A.B. Pleasants

Metabolic plasticity during mammalian development is directionally dependent on early nutritional status.

Developmental plasticity in response to environmental cues can take the form of polyphenism, as for the discrete morphs of some insects, or of an apparently continuous spectrum of phenotype, as for most mammalian traits. The metabolic phenotype of adult rats, including the propensity to obesity, hyperinsulinemia, and hyperphagia, shows plasticity in response to prenatal nutrition and to neonatal administration of the adipokine leptin. Here, we report that the effects of neonatal leptin on hepatic gene expression and epigenetic status in adulthood are directionally dependent on the animals nutritional status in utero. These results demonstrate that, during mammalian development, the direction of the response to one cue can be determined by previous exposure to another, suggesting the potential for a discontinuous distribution of environmentally induced phenotypes, analogous to the phenomenon of polyphenism.

Pre- and postnatal nutritional histories influence reproductive maturation and ovarian function in the rat.

Background While prepubertal nutritional influences appear to play a role in sexual maturation, there is a need to clarify the potential contributions of maternal and childhood influences in setting the tempo of reproductive maturation. In the present study we employed an established model of nutritional programming to evaluate the relative influences of prenatal and postnatal nutrition on growth and ovarian function in female offspring. Methods Pregnant Wistar rats were fed either a calorie-restricted diet, a high fat diet, or a control diet during pregnancy and/or lactation. Offspring then were fed either a control or a high fat diet from the time of weaning to adulthood. Pubertal age was monitored and blood samples collected in adulthood for endocrine analyses. Results We report that in the female rat, pubertal timing and subsequent ovarian function is influenced by the animals nutritional status in utero, with both maternal caloric restriction and maternal high fat nutrition resulting in early pubertal onset. Depending on the offsprings nutritional history during the prenatal and lactational periods, subsequent nutrition and body weight gain did not further influence offspring reproductive tempo, which was dominated by the effect of prenatal nutrition. Whereas maternal calorie restriction leads to early pubertal onset, it also leads to a reduction in adult progesterone levels later in life. In contrast, we found that maternal high fat feeding which also induces early maturation in offspring was associated with elevated progesterone concentrations. Conclusions These observations are suggestive of two distinct developmental pathways leading to the acceleration of pubertal timing but with different consequences for ovarian function. We suggest different adaptive explanations for these pathways and for their relationship to altered metabolic homeostasis.

The distribution of urine deposited on a pasture from grazing animals

Intensive agricultural production practices are known to cause far-reaching effects on water quality. The current paper addresses and quantifies these effects caused by high stocking rates. A set of stochastic difference equations describing the development of the proportion of a grazed field either unaffected by urine deposition, or affected by multiple (1, 2, ...) urine depositions is described. A solution to this set of equations is found for the expected value of multiple (0, 1, 2, ...) urine depositions, and the variances of these depositions. It is assumed that an animal voids urine with a Poisson probability distribution, and that each urine deposition covers a random area with a Gaussian probability density. Given these reasonable assumptions, the probability distributions for each multiplicity of patch distribution can be found numerically. The utility of the results obtained is illustrated for a problem in assessing the nitrogen (N) pollution of ground water from different grazing strategies. It is demonstrated quantitatively that mob stocking (typical of winter management regimes in New Zealand) is often caused by rotational grazing. The latter is often used to optimize grass growth and intake, especially in winter. This increases (more than linearly) the level of N pollution in ground water. This is because of the increased frequency of multiple urine depositions, i.e. more than one urine deposition on the same patch of land in a short time.

Qualitative theory of the spread of a new gene into a resident population

This work addresses the problems that arise in the estimation of the risk of invader/unwanted GMO spread and the optimal release of desired genes into a population through the release of transgenic individuals. On the basis of a general model of the propagation of an advantageous allele through a population we analyze the thresholds and critical aggregations in gene frequency necessary for the spread of new gene carriers. It is shown that if the invader appears at one place in the ecosystem then it will not spread throughout the ecosystem unless it exceeds some critical threshold, where the critical threshold is defined in terms of both the amount and distribution of the invader. The value of the critical threshold will depend on the fitness of the invader relative to the fitness of the resident organisms in the ecosystem and the mechanism of its dispersion. It is also shown that typically an invader will not spread symmetrically, even if the environment is isotropic, but rather develops clusters that form filaments within the ecosystem. We also demonstrate that if the invader aggregation is sufficiently large then after an initial period the advance of the invader into the resident population takes the form of a traveling wave. The speed of this wave tends to a speed characteristic of the relative fitness and dispersive mechanisms of the invader.

Population growth as a nonlinear stochastic process

The evolution of the probability density of a biological population is described using nonlinear stochastic differential equations for the growth process and the related Fokker-Planck equations for the time-dependent probability densities. It is shown that the effect of the initial conditions disappears rapidly from the evolution of the mean of the process. But the behaviour of the variance depends on the initial condition. It may monotonically increase, reaching its maximum in the steady state, or have a rather complicated evolution reaching the maximum near the point where growth rates (not population size) is maximal. The variance then decreases to its steady-state value. This observation has implications for risk assessments associated with growing populations, such as microbial populations, which cause food poisoning if the population size reaches a critical level.

A simple model for optimizing rotational grazing

Abstract A simple mathematical model has been formulated to model a simple rotational grazing system of two fields, where a mob of animals is grazed first in one field, then the other. By using linear functions for the rate of herbage mass accumulation and for the rate of animal herbage intake, this system may be solved explicitly to yield expressions for (1) the total intake per animal over the time period, and (2) the total remaining herbage after grazing. Regarding the swap over time as an optimal control variable, these expressions can be optimized. The results are analysed for various initial conditions, including stocking rate, initial biomass in each field, and field Comparisons are made with continuous grazing. Extensions to the model are discussed.

THE ALLOMETRIC HYPOTHESIS WHEN THE SIZE VARIABLE IS UNCERTAIN: ISSUES IN THE STUDY OF CARCASS COMPOSITION BY SERIAL SLAUGHTER

(Received 21 February 1995; revised 17 July 1995)AbstractThe allometric hypothesis which relates the shape (y) of biological organs to the size ofthe plant or animal (x), as a function of the relative growth rates, is ubiquitous in biology.This concept has been especially useful in studies of carcass composition of farm animals,and is the basis for the definition of maintenance requirements in animal nutrition.When the size variable is random the differential equation describing the relative growthrates of organs becomes a stochastic differential equation, with a solution different fromthat of the deterministic equation normally used to describe allometry. This is important instudies of carcass composition where animals are slaughtered in different sizes and ages,introducing variance between animals into the size variable.This paper derives an equation that relates values of the shape variable to the expectedvalues of the size variable at any point. This is the most easily interpreted relationshipin many applications of the allometric hypothesis such as the study of the development ofcarcass composition in domestic animals by serial slaughter. The change in the estimatesof the coefficients of the allometric equation found through the usual deterministc equationis demonstrated under additive and multiplicative errors. The inclusion of a factor basedon the reciprocal of the size variable to the usual log - log regression equation is shownto produce unbiased estimates of the parameters when the errors can be assumed to bemultiplicative.The consequences of stochastic size variables in the study of carcass composition arediscussed.

Modelling pasture mass through time in a managed grazing system subject to perturbations resulting from complexity in natural biological processes

Abstract Variation is a characteristic of biological systems which may be due to both inaccuracies in measurement and the complexity of the interactions involved. The complexity of the interactions means that any abstraction of a biological system into a model often includes considerable uncertainty. Traditionally this uncertainty has been modelled by probabilistic methods. When dynamical systems are used to describe the evolution of biological processes it is necessary to consider the variation resulting from the impact of variables that are ignored in the formulation. Typically these variables are ignored because they act on a time scale faster than that of the abstraction. However, these fast variables can still affect the evolution of the system. This fast variable affect can be modelled using stochastic differential equations which incorporate the uncertainty due to complexity in the natural system. Solutions of stochastic differential equations may differ from the corresponding deterministic equations. Stochastic differential equations introduce a number of modelling issues not present in the deterministic case. These issues are reviewed using a model of a pasture grazing system. It is shown that the mode of the probability density which is the solution of the stochastic differential equation is an important statistic in the dynamical case. The importance of the first passage time in modelling complex ecological systems subject to uncertainty is also discussed.

The evolution of a truncated gaussian probability density through time-modelling animal liveweights after selection

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian.

Linear Models with Response Functions Based on the Laplace Distribution: Statistical Formulae and Their Application to Epigenomics

The statistical application considered here arose in epigenomics, linking the DNA methylation proportions measured at specific genomic sites to characteristics such as phenotype or birth order. It was found that the distribution of errors in the proportions of chemical modification (methylation) on DNA, measured at CpG sites, may be successfully modelled by a Laplace distribution which is perturbed by a Hermite polynomial. We use a linear model with such a response function. Hence, the response function is known, or assumed well estimated, but fails to be differentiable in the classical sense due to the modulus function. Our problem was to estimate coefficients for the linear model and the corresponding covariance matrix and to compare models with varying numbers of coefficients. The linear model coefficients may be found using the (derivative-free) simplex method, as in quantile regression. However, this theory does not yield a simple expression for the covariance matrix of the coefficients of the linear model. Assuming response functions which are except where the modulus function attains zero, we derive simple formulae for the covariance matrix and a log-likelihood ratio statistic, using generalized calculus. These original formulae enable a generalized analysis of variance and further model comparisons.