Optimal management of agricultural systems

To remain competitive, many agricultural systems are now being run along business lines. Systems methodologies are being incorporated, and here evolutionary computation is a valuable tool for identifying more profitable or sustainable solutions. However, agricultural models typically pose some of the more challenging problems for optimisation. This chapter outlines these problems, and then presents a series of three case studies demonstrating how they can be overcome in practice. Firstly, increasingly complex models of Australian livestock enterprises show that evolutionary computation is the only viable optimisation method for these large and difficult problems. On-going research is taking a notably efficient and robust variant, differential evolution, out into real-world systems. Next, models of cropping systems in Australia demonstrate the challenge of dealing with competing objectives, namely maximising farm profit whilst minimising resource degradation. Pareto methods are used to illustrate this trade-off, and these results have proved to be most useful for farm managers in this industry. Finally, land-use planning in the Netherlands demonstrates the size and spatial complexity of real-world problems. Here, GIS-based optimisation techniques are integrated with Pareto methods, producing better solutions which were acceptable to the competing organizations. These three studies all show that evolutionary computation remains the only feasible method for the optimisation of large, complex agricultural problems. An extra benefit is that the resultant population of candidate solutions illustrates trade-offs, and this leads to more informed discussions and better education of the industry decision-makers.

The accuracy of varietal selection using factor analytic models for multi-environment plant breeding trials

Modeling of cultivar x trial effects for multienvironment trials (METs) within a mixed model framework is now common practice in many plant breeding programs. The factor analytic (FA) model is a parsimonious form used to approximate the fully unstructured form of the genetic variance-covariance matrix in the model for MET data. In this study, we demonstrate that the FA model is generally the model of best fit across a range of data sets taken from early generation trials in a breeding program. In addition, we demonstrate the superiority of the FA model in achieving the most common aim of METs, namely the selection of superior genotypes. Selection is achieved using best linear unbiased predictions (BLUPs) of cultivar effects at each environment, considered either individually or as a weighted average across environments. In practice, empirical BLUPs (E-BLUPs) of cultivar effects must be used instead of BLUPs since variance parameters in the model must be estimated rather than assumed known. While the optimal properties of minimum mean squared error of prediction (MSEP) and maximum correlation between true and predicted effects possessed by BLUPs do not hold for E-BLUPs, a simulation study shows that E-BLUPs perform well in terms of MSEP.

Optimal eradication: when to stop looking for an invasive plant

The notion of being sure that you have completely eradicated an invasive species is fanciful because of imperfect detection and persistent seed banks. Eradication is commonly declared either on an ad hoc basis, on notions of seed bank longevity, or on setting arbitrary thresholds of 1% or 5% confidence that the species is not present. Rather than declaring eradication at some arbitrary level of confidence, we take an economic approach in which we stop looking when the expected costs outweigh the expected benefits. We develop theory that determines the number of years of absent surveys required to minimize the net expected cost. Given detection of a species is imperfect, the optimal stopping time is a trade-off between the cost of continued surveying and the cost of escape and damage if eradication is declared too soon. A simple rule of thumb compares well to the exact optimal solution using stochastic dynamic programming. Application of the approach to the eradication programme of Helenium amarum reveals that the actual stopping time was a precautionary one given the ranges for each parameter.

Soil carbon stock in the tropical rangelands of Australia: Effects of soil type and grazing pressure, and determination of sampling requirement.

On-going, high-profile public debate about climate change has focussed attention on how to monitor the soil organic carbon stock (C(s)) of rangelands (savannas). Unfortunately, optimal sampling of the rangelands for baseline C(s) - the critical first step towards efficient monitoring - has received relatively little attention to date. Moreover, in the rangelands of tropical Australia relatively little is known about how C(s) is influenced by the practice of cattle grazing. To address these issues we used linear mixed models to: (i) unravel how grazing pressure (over a 12-year period) and soil type have affected C(s) and the stable carbon isotope ratio of soil organic carbon (delta(13)C) (a measure of the relative contributions of C(3) and C(4) vegetation to C(s)); (ii) examine the spatial covariation of C(s) and delta(13)C; and, (iii) explore the amount of soil sampling required to adequately determine baseline C(s). Modelling was done in the context of the material coordinate system for the soil profile, therefore the depths reported, while conventional, are only nominal. Linear mixed models revealed that soil type and grazing pressure interacted to influence C(s) to a depth of 0.3 m in the profile. At a depth of 0.5 m there was no effect of grazing on C(s), but the soil type effect on C(s) was significant. Soil type influenced delta(13)C to a soil depth of 0.5 m but there was no effect of grazing at any depth examined. The linear mixed model also revealed the strong negative correlation of C(s) with delta(13)C, particularly to a depth of 0.1 m in the soil profile. This suggested that increased C(s) at the study site was associated with increased input of C from C(3) trees and shrubs relative to the C(4) perennial grasses; as the latter form the bulk of the cattle diet, we contend that C sequestration may be negatively correlated with forage production. Our baseline C(s) sampling recommendation for cattle-grazing properties of the tropical rangelands of Australia is to: (i) divide the property into units of apparently uniform soil type and grazing management; (ii) use stratified simple random sampling to spread at least 25 soil sampling locations about each unit, with at least two samples collected per stratum. This will be adequate to accurately estimate baseline mean C(s) to within 20% of the true mean, to a nominal depth of 0.3 m in the profile.

Fishing power increases continue in Queensland's east coast trawl fishery, Australia

The Queensland east coast trawl fishery is by far the largest prawn and scallop otter trawl fleet in Australia in terms of number of vessels, with 504 vessels licensed to fish for species including tiger prawns, endeavour prawns, red spot king prawns, eastern king prawns and saucer scallops by the end of 2004. The vessel fleet has gradually upgraded characteristics such as engine power and use of propeller nozzles, quad nets, global positioning systems (GPS) and computer mapping software. These changes, together with the ever-changing profile of the fleet, were analysed by linear mixed models to quantify annual efficiency increases of an average vessel at catching prawns or scallops. The analyses included vessel characteristics (treated as fixed effects) and vessel identifier codes (treated as random effects). For the period from 1989 to 2004 the models estimated overall fishing power increases of 6% in the northern tiger, 6% in the northern endeavour, 12% in the southern tiger, 18% in the red spot king, 46% in the eastern king prawn and 15% in the saucer scallop sector. The results illustrate the importance of ongoing monitoring of vessel and fleet characteristics and the need to use this information to standardise catch rate indices used in stock assessment and management.

Deriving optimal fishing effort for managing Australia's Moreton Bay multispecies trawl fishery with aggregated effort data

Deriving an estimate of optimal fishing effort or even an approximate estimate is very valuable for managing fisheries with multiple target species. The most challenging task associated with this is allocating effort to individual species when only the total effort is recorded. Spatial information on the distribution of each species within a fishery can be used to justify the allocations, but often such information is not available. To determine the long-term overall effort required to achieve maximum sustainable yield (MSY) and maximum economic yield (MEY), we consider three methods for allocating effort: (i) optimal allocation, which optimally allocates effort among target species; (ii) fixed proportions, which chooses proportions based on past catch data; and (iii) economic allocation, which splits effort based on the expected catch value of each species. Determining the overall fishing effort required to achieve these management objectives is a maximizing problem subject to constraints due to economic and social considerations. We illustrated the approaches using a case study of the Moreton Bay Prawn Trawl Fishery in Queensland (Australia). The results were consistent across the three methods. Importantly, our analysis demonstrated the optimal total effort was very sensitive to daily fishing costs—the effort ranged from 9500–11 500 to 6000–7000, 4000 and 2500 boat-days, using daily cost estimates of $0, $500, $750, and $950, respectively. The zero daily cost corresponds to the MSY, while a daily cost of $750 most closely represents the actual present fishing cost. Given the recent debate on which costs should be factored into the analyses for deriving MEY, our findings highlight the importance of including an appropriate cost function for practical management advice. The approaches developed here could be applied to other multispecies fisheries where only aggregated fishing effort data are recorded, as the literature on this type of modelling is sparse.