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.     

Genetic variation and divergence of the sibling pair of cyprinid fishes, Notropis cornutus and N. chrysocephalus

Horizontal starch gel electrophoresis was used to estimate the amount of genetic divergence between Notropis cornutus and N. chrysocephalus. Measures of genetic identity (1) and distance (D) were 0.881 and 0.127 ± 0.055 (s.e.), respectively. These estimates correspond more closely to the sibling species status of these taxa than other previously reported estimates. Notropis cornutus was found to be significantly more variable than N. chrysocephalus electrophoretically and morphologically. Assuming the existence of an electrophoretic clock, the time of divergence was calculated to be roughly 1.9–2.5 million years. This estimate corresponds very closely to a previously hypothesized late Pliocene divergence.     

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.     

A population genetic study of the Banks and Torres Islands (Vanuatu) and of the Santa Cruz Islands and polynesian outliers (Solomon Islands)

As part of a multidisciplinary survey of populations in the Banks and Torres Islands of Vanuatu and the Southern and Central Districts of the Solomon Islands, nearly 2,400 persons have been tested for ABO blood groups and a number of serum protein and red cell enzyme genetic marker systems. For the ABO system, the populations are characterized in general by high gene O and low gene B frequencies except in two of the Polynesian Outlier Islands, Rennell and Bellona, which have high frequencies of B. Among the serum proteins, several alleles have distributions indicating significant movement of people between islands. These include Albumin ^{New Guinea} and the transferrin alleles Tf, and Tf, and Tf. Similar specific alleles for red cell enzymes also show distributions reflecting interisland population movement as well as contact with persons from outside the southern Pacific region. Examples are ACP in the acid phosphatase system, PGM and PGM, PGM and PGM, PGK⁴ and also HbJ^Tongariki. The data available for 11 polymorphic systems were used to generate genetic distances. Of the four Polynesian Outlier Islands, Anuta is most remote genetically, with Rennell and Bellona also relatively isolated. The fourth Polynesian Outlier, Tikopia, occupies a position genetically close to the Melanesian populations of the Banks and Torres Islands and the southern Solomons. The history of early European contact and voyaging in the Pacific, as well as archaeological and linguistic evidence and local legends, indicate that significant movements of people occurred between islands and provided opportunities for genes to be introduced from Europeans, Africans, and Asians. The genetic marker studies give evidence for genes from all these sources, though at a low level. Despite this admixture, the Polynesian Outlier and Melanesian populations have preserved their own distinctive genetic patterns.     

Studies on the complex formed between glucagon and dicaprylphosphatidylcholine

The interaction between glucagon and dicaprylphosphatidylcholine (DCPC) was studied by fluorescence, circular dichroism and calorimetry, as well as by ¹H- and ³¹P-nuclear magnetic resonance. The water-soluble lipid-protein complex was also characterized by gel filtration and ultracentrifugation. The complex appeared to be monodisperse by sedimentation equilibrium measurements, with a molecular weight of (4.55 ± 0.57)·10⁴. This complex contained approximately 7 molecules of glucagon and 35 molecules of phospholipid. Proton-decoupled ³¹P-NMR spectra of the phospholipid in the lipid-protein complex display narrower resonances than those of sonicated vesicles of DCPC, and ¹H-³¹P coupling could be detected in proton coupled spectra. These NMR results, together with gel-filtration results, suggest that glucagon ‘solubilizes’ phospholipid aggregates, forming a lipid-protein complex which is smaller than sonicated preparations of DCPC. ¹H-NMR resonance of both the methionine methyl group (met-27) and the aromatic envelope of glucagon are broadened by the phospolipid, indicating that the C-terminal region and the aromatic residues are involved in the interaction with the phospholipid. Nuclear magnetic resonance titrations of the imidazole ring C(2) and C(4) protons of the histidine residue of glucagon show that DCPC lowers the pK of the imidazole. The alterations caused by the phospholipid in the far and near ultraviolet CD spectra of glucagon reflect, respectively, the increased helix content of the hormone and the fact that the aromatic residues are located in a more structured environment. The phospholipid also alters the fluorescence properties of glucagon, shifting the fluorescence emission maximum of the hormone to shorter wavelength, and enhancing its relative intensity. This suggests that the fluorophore is experiencing a more hydrophobic environment in the presence of the lipid. Binding of glucagon to the phospholipid was analysed by Scatchard plots of the enhancement of fluorescence caused by the phospholipid and showed that the equilibrium binding constants of glucagon to DCPC are (4.4 ± 0.5)·10⁴M^?1 and (7.5±0.5)·10⁴M^?1, at 15°C and 25°C, respectively. The average number of moles of phospholipid bound per mole of glucagon is 4.4±0.6. The isothermal enthalpy of reaction of glucagon with DCPC is ?20.5 kcal/mol of glucagon at 25°C and ?32.5 kcal/mol of glucagon at 15°C. The observed enthalpies can arise from glucagon-induced cyrstallization of the phospholipid, from the non-covalent interactions between the peptide and lipid as well as from the lipid-induced conformational change in the protein. These results demonstrate that, unlike the complexes formed between glucagon and phospholipids which form more stable bilayers, the complex formed between glucagon and DCPC is stable over a wide range of temperatures, including temperatures well above the phase transition.     

Dissimilarity for partially ranked data and its application to cover-abundance data

Cover-abundance estimates are commonly employed in phytosociological investigations to record the performance of species. Because the coded values are on an ordinal scale of measure, various authors have suggested that some transformation is necessary before such values can be used for classification and ordination. However, it is not clear that transformation is a sufficient treatment, and it would seem preferable to use ordinal data directly. In this paper we examine such direct use of partial rankings and show that several dissimilarity measures can be defined for this case without invoking any transformations. They include dissimilarity measures associated with various rank correlation measures and with distances between strings; all the measure are variant forms of Hausdorf's interset distance. Certain other kinds of data, such as those employing dominant and subdominant species and the dry-weight-rank estimation of biomass, are also on an ordinal scale and could be analysed using similar techniques.To illustrate the approach, a string dissimilarity measure is used to analyse a set of data from Slovakian grasslands which appear to reflect a simple gradient. The original data were recorded with 10 classes of performance and are analysed using hierarchical and nondeterministic, overlapping, classifications.     

玉米自交系间遗传距离与产量杂种优势,杂种产量的关系

以13个玉米自交系及其按双列杂交配制的78个单交种为材料,研究性状选择、亲本选择对遗传距离与产量杂种优势、杂种产量关系的影响,结果表明:(1)当性状数较少时,遗传距离与产量杂种优势、杂种产量的关系因性状的不同而异;当性状数较多时,遗传距离与产量杂种优势、杂种产量的关系为抛物线,受性状影响较小;(2)当所选亲本材料的遗传差异较大时,遗传距离与产量杂种优势的关系为抛物线;当所选亲本材料的遗传差异较小时,遗传距离与产量杂种优势的关系为直线或不相关。     

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