentrations of sulfide and sulfate in acidic environments over a broad temperature range, this putative metabolism can be exergonic ( ΔG _r <0), yielding ~30–50 kJ mol⁻¹. We suggest that this may be sufficient energy to support a chemolithotrophic metabolism currently missing from the literature. Other versions of this metabolism, comproportionation to thiosulfate (H₂S + ⇌ + H₂O) and to sulfite (H₂S + 3 ⇌ 4 + 2H⁺), are only moderately exergonic or endergonic even at ideal geochemical conditions. Natural and impacted environments, including sulfidic karst systems, shallow-sea hydrothermal vents, sites of acid mine drainage, and acid–sulfate crater lakes, may be ideal hunting grounds for finding microbial sulfur comproportionators.