Thermal requirements, field mortality and population phenology modelling of Paropsis atomaria Olivier, an emergent pest in subtropical hardwood plantations

Paropsis atomaria is a recently emerged pest of eucalypt plantations in subtropical Australia. Its broad host range of at least 20 eucalypt species and wide geographical distribution provides it the potential to become a serious forestry pest both within Australia and, if accidentally introduced, overseas. Although populations of P. atomaria are genetically similar throughout its range, population dynamics differ between regions. Here, we determine temperature-dependent developmental requirements using beetles sourced from temperate and subtropical zones by calculating lower temperature thresholds, temperature-induced mortality, and day-degree requirements. We combine these data with field mortality estimates of immature life stages to produce a cohort-based model, ParopSys, using DYMEX™ that accurately predicts the timing, duration, and relative abundance of life stages in the field and number of generations in a spring–autumn (September–May) field season. Voltinism was identified as a seasonally plastic trait dependent upon environmental conditions, with two generations observed and predicted in the Australian Capital Territory, and up to four in Queensland. Lower temperature thresholds for development ranged between 4 and 9 °C, and overall development rates did not differ according to beetle origin. Total immature development time (egg–adult) was approximately 769.2 ± S.E. 127.8 DD above a lower temperature threshold of 6.4 ± S.E. 2.6 °C. ParopSys provides a basic tool enabling forest managers to use the number of generations and seasonal fluctuations in abundance of damaging life stages to estimate the pest risk of P. atomaria prior to plantation establishment, and predict the occurrence and duration of damaging life stages in the field. Additionally, by using local climatic data the pest potential of P. atomaria can be estimated to predict the risk of it establishing if accidentally introduced overseas. Improvements to ParopSys’ capability and complexity can be made as more biological data become available.

Context-Based Modelling of Interferometric Signals for the Assessment of Tear-Film Suface Quality

Modelling of interferometric signals related to tear film surface quality is considered. In the context of tear film surface quality estimation in normal healthy eyes, two clinical parameters are of interest: the build-up time, and the average interblink surface quality. The former is closely related to the signal derivative while the latter to the signal itself. Polynomial signal models, chosen for a particular set of noisy interferometric measurements, can be optimally selected, in some sense, with a range of information criteria such as AIC, MDL, Cp, and CME. Those criteria, however, do not always guarantee that the true derivative of the signal is accurately represented and they often overestimate it. Here, a practical method for judicious selection of model order in a polynomial fitting to a signal is proposed so that the derivative of the signal is adequately represented. The paper highlights the importance of context-based signal modelling in model order selection.

Mathematical modelling of muscle recruitment and function in the lumbar spine

Low back pain is an increasing problem in industrialised countries and although it is a major socio-economic problem in terms of medical costs and lost productivity, relatively little is known about the processes underlying the development of the condition. This is in part due to the complex interactions between bone, muscle, nerves and other soft tissues of the spine, and the fact that direct observation and/or measurement of the human spine is not possible using non-invasive techniques. Biomechanical models have been used extensively to estimate the forces and moments experienced by the spine. These models provide a means of estimating the internal parameters which can not be measured directly. However, application of most of the models currently available is restricted to tasks resembling those for which the model was designed due to the simplified representation of the anatomy. The aim of this research was to develop a biomechanical model to investigate the changes in forces and moments which are induced by muscle injury. In order to accurately simulate muscle injuries a detailed quasi-static three dimensional model representing the anatomy of the lumbar spine was developed. This model includes the nine major force generating muscles of the region (erector spinae, comprising the longissimus thoracis and iliocostalis lumborum; multifidus; quadratus lumborum; latissimus dorsi; transverse abdominis; internal oblique and external oblique), as well as the thoracolumbar fascia through which the transverse abdominis and parts of the internal oblique and latissimus dorsi muscles attach to the spine. The muscles included in the model have been represented using 170 muscle fascicles each having their own force generating characteristics and lines of action. Particular attention has been paid to ensuring the muscle lines of action are anatomically realistic, particularly for muscles which have broad attachments (e.g. internal and external obliques), muscles which attach to the spine via the thoracolumbar fascia (e.g. transverse abdominis), and muscles whose paths are altered by bony constraints such as the rib cage (e.g. iliocostalis lumborum pars thoracis and parts of the longissimus thoracis pars thoracis). In this endeavour, a separate sub-model which accounts for the shape of the torso by modelling it as a series of ellipses has been developed to model the lines of action of the oblique muscles. Likewise, a separate sub-model of the thoracolumbar fascia has also been developed which accounts for the middle and posterior layers of the fascia, and ensures that the line of action of the posterior layer is related to the size and shape of the erector spinae muscle. Published muscle activation data are used to enable the model to predict the maximum forces and moments that may be generated by the muscles. These predictions are validated against published experimental studies reporting maximum isometric moments for a variety of exertions. The model performs well for fiexion, extension and lateral bend exertions, but underpredicts the axial twist moments that may be developed. This discrepancy is most likely the result of differences between the experimental methodology and the modelled task. The application of the model is illustrated using examples of muscle injuries created by surgical procedures. The three examples used represent a posterior surgical approach to the spine, an anterior approach to the spine and uni-lateral total hip replacement surgery. Although the three examples simulate different muscle injuries, all demonstrate the production of significant asymmetrical moments and/or reduced joint compression following surgical intervention. This result has implications for patient rehabilitation and the potential for further injury to the spine. The development and application of the model has highlighted a number of areas where current knowledge is deficient. These include muscle activation levels for tasks in postures other than upright standing, changes in spinal kinematics following surgical procedures such as spinal fusion or fixation, and a general lack of understanding of how the body adjusts to muscle injuries with respect to muscle activation patterns and levels, rate of recovery from temporary injuries and compensatory actions by other muscles. Thus the comprehensive and innovative anatomical model which has been developed not only provides a tool to predict the forces and moments experienced by the intervertebral joints of the spine, but also highlights areas where further clinical research is required.

Mathematical modelling in the early school years

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the Butter Beans Problem and the Airplane Problem). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data, together with background information containing specific criteria to be considered in the solution process. Four classes of third-graders (8 years of age) and their teachers participated in the 6-month program, which included preparatory modelling activities along with professional development for the teachers. In discussing our findings we address: (a) Ways in which the children applied their informal, personal knowledge to the problems; (b) How the children interpreted the tables of data, including difficulties they experienced; (c) How the children operated on the data, including aggregating and comparing data, and looking for trends and patterns; (c) How the children developed important mathematical ideas; and (d) Ways in which the children represented their mathematical understandings.

Young children's early modelling with data

An educational priority of many nations is to enhance mathematical learning in early childhood. One area in need of special attention is that of statistics. This paper argues for a renewed focus on statistical reasoning in the beginning school years, with opportunities for children to engage in data modelling activities. Such modelling involves investigations of meaningful phenomena, deciding what is worthy of attention (i.e., identifying complex attributes), and then progressing to organising, structuring, visualising, and representing data. Results are reported from the first year of a three-year longitudinal study in which three classes of first-grade children and their teachers engaged in activities that required the creation of data models. The theme of “Looking after our Environment,” a component of the children’s science curriculum at the time, provided the context for the activities. Findings focus on how the children dealt with given complex attributes and how they generated their own attributes in classifying broad data sets, and the nature of the models the children created in organising, structuring, and representing their data.

Interdisciplinary modelling

This article examines one approach to promoting creative and flexible use of mathematical ideas within an interdisciplinary context in the primary curriculum, namely, through modelling. Three classes of fifth-grade children worked on a modelling problem, The First Fleet (Australia’s settlement), situated within the curriculum domains of science and studies of society and environment. Reported here are the cycles of development displayed by one group of children as they worked the problem, together with the range of models created across the classes. Children developed mathematisation processes that extended beyond their regular curriculum, including identifying and prioritising key problem elements, exploring relationships among elements, quantifying qualitative data, ranking and aggregating data, and creating and working with weighted scores. Aspects of Goldin’s (2000, 2007) affective structures also appeared to play an important role in the children's mathematical developments.