Quasi-stationarity in populations that are subject to large-scale mortality or emigration

We shall examine a model, first studied by Brockwell et al. [Adv Appl Probab 14 (1982) 709.], which can be used to describe the longterm behaviour of populations that are subject to catastrophic mortality or emigration events. Populations can suffer dramatic declines when disease, such as an introduced virus, affects the population, or when food shortages occur, due to overgrazing or fluctuations in rainfall. However, perhaps surprisingly, such populations can survive for long periods and, although they may eventually become extinct, they can exhibit an apparently stationary regime. It is useful to be able to model this behaviour. This is particularly true of the ecological examples that motivated the present study, since, in order to properly manage these populations, it is necessary to be able to predict persistence times and to estimate the conditional probability distribution of population size. We shall see that although our model predicts eventual extinction, the time till extinction can be long and the stationary exhibited by these populations over any reasonable time scale can be explained using a quasistationary distribution. (C) 2001 Elsevier Science Ltd. All rights reserved.

Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Toxicity and uptake mechanism of cylindrospermopsin and lophyrotomin in primary rat hepatocytes

The toxicities and uptake mechanisms of two hepatotoxins, namely cylindrospermopsin and lophyrotomin, were investigated on primary rat hepatocytes by using microcystin-LIZ (a well-known hepatotoxin produced by cyanobacteria) as a comparison. Isolated rat hepatocytes were incubated with different concentrations of hepatotoxins for 0, 24, 48 and 72 h. The cell viability was assayed by the tetrazolium-based (MTT) assay. Microcystin-LR, cylindrospermopsin and lophyrotomin all exhibited toxic effects on the primary rat hepatocytes with 72-h LC50 of 8, 40 and 560 ng/ml, respectively. The involvement of the bile acid transport system in the hepatotoxin-induced toxicities was tested in the presence of two bile acids, cholate and taurocholate. Results showed that the bile acid transport system was responsible for the uptake, and facilitated the subsequent toxicities of lophyrotomin on hepatocytes. This occurred to a much lesser extent with cylindrospermopsin. With its smaller molecular weight, passive diffusion might be one of the possible mechanisms for cylindrospermopsin uptake into hepatocytes. This was supported by incubating a permanent cell line, KB (devoid of bile acid transport system), with cylindrospermopsin which showed cytotoxic effects. No inhibition of protein phosphatase 2A by cylindrospermopsin or lophyrotomin was found. This indicated that other toxic mechanisms besides protein phosphatase inhibition were producing the toxicities of cylindrospermopsin and lophyrotomin, and that they were unlikely to be potential tumor promoters. (C) 2001 Elsevier Science Ltd. All rights reserved.

Liquid distribution in wet granulation: dimensionless spray flux

This study investigates binder distribution in wet granulation and focuses on the nucleation zone, which is the area where the liquid binder and powder surface come into contact and form the initial nuclei. An equipment independent parameter, dimensionless spray flux Psi (a), is defined to characterise the most important process parameters in the nucleation process: solution flowrate, powder flux, and binder drop size. Ex-granulator experiments are used to study the relationship between dimensionless spray flux, process variables and the coverage of binder fluid on the powder surface. Lactose monohydrate powder on a variable speed riffler passed under a flat spray once only. Water and 7% HPC solution at two spray pressures were used as binders. Experiments with red dye and image analysis demonstrate that changes in dimensionless spray flux correlate with a measurable difference in powder surface coverage. Nucleation experiments show that spray flux controls the size and shape of the nuclei size distribution. At low Psi (a), the system operates in the drop controlled regime, where one drop forms one nucleus and the nuclei size distribution is narrow. At higher Psi (a), the powder surface cakes creating a broader size distribution. For controlled nucleation with the narrowest possible size distribution, it is recommended that the dimensionless spray flux be less than 0.1 to be in the drop-controlled regime. (C) 2001 Elsevier Science S.A. All rights reserved.

Growth regime map for liquid-bound granules: further development and experimental validation

An attempt was made to quantify the boundaries and validate the granule growth regime map for liquid-bound granules recently proposed by Iveson and Litster (AlChE J. 44 (1998) 1510). This regime map postulates that the type of granule growth behaviour is a function of only two dimensionless groups: the amount of granule deformation during collision (characterised by a Stokes deformation number, St(def)) and the maximum granule pore saturation, s(max). The results of experiments performed with a range of materials (glass ballotini, iron ore fines, copper chalcopyrite powder and a sodium sulphate and cellulose mixture) using both drum and high shear mixer granulators were examined. The drum granulation results gave good agreement with the proposed regime map. The boundary between crumb and steady growth occurs at St(def) of order 0.1 and the boundary between steady and induction growth occurs at St(def) of order 0.001. The nucleation only boundary occurs at pore saturations that increase from 70% to 80% with decreasing St(def). However, the high shear mixer results all had St(def) numbers which were too large. This is most likely to be because the chopper tip-speed is an over-estimate of the average impact velocity granules experience and possibly also due to the dynamic yield strength of the materials being significantly greater than the yield strengths measured at low strain rates. Hence, the map is only a useful tool for comparing the granulation behaviour of different materials in the same device. Until we have a better understanding of the flow patterns and impact velocities in granulators, it cannot be used to compare different types of equipment. Theoretical considerations also revealed that several of the regime boundaries are also functions of additional parameters not explicitly contained on the map, such as binder viscosity. (C) 2001 Elsevier Science B.V. All rights reserved.

Nucleation, growth and breakage phenomena in agitated wet granulation processes: a review

Wet agglomeration processes have traditionally been considered an empirical art, with great difficulties in predicting and explaining observed behaviour. Industry has faced a range of problems including large recycle ratios, poor product quality control, surging and even the total failure of scale up from laboratory to full scale production. However, in recent years there has been a rapid advancement in our understanding of the fundamental processes that control granulation behaviour and product properties. This review critically evaluates the current understanding of the three key areas of wet granulation processes: wetting and nucleation, consolidation and growth, and breakage and attrition. Particular emphasis is placed on the fact that there now exist theoretical models which predict or explain the majority of experimentally observed behaviour. Provided that the correct material properties and operating parameters are known, it is now possible to make useful predictions about how a material will granulate. The challenge that now faces us is to transfer these theoretical developments into industrial practice. Standard, reliable methods need to be developed to measure the formulation properties that control granulation behaviour, such as contact angle and dynamic yield strength. There also needs to be a better understanding of the flow patterns, mixing behaviour and impact velocities in different types of granulation equipment. (C) 2001 Elsevier Science B.V. All rights reserved.

Advances in application of climate prediction in agriculture

Agricultural ecosystems and their associated business and government systems are diverse and varied. They range from farms, to input supply businesses, to marketing and government policy systems, among others. These systems are dynamic and responsive to fluctuations in climate. Skill in climate prediction offers considerable opportunities to managers via its potential to realise system improvements (i.e. increased food production and profit and/or reduced risks). Realising these opportunities, however, is not straightforward as the forecasting skill is imperfect and approaches to applying the existing skill to management issues have not been developed and tested extensively. While there has been much written about impacts of climate variability, there has been relatively little done in relation to applying knowledge of climate predictions to modify actions ahead of likely impacts. However, a considerable body of effort in various parts of the world is now being focused on this issue of applying climate predictions to improve agricultural systems. In this paper, we outline the basis for climate prediction, with emphasis on the El Nino-Southern Oscillation phenomenon, and catalogue experiences at field, national and global scales in applying climate predictions to agriculture. These diverse experiences are synthesised to derive general lessons about approaches to applying climate prediction in agriculture. The case studies have been selected to represent a diversity of agricultural systems and scales of operation. They also represent the on-going activities of some of the key research and development groups in this field around the world. The case studies include applications at field/farm scale to dryland cropping systems in Australia, Zimbabwe, and Argentina. This spectrum covers resource-rich and resource-poor farming with motivations ranging from profit to food security. At national and global scale we consider possible applications of climate prediction in commodity forecasting (wheat in Australia) and examine implications on global wheat trade and price associated with global consequences of climate prediction. In cataloguing these experiences we note some general lessons. Foremost is the value of an interdisciplinary systems approach in connecting disciplinary Knowledge in a manner most suited to decision-makers. This approach often includes scenario analysis based oil simulation with credible models as a key aspect of the learning process. Interaction among researchers, analysts and decision-makers is vital in the development of effective applications all of the players learn. Issues associated with balance between information demand and supply as well as appreciation of awareness limitations of decision-makers, analysts, and scientists are highlighted. It is argued that understanding and communicating decision risks is one of the keys to successful applications of climate prediction. We consider that advances of the future will be made by better connecting agricultural scientists and practitioners with the science of climate prediction. Professions involved in decision making must take a proactive role in the development of climate forecasts if the design and use of climate predictions are to reach their full potential. (C) 2001 Elsevier Science Ltd. All rights reserved.

Increasing profits and reducing risks in crop production using participatory systems simulation approaches

The development of cropping systems simulation capabilities world-wide combined with easy access to powerful computing has resulted in a plethora of agricultural models and consequently, model applications. Nonetheless, the scientific credibility of such applications and their relevance to farming practice is still being questioned. Our objective in this paper is to highlight some of the model applications from which benefits for farmers were or could be obtained via changed agricultural practice or policy. Changed on-farm practice due to the direct contribution of modelling, while keenly sought after, may in some cases be less achievable than a contribution via agricultural policies. This paper is intended to give some guidance for future model applications. It is not a comprehensive review of model applications, nor is it intended to discuss modelling in the context of social science or extension policy. Rather, we take snapshots around the globe to 'take stock' and to demonstrate that well-defined financial and environmental benefits can be obtained on-farm from the use of models. We highlight the importance of 'relevance' and hence the importance of true partnerships between all stakeholders (farmer, scientists, advisers) for the successful development and adoption of simulation approaches. Specifically, we address some key points that are essential for successful model applications such as: (1) issues to be addressed must be neither trivial nor obvious; (2) a modelling approach must reduce complexity rather than proliferate choices in order to aid the decision-making process (3) the cropping systems must be sufficiently flexible to allow management interventions based on insights gained from models. The pro and cons of normative approaches (e.g. decision support software that can reach a wide audience quickly but are often poorly contextualized for any individual client) versus model applications within the context of an individual client's situation will also be discussed. We suggest that a tandem approach is necessary whereby the latter is used in the early stages of model application for confidence building amongst client groups. This paper focuses on five specific regions that differ fundamentally in terms of environment and socio-economic structure and hence in their requirements for successful model applications. Specifically, we will give examples from Australia and South America (high climatic variability, large areas, low input, technologically advanced); Africa (high climatic variability, small areas, low input, subsistence agriculture); India (high climatic variability, small areas, medium level inputs, technologically progressing; and Europe (relatively low climatic variability, small areas, high input, technologically advanced). The contrast between Australia and Europe will further demonstrate how successful model applications are strongly influenced by the policy framework within which producers operate. We suggest that this might eventually lead to better adoption of fully integrated systems approaches and result in the development of resilient farming systems that are in tune with current climatic conditions and are adaptable to biophysical and socioeconomic variability and change. (C) 2001 Elsevier Science Ltd. All rights reserved.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Cloud-point extraction and preconcentration of cyanobacterial toxins (microcystins) from natural waters using a cationic surfactant

A new cloud-point extraction and preconcentration method, using a cationic, surfactant, Aliquat-336 (tricaprylyl-methy;ammonium chloride), his-been developed for the determination of cyanobacterial toxins, microcystins, in natural waters. Sodium sulfate was used to induce phase separation at 25 degreesC. The phase behavior of Aliquat-336 with respect to concentration of Na2SO4 was studied. The cloud-point system revealed a very high phase volume ratio compared to other established systems of nonionic, anionic, and cationic surfactants: At pH 6-7, it showed an outstanding selectivity in ahalyte extraction for anionic species. Only MC-LR and MC-YR, which are known to be predominantly anionic, were extracted (with averaged recoveries of 113.9 +/- 9% and 87.1 +/- 7%, respectively). MC-RR, which is likely to be amphoteric at the above pH range, was. not cle tectable in.the extract. Coupled to HPLC/UV separation and detection, the cloud-point extraction method (with 2.5 mM Aliquat-336 and 75 mM Na2SO4 at 25 degreesC) offered detection limits of 150 +/- 7 and 470 +/- 72 pg/mL for MC-LR and MC-YR, respectively, in 25 mL of deionized water. Repeatability of the method was 7.6% for MC-LR and 7.3% for MC-YR: The cloud-point extraction process can be. completed within 10-15 min with no cleanup steps required. Applicability of the new method to the determination of microcystins in real samples was demonstrated using natural surface waters, collected from a local river and a local duck pond spiked with realistic. concentrations of microcystins. Effects of salinity and organic matter (TOC) content in the water sample on the extraction efficiency were also studied.

Genotoxicity investigation of a cyanobacterial toxin, cylindrospermopsin

Cylindrospermopsin (CYN), a potent cyanobacterial hepatotoxin produced by Cylindrospermopsis raciborskii and other cyanobacteria, is regularly found in water supplies in many parts of the world, and has been associated with the intoxication of humans and livestock. In this study, Balb/c mice were injected via the intraperitoneal (IP) route with a single dose of 0.2 mg/kg CYN. Animals were sacrificed at 6, 12, 24, 48 and 72 It. DNA was isolated from the mouse livers, and examined for strand breakage by alkaline gel electrophoresis (pH 12). Significant DNA strand breakage was observed in the mouse liver exposed to CYN, suggesting that induction of DNA strand breakage is probably one of the key mechanisms for CYN genotoxicity. (C) 2002 Elsevier Science Ltd. All rights reserved.