Estimation in a multiplicative mixed model involving a genetic relationship matrix.

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.

Estimation of light interception in research environments: A joint approach using directional light sensors and 3D virtual plants applied to sunflower (Helianthus annuus) and Arabidopsis thaliana in natural and artificial conditions

Light interception is a major factor influencing plant development and biomass production. Several methods have been proposed to determine this variable, but its calculation remains difficult in artificial environments with heterogeneous light. We propose a method that uses 3D virtual plant modelling and directional light characterisation to estimate light interception in highly heterogeneous light environments such as growth chambers and glasshouses. Intercepted light was estimated by coupling an architectural model and a light model for different genotypes of the rosette species Arabidopsis thaliana (L.) Heynh and a sunflower crop. The model was applied to plants of contrasting architectures, cultivated in isolation or in canopy, in natural or artificial environments, and under contrasting light conditions. The model gave satisfactory results when compared with observed data and enabled calculation of light interception in situations where direct measurements or classical methods were inefficient, such as young crops, isolated plants or artificial conditions. Furthermore, the model revealed that A. thaliana increased its light interception efficiency when shaded. To conclude, the method can be used to calculate intercepted light at organ, plant and plot levels, in natural and artificial environments, and should be useful in the investigation of genotype-environment interactions for plant architecture and light interception efficiency. This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Non-specific conducting polymer-based array capable of monitoring odour emissions from a biofiltration system in a piggery building

A commercial non-specific gas sensor array system was evaluated in terms of its capability to monitor the odour abatement performance of a biofiltration system developed for treating emissions from a commercial piggery building. The biofiltration system was a modular system comprising an inlet ducting system, humidifier and closed-bed biofilter. It also included a gravimetric moisture monitoring and water application system for precise control of moisture content of an organic woodchip medium. Principal component analysis (PCA) of the sensor array measurements indicated that the biofilter outlet air was significantly different to both inlet air of the system and post-humidifier air. Data pre-processing techniques including normalising and outlier handling were applied to improve the odour discrimination performance of the non-specific gas sensor array. To develop an odour quantification model using the sensor array responses of the non-specific sensor array, PCA regression, artificial neural network (ANN) and partial least squares (PLS) modelling techniques were applied. The correlation coefficient (r(2)) values of the PCA, ANN, and PLS models were 0.44, 0.62 and 0.79, respectively.

Parameter estimation and sensitivity analysis of fat deposition models in beef steers using acslXtreme.

The Davis Growth Model (a dynamic steer growth model encompassing 4 fat deposition models) is currently being used by the phenotypic prediction program of the Cooperative Research Centre (CRC) for Beef Genetic Technologies to predict P8 fat (mm) in beef cattle to assist beef producers meet market specifications. The concepts of cellular hyperplasia and hypertrophy are integral components of the Davis Growth Model. The net synthesis of total body fat (kg) is calculated from the net energy available after accounting tor energy needs for maintenance and protein synthesis. Total body fat (kg) is then partitioned into 4 fat depots (intermuscular, intramuscular, subcutaneous, and visceral). This paper reports on the parameter estimation and sensitivity analysis of the DNA (deoxyribonucleic acid) logistic growth equations and the fat deposition first-order differential equations in the Davis Growth Model using acslXtreme (Hunstville, AL, USA, Xcellon). The DNA and fat deposition parameter coefficients were found to be important determinants of model function; the DNA parameter coefficients with days on feed >100 days and the fat deposition parameter coefficients for all days on feed. The generalized NL2SOL optimization algorithm had the fastest processing time and the minimum number of objective function evaluations when estimating the 4 fat deposition parameter coefficients with 2 observed values (initial and final fat). The subcutaneous fat parameter coefficient did indicate a metabolic difference for frame sizes. The results look promising and the prototype Davis Growth Model has the potential to assist the beef industry meet market specifications.

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.

Simple software processes and tests improve the reliability and usefulness of a model.

Models are abstractions of reality that have predetermined limits (often not consciously thought through) on what problem domains the models can be used to explore. These limits are determined by the range of observed data used to construct and validate the model. However, it is important to remember that operating the model beyond these limits, one of the reasons for building the model in the first place, potentially brings unwanted behaviour and thus reduces the usefulness of the model. Our experience with the Agricultural Production Systems Simulator (APSIM), a farming systems model, has led us to adapt techniques from the disciplines of modelling and software development to create a model development process. This process is simple, easy to follow, and brings a much higher level of stability to the development effort, which then delivers a much more useful model. A major part of the process relies on having a range of detailed model tests (unit, simulation, sensibility, validation) that exercise a model at various levels (sub-model, model and simulation). To underline the usefulness of testing, we examine several case studies where simulated output can be compared with simple relationships. For example, output is compared with crop water use efficiency relationships gleaned from the literature to check that the model reproduces the expected function. Similarly, another case study attempts to reproduce generalised hydrological relationships found in the literature. This paper then describes a simple model development process (using version control, automated testing and differencing tools), that will enhance the reliability and usefulness of a model.

Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual’s previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag–recapture data and tag–recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

An improved simulation model to predict pre-harvest aflatoxin risk in maize

Aflatoxin is a potent carcinogen produced by Aspergillus flavus, which frequently contaminates maize (Zea mays L.) in the field between 40° north and 40° south latitudes. A mechanistic model to predict risk of pre-harvest contamination could assist in management of this very harmful mycotoxin. In this study we describe an aflatoxin risk prediction model which is integrated with the Agricultural Production Systems Simulator (APSIM) modelling framework. The model computes a temperature function for A. flavus growth and aflatoxin production using a set of three cardinal temperatures determined in the laboratory using culture medium and intact grains. These cardinal temperatures were 11.5 °C as base, 32.5 °C as optimum and 42.5 °C as maximum. The model used a low (≤0.2) crop water supply to demand ratio—an index of drought during the grain filling stage to simulate maize crop's susceptibility to A. flavus growth and aflatoxin production. When this low threshold of the index was reached the model converted the temperature function into an aflatoxin risk index (ARI) to represent the risk of aflatoxin contamination. The model was applied to simulate ARI for two commercial maize hybrids, H513 and H614D, grown in five multi-location field trials in Kenya using site specific agronomy, weather and soil parameters. The observed mean aflatoxin contamination in these trials varied from <1 to 7143 ppb. ARI simulated by the model explained 99% of the variation (p ≤ 0.001) in a linear relationship with the mean observed aflatoxin contamination. The strong relationship between ARI and aflatoxin contamination suggests that the model could be applied to map risk prone areas and to monitor in-season risk for genotypes and soils parameterized for APSIM.

An improved simulation model to predict pre-harvest aflatoxin risk in maize

Aflatoxin is a potent carcinogen produced by Aspergillus flavus, which frequently contaminates maize (Zea mays L.) in the field between 40° north and 40° south latitudes. A mechanistic model to predict risk of pre-harvest contamination could assist in management of this very harmful mycotoxin. In this study we describe an aflatoxin risk prediction model which is integrated with the Agricultural Production Systems Simulator (APSIM) modelling framework. The model computes a temperature function for A. flavus growth and aflatoxin production using a set of three cardinal temperatures determined in the laboratory using culture medium and intact grains. These cardinal temperatures were 11.5 °C as base, 32.5 °C as optimum and 42.5 °C as maximum. The model used a low (≤0.2) crop water supply to demand ratio—an index of drought during the grain filling stage to simulate maize crop's susceptibility to A. flavus growth and aflatoxin production. When this low threshold of the index was reached the model converted the temperature function into an aflatoxin risk index (ARI) to represent the risk of aflatoxin contamination. The model was applied to simulate ARI for two commercial maize hybrids, H513 and H614D, grown in five multi-location field trials in Kenya using site specific agronomy, weather and soil parameters. The observed mean aflatoxin contamination in these trials varied from <1 to 7143 ppb. ARI simulated by the model explained 99% of the variation (p ≤ 0.001) in a linear relationship with the mean observed aflatoxin contamination. The strong relationship between ARI and aflatoxin contamination suggests that the model could be applied to map risk prone areas and to monitor in-season risk for genotypes and soils parameterized for APSIM.

Maximum likelihood estimation of natural mortality and quantification of temperature effects on catchability of brown tiger prawn (Penaeus esculentus) in Moreton Bay (Australia) using logbook data

It is common to model the dynamics of fisheries using natural and fishing mortality rates estimated independently using two separate analyses. Fishing mortality is routinely estimated from widely available logbook data, whereas natural mortality estimations have often required more specific, less frequently available, data. However, in the case of the fishery for brown tiger prawn (Penaeus esculentus) in Moreton Bay, both fishing and natural mortality rates have been estimated from logbook data. The present work extended the fishing mortality model to incorporate an eco-physiological response of tiger prawn to temperature, and allowed recruitment timing to vary from year to year. These ecological characteristics of the dynamics of this fishery were ignored in the separate model that estimated natural mortality. Therefore, we propose to estimate both natural and fishing mortality rates within a single model using a consistent set of hypotheses. This approach was applied to Moreton Bay brown tiger prawn data collected between 1990 and 2010. Natural mortality was estimated by maximum likelihood to be equal to 0.032 ± 0.002 week−1, approximately 30% lower than the fixed value used in previous models of this fishery (0.045 week−1).