Variance component tests of multivariate mediation effects under composite null hypotheses

Mediation effects of multiple mediators are determined by two associations: one between an exposure and mediators (‐) and the other between the mediators and an outcome conditional on the exposure (‐). The test for mediation effects is conducted under a composite null hypothesis, that is, either one of the ‐ and ‐ associations is zero or both are zeros. Without accounting for the composite null, the type 1 error rate within a study containing a large number of multimediator tests may be much less than the expected. We propose a novel test to address the issue. For each mediation test , , we examine the ‐ and ‐ associations using two separate variance component tests. Assuming a zero‐mean working distribution with a common variance for the element‐wise ‐ (and ‐) associations, score tests for the variance components are constructed. We transform the test statistics into two normally distributed statistics under the null. Using a recently developed result, we conduct hypothesis tests accounting for the composite null hypothesis by adjusting for the variances of the normally distributed statistics for the ‐ and ‐ associations. Advantages of the proposed test over other methods are illustrated in simulation studies and a data application where we analyze lung cancer data from The Cancer Genome Atlas to investigate the smoking effect on gene expression through DNA methylation in 15 114 genes.     

A robust removing unwanted variation–testing procedure via γ‐divergence

Identification of differentially expressed genes (DE genes) is commonly conducted in modern biomedical research. However, unwanted variation inevitably arises during the data collection process, which can make the detection results heavily biased. Various methods have been suggested for removing the unwanted variation while keeping the biological variation to ensure a reliable analysis result. Removing unwanted variation (RUV) has recently been proposed for this purpose, which works by virtue of negative control genes. On the other hand, outliers frequently appear in modern high‐throughput genetic data, which can heavily affect the performances of RUV and its downstream analysis. In this work, we propose a robust RUV‐testing procedure (a robust RUV procedure to remove unwanted variance, followed by a robust testing procedure to identify DE genes) via $\gamma$‐divergence. The advantages of our method are twofold: (a) it does not involve any modeling for the outlier distribution, which makes it applicable to various situations; (b) it is easy to implement in the sense that its robustness is controlled by a single tuning parameter $\gamma$ of $\gamma$‐divergence, and a data‐driven criterion is developed to select $\gamma$. When applied to real data sets, our method can successfully remove unwanted variation, and was able to identify more DE genes than conventional methods.     

On construction of single‐arm two‐stage designs with consideration of both response and toxicity

When establishing a treatment in clinical trials, it is important to evaluate both effectiveness and toxicity. In phase II clinical trials, multinomial data are collected in m‐stage designs, especially in two‐stage () design. Exact tests on two proportions, for the response rate and for the nontoxicity rate, should be employed due to limited sample sizes. However, existing tests use certain parameter configurations at the boundary of null hypothesis space to determine rejection regions without showing that the maximum Type I error rate is achieved at the boundary of null hypothesis. In this paper, we show that the power function for each test in a large family of tests is nondecreasing in both and ; identify the parameter configurations at which the maximum Type I error rate and the minimum power are achieved and derive level‐α tests; provide optimal two‐stage designs with the least expected total sample size and the optimization algorithm; and extend the results to the case of . Some R‐codes are given in the Supporting Information.     

Nitrate or ammonium: Influences of nitrogen source on the physiology of a green alga

In freshwaters, algal species are exposed to different inorganic nitrogen (N_i) sources whose incorporation varies in biochemical energy demand. We hypothesized that due to the lesser energy requirement of ammonium ()‐use, in contrast to nitrate ()‐use, more energy remains for other metabolic processes, especially under CO₂‐ and phosphorus (P_i) limiting conditions. Therefore, we tested differences in cell characteristics of the green alga Chlamydomonas acidophila grown on or under covariation of CO₂ and P_i‐supply in order to determine limitations, in a full‐factorial design. As expected, results revealed higher carbon fixation rates for ‐grown cells compared to growth with under low CO₂ conditions. ‐grown cells accumulated more of the nine analyzed amino acids, especially under P_i‐limited conditions, compared to cells provided with . This is probably due to a slower protein synthesis in cells provided with . In contrast to our expectations, compared to ‐grown cells ‐grown cells had higher photosynthetic efficiency under P_i‐limitation. In conclusion, growth on the N_i‐source did not result in a clearly enhanced C_i‐assimilation, as it was highly dependent on P_i and CO₂ conditions (replete or limited). Results are potentially connected to the fact that C. acidophila is able to use only CO₂ as its inorganic carbon (C_i) source.     

Mortality process in relation to aggregation in the southern green stink bug

A simple experiment of simulation was done to analyze the natural mortality process of young larval colonies and egg masses of the southern green stink bug. In this experiment, a degree of contagiousness was allowed in regard to the action of a mortality factor, and was defined as the mean number killed per a colony or an egg mass by the mortality factor within a unit time and the number killed per a colony was assumed to follow the Poisson series with the mean . Thus each component of the Poisson series was opposed to each colony or egg mass which was taken at random from 162 egg masses, 135 and 117 colonies of the first and the second instar larvae, respectively. It was revealed that mortality factors in the field did not act with a small degree of contagiosness, e. g., on all colonies or egg masses, but acted with a large degree of contagiousness, e. g., on some of the colonies or egg masses. Thus differential survival somewhat in all or none way occurred among the insect colonies irrespective of their initial sizes. These results were well explained by taking actual mortality factors into account.     

Activation of Terminal Components of Human Complement by a Trypsin-Activated Complex of Human Factor B and Cobra Venom Factor

Cleavage of C3 by CVF-B? was demonstrated by hemolytic, immunoelectrophoretic and immune adherence reactions. No cleavage of C5 was detected by immunoelectrophoresis, but C5 hemolytic activity, assayed with decreased although less than C3 hemolytic activity. The co-existence of C3 with limiting amounts of C5 did not reduce the final degree of hemolysis of guinea pig erythrocytes (GPE) induced by late-acting components C6 through C9 and CVF-B?. Thus, a CVF-B? hemolytic system composed of GPE, C5 through C9 and CVF-B? provided a method for titration of terminal components of human complement. CVF-B? was able to generate hemolytically active sites of on GPE by activation of C5, C6 and C7. The complex in the fluid-phase decayed within 1 min but on GPE was quite stable. Originally insensitive sheep erythrocytes became sensitive to the CVF-B? hemolytic system if C3b sites were present, suggesting that cell-bound C3b played a role in orienting the positions of to be fixed. CVF-B? could be recovered quantitatively from the supernatant of the reaction mixture in which the hemolytically active intermediate GPEC- had been formed through the interaction between C5 to C8 and CVF-B?.     

Biological nascent evolution of snail bone and collagen revealed by nonlinear optical microscopy

Using nonlinear optical microscopy of coherent antistokes Raman scattering (CARS), second harmonic generation (SHG) and two‐photo excitation fluorescence, we in situ observed how the collagen and the bone grow synergistically and competitively during nascent biological evolution. The and ions were first observed to be dispersed in the liquid environment, and the collagen was observed 2 days later. With the help of the collagen, the and ions gradually moved closer to the collagen, and then the bone was produced in the forms of CaCO₃ and CaPO₃. When the bone was completed with the help of the collagen, the collagen gradually disappeared. The biological evolution of snail bone and collagen can be well revealed by CARS and SHG, and in addition, the biological evolution of structure and morphology can be clearly observed day by day.     

Collagen chirality and three‐dimensional orientation studied with polarimetric second‐harmonic generation microscopy

Polarization‐dependent second‐harmonic generation (P‐SHG) microscopy is used to characterize molecular nonlinear optical properties of collagen and determine a three‐dimensional (3D) orientation map of collagen fibers within a pig tendon. C₆ symmetry is used to determine the nonlinear susceptibility tensor components ratios in the molecular frame of reference and , where the latter is a newly extracted parameter from the P‐SHG images and is related to the chiral structure of collagen. The is observed for collagen fibers tilted out of the image plane, and can have positive or negative values, revealing the relative polarity of collagen fibers within the tissue. The P‐SHG imaging was performed using a linear polarization‐in polarization‐out (PIPO) method on thin sections of pig tendon cut at different angles. The nonlinear chiral properties of collagen can be used to construct the 3D organization of collagen in the tissue and determine the orientation‐independent molecular susceptibility ratios of collagen fibers in the molecular frame of reference.      

MATERNAL INHERITANCE AND ITS EFFECT ON ADAPTIVE EVOLUTION: A QUANTITATIVE GENETIC ANALYSIS OF MATERNAL EFFECTS IN A NATURAL PLANT POPULATION

A mother can influence a trait in her offspring both by the genes she transmits (Mendelian inheritance) and by maternal attributes that directly affect that trait in her offspring (maternal inheritance). Maternal inheritance can alter the direction, rate, and duration of adaptive evolution from standard Mendelian models and its impact on adaptive evolution is virtually unexplored in natural populations. In a hierarchical quantitative genetic analysis to determine the magnitude and structure of maternal inheritance in the winter annual plant, Collinsia verna, I consider three potential models of inheritance. These range from a standard Mendelian model estimating only direct (i.e., Mendelian) additive and environmental variance components to a maternal inheritance model estimating six additive and environmental variance components: direct additive and environmental variances; maternal additive and environmental variances; and the direct-maternal additive () and environmental covariances. The structure of maternal inheritance differs among the 10 traits considered at four stages in the life cycle. Early in the life cycle, seed weight and embryo weight display substantial , a negative , and a positive . Subsequently, cotyledon diameter displays and of roughly the same magnitude and negative . For fall rosettes, leaf number and length are best described by a Mendelian model. In the spring, leaf length displays maternal inheritance with significant and and a negative . All maternally inherited traits show significant negative . Predicted response to selection under maternal inheritance depends on and as well as . Negative results in predicted responses in the opposite direction to selection for seed weight and embryo weight and predicted responses near zero for all subsequent maternally inherited traits. Maternal inheritance persists through the life cycle of this annual plant for a number of size-related traits and will alter the direction and rate of evolutionary response in this population.     

Evaluating interactions between space‐use sharing and defence under increasing density conditions for the group‐territorial Red‐cockaded Woodpecker Leuconotopicus borealis

Information about how bird species respond to increasing density conditions through either space‐use sharing or increased territoriality, and how those changes affect fitness, is essential for effective conservation planning. We used a case study of endangered Red‐cockaded Woodpeckers Leuconotopicus borealis (RCW) to address these questions. We documented over 36 000 locations from 44 RCW groups in three density conditions on two sites in South Carolina, USA, between April 2013 and March 2015. The frequency of neighbouring group interactions differed among density conditions and was highest for high‐density groups. RCW home‐ranges and core‐areas were larger under low‐density conditions ( = 88.4 ha,  = 21.0 ha) than under medium ( = 68.29 ha,  = 16.6 ha) and high‐density ( = 76.3 ha,  = 18.6 ha) conditions. Neighbouring RCWs maintained overlapping home‐ranges with nearly exclusive core‐areas across density conditions, but overlap tended to increase as neighbouring group density increased. Under high‐density conditions, home‐range overlap correlated inversely with clutch size (β ± se = ?0.19 ± 0.09), nestling production (β ± se = ?0.37 ± 0.09) and fledgling production (β ± se = ?0.34 ± 0.08). Our results indicate that RCWs dedicate more effort to territorial defence under high‐density conditions, potentially at the expense of greater foraging efficiency and time allocated to reproduction, as evidenced by reduced fitness. Large home‐range overlap indicated limited territoriality farther away from cavity trees, but the existence of exclusive core‐areas suggests that RCW groups defend habitat closer to cavity trees. Thiessen partitions used to allocate critical foraging habitat offered comprehensive habitat protection for RCW but appear flawed for spatially explicit habitat assessments because they do not accurately delineate space used by individual RCW groups.     

THE MAINTENANCE OF POLYGENIC VARIATION IN FINITE POPULATIONS

Models of the maintenance of genetic variance in a polygenic trait have usually assumed that population size is infinite and that selection is weak. Consequently, they will overestimate the amount of variation maintained in finite populations. I derive approximations for the equilibrium genetic variance, in finite populations under weak stabilizing selection for triallelic loci and for an infinite “rare alleles” model. These are compared to results for neutral characters, to the “Gaussian allelic” model, and to Wright's approximation for a biallelic locus under arbitrary selection pressures. For a variety of parameter values, the three-allele, Gaussian, and Wrightian approximations all converge on the neutral model when population size is small. As expected, far less equilibrium genetic variance can be maintained if effective population size, N, is on the order of a few hundred than if N is infinite. All of the models predict that comparisons among populations with N less than about 10⁴ should show substantial differences in . While it is easier to maintain absolute when alleles interact to yield dominance or overdominance for fitness, less additivity also makes more susceptible to differences in N. I argue that experimental data do not seem to reflect the predicted degree of relationship between N and . This calls into question the ability of mutation-selection balance or simple balancing selection to explain observed . The dependence of on N could be used to test the adequacy of mutation-selection balance models.     

Additive genetic variance for lifetime fitness and the capacity for adaptation in an annual plant

The immediate capacity for adaptation under current environmental conditions is directly proportional to the additive genetic variance for fitness, V_A(W). Mean absolute fitness, , is predicted to change at the rate , according to Fisher's Fundamental Theorem of Natural Selection. Despite ample research evaluating degree of local adaptation, direct assessment of V_A(W) and the capacity for ongoing adaptation is exceedingly rare. We estimated V_A(W) and in three pedigreed populations of annual Chamaecrista fasciculata, over three years in the wild. Contrasting with common expectations, we found significant V_A(W) in all populations and years, predicting increased mean fitness in subsequent generations (0.83 to 6.12 seeds per individual). Further, we detected two cases predicting “evolutionary rescue,” where selection on standing V_A(W) was expected to increase fitness of declining populations (< 1.0) to levels consistent with population sustainability and growth. Within populations, inter‐annual differences in genetic expression of fitness were striking. Significant genotype‐by‐year interactions reflected modest correlations between breeding values across years, indicating temporally variable selection at the genotypic level that could contribute to maintaining V_A(W). By directly estimating V_A(W) and total lifetime , our study presents an experimental approach for studies of adaptive capacity in the wild.     

Biophysical analysis of the dynamics of calmodulin interactions with neurogranin and Ca2+/calmodulin‐dependent kinase II

Calmodulin (CaM) functions depend on interactions with CaM‐binding proteins, regulated by . Induced structural changes influence the affinity, kinetics, and specificities of the interactions. The dynamics of CaM interactions with neurogranin (Ng) and the CaM‐binding region of /calmodulin‐dependent kinase II (CaMKII_290−309) have been studied using biophysical methods. These proteins have opposite dependencies for CaM binding. Surface plasmon resonance biosensor analysis confirmed that and CaM interact very rapidly, and with moderate affinity ( ). Calmodulin‐CaMKII_290−309 interactions were only detected in the presence of , exhibiting fast kinetics and nanomolar affinity ( ). The CaM–Ng interaction had higher affinity under ‐depleted ( and k ₋₁ = 1.6 × 10⁻¹s⁻¹) than ‐saturated conditions ( ). The IQ motif of Ng (Ng₂₇₋₅₀) had similar affinity for CaM as Ng under ‐saturated conditions ( ), but no interaction was seen under ‐depleted conditions. Microscale thermophoresis using fluorescently labeled CaM confirmed the surface plasmon resonance results qualitatively, but estimated lower affinities for the Ng ( ) and CaMKII_290−309( ) interactions. Although CaMKII_290−309 showed expected interaction characteristics, they may be different for full‐length CaMKII. The data for full‐length Ng, but not Ng₂₇₋₅₀, agree with the current model on Ng regulation of /CaM signaling.     

Improved estimates of global terrestrial photosynthesis using information on leaf chlorophyll content

The terrestrial biosphere plays a critical role in mitigating climate change by absorbing anthropogenic CO₂ emissions through photosynthesis. The rate of photosynthesis is determined jointly by environmental variables and the intrinsic photosynthetic capacity of plants (i.e. maximum carboxylation rate; ). A lack of an effective means to derive spatially and temporally explicit has long hampered efforts towards estimating global photosynthesis accurately. Recent work suggests that leaf chlorophyll content (Chl_leaf) is strongly related to , since Chl_leaf and are both correlated with photosynthetic nitrogen content. We used medium resolution satellite images to derive spatially and temporally explicit Chl_leaf, which we then used to parameterize within a terrestrial biosphere model. Modelled photosynthesis estimates were evaluated against measured photosynthesis at 124 eddy covariance sites. The inclusion of Chl_leaf in a terrestrial biosphere model improved the spatial and temporal variability of photosynthesis estimates, reducing biases at eddy covariance sites by 8% on average, with the largest improvements occurring for croplands (21% bias reduction) and deciduous forests (15% bias reduction). At the global scale, the inclusion of Chl_leaf reduced terrestrial photosynthesis estimates by 9 PgC/year and improved the correlations with a reconstructed solar‐induced fluorescence product and a gridded photosynthesis product upscaled from tower measurements. We found positive impacts of Chl_leaf on modelled photosynthesis for deciduous forests, croplands, grasslands, savannas and wetlands, but mixed impacts for shrublands and evergreen broadleaf forests and negative impacts for evergreen needleleaf forests and mixed forests. Our results highlight the potential of Chl_leaf to reduce the uncertainty of global photosynthesis but identify challenges for incorporating Chl_leaf in future terrestrial biosphere models.     

RISK OF POPULATION EXTINCTION FROM FIXATION OF NEW DELETERIOUS MUTATIONS

The fixation of new deleterious mutations is analyzed for a randomly mating population of constant size with no environmental or demographic stochasticity. Mildly deleterious mutations are far more important in causing loss of fitness and eventual extinction than are lethal and semilethal mutations in populations with effective sizes, N_e, larger than a few individuals. If all mildly deleterious mutations have the same selection coefficient, s against heterozygotes and 2s against homozygotes, the mean time to extinction, , is asymptotically proportional to for 4N_es > 1. Nearly neutral mutations pose the greatest risk of extinction for stable populations, because the magnitude of selection coefficient that minimizes is about ? = 0.4/N_e. The influence of variance in selection coefficients among mutations is analyzed assuming a gamma distribution of s, with mean and variance . The mean time to extinction increases with variance in selection coefficients if is near ?, but can decrease greatly if is much larger than ?. For a given coefficient of variation of , the mean time to extinction is asymptotically proportional to for . When s is exponentially distributed, (c = 1) is asymptotically proportional to . These results in conjunction with data on the rate and magnitude of mildly deleterious mutations in Drosophila melanogaster indicate that even moderately large populations, with effective sizes on the order of N_e = 10³, may incur a substantial risk of extinction from the fixation of new mutations.     

Differential responses of two wetland graminoids to high ammonium at different pH values

Enhanced soil ammonium () concentrations in wetlands often lead to graminoid dominance, but species composition is highly variable. Although is readily taken up as a nutrient, several wetland species are known to be sensitive to high concentrations or even suffer toxicity, particularly at low soil pH. More knowledge about differential graminoid responses to high availability in relation to soil pH can help to better understand vegetation changes. The responses of two wetland graminoids, Juncus acutiflorus and Carex disticha, to high (2 mmol·l^?1) versus control (20 μmol·l^?1) concentrations were tested in a controlled hydroponic set up, at two pH values (4 and 6). A high concentration did not change total biomass for these species at either pH, but increased C allocation to shoots and increased P uptake, leading to K and Ca limitation, depending on pH treatment. More than 50% of N taken up by C. disticha was invested in N‐rich amino acids with decreasing C:N ratio, but only 10% for J. acutiflorus. Although both species appeared to be well adapted to high loadings in the short term, C. disticha showed higher classic detoxifying responses that are early warning indicators for decreased tolerance in the long term. In general, the efficient aboveground biomass allocation, P uptake and N detoxification explain the competitive strength of wetland graminoids at the expense of overall biodiversity at high loading. In addition, differential responses to enhanced affect interspecific competition among graminoids and lead to a shift in vegetation composition.     

The importance of non-linearity: A comment on the views of Taylor

Taylor's (1984) view that his power law is better measurement of the distribution pattern of animals than 1/k, I_ρ and relation because almost all the data on means and variances of given species could be fitted by the power low, was critisized. Changes in values of 1/k, I_ρ and suggest the change of distribution pattern of the species, but the data can still be fitted by the power law because of the great linearizing power of log-log plots, and, using the power law only, we shall overlook the information on the meaningful changes in the distribution pattern.     

The Arabidopsis root stele transporter NPF2.3 contributes to nitrate translocation to shoots under salt stress

In most plants, constitutes the major source of nitrogen, and its assimilation into amino acids is mainly achieved in shoots. Furthermore, recent reports have revealed that reduction of translocation from roots to shoots is involved in plant acclimation to abiotic stress. NPF2.3, a member of the NAXT (nitrate excretion transporter) sub‐group of the NRT1/PTR family (NPF) from Arabidopsis, is expressed in root pericycle cells, where it is targeted to the plasma membrane. Transport assays using NPF2.3‐enriched Lactococcus lactis membranes showed that this protein is endowed with transport activity, displaying a strong selectivity for against Cl^?. In response to salt stress, translocation to shoots is reduced, at least partly because expression of the root stele transporter gene NPF7.3 is decreased. In contrast, NPF2.3 expression was maintained under these conditions. A loss‐of‐function mutation in NPF2.3 resulted in decreased root‐to‐shoot translocation and reduced shoot content in plants grown under salt stress. Also, the mutant displayed impaired shoot biomass production when plants were grown under mild salt stress. These mutant phenotypes were dependent on the presence of Na⁺ in the external medium. Our data indicate that NPF2.3 is a constitutively expressed transporter whose contribution to translocation to the shoots is quantitatively and physiologically significant under salinity.     

Partial genotyping at polymorphic markers can improve heritability estimates in sibling groups

Accurate estimates of heritability () are necessary to assess adaptive responses of populations and evolution of fitness‐related traits in changing environments. For plants, estimates generally rely on maternal progeny designs, assuming that offspring are either half‐sibs or unrelated. However, plant mating systems often depart from half‐sib assumptions, this can bias estimates. Here, we investigate how to accurately estimate in nonmodel species through the analysis of sibling designs with a moderate genotyping effort. We performed simulations to investigate how microsatellite marker information available for only a subset of offspring can improve estimates based on maternal progeny designs in the presence of nonrandom mating, inbreeding in the parental population or maternal effects. We compared the basic family method, considering or not adjustments based on average relatedness coefficients, and methods based on the animal model. The animal model was used with average relatedness information, or with hybrid relatedness information: associating one‐generation pedigree and family assumptions, or associating one‐generation pedigree and average relatedness coefficients. Our results highlighted that methods using marker‐based relatedness coefficients performed as well as pedigree‐based methods in the presence of nonrandom mating (i.e. unequal male reproductive contributions, selfing), offering promising prospects to investigate in situ heritabilities in natural populations. In the presence of maternal effects, only the use of pairwise relatednesses through pedigree information improved the accuracy of estimates. In that case, the amount of father‐related offspring in the sibling design is the most critical. Overall, we showed that the method using both one‐generation pedigree and average relatedness coefficients was the most robust to various ecological scenarios.