Envelope methodology can provide substantial efficiency gains in multivariate statistical problems, but in some applications the estimation of the envelope dimension can induce selection volatility that may mitigate those gains. Current envelope methodology does not account for the added variance that can result from this selection. In this article, we circumvent dimension selection volatility through the development of a weighted envelope estimator. Theoretical justification is given for our estimator and validity of the residual bootstrap for estimating its asymptotic variance is established. A simulation study and an analysis on a real data set illustrate the utility of our weighted envelope estimator.

The epigenetic information encoded in the genomic DNA methylation pattern is translated by methylcytosine binding proteins like MeCP2 into chromatin topology and structure and gene activity states. We have shown previously that the MeCP2 level increases during differentiation and that it causes large-scale chromatin reorganization, which is disturbed by MeCP2 Rett syndrome mutations. Phosphorylation and other posttranslational modifications of MeCP2 have been described recently to modulate its function. Here we show poly(ADP-ribosyl)ation of endogenous MeCP2 in mouse brain tissue. Consequently, we found that MeCP2 induced aggregation of pericentric heterochromatin and that its chromatin accumulation was enhanced in poly(ADP-ribose) polymerase (PARP) 1−/− compared with wild-type cells. We mapped the poly(ADP-ribosyl)ation domains and engineered MeCP2 mutation constructs to further analyze potential effects on DNA binding affinity and large-scale chromatin remodeling. Single or double deletion of the poly(ADP-ribosyl)ated regions and PARP inhibition increased the heterochromatin clustering ability of MeCP2. Increased chromatin clustering may reflect increased binding affinity. In agreement with this hypothesis, we found that PARP-1 deficiency significantly increased the chromatin binding affinity of MeCP2 in vivo. These data provide novel mechanistic insights into the regulation of MeCP2-mediated, higher-order chromatin architecture and suggest therapeutic opportunities to manipulate MeCP2 function.

The multivariate linear regression model is an important tool for investigating relationships between several response variables and several predictor variables. The primary interest is in inference about the unknown regression coefficient matrix. We propose multivariate bootstrap techniques as a means for making inferences about the unknown regression coefficient matrix. These bootstrapping techniques are extensions of those developed in Freedman [1981], which are only appropriate for univariate responses. Extensions to the multivariate linear regression model are made without proof. We formalize this extension and prove its validity. A real data example and two simulated data examples which offer some finite sample verification of our theoretical results are provided.

Most studies of phenotypic selection do not estimate selection or fitness surfaces for multiple components of fitness within a unified statistical framework. This makes it difficult or impossible to assess how selection operates on traits through variation in multiple components of fitness. We describe a new generation of aster models that can evaluate phenotypic selection by accounting for timing of life-history transitions and their effect on population growth rate, in addition to survival and reproductive output. We use this approach to estimate selection on body size and development time for a field population of the herbivorous insect, Manduca sexta (Lepidoptera: Sphingidae). Estimated fitness surfaces revealed strong and significant directional selection favoring both larger adult size (via effects on egg counts) and more rapid rates of early larval development (via effects on larval survival). Incorporating the timing of reproduction and its influence on population growth rate into the analysis resulted in larger values for size in early larval development at which fitness is maximized, and weaker selection on size in early larval development. These results illustrate how the interplay of different components of fitness can influence selection on size and development time. This integrated modeling framework can be readily applied to studies of phenotypic selection via multiple fitness components in other systems.

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