Structured modelling of animal cells

Recent advances in computer technology have promoted the design and use of detailed, computer-based models for biological systems. For many non-biological systems, the complexity of such simulations may be considered inappropriate and unwieldy, but in biological systems, and more specifically in animal cell culture, this level of complexity simply mimics what is only beginning to be understood about metabolic processs. With this in mind, we contend that complex, structured models are vital tools in the investigation of fundamental biological processes. An example of such a simulation, which describes the commercial production of therapeutic proteins by animal cell cultures, is considered.     

Predictive models for phosphorus retention in wetlands

The potential of wetlands to efficiently remove (i.e., act as a nutrient sink) or to transform nutrients like phosphorus under high nutrient loading has resulted in their consideration as a cost-effective means of treating wastewater on the landscape. Few predictive models exist which can accurately assess P retention capacity. An analysis of the north American data base (NADB) allowed us to develop a mass loading model that can be used to predict P storage and effluent concentrations from wetlands. Phosphorus storage in wetlands is proportional to P loadings but the output total phosphorus (TP) concentrations increase exponentially after a P loading threshold is reached. The threshold P assimilative capacity based on the NADB and a test site in the Everglades is approximately 1 g m^–2 yr^–1. We hypothesize that once loadings exceed 1 g m^–2 yr^–1 and short-term mechanisms are saturated, that the mechanisms controlling the uptake and storage of P in wetlands are exceeded and effluent concentrations of TP rise exponentially. We propose a One Gram Rule for freshwater wetlands and contend that this loading is near the assimilative capacity of wetlands. Our analysis further suggests that P loadings must be reduced to 1 g m^–2 yr^–1 or lower within the wetland if maintaining long-term low P output concentrations from the wetlands is the central goal. A carbon based phosphorus retention model developed for peatlands and tested in the Everglades of Florida provided further evidence of the proposed One Gram Rule for wetlands. This model is based on data from the Everglades areas impacted by agricultural runoff during the past 30 years. Preliminary estimates indicate that these wetlands store P primarily as humic organic-P, insoluble P, and Ca bound P at 0.44 g m^–2 yr^–1 on average. Areas loaded with 4.0 g m^–2 yr^–1 (at water concentrations>150 g·L^–1 TP) stored 0.8 to 0.6 g m^–2 yr^–1 P, areas loaded with 3.3 g m^–2 yr^–1 P retained 0.6 to 0.4 g m^–2 yr^–1 P, and areas receiving 0.6 g m^–2 yr^–1 P retained 0.3 to 0.2 g m^–2 yr^–1. The TP water concentrations in the wetland did not drop below 50 g·L^–1 until loadings were below 1 g m² yr^–1 P.     

The expected effects of climate change on wheat development

Air temperature and the atmospheric concentrations of carbon dioxide are expected to rise. These two factor have a great potential to affect development, growth and yield of crops, including wheat. Rising air temperature may affect wheat development more than rising atmospheric CO₂ as there is not yet evidence that elevated CO₂ concentrations can directly induce changes in wheat development. In winter wheat, temperature has a complex effect on development due to its strong interaction with vernalization and photoperiod. In this paper, potential effects of rising temperature on the development of winter wheat from sowing to heading are considered in the light of this complex controlling mechanism. Data from a large series of field trials made in Romania is analysed at first and, subsequently, the IATA-Wheat Phenology model is used to calculate the impact of air warming on wheat development under different climate change scenarios. Data from the field trials showed very clearly the occurrence of a complex temperature/photoperiod/vernalization interaction for field sown crops and demostrated that the photoperiodic and vernalization responses have a key role in controlling the duration of the emergence-heading period. Temperature plays, instead, a central role in controlling seed germination and crop emergence as well as leaf inititiation and leaf appearance rate. The results of model analysis showed very well that the impact of an even or uneven distribution of warning effects may be very different. In the first case, the model predicted that the duration of the vegetative period was at least partly reduced in some years. In the second case, the model suggested that if warming will be more pronounced in winter than in spring, as predicted for some areas of the world by General Circulation Models, we may expect an increase in the duration of the vegetative phase of growth. On the contrary, in case of a spring warming but unchanged winter temperatures, we may expect a substantial decrease in the duration of the vegetative period.     

Models to predict lake annual mean total phosphorus

A lake is a product of processes in its watershed, and these relationships should be empirically quantifiable. Yet few studies have made that attempt. This study quantifies and ranks variables of significance to predict annual mean values of total phosphorus (TP) in small glacial lakes. Several new empirical models based on water chemistry variables, on map parameters of the lake and its catchment, and combinations of such variables are presented. Each variable provides only a limited (statistical) explanation of the variation in annual mean values of TP among lakes. The models are markedly improved by accounting for the distribution of the characteristics (e.g., the mires) in the watershed. The most important map parameters were the proportion of the watershed lying close to the lake covered by rocks and open land (as determined with the drainage area zonation method), relief of the drainage area, lake area and mean depth. These empirical models can be used to predict annual mean TP but only for lakes of the same type. The model based on map parameters (r ²=0.56) appears stable. The effects of other factors/variables not accounted for in the model (like redox-induced internal loading and anthropogenic sources) on the variation in annual mean TP may then be estimated quantitatively by residual analysis. A new mixed model (which combines a dynamic mass-balance approach with empirical knowledge) was also developed. The basic objective was to put the empirical results into a dynamic framework, thereby increasing predictive accuracy. Sensitivity tests of the mixed model indicate that it works as intended. However, comparisons against independent data for annual mean TP show that the predictive power of the mixed model is low, likely because crucial model variables, like sedimentation rate, runoff rate, diffusion rate and precipitation factor, cannot be accurately predicted. These model variables vary among lakes, but this mixed model, like most dynamic models, assumed that they are constants.     

Ecological optima and tolerances of Thelypteris limbosperma,Athyrium distentifolium,and Matteuccia struthiopteris along environmental gradients in Western Norway

The distribution and abundance of Thelypteris limbosperma, Athyrium distentifolium, and Matteuccia struthiopteris are modelled statistically in relation to 14 environmental variables along the major climatic, topographic, and edaphic gradients in western Norway. The data are from 624 stands from which measurements or estimates of mean January and mean July temperatures, humidity, altitude, aspect, and slope are available. From 182 of these stands eight soil variables have also been measured. The species responses are quantified by two numerical methods: Gaussian logit regression and weighted averaging (WA) regression. The estimated WA optima suggest that A. distentifolium has an ecological preference for low July and January temperatures, high altitudes, and soils of low-medium pH and base content. The species shows statistically significant Gaussian responses with summer temperature, humidity (= Martonnes humidity index), altitude, slope, aspect, pH, cation exchange capacity, and base saturation with optima of 8.7 °C, 188.9, 1220 m, 28°, 29°, 4.8, 13.77 mEq 100 g dry soil^-1, and 13.4%, respectively. These suggest that the occurrence and relative abundance of A. distentifolium are well predicted by summer temperature, topography, and soil pH and base status. T. limbosperma has WA optima that suggest that it favours moderately high winter and summer temperatures, high humidity, medium altitude, and soils of low pH and base content. It has significant Gaussian responses to summer temperature (optimum =12.6 °C), winter temperature (-1.8 °C), humidity (179.2), altitude (459.5 m), slope (22.5°), and Na (0.7 mg 100 g dry soil^-1). These suggest that climatic factors, altitude, and slope are significant predictors for its occurrence and abundance. M. struthiopteris has high WA optima for summer temperature, pH, Ca, Mg, K, Na, cation exchange capacity (CEC), and base saturation, and a low optima for humidity and winter temperature. Of these, summer temperature (16.0 °C), Ca (63.1 mg 100 g dry soil^-1), Mg (41.0 mg 100 g dry soil^-1), K (23.6 mg 100 g dry soil^-1), Na (5.0 mg 100 g dry soil^-1), CEC (60.7 mEq 100 g dry soil^-1), and base saturation (56.3%) have significant Gaussian logit responses, as do aspect (150.2°) and loss-on-ignition (9.4%). These results suggest that the occurrence and relative abundance of M. struthiopteris are well predicted by high soil base cations, a generally southern aspect, low organic content in the soil, and high July temperatures.     

A protocol for classifying regional dynamics,exemplified by using woodland birds in southeastern Australia

Abstract Communities of forest and woodland birds are usually studied intensively at only one or a few locations. This provides a perspective that perhaps emphasizes local phenomena at the expense of placing local dynamics in the context of processes operating at the landscape or regional scale. The present paper seeks to redress partially this imbalance by studying the dynamics of individual bird species among several habitat types (all Eucalyptus-dominated forests or woodlands) over the annual cycle. This regional-scale (250km), continental study reveals that species exhibit idiosyncratic dynamics of various kinds: restricted or more ubiquitous occupation of habitats and three forms of seasonal dynamics at the regional scale (resident, migrant and itinerant). By using this classificatory scheme, it becomes evident that the bird communities found in different habitats consist of diverse collections of strategists and that the level of diversity differs among habitat types. The difficulties that many field workers have had in reconciling their observations with community theory most likely reflect the underlying dynamism of bird communities, especially in the temperate regions on continents where seasonal fluxes are pronounced.     

Self-Reported Substantial 1-Year Weight Change Among Men and Women in the United States

Population-based data have not been readily available on relatively short-term changes in weight. Therefore, we sought to determine the nature of self-reported substantial (> 10%) weight change over one year in a representative sample of the US population which participated in the 1989 National Health Interview Survey (NHIS). Across all ages, a larger proportion of women than men reported both weight loss as well as weight gain of any amount (18.9% vs. 16.1% for weight loss and 20.0% vs. 16.1% for weight gain). In sex-specific logistic regression analyses, significant risk factors common to both sexes for substantial weight loss included divorced/separated marital status, smoking, increased number of blood pressure checks, increased BMI (body mass index) and increased number of bed days. Black race reduced the risk of weight loss for both men and women. Sex-specific risk factors for weight loss in men only were widowhood or never married marital status, while increasing age was a protective factor in women only. Concerning weight gain > 10% over the past year, increased number of blood pressure checks and having one or more diabetic parents were significant risk factors among both men and women; while never being married, increased age, BMI, and education exerted a protective effect in both sexes. For women only, risk factors for weight gain included black race, increased number of contacts with a health professional, and being unemployed. Intention to lose weight was associated with both weight gain and weight loss in both sexes, although it did not serve as a confounder in any of these relationships. A greater likelihood of substantial weight loss among women relative to men was diminished for persons with higher BMI, higher number of blood pressure checks, being widowed, divorced or separated, and intention to lose weight. A greater likelihood of substantial weight gain among women relative to men was diminished for persons with low BMI. The results of this cross-sectional study of weight change, involving a one-year follow-up period, generally correspond with the results obtained by longitudinal studies involving a longer follow-up.     

向日葵籽实产量预测数学模型的研究

根据2年10个点次的田间试验结果建立了由数粒法、盘重法和盘径法预测向日葵籽实产量的回归数学模型,并根据1994年4个点次的产量实测结果对各模型的可靠性进行了验证．结果表明,三种方法建立的模型均有效、可靠．但在我国向日葵科研和生产实践中,以盘径法最为实用,建议推广应用．     

On some formulas in a partnership model from the perspective of a semi-Markov process

Many deterministic models of sexually transmitted diseases, as well as population models in general, contain elements of stochastic or statistical reasoning. An example of such a model is that of Dietz and Hadeler (1988) concerning sexually transmitted diseases in which there is partnership formation and dissolution. Among the interesting formulas in this paper, which enter into the analysis of the model, are those for the expected number of partners a male or female has during a lifetime. To a probabilist such formulas suggest the possibility that some stochastic process may be constructed so as to yield these formulas as well as others that may be of interest. The principal purpose of this paper is to demonstrate that such a stochastic process does indeed exist in the form of a three state semi-Markov process in continuous time with stationary laws of evolution and with a one-step density matrix determined by four parameters which were interpreted as constant latent risk functions in the classical theory of competing risks. This construction of a semi-Markov process not only provides a framework for the systematic derivation of the formulas of Dietz and Hadeler but also suggests pathways,for extensions to the age-dependent case.This research was partially supported by NATO Grant D.890350     

A cross-diffusion model of forest boundary dynamics

A simple mathematical model of mono-species forest with two age classes which takes into account seed production and dispersal is presented in the paper. This reaction — diffusion type model is then reduced by means of an asymptotic procedure to a lower dimensional reaction — cross-diffusion model. The existence of standing and travelling wave front solutions corresponding to the forest boundary is shown for the later model. On the basis of the analysis, possible changes in forest boundary dynamics caused by antropogenic impacts are discussed.