Increased recombination in a multi-locus system during environmental fluctuations

The role of variability of environment as a factor of recombination evolution is studied. It was shown that selection in multilocus system under cyclic or random fluctuations of external conditions results in rapid increase in recombination frequency, even under free recombination between the rec-modificator and the selected system (SS). If so, pair-vise linkage disequilibrium coefficients have unchanged signs and are negative, and the advantage of rec+ alleles is provided by changes in signs of disequilibriums of higher order. The low frequency environmental fluctuations maintain recombination as it is, while high frequency ones induce the substitution of the low level by high. It was established that the recombination promoting mechanism of crossing-over maintenance, due to elimination of non-optimal allelic combinations of SS loci under temporal optimum variations, may be accomplished by smaller genetic load, than under elimination of deleterious mutations.     

Stochastic compartmental model with branching particles

A multi-compartmental model with particles producing offspring according to the Markov branching process has been studied. Explicit results are given for the two-compartmental system and for irreversible general multicompartmental systems. The known models in stochastic compartmental analysis are shown to be particular cases of this model and applications are cited.     

Stochastic compartmental models with banching and immigrant particles

A multicompartmental model in which particles enter the system from the environment and reproduce according to a Markov branching process has been considered. Explicit expressions have been obtained for the mean vector and the correlation structure for the numbers of particles in different compartments in different time points of the system. Growth rates of the mean vector and some special cases of the system are also discussed.     

Stochastic processes in particle-number fluctuations in an electron-photon shower

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F(t,G,F, ¦α?β¦) (1) ¦α?β¦dF/dt=g(t,G,F, ¦α?β¦)G(o,¦α?β¦)=k ₁,G(∞,¦α?β¦)=k ₂ (2) as ¦α?β¦→ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower. A solution of the system (1) satisfying the boundary conditions (2) is constructed so that specified limiting conditions are fulfilled.     

On the completely symmetric compartmental system

The completely symmetrical system is defined as having identical transfer coefficients between pairs of compartments and the same loss coefficient for each compartment. The eigenvalues and eigenvector are explicitly found along with the inverses of the system matrix and the matrix of eigenvectors. Many properties, special instances of more general theorems, can be seen at once from the explicit analytic solution of the initial value, washout and washin problems. The system serves as a known case for testing estimation procedures, algorithms for solutions of linear systems, eigenvalue-eigenvector and inversion routines and is of considerable tutorial value.     

Genomics of cellular proliferation in periodic environmental fluctuations

Living systems control cell growth dynamically by processing information from their environment. Although responses to a single environmental change have been intensively studied, little is known about how cells react to fluctuating conditions. Here, we address this question at the genomic scale by measuring the relative proliferation rate (fitness) of 3,568 yeast gene deletion mutants in out‐of‐equilibrium conditions: periodic oscillations between two environmental conditions. In periodic salt stress, fitness and its genetic variance largely depended on the oscillating period. Surprisingly, dozens of mutants displayed pronounced hyperproliferation under short stress periods, revealing unexpected controllers of growth under fast dynamics. We validated the implication of the high‐affinity cAMP phosphodiesterase and of a regulator of protein translocation to mitochondria in this group. Periodic oscillations of extracellular methionine, a factor unrelated to salinity, also altered fitness but to a lesser extent and for different genes. The results illustrate how natural selection acts on mutations in a dynamic environment, highlighting unsuspected genetic vulnerabilities to periodic stress in molecular processes that are conserved across all eukaryotes.     

Stochastic fluctuations in frequency-dependent selection: a one-locus, two-allele and two-phenotype model

Stochastic fluctuations in a simple frequency-dependent selection model with one-locus, two-alleles and two-phenotypes are investigated. The steady-state statistics of allele frequencies for an interior stable phenotypic equilibrium are shown to be similar to the stochastic fluctuations in standard evolutionary game dynamics [Tao, Y., Cressman, R., 2007. Stochastic fluctuations through intrinsic noise in evolutionary game dynamics. Bull. Math. Biol. 69, 1377-1399]. On the other hand, for an interior stable phenotypic or genotypic equilibrium, our main results show that the deterministic model cannot be used to predict the expectation of phenotypic frequency. The variance of phenotypic frequency for an interior stable genotypic equilibrium is more sensitive to the expected population size than for an interior stable phenotypic equilibrium. Furthermore, the stochastic fluctuations of allele frequency and phenotypic frequency can be considered approximately independent of each other for these genotypic equilibria, but not for phenotypic.     

The role of nonreal eigenvalues in the identification of cycles in a compartmental system

The paper concerns the relationship between the cycles in the graph of a compartmental system and the modes of the impulse response function associated with an input-output experiment. Suppose that there is at least one oscillatory mode, e^μtcos(vt - α). Let e^?t be the slowest mode. The main result is that the system contains a cycle of length 3 or longer and that the length of the longest cycle is at least π/tan^-1[¦v¦/(?-μ)]. The paper also deals with the problem of estimating the cycle length from discrete data.     

Effect of environmental fluctuations on invasion fronts

We determine the density profile and velocity of invasion fronts in one-dimensional infinite habitats in the presence of environmental fluctuations. The population dynamics is reformulated in terms of a stochastic reaction-diffusion equation and is reduced to a deterministic equation that incorporates the systematic contributions of the noise. We obtain analytical expressions for the front profile and velocity by constructing a variational principle. The effect of the noise differs, depending on whether it affects the density-independent growth rate, the intraspecific competition term or the Allee threshold. Fluctuations in the density-independent growth rate increase the invasion velocity and the population density of the invaded area. Fluctuations in the competition term also change the population density of the invaded area, but modify the invasion velocity only for certain initial conditions. Fluctuations in the Allee threshold can induce pulled or pushed invasion fronts as well as invasion failure. We compare our analytical results with numerical solutions of the stochastic partial differential equations and show that our procedure proves useful in dealing with reaction-diffusion equations with multiplicative noise.     

Kinetic compartmental analysis of carnitine metabolism in the dog

This study was undertaken to quantitate the dynamic parameters of carnitine metabolism in the dog. Six mongrel dogs were given intravenous injections of L-[methyl-3H]carnitine and the specific radioactivity of carnitine was followed in plasma and urine for 19-28 days. The data were analyzed by kinetic compartmental analysis. A three-compartment, open-system model [(a) extracellular fluid, (b) cardiac and skeletal muscle, (c) other tissues, particularly liver and kidney] was adopted and kinetic parameters (carnitine flux, pool sizes, kinetic constants) were derived. In four of six dogs the size of the muscle carnitine pool obtained by kinetic compartmental analysis agreed (+/- 5%) with estimates based on measurement of carnitine concentrations in different muscles. In three of six dogs carnitine excretion rates derived from kinetic compartmental analysis agreed (+/- 9%) with experimentally measured values, but in three dogs the rates by kinetic compartmental analysis were significantly higher than the corresponding rates measured directly. Appropriate chromatographic analyses revealed no radioactive metabolites in muscle or urine of any of the dogs. Turnover times for carnitine were (mean +/- SEM): 0.44 +/- 0.05 h for extracellular fluid, 232 +/- 22 h for muscle, and 7.9 +/- 1.1 h for other tissues. The estimated flux of carnitine in muscle was 210 pmol/min/g of tissue. Whole-body turnover time for carnitine was 62.9 +/- 5.6 days (mean +/- SEM). Estimated carnitine biosynthesis ranged from 2.9 to 28 mumol/kg body wt/day. Results of this study indicate that kinetic compartmental analysis may be applicable to study of human carnitine metabolism.     

Impact of density and environmental factors on population fluctuations in a migratory passerine

1. Populations of plants and animals typically fluctuate because of the combined effects of density-dependent and density-independent processes. The study of these processes is complicated by the fact that population sizes are typically not known exactly, because population counts are subject to sampling variance. Although the existence of sampling variance is broadly acknowledged, relatively few studies on time-series data have accounted for it, which can result in wrong inferences about population processes. 2. To increase our understanding of population dynamics, we analysed time series from six Central European populations of the migratory red-backed shrike Lanius collurio by simultaneously assessing the strength of density dependence, process and sampling variance. In addition, we evaluated hypotheses predicting effects of factors presumed to operate on the breeding grounds, at stopover sites in eastern Africa during fall and spring migration and in the wintering grounds in southern Africa. We used both simple and state-space formulations of the Gompertz equation to model population size. 3. Across populations and modelling approaches, we found consistent evidence for negative density-dependent population regulation. Further, process variance contributed substantially to variation in population size, while sampling variance did not. Environmental conditions in eastern and southern Africa appear to influence breeding population size, as rainfall in the Sahel during fall migration and in the south African wintering areas were positively related to population size in the following spring in four of six populations. In contrast, environmental conditions in the breeding grounds were not related to population size. 4. Our findings suggest negative density-dependent regulation of red-backed shrike breeding populations and are consistent with the long-standing hypothesis that conditions in the African staging and wintering areas influence population numbers of species breeding in Europe. 5. This study highlights the importance of jointly investigating density-dependent and density-independent processes to improve our understanding of factors influencing population fluctuations in space and time.     

Stochastic simulations of a multi-group compartmental model for Johne's disease on US dairy herds with test-based culling intervention

Infection elimination may be an important goal of control programs. Only in stochastic infection models can true infection elimination be observed as a fadeout. The phenomena of fadeout and variable prevalence are important in understanding the transmission dynamics of infectious diseases and these phenomena are essential to evaluate the effectiveness of control measures. To investigate the stochastic dynamics of Mycobacterium avium subsp. paratuberculosis (MAP) infection on US dairy herds with test-based culling intervention, we developed a multi-group stochastic compartmental model (a continuous time Markov chain model) with both horizontal and vertical transmission. The stochastic model predicted fadeout and within-herd prevalence to have a large variance. Although test-based culling intervention generally decreased prevalence over time, it took longer than desired by producers to eliminate the endemic MAP infection from a herd. Uncertainty analysis showed that, using annual culture test and culling of only high shedders or culling of both low and high shedders with a 12-month delay in culling of low shedders, MAP infection persisted in many herds beyond 20 years. While using semi-annual culture test and culling of low and high shedders with a 6-month delay in culling of low shedders, MAP infection in many herds would be extinct within 20 years. Sensitivity analysis of the cumulative density function of fadeout suggested that combining test-based culling intervention and reduction of transmission rates through improved management between susceptible calves and shedding animals may be more effective than either alone in eliminating endemic MAP infection. We also discussed the effects of other factors such as herd size, heifer replacement, and adult cow infection on the probability of fadeout.     

Stochastic compartmental modeling and parameter estimation with application to cancer treatment follow-up studies

In this paper we use marginal probabilities to derive expressions for the means, variances and covariances ofm-compartment systems. We also present an efficient algorithm for the estimation of the parameters of the system using time series data when measurements are available fromk of them compartments. An application of the analysis and parameter estimation procedure for a model representing the results of a cancer treatment follow-up study is given. Supported in part by NSF Grant Number DCR74-17282.     

Physiological compartmental analysis of alpha-linolenic acid metabolism in adult humans

A physiological compartmental model of alpha-linolenic acid metabolism was derived from the plasma concentration-time curves for d5-18:3n-3, d5-20:5n-3, d5-22:5n-3, and d5-22:6n-3 in eight healthy subjects. Subjects received a 1-g oral dose of an isotope tracer of alpha-linolenate (d5-18:3n-3 ethyl ester) while subsisting on a rigorously controlled beef-based diet. By utilizing the Windows Simulation and Analysis Modeling program, kinetic parameters were determined for each subject. Half-lives and mean transit times of the n-3 fatty acids in the plasma were also determined. The model predicted plasma values for the n-3 fatty acids in good accordance with the measured steady state concentrations and also predicted dietary linolenic acid intake for each subject in accordance with values determined by lipid analysis of the diet. Only about 0.2% of the plasma 18:3n-3 was destined for synthesis of 20:5n-3, approximately 63% of the plasma 20:5n-3 was accessible for production of 22:5n-3, and 37% of 22:5n-3 was available for synthesis of 22:6n-3. The inefficiency of the conversion of 18:3n-3 to 20:5n-3 indicates that the biosynthesis of long-chain n-3 PUFA from alpha-linolenic acid is limited in healthy individuals. In contrast, the much greater rate of transfer of mass from the plasma 20:5n-3 compartment to 22:5n-3 suggests that dietary eicosapentaenoic acid may be well utilized in the biosynthesis of 22:6n-3 in humans.     

A note on the use of a stochastic mammillary compartmental model as an environmental safety model

Environmental safety testing typically requires procedures for extrapolating from the relatively high experimental to the very low use doses of potentially harmful substances. In the present paper, a stochastic mammillary compartmental model for environmental safety testing is proposed and extrapolation procedures based on its dose-response relationship are developed. The proposed model is a direct generalization of one of the basic safety models, the one-hit model, in that a harmful reaction is assumed to occur if at any time any of the peripheral compartments attains a specified threshold of particles. Consideration of a closed model yields an upper bound on the probability of attaining a certain threshold level, thus providing a conservative procedure for extrapolating to a low dose, while a lower bound obtained from a related open model provides a useful monitoring device as to the sharpness of the upper, bound. The extrapolation procedure is illustrated with simulated data and approximations for initial values are developed.     

A compartmental analysis of circulatory lymphocytes in the spleen.

A tentative model describing the passage of circulatory lymphocytes through the spleen is formulated in accord with known anatomical features. In order to preserve isomorphism between the model and the splenic system, the model is formulated in compartmental form and its design allows alternative routes and modes of lymphocyte transit to be considered. The simultaneous differential equations arising from the model are solved using an analogue computer which also provides the means whereby the performance of the model may be compared with suitable dynamic data drawn from literature. This not only allows the selection of a particular configuration of the model in preference to its alternatives, but also allows the numerical determination of certain unknown parameters. In the case of the rat spleen, best agreement between model and experimental data is obtained when between 10 and 25% of the total lymphocyte flux in the model spleen passes through the marginal zone where the average dwell time of the lymphocytes is about 50 min. The white pulp receives a lymphocyte flux from the marginal zone amounting to about 10% of the total splenic flux and the white pulp lymphocytes are sequestered for a period of 4-6 hr before release to the venous circulation. The red pulp receives 90% of the total splenic flux but the majority of lymphocytes find transit through the red pulp in less than 5 min. The remaining flux of lymphocytes, amounting to 10% of the splenic input, is delayed in transit through the red pulp by 2-3 hr before release to the venous circulation.