Prediction of complex traits: Conciliating genetics and statistics

Heterosis and Hybrid Crop Breeding: A Multidisciplinary Review

Although hybrid crop varieties are among the most popular agricultural innovations, the rationale for hybrid crop breeding is sometimes misunderstood. Hybrid breeding is slower and more resource-intensive than inbred breeding, but it allows systematic improvement of a population by recurrent selection and exploitation of heterosis simultaneously. Inbred parental lines can identically reproduce both themselves and their F1 progeny indefinitely, whereas outbred lines cannot, so uniform outbred lines must be bred indirectly through their inbred parents to harness heterosis. Heterosis is an expected consequence of whole-genome non-additive effects at the population level over evolutionary time. Understanding heterosis from the perspective of molecular genetic mechanisms alone may be elusive, because heterosis is likely an emergent property of populations. Hybrid breeding is a process of recurrent population improvement to maximize hybrid performance. Hybrid breeding is not maximization of heterosis per se, nor testing random combinations of individuals to find an exceptional hybrid, nor using heterosis in place of population improvement. Though there are methods to harness heterosis other than hybrid breeding, such as use of open-pollinated varieties or clonal propagation, they are not currently suitable for all crops or production environments. The use of genomic selection can decrease cycle time and costs in hybrid breeding, particularly by rapidly establishing heterotic pools, reducing testcrossing, and limiting the loss of genetic variance. Open questions in optimal use of genomic selection in hybrid crop breeding programs remain, such as how to choose founders of heterotic pools, the importance of dominance effects in genomic prediction, the necessary frequency of updating the training set with phenotypic information, and how to maintain genetic variance and prevent fixation of deleterious alleles.

Estimating variance components in population scale family trees

The rapid digitization of genealogical and medical records enables the assembly of extremely large pedigree records spanning millions of individuals and trillions of pairs of relatives. Such pedigrees provide the opportunity to investigate the sociological and epidemiological history of human populations in scales much larger than previously possible. Linear mixed models (LMMs) are routinely used to analyze extremely large animal and plant pedigrees for the purposes of selective breeding. However, LMMs have not been previously applied to analyze population-scale human family trees. Here, we present Sparse Cholesky factorIzation LMM (Sci-LMM), a modeling framework for studying population-scale family trees that combines techniques from the animal and plant breeding literature and from human genetics literature. The proposed framework can construct a matrix of relationships between trillions of pairs of individuals and fit the corresponding LMM in several hours. We demonstrate the capabilities of Sci-LMM via simulation studies and by estimating the heritability of longevity and of reproductive fitness (quantified via number of children) in a large pedigree spanning millions of individuals and over five centuries of human history. Sci-LMM provides a unified framework for investigating the epidemiological history of human populations via genealogical records.