A multivariate growth curve model for pregnancy

A model is proposed for consecutive multivariate observations of pregnancy-related quantities for a particular mother assuming proportionally with an underlying univariate growth process. Apart from the longitudinal aspect of the multivariate time series, the cross-sectional distribution of growth curves is also discussed. The model is examined as regards problems of estimation and model checking, and the results are applied to data consisting of bivariate time series of symphyseal fundal distances and fetal weight estimates from 91 mothers. We find some evidence in the data on departures from the model.     

A general multilocus two-allele model for epistatic selection

Observations show that evolutionary processes often relate to multilocus epistatic selection. Here we develop further the approach suggested earlier by Zhivotovsky and Gavrilets to admit arbitrary multilocus epistasis. The obtained dynamic equations for allelic frequencies and gametic disequilibria are represented in a simple form. If selection is weak, this result extends Wright’s evolutionary equation to the case of cis-trans effects and sex differences in both recombination rates and genotypic fitnesses. Additionally to Wright’s equations for allelic frequencies, we derive equations for the gametic disequilibrium terms. We also give a general expression for the gametic disequilibria in a quasi-linkage state.     

A general model for aerobic yeast growth: batch growth

A general model for aerobic yeast growth in batch culture is presented. It is based on the concept that the aerobic metabolism of all yeasts is determined by the relative sizes of the transport rate of sugar into the cell and the transport rate of respiratory intermediates into the mitochondrion. If the rate of sugar uptake rate exceeds the rate of transport of respiratory intermediates into the mitochondrion (as in Saccharomyces cerevisiae, S. uvarum, and S. pombe), the metabolism exhibits the features of ethanol excretion and limited specific oxygen uptake rate. If the rate of transport of respiratory intermediates into the mitochondrion is of the same order as the transport of sugar into the cell (as in Candida utilis), the metabolism is characterized by little or no ethanol excretion and a much higher specific oxygen uptake rate. Batch data from an extensive range of yeast and carbon sources is used to illustrate the use of this model. The ability of this model to fit such an extensive range of experimental data suggests that it can be used as a generalized model for aerobic yeast growth.     

A general Akaike-type criterion for model selection in robust regression

Akaike's procedure (1970) for selecting a model minimises anestimate of the expected squared error in predicting new, independentobservations. This selection criterion was designed for modelsfitted by least squares. A different model-fitting technique,such as least absolute deviation regression, requires an appropriatemodel selection procedure. This paper presents a general Akaike-typecriterion applicable to a wide variety of loss functions formodel fitting. It requires only that the function be convexwith a unique minimum, and twice differentiable in expectation.Simulations show that the estimators proposed here well approximatetheir respective prediction errors.     

A general model for host plant selection in phytophagous insects

We develop a general theoretical framework for exploring the host plant selection behaviour of herbivorous insects. This model can be used to address a number of questions, including the evolution of specialists, generalists, preference hierarchies, and learning. We use our model to: (i) demonstrate the consequences of the extent to which the reproductive success of a foraging female is limited by the rate at which they find host plants (host limitation) or the number of eggs they carry (egg limitation); (ii) emphasize the different consequences of variation in behaviour before and after landing on (locating) a host (termed pre- and post-alighting, respectively); (iii) show that, in contrast to previous predictions, learning can be favoured in post-alighting behaviour--in particular, individuals can be selected to concentrate oviposition on an abundant low-quality host, whilst ignoring a rare higher-quality host; (iv) emphasize the importance of interactions between mechanisms in favouring specialization or learning.     

A general model for selection among modules in haplo-diploid life histories

Genetic variation resulting from changes during somatic development in modular organisms may be inherited by subsequent generations due to the late development of their germ line. As a consequence, both sexually and asexually produced offspring may be genetically variable. The presence of heritable intraclonal variation and the great life history variation among modular organisms requires that evolutionary theory does not limit selection to only that occurring among individuals resulting from meiosis and zygote formation. To allow for variation within clonal lineages, and encompass a wide variety of life histories, we construct a simple model of selection among modules in life histories that contain both haploid and diploid phases, such as that seen among many multicellular algae. Selection among modules is a demographic process with module performance depending on its genotype at a single locus with two alleles. The model is used to simulate the spread of a beneficial allele in life histories that vary in the relative amount of sexual and asexual reproduction. The time taken for allele fixation is shown to depend on both demographic and genetic factors.     

An asymptotic theory for model selection inference in general semiparametric problems

Hjort & Claeskens (2003) developed an asymptotic theoryfor model selection, model averaging and subsequent inferenceusing likelihood methods in parametric models, along with associatedconfidence statements. In this article, we consider a semiparametricversion of this problem, wherein the likelihood depends on parametersand an unknown function, and model selection/averaging is tobe applied to the parametric parts of the model. We show thatall the results of Hjort & Claeskens hold in the semiparametriccontext, if the Fisher information matrix for parametric modelsis replaced by the semiparametric information bound for semiparametricmodels, and if maximum likelihood estimators for parametricmodels are replaced by semiparametric efficient profile estimators.Our methods of proof employ Le Cam's contiguity lemmas, leadingto transparent results. The results also describe the behaviourof semiparametric model estimators when the parametric componentis misspecified, and also have implications for pointwise-consistentmodel selectors.     

A general model for ontogenetic growth under food restriction

Food restriction (FR) retards animals' growth. Understanding the underlying mechanisms of this phenomenon is important to conceptual problems in life-history theory, as well as to applied problems in animal husbandry and biomedicine. Despite a considerable amount of empirical data published since the 1930s, there is no relevant general theoretical framework that predicts how animals vary their energy budgets and life-history traits under FR. In this paper, we develop such a general quantitative model based on fundamental principles of metabolic energy allocation during ontogeny. This model predicts growth curves under varying conditions of FR, such as the compensatory growth, different age at which FR begins, its degree and its duration. Our model gives a quantitative explanation for the counterintuitive phenomenon that under FR, lower body temperature and lower metabolism lead to faster growth and larger adult size. This model also predicts that the animals experiencing FR reach the same fraction of their adult mass at the same age as their ad libitum counterparts. All predictions are well supported by empirical data from mammals and birds of varying body size, under different conditions of FR.     

A general model of the relation between phenotypic selection and genetic response

The phenotypic view of selection assumes that genetic responses can be predicted from selective forces and heritability — or in the classical quantitative genetic equation: R = h²S. However, data on selection in bird populations show that often no selection responses is found, despite consistent selective forces on phenotypes and significant heritable variation. Such discrepancies may arise due to the assumption that selection only acts on observed phenotypes. We derive a general selection equation that takes into account the possibility that some relevant (internal or external) traits are not measured. This equation shows that the classic equation applies if selection directly acts on the measured, phenotypic traits. This is not the case when, for instance, there are unknown internal genetic trade-offs, or unknown common environmental factors affecting both trait and fitness. In such cases, any relationship between phenotypic selection and genetic response is possible. Fortunately, the classical model can be tested by comparing phenotypic and genetic covariances between traits and fitness; an indication that important internal or external traits are missing can thus be obtained. Such an analysis was indeed found in the literature; for selection on fledging weight in Great Tits it yielded valuable extra information.     

Maintenance energy: a general model for energy-limited and energy-sufficient growth

The new model proposed to account for the energy requirement for growth includes both a constant maintenance energy term (m) independent of the specific growth rate and a term (m′) which decreases linearly with increase in specific growth rate and becomes zero at the maximum specific growth rate. The available data for testing the model do not deviate significantly from the relations predicted. Consistent values of the maximum growth yield (Y _G) can be derived, irrespective of whether the cultures are energy limited or energy sufficient. Attention is drawn to the possibility that the constant maintenance energy term may be estimated from the maximum specific growth rate.     

Saguaro (Carnegiea gigantea, Cactaceae) age-height relationships and growth: the development of a general growth curve

Because the growth rate of saguaros varies across different environments, past studies on saguaro population structure required extensive data collection (often over many decades) followed by site-specific analysis to estimate age at the sampled locale. However, when height-growth data from different populations are compared, the overall shape of the growth curves is similar. In this study, a formula was developed to establish saguaro age-height relationships (using stepwise regression) that can be applied to any saguaro population and only requires a site-specific factor to adjust the curve to the local growth rate. This adjustment factor can be established more efficiently and requires less data than the full analyses required for previous studies. Saguaro National Park East (SNP-E) was used as the baseline factor, set to 1.0. Results yielded a factor of 0.743 for SNP West. When the formula was applied to 10-yr interval data from Organ Pipe Cactus National Monument (OPCNM) in Arizona, USA, this location had a factor of 0.617 (relative to SNP-E). With this formula and relatively little field sampling, the age of any individual saguaro (whether the individual was sampled or not) in any population can be estimated.     

A general model for aerobic yeast growth: continuous culture

A general model for the aerobic growth of yeast in continuous culture is presented. The model is capable of simulating the complete range of metabolic responses observed for yeast growth in continuous culture including respiratory repression, saturated respiratory capacity, and respiratory depression.It is postulated that respiratory depression is the result of the adaptation (increase in capacity of the respiratory intermediate transport proteins located at the mitochondrial membrane). Respiratory repression and subsequent saturated respiratory capacity is postulated to be the result of the gradual transfer of biosynthetic intermediates provision from the mitochondrion to the cytoplasm or, possibly, the adaptation (increase) in the capacity of the cell to excrete ethnol. It is difficult to provide a definitive experimental verification of these postulates.Irrespective of the biochemical basis of respiratory repression and depression, the model described is capable of simulating the complete range of metabolic responses obtained for yeast growth in continuous culture. It is the only model reported in the literature capable of achieving this.     

A mathematical model for the survivorship curve

A mathematical function describing the various kinds of survivorship curve is formulated with the useful parameter, environmental capacity. Three types of the survivorship curve illlustrated byDeevey can be obtained from changing the value of this function. When a cohort is large and the competition occurs in the scramble type, this function shows the third type ofDeevy 's and this to the first type in the case of low density and the contest type of competition. But the second type would rather be obtained by the action of density independent agencies.     

The effects of selection for different combinations of weights at two ages on the growth curve of mice

Summary The weights of mice in lines selected for different combinations of high and low body weights at 5 and at 10 weeks of age were recorded from 3 to 21 weeks of age. The average growth curve for each line was computed using the Gompertz function. The growth curves of lines selected for high or low weight at a single age (ST lines) showed large differences in estimates of mature size and small differences in estimates of maturing rate, i.e. of the relative rate of growth to maturity. The growth curves of lines selected by independent culling for divergent combinations of deviations of opposite sign in 5- and 10-week weights (ICL lines) showed little difference in estimates of mature size and a large difference in estimates of maturing rate. The growth curves of lines selected by index for divergence in 5-week weight with no change in 10-week-weight or for divergence in 10-week-weight with no change in 5-week weight showed large differences in estimates of mature size and large differences in estimates of the maturing rate. The relationship between mature size and maturing rate was affected in different ways by the three types of selection.     

A general framework for marker-assisted selection

Early simulation studies have showed that the inclusion of epistatic components (especially the additive-by-additive effects) into marker-assisted selection (MAS) can improve selection efficiency for a short-term breeding program. In this study I extend Lande and Thompson's theory to incorporate both additive and non-additive effects into MAS with reference to the mass selection case. Four different indices are analytically examined in terms of the type of genetic components involved in the marker scores: phenotype-, general combining ability (GCA)-, and GCA and reciprocal effects-based marker scores. The phenotype-based marker index is applicable to any population of non-random mating, while the other three indices are applicable to the synthetic population derived from diallel crosses. All these indices may have higher selection efficiencies than the index with solely additive effects-associated markers as long as the detectable transient non-additive effects are present. The improvement in selection efficiency depends on the magnitude of non-additive variances and the proportion of them explained by markers. The index with the phenotype-based marker scores operates on the whole of the additive and non-additive effects, and has the largest selection efficiency. The indices with the GCA-based marker scores operate only on additive and additive-by-additive genetic variation and have relatively small selection efficiencies. Inclusion of the markers from organelle genomes can also increase selection efficiency, depending upon the proportion of the total genetic variation attributable to organelle genomes and the proportion of them explained by organelle genomic markers. Sharing of markers among different marker scores does not facilitate the improvement of selection efficiency.