Multiple-trait BLUP in longitudinal data analysis on Jatropha curcas breeding for bioenergy
Introduction
The search for sustainable fuels has become a frequent topic in numerous world conferences. In this scenario, Jatropha curcas L. stands out as one of the main species from which biodiesel can be produced by virtue of its adaptability to different environments; its tolerance to drought, which enable its cultivation in low-fertile and non-irrigated soils (Laviola et al., 2017); and production life of more than 50 years (Nithiyanantham et al., 2012). Moreover, it has a higher capacity to transform oil into biodiesel compared with other species (Pu et al., 2011).
Despite being a species with great potential for biodiesel production, little research has been done on the breeding of Jatropha curcas. Recently, studies have been undertaken with a view to selecting genotypes using information of only one harvest (Junqueira et al., 2016); using several harvests independently (Bhering et al., 2013); or based on temporal stability and adaptability of genetic values (Alves et al., 2018a, 2018b). However, because Jatropha curcas is a perennial species that produces for many years, statistical methodologies that efficiently evaluate longitudinal data are necessary to allow for a more accurate genetic selection (Peixoto et al., 2016).
Longitudinal data analysis has a few peculiarities, as the many harvests are correlated with each other and because there may be heterogeneity of variances and covariances between them (Mrode, 2014). The interest in analyses of this sort of data usually lies in the prediction of genetic values across all harvests as well as in the identification of a covariance structure over time (Resende et al., 2014). In plant breeding, longitudinal data associated with harvests are usually analyzed via repeatability models (Resende et al., 2014).
However, the multiple-trait Best Linear Unbiased Prediction (BLUP) — also known as the model with an unstructured covariance matrix — can be a very efficient alternative, because it uses all pieces of information simultaneously and treats repeated measures as different and correlated traits, considering their heritabilities and genetic and residual correlations (Mrode, 2014; Resende et al., 2014). This covariance structure is applied to all random factors of the statistical model such as genotype effects, plot effects, and residual effects (Gilmour et al., 2004). In this scenario, the present study proposes to analyze longitudinal data via multiple-trait Best Linear Unbiased Prediction (BLUP) for the genetic improvement of Jatropha curcas.
Section snippets
Experimental data
The experiment was implemented in November 2008 as a randomized-block design with two blocks and five plants per plot that were arranged in rows spaced 4 m apart, with 2 m spacing between plants. The experiment was conducted in the experimental field of Embrapa Cerrados, located in Planaltina, DF - Brazil (15°35′30″ S and 47°42′30″ W; 1007 m asl). All management practices were based on Carels et al. (2012). The experiment consisted of an evaluation of the performance of 730 individuals of 73
Results
The standard errors of the estimates of the variance components revealed that all the random effects of the statistical model are statistically significant (i.e., they differ from zero) (Table 1). An increase was observed in the magnitude of genetic variance between family means and, consequently, in additive genetic variance between family means throughout the harvests, except for that of 2013. On the other hand, heritability between family means did not follow any pattern, ranging from 0.33
Discussion
BLUP assumes that variance components are known (Henderson, 1975). However, in practice, variance components are unknown and should thus be estimated in the most reliable way possible so that estimates can properly replace the parameters. In this case, the standard procedure for estimating variance components, under the approach of linear mixed models, is REML (Patterson and Thompson, 1971). Therefore, the genetic evaluation consists of using these methodologies together — the so-called
Conclusion
Genetic correlations of low to moderate magnitude were observed between pairs of harvests.
The Multiple-trait BLUP / Additive Index procedure allowed for the selection of superior families based on the predicted genetic values, considering all the harvests. Therefore, it can be efficiently applied in the breeding of Jatropha curcas.
Acknowledgments
The authors thank CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for their financial support.
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