Annual forecasting of the Australian macadamia crop - integrating tree census data with statistical climate-adjustment models

To facilitate marketing and export, the Australian macadamia industry requires accurate crop forecasts. Each year, two levels of crop predictions are produced for this industry. The first is an overall longer-term forecast based on tree census data of growers in the Australian Macadamia Society (AMS). This data set currently accounts for around 70% of total production, and is supplemented by our best estimates of non-AMS orchards. Given these total tree numbers, average yields per tree are needed to complete the long-term forecasts. Yields from regional variety trials were initially used, but were found to be consistently higher than the average yields that growers were obtaining. Hence, a statistical model was developed using growers' historical yields, also taken from the AMS database. This model accounted for the effects of tree age, variety, year, region and tree spacing, and explained 65% of the total variation in the yield per tree data. The second level of crop prediction is an annual climate adjustment of these overall long-term estimates, taking into account the expected effects on production of the previous year's climate. This adjustment is based on relative historical yields, measured as the percentage deviance between expected and actual production. The dominant climatic variables are observed temperature, evaporation, solar radiation and modelled water stress. Initially, a number of alternate statistical models showed good agreement within the historical data, with jack-knife cross-validation R2 values of 96% or better. However, forecasts varied quite widely between these alternate models. Exploratory multivariate analyses and nearest-neighbour methods were used to investigate these differences. For 2001-2003, the overall forecasts were in the right direction (when compared with the long-term expected values), but were over-estimates. In 2004 the forecast was well under the observed production, and in 2005 the revised models produced a forecast within 5.1% of the actual production. Over the first five years of forecasting, the absolute deviance for the climate-adjustment models averaged 10.1%, just outside the targeted objective of 10%.

Mixture of time-dependent growth models with an application to blue swimmer crab length-frequency data

Understanding how aquatic species grow is fundamental in fisheries because stock assessment often relies on growth dependent statistical models. Length-frequency-based methods become important when more applicable data for growth model estimation are either not available or very expensive. In this article, we develop a new framework for growth estimation from length-frequency data using a generalized von Bertalanffy growth model (VBGM) framework that allows for time-dependent covariates to be incorporated. A finite mixture of normal distributions is used to model the length-frequency cohorts of each month with the means constrained to follow a VBGM. The variances of the finite mixture components are constrained to be a function of mean length, reducing the number of parameters and allowing for an estimate of the variance at any length. To optimize the likelihood, we use a minorization–maximization (MM) algorithm with a Nelder–Mead sub-step. This work was motivated by the decline in catches of the blue swimmer crab (BSC) (Portunus armatus) off the east coast of Queensland, Australia. We test the method with a simulation study and then apply it to the BSC fishery data.

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.

Statistical forecasting of the Australian macadamia crop

Three types of forecasts of the total Australian production of macadamia nuts (t nut-in-shell) have been produced early each year since 2001. The first is a long-term forecast, based on the expected production from the tree census data held by the Australian Macadamia Society, suitably scaled up for missing data and assumed new plantings each year. These long-term forecasts range out to 10 years in the future, and form a basis for industry and market planning. Secondly, a statistical adjustment (termed the climate-adjusted forecast) is made annually for the coming crop. As the name suggests, climatic influences are the dominant factors in this adjustment process, however, other terms such as bienniality of bearing, prices and orchard aging are also incorporated. Thirdly, industry personnel are surveyed early each year, with their estimates integrated into a growers and pest-scouts forecast. Initially conducted on a 'whole-country' basis, these models are now constructed separately for the six main production regions of Australia, with these being combined for national totals. Ensembles or suites of step-forward regression models using biologically-relevant variables have been the major statistical method adopted, however, developing methodologies such as nearest-neighbour techniques, general additive models and random forests are continually being evaluated in parallel. The overall error rates average 14% for the climate forecasts, and 12% for the growers' forecasts. These compare with 7.8% for USDA almond forecasts (based on extensive early-crop sampling) and 6.8% for coconut forecasts in Sri Lanka. However, our somewhatdisappointing results were mainly due to a series of poor crops attributed to human reasons, which have now been factored into the models. Notably, the 2012 and 2013 forecasts averaged 7.8 and 4.9% errors, respectively. Future models should also show continuing improvement, as more data-years become available.