The importance of modelling heterogeneity in complex disease: application to NIMH Schizophrenia Genetics Initiative data

As for other complex diseases, linkage analyses of schizophrenia (SZ) have produced evidence for numerous chromosomal regions, with inconsistent results reported across studies. The presence of locus heterogeneity appears likely and may reduce the power of linkage analyses if homogeneity is assumed. In addition, when multiple heterogeneous datasets are pooled, inter-sample variation in the proportion of linked families (alpha) may diminish the power of the pooled sample to detect susceptibility loci, in spite of the larger sample size obtained. We compare the significance of linkage findings obtained using allele-sharing LOD scores (LOD(exp))-which assume homogeneity-and heterogeneity LOD scores (HLOD) in European American and African American NIMH SZ families. We also pool these two samples and evaluate the relative power of the LOD(exp) and two different heterogeneity statistics. One of these (HLOD-P) estimates the heterogeneity parameter alpha only in aggregate data, while the second (HLOD-S) determines alpha separately for each sample. In separate and combined data, we show consistently improved performance of HLOD scores over LOD(exp). Notably, genome-wide significant evidence for linkage is obtained at chromosome 10p in the European American sample using a recessive HLOD score. When the two samples are combined, linkage at the 10p locus also achieves genome-wide significance under HLOD-S, but not HLOD-P. Using HLOD-S, improved evidence for linkage was also obtained for a previously reported region on chromosome 15q. In linkage analyses of complex disease, power may be maximised by routinely modelling locus heterogeneity within individual datasets, even when multiple datasets are combined to form larger samples.

Marker selection by Akaike information criterion and Bayesian information criterion

We carried out a discriminant analysis with identity by descent (IBD) at each marker as inputs, and the sib pair type (affected-affected versus affected-unaffected) as the output. Using simple logistic regression for this discriminant analysis, we illustrate the importance of comparing models with different number of parameters. Such model comparisons are best carried out using either the Akaike information criterion (AIC) or the Bayesian information criterion (BIC). When AIC (or BIC) stepwise variable selection was applied to the German Asthma data set, a group of markers were selected which provide the best fit to the data (assuming an additive effect). Interestingly, these 25-26 markers were not identical to those with the highest (in magnitude) single-locus lod scores.

An explicit finite element modelling method for masonry walls under out-of-plane loading

An explicit finite element modelling method is formulated using a layered shell element to examine the behaviour of masonry walls subject to out-of-plane loading. Masonry is modelled as a homogenised material with distinct directional properties that are calibrated from datasets of a “C” shaped wall tested under pressure loading applied to its web. The predictions of the layered shell model have been validated using several out-of-plane experimental datasets reported in the literature. Profound influence of support conditions, aspect ratio, pre-compression and opening to the strength and ductility of masonry walls is exhibited from the sensitivity analyses performed using the model.

Modelling temperature, photoperiod and vernalization responses of Brunonia australis (Goodeniaceae) and Calandrinia sp (Portulacaceae) to predict flowering time

Crop models for herbaceous ornamental species typically include functions for temperature and photoperiod responses, but very few incorporate vernalization, which is a requirement of many traditional crops. This study investigated the development of floriculture crop models, which describe temperature responses, plus photoperiod or vernalization requirements, using Australian native ephemerals Brunonia australis and Calandrinia sp. A novel approach involved the use of a field crop modelling tool, DEVEL2. This optimization program estimates the parameters of selected functions within the development rate models using an iterative process that minimizes sum of squares residual between estimated and observed days for the phenological event. Parameter profiling and jack-knifing are included in DEVEL2 to remove bias from parameter estimates and introduce rigour into the parameter selection process. Development rate of B. australis from planting to first visible floral bud (VFB) was predicted using a multiplicative approach with a curvilinear function to describe temperature responses and a broken linear function to explain photoperiod responses. A similar model was used to describe the development rate of Calandrinia sp., except the photoperiod function was replaced with an exponential vernalization function, which explained a facultative cold requirement and included a coefficient for determining the vernalization ceiling temperature. Temperature was the main environmental factor influencing development rate for VFB to anthesis of both species and was predicted using a linear model. The phenology models for B. australis and Calandrinia sp. described development rate from planting to VFB and from VFB to anthesis in response to temperature and photoperiod or vernalization and may assist modelling efforts of other herbaceous ornamental plants. In addition to crop management, the vernalization function could be used to identify plant communities most at risk from predicted increases in temperature due to global warming.

A participatory whole farm modelling approach to understand impacts and increase preparedness to climate change in Australia

This study presents the use of a whole farm model in a participatory modelling research approach to examine the sensitivity of four contrasting case study farms to a likely climate change scenario. The newly generated information was used to support discussions with the participating farmers in the search for options to design more profitable and sustainable farming systems in Queensland Australia. The four case studies contrasted in key systems characteristics: opportunism in decision making, i.e. flexible versus rigid crop rotations; function, i.e. production of livestock or crops; and level of intensification, i.e. dryland versus irrigated agriculture. Tested tactical and strategic changes under a baseline and climate change scenario (CCS) involved changes in the allocation of land between cropping and grazing enterprises, alternative allocations of limited irrigation water across cropping enterprises, and different management rules for planting wheat and sorghum in rainfed cropping. The results show that expected impacts from a likely climate change scenario were evident in the following increasing order: the irrigated cropping farm case study, the cropping and grazing farm, the more opportunistic rainfed cropping farm and the least opportunistic rainfed cropping farm. We concluded that in most cases the participating farmers were operating close to the efficiency frontier (i.e. in the relationship between profits and risks). This indicated that options to adapt to climate change might need to evolve from investments in the development of more innovative cropping and grazing systems and/or transformational changes on existing farming systems. We expect that even though assimilating expected changes in climate seems to be rather intangible and premature for these farmers, as innovations are developed, adaptation is likely to follow quickly. The multiple interactions among farm management components in complex and dynamic farm businesses operating in a variable and changing climate, make the use of whole farm participatory modelling approaches valuable tools to quantify benefits and trade-offs from alternative farming systems designs in the search for improved profitability and resilience.

Individual-based modelling of the efficacy of fumigation tactics to control lesser grain borer (Rhyzopertha dominica) in stored grain

Increasing resistance to phosphine (PH 3) in insect pests, including lesser grain borer (Rhyzopertha dominica) has become a critical issue, and development of effective and sustainable strategies to manage resistance is crucial. In practice, the same grain store may be fumigated multiple times, but usually for the same exposure period and concentration. Simulating a single fumigation allows us to look more closely at the effects of this standard treatment.We used an individual-based, two-locus model to investigate three key questions about the use of phosphine fumigant in relation to the development of PH 3 resistance. First, which is more effective for insect control; long exposure time with a low concentration or short exposure period with a high concentration? Our results showed that extending exposure duration is a much more efficient control tactic than increasing the phosphine concentration. Second, how long should the fumigation period be extended to deal with higher frequencies of resistant insects in the grain? Our results indicated that if the original frequency of resistant insects is increased n times, then the fumigation needs to be extended, at most, n days to achieve the same level of insect control. The third question is how does the presence of varying numbers of insects inside grain storages impact the effectiveness of phosphine fumigation? We found that, for a given fumigation, as the initial population number was increased, the final survival of resistant insects increased proportionally. To control initial populations of insects that were n times larger, it was necessary to increase the fumigation time by about n days. Our results indicate that, in a 2-gene mediated resistance where dilution of resistance gene frequencies through immigration of susceptibles has greater effect, extending fumigation times to reduce survival of homozygous resistant insects will have a significant impact on delaying the development of resistance. © 2012 Elsevier Ltd.

A Paddock to reef monitoring and modelling framework for the Great Barrier Reef: Paddock and catchment component

Targets for improvements in water quality entering the Great Barrier Reef (GBR) have been set through the Reef Water Quality Protection Plan (Reef Plan). To measure and report on progress towards the targets set a program has been established that combines monitoring and modelling at paddock through to catchment and reef scales; the Paddock to Reef Integrated Monitoring, Modelling and Reporting Program (Paddock to Reef Program). This program aims to provide evidence of links between land management activities, water quality and reef health. Five lines of evidence are used: the effectiveness of management practices to improve water quality; the prevalence of management practice adoption and change in catchment indicators; long-term monitoring of catchment water quality; paddock & catchment modelling to provide a relative assessment of progress towards meeting targets; and finally marine monitoring of GBR water quality and reef ecosystem health. This paper outlines the first four lines of evidence. (C) 2011 Elsevier Ltd. All rights reserved.

Stochastic modelling of monthly rainfall

A transformation is suggested which can transform a non-Gaussian monthly hydrological time series into a Gaussian one. The suggested approach is verified with data of ten Indian rainfall time series. Incidentally, it is observed that once the deterministic trends are removed, the transformation leads to an uncorrelated process for monthly rainfall. The procedure for normalization is general enough in that it should be also applicable to river discharges. This is verified to a limited extent by considering data of two Indian river discharges.

Managing glyphosate resistance in Australian cotton farming: modelling shows how to delay evolution and maintain long-term population control

Glyphosate resistance is a rapidly developing threat to profitability in Australian cotton farming. Resistance causes an immediate reduction in the effectiveness of in-crop weed control in glyphosate-resistant transgenic cotton and summer fallows. Although strategies for delaying glyphosate resistance and those for managing resistant populations are qualitatively similar, the longer resistance can be delayed, the longer cotton growers will have choice over which tactics to apply and when to apply them. Effective strategies to avoid, delay, and manage resistance are thus of substantial value. We used a model of glyphosate resistance dynamics to perform simulations of resistance evolution in Sonchus oleraceus (common sowthistle) and Echinochloa colona (awnless barnyard grass) under a range of resistance prevention, delaying, and management strategies. From these simulations, we identified several elements that could contribute to effective glyphosate resistance prevention and management strategies. (i) Controlling glyphosate survivors is the most robust approach to delaying or preventing resistance. High-efficacy, high-frequency survivor control almost doubled the useful lifespan of glyphosate from 13 to 25 years even with glyphosate alone used in summer fallows. (ii) Two non-glyphosate tactics in-crop plus two in-summer fallows is the minimum intervention required for long-term delays in resistance evolution. (iii) Pre-emergence herbicides are important, but should be backed up with non-glyphosate knockdowns and strategic tillage; replacing a late-season, pre-emergence herbicide with inter-row tillage was predicted to delay glyphosate resistance by 4 years in awnless barnyard grass. (iv) Weed species' ecological characteristics, particularly seed bank dynamics, have an impact on the effectiveness of resistance strategies; S. oleraceus, because of its propensity to emerge year-round, was less exposed to selection with glyphosate than E. colona, resulting in an extra 5 years of glyphosate usefulness (18 v. 13 years) even in the most rapid cases of resistance evolution. Delaying tactics are thus available that can provide some or many years of continued glyphosate efficacy. If glyphosate-resistant cotton cropping is to remain profitable in Australian farming systems in the long-term, however, growers must adapt to the probability that they will have to deal with summer weeds that are no longer susceptible to glyphosate. Robust resistance management systems will need to include a diversity of weed control options, used appropriately.

Assessing the sustainability of wheat-based cropping systems using simulation modelling: sustainability

Concepts of agricultural sustainability and possible roles of simulation modelling for characterising sustainability were explored by conducting, and reflecting on, a sustainability assessment of rain-fed wheat-based systems in the Middle East and North Africa region. We designed a goal-oriented, model-based framework using the cropping systems model Agricultural Production Systems sIMulator (APSIM). For the assessment, valid (rather than true or false) sustainability goals and indicators were identified for the target system. System-specific vagueness was depicted in sustainability polygons-a system property derived from highly quantitative data-and denoted using descriptive quantifiers. Diagnostic evaluations of alternative tillage practices demonstrated the utility of the framework to quantify key bio-physical and chemical constraints to sustainability. Here, we argue that sustainability is a vague, emergent system property of often wicked complexity that arises out of more fundamental elements and processes. A 'wicked concept of sustainability' acknowledges the breadth of the human experience of sustainability, which cannot be internalised in a model. To achieve socially desirable sustainability goals, our model-based approach can inform reflective evaluation processes that connect with the needs and values of agricultural decision-makers. Hence, it can help to frame meaningful discussions, from which actions might emerge.