Stochastic growth models for analyzing crustacean data

The contemporary methodology for growth models of organisms is based on continuous trajectories and thus it hinders us from modelling stepwise growth in crustacean populations. Growth models for fish are normally assumed to follow a continuous function, but a different type of model is needed for crustacean growth. Crustaceans must moult in order for them to grow. The growth of crustaceans is a discontinuous process due to the periodical shedding of the exoskeleton in moulting. The stepwise growth of crustaceans through the moulting process makes the growth estimation more complex. Stochastic approaches can be used to model discontinuous growth or what are commonly known as "jumps" (Figure 1). However, in stochastic growth model we need to ensure that the stochastic growth model results in only positive jumps. In view of this, we will introduce a subordinator that is a special case of a Levy process. A subordinator is a non-decreasing Levy process, that will assist in modelling crustacean growth for better understanding of the individual variability and stochasticity in moulting periods and increments. We develop the estimation methods for parameter estimation and illustrate them with the help of a dataset from laboratory experiments. The motivational dataset is from the ornate rock lobster, Panulirus ornatus, which can be found between Australia and Papua New Guinea. Due to the presence of sex effects on the growth (Munday et al., 2004), we estimate the growth parameters separately for each sex. Since all hard parts are shed too often, the exact age determination of a lobster can be challenging. However, the growth parameters for the aforementioned moult processes from tank data being able to estimate through: (i) inter-moult periods, and (ii) moult increment. We will attempt to derive a joint density, which is made up of two functions: one for moult increments and the other for time intervals between moults. We claim these functions are conditionally independent given pre-moult length and the inter-moult periods. The variables moult increments and inter-moult periods are said to be independent because of the Markov property or conditional probability. Hence, the parameters in each function can be estimated separately. Subsequently, we integrate both of the functions through a Monte Carlo method. We can therefore obtain a population mean for crustacean growth (e. g. red curve in Figure 1). [GRAPHICS]

Does the size of subsamples taken from multispecies trawl catches affect estimates of catch composition and abundance?

Although subsampling is a common method for describing the composition of large and diverse trawl catches, the accuracy of these techniques is often unknown. We determined the sampling errors generated from estimating the percentage of the total number of species recorded in catches, as well as the abundance of each species, at each increase in the proportion of the sorted catch. We completely partitioned twenty prawn trawl catches from tropical northern Australia into subsamples of about 10 kg each. All subsamples were then sorted, and species numbers recorded. Catch weights ranged from 71 to 445 kg, and the number of fish species in trawls ranged from 60 to 138, and invertebrate species from 18 to 63. Almost 70% of the species recorded in catches were "rare" in subsamples (less than one individual per 10 kg subsample or less than one in every 389 individuals). A matrix was used to show the increase in the total number of species that were recorded in each catch as the percentage of the sorted catch increased. Simulation modelling showed that sorting small subsamples (about 10% of catch weights) identified about 50% of the total number of species caught in a trawl. Larger subsamples (50% of catch weight on average) identified about 80% of the total species caught in a trawl. The accuracy of estimating the abundance of each species also increased with increasing subsample size. For the "rare" species, sampling error was around 80% after sorting 10% of catch weight and was just less than 50% after 40% of catch weight had been sorted. For the "abundant" species (five or more individuals per 10 kg subsample or five or more in every 389 individuals), sampling error was around 25% after sorting 10% of catch weight, but was reduced to around 10% after 40% of catch weight had been sorted.

On Systems Thinking, Systems Biology, and the in Silico Plant

The recent summary report of a Department of Energy Workshop on Plant Systems Biology (P.V. Minorsky [2003] Plant Physiol 132: 404-409) offered a welcomed advocacy for systems analysis as essential in understanding plant development, growth, and production. The goal of the Workshop was to consider methods for relating the results of molecular research to real-world challenges in plant production for increased food supplies, alternative energy sources, and environmental improvement. The rather surprising feature of this report, however, was that the Workshop largely overlooked the rich history of plant systems analysis extending over nearly 40 years (Sinclair and Seligman, 1996) that has considered exactly those challenges targeted by the Workshop. Past systems research has explored and incorporated biochemical and physiological knowledge into plant simulation models from a number of perspectives. The research has resulted in considerable understanding and insight about how to simulate plant systems and the relative contribution of various factors in influencing plant production. These past activities have contributed directly to research focused on solving the problems of increasing biomass production and crop yields. These modeling approaches are also now providing an avenue to enhance integration of molecular genetic technologies in plant improvement (Hammer et al., 2002).

A spatially explicit multi-competitor coexistence model of penaeid (shrimp) distribution on the Australian Great Barrier Reef

A spatially explicit multi-competitor coexistence model was developed for meta-populations of prawns (shrimp) occupying habitat patches across the Great Barrier Reef, where dispersal was localised and dispersal rates varied between species. Prawns were modelled as individuals moving to and from patches or cells according to pre-set decision rules. The landscape was simulated as a matrix of cells with each cell having a spatially explicit survival index for each species. Mixed species prawn assemblages moved over this simplified spatially explicit landscape. A low level of chronic random environmental disturbance was assumed (cyclone and tropical storm damage) with additional acute spatially confined disturbance due to commercial trawling, modelled as an increase in mortality affecting inter-specific competition. The general form of the results was for increased disturbance to favour good-colonising "generalist" species at the expense of good-competitor "specialists". Increasing fishing mortality (local patch extinctions) combined with poor colonising ability resulted in low equilibrium abundance for even the best competitor, while in the same circumstances the poorest competitor but best coloniser could have the highest equilibrium abundance. This mimics the switch from high-value prawn species to lower-value prawn species as trawl effort increases, reflected in historic catch and effort logbook data and reported anecdotaly from the north Queensland trawl fleet. To match the observed distribution and behaviour of prawn assemblages, a combination inter-species competition, a spatially explicit landscape, and a defined pattern of disturbance (trawling) was required. Modelling this combination could simulate not only general trends in spatial distribution of each of prawn species but also localised concentrations observed in the survey data

Exploring profit - Sustainability trade-offs in cropping systems using evolutionary algorithms

Models that implement the bio-physical components of agro-ecosystems are ideally suited for exploring sustainability issues in cropping systems. Sustainability may be represented as a number of objectives to be maximised or minimised. However, the full decision space of these objectives is usually very large and simplifications are necessary to safeguard computational feasibility. Different optimisation approaches have been proposed in the literature, usually based on mathematical programming techniques. Here, we present a search approach based on a multiobjective evaluation technique within an evolutionary algorithm (EA), linked to the APSIM cropping systems model. A simple case study addressing crop choice and sowing rules in North-East Australian cropping systems is used to illustrate the methodology. Sustainability of these systems is evaluated in terms of economic performance and resource use. Due to the limited size of this sample problem, the quality of the EA optimisation can be assessed by comparison to the full problem domain. Results demonstrate that the EA procedure, parameterised with generic parameters from the literature, converges to a useable solution set within a reasonable amount of time. Frontier ‘‘peels’’ or Pareto-optimal solutions as described by the multiobjective evaluation procedure provide useful information for discussion on trade-offs between conflicting objectives.

A new data source for fisheries resource assessment: genetic estimates of the effective number of spawners. Final Report to the Fisheries Research and Development Corporation.

The development of innovative methods of stock assessment is a priority for State and Commonwealth fisheries agencies. It is driven by the need to facilitate sustainable exploitation of naturally occurring fisheries resources for the current and future economic, social and environmental well being of Australia. This project was initiated in this context and took advantage of considerable recent achievements in genomics that are shaping our comprehension of the DNA of humans and animals. The basic idea behind this project was that genetic estimates of effective population size, which can be made from empirical measurements of genetic drift, were equivalent to estimates of the successful number of spawners that is an important parameter in process of fisheries stock assessment. The broad objectives of this study were to 1. Critically evaluate a variety of mathematical methods of calculating effective spawner numbers (Ne) by a. conducting comprehensive computer simulations, and by b. analysis of empirical data collected from the Moreton Bay population of tiger prawns (P. esculentus). 2. Lay the groundwork for the application of the technology in the northern prawn fishery (NPF). 3. Produce software for the calculation of Ne, and to make it widely available. The project pulled together a range of mathematical models for estimating current effective population size from diverse sources. Some of them had been recently implemented with the latest statistical methods (eg. Bayesian framework Berthier, Beaumont et al. 2002), while others had lower profiles (eg. Pudovkin, Zaykin et al. 1996; Rousset and Raymond 1995). Computer code and later software with a user-friendly interface (NeEstimator) was produced to implement the methods. This was used as a basis for simulation experiments to evaluate the performance of the methods with an individual-based model of a prawn population. Following the guidelines suggested by computer simulations, the tiger prawn population in Moreton Bay (south-east Queensland) was sampled for genetic analysis with eight microsatellite loci in three successive spring spawning seasons in 2001, 2002 and 2003. As predicted by the simulations, the estimates had non-infinite upper confidence limits, which is a major achievement for the application of the method to a naturally-occurring, short generation, highly fecund invertebrate species. The genetic estimate of the number of successful spawners was around 1000 individuals in two consecutive years. This contrasts with about 500,000 prawns participating in spawning. It is not possible to distinguish successful from non-successful spawners so we suggest a high level of protection for the entire spawning population. We interpret the difference in numbers between successful and non-successful spawners as a large variation in the number of offspring per family that survive – a large number of families have no surviving offspring, while a few have a large number. We explored various ways in which Ne can be useful in fisheries management. It can be a surrogate for spawning population size, assuming the ratio between Ne and spawning population size has been previously calculated for that species. Alternatively, it can be a surrogate for recruitment, again assuming that the ratio between Ne and recruitment has been previously determined. The number of species that can be analysed in this way, however, is likely to be small because of species-specific life history requirements that need to be satisfied for accuracy. The most universal approach would be to integrate Ne with spawning stock-recruitment models, so that these models are more accurate when applied to fisheries populations. A pathway to achieve this was established in this project, which we predict will significantly improve fisheries sustainability in the future. Regardless of the success of integrating Ne into spawning stock-recruitment models, Ne could be used as a fisheries monitoring tool. Declines in spawning stock size or increases in natural or harvest mortality would be reflected by a decline in Ne. This would be good for data-poor fisheries and provides fishery independent information, however, we suggest a species-by-species approach. Some species may be too numerous or experiencing too much migration for the method to work. During the project two important theoretical studies of the simultaneous estimation of effective population size and migration were published (Vitalis and Couvet 2001b; Wang and Whitlock 2003). These methods, combined with collection of preliminary genetic data from the tiger prawn population in southern Gulf of Carpentaria population and a computer simulation study that evaluated the effect of differing reproductive strategies on genetic estimates, suggest that this technology could make an important contribution to the stock assessment process in the northern prawn fishery (NPF). Advances in the genomics world are rapid and already a cheaper, more reliable substitute for microsatellite loci in this technology is available. Digital data from single nucleotide polymorphisms (SNPs) are likely to super cede ‘analogue’ microsatellite data, making it cheaper and easier to apply the method to species with large population sizes.

Assessing the cost-effectiveness of water quality interventions in South-East Queensland

The focus of this article is on the cost-effectiveness of mitigation strategies to reduce pollution loads and improve water quality in South-East Queensland. Scenarios were developed about the types of catchment interventions that could be considered, and the resulting changes in water quality indicators that may result. Once these catchment scenarios were modelled, the range of expected outcomes was assessed and the costs of mitigation interventions were estimated. Strategies considered include point and non-point source interventions. Predicted reductions in pollution levels were calculated for each action based on the expected population growth. The cost of the interventions included the full investment and annual running costs as well as planned public investment by the state agencies. Cost-effectiveness of strategies is likely to vary according to whether suspended sediments, nitrogen or phosphorus loads are being targeted.

Assessing the relationship between shire winter crop yield and seasonal variability of the MODIS NDVI and EVI images

Australian researchers have been developing robust yield estimation models, based mainly on the crop growth response to water availability during the crop season. However, knowledge of spatial distribution of yields within and across the production regions can be improved by the use of remote sensing techniques. Images of Moderate Resolution Imaging Spectroradiometer (MODIS) vegetation indices, available since 1999, have the potential to contribute to crop yield estimation. The objective of this study was to analyse the relationship between winter crop yields and the spectral information available in MODIS vegetation index images at the shire level. The study was carried out in the Jondaryan and Pittsworth shires, Queensland , Australia . Five years (2000 to 2004) of 250m resolution, 16-day composite of MODIS Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) images were used during the winter crop season (April to November). Seasonal variability of the profiles of the vegetation index images for each crop season using different regions of interest (cropping mask) were displayed and analysed. Correlation analysis between wheat and barley yield data and MODIS image values were also conducted. The results showed high seasonal variability in the NDVI and EVI profiles, and the EVI values were consistently lower than those of the NDVI. The highest image values were observed in 2003 (in contrast to 2004), and were associated with rainfall amount and distribution. The seasonal variability of the profiles was similar in both shires, with minimum values in June and maximum values at the end of August. NDVI and EVI images showed sensitivity to seasonal variability of the vegetation and exhibited good association (e.g. r = 0.84, r = 0.77) with winter crop yields.

Simulating crop-parasitic weed interactions using APSIM: Model evaluation and application

The parasitic weed Orobanche crenata inflicts major damage on faba bean, lentil, pea and other crops in Mediterranean environments. The development of methods to control O. crenata is to a large extent hampered by the complexity of host-parasite systems. Using a model of host-parasite interactions can help to explain and understand this intricacy. This paper reports on the evaluation and application of a model simulating host-parasite competition as affected by environment and management that was implemented in the framework of the Agricultural Production Systems Simulator (APSIM). Model-predicted faba bean and O. crenata growth and development were evaluated against independent data. The APSIM-Fababean and -Parasite modules displayed a good capability to reproduce effects of pedoclimatic conditions, faba bean sowing date and O. crenata infestation on host-parasite competition. The r(2) values throughout exceeded 0.84 (RMSD: 5.36 days) for phenological, 0.85 (RMSD: 223.00 g m(-2)) for host growth and 0.78 (RMSD: 99.82 g m(-2)) for parasite growth parameters. Inaccuracies of simulated faba bean root growth that caused some bias of predicted parasite number and host yield loss may be dealt with by more flexibly simulating vertical root distribution. The model was applied in simulation experiments to determine optimum sowing windows for infected and non-infected faba bean in Mediterranean environments. Simulation results proved realistic and testified to the capability of APSIM to contribute to the development of tactical approaches in parasitic weed control.

Modeling chickpea growth and development: Nitrogen accumulation and use

Quantitative information regarding nitrogen (N) accumulation and its distribution to leaves, stems and grains under varying environmental and growth conditions are limited for chickpea (Cicer arietinum L.). The information is required for the development of crop growth models and also for assessment of the contribution of chickpea to N balances in cropping systems. Accordingly, these processes were quantified in chickpea under different environmental and growth conditions (still without water or N deficit) using four field experiments and 1325 N measurements. N concentration ([N]) in green leaves was 50 mg g-1 up to beginning of seed growth, and then it declined linearly to 30 mg g-1 at the end of seed growth phase. [N] in senesced leaves was 12 mg g-1. Stem [N] decreased from 30 mg g-1 early in the season to 8 mg g-1 in senesced stems at maturity. Pod [N] was constant (35 mg g-1), but grain [N] decreased from 60 mg g-1 early in seed growth to 43 mg g-1 at maturity. Total N accumulation ranged between 9 and 30 g m-2. N accumulation was closely linked to biomass accumulation until maturity. N accumulation efficiency (N accumulation relative to biomass accumulation) was 0.033 g g-1 where total biomass was -2 and during early growth period, but it decreased to 0.0176 g g-1 during the later growth period when total biomass was >218 g m-2. During vegetative growth (up to first-pod), 58% of N was partitioned to leaves and 42% to stems. Depending on growth conditions, 37-72% of leaf N and 12-56% of stem N was remobilized to the grains. The parameter estimates and functions obtained in this study can be used in chickpea simulation models to simulate N accumulation and distribution.

Managing the risk of glyphosate resistance in Australian glyphosate-resistant cotton production systems

BACKGROUND: Glyphosate-resistant cotton varieties are an important tool for weed control in Australian cotton production systems. To increase the sustainability of this technology and to minimise the likelihood of resistance evolving through its use, weed scientists, together with herbicide regulators, industry representatives and the technology owners, have developed a framework that guides the use of the technology. Central to this framework is a crop management plan (CMP) and grower accreditation course. A simulation model that takes into account the characteristics of the weed species, initial gene frequencies and any associated fitness penalties was developed to ensure that the CMP was sufficiently robust to minimise resistance risks. RESULTS: The simulations showed that, when a combination of weed control options was employed in addition to glyphosate, resistance did not evolve over the 30 year period of the simulation. CONCLUSION: These simulations underline the importance of maintaining an integrated system for weed management to prevent the evolution of glyphosate resistance, prolonging the use of glyphosate-resistant cotton.

Simulating pasture growth rates in Australian and New Zealand grazing systems

DairyMod, EcoMod, and the SGS Pasture Model are mechanistic biophysical models developed to explore scenarios in grazing systems. The aim of this manuscript was to test the ability of the models to simulate net herbage accumulation rates of ryegrass-based pastures across a range of environments and pasture management systems in Australia and New Zealand. Measured monthly net herbage accumulation rate and accumulated yield data were collated from ten grazing system experiments at eight sites ranging from cool temperate to subtropical environments. The local climate, soil, pasture species, and management (N fertiliser, irrigation, and grazing or cutting pattern) were described in the model for each site, and net herbage accumulation rates modelled. The model adequately simulated the monthly net herbage accumulation rates across the range of environments, based on the summary statistics and observed patterns of seasonal growth, particularly when the variability in measured herbage accumulation rates was taken into account. Agreement between modelled and observed growth rates was more accurate and precise in temperate than in subtropical environments, and in winter and summer than in autumn and spring. Similarly, agreement between predicted and observed accumulated yields was more accurate than monthly net herbage accumulation. Different temperature parameters were used to describe the growth of perennial ryegrass cultivars and annual ryegrass; these differences were in line with observed growth patterns and breeding objectives. Results are discussed in the context of the difficulties in measuring pasture growth rates and model limitations.

Analysis of high yielding maize production - A study based on a commercial crop

This paper reports on the use of APSIM - Maize for retrospective analysis of performance of a high input, high yielding maize crop and analysis of predicted performance of maize grown with high inputs over the long-term (>100 years) for specified scenarios of environmental conditions (temperature and radiation) and agronomic inputs (sowing date, plant population, nitrogen fertiliser and irrigation) at Boort, Victoria, Australia. It uses a high yielding (17 400 kg/ha dry grain, 20 500 kg/ha at 15% water) commercial crop grown in 2004-05 as the basis of the study. Yield for the agronomic and environmental conditions of 2004-05 was predicted accurately, giving confidence that the model could be used for the detailed analyses undertaken. The analysis showed that the yield achieved was close to that possible with the conditions and agronomic inputs of 2004-05. Sowing dates during 21 September to 26 October had little effect on predicted yield, except when combined with reduced temperature. Single year and long-term analyses concluded that a higher plant population (11 plants/m2) is needed to optimise yield, but that slightly lower N and irrigation inputs are appropriate for the plant population used commercially (8.4 plants/m2). Also, compared with changes in agronomic inputs increases in temperature and/or radiation had relatively minor effects, except that reduced temperature reduces predicted yield substantially. This study provides an approach for the use of models for both retrospective analysis of crop performance and assessment of long-term variability of crop yield under a wide range of agronomic and environmental conditions.

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.

Insecticide resistance and implications for future aphid management in Australian grains and pastures: A review

Aphids can cause substantial damage to cereals, oilseeds and legumes through direct feeding and through the transmission of plant pathogenic viruses. Aphid-resistant varieties are only available for a limited number of crops. In Australia, growers often use prophylactic sprays to control aphids, but this strategy can lead to non-target effects and the development of insecticide resistance. Insecticide resistance is a problem in one aphid pest of Australian grains in Australia, the green peach aphid (Myzus persicae). Molecular analyses of field-collected samples demonstrate that amplified E4 esterase resistance to organophosphate insecticides is widespread in Australian grains across Australia. Knockdown resistance to pyrethroids is less abundant, but has an increased frequency in areas with known frequent use of these insecticides. Modified acetylcholinesterase resistance to dimethyl carbamates, such as pirimicarb, has not been found in Australia, nor has resistance to imidacloprid. Australian grain growers should consider control options that are less likely to promote insecticide resistance, and have reduced impacts on natural enemies. Research is ongoing in Australia and overseas to provide new strategies for aphid management in the future.