Modelling the movement of interacting cell populations: A moment dynamics approach

Mathematical models describing the movement of multiple interacting subpopulations are relevant to many biological and ecological processes. Standard mean-field partial differential equation descriptions of these processes suffer from the limitation that they implicitly neglect to incorporate the impact of spatial correlations and clustering. To overcome this, we derive a moment dynamics description of a discrete stochastic process which describes the spreading of distinct interacting subpopulations. In particular, we motivate our model by mimicking the geometry of two typical cell biology experiments. Comparing the performance of the moment dynamics model with a traditional mean-field model confirms that the moment dynamics approach always outperforms the traditional mean-field approach. To provide more general insight we summarise the performance of the moment dynamics model and the traditional mean-field model over a wide range of parameter regimes. These results help distinguish between those situations where spatial correlation effects are sufficiently strong, such that a moment dynamics model is required, from other situations where spatial correlation effects are sufficiently weak, such that a traditional mean-field model is adequate.

A new semi-dwarfing gene identified by molecular mapping of quantitative trait loci in barley.

Semi-dwarfing genes have been widely used in spring barley (Hordeum vulgare L.) breeding programs in many parts of the world, but the success in developing barley cultivars with semi-dwarfing genes has been limited in North America. Exploiting new semi-dwarfing genes may help in solving this dilemma. A recombinant inbred line population was developed by crossing ZAU 7, a semi-dwarf cultivar from China, to ND16092, a tall breeding line from North Dakota. To identify quantitative trait loci (QTL) controlling plant height, a linkage map comprised of 111 molecular markers was constructed. Simple interval mapping was performed for each of the eight environments. A consistent QTL for plant height was found on chromosome 7HL. This QTL is not associated with maturity and rachis internode length. We suggest the provisional name Qph-7H for this QTL. Qph-7H from ZAU 7 reduced plant height to about 3/4 of normal; thus, Qph-7H is considered a semi-dwarfing gene. Other QTLs for plant height were found, but their expression was variable across the eight environments tested.

Analysis and Modelling of the Effects of Water Stress on Maize Growth and Yield in Dryland Conditions.

It is essential to provide experimental evidence and reliable predictions of the effects of water stress on crop production in the drier, less predictable environments. A field experiment undertaken in southeast Queensland, Australia with three water regimes (fully irrigated, rainfed and irrigated until late canopy expansion followed by rainfed) was used to compare effects of water stress on crop production in two maize (Zea mays L.) cultivars (Pioneer 34N43 and Pioneer 31H50). Water stress affected growth and yield more in Pioneer 34N43 than in Pioneer 31H50. A crop model APSIM-Maize, after having been calibrated for the two cultivars, was used to simulate maize growth and development under water stress. The predictions on leaf area index (LAI) dynamics, biomass growth and grain yield under rain fed and irrigated followed by rain fed treatments was reasonable, indicating that stress indices used by APSIM-Maize produced appropriate adjustments to crop growth and development in response to water stress. This study shows that Pioneer 31H50 is less sensitive to water stress and thus a preferred cultivar in dryland conditions, and that it is feasible to provide sound predictions and risk assessment for crop production in drier, more variable conditions using the APSIM-Maize model.

High resolution satellite imagery and GPS collars can help assist in the assessment of patch selection by grazing cattle in semi-arid savannas.

The selection of different patch types for grazing by cattle in tropical savannas is well documented. Advances in high resolution satellite imagery and computing power now allow us to identify patch types over an entire paddock, combined with GPS collars as a non instrusive method of capturing positional data, an accurate and comprehensive picture of landscape use by cattle can be quantified.

Patch selection by cattle can be quantified using satellite imagery and GPS in extensive, semi-arid savannas.

Patch selection by grazing animals is difficult to quantify, particularly in large, extensive paddocks like those in northern Australia. However, advances in high resolution satellite imagery now allow identification of patch types over an entire paddock which combined with GPS collars to capture positional data, can give an accurate and comprehensive picture of landscape use by cattle.

Modelling the distribution and relative abundance of feral camels in the Northern Territory using count data

The objectives of this study were to predict the potential distribution, relative abundance and probability of habitat use by feral camels in southern Northern Territory. Aerial survey data were used to model habitat association. The characteristics of ‘used’ (where camels were observed) v. ‘unused’ (pseudo-absence) sites were compared. Habitat association and abundance were modelled using generalised additive model (GAM) methods. The models predicted habitat suitability and the relative abundance of camels in southern Northern Territory. The habitat suitability maps derived in the present study indicate that camels have suitable habitat in most areas of southern Northern Territory. The index of abundance model identified areas of relatively high camel abundance. Identifying preferred habitats and areas of high abundance can help focus control efforts.

Best use modelling for sustainable Australia sports field surfaces

The Best Use Modelling for Sustainable Australian Sports Field Surfaces project has achieved significant success. The project has attracted participation from councils throughout Australia, with in excess of 300 sports fields evaluated from 18 councils to date. An important project component is the derivation of a recommended standard procedure for specifying the performance of playing surfaces. An associated step has been to establish recommended playing surface performance standards for community level sports fields. The derived modelling also provides information on the expected usage and associated costs of different sports surface development options. This is expected to assist the Australian turf production industry through demonstrating to councils that cost effective natural turf options exist that can meet higher usage expectation (as a viable alternative to synthetic turf). A web-accessed data base system will be made available to councils from January 2010 on (reference to www.passturf.com). This system will enable participating councils to record and analyse field performance over time. The system is considered world-leading, and will help keep the Australian parks industry to the international forefront. Tools developed as part of the project offer councils the opportunity to internally assess the performance of their current sports field provision, to identify any deficiencies and to determine the best corrective measure if any deficiency is identified. This is expected to offer community benefits to both sports facility providers and facility user groups. In turn this will aid the provision of affordable community access to safe and good quality playing surfaces. Tools and associated information material will be made available to councils throughout Australia by the end of this year, via the Parks and Leisure Aust. web site. The Best Use Modelling Project is work in progress. On-going input will be needed to ensure the web-accessed database software is as user friendly as possible, new performance testing data will need to be inputted, and tools provided to participating councils updated. Through the support of HAL there is now a well-structured, nationally-supported system in place for benchmarking playing surfaces and for assisting councils to optimise their resource allocation to sports field upgrade or maintenance work.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

Modelling the nitrogen-driven trade-off between nitrogen utilisation efficiency and water use efficiency of wheat in eastern Australia.

The nitrogen-driven trade-off between nitrogen utilisation efficiency (yield per unit nitrogen uptake) and water use efficiency (yield per unit evapotranspiration) is widespread and results from well established, multiple effects of nitrogen availability on the water, carbon and nitrogen economy of crops. Here we used a crop model (APSIM) to simulate the yield, evapotranspiration, soil evaporation and nitrogen uptake of wheat, and analysed yield responses to water, nitrogen and climate using a framework analogous to the rate-duration model of determinate growth. The relationship between modelled grain yield (Y) and evapotranspiration (ET) was fitted to a linear-plateau function to derive three parameters: maximum yield (Ymax), the ET break-point when yield reaches its maximum (ET#), and the rate of yield response in the linear phase ([Delta]Y/[Delta]ET). Against this framework, we tested the hypothesis that nitrogen deficit reduces maximum yield by reducing both the rate ([Delta]Y/[Delta]ET) and the range of yield response to evapotranspiration, i.e. ET# - Es, where Es is modelled median soil evaporation. Modelled data reproduced the nitrogen-driven trade-off between nitrogen utilisation efficiency and water use efficiency in a transect from Horsham (36°S) to Emerald (23°S) in eastern Australia. Increasing nitrogen supply from 50 to 250 kg N ha-1 reduced yield per unit nitrogen uptake from 29 to 12 kg grain kg-1 N and increased yield per unit evapotranspiration from 6 to 15 kg grain ha-1 mm-1 at Emerald. The same increment in nitrogen supply reduced yield per unit nitrogen uptake from 30 to 25 kg grain kg-1 N and increased yield per unit evapotranspiration from 6 to 25 kg grain ha-1 mm-1 at Horsham. Maximum yield ranged from 0.9 to 6.4 t ha-1. Consistent with our working hypothesis, reductions in maximum yield with nitrogen deficit were associated with both reduction in the rate of yield response to ET and compression of the range of yield response to ET. Against the notion of managing crops to maximise water use efficiency in low rainfall environments, we emphasise the trade-off between water use efficiency and nitrogen utilisation efficiency, particularly under conditions of high nitrogen-to-grain price ratio. The rate-range framework to characterise the relationship between yield and evapotranspiration is useful to capture this trade-off as the parameters were responsive to both nitrogen supply and climatic factors.

Resilience of a high-conservation-value, semi-arid grassland on fertile clay soils to burning, mowing and ploughing.

In grassland reserves, managed disturbance is often necessary to maintain plant species diversity. We carried out experiments to determine the impact of fire, kangaroo grazing, mowing and disc ploughing on grassland species richness and composition in a nature reserve in semi-arid eastern Australia. Vegetation response was influenced by winter-spring drought after establishment of the experiments, but moderate rainfall followed in late summer-autumn. Species composition varied greatly between sampling times, and the variability due to rainfall differences between seasons and years was greater than the effects of fire, kangaroo grazing, mowing or disc ploughing. In the fire experiment, species richness and composition recovered more rapidly after spring than autumn burning. Species richness and composition were similar to control sites within 12 months of burning and mowing, suggesting that removal of the dominant grass canopy is unnecessary to enhance plant diversity. Two fires (separated by 3 years) and post-fire kangaroo grazing had only minor influence on species richness and composition. Even disc ploughing caused only a small reduction in native richness. The minor impact of ploughing was explained by the small areas that were ploughed, the once-off nature of the treatment, and the high degree of natural movement and cracking in these shrink-swell soils. Recovery of the composition and richness of these grasslands was rapid because of the high proportion of perennial species that resprout vegetatively after fire and mowing. There appears to be little conservation benefit from fire, mowing or ploughing ungrazed areas, as we could identify no native plant species dependent on frequent disturbance for persistence in this grassland community. However, the ability of the Astrebla- and Dichanthium-dominated grasslands to recover quickly after disturbance, given favourable seasonal conditions, suggests that they are well adapted to natural disturbances (e.g. droughts, fire, flooding and native grazing).

Characterisation of wood properties and transverse anatomy for vacuum drying modelling of commercially important Australian hardwood species.

Characterisation and investigation of a number of key wood properties, critical for further modelling work, has been achieved. The key results were: • Morphological characterisation, in terms of fibre cell wall thickness and porosity, was completed. A clear difference in fibre porosity, size, wall thickness and orientation was evident between species. Results were consistent with published data for other species. • Viscoelastic properties of wood were shown to differ greatly between species and in the radial and tangential directions, largely due to anatomical and chemical variations. Consistent with published data, the radial direction shows higher stiffness, internal friction and glass transition temperature than the tangential directions. The loss of stiffness over the measured temperature range was greater in the tangential direction than the radial direction. Due to time dependant molecular relaxation, the storage modulus and glass transition temperature decreased with decreasing test frequency, approaching an asymptotic limit. Thus the viscoelastic properties measured at lower frequencies are more representative of static material. • Dynamic interactions between relative humidity, moisture content and shrinkage of four Australian hardwood timbers can be accurately monitored on micro-samples using a specialised experimental device developed by AgroParisTech – ENGREF. The device generated shrinkage data that varied between species but were consistent (repeatable) within a species. Collapse shrinkage was clearly evident with this method for Eucalyptus obliqua, but not with other species, consistent with industrial seasoning experience. To characterise the wood-water relations of this species, free of collapse, thinner sample sections (in the R-T plane) should be used.

Unsteady flow of a dilute suspension in a semi-infinite contracting or expanding pipe

In the present paper an exact similar solution of the Navier-Stokes equation for unsteady flow of a dilute suspension in a semi-infinite contracting or expanding circular pipe is presented. The effects of the Schmidt number (Sc), Reynolds number (|ε|), the volume fraction (α) and the relaxation time (τ) of the particulate phase on the flow characteristics are examined. The presence of the solid particles has been observed to influence the flow behaviour significantly. These solutions are valid down to the state of a completely collapsed pipe, since the nonlinearity is retained fully. The results may help understanding the flow near the heart and certain forced contractions or expansions of valved veins.

Iterative modelling for stress analysis of composite laminates

The importance of interlaminar stresses has prompted a fresh look at the theory of laminated plates. An important feature in modelling such laminates is the need to provide for continuity of some strains and stresses, while at the same time allowing for the discontinuities in the others. A new modelling possibility is examined in this paper. The procedure allows for discontinuities in the in-plane stresses and transverse strains and continuity in the in-plane strains and transverse stresses. This theory is in the form of a heirarchy of formulations each representing an iterative step. Application of the theory is illustrated by considering the example of an infinite laminated strip subjected to sinusoidal loading.

Numerical modelling of deformation behaviour of red blood cells in microvessels using the coupled SPH-DEM method

This thesis developed an advanced computational model to investigate the motion and deformation properties of red blood cells in capillaries. The novel model is based on the meshfree particle methods and is capable of modelling the large deformation of red blood cells moving through blood vessels. The developed model was employed to simulate the deformation behaviour of healthy and malaria infected red blood cells as well as the motion of red blood cells in stenosed capillaries.

Environment characterization as an aid to wheat improvement: interpreting genotype-environment interactions by modelling water-deficit patterns in North-Eastern Australia.

Genotype-environment interactions (GEI) limit genetic gain for complex traits such as tolerance to drought. Characterization of the crop environment is an important step in understanding GEI. A modelling approach is proposed here to characterize broadly (large geographic area, long-term period) and locally (field experiment) drought-related environmental stresses, which enables breeders to analyse their experimental trials with regard to the broad population of environments that they target. Water-deficit patterns experienced by wheat crops were determined for drought-prone north-eastern Australia, using the APSIM crop model to account for the interactions of crops with their environment (e.g. feedback of plant growth on water depletion). Simulations based on more than 100 years of historical climate data were conducted for representative locations, soils, and management systems, for a check cultivar, Hartog. The three main environment types identified differed in their patterns of simulated water stress around flowering and during grain-filling. Over the entire region, the terminal drought-stress pattern was most common (50% of production environments) followed by a flowering stress (24%), although the frequencies of occurrence of the three types varied greatly across regions, years, and management. This environment classification was applied to 16 trials relevant to late stages testing of a breeding programme. The incorporation of the independently-determined environment types in a statistical analysis assisted interpretation of the GEI for yield among the 18 representative genotypes by reducing the relative effect of GEI compared with genotypic variance, and helped to identify opportunities to improve breeding and germplasm-testing strategies for this region.