Weighting indicators of tourism sustainability: A critical note

Indicator weighting is an important issue in the measurement of tourism sustainability. Its importance derives from the fact that weights can have a significant effect on the rankings of analysed regions and subsequent policymaking. This is because relative indicator weights may significantly differ depending on the chosen weighting procedure. Relevant studies have however not paid particular attention to this issue so far, which is a gap this note aims to fill. An illustrative comparison of indicator weights from available studies further indicates potentially serious problems with some commonly used weighting procedures.     

7. Global support and coordination: conserving germplasm of world crop species and their relatives

The awareness of the importance of plant biodiversity has been considerably raised in both developed and developing countries over the last decade. Some of the debate has not been helpful in fostering collaboration or progress towards a more rational support network. The paper attempts to identify and categorize existing efforts in operation in a wide range of institutions and bodies ranging from essentially environmentally orientated to crop-based organizations. Current funding and training initiatives are discussed.     

Describing Ordinal Odds Ratios for Stratified r × c Tables

For an r × ctable with ordinal responses, odds ratios are commonly used to describe the relationship between the row and column variables. This article shows two types of ordinal odds ratios where local‐global odds ratios are used to compare several groups on a c‐category ordinal response and a global odds ratio is used to measure the global association between a pair of ordinal responses. When there is a stratification factor, we consider Mantel‐Haenszel (MH) type estimators of these odds ratios to summarize the association from several strata. Like the ordinary MH estimator of the common odds ratio for several 2 × 2 contingency tables, the estimators are used when the association is not expected to vary drastically among the strata. Also, the estimators are consistent under the ordinary asymptotic framework in which the number of strata is fixed and also under sparse asymptotics in which the number of strata grows with the sample size. Compared to the maximum likelihood estimators, simulations find that the MH type estimators perform better especially when each stratum has few observations. This article provides variances and covariances formulae for the local‐global odds ratios estimators and applies the bootstrap method to obtain a standard error for the global odds ratio estimator. At the end, we discuss possible ways of testing the homogeneity assumption.     

Global convergence properties in multilocus viability selection models: the additive model and the Hardy-Weinberg law

A natural coordinate system is introduced for the analysis of the global stability of the Hardy-Weinberg (HW) polymorphism under the general multilocus additive viability model. A global convergence criterion is developed and used to prove that the HW polymorphism is globally stable when each of the loci is diallelic, provided the loci are overdominant and the multilocus recombination is positive. As a corollary the multilocus Hardy-Weinberg law for neutral selection is derived.Research supported in part by NIH grants GM 39907-01, GM 10452-26 and NSF Grant DMS 86-06244Research supported in part by a US-Israel Binational Science Foundation grant 85-00021 and NIH grant GM 28016     

Analysis of a disease transmission model in a population with varying size

An S I R S epidemiological model with vital dynamics in a population of varying size is discussed. A complete global analysis is given which uses a new result to establish the nonexistence of periodic solutions. Results are discussed in terms of three explicit threshold parameters which respectively govern the increase of the total population, the existence and stability of an endemic proportion equilibrium and the growth of the infective population. These lead to two distinct concepts of disease eradication which involve the total number of infectives and their proportion in the population.Partially supported by NSF Grant No. DMS-8703631. This work was done while this author was visiting the University of VictoriaResearch supported in part by NSERC A-8965     

Early-blocked sporulation mutations alter expression of enzymes under carbon control in Bacillus subtilis

Summary The physiological roles of the gene subset defined by early-blocked sporulation mutations (spo0) and their second-site suppressor alleles (rvtA11 and crsA47) remain cryptic for both vegetative and sporulating Bacillus subtilis cells. To test the hypothesis that spo0 gene products affect global regulation, we assayed the levels of carbon- and nitrogen-sensitive enzymes in wild-type and spo0 strains grown in a defined minimal medium containing various carbon and nitrogen sources. All the spo0 mutations (except spo0J) affected both histidase and arabinose isomerase levels in an unexpected way: levels of both carbon-sensitive enzymes were two- to six-fold higher in spo0 strains compared to wild type, when cells were grown on the derepressing carbon sources arabinose or maltose. There was no difference in enzyme levels with glucose-grown cells, nor was there a significant difference in levels of the carbonindependent enzymes glutamine synthetase and glucose-6-phosphate dehydrogenase. This effect was not due to a slower growth rate for the spo0 mutants on the poor carbon and nitrogen sources used. The levels of carbon-sensitive enzymes were not simply correlated with sporulation ability in genetically suppressed spo0 mutants, but the rvtA and crsA suppressors each had such marked effects on wild-type growth and enzyme levels that these results were difficult to interpret. We conclude that directly or indirectly the spo0 mutations, although blocking the sporulation process, increase levels of carbon-sensitive enzymes, possibly at the level of gene expression.     

A threshold result for an epidemiological model

A threshold parameter R ₀ is identified for an SIRS epidemiological model which has nonlinear incidence and a distributed delay for transfer out of the removed class. For R ₀ < 1, the disease free equilibrium is proved to be the global attractor for all solutions.Research supplied in part by NSERC A-8965     

A model of a myelinated nerve axon: threshold behaviour and propagation

A model of a myelinated nerve axon is developed on the basis of FitzHugh-Nagumo dynamics under the assumption that the nodes of Ranvier are of small but finite width. It is shown that a periodic excited state may not exist if the width of the nodes is too small and the leakage across the myelin sheath is too great. The propagation of a super threshold pulse is prevented in the absence of nodes. Global stability of the resting equilibrium state is investigated as well as the propagation of wave front, type solutions.