Better Estimates of Genetic Covariance Matrices by “Bending” Using Penalized Maximum Likelihood

Obtaining accurate estimates of the genetic covariance matrix for multivariate data is a fundamental task in quantitative genetics and important for both evolutionary biologists and plant or animal breeders. Classical methods for estimating are well known to suffer from substantial sampling errors; importantly, its leading eigenvalues are systematically overestimated. This article proposes a framework that exploits information in the phenotypic covariance matrix in a new way to obtain more accurate estimates of . The approach focuses on the “canonical heritabilities” (the eigenvalues of ), which may be estimated with more precision than those of because is estimated more accurately. Our method uses penalized maximum likelihood and shrinkage to reduce bias in estimates of the canonical heritabilities. This in turn can be exploited to get substantial reductions in bias for estimates of the eigenvalues of and a reduction in sampling errors for estimates of . Simulations show that improvements are greatest when sample sizes are small and the canonical heritabilities are closely spaced. An application to data from beef cattle demonstrates the efficacy this approach and the effect on estimates of heritabilities and correlations. Penalized estimation is recommended for multivariate analyses involving more than a few traits or problems with limited data.QUANTITATIVE geneticists, including evolutionary biologists and plant and animal breeders, are increasingly dependent on multivariate analyses of genetic variation, for example, to understand evolutionary constraints and design efficient selection programs. New challenges arise when one moves from estimating the genetic variance of a single phenotype to the multivariate setting. An important but unresolved issue is how best to deal with sampling variation and the corresponding bias in the eigenvalues of estimates for the genetic covariance matrix, . It is well known that estimates for the largest eigenvalues of a covariance matrix are biased upward and those for the smallest eigenvalues are biased downward (Lawley 1956; Hayes and Hill 1981). For genetic problems, where we need to estimate at least two covariance matrices simultaneously, this tends to be exacerbated, especially for . In turn, this can result in invalid estimates of , i.e., estimates with negative eigenvalues, and can produce systematic errors in predictions for the response to selection.There has been longstanding interest in “regularization” of covariance matrices, in particular for cases where the ratio between the number of observations and the number of variables is small. Various studies recently employed such techniques for the analysis of high-dimensional, genomic data. In general, this involves a compromise between additional bias and reduced sampling variation of “improved” estimators that have less statistical risk than standard methods (Bickel and Li 2006). For instance, various types of shrinkage estimators of covariance matrices have been suggested that counteract bias in estimates of eigenvalues by shrinking all sample eigenvalues toward their mean. Often this is equivalent to a weighted combination of the sample covariance matrix and a target matrix, assumed to have a simple structure. A common choice for the latter is an identity matrix. This yields a ridge regression type formulation (Hoerl and Kennard 1970). Numerous simulation studies in a variety of settings are available, which demonstrate that regularization can yield closer agreement between estimated and population covariance matrices, less variable estimates of model terms, or improved performance of statistical tests.In quantitative genetic analyses, we attempt to partition observed, overall (phenotypic) covariances into their genetic and environmental components. Typically, this results in strong sampling correlations between them. Hence, while the partitioning into sources of variation and estimates of individual covariance matrices may be subject to substantial sampling variances, their sum, i.e., the phenotypic covariance matrix, can generally be estimated much more accurately. This has led to suggestions to “borrow strength” from estimates of phenotypic components to estimate the genetic covariances. In particular, Hayes and Hill (1981) proposed a method termed “bending” that involved regressing the eigenvalues of the product of the genetic and the inverse of the phenotypic covariance matrix toward their mean. One objective of this procedure was to ensure that estimates of the genetic covariance matrix from an analysis of variance were positive definite. In addition, the authors showed by simulation that shrinking eigenvalues even further than needed to make all values nonnegative could improve the achieved response to selection when using the resulting estimates to derive weights for a selection index, especially for estimation based on small samples. Subsequent work demonstrated that bending could also be advantageous in more general scenarios such as indexes that included information from relatives (Meyer and Hill 1983).Modern, mixed model (“animal model”)-based analyses to estimate genetic parameters using maximum likelihood or Bayesian methods generally constrain estimates to the parameter space, so that—at the expense of introducing some bias—estimates of covariance matrices are positive semidefinite. However, the problems arising from substantial sampling variation in multivariate analyses remain. In spite of increasing applications of such analyses in scenarios where data sets are invariably small, e.g., the analysis of data from natural populations (e.g., Kruuk et al. 2008), there has been little interest in regularization and shrinkage techniques in genetic parameter estimation, other than through the use of informative priors in a Bayesian context. Instead, suggestions for improved estimation have focused on parsimonious modeling of covariance matrices, e.g., through reduced rank estimation or by imposing a known structure, such as a factor-analytic structure (Kirkpatrick and Meyer 2004; Meyer 2009), or by fitting covariance functions for longitudinal data (Kirkpatrick et al. 1990). While such methods can be highly advantageous when the underlying assumptions are at least approximately correct, data-driven methods of regularization may be preferable in other scenarios.This article explores the scope for improved estimation of genetic covariance matrices by implementing the equivalent to bending within animal model-type analyses. We begin with a review of the underlying statistical principles (which the impatient reader might skip), examining the concept of improved estimation, its implementation via shrinkage estimators or penalized estimation, and selected applications. We then describe a penalized restricted maximum-likelihood (REML) procedure for the estimation of genetic covariance matrices that utilizes information from its phenotypic counterparts and present a simulation study demonstrating the effect of penalties on parameter estimates and their sampling properties. The article concludes with an application to a problem relevant in genetic improvement of beef cattle and a discussion.     

Rotifer–crustacean interactions in a pseudokarstic lake: influence of hydrology

Zooplankton abundance was related to hydrological and environmental variables in a hydrologically dynamic lake fed by a pseudokarstic aquifer. The study period (2002–2006) in Lake Tovel covered different hydrological situations with water residence time (WRT) having the lowest values in 2002 and the highest values in 2003. WRT was negatively correlated with silica concentrations and algal biovolume. Furthermore, the biovolume of small algae was highest in spring and summer, while large algae did not show any pattern. In multivariate analysis, high abundance of crustacean species in autumn and winter was positively related to WRT and negatively to algal biovolume, while high abundance of rotifer species in spring and summer was negatively related to WRT and positively to algal biovolume. With the exception of Keratella cochlearis and Gastropus stylifer, rotifers showed a pattern of crustacean avoidance, and three groups were distinguished: (i) Ascomorpha ecaudis and Polyarthra dolichoptera, (ii) Asplanchna priodonta and Synchaeta spp., and (iii) Filinia terminalis and Keratella quadrata. These groups were associated with different food sources and depths. We suggest that WRT influenced the rotifer–crustacean relationship by wash-out effects and competition for food resources. The dynamics of single rotifer species were attributable to specific feeding requirements and adaptations. In summary, WRT determined the platform for abiotic and biotic interactions that influenced population dynamics of crustaceans and rotifers.     

Hierarchical Bayesian Spatio–Temporal Analysis of Climatic and Socio–Economic Determinants of Rocky Mountain Spotted Fever

This study aims to examine the spatio-temporal dynamics of Rocky Mountain spotted fever (RMSF) prevalence in four contiguous states of Midwestern United States, and to determine the impact of environmental and socio–economic factors associated with this disease. Bayesian hierarchical models were used to quantify space and time only trends and spatio–temporal interaction effect in the case reports submitted to the state health departments in the region. Various socio–economic, environmental and climatic covariates screened a priori in a bivariate procedure were added to a main–effects Bayesian model in progressive steps to evaluate important drivers of RMSF space-time patterns in the region. Our results show a steady increase in RMSF incidence over the study period to newer geographic areas, and the posterior probabilities of county-specific trends indicate clustering of high risk counties in the central and southern parts of the study region. At the spatial scale of a county, the prevalence levels of RMSF is influenced by poverty status, average relative humidity, and average land surface temperature (>35°C) in the region, and the relevance of these factors in the context of climate–change impacts on tick–borne diseases are discussed.     

Probing Structure–Function Relationships of Serine Hydrolases and Proteases with Carbamate and Thiocarbamate Inhibitors

Benzene-1,3-di-N-n-octylcarbamate (1), benzene-1-hydroxyl-3-N-n-octylcarbamate (2), benzene-1,3-di-N-n-ocztylthiocarbamate (3), and benzene-1-hydroxyl-3-N-n-octylthiocarbamate (4) are synthesized from 1,3-benzene-diol and are characterized as the pseudo-substrate inhibitors of acetylcholinesterase, butyrylcholinesterase, cholesterol esterase, lipase, trypsin, and chymotrypsin. For these six enzyme inhibitions by 1-4, the pKi values are linearly correlated with their log ki values - Br?nsted plots. Therefore, 1-4 inhibit these enzymes through a common mechanism. Moreover, both pKi and log ki values for the inhibitions by 1,3, and 4 are linearly correlated with both pKi and log ki values for the inhibitions by 2, respectively. Thus, the pKi values for the inhibitions by 2 are defined as the nucleophilicity constants of these enzymes (nenzyme). The log k2 values for the inhibitions by 1-4 are also linearly correlated with the nenzyme values. Therefore, the nucleophilicity for serine hydrolases and proteases toward 1-4 also applies the Swain-Scott correlations.     

Evolutionary Dynamics of ‘the’ Bdelloid and Monogonont Rotifer Life-history Patterns

Substantial differences in both life-table characteristics and reproductive patterns distinguish bdelloid from monogonont rotifers. Bdelloids reproduce only asexually, whereas most monogononts are cyclical parthenogens. We explore some of the adaptive consequences of these life-history differences using a computer model to simulate the evolutionary acquisition of new beneficial mutations. A one-locus mutation-selection regime based on the life-history characteristics of bdelloids indicates that asexuals can maintain higher levels of both allelic and genotypic diversity over a longer time period than obligate sexuals. These results are produced by differences in the magnitude of random genetic drift (RGD) associated with the different types of reproduction. Cyclical parthenogens have significantly higher evolutionary rates than sexual forms in a single-locus model, but incorporate beneficial mutations more slowly than sexuals in a two-locus simulation. Our results are therefore strongly influenced by the number of loci being evaluated as well as the pattern of reproduction. The asexual life history was found to maintain higher levels of allelic diversity than any pattern including sexual reproduction. This intriguing finding is amplified as the number of loci undergoing selection is increased. We end by considering the adaptive consequences of the remarkably divergent life histories found in typical bdelloid and monogonont rotifers.     

The Use of the Expectation–Maximization (EM) Algorithm for Maximum Likelihood Estimation of Gametic Frequencies of Multilocus Polymorphic Codominant Systems Based on Sampled Population Data

Estimation of gametic frequencies in multilocus polymorphic systems based on the numerical distribution of multilocus genotypes in a population sample (analysis without pedigrees) is difficult because some gametes are not recognized in the data obtained. Even in the case of codominant systems, where all alleles can be recognized by genotypes, so that direct estimation of the frequencies of genes (alleles) is possible (complete data), estimation of the frequencies of multilocus gametes based on the data on multilocus genotypes is sometimes impossible, whether population data or even family data are used for studying genotypic segregation or analysis of linkage (incomplete data). Such incomplete data are analyzed based on the corresponding genetic models using the expectation–maximization (EM) algorithm. In this study, the EM algorithm based on the random-marriage model for a nonsubdivided population was used to estimate gametic frequencies. The EM algorithm used in the study does not set any limitations on the number of loci and the number of alleles of each locus. Locus and alleles are identified by numeration making possible to arrange loops. In each combination of alleles for a given combination of m out of L loci (L is the total number of loci studied), all alleles are assigned value 1, and the remaining alleles are assigned value 0. The sum of zeros and unities for each gamete is its gametic value (h), and the sum of the gametic values of the gametes that form a given genotype is the genotypic value (g) of this genotype. Then, gametes with the sameh are united into a single class, which reduces the number of the estimated parameters. In a general case of m loci, this procedure yields m + 1 classes of gametes and 2m + 1 classes of genotypes with genotypic valuesg = 0, 1, 2,... 2m. The unknown frequencies of them + 1 classes of gametes can be represented as functions of the gametic frequencies whose maximum likelihood estimations (MLEs) have been obtained in all previous EM procedures and the only unknown frequency (P _m(m)) that is to be estimated in the given EM procedure. At the expectation step, the expected frequencies (F _m(g) of the genotypes with genotypic valuesg are expressed in terms of the products of the frequencies of m + 1 classes of gametes. The data on genotypes are the numbers (n _g) of individuals with genotypic values g = 0, 1, 2, 3, ..., 2m. The maximization step is the maximization of the logarithm of the likelihood function (LLF) for n _g values. Thus, the EM algorithm is reduced, in each case, to solution of only one equation with one unknown parameter with the use of the n _g values, i.e., the numbers of individuals after the corresponding regrouping of the data on the individuals" genotypes. Treatment of the data obtained by Kurbatova on the MNSs and Rhesus systems with alleles C, C ^w , c, D, d, E, e with the use of Weir's EM algorithm and the EM algorithm suggested in this study yielded similar results. However, the MLEs of the parameters obtained with the use of either algorithm often converged to a wrong solution: the sum of the frequencies of all gametes (4 and 12 gametes for MNSs and Rhesus, respectively) was not equal to 1.0 even if the global maximum of LLF was reached for each of them (as it was for MNSs with the use of Weir's EM algorithm), with each parameter falling within admissible limits (e.g., 0, min(P _N, P _s) for P _Ns). The ² function is suggested to be used as a goodness-of-fit function for the distribution of genotypes in a sample in order to select acceptable solutions. However, the minimum of this function only guarantee the acceptability of solutions if all limitations on the parameters are met: the sum of estimations of gametic frequencies is 1.0, each frequency falls within the admissible limits, and the gametic algebra is complied with (none of the frequencies is negative).     

Anti-Barnacle Activities of Isothiocyanates Derived from β-Citronellol and Their Structure–Activity Relationships

Antifouling agents with low toxicity are in high demand for sustaining marine industries and the environment. This study aimed to synthesize 15 isothiocyanates derived from β-citronellol and evaluate their antifouling activities and toxicities against cypris larvae of the barnacle Amphibalanus amphitrite. The synthesized isothiocyanates exhibited effective antifouling activities (EC₅₀=0.10–3.33 μg mL⁻¹) with high therapeutic ratios (LC₅₀/EC₅₀ >30). Four isothiocyanates with an amide or isocyano group showed great potential as effective antifouling agents (EC₅₀=0.10–0.32 μg mL⁻¹, LC₅₀/EC₅₀=104–833). The enantiomers of the isothiocyanates only slightly differed in their antifouling activities. These results may serve as a basis for further research and development of β-citronellol-derived isothiocyanates as effective low-toxic antifouling agents. To the best of our knowledge, this study is the first to report the antifouling activities of isothiocyanates derived from accessible natural products.     

Mink Growth Hormone Structural–Functional Relationships: Effects of Renaturing and Storage Conditions

Fourier-transform infrared spectroscopy, in vitro bioassay and enzyme-linked immunoassay were used to study the structural-functional relationships of recombinant mink growth hormone (mGH), refolded and stored under different conditions. Porcine GH (pGH) was synthesized and used as an example. These two hormones, when refolded and stored the same way, had the same secondary structures, biological and immunological efficacy, and biological potency. Only the immunological potency differed, mGH being significantly less potent than pGH. Renaturation pH and storing frozen or at 4 °C in 5% glycerol did not affect either the secondary structure or the activity. However, freeze-drying raised the content of buried α-helices and lowered that of solvated α-helices and of unordered structures. These conformational changes were associated with a reduction of immunological and biological potency of mGH and of immunological potency of pGH. These findings provide original information on the secondary structure of mGH, and show that conformational changes induced by lyophilization adversely affect its activity.     

Dose–Risk and Duration–Risk Relationships between Aspirin and Colorectal Cancer: A Meta-Analysis of Published Cohort Studies

Background

In previous meta-analyses, aspirin use has been associated with reduced risk of colorectal cancer. However, uncertainty remains on the exact dose–risk and duration–risk relationships.

Methods

We identified studies by searching several English and Chinese electronic databases and reviewing relevant articles. The dose-response meta-analysis was performed by linear trend regression and restricted cubic spline regression. Subgroup analyses were conducted to explore possible heterogeneity among studies. Potential heterogeneity was calculated as Q statistic and I ² value. Publication bias was evaluated using funnel plots and quantified by the Begg’s and Egger’s test.

Results

Twelve studies were included in this meta-analysis. An inverse association between aspirin use and colorectal cancer was observed in both the overall group (RR = 0.74, 95% CI 0.64–0.83 for aspirin dose; RR = 0.80, 95% CI 0.75–0.85 for frequency of aspirin use; RR = 0.75, 95% CI 0.68–0.81 for years of aspirin use) and subgroups stratified by sex and cancer site. The dose-response meta-analysis showed that there was a 20% statistically significant decreased risk of colorectal cancer for 325 mg aspirin per day increment, 18% decreased risk for 7 times aspirin per week increment and 18% decreased risk for 10 years aspirin increment.

Conclusion

Long-term (>5 years), low-dose (75–325 mg per day) and regular aspirin use (2–7 times per week) can effectively reduce the risk of colorectal cancer.     

Structure–Function Relationships of the Vasopressin Prohormone Domains

1. In this review the structure–function relationships of the different vasopressin prohormone domains are dated and discussed, with special reference to the neurophysin and glycopeptide domains.2. The primary structures of the currently known neurophysins and glycopeptide sequences are compared and discussed.3. The hormone-binding and aggregational properties of neurophysin are reviewed and related to a possible function within the regulated secretory pathway.4. It is proposed, based on the properties reviewed here as well as our own data shown here, that the sorting of the vasopressin prohormone is initiated by hormone binding, which triggers aggregation of the prohormone into the characteristic dense cores of the regulated secretory pathway.5. This may suggest that prohormone sorting into the regulated secretory pathway is, in general, determined by noncovalent, intramolecular interactions that promote aggregation.     

Experimental Models of Protein–RNA Interaction: Isolation and Analyses of tRNAPhe and U1 snRNA-Binding Peptides from Bacteriophage Display Libraries

Peptides that bind either U1 small nuclear RNA (U1 snRNA) or the anticodon stem and loop of yeast tRNA^Phe (tRNA _AC ^Phe ) were selected from a random-sequence, 15-amino acid bacteriophage display library. An experimental system, including an affinity selection method, was designed to identify primary RNA-binding peptide sequences without bias to known amino acid sequences and without incorporating nonspecific binding of the anionic RNA backbone. Nitrocellulose binding assays were used to evaluate the binding of RNA by peptide-displaying bacteriophage. Amino acid sequences of RNA-binding bacteriophage were determined from the foreign insert DNA sequences, and peptides corresponding to the RNA-binding bacteriophage inserts were chemically synthesized. Peptide affinities for the RNAs (K _d ? 0.1–5.0 μM) were analyzed successfully using fluorescence and circular dichroism spectroscopies. These methodologies demonstrate the feasibility of rapidly identifying, isolating, and initiating the analyses of small peptides that bind to RNAs in an effort to define better the chemistry, structure, and function of protein–RNA complexes.     

DCCP and DICP： Construction and Analyses of Databases for Copper- and Iron-Chelating Proteins

Copper and iron play important roles in a variety of biological processes, especially when being chelated with proteins. The proteins involved in the metal binding, transporting and metabolism have aroused much interest. To facilitate the study on this topic, we constructed two databases （DCCP and DICP） containing the known copper- and iron-chelating proteins~ which are freely available from the website http：//sdbi.sdut.edu.cn/en. Users can conveniently search and browse all of the entries in the databases. Based on the two databases, bioinformatic analyses were performed, which provided some novel insights into metalloproteins.     

Low Genetic Differentiation of and Close Evolutionary Relationships between Anas platyrhynchos and Anas poecilorhyncha: RAPD–PCR Evidence

Using RAPD–PCR, we examined genetic diversity and phylogenetic relationships in two groups of river ducks: Anas platyrhynchos, A. poecilorhyncha, A. streperaand A. crecca, A. formosa, A. querquedula. Molecular taxon-specific markers were found for teals (A. crecca, A. formosa, A. querquedula) and gadwall (A. strepera). Each of the species examined was shown to exhibit high genetic diversity. The mean levels of intraspecific genetic polymorphism in the groups of mallards (P = 77%) and teals (P = 74.5%) were approximately equal whereas the mean interspecific genetic distances in teals were significantly higher than in mallards (D = 0.432 and D= 0.336, respectively). The levels of interspecific genetic differentiation in the species groups were also different. The genetic distances between the teal species and between gadwall and mallards were equal to 0.668–0.971 while the genetic distance between mallard A. platyrhynchos and spot-billed duck A. poecilorhyncha was 0.401, which slightly exceeds the intraspecific values for mallards (0.356–0.377). The RAPD patterns for this species pair showed high variability and a lack of fixed differences. This was adequately reflected on both intra- and interspecific differences and on phylogenetic constructions in which the morphological species did not form their own clusters but were intermixed. In contrast to mallards, the other species, which showed high genetic variability, were reliably separated in phenogenetic and phylogenetic reconstructions. The possible explanations of the low genetic differentiation of A. platyrhynchos and A. poecilorhynchaare discussed.     

Structure–Function Relationships in the Evolutionary Framework of Spermine Oxidase

Spermine oxidase is a FAD-dependent enzyme that specifically oxidizes spermine, and plays a central role in the highly regulated catabolism of polyamines in vertebrates. The spermine oxidase substrate is specifically spermine, a tetramine that plays mandatory roles in several cell functions, such as DNA synthesis, cellular proliferation, modulation of ion channels function, cellular signalling, nitric oxide synthesis and inhibition of immune responses. The oxidative products of spermine oxidase activity are spermidine, H₂O₂ and the aldehyde 3-aminopropanal that spontaneously turns into acrolein. In this study the reconstruction of the phylogenetic relationships among spermine oxidase proteins from different vertebrate taxa allowed to infer their molecular evolutionary history, and assisted in elucidating the conservation of structural and functional properties of this enzyme family. The amino acid residues, which have been hypothesized or demonstrated to play a pivotal role in the enzymatic activity, and substrate specificity are here analysed to obtain a comprehensive and updated view of the structure–function relationships in the evolution of spermine oxidase.