A Stochastic Model for Coupled Enzyme System

The molecular biology of transformed cancer cells singles out key enzymes as sensitive targets of anti-cancer drugs. Here we use one substrate–one intermediate–one final product model for a coupled enzyme system. The transfer rates for the mechanism are taken as continuous but subject to random fluctuations. Explicit formulae for the first moments of the distribution of the process are obtained. These formulae allow us to take into account not only the variability between the subjects, but also the variability of the process for a single subject. The present results allow us also to build the prediction interval for a particular time period given the observations for some preceding moments.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

A Stochastic Model for Estimating Adolescent Sterility Among Married Women

In this paper a stochastic model is presented for the time to the first conception of a cohort of married women. By identifying three states “adolescent sterility”, “ovulation” and “conceived”, into which the women can be placed, the model incorporates individual differences for the women in the “adolescent sterility” state which allow for the individual characteristics to affect the conversion of these women into the “ovulation” state. Using straightforward probabilistic arguments it is shown that the model provides a close fit to recently published data, compares favorably with previously published models on the same subject and it is useful for planning purposes in predicting future developments.     

随机时滞Lotka-Volterra模型数值解的收敛性

通常情况下,随机时滞Lotka-Volterra模型没有解析解,因而数值逼近方法是研究其性质的有效工具.本文根据Euler数值方法,利用鞅不等式和Ito公式讨论了一类随机时滞Lotka-Volterra模型数值解的收敛性,给出了数值解收敛于解析解的条件.最后通过数值算例对数值计算方法进行了验证.     

A Stochastic Model for Estimating Adolescent Sterility

In this article, a simple stochastic model for the time to first conception of a cohort of married women is developed, by identifying three states, ‘adolescent sterile’, ‘ovulating’ and ‘conceived‘, into which they can be placed. It is demonstrated that the model provides a close fit to observed data. The estimates of the parameters in the model, can be used to calculate the number of women in each state at different points of time and also to obtain estimates of the probabilities of conception for the two categories of women, adolescent sterile and biologically mature.     

A Stochastic Epidemic Model with Seasonal Variations in Infection Rate

In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non-stationary Ornstein-Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.     

A Stochastic Model of Oscillatory Blood Testosterone Levels

A continuous-time, discrete-state stochastic model of testosterone secretion in men is considered. Blood levels of testosterone in men fluctuate periodically with a period of 2–3 h. The deterministic model, on which the stochastic model considered here is based, is well studied and has been shown to have a globally stable fixed point. Thus, no sustained oscillations are possible in the deterministic case. However, the stochastic model does observe periodic, pulsatile behavior. This demonstrates how oscillations can occur due to a switching behavior dependent on the random degradation of testosterone molecules in the system. The Gillespie algorithm is used to simulate the hormone secretion model. Important parameters of the model are discussed and results from the model are compared to experimental observations.     

Infanticide Avoidance by the Granary Weevil, <Emphasis Type="Italic">Sitophilus granarius</Emphasis> (L.) (Coleoptera: Curculionidae): The Role of Harbourage Markers,Oviposition Markers,and Egg-Plugs

In dual choice experiments, adult female granary weevils, Sitophilus granarius L. (Coleoptera: Curculionidae), demonstrated no feeding preference for wheat that had been previously exposed to male and female conspecifics but avoided feeding on grain parasitized with related or unrelated conspecific eggs. Feeding avoidance was lost if egg-parasitized grains possessed an additional unsealed oviposition cavity. Females also preferred to consume artificially damaged grains over undamaged grains. These results suggest that a harbourage-derived feeding deterrent does not exist but an oviposition-derived feeding deterrent does, and that this deterrent protects S. granarius conspecifics from infanticide regardless of their relationship to the adult insect. Egg-plugs may also serve to reduce infanticide by preventing the release of phagostimulatory compounds from oviposition-damaged wheat.     

A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite

This paper considers a generalized birth process {X^m(t), t > 0} and presents a new stochastic model for the number of eggs laid by a parasite on a host. Also, given an underlying distribution for the number of visits between parasites and a host, this distribution is generalized by the distribution of the number of eggs per visit laid on the host. If a certain number of eggs are already present on the host, a parasite such as a Japanese weevil, may avoid oviposition in subsequent visits (see JANARDAN (1980)) to the same host. A class of generalized distributions are presented to model such situations. The case of a single egg laying parasite and a Poisson distribution for the number of visits of the parasite to the same host yields a distribution of particular interest. In order to develop this model, certain lemmas are derived. Finally a characteristic property of this stochastic model is presented.     

A Stochastic Compartmental Model with Long Lasting Infusion

Most of the compartmental models in current use to model pharmacokinetic systems are deterministic. Stochastic formulations of pharmacokinetic compartmental models introduce stochasticity through either a probabilistic transfer mechanism or the randomization of the transfer rate constants. In this paper we consider a linear stochastic differential equation (LSDE) which represents a stochastic version of a one‐compartment linear model when input function undergoes random fluctuations. The solution of the LSDE, its mean value and covariance structure are derived. An explicit likelihood function is obtained either when the process is observed continuously over a period of time or when sampled data are available, as it is generally feasible. We discuss some asymptotic properties of the maximum likelihood estimators for the model parameters. Furthermore we develop expressions for two random variables of interest in pharmacokinetics: the area under the time‐concentration curve, M₀(T), and the plateau concentration, x_ss. Finally the estimation procedure is illustrated by an application to real data.     

A Stochastic Spatial Dynamical Model for Aedes Aegypti

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.     

A Stochastic Model for the Synthesis and Degradation of Natural Organic Matter. Part I. Data Structures and Reaction Kinetics

Here we present a stochastic biogeochemical model for the formation, transformation and mineralization of natural organic matter (NOM). The model is agent-based, with each software agent representing a single molecule of defined composition. Molecular properties and reactivities are estimated from composition and environmental parameters. Environmental parameters including temperature, pH, light intensity, dissolved O₂, moisture and enzyme activities are user controlled. Time is treated in discrete steps, and during each step potential reaction probabilities are evaluated for each molecule based on its structure and the environmental parameters. When reactions occur, the molecular composition is modified accordingly. The model uses small natural products and biopolymers for inputs, and the composition of the molecules produced is constrained only by the inputs and reaction stoichiometries, not by pre-defined structures. Example simulations using the program AlphaStep are presented, in which the breakdown of biopolymers and the condensation of small molecules both lead to molecular assemblages with elemental composition and average properties similar to those of aquatic NOM. This batch-reactor model can be expanded to include spatial information and environmental feedback.     

Oviposition behaviour in Drosophila melanogaster: Genetic and behavioural decoupling between oviposition acceptance and preference for natural fruits

In phytophagous insects, oviposition behaviour is an important component of habitat selection and, given the multiplicity of genetic and environmental factors affecting its expression, is defined as a complex character resulting from the sum of interdependent traits. Here, we study two components of egg-laying behaviour: oviposition acceptance (OA) and oviposition preference (OP) in Drosophila melanogaster using three natural fruits as resources (grape, tomato and orange) by means of no-choice and two-choice experiments, respectively. This experimental design allowed us to show that the results obtained in two-choice assays (OP) cannot be accounted for by those resulting from no-choice assays (OA). Since the genomes of all lines used are completely sequenced, we perform a genome-wide association study to identify and characterize the genetic underpinnings of these oviposition behaviour traits. The analyses revealed different candidate genes affecting natural genetic variation of both OA and OP traits. Moreover, our results suggest behavioural and genetic decoupling between OA and OP and that egg-laying behaviour is plastic and context-dependent. Such independence in the genetic architectures of OA and OP variation may influence different aspects of oviposition behaviour, including plasticity, canalization, host shift and maintenance of genetic variability, which contributes to the adoption of adaptive strategies during habitat selection.     

Postcopulatory Behavior in Libellula pulchella Drury (Odonata: Libellulidae) and Female Tactics for Avoiding Male Interference with Oviposition

Postcopulatory behavior was studied in Libellula pulchella, a North American dragonfly in which ovipositing females face frequent harassment by unpaired males seeking matings. Although males performed noncontact guarding of their mates after copulation, females received minimal protection since their guarders tended to leave on extended chases of other males when harassment was intense. Ovipositions by unguarded females were even more likely to be terminated by harassment and were disrupted sooner. Female tactics to minimize interference included rapid escape flights, repeated return visits to the water within short time periods, perching when severerly harassed, and proceeding with mating when clasped. Female use of multiple oviposition sites is discussed in the context of guarding effectiveness and mate recognition by males.     

Oviposition decreased in response to enriched water: a field study of the pitcher-plant mosquito, Wyeomyia smithii

Abstract.  1. Environmental cues are known to influence oviposition behaviour in mosquitoes, with important consequences for larval survival and insect population dynamics. Enriched microhabitats have been shown to be preferred oviposition sites.
2. In a field experiment designed to determine whether ovipositing mosquitoes are sensitive to different levels of nutrient enrichment, new pitcher-plant ( Sarracenia purpurea ) leaves were opened and enriched with 0, 2, or 20 dead ants, and the number of pitcher-plant mosquito ( Wyeomyia smithii ) larvae resulting from subsequent oviposition were measured.
3. Oviposition rates were higher in leaves with low levels of enrichment (0 and 2 ants per leaf), although larval development was enhanced at the highest enrichment level.
4. Results suggest that, although these mosquito larvae are nutrient limited, ovipositing females preferentially avoid highly enriched leaves. This counterintuitive result may be due to low oxygen concentrations or a masked cue in enriched leaves, and contrasts with other oviposition studies.     

A Stochastic Model of Gene Evolution with Time Dependent Pseudochaotic Mutations

We develop here a new class of stochastic models of gene evolution in which a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some time dependent substitution probabilities. Therefore, at each time t, the numbers and the types of mutable trinucleotides are unknown. Thus, the mutation matrix changes at each time t. This pseudochaotic model developed generalizes the standard model in which all the trinucleotides mutate at each time t. It determines the occurrence probabilities at time t of trinucleotides which pseudochaotically mutate according to 3 time dependent substitution parameters associated with the 3 trinucleotide sites. The main result proves that under suitable assumptions, this pseudochaotic model converges to a uniform probability vector identical to that of the standard model. Furthermore, an application of this pseudochaotic model allows an evolutionary study of the 3 circular codes identified in both eukaryotic and prokaryotic genes. A circular code is a particular set of trinucleotides whose main property is the retrieval of the frames in genes locally, i.e., anywhere in genes and particularly without start codons, and automatically with a window of a few nucleotides. After a certain evolutionary time and with particular time dependent functions for the 3 substitution parameters, precisely an exponential decrease in the 1st and 2nd trinucleotide sites and an exponential increase in the 3rd one, this pseudochaotic model retrieves the main statistical properties of the 3 circular codes observed in genes. Furthermore, it leads to a circular code asymmetry stronger than the standard model (nonpseudochaotic) and, therefore, to a better correlation with the genes.     

Feeding and oviposition preferences of the Sweet Potato Weevil, Cylas formicarius elegantulus, on the outer periderm and exposed inner core of storage roots of selected Sweet Potato cultivars

Cores from sweet potato (Ipomoea batatas L.) storage roots, with either the outer periderm or inner core exposed, were presented to female sweet potato weevils, Cylas formicarius elegantulus (Summers) (Coleoptera: Curculionidae) in cage preference tests. Tests with weevils of different ages showed that feeding was constant 21 to 76 days after emergence, while oviposition showed a slight peak between 21 and 45 days. Differences in the levels of feeding and oviposition were noted for the periderms of four sweet potato cultivars, but these differences were not evident for the inner cores. Oviposition was reduced to low levels on the inner core and, therefore, the oviposition stimulant appears to reside in the root periderm. Feeding did occur on the inner cores, but at a reduced level compared to the root periderm in preference tests where both were available. Inner root cores have a potential use in the elucidation of the oviposition stimulant of the sweet potato weevil.

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Résumé Des coeurs de racines tubéreuses d'I. batatas ont été proposés, soit avec leur périderme externe, soit avec la partie interne du coeur seule, à des femelles du charançon, C. formicarius elegantulus Summers, dans des cages pour expériences sur le choix. Les coeurs étaient prélevés à l'emportepièce pour liège dans des racines stockées et, après tirage au hasard, les expériences ont été distribuées dans des plaques à 24 puits pour cultures de tissus.L'alimentation des charançons de différents âges était constante du 21ème au 47ème jour après l'émergence, tandis que la ponte était maximale entre les 25ème et 45ème jours. Des différences quantitives quant à l'alimentation et à la ponte ont été observées avec les péridermes de 4 cultivars: Centennial, Jewel, Resisto et Regal; ces différences n'étaient pas nettes pour les parties profondes du coeur.La ponte était réduite à un niveau bas avec la partie interne du coeur; il semble ainsi qu'un stimulant de la ponte soit contenu dans de périderme de la racine. L'alimentation s'est effectuée sur la partie centrale du coeur, mais moins que sur le périderme, quand les deux étaient disponibles dans des expériences de choix. La ponte paraît un meilleur critère que l'alimentation, pour comparer les résistance variétales. La partie intérieure du coeur peut être utilisée pour connaître le stimulant le stimulant de la ponte de C. formicarius elegantulus.

     

Influence of Seed Size on Exploitation by the Rice Weevil, Sitophilus oryzae

Oviposition decisions and their fitness consequences for the seed parasite Sitophilus oryzae (L.) (Coleoptera: Curculionidae) were investigated. Female S. oryzae lay eggs inside seeds such as wheat [Triticum aestivum (L.)]. Because larvae develop to adult within a single seed, the resources available are determined by the behavior of the female parent and characteristics of the seed in which the egg was deposited. Females were demonstrated to lay more eggs in kernels 20 mg. Females initiated the chewing of oviposition holes in shriveled kernels but were less likely to oviposit in them. Progeny size increased with increasing seed size, but the probability of an adult emerging was not affected. Females accepted large kernels more quickly than small kernels and this contributed to increased oviposition in large kernels. The increase in the number of eggs per kernel appears to result from an increase in number of visits resulting in oviposition rather than an increase in the number of eggs laid during a visit.     

Novel Fraction Collector for Studying the Oviposition Rhythm in the Turnip Moth

Turnip moths, Agrotis segetum (Schiff.) (Lepidoptera: Noctuidae), were held in a transparent plastic box with a window opening to a rotating paper drum upon which the females could lay eggs. A novel fraction collector, consisting of a standard 24-hr wall timer and simple electronic circuit, served to rotate the paper in hourly increments. The entire apparatus was housed in an environmental chamber on a 16 hr light: 8 hr dark photoperiod at constant 23.7°C and 55% r.h. Under these conditions a circadian rhythm of egg laying was indicated with a mean activity time 0.2 hr before dark and standard deviation of 2.1 hr. The relative egg productions during the second to seventh day of oviposition peaked on the third day. Differences in the circadian rhythms of mating and oviposition are considered in terms of ecological fitness.     

Oviposition by the African migratory locust, Locusta migratoria migratorioides, in a crop environment in South Africa

Oviposition by the African migratory locust, Locusta migratoria migratorioides (Orthoptera: Acrididae), was studied in maize and wheat crops on the Orange Free State Highveld. Maize was shown to be the most important oviposition habitat with peak laying taking place in autumn and early winter when highest pod densities were recorded. Laying was mainly concentrated along the middle of the crop interrows in maize and within clearings in the wheat crop. Despite the uniform layout of these crops, the distribution of egg pods was found to be aggregated. Non-reproductive behaviour, such as locust aggregation, basking and feeding, as well as environmental factors appeared to influence the distribution of egg pods in these crops. Secondary selection for optinum soil moisture and compaction on the laying site enhanced the aggregation of pods.