Mathematical methods for spatially cohesive reserve design

The problem of designing spatially cohesive nature reserve systems that meet biodiversity objectives is formulated as a nonlinear integer programming problem. The multiobjective function minimises a combination of boundary length, area and failed representation of the biological attributes we are trying to conserve. The task is to reserve a subset of sites that best meet this objective. We use data on the distribution of habitats in the Northern Territory, Australia, to show how simulated annealing and a greedy heuristic algorithm can be used to generate good solutions to such large reserve design problems, and to compare the effectiveness of these methods.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

Allozyme electrophoresis still represents a powerful technique in the management of coral reefs

Understanding genetic variability and gene flow between populations of scleractinian corals separated by one to several hundred kilometers is crucially important as we head into a century of climate change in which an understanding of the connectivity of populations is a critically important question in management. Genetic methods that directly use molecular variance in the DNA should offer greater precision in detecting differences among individuals and populations than the more traditional allozyme electrophoresis. However, this paper highlights the point that the limited number of DNA markers that have been identified for scleractinian coral genetic studies do not necessarily offer greater precision than that offered by allozymes. In fact, at present allozyme electrophoresis yields greater information than the eight different DNA markers used in this study. Given the relative ease of use of allozymes and the wealth of comparable data sets from numerous previously published studies, allozyme electrophoresis should not be dismissed for population structure and connectivity studies on coral reefs. While continued effort should be placed into searching for new DNA markers, until a more sensitive DNA marker becomes available for scleractinian corals, allozyme electrophoresis remains a powerful and relevant technique for understanding the connectivity of coral population studies.

Colorectal cancer screening in Australia: an economic evaluation of a potential biennial screening program using faecal occult blood tests

Objective: To evaluate whether the introduction of a national, co-ordinated screening program using the faecal occult blood test represents 'value-for-money' from the perspective of the Australian Government as third-party funder. Methods: The annual equivalent costs and consequences of a biennial screening program in 'steady-state' operation were estimated for the Australian population using 1996 as the reference year. Disability-adjusted life years (DALYs) and the years of life lost (YLLs) averted, and the health service costs were modelled, based on the epidemiology and the costs of colorectal cancer in Australia together with the mortality reduction achieved in randomised controlled trials. Uncertainty in the model was examined using Monte Carlo simulation methods. Results: We estimate a minimum or 'base program' of screening those aged 55 to 69 years could avert 250 deaths per annum (95% uncertainty interval 99-400), at a gross cost of $A55 million (95% UI $A46 million to $A96 million) and a gross incremental cost-effectiveness ratio of $A17,000/DALY (95% UI $A13,000/DALY to $A52,000/DALY). Extending the program to include 70 to 74-year-olds is a more effective option (cheaper and higher health gain) than including the 50 to 54-year-olds. Conclusions: The findings of this study support the case for a national program directed at the 55 to 69-year-old age group with extension to 70 to 74-year-olds if there are sufficient resources. The pilot tests recently announced in Australia provide an important opportunity to consider the age range for screening and the sources of uncertainty, identified in the modelled evaluation, to assist decisions on implementing a full national program.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

Cost-effectiveness of cognitive-behavioural therapy and drug interventions for major depression

Objective: Antidepressant drugs and cognitive-behavioural therapy (CBT) are effective treatment options for depression and are recommended by clinical practice guidelines. As part of the Assessing Cost-effectiveness - Mental Health project we evaluate the available evidence on costs and benefits of CBT and drugs in the episodic and maintenance treatment of major depression. Method: The cost-effectiveness is modelled from a health-care perspective as the cost per disability-adjusted life year. Interventions are targeted at people with major depression who currently seek care but receive non-evidence based treatment. Uncertainty in model inputs is tested using Monte Carlo simulation methods. Results: All interventions for major depression examined have a favourable incremental cost-effectiveness ratio under Australian health service conditions. Bibliotherapy, group CBT, individual CBT by a psychologist on a public salary and tricyclic antidepressants (TCAs) are very cost-effective treatment options falling below $A10 000 per disability-adjusted life year (DALY) even when taking the upper limit of the uncertainty interval into account. Maintenance treatment with selective serotonin re-uptake inhibitors (SSRIs) is the most expensive option (ranging from $A17 000 to $A20 000 per DALY) but still well below $A50 000, which is considered the affordable threshold. Conclusions: A range of cost-effective interventions for episodes of major depression exists and is currently underutilized. Maintenance treatment strategies are required to significantly reduce the burden of depression, but the cost of long-term drug treatment for the large number of depressed people is high if SSRIs are the drug of choice. Key policy issues with regard to expanded provision of CBT concern the availability of suitably trained providers and the funding mechanisms for therapy in primary care.

Erosion/productivity modelling of maize farming in the Philippine uplands part II: Simulation of alternative farming methods

A version of the Agricultural Production Systems Simulator (APSIM) capable of simulating the key agronomic aspects of intercropping maize between legume shrub hedgerows was described and parameterised in the first paper of this series (Nelson et al., this issue). In this paper, APSIM is used to simulate maize yields and soil erosion from traditional open-field farming and hedgerow intercropping in the Philippine uplands. Two variants of open-field farming were simulated using APSIM, continuous and fallow, for comparison with intercropping maize between leguminous shrub hedgerows. Continuous open-field maize farming was predicted to be unsustainable in the long term, while fallow open-field farming was predicted to slow productivity decline by spreading the effect of erosion over a larger cropping area. Hedgerow intercropping was predicted to reduce erosion by maintaining soil surface cover during periods of intense rainfall, contributing to sustainable production of maize in the long term. In the third paper in this series, Nelson et al. (this issue) use cost-benefit analysis to compare the economic viability of hedgerow intercropping relative to traditional open-field farming of maize in relatively inaccessible upland areas. (C) 1998 Elsevier Science Ltd. All rights reserved.

Cost effectiveness of adding magnetic resonance imaging to the usual management of suspected scaphoid fractures

Objective: To determine the cost effectiveness of a magnetic resonance imaging scan (MRI) within 5 days of injury compared with the usual management of occult scaphoid fracture. Methods: All patients with suspected scaphoid fractures in five hospitals were invited to participate in a randomised controlled trial of usual treatment with or without an MRI scan. Healthcare costs were compared, and a cost effectiveness analysis of the use of MRI in this scenario was performed. Results: Twenty eight of the 37 patients identified were randomised: 17 in the control group, 11 in the MRI group. The groups were similar at baseline and follow up in terms of number of scaphoid fractures, other injuries, pain, and function. Of the patients without fracture, the MRI group had significantly fewer days immobilised: a median of 3.0 (interquartile range 3.0-3.0) v 10.0 (7-12) in the control group (p = 0.006). The MRI group used fewer healthcare units (median 3.0, interquartile range 2.0-4.25) than the control group (5.0, 3.0-6.5) (p = 0.03 for the difference). However, the median cost of health care in the MRI group ($594.35 AUD, $551.35-667.23) was slightly higher than in the control group ($428.15, $124.40-702.65) (p = 0.19 for the difference). The mean incremental cost effectiveness ratio derived from this simulation was that MRI costs $44.37 per day saved from unnecessary immobilisation (95% confidence interval $4.29 to $101.02). An illustrative willingness to pay was calculated using a combination of the trials measure of the subjects' individual productivity losses and the average daily earnings. Conclusions: Use of MRI in the management of occult scaphoid fracture reduces the number of days of unnecessary immobilisation and use of healthcare units. Healthcare costs increased non-significantly in relation to the use of MRI in this setting. However, when productivity losses are considered, MRI may be considered cost effective, depending on the individual case.

Using clusters of computers for large QU-GENE simulation experiments

The QU-GENE Computing Cluster (QCC) is a hardware and software solution to the automation and speedup of large QU-GENE (QUantitative GENEtics) simulation experiments that are designed to examine the properties of genetic models, particularly those that involve factorial combinations of treatment levels. QCC automates the management of the distribution of components of the simulation experiments among the networked single-processor computers to achieve the speedup.

An atomistic simulation of solid state sintering using Monte Carlo methods

This paper presents results on the simulation of the solid state sintering of copper wires using Monte Carlo techniques based on elements of lattice theory and cellular automata. The initial structure is superimposed onto a triangular, two-dimensional lattice, where each lattice site corresponds to either an atom or vacancy. The number of vacancies varies with the simulation temperature, while a cluster of vacancies is a pore. To simulate sintering, lattice sites are picked at random and reoriented in terms of an atomistic model governing mass transport. The probability that an atom has sufficient energy to jump to a vacant lattice site is related to the jump frequency, and hence the diffusion coefficient, while the probability that an atomic jump will be accepted is related to the change in energy of the system as a result of the jump, as determined by the change in the number of nearest neighbours. The jump frequency is also used to relate model time, measured in Monte Carlo Steps, to the actual sintering time. The model incorporates bulk, grain boundary and surface diffusion terms and includes vacancy annihilation on the grain boundaries. The predictions of the model were found to be consistent with experimental data, both in terms of the microstructural evolution and in terms of the sintering time. (C) 2002 Elsevier Science B.V. All rights reserved.

Genetic assignment methods for the direct, real-time estimation of migration rate: a simulation-based exploration of accuracy and power

Genetic assignment methods use genotype likelihoods to draw inference about where individuals were or were not born, potentially allowing direct, real-time estimates of dispersal. We used simulated data sets to test the power and accuracy of Monte Carlo resampling methods in generating statistical thresholds for identifying F-0 immigrants in populations with ongoing gene flow, and hence for providing direct, real-time estimates of migration rates. The identification of accurate critical values required that resampling methods preserved the linkage disequilibrium deriving from recent generations of immigrants and reflected the sampling variance present in the data set being analysed. A novel Monte Carlo resampling method taking into account these aspects was proposed and its efficiency was evaluated. Power and error were relatively insensitive to the frequency assumed for missing alleles. Power to identify F-0 immigrants was improved by using large sample size (up to about 50 individuals) and by sampling all populations from which migrants may have originated. A combination of plotting genotype likelihoods and calculating mean genotype likelihood ratios (D-LR) appeared to be an effective way to predict whether F-0 immigrants could be identified for a particular pair of populations using a given set of markers.

Data mining and simulation: a grey relationship demonstration

Fuzzy data has grown to be an important factor in data mining. Whenever uncertainty exists, simulation can be used as a model. Simulation is very flexible, although it can involve significant levels of computation. This article discusses fuzzy decision-making using the grey related analysis method. Fuzzy models are expected to better reflect decision-making uncertainty, at some cost in accuracy relative to crisp models. Monte Carlo simulation is used to incorporate experimental levels of uncertainty into the data and to measure the impact of fuzzy decision tree models using categorical data. Results are compared with decision tree models based on crisp continuous data.