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.

Prediction of breeding values for average fruit weight in mango using a multivariate individual mixed model

Mango is an important horticultural fruit crop and breeding is a key strategy to improve ongoing sustainability. Knowledge of breeding values of potential parents is important for maximising progress from breeding. This study successfully employed a mixed linear model methods incorporating a pedigree to predict breeding values for average fruit weight from highly unbalanced data for genotypes planted over three field trials and assessed over several harvest seasons. Average fruit weight was found to be under strong additive genetic control. There was high correlation between hybrids propagated as seedlings and hybrids propagated as scions grafted onto rootstocks. Estimates of additive genetic correlation among trials ranged from 0.69 to 0.88 with correlations among harvest seasons within trials greater than 0.96. These results suggest that progress from selection for broad adaptation can be achieved, particularly as no repeatable environmental factor that could be used to predict G x E could be identified. Predicted breeding values for 35 known cultivars are presented for use in ongoing breeding programs.

CIMMYT-selected derived synthetic bread wheats for rainfed environments: Yield evaluation in Mexico and Australia.

Synthetic backcrossed-derived bread wheats (SBWs) from CIMMYT were grown in the Northwest of Mexico at Centro de Investigaciones Agrícolas del Noroeste (CIANO) and sites across Australia during three seasons. During three consecutive years Australia received “shipments” of different SBWs from CIMMYT for evaluation. A different set of lines was evaluated each season, as new materials became available from the CIMMYT crop enhancement program. These consisted of approximately 100 advanced lines (F7) per year. SBWs had been top and backcrossed to CIMMYT cultivars in the first two shipments and to Australian wheat cultivars in the third one. At CIANO, the SBWs were trialled under receding soil moisture conditions. We evaluated both the performance of each line across all environments and the genotype-by-environment interaction using an analysis that fits a multiplicative mixed model, adjusted for spatial field trends. Data were organised in three groups of multienvironment trials (MET) containing germplasm from shipment 1 (METShip1), 2 (METShip2), and 3 (METShip3), respectively. Large components of variance for the genotype × environment interaction were found for each MET analysis, due to the diversity of environments included and the limited replication over years (only in METShip2, lines were tested over 2 years). The average percentage of genetic variance explained by the factor analytic models with two factors was 50.3% for METShip1, 46.7% for METShip2, and 48.7% for METShip3. Yield comparison focused only on lines that were present in all locations within a METShip, or “core” SBWs. A number of core SBWs, crossed to both Australian and CIMMYT backgrounds, outperformed the local benchmark checks at sites from the northern end of the Australian wheat belt, with reduced success at more southern locations. In general, lines that succeeded in the north were different from those in the south. The moderate positive genetic correlation between CIANO and locations in the northern wheat growing region likely reflects similarities in average temperature during flowering, high evaporative demand, and a short flowering interval. We are currently studying attributes of this germplasm that may contribute to adaptation, with the aim of improving the selection process in both Mexico and Australia.

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.

Detection and use of QTL for complex traits in multiple environments.

QTL mapping methods for complex traits are challenged by new developments in marker technology, phenotyping platforms, and breeding methods. In meeting these challenges, QTL mapping approaches will need to also acknowledge the central roles of QTL by environment interactions (QEI) and QTL by trait interactions in the expression of complex traits like yield. This paper presents an overview of mixed model QTL methodology that is suitable for many types of populations and that allows predictive modeling of QEI, both for environmental and developmental gradients. Attention is also given to multi-trait QTL models which are essential to interpret the genetic basis of trait correlations. Biophysical (crop growth) model simulations are proposed as a complement to statistical QTL mapping for the interpretation of the nature of QEI and to investigate better methods for the dissection of complex traits into component traits and their genetic controls.

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.

Predicting Additive and Non-additive Genetic Effects from Trials Where Traits Are Affected by Interplot Competition

There are two key types of selection in a plant breeding program, namely selection of hybrids for potential commercial use and the selection of parents for use in future breeding. Oakey et al. (in Theoretical and Applied Genetics 113, 809-819, 2006) showed how both of these aims could be achieved using pedigree information in a mixed model analysis in order to partition genetic effects into additive and non-additive effects. Their approach was developed for field trial data subject to spatial variation. In this paper we extend the approach for data from trials subject to interplot competition. We show how the approach may be used to obtain predictions of pure stand additive and non-additive effects. We develop the methodology in the context of a single field trial using an example from an Australian sorghum breeding program.

Resistance to Fusarium oxysporum f. sp fragariae and Predicted Breeding Values in Strawberry

Fusarium wilt of strawberry, incited by Fusarium oxysporum f. sp. fragariae (Fof), is a major disease of the cultivated strawberry (Fragaria xananassa) worldwide. An increase in disease outbreaks of the pathogen in Western Australia and Queensland plus the search for alternative disease management strategies place emphasis on the development of resistant cultivars. In response, a partial incomplete diallel cross involving four parents was performed for use in glasshouse resistance screenings. The resulting progeny were evaluated for their susceptibility to Fof. Best-performing progeny and suitability of progenies as parents were determined using data from disease severity ratings and analyzed using a linear mixed model incorporating a pedigree to produce best linear unbiased predictions of breeding values. Variation in disease response, ranging from highly susceptible to resistant, indicates a quantitative effect. The estimate of the narrow-sense heritability was 0.49 +/- 0.04 (SE), suggesting the population should be responsive to phenotypic recurrent selection. Several progeny genotypes have predicted breeding values higher than any of the parents. Knowledge of Fof resistance derived from this study can help select best parents for future crosses for the development of new strawberry cultivars with Fof resistance.

A retrospective study of vase life determinants for cut Acacia holosericea foliage

Short and variable vase life of cut Acacia holosericea foliage stems limits its commercial potential. Retrospective evaluation of factors affecting the vase life of this cut foliage line was assessed using primary data collected from 30 individual experiments. These data had been collected by four different researchers over 17 months, from late Summer to mid Winter across two consecutive years. Vase life data of cut A. holosericea stems held in deionised water (DIW) was analysed for general vase life variation and to define the most influential factor affecting vase life of the cut stems. Meanwhile, vase life of cut stems exposed to various chemical and physical postharvest treatments was analysed using meta-analysis to evaluate their efficacy in prolonging vase life of the stems. The overall mean vase life (±standard deviation) of cut A. holosericea stems was 6.4 ± 1.2 days (n = 30 trials). Longer vase life of ≥7 days was obtained from cut stems harvested at vegetative and flowering stage, which was between Summer and Autumn. Cut stems harvested at fruiting stage, between Winter and Spring displayed shorter vase life of ≤5.5 days. Mixed model analysis indicated that vase life variation of the cut stems was mostly determined by season (P < 0.001). In averaged, postharvest treatments increased vase life 1.4-fold compared to stems in DIW, with 68.32% had a large positive treatment effect size (d). Among the treatments, nano silver (NS) and copper (Cu2+) were the most beneficial to vase life. Retrospective analysis was found to be beneficial for identifying conditions and targeting practices to maximise the vase life of cut A. holosericea and, potentially for other species.

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

Growth and species interactions of Eucalyptus pellita in a mixed and monoculture plantation in the humid tropics of north Queensland

This study investigated whether mixed-species designs can increase the growth of a tropical eucalypt when compared to monocultures. Monocultures of Eucalyptus pellita (E) and Acacia peregrina (A) and mixtures in various proportions (75E:25A, 50E:50A, 25E:75A) were planted in a replacement series design on the Atherton Tablelands of north Queensland, Australia. High mortality in the establishment phase due to repeated damage by tropical cyclones altered the trial design. Effects of experimental designs on tree growth were estimated using a linear mixed-effects model with restricted maximum likelihood analysis (REML). Volume growth of individual eucalypt trees were positively affected by the presence of acacia trees at age 5 years and this effect generally increased with time up to age 10 years. However, the stand volume and basal area increased with increasing proportions of E. pellita, due to its larger individual tree size. Conventional analysis did not offer convincing support for mixed-species designs. Preliminary individual-based modelling using a modified Hegyi competition index offered a solution and an equation that indicates acacias have positive ecological interactions (facilitation or competitive reduction) and definitely do not cause competition like a eucalypt. These results suggest that significantly increased in growth rates could be achieved with mixed-species designs. This statistical methodology could enable a better understanding of species interactions in similarly altered experiments, or undesigned mixed-species plantations.

Improved models for estimating temporal changes in carbon sequestration in above-ground biomass of mixed-species environmental plantings

Plantings of mixed native species (termed 'environmental plantings') are increasingly being established for carbon sequestration whilst providing additional environmental benefits such as biodiversity and water quality. In Australia, they are currently one of the most common forms of reforestation. Investment in establishing and maintaining such plantings relies on having a cost-effective modelling approach to providing unbiased estimates of biomass production and carbon sequestration rates. In Australia, the Full Carbon Accounting Model (FullCAM) is used for both national greenhouse gas accounting and project-scale sequestration activities. Prior to undertaking the work presented here, the FullCAM tree growth curve was not calibrated specifically for environmental plantings and generally under-estimated their biomass. Here we collected and analysed above-ground biomass data from 605 mixed-species environmental plantings, and tested the effects of several planting characteristics on growth rates. Plantings were then categorised based on significant differences in growth rates. Growth of plantings differed between temperate and tropical regions. Tropical plantings were relatively uniform in terms of planting methods and their growth was largely related to stand age, consistent with the un-calibrated growth curve. However, in temperate regions where plantings were more variable, key factors influencing growth were planting width, stand density and species-mix (proportion of individuals that were trees). These categories provided the basis for FullCAM calibration. Although the overall model efficiency was only 39-46%, there was nonetheless no significant bias when the model was applied to the various planting categories. Thus, modelled estimates of biomass accumulation will be reliable on average, but estimates at any particular location will be uncertain, with either under- or over-prediction possible. When compared with the un-calibrated yield curves, predictions using the new calibrations show that early growth is likely to be more rapid and total above-ground biomass may be higher for many plantings at maturity. This study has considerably improved understanding of the patterns of growth in different types of environmental plantings, and in modelling biomass accumulation in young (<25. years old) plantings. However, significant challenges remain to understand longer-term stand dynamics, particularly with temporal changes in stand density and species composition. © 2014.