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Biomedical subjects

R A Desharnais

Publications and source records attributed to R A Desharnais.

7 recordsLinked to original sources

Lattice effects observed in chaotic dynamics of experimental populations.

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated much ecological research; yet discrete-state models with bounded population size can display only cyclic behavior. Motivated by data from a population experiment, we compared the predictions of discrete-state and continuous-state population models. Neither the discrete- nor continuous-state models completely account for the data. Rather, the observed dynamics are explained by a stochastic blending of the chaotic dynamics predicted by the continuous-state model and the cyclic dynamics predicted by the discrete-state models. We suggest that such lattice effects could be an important component of natural population fluctuations.

Animals↗

Resonant population cycles in temporally fluctuating habitats.

Experiments with the flour beetle Tribolium have revealed that animal numbers were larger in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volume of the same average size. In this paper we derive and analyze a discrete stage-structured mathematical model that explains this phenomenon as a kind of resonance effect. Habitat volume is incorporated into the model by the assumption that all rates of cannibalism (larvae on eggs, adults on eggs and pupae) are inversely proportional to the volume of the culture medium. We tested this modeling assumption by conducting and statistically analyzing laboratory experiments. For parameter estimates derived from experimental data, our model indeed predicts, under certain circumstances, a larger (cycle-average) total population abundance when the habitat volume periodically fluctuates than when the habitat volume is held constant at the average volume. The model also correctly predicts certain phase relationships and transient dynamics observed in data. The analyses involve a thorough integration of mathematics, statistical methods, biological details and experimental data.

Animals↗

Quantitative in situ hybridization to measure single-cell changes in vasopressin and oxytocin mRNA levels after osmotic stimulation.

1. The measurement of cellular mRNA content by quantitative in situ hybridization is a valuable approach to the study of gene expression in brain since this tissue exhibits a high degree of phenotypic heterogeneity. 2. The cellular content of vasopressin and oxytocin mRNA in hypothalamo-neurohypophysial system neurons was altered by maintaining rats for 24 hr on 2% sodium chloride water. 3. Statistical and graphical techniques were then used to analyze cell by cell how mRNA levels were altered as a result of osmotic stimulation. We propose that the negative binomial probability distribution is a suitable model to describe how mRNA content varies across a defined cell population. For both measures of oxytocin and vasopressin mRNA levels, maximum-likelihood estimation indicated that this model adequately described empirical findings obtained from rats drinking tap water or salt water. 4. Both graphical and statistical analyses suggested how the defined neural system responds to osmotic stimulation: mRNA content was altered as a multiplicative function of "initial state." The utility and limitations of the quantitative approach are discussed.

Animals↗

Graphical and statistical approaches to data analysis for in situ hybridization.

Quantification of gene expression in a morphological context is an invaluable tool for neurobiological investigation. The ability to measure the quantity of specific mRNA molecules at the level of the single neuron permits one to monitor the modulation of complex cell synthetic activity of intact neuron populations. The cells of interest can be contiguous or dispersed in functionally significant patterns throughout a broad anatomical region of the brain. The application of quantitative in situ hybridization is technically difficult and labor intensive. Nevertheless, it has great utility for investigating gene expression from a structural perspective. (1) In situ hybridization permits one to ask questions concerning the anatomical pattern of neuronal gene expression. (2) It permits analyses concerning the initiation of expression, cell location, cell type, and alterations of level of expression within a spatial and temporal context. (3) In cases where blotting methods suggest a message exists at low copy, in situ hybridization permits queries at the single-cell level. For example, in situ hybridization can determine if very few cells are expressing the gene product or if many neurons dispersed throughout a brain region exhibit low mRNA copy number/cell. Quantitative analyses also allow detailed investigation of cell response to physiologically meaningful stimulation. Our application of statistical and numerical methods is a demonstration of the utility of probabilistic models; the mixture distribution accounted for data from both labeled and unlabeled sources. In agreement with many previous investigations, grain density over an unlabeled uniform source (oxytocinergic cells) was suitably described by the Poisson distribution. The population of labeled vasopressinergic cells, however, was best described by the negative binomial distribution. Previous investigations from different fields of biology show that the negative binomial can be used to describe many biological phenomena, and this distribution was considered in at least two previous investigations to evaluate autoradiographic data which did not fit the Poisson function. From a theoretical perspective, the probabilistic relationship between beta-particle decay (a Poisson function) and the distribution of message levels among individual neurons in a cell group (gamma distribution) prompts consideration of the negative binomial. For both data sets the observed variances were larger than the mean, and the labeled portion of the data sets exhibited positive skewness.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

Life not lived due to disequilibrium in heterogeneous age-structured populations.

Three models of age-structured populations with demographically heterogeneous subpopulations are analyzed. In the first model, each subpopulation has its own age-specific vital rates which are fixed in time. In the second model, the vital rates of each subpopulation are uniformly inhibited by increasing total numbers of individuals. In the third, the vital rates of groups of subpopulations are inhibited by the total numbers of individuals in other groups of subpopulations with an intensity that depends on the interacting pair of groups. Three functions are defined to measure disequilibrium in the subpopulation frequencies, subpopulation age structures, and total population size. For the first model, we show that disequilibrium will shift the trajectory of the total numbers of individuals forward or backward in time by an asymptotic constant that is proportional to the sum of the disequilibrium measures. For the second model, we establish sufficient conditions for the existence of a globally stable equilibrium and we show that disequilibrium will result in a finite loss or gain in life which is proportional to the sum of the disequilibrium measures. For the last model, we show that the loss or gain in life for each group of subpopulations is a linear combination over all groups of the sums of the three disequilibrium measures. We illustrate these results with numerical examples and give possible biological interpretations of the models. We relate these new results to previous work on the cost of natural selection and measures of demographic disequilibrium.

Age Factors↗

Natural selection, fitness entropy, and the dynamics of coevolution.

The coevolutionary dynamics of interacting populations were studied by combining continuous time Lotka-Volterra models of population growth with single-locus genetic models of weak selection. The effects of natural selection on population growth were evaluated using Ginzburg's fitness entropy function as a measure of the deviation of a population's initial allele frequencies from their polymorphic equilibrium values. This entropy measure was used to relate the dynamics of a community composed of evolving populations to the dynamics of a "reference community" whose populations are initially in genetic equilibrium. Specifically, a quantity called the "selective difference area" was defined as the total difference between the population size trajectories of a reference and evolving population. The selective difference area represents the amount of extra life a species would realize if the entire community were at genetic equilibrium. It was shown that this selective difference area is a simple linear function of the initial fitness entropies of each species. This prediction is independent of the strength of selection and holds for any arbitrary set of initial population densities. Numerical examples were presented to illustrate the results. Under the assumption of weak selection, a generalization for arbitrary population growth models was outlined.

Biological Evolution↗