Extinction times for a general birth, death and catastrophe process

The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times.

General practitioners with special interests: risk of a good thing becoming bad?

There is a long tradition of some general practitioners developing areas of special interest within their mainstream generalist practice. General practice is now becoming increasingly fragmented, with core components being delivered as separate and standalone services (eg, travel medicine, skin cancer, women's health). Although this fragmentation seems to meet a need for some patients and doctors, potential problems need careful consideration and response. These include loss of generalist skills among GPs, fewer practitioners working in less well-remunerated areas, such as nursing home visits, and issues related to standards of care and training.

Variation among Australian accessions of the wild mungbean (Vigna radiata ssp sublobata) for traits of agronomic, adaptive, or taxonomic interest

The wild mungbean, Vigna radiata ssp. sublobata, is an 'old world' tropical species indigenous throughout the better watered areas of northern Australia. Variation among 115 accessions, mainly from Australia, West Timor, and Papua New Guinea, was evaluated for several diverse traits. The plants were cultivated in the field at 2 sowing dates, at both a tropical and a subtropical location, with 6 accessions from India and a mungbean cultivar for comparison. Substantial variation was identified for traits of potential agronomic, adaptive, or taxonomic interest. For some traits, like phenology, the variation appeared to be systematic, with plausible underlying physiological and/or adaptive explanation. Among accessions, wild type traits, like prostrate habit, more gracile morphology, twining form, and small hard seeds, tended to be associated. There was a general geographic trend for lines collected from locations more remote from where mungbean has historically been cultivated to show greater expression of wild type traits, with few 'traits of domestication' evident in the Australian accessions. Some of the identified variation, e. g. higher seed protein content, hardseededness, and putative disease resistance, may be of value in mungbean variety improvement. A more targetted evaluation of the collection would likely reveal other adaptations, especially tolerance to environmental stresses. As such, the wild accessions are a potentially valuable if under-utilised germplasm resource.