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.

Reassessing spatial and temporal dynamics of kangaroo populations

Long-running datasets from aerial surveys of kangaroos (Macropus giganteus, Macropus [uliginosus, Macropus robustus and Macropus rufus) across Queensland, New South Wales and South Australia have been analysed, seeking better predictors of rates of increase which would allow aerial surveys to be undertaken less frequently than annually. Early models of changes in kangaroo numbers in response to rainfall had shown great promise, but much variability. We used normalised difference vegetation index (NDVI) instead, reasoning that changes in pasture condition would provide a better predictor than rainfall. However, except at a fine scale, NDVI proved no better; although two linked periods of rainfall proved useful predictors of rates of increase, this was only in some areas for some species. The good correlations reported in earlier studies were a consequence of data dominated by large droughtinduced adult mortality, whereas over a longer time frame and where changes between years are less dramatic, juvenile survival has the strongest influence on dynamics. Further, harvesting, density dependence and competition with domestic stock are additional and important influences and it is now clear that kangaroo movement has a greater influence on population dynamics than had been assumed. Accordingly, previous conclusions about kangaroo populations as simple systems driven by rainfall need to be reassessed. Examination of this large dataset has permitted descriptions of shifts in distribution of three species across eastern Australia, changes in dispersion in response to rainfall, and an evaluation of using harvest statistics as an index of density and harvest rate. These results have been combined into a risk assessment and decision theory framework to identify optimal monitoring strategies.

Impacts of grazing management options on pasture and animal productivity in a Heteropogon contortus (black speargrass) pasture in central Queensland. 2. Population dynamics of Heteropogon contortus and Stylosanthes scabra cv. Seca.

The dynamics of Heteropogon contortus and Stylosanthes scabra cv. Seca populations were studied in a subset of treatments in an extensive grazing study conducted in central Queensland between 1988 and 2001. These treatments were 4 stocking rates in native pasture and 2 of these stocking rates in legume oversown and supplement/spring burning treatments. For the 1999-2000 summer, population data for H. contortus in 5 of these native pasture and supplement/burning treatments were compared with those for an additional burnt treatment. Seasonal rainfall throughout this study was below the long-term mean and mean annual pasture utilisation ranged from 24 to 61%. Increasing stocking rate from 5 to 2 ha/steer in native pasture reduced H. contortus plant density. Increasing stocking rate reduced seedling recruitment as a result of its effect on soil seedbanks. Seedling recruitment was the major determinant of change in plant density, although some individual H. contortus plants did survive throughout the study. Burning in spring 1999, particularly at light stocking rate, promoted seedling recruitment above that in both unburnt native and legume oversown pasture and resulted in increased H. contortus plant density. In the legume oversown treatments, S. scabra cv. Seca density increased rapidly from 15 plants/m2 in 1988 to 140 plants/m2 in 2001 following a lag phase between 1988 and 1993. This increased S. scabra density was associated with an eventual decline in H. contortus plant density through reduced seedling recruitment. It was concluded that H. contortus population density is sustainable at stocking rates of 4 and 5 ha/steer (30% pasture utilisation) and that spring burning at light stocking rate can promote H. contortus populations. Increasing densities of S. scabra need to be managed to prevent its dominance.

Net radiation dynamics: performance of 20 daily net radiation models as related to model structure and intricacy in two climates.

We compared daily net radiation (Rn) estimates from 19 methods with the ASCE-EWRI Rn estimates in two climates: Clay Center, Nebraska (sub-humid) and Davis, California (semi-arid) for the calendar year. The performances of all 20 methods, including the ASCE-EWRI Rn method, were then evaluated against Rn data measured over a non-stressed maize canopy during two growing seasons in 2005 and 2006 at Clay Center. Methods differ in terms of inputs, structure, and equation intricacy. Most methods differ in estimating the cloudiness factor, emissivity (e), and calculating net longwave radiation (Rnl). All methods use albedo (a) of 0.23 for a reference grass/alfalfa surface. When comparing the performance of all 20 Rn methods with measured Rn, we hypothesized that the a values for grass/alfalfa and non-stressed maize canopy were similar enough to only cause minor differences in Rn and grass- and alfalfa-reference evapotranspiration (ETo and ETr) estimates. The measured seasonal average a for the maize canopy was 0.19 in both years. Using a = 0.19 instead of a = 0.23 resulted in 6% overestimation of Rn. Using a = 0.19 instead of a = 0.23 for ETo and ETr estimations, the 6% difference in Rn translated to only 4% and 3% differences in ETo and ETr, respectively, supporting the validity of our hypothesis. Most methods had good correlations with the ASCE-EWRI Rn (r2 > 0.95). The root mean square difference (RMSD) was less than 2 MJ m-2 d-1 between 12 methods and the ASCE-EWRI Rn at Clay Center and between 14 methods and the ASCE-EWRI Rn at Davis. The performance of some methods showed variations between the two climates. In general, r2 values were higher for the semi-arid climate than for the sub-humid climate. Methods that use dynamic e as a function of mean air temperature performed better in both climates than those that calculate e using actual vapor pressure. The ASCE-EWRI-estimated Rn values had one of the best agreements with the measured Rn (r2 = 0.93, RMSD = 1.44 MJ m-2 d-1), and estimates were within 7% of the measured Rn. The Rn estimates from six methods, including the ASCE-EWRI, were not significantly different from measured Rn. Most methods underestimated measured Rn by 6% to 23%. Some of the differences between measured and estimated Rn were attributed to the poor estimation of Rnl. We conducted sensitivity analyses to evaluate the effect of Rnl on Rn, ETo, and ETr. The Rnl effect on Rn was linear and strong, but its effect on ETo and ETr was subsidiary. Results suggest that the Rn data measured over green vegetation (e.g., irrigated maize canopy) can be an alternative Rn data source for ET estimations when measured Rn data over the reference surface are not available. In the absence of measured Rn, another alternative would be using one of the Rn models that we analyzed when all the input variables are not available to solve the ASCE-EWRI Rn equation. Our results can be used to provide practical information on which method to select based on data availability for reliable estimates of daily Rn in climates similar to Clay Center and Davis.

Collaborative learning approach to introduce computational fluid dynamics

This paper presents the design, implementation and evaluation of a collaborative learning activity designed to replace traditional face-to-face lectures in a large classroom. This activity aims to better engage the students with their learning and improve the students’ experience and outcomes. This project is implemented in the Fluid Mechanics unit of the Mechanical Engineering degree at the Queensland University of Technology to introduce students with the concept, terminology and process of Computational Fluid Dynamics (CFD). The approach integrates a constructive collaborative assignment which is a key element in the overall quality of teaching and learning, and an integral component of the students’ experience. A detailed survey, given to the students, showed an overall high level of satisfaction. However, the results also highlighted the gap between students’ expectations both for contents and assignment and teacher expectations. Discussions to address this issue are presented in the paper based on a critical reflection.

A molecular dynamics investigation of the structure of PbO---PbF2 glasses*1

The structure of PbO---PbF2 glasses has been studied using molecular dynamics (MD). The existence of [OPb4] structural units is observed over the entire glass-forming range, in conformity with a model proposed earlier based on various structural investigations of this system. Various other features of the structural model are also supported by the MD calculations.

A conformational approach to the study of the dynamics of enzyme inhibition: studies on thermolysin

The preferred conformations of β-phenylpropionyl-Image -phenylalanine (β-PPP) and N-carbobenzoxy-L-phenylalanine (Cbz-Phe), two inhibitors of thermolysin, have been determined by computing potential energy using empirial potential energy functions. Of the 15 to 20 conformations that are favoured for each of these inhibitors only a few have the right conformation to reach the active site of the enzyme. The conformer of β-PPP that initiates binding with the enzyme is different from the bound one, while for Cbz-Phe the bound and initiating conformers are quite similar. Thus, β-PPP favours the ‘induced fit’ model while Cbz-Phe follows the ‘lock and key’ model of binding. The inhibitors differ in their alignment at the active site.

Isomerization Dynamics In Solution In The Absence Of An Activation Barrier - Evaluation Of The Potential Parameters

We analyze recent experimental results of Sundström and Gillbro by using the theory of Bagchi, Fleming and Oxtoby. The experimental results are in good agreement with this theory, but not with the earlier theory of Förster and Hoffmann. By fitting the new experimental results to the theory, we obtain approximate estimates of the frequency of the excited surface (assumed harmonic) and the width of the sink function.

The spatiotemporal dynamics of Tribolium castaneum (Herbst): adult flight and gene flow.

Tribolium castaneum (Herbst) has been used as a model organism to develop and test important ecological and evolutionary concepts and is also a major pest of grain and grain products globally. This beetle species is assumed to be a good colonizer of grain storages through anthropogenic movement of grain, and active dispersal by flight is considered unlikely. Studies using T. castaneum have therefore used confined or walking insects. We combine an ecological study of dispersal with an analysis of gene flow using microsatellites to investigate the spatiotemporal dynamics and adult flight of T. castaneum in an ecological landscape in eastern Australia. Flying beetles were caught in traps at grain storages and in fields at least 1 km from the nearest stored grain at regular intervals for an entire year. Significantly more beetles were trapped at storages than in fields, and almost no beetles were caught in native vegetation reserves many kilometres from the nearest stored grain. Genetic differentiation between beetles caught at storages and in fields was low, indicating that although T. castaneum is predominantly aggregated around grain storages, active dispersal takes place to the extent that significant gene flow occurs between them, mitigating founder effects and genetic drift. By combining ecological and molecular techniques, we reveal much higher levels of active dispersal through adult flight in T. castaneum than previously thought. We conclude that the implications of adult flight to previous and future studies on this model organism warrant consideration.

Impact of control strategies on bellyache bush (Jatropha gossypiifolia L.) mortality, seedling recruitment, population dynamics, pasture yield and cost analysis

Bellyache bush (Jatropha gossypiifolia L.) is an invasive weed that has the potential to greatly reduce biodiversity and pasture productivity in northern Australia’s rangelands. This paper reports an approach to develop best practice options for controlling medium to dense infestations of bellyache bush using combinations of control methods. The efficacy of five single treatments including foliar spraying, slashing, stick raking, burning and do nothing (control) were compared against 15 combinations of these treatments over 4 successive years. Treatments were evaluated using several attributes, including plant mortality, changes in population demographics, seedling recruitment, pasture yield and cost of treatment. Foliar spraying once each year for 4 years proved the most cost-effective control strategy, with no bellyache bush plants recorded at the end of the study. Single applications of slashing, stick raking and to a lesser extent burning, when followed up with foliar spraying also led to significantly reduced densities of bellyache bush and changed the population from a growing one to a declining one. Total experimental cost estimates over 4 successive years for treatments where burning, stick raking, foliar spraying, and slashing were followed with foliar spraying were AU$408, AU$584, AU$802 and AU$789 ha–1, respectively. Maximum pasture yield of 5.4 t ha–1 occurred with repeated foliar spraying. This study recommends that treatment combinations using either foliar spraying alone or as a follow up with slashing, stick raking or burning are best practice options following consideration of the level of control, changes in pasture yield and cost effectiveness.

A Newton-Euler formulation for the inverse dynamics of the Stewart platform manipulator

This paper presents an inverse dynamic formulation by the Newton–Euler approach for the Stewart platform manipulator of the most general architecture and models all the dynamic and gravity effects as well as the viscous friction at the joints. It is shown that a proper elimination procedure results in a remarkably economical and fast algorithm for the solution of actuator forces, which makes the method quite suitable for on-line control purposes. In addition, the parallelism inherent in the manipulator and in the modelling makes the algorithm quite efficient in a parallel computing environment, where it can be made as fast as the corresponding formulation for the 6-dof serial manipulator. The formulation has been implemented in a program and has been used for a few trajectories planned for a test manipulator. Results of simulation presented in the paper reveal the nature of the variation of actuator forces in the Stewart platform and justify the dynamic modelling for control.

A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements. the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.

Telomere dynamics in the Sydney rock oyster (Saccostrea glomerata): an investigation into the effects of age, tissue type, location and time of sampling.

Telomere length has been purported as a biomarker for age and could offer a non-lethal method for determining the age of wild-caught individuals. Molluscs, including oysters and abalone, are the basis of important fisheries globally and have been problematic to accurately age. To determine whether telomere length could provide an alternative means of ageing molluscs, we evaluated the relationship between telomere length and age using the commercially important Sydney rock oyster (Saccostrea glomerata). Telomere lengths were estimated from tissues of known age individuals from different age classes, locations and at different sampling times. Telomere length tended to decrease with age only in young oysters less than 18 months old, but no decrease was observed in older oysters aged 2-4 years. Regional and temporal differences in telomere attrition rates were also observed. The relationship between telomere length and age was weak, however, with individuals of identical age varying significantly in their telomere length making it an imprecise age biomarker in oysters.

Fluid dynamics of the monsoon

The monsoonal regions of the world are characterized by a seasonal reversal in the direction of winds associated with the excursion of the equatorial trough (or the ITCZ) in response to the variation in the latitude of maximum insolation. This monsoonal circulation is a planetary scale phenomenon. However, the associated precipitation is critically dependent on the organization of the cumulus clouds (typically a few kilometers in horizontal extent) over the scale of synoptic vortices (typically a few hundred kilometers in horizontal extent). Thus modelling of the seasonal transitions and intraseasonal fluctuations requires an understanding of the fluid mechanics of these three scales of organizations and their interactions. The present paper is an attempt to outline the current state of understanding of these phenomena.