The reliability of approximate reduction techniques in population models with two time scales

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time scales are very different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one.The results are illustrated by some numerical simulations corresponding to the reduction of a Leslie type model for a population structured in two age classes and living in a two patch system.     

Spreading speeds of spatially periodic integro-difference models for populations with nonmonotone recruitment functions

An idea used by Thieme (J. Math. Biol. 8, 173-187, 1979) is extended to show that a class of integro-difference models for a periodically varying habitat has a spreading speed and a formula for it, even when the recruitment function R(u, x) is not nondecreasing in u, so that overcompensation occurs. Numerical simulations illustrate the behavior of solutions of the recursion whose initial values vanish outside a bounded set.     

Stochastic differential equation models for spatially distributed neurons and propagation of chaos for interacting systems.

Distribution or nuclear space-valued stochastic differential equations (SDEs) (diffusions as well as discontinuous equations) are discussed as stochastic models for the behavior of voltage potentials of spatially distributed neurons. A propagation of chaos result is obtained for an interacting system of Hilbert space-valued SDEs.     

Linear discrete population models with two time scales in fast changing environments II: non-autonomous case

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system.     

Agricultural disturbance response models for invertebrate and algal metrics from streams at two spatial scales within the U.S.

As part of the USGS study of nutrient enrichment of streams in agricultural regions throughout the United States, about 30 sites within each of eight study areas were selected to capture a gradient of nutrient conditions. The objective was to develop watershed disturbance predictive models for macroinvertebrate and algal metrics at national and three regional landscape scales to obtain a better understanding of important explanatory variables. Explanatory variables in models were generated from landscape data, habitat, and chemistry. Instream nutrient concentration and variables assessing the amount of disturbance to the riparian zone (e.g., percent row crops or percent agriculture) were selected as most important explanatory variable in almost all boosted regression tree models regardless of landscape scale or assemblage. Frequently, TN and TP concentration and riparian agricultural land use variables showed a threshold type response at relatively low values to biotic metrics modeled. Some measure of habitat condition was also commonly selected in the final invertebrate models, though the variable(s) varied across regions. Results suggest national models tended to account for more general landscape/climate differences, while regional models incorporated both broad landscape scale and more specific local-scale variables.     

Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour

Circadian rhythms are endogenous oscillations that occur with a period close to 24 h in nearly all living organisms. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a deterministic model previously proposed for circadian oscillations of the PER and TIM proteins and their mRNAs in Drosophila. The model is based on repression of the per and tim genes by a complex between the PER and TIM proteins. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity from a bifurcation point beyond which the system evolves to stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic model also reproduces the evolution to a strange attractor in conditions where the deterministic PER-TIM model admits chaotic behaviour. The difference between periodic oscillations of the limit cycle type and aperiodic oscillations (i.e. chaos) persists in the presence of molecular noise, as shown by means of Poincaré sections. The progressive obliteration of periodicity observed as the number of molecules decreases can thus be distinguished from the aperiodicity originating from chaotic dynamics. As long as the numbers of molecules involved in the oscillations remain sufficiently large (of the order of a few tens or hundreds, or more), stochastic models therefore provide good agreement with the predictions of the deterministic model for circadian rhythms.     

Anxiolytic effect of berberine on exploratory activity of the mouse in two experimental anxiety models: interaction with drugs acting at 5-HT receptors

The aim of this study was to assess the anxiolytic effect of berberine (abbrev. BER) using two experimental anxiety models in the mouse. In the black and white test of anxiety, berberine (100, 500 mg/kg) produced an increase in the first time entry, time spent in the white section, and total changes between two compartments. On the other hand, in the elevated plus-maze test, berberine (100, 500 mg/kg) produced an increase in the time spent and arm entries in the open arms, and a decrease in the time spent and arm entries in the closed arms. Berberine (500 mg/kg) decreased locomotor activity in mice. Furthermore, BER at 100, 500 mg/kg decreased concentrations of NE, DA and 5-HT, and increased the concentrations of VMA, HVA and 5-HIAA in the brain stem. BER also attenuated the anxiogenic effect of WAY-100635, 8-OH DPAT and DOI and enhanced the anxiolytic effect of BUS, p-MPPI and RIT in the elevated plus-maze. These results suggested that berberine at 100 mg/kg had a significant anxiolytic-like effect, which was similar to that observed with 1 mg/kg diazepam and 2 mg/kg buspirone. The anxiolytic mechanism of BER might be related to the increase in turnover rates of monoamines in the brain stem and decreased serotonergic system activity. Moreover, BER decreased serotonergic system activity via activation of somatodendritic 5-HT1A autoreceptors and inhibition of postsynaptic 5-HT1A and 5-HT2 receptors.     

Dynamics of cellular retinoic acid binding protein I on multiple time scales with implications for ligand binding

Cellular retinoic acid binding protein I (CRABPI) belongs to the family of intracellular lipid binding proteins (iLBPs), all of which bind a hydrophobic ligand within an internal cavity. The structures of several iLBPs reveal minimal structural differences between the apo (ligand-free) and holo (ligand-bound) forms, suggesting that dynamics must play an important role in the ligand recognition and binding processes. Here, a variety of nuclear magnetic resonance (NMR) spectroscopy methods were used to systematically study the dynamics of both apo and holo CRABPI at various time scales. Translational and rotational diffusion constant measurements were used to study the overall motions of the proteins. Both apo and holo forms of CRABPI tend to self-associate at high (1.2 mM) concentrations, while at low concentrations (0.2 mM), they are predominantly monomeric. Rapid amide exchange rate and laboratory frame relaxation rate measurements at two spectrometer field strengths (500 and 600 MHz) were used to probe the internal motions of the individual residues. Several residues in the apo form, notably within the ligand recognition region, exhibit millisecond time scale motions that are significantly arrested in the holo form. In contrast, no significant differences in the high-frequency motions were observed between the two forms. These results provide direct experimental evidence for dynamics-induced ligand recognition and binding at a specifically defined time scale. They also exemplify the importance of dynamics in providing a more comprehensive understanding of how a protein functions.     

A method for determining the heart moving electric center on surface distributed models of the cardioelectric generator

Using mathematical models of the bioelectric generators of the heart with surface distributed configurations, it was shown that the coordinates of the moving electric center of the heart can facilitate the recognition of the global spatial position of electrogenic zones in the myocardium. These coordinates were determined by the previously proposed method from the cardioelectric potential measured noninvasively with a multichannel lead system in the framework of electrocardiographic mapping.     

Evidence for stabilising selection acting on flowering time in Arum maculatum (Araceae): the influence of phylogeny on adaptation

The relationship between flowering time and reproductive success was investigated in the fly-pollinated, monoecious perennial herb Arum maculatum L. (Araceae). This species temporarily traps its principle pollinator, a psychodid midge. Probability of fruit set was analysed in relation to early, peak and late periods of the flowering phenology of four British populations between 1992 and 1997. In three out of five cases, plants which flowered during early and late periods were significantly less likely to set fruit. In addition, one population showed a similar relationship for percentage fruit set of individual inflorescences, and seeds from peak-flowering plants were significantly heavier. There was no variation in number of female flowers per inflorescence over the flowering season. Probability of fruit set appears to be mediated by the likelihood of trapping psychodid midges that have previously been trapped and picked up pollen, an unlikely event during early and late flowering periods when few inflorescences are open. The majority of plants in all populations produce only one inflorescence which means that timing of flowering may be crucial to reproductive success. We interpret our findings as evidence that stabilising selection may be acting on some populations and/or during some years. The ultimate cause, however, can be related to the very short (12–18 h) female phase of each inflorescence, a phylogenetically conservative trait within the Araceae. Received: 19 August 1998 / 15 February 1999     

Living on three time scales: the dynamics of plasma cell and antibody populations illustrated for hepatitis a virus

Understanding the mechanisms involved in long-term persistence of humoral immunity after natural infection or vaccination is challenging and crucial for further research in immunology, vaccine development as well as health policy. Long-lived plasma cells, which have recently been shown to reside in survival niches in the bone marrow, are instrumental in the process of immunity induction and persistence. We developed a mathematical model, assuming two antibody-secreting cell subpopulations (short- and long-lived plasma cells), to analyze the antibody kinetics after HAV-vaccination using data from two long-term follow-up studies. Model parameters were estimated through a hierarchical nonlinear mixed-effects model analysis. Long-term individual predictions were derived from the individual empirical parameters and were used to estimate the mean time to immunity waning. We show that three life spans are essential to explain the observed antibody kinetics: that of the antibodies (around one month), the short-lived plasma cells (several months) and the long-lived plasma cells (decades). Although our model is a simplified representation of the actual mechanisms that govern individual immune responses, the level of agreement between long-term individual predictions and observed kinetics is reassuringly close. The quantitative assessment of the time scales over which plasma cells and antibodies live and interact provides a basis for further quantitative research on immunology, with direct consequences for understanding the epidemiology of infectious diseases, and for timing serum sampling in clinical trials of vaccines.     

A computer programme for the determination of the kinetic constants of two enzymes acting simultaneously on the same substrate.

A computer programme permitting rapid and accurate estimation of the kinetic parameters (apparent K_m and V_m) of two enzymes acting simultaneously on the same substrate is described. No starting estimates of the parameters are required. The only additional parameter needed is an inflexional substrate concentration. This is obtained from the last half of the segment of major curvature on the Lineweaver-Burk plot, which is not linear under these conditions. The value of this substrate concentration need not be precisely determined. This procedure is shown to give significantly better results than general non-linear regression procedures. The programme is written in the Fortran IV language.     

A preliminary study on habitat selection of the Japanese serow (Capricornis crispus) at two temporal scales,season and time of day,in a montane forest

Journal of Ethology - Habitat selection has a significant influence on animals’ fitness, and has been well studied in various ungulates. A trade-off between the access to forage and to...     

Host influences on sex ratio, longevity, and egg load of two Metaphycus species parasitic on soft scales: implications for insectary rearing

Metaphycus flavus (Howard) and M. stanleyi Compere (Hymenoptera: Encyrtidae) are currently being screened for use as augmentative biological control agents of citrus-infesting soft scales (Homoptera: Coccidae). Two factors were investigated, host quality-dependent sex allocation and local mate competition, which likely influence these parasitoid's sex allocation strategies and are therefore of interest for their mass-rearing. The results of these studies suggested that, under the mass-rearing protocol that is envisioned for these parasitoids, offspring sex ratios in both M. flavus and M. stanleyi are dominated by host quality (= size) influences, but not by interactions with other females. These results indicated that host size strongly influences offspring sex ratios and brood sizes; larger hosts led to more female offspring and larger broods. In contrast, increasing the number of parental females did not lead to fewer female offspring as expected under local mate competition. Additionally, within-brood sex ratios did not vary with brood size; this result is inconsistent with expected sex ratios due to local mate competition. Other results also indicated that host quality was a dominant influence on M. flavus' and M. stanleyi's sex ratios. Larger hosts led to a larger size in the emerging wasps, and larger wasps had greater egg loads and lived longer than smaller wasps. However, wasp longevity, and the influence of wasp size on longevity were mediated by a wasp's diet. Metaphycus flavus females lived the longest when they had access to hosts, honey, and water, followed by honey and water, and shortest when they had access to water alone; M. stanleyi females lived longest with honey and water, followed by hosts, honey, and water, and shortest with water alone. Greater wasp size led to greater longevity in females only when they had access to food (honey, or hosts and honey). Finally, other results suggested that both M. flavus and M. stanleyi are facultatively gregarious. Wasp size did not decrease with brood size as expected under superparasitism. Overall, the results of these studies suggested that holding newly emerged females of both M. flavus and M. stanleyi for several days in the presence of an appropriate food source before field release could enhance a female's performance as an augmentative biological control agent. It increases their initial life expectancy following release, and maximizes the females' egg load (both Metaphycus species) and resources for replacing oviposited eggs (M. flavus only).     

Non-linear mixed models for repeated data assessment of time and temperature effects on conidia production in the fungus Valdensinia heterodoxa

Valdensinia heterodoxaPeyr. has potential for application as abiological control agent of salal (Gaultheria shallon Pursh) in regeneratingforests in the Pacific Northwest region ofNorth America. Conidia production of twoisolates of Valdensinia heterodoxa wasexamined at four temperature levels during a12-day period. Conidia production was stronglyinfluenced by both temperature (with an optimumbetween 16 and 19 °C) and time (peakedat day 9). Replicate (five) variance was highlyheterogeneous and made a conventional approachto the statistical analyses unsuccessful.However, newly developed generalized nonlinearmodels succeeded in identifying significantdifferences between isolates in theirtemperature specificity. One model was based ona time-dependent Poisson process (logisticmodel) modified by an independent nonlineartemperature function (a scaled gamma function).The other was a nonlinear growth model withfixed (time, isolate) and random (replicate)effects. We believe that nonlinear mixed modelsoffer an attractive framework for analysis oflongitudinal count data common in growth andreproduction studies.     

以小时为步长的大兴安岭兴安落叶松林地表可燃物含水率预测模型

应用时滞平衡含水率法(包括Nelson和Simard两种)及气象要素回归法,以小时为步长对大兴安岭地区阳坡上部落叶松林下地表细小死可燃物进行动态含水率测定,分析了不同郁闭度林分的预测误差.结果表明:以小时为步长的可燃物含水率预测方法适用于大兴安岭地区的典型落叶松林分,Simard法预测平均绝对误差为1.1%,平均相对误差为8.5%,低于Nelson法和传统的气象要素回归法,接近同类研究的误差范围;同一坡度、坡位上,不同郁闭度下的可燃物含水率变化差异较大,使用以小时为步长的可燃物含水率预测方法,应根据不同地区林分和地点选择合适的平衡含水率模型,或建立基于林分的可燃物含水率模型.     

Peptide arrays on cellulose support: SPOT synthesis, a time and cost efficient method for synthesis of large numbers of peptides in a parallel and addressable fashion

Peptide synthesis on cellulose using SPOT technology allows the parallel synthesis of large numbers of addressable peptides in small amounts. In addition, the cost per peptide is less than 1% of peptides synthesized conventionally on resin. The SPOT method follows standard fluorenyl-methoxy-carbonyl chemistry on conventional cellulose sheets, and can utilize more than 600 different building blocks. The procedure involves three phases: preparation of the cellulose membrane, stepwise coupling of the amino acids and cleavage of the side-chain protection groups. If necessary, peptides can be cleaved from the membrane for assays performed using soluble peptides. These features make this method an excellent tool for screening large numbers of peptides for many different purposes. Potential applications range from simple binding assays, to more sophisticated enzyme assays and studies with living microbes or cells. The time required to complete the protocol depends on the number and length of the peptides. For example, 400 9-mer peptides can be synthesized within 6 days.     

Reproductive fitness and artificial selection in animal breeding: culling on fitness prevents a decline in reproductive fitness in lines of Drosophila melanogaster selected for increased inebriation time

Summary The maintenance of reproductive fitness in lines subjected to artificial selection is one of the major problems in animal breeding. The decline in reproductive performance has neither been predictable from heritabilities and genetic correlations, nor have conventional selection indices been adequate to avoid the problem. Gowe (1983) has suggested that the heritabilities of reproductive traits are non-linear, with heritabilities being higher on the lower fitness side. Consequently, he has predicted that culling on reproductive fitness in artificial selection lines will be effective in preventing the usual declines in fitness. An experimental evaluation of Gowe's prediction has been carried out by comparing fitnesses of replicated lines of three treatments: selection for increased inebriation time without culling on fitness (HO), selection for inebriation time with culling of 20% (4/20) of selected females on reproductive fitness (HS), and unselected controls (C). Response to selection for inebriation time in the two selection treatments was similar. After 25 generations, the competitive index, a measure of reproductive fitness, was significantly lower in the HO treatment than the HS treatment, while the HS treatment did not differ from the control lines or the base population. These results demonstrate for the first time that culling on reproductive fitness in selection lines can be used to prevent the usual decline in reproductive performance.