Peyton Cook

Accurate and statistically verified quantification of relative mRNA abundances using SYBR Green I and real-time RT-PCR

Among the many methods currently available for quantifying mRNA transcript abundance, reverse transcription-polymerase chain reaction (RT-PCR) has proved to be the most sensitive. Recently, several protocols for real-time relative RT-PCR using the reporter dye SYBR Green I have appeared in the literature. In these methods, sample and control mRNA abundance is quantified relative to an internal reference RNA whose abundance is known not to change under the differing experimental conditions. We have developed new data analysis procedures for the two most promising of these methodologies and generated data appropriate to assess both the accuracy and precision of the two protocols. We demonstrate that while both methods produce results that are precise when 18S rRNA is used as an internal reference, only one of these methods produces consistently accurate results. We have used this latter system to show that mRNA abundances can be accurately measured and strongly correlate with cell surface protein and carbohydrate expression as assessed by flow cytometry under different conditions of B cell activation.

SAS programs for real-time RT-PCR having multiple independent samples.

Relative real-time reverse transcription PCR (RT-PCR) has become an important tool for quantifying changes in messenger RNA (mRNA) populations following differential development or stimulation of tissues or cells. However, the best methods for conducting such experiments and analyzing the resultant data remain an issue of discussion. In this report we describe an appropriate experimental methodology and the computer programs necessary to generate a meaningful statistical analysis of the combined biological and experimental variability in such experiments. Specifically, logarithmic transformations of raw fluorescence data from the log-linear portion of real-time PCR growth curves for both target and reference genes are analyzed using a SAS/STAT Mixed Procedure program specifically designed to give a point estimate of the relative expression ratio of the target gene with associated 95% confidence interval. The program code is open-source and is printed in the text.

The importance of overwinter aggregation for reproductive success of monarch butterflies (Danaus plexippus L.)

A model of monarch bufferfly mating in overwinter aggregations is presented. Mating success each day is predicted to be a function of second-order kinetics. Therefore, increased density increases each individuals frequency of mating. Since multiple mating of females is critical for female energetics in overwinter populations (and in turn fecundity), and mating frequency is based on second-order kinetics, aggregations play an indispensable role in the reproduction dynamics of overwintering Danaus plexippus.

Bayesian Statistics Using Mathematica

Abstract We illustrate the use of the Mathematica software system (programming language) for performing Bayesian calculations of the sort encountered in introductory presentations of Bayesian statistics. In particular, we show the ease with which one can do numerical computation, graphics, and symbolic computation to analyze one- and two-dimensional probability density functions. Our illustrations involve a time series problem using oxygen uptake data taken from a burn patient.

A Bayesian analysis of regression models with continuous errors with application to longitudinal studies.

We employ a regression model with errors that follow a continuous autoregressive process to analyse longitudinal studies. In this way, unequally spaced observations do not present a problem in the analysis. We employ a Bayesian approach, where our inferences are based on a direct resampling process that generates values from the posterior distribution of the parameters of the model. We illustrate these Bayesian inferences with an analysis of a longitudinal study that involves the regression of foetal head circumference on menstrual age. Using these same data, we contrast the Bayesian approach with a maximum likelihood technique.

Bayesian estimation of the mean of an autoregressive process

The marginal posterior probability density function (pdf) for the mean of a stationary pth order Gaussian autoregressive process is derived using the conditional likelihood function. While the posterior pdf provides a small sample analysis, the pdf is not well known and must be analyzed numerically. This is relatively easy since it is a function of only one variable. Two sets of examples are presented. The first set involves synthetic data generated by computer, and the second set deals with energy expenditure data on a bum patient.

Bayesian analysis of threshold autoregressions

A nonasymptotic Bayesian approach is developed for analysis of data from threshold autoregressive processes with two regimes. Using the conditional likelihood function, the marginal posterior distribution for each of the parameters is derived along with posterior means and variances. A test for linear functions of the autoregressive coefficients is presented. The approach presented uses a posterior p-value averaged over the values of the threshold. The one-step ahead predictive distribution is derived along with the predictive mean and variance. In addition, equivalent results are derived conditional upon a value of the threshold. A numerical example is presented to illustrate the approach.

Africanized honey bee response to differences in reward frequency

SUMMARYDifferences in predation pressure and floral resources exist among the endemic ranges of Apis mellifera subspecies. Those environmental differences should select for heterogeneity in forager flower fidelity among honey bee subspecies, particularly when reward frequency differences are associated with competing flower types. We tested that evolutionary model by examining the foraging behaviour of Africanized honey bees (AHB), and by comparing our observations with those recorded for Italian (A. m. ligustica) and Caucasian honey bees (A. m. caucasica). The response of AHB (A. m. scutel- lata hybrid/introgressant) to reward frequency differences among flower colours was examined using artificial flower patches. Each patch contained blue, white, and yellow flowers. When rewards offered by all three flower- morphs were identical, some foragers restricted visitation to blue and white flowers, while others showed fidelity to yellow flowers. Bees visiting blue and white flowers did not show a preference fo...

A bayesian analysis of the mixed linear model

The mixed model is defined. The exact posterior distribution for the fixed effect vector is obtained. The exact posterior distribution for the error variance is obtained. The exact posterior mean and variance of a Bayesian estimator for the variances of random effects is also derived. All computations are non-iterative and avoid numerical integrations.

Nectar quality perception by honey bees (Apis mellifera ligustica).

In exploring how foragers perceive rewards, we often find that well-motivated individuals are not too choosy and unmotivated individuals are unreliable and inconsistent. Nevertheless, when given a choice we see that individuals can clearly distinguish between rewards. Here we develop the logic of using responses to two-choice problems as a derivative function of perceived reward, and utilize this model to examine honey bee perception of nectar quality. Measuring the derivative allows us to deduce the perceived reward function. The derivative function of the perceived reward equation gives the rate of change of the reward perceived for each reward value. This approach depends on presenting free-flying foragers with a series of two different rewards presented simultaneously (i.e., two-choice, binomial tests). We also examine how honey bees integrate information from a range of reward qualities to formulate a functional response. Results suggest that honey bees overestimate higher quality rewards and that direct comparison is an important step in the integration of information from a range of rewards.