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Aim: Higher-elevation areas on islands and continental mountains tend to be separated by longer distances, predicting higher endemism at higher elevations; our study is the first to test the generality of the predicted pattern. We also compare it empirically with contrasting expectations from hypotheses invoking higher speciation with area, temperature and species richness. Location: Thirty-two insular and 18 continental elevational gradients from around the world. Methods: We compiled entire floras with elevation-specific occurrence information, and calculated the proportion of native species that are endemic ('percent endemism') in 100-m bands, for each of the 50 elevational gradients. Using generalized linear models, we tested the relationships between percent endemism and elevation, isolation, temperature, area and species richness. Results: Percent endemism consistently increased monotonically with elevation, globally. This was independent of richness—elevation relationships, which had varying shapes but decreased with elevation at high elevations. The endemism—elevation relationships were consistent with isolation-related predictions, but inconsistent with hypotheses related to area, richness and temperature. Main conclusions: Higher per-species speciation rates caused by increasing isolation with elevation are the most plausible and parsimonious explanation for the globally consistent pattern of higher endemism at higher elevations that we identify. We suggest that topography-driven isolation increases speciation rates in mountainous areas, across all elevations and increasingly towards the equator. If so, it represents a mechanism that may contribute to generating latitudinal diversity gradients in a way that is consistent with both present-day and palaeontological evidence.

Background Microbiome/metagenomic data have specific characteristics, including varying total sequence reads, over-dispersion, and zero-inflation, which require tailored analytic tools. Many microbiome/metagenomic studies follow a longitudinal design to collect samples, which further complicates the analysis methods needed. A flexible and efficient R package is needed for analyzing processed multilevel or longitudinal microbiome/metagenomic data. Results NBZIMM is a freely available R package that provides functions for setting up and fitting negative binomial mixed models, zero-inflated negative binomial mixed models, and zero-inflated Gaussian mixed models. It also provides functions to summarize the results from fitted models, both numerically and graphically. The main functions are built on top of the commonly used R packages nlme and MASS, allowing us to incorporate the well-developed analytic procedures into the framework for analyzing over-dispersed and zero-inflated count or proportion data with multilevel structures (e.g., longitudinal studies). The statistical methods and their implementations in NBZIMM particularly address the data characteristics and the complex designs in microbiome/metagenomic studies. The package is freely available from the public GitHub repository https://github.com/nyiuab/NBZIMM . Conclusion The NBZIMM package provides useful tools for complex microbiome/metagenomics data analysis.

A general method for constructing low‐rank tensor product smooths for use as components of generalized additive models or generalized additive mixed models is presented. A penalized regression approach is adopted in which tensor product smooths of several variables are constructed from smooths of each variable separately, these “marginal” smooths being represented using a low‐rank basis with an associated quadratic wiggliness penalty. The smooths offer several advantages: (i) they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates, making them useful when there is no “natural” way to scale covariates relative to each other; (ii) they have a useful tuneable range of smoothness, unlike single‐penalty tensor product smooths that are scale invariant; (iii) the relatively low rank of the smooths means that they are computationally efficient; (iv) the penalties on the smooths are easily interpretable in terms of function shape; (v) the smooths can be generated completely automatically from any marginal smoothing bases and associated quadratic penalties, giving the modeler considerable flexibility to choose the basis penalty combination most appropriate to each modeling task; and (vi) the smooths can easily be written as components of a standard linear or generalized linear mixed model, allowing them to be used as components of the rich family of such models implemented in standard software, and to take advantage of the efficient and stable computational methods that have been developed for such models. A small simulation study shows that the methods can compare favorably with recently developed smoothing spline ANOVA methods.

Background The use of mixed effect models with a specific functional form such as the Sigmoidal Mixed Model and the Piecewise Mixed Model (or Changepoint Mixed Model) with abrupt or smooth random change allows the interpretation of the defined parameters to understand longitudinal trajectories. Currently, there are no interface R packages that can easily fit the Sigmoidal Mixed Model allowing the inclusion of covariates or incorporating recent developments to fit the Piecewise Mixed Model with random change. Results To facilitate the modeling of the Sigmoidal Mixed Model, and Piecewise Mixed Model with abrupt or smooth random change, we have created an R package called nlive. All needed pieces such as functions, covariance matrices, and initials generation were programmed. The package was implemented with recent developments such as the polynomial smooth transition of the piecewise mixed model with improved properties over Bacon-Watts, and the stochastic approximation expectation-maximization (SAEM) for efficient estimation. It was designed to help interpretation of the output by providing features such as annotated output, warnings, and graphs. Functionality, including time and convergence, was tested using simulations. We provided a data example to illustrate the package use and output features and interpretation. The package implemented in the R software is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=nlive . Conclusions The nlive package for R fits the Sigmoidal Mixed Model and the Piecewise Mixed: abrupt and smooth. The nlive allows fitting these models with only five mandatory arguments that are intuitive enough to the less sophisticated users.

Contrasting trajectories of biodiversity loss and urban expansion make it imperative to understand biodiversity persistence in cities. Size‐, local‐, and landscape‐level habitat factors of greenspaces in cities may be critical for future design and management of urban greenspaces in conserving bird biodiversity. Most current understanding of bird communities in cities has come from disparate analyses of single cities, over relatively short time periods, producing limited understanding of processes and characteristics of bird patterns for improved biodiversity management of the world's cities. We analyzed bird biodiversity in 112 urban greenspaces from 51 cities across eight countries, using eBird, a broadscale citizen science project. Species richness and Shannon diversity were used as response variables, while percent tree cover, percent water cover, and vegetation index were used as habitat predictor variables at both a landscape (5 and 25 km radius) and local‐scale level (specific to an individual greenspace) in the modeling process, retrieved using Google Earth Engine. Area of a greenspace was the most important predictor of bird biodiversity, underlining the critical importance of habitat area as the most important factor for increasing bird biodiversity and mitigating loss from urbanization. Surprisingly, distance from the city center and distance from the coast were not significantly related to bird biodiversity. Landscape‐scale habitat predictors were less related to bird biodiversity than local‐scale habitat predictors. Ultimately, bird biodiversity loss could be mitigated by protecting and developing large greenspaces with varied habitat in the world's cities.

A major challenge in the analysis of plant breeding multi-environment datasets is the provision of meaningful and concise information for variety selection in the presence of variety by environment interaction (VEI). This is addressed in the current paper by fitting a factor analytic linear mixed model (FALMM) then using the fundamental factor analytic parameters to define groups of environments in the dataset within which there is minimal crossover VEI, but between which there may be substantial crossover VEI. These groups are consequently called interaction classes (iClasses). Given that the environments within an iClass exhibit minimal crossover VEI, it is then valid to obtain predictions of overall variety performance (across environments) for each iClass. These predictions can then be used not only to select the best varieties within each iClass but also to match varieties in terms of their patterns of VEI across iClasses. The latter is aided with the use of a new graphical tool called an iClass Interaction Plot. The ideas are introduced in this paper within the framework of FALMMs in which the genetic effects for different varieties are assumed independent. The application to FALMMs which include information on genetic relatedness is the subject of a subsequent paper.

Quantifying sex-specific additive genetic variance (VA) in fitness, and the cross-sex genetic correlation (rA), is prerequisite to predicting evolutionary dynamics and the magnitude of sexual conflict. Further, quantifying VA and rA in underlying fitness components, and genetic consequences of immigration and resulting gene flow, is required to identify mechanisms that maintain VA in fitness. However, these key parameters have rarely been estimated in wild populations experiencing natural environmental variation and immigration. We used comprehensive pedigree and life-history data from song sparrows (Melospiza melodia) to estimate VA and rA in sex-specific fitness and underlying fitness components, and to estimate additive genetic effects of immigrants alongside inbreeding depression. We found evidence of substantial VA in female and male fitness, with a moderate positive crosssex rA. There was also substantial VA in male but not female adult reproductive success, and moderate VA in juvenile survival but not adult annual survival. Immigrants introduced alleles with negative additive genetic effects on local fitness, potentially reducing population mean fitness through migration load, but alleviating expression of inbreeding depression. Our results show that VA for fitness can be maintained in the wild, and be broadly concordant between the sexes despite marked sex-specific VA in reproductive success.

Water stress during reproductive growth is a major yield constraint for wheat (Triticum aestivum L). We previously established a controlled environment drought tolerance phenotyping method targeting the young microspore stage of pollen development. This method eliminates stress avoidance based on flowering time. We substituted soil drought treatments by a reproducible osmotic stress treatment using hydroponics and NaCl as osmolyte. Salt exclusion in hexaploid wheat avoids salt toxicity, causing osmotic stress. A Cranbrook x Halberd doubled haploid (DH) population was phenotyped by scoring spike grain numbers of unstressed (SGNCon) and osmotically stressed (SGNTrt) plants. Grain number data were analyzed using a linear mixed model (LMM) that included genetic correlations between the SGNCon and SGNTrt traits. Viewing this as a genetic regression of SGNTrt on SGNCon allowed derivation of a stress tolerance trait (SGNTol). Importantly, and by definition of the trait, the genetic effects for SGNTol are statistically independent of those for SGNCon. Thus they represent non-pleiotropic effects associated with the stress treatment that are independent of the control treatment. QTL mapping was conducted using a whole genome approach in which the LMM included all traits and all markers simultaneously. The marker effects within chromosomes were assumed to follow a spatial correlation model. This resulted in smooth marker profiles that could be used to identify positions of putative QTL. The most influential QTL were located on chromosome 5A for SGNTol (126cM; contributed by Halberd), 5A for SGNCon (141cM; Cranbrook) and 2A for SGNTrt (116cM; Cranbrook). Sensitive and tolerant population tail lines all showed matching soil drought tolerance phenotypes, confirming that osmotic stress is a valid surrogate screening method.

In applying a hierarchical mixed model to genome-wide association analysis (GWAS) of longitudinal data, dimensionality reduction through modeling repeated measurements improves both computational efficiency and statistical power. Legendre polynomials can flexibly fit population growth trajectories, but higher orders substantially increase computational complexity. Instead of using Legendre polynomials, we first estimated fewer individual-specific parameters using biologically meaningful non-linear models and then associated these phenotypic regressions with genetic markers using a multivariate linear mixed model (mvLMM). After performing a canonical transformation of the regressions based on the pre-estimated covariance matrices under the null genomic mvLMM, we decomposed the mvLMM into mutually independent univariate models and incorporated EMMAX to enable rapid genome-wide mixed-model associations for each transformed phenotype. Simulations for longitudinal association analysis in maize and GWAS for the growth trajectories of body weights in mice demonstrated the advantages of hierarchical non-linear mixed models in computing efficiency and statistical power for detecting quantitative trait loci (QTL), compared with mvLMM for multiple growth points and the hierarchical random regression model using Legendre polynomials as sub-models.

Background Intensive care unit (ICU) length of stay (LOS) and the risk adjusted equivalent (RALOS) have been used as quality metrics. The latter measures entail either ratio or difference formulations or ICU random effects (RE), which have not been previously compared. Methods From calendar year 2016 data of an adult ICU registry-database (Australia & New Zealand Intensive Care Society (ANZICS) CORE), LOS predictive models were established using linear (LMM) and generalised linear (GLMM) mixed models. Model fixed effects quality-metric formulations were estimated as RALOSR for LMM (geometric mean derived from log(ICU LOS)) and GLMM (day) and observed minus expected ICU LOS (OMELOS from GLMM). Metric confidence intervals (95%CI) were estimated by bootstrapping; random effects (RE) were predicted for LMM and GLMM. Forest-plot displays of ranked quality-metric point-estimates (95%CI) were generated for ICU hospital classifications (metropolitan, private, rural/regional, and tertiary). Robust rank confidence sets (point estimate and 95%CI), both marginal (pertaining to a singular ICU) and simultaneous (pertaining to all ICU differences), were established. Results The ICU cohort was of 94,361 patients from 125 ICUs (metropolitan 16.9%, private 32.8%, rural/regional 6.4%, tertiary 43.8%). Age (mean, SD) was 61.7 (17.5) years; 58.3% were male; APACHE III severity-of-illness score 54.6 (25.7); ICU annual patient volume 1192 (702) and ICU LOS 3.2 (4.9). There was no concordance of ICU ranked model predictions, GLMM versus LMM, nor for the quality metrics used, RALOSR, OMELOS and site-specific RE for each of the ICU hospital classifications. Furthermore, there was no concordance between ICU ranking confidence sets, marginal and simultaneous for models or quality metrics. Conclusions Inference regarding adjusted ICU LOS was dependent upon the statistical estimator and the quality index used to quantify any LOS differences across ICUs. That is, there was no “one best model”; thus, ICU “performance” is determined by model choice and any rankings thereupon should be circumspect.