A multivariate model for growth of populations

The “random environment” concept is used to model the growth of several interdependent populations. The vital rates are assumed to follow a multi-variate Ornstein-Uhlenbeck process; important properties of this process and of the integrated process (representing log of population growth) are developed. Application to a predator-prey situation is considered and a technique for the estimation of unknown parameters is developed.     

Tests and model selection for the general growth curve model

The model considered here is a generalized multivariate analysis of variance model useful especially for many types of growth curve problems including biological growth and technology substitution. It is defined as Yp x N = Xp x m tau m x r Ar x N + epsilon p x N, where tau is unknown, and X and A are known design matrices of ranks m less than p and r less than N, respectively. Furthermore, the columns of epsilon are independent p-variate normal with mean vector 0 and common covariance matrix sigma. In general, p is the number of time (or spatial) points observed on each of the N cases, (m - 1) is the degree of polynomial in time, and r is the number of groups. The main focus of this paper is the selection of models for the general growth curve model with regard to the covariance matrix sigma. Likelihood ratio tests and selection procedures based on sample reuse and predictions are proposed. Special emphasis is on the serial covariance structure for sigma, which has been shown to be quite important in the prediction of biological data and technology substitution data. One-population and K-population problems are considered. Some of the results are illustrated with two sets of biological data.     

A multivariate model for ordinal trait analysis

Many economically important characteristics of agricultural crops are measured as ordinal traits. Statistical analysis of the genetic basis of ordinal traits appears to be quite different from regular quantitative traits. The generalized linear model methodology implemented via the Newton-Raphson algorithm offers improved efficiency in the analysis of such data, but does not take full advantage of the extensive theory developed in the linear model arena. Instead, we develop a multivariate model for ordinal trait analysis and implement an EM algorithm for parameter estimation. We also propose a method for calculating the variance-covariance matrix of the estimated parameters. The EM equations turn out to be extremely similar to formulae seen in standard linear model analysis. Computer simulations are performed to validate the EM algorithm. A real data set is analyzed to demonstrate the application of the method. The advantages of the EM algorithm over other methods are addressed. Application of the method to QTL mapping for ordinal traits is demonstrated using a simulated baclcross (BC) population.     

A multivariate prediction model for microarray cross-hybridization

Background  

Expression microarray analysis is one of the most popular molecular diagnostic techniques in the post-genomic era. However, this technique faces the fundamental problem of potential cross-hybridization. This is a pervasive problem for both oligonucleotide and cDNA microarrays; it is considered particularly problematic for the latter. No comprehensive multivariate predictive modeling has been performed to understand how multiple variables contribute to (cross-) hybridization.     

A model for noninhibitory microbial growth

A model for noninhibitory microbial growth has been developed which is superior to the Monod model in that it can predict the decline in steady-state growth yields at both the slow and the fast specific growth rates. The model parameters are evaluated from data obtained for steady-state, phenol-limited Pseudomonas putida growth using a conventional 1-dm(3) cheniostat. The model also has been successfully applied to Mor and Fiechter's data for cheniostat yeast cultures.     

A model for diauxic growth.

A model is developed to predict batch and continuous culture behavior of fermentations on two different carbon and energy sources. The basic assumption of the model is that the permease for the favored substrate is constitutive, whereas the premease for the second substrate is subject to induction and catabolite repression. Simulations of the model show features of diauxic growth described in the literature.     

A continuum model for root growth

This paper presents a study of a simple one-dimensional continuum model for growth of the plant root. A fundamental constitutive equation is derived. The model is studied by means of various special cases of increasing complexity. Asymptotic expansions are used to derive approximate solutions to the equation of the model under the fundamental assumption that cell wall thickness is small in comparison with the diameter of the cell. The basic results of the study may be summarized as follows. The observed growth pattern of the root cannot be modelled by a mechanical system whose properties are independent of position on the root. The observed pattern can be modelled by a simple mechanical system in which, for example, cell wall yield stress first decreases and then increases. Two fundamental observations are made based on the modelling study. The first is that any mechanical model must take into account the convective displacement from the tip of points along the root. The second is that in describing growth, data on cell wall mechanical properties are meaningless without corresponding data on cell water potential, and vice versa.     

A model for energy-sufficient culture growth

Pirt's maintenance model has been widely accepted for the effects of growth rate and maintenance on growth yield. However, the interpretation of parameters in Pirt's model as biological constants is difficult for energy-sufficient culture growth. In this study, a mechanistic model for the growth energetics of energy-sufficient chemostat cultures is proposed and verified with literature data. In the model, the overutilization of the energy substrate in energy-sufficient culture growth is attributed to the defective regulation of the energy substrate metabolism and energy uncoupling. The model also uses an "energy surplus" concept to collectively represent the effects of energy excessiveness. The proposed model provides a better quantitative understanding of the maximum growth yield and maintenance of energy-sufficient cultures. It also explains the glucose concentration effect reported in the literature.     

The photosynthesis-light curve: A simple analog model

An analog model of the photosynthesis-light curve is presented and applied to published data. Previous equations have been constructed with parameters having geometric rather than biologic definition. The present study defines each parameter as an analog of a hypothetical photosynthetic system. The model is constructed of two stages, a light stage composed of photosynthetic factories, N, with probability P of intercepting a given amount of light, and a dark stage approximated by the Michaelis-Menten equation. An index of the speed of the dark stage, relative to the potential speed of the light stage is provided. The model describes a family of photosynthesis-light curves and can be applied to data to interpret changes in the photosynthetic system from changes in the shape of the curve.     

Exploratory data analysis of DNA microarrays by multivariate curve resolution

In this work, the application of a multivariate curve resolution procedure based on alternating least squares optimization (MCR-ALS) for the analysis of data from DNA microarrays is proposed. For this purpose, simulated and publicly available experimental data sets have been analyzed. Application of MCR-ALS, a method that operates without the use of any training set, has enabled the resolution of the relevant information about different cancer lines classification using a set of few components; each of these defined by a sample and a pure gene expression profile. From resolved sample profiles, a classification of samples according to their origin is proposed. From the resolved pure gene expression profiles, a set of over- or underexpressed genes that could be related to the development of cancer diseases has been selected. Advantages of the MCR-ALS procedure in relation to other previously proposed procedures such as principal component analysis are discussed.