A graph-theoretic method for the basic reproduction number in continuous time epidemiological models

In epidemiological models of infectious diseases the basic reproduction number is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for can be obtained from the digraphs in the reduction process.     

Reidentification of the keratinase-producing facultatively alkaliphilic Bacillus sp. AH-101 as Bacillus halodurans

Alkaliphilic Bacillus sp. AH-101 was characterized in terms of physiological and biochemical characteristics, and 16S rDNA sequence homology and DNA–DNA hybridization analyses were performed. Phylogenetic analysis of strain AH-101 based on comparison of 16S rDNA sequences revealed that this strain is closely related to Bacillus halodurans. DNA–DNA hybridization of AH-101 and related Bacillus reference strains showed that the highest level of DNA–DNA relatedness (88%) was found between strain AH-101 and the B. halodurans type strain (DSM497). Our findings demonstrate that strain AH-101 is a member of the species B. halodurans. Received: June 10, 1999 / Accepted: August 6, 1999     

All that glisters is not galled

Galled trees, evolutionary networks with isolated reticulation cycles, have appeared under several slightly different definitions in the literature. In this paper, we establish the actual relationships between the main four such alternative definitions: namely, the original galled trees, level-1 networks, nested networks with nesting depth 1, and evolutionary networks with arc-disjoint reticulation cycles.     

Radial distribution of Ni in stemwood of Quercus ilex L. trees grown on serpentine and sandy loam (umbric leptosol) soils of NE-Portugal

Concentrations of Ni were determined in xylem and phloem of Quercus ilex trees growing on serpentine and sandy loam soils of northeast Portugal. Radial distribution patterns of Ni in stemwood were compared to variations in annual growth increments of the trees.Concentrations of Ni in xylem and phloem were higher in Q. ilex from serpentine soil, when compared with Q. ilex of a sandy loam soil.The radial distributions of Ni showed large variations among the trees, although they all grew in the same area within a short distance from each other. These differences can be caused by small-scale spatial variations in the soil. Therefore, the use of such radial Ni distributions for a retrospective biomonitoring of the Ni pollution of larger areas appears questionable.     

Molecular markers reveal a strong genetic differentiation between two European relic tree species: Zelkova abelicea (Lam.) Boissier and Z. sicula Di Pasquale, Garfì & Quézel (Ulmaceae)

Chloroplast (trnL) and ribosomal (ITS2)sequences and chloroplast DNA (PCR-RFLP andSSR) markers were analysed in two relicUlmaceae tree species: Zelkova abelicea,from Crete, and Z. sicula, from Sicily.The analysis of the plastidial trnLintron and of ITS2 ribosomal sequences revealedtheir divergence from the related speciesZ. carpinifolia, widespread in the Caucasianregion; one base substitution in the trnLintron was detected between the twoMediterranean species, thus suggesting theirrecent separation. Molecular markers(plastidial PCR-RFLP and SSR) showed an evidentgenetic differentiation between Z. siculaand Z. abelicea, the two species beingcharacterised by different haplotypes. Nowithin population variation was detected usingdifferent chloroplast markers inZ. abelicea and Z. sicula. Paleobotanicaldata proved that the genus Zelkova wasabundant and widespread in central Italy untilit became extinct in the continental part ofEurope during last glaciation events andsurvived only in two Mediterranean islands. Thesegregation of the two Mediterranean relicspecies might have occurred as a consequence ofthe strong reduction of their distribution andthe following geographic isolation. Geneticdrift may have determined the drastic reductionof within stand diversity as observed in othersmall, peripheral and geographically isolatedplant populations. The priorities forconservation programs are discussed in thelight of the different genetic resourcesrepresented by the two taxa.     

Shear effects on failure of hollow trees

It is shown that bending stresses in a non-cracked hollow trunk can never explain failure. Consequently, stem breakage due to bending stress cannot be primary failure. It is shown by field studies and simple theoretical assessments that the initiation of a longitudinal shear crack is primarily responsible for failure. Due to cracking, the bending stresses increase and failure by bending happens as secondary failure. As a result, bending theory of a non-cracked closed circular pipe is inappropriate to describe failure of hollow trees. In the appendix is shown the reason for high shear stresses at the tree base and why the shear stresses increase more due to hollowness than to bending stresses.