Stability in cyclic epidemic models

A general formulation for a family of cyclic epidemic models with density-dependent feedback mechanisms and removed classes is presented. A parameter, , related to the basic reproductive rate determines the asymptotic behaviour of solutions of the model. It is shown that if <1 the trivial solution is globally stable, and if >1 it is conditionally stable. The results are applied to a set of differential equations that has been used to model the life cycle of a parasite that has two hosts.     

General method for the derivation and numerical solution of epithelial transport models

Summary A general method is presented for the formulation and numerical evaluation of mathematical models describing epithelial transport. The method is based on the principles of conservation of mass, and maintenance of electroneutrality within the cells and bathing solutions. It is therefore independent of the specific membrane transport mechanisms, and can be used to evaluate different models describing arbitrary transport processes (including passive, active and cotransport processes). Detailed numerical methods are presented that allow computation of steady-state and transient responses under open-circuit, current-clamp and voltage-clamp conditions, using a general-purpose laboratory minicomputer. To evaluate the utility of this approach, a specific model is presented that is consistent with the Koefoed-Johnson and Ussing hypothesis of sodium transport in tight epithelia (Acta Physiol. Scand. 42:298–308, 1958). This model considers passive transport of an arbitrary number of permeant solutes, active transport of sodium and potassium, and osmotically induced water transport across the apical and basolateral membranes. Results of the model are compared to published experimental measurements in rabbit urinary bladder epithelium.     

Models for age structured populations with distributed maturation rates

In the use of age structured population models for agricultural applications such as the modeling of crop-pest interactions it is often essential that the model take into account the distribution in maturation rates present in some or all of the populations. The traditional method for incorporating distributed maturation rates into crop and pest models has been the so-called distributed delay method. In this paper we review the application of the distributed delay formalism to the McKendrick equation of an age structured population. We discuss the mathematical properties of the system of ordinary differential equations arising out of the distributed delay formalism. We then discuss an alternative method involving modification of the Leslie matrix.     

Territoriality and fighting in a colonial thrips, Hoplothrips pedicularius, and sexual dimorphism in Thysanoptera

ABSTRACT.

• 1 Hoplothrips pedicularius (Haliday) (Thysanoptera: Phlaeothripidae), a tubuliferan thrips in which males possess greatly enlarged forelegs, lives in colonies on Stereum fungus.
• 2 Females oviposit onto communal egg masses, and males fight by grasping and stabbing with their forelegs in territorial defence of oviposition areas. Prolonged escalated fights occur between males who are of similar size.
• 3 Larger males usually win fights and become dominant at the oviposition area. Dominant males secure 80% of matings, and mate most frequently during oviposition periods, with an ovipositing female.
• 4 Smaller, subordinate males avoid fights and attempt to 'sneak’copulations. However, they occasionally challenge the dominant male. Challenges tend to follow copulations by the subordinate male and occur more frequently between males who are of similar size.
• 5 Subordinate males who eventually leave the oviposition area are larger than those who remain, have frequently challenged the dominant male, and have more frequently been stabbed.
• 6 Sexual dimorphism in thrips is associated with gregariousness, claustral habitats, female-biased sex ratios, and male winglessness. In thrips genera in which males exhibit foreleg armature, males are larger relative to females. The ecological circumstances promoting sexual dimorphism and male fighting in spatially-structured populations are discussed.

     

岛屿生物地理学理论：模型与应用

前言岛屿有许多显著特征,如地理隔离,生物类群简单。这些特点为重复性研究和统计学分析奠定了基础,从而有利于许多深入而细致的生物学研究。因此,岛屿为发展和检验自然选择、物种形成及演化,以及生物地理学和生态学诸领域的理论和假设,提供了重要的自然实验室。岛屿生物地理学理论(MacArthurwilson学说)即为岛屿生物学研究中所产生的著名理论之一。该理论发展之     

Simulated and measured nitrogen conditions in a manured and fertilised soil

The governing factors for soil nitrogen dynamics were identified with a simulation model. In addition, the model was used to interpret measurements from a plot fertilisation experiment in southwest Sweden.Simulated moisture and temperature conditions were the driving variables for the simulation of soil nitrogen dynamics and leaching during a 6-year period. The results of the simulation were compared with monthly observations on two plots with grain crops, one with liquid manure and commercial fertilisers applied and one with commercial fertilisers only.Simulated temporal variations of the nitrate and ammonium storages generally agreed with observations. The dominant role of the crops as a determinant of soil nitrogen conditions was demonstrated. A higher leaching loss from the plot with application of commerical fertilisers only occurred both in simulations and measurements compared to the plot with application of both commercial fertilisers and manure. The main reason was the higher N-application in the former treatment.The effect of water flows in macropores was interpreted as a delay of simulated leaching compared to observed leaching on some occasions in summer and early autumn. No direct effect of the macropores on the yearly rates of leaching could be seen.     

Anion exchange reactions in bacteria

Bacterial anion exchange now includes both carboxylate-linked reactions, in which there is an antiport of mono- and dicarboxylic acids, and Pi-linked reactions that build on phosphate (Pi) and organic phosphates. To illustrate the general features of this expanding class, this article discussed the biochemistry, physiology, and molecular biology of Pi-linked antiporters that accept glucose 6-phosphate (G6P) as their primary substrate. Kinetic and biochemical analysis suggsts that Pi-linked exchangers have a bifunctional active site that accepts a pair of negative charges. For this reason, exchange stoichiometry moves between the limits of 2:1 and 2:2 to reflect the ratio of mono- and divalent substrates at either membrane surface. This results in a particularly interesting reaction sequencein vivo, where, because cytosolic pH is relatively alkaline, one can expect the asymmetric exchange of two monovalent G6P anions against a single divalent G6P. In this way, an otherwise futile self-exchange of G6P gives a net flux driven (indirectly) by the pH gradient. Despite this biochemical and physiological complexity, Pi-linked carriers resemble all other secondary carriers at a molecular level. Indeed, sequence analysis leads one to infer a common (albeit low resolution) structural theme in which each functional unit has two sets of six trans-membrane helices separated by a central hydrophilic loop. Present examples show that this topology can derive from either a single protein, as is typical in bacteria, or from pairs of identical subunits, as found in mitochondria and chloroplasts. The finding of this common structure should make it possible to build detailed structural models that have implications for all membrane carrier proteins.     

Modeling in the museum: On the role of remnant models in the work of Joseph Grinnell

Accounts of the relation between theories and models in biology concentrate on mathematical models. In this paper I consider the dual role of models as representations of natural systems and as a material basis for theorizing. In order to explicate the dual role, I develop the concept of a remnant model, a material entity made from parts of the natural system(s) under study. I present a case study of an important but neglected naturalist, Joseph Grinnell, to illustrate the extent to which mundane practices in a museum setting constitute theorizing. I speculate that historical and sociological analyses of institutions can play a specific role in the philosophical analysis of model-building strategies.     

Hydration of 3-cyanopyridine to nicotinamide by crude extract nitrile hydratase

Summary The kinetic and stability characteristics of crude extract nitrile hydratase fromBrevibacterium R-312 were studied for the hydration of 3-cyanopyridine to nicotinamide. The enzyme was substrate and product inhibited and had the following kinetic constants:K _m =28 mM;K _p =36 mM;K _s =155 mM;V _m =5.8 mol/min/mg protein (25°C). Itsmaximum temperature and pH (phosphate buffer) were 35°C and 8.0, respectively and it had half-lives of 50 days, 10 days and 1 day at 4°C, 10°C and 25°C, respectively. The crude extract also exhibited amidase activity on nicotinamide, but it became significant only at nicotinamide concentrations greater than 300 mM. Mathematical models for batch and fed-batch hydrations were developed to account for substrate and product inhibitions and for enzyme decay. They predicted to within 10% experimental results for initial substrate and final product concentrations up to 300 mM; the accuracies decreased at higher concentrations primarily because of the relatively rapid hydrolysis of nicotinamide.