Introduction
Plant traits are often correlated, either positively or negatively, which has been ecologically explained to reflect the trade‐offs in biological functions and resource allocation, and allometric scaling (Freschet et al., 2015; Agrawal, 2020). The traits could become correlated due to common evolutionary processes such as correlated selection (Armbruster et al., 2014). The plant height and seed size scaling are manifested as a positive correlation between the two traits, and it sits within the broad allometric scaling that describes the relative growth rates of different body parts following a positive correlation of an individual organ versus total body size. Allometric scaling emerges as one of a seemly universal law in biology from genomes to ecosystems (West & Brown, 2005). Over the past century, many morphological, ecological, and evolutionary size-correlated trends have been observed across organisms and life forms (Kleiber, 1947, 1975; McMahon & Bonner, 1983; Schmidt-Nielson, 1984; Niklas, 1994; Brown & West, 2000; Moles et al., 2004; Novack-Gottshall., 2008; Vasseur et al., 2018). Various of conceptual frameworks have been proposed when seeking the underlying mechanisms of the broadly observed allometric scaling (e.g. Charnov et al., 1993; Blum, 1977; West et al., 1997; Darveau et al., 2002; Weibel, 2002, Niklas, 2004; Moles et al. 2005; Grubb et al. 2005; Rees & Veranble, 2007; Falster et al. 2008, Veranble and Rees, 2009, Westoby et al., 2009). The mechanism underlying the scaling law and traits correlation requires genetic explanations, but that is less explored in the current research endeavour.
Pleiotropy has been proposed as a significant mechanism leading to trait correlation (Saltz et al., 2017). Pleiotropy is defined as the phenomenon in which a genetic variant influences two or more phenotypic traits. The pleiotropic genetic variant may only have a single function, but it is involved in multiple biological processes; alternatively, the variant could have multiple functions that are related to different traits (Blow & Hoffmann, 2005; Hine et al., 2014; Saltz et al., 2017). Trait correlation could also be the effect of genetic linkage, e.g. the co-selection of gene variants closely linked to selected loci of interest in the chromosome leading the correlation of trait expression, as physical linkage based correlations can be stable over many generations in species with low recombination rate (Agrawal et al., 2010; Langridge & Fleury, 2011). The recent advancements of high throughput genotyping and large scale phenotyping offers an opportunity to decipher the different genetic basis of trait correlation. Genome-wide association studies (GWAS) reveal single nucleotides polymorphisms (SNPs) that are significantly associated with a particular phenotype (Xiao et al., 2017), therefore allows identifying genetic variants that influence more than one trait. Further, if the physical position on the chromosome of the responsible genetic variants is known, their genetic linkage can be examined. Recently, genomic structural equation modelling (genomic SEM) emerges as a powerful method for deciphering the joint genetic architecture of multiple traits. Genomic SEM models shared genetic architecture across multiple phenotypes with factors representing broad genetic liabilities through common factors analysis (Grotzinger et al., 2019). Therefore, genomic SEM offers an opportunity to not only directly explore pleiotropy as a genetic explanation on trait correlation, but also to describe pleiotropic genetic variants that may have driven the trait correlation.
Moreover, plant height and seed size (weight) are important agronomic traits in cereal crops and pulses. The pattern and evolution of plant height and seeds weight scaling might be affected by direct selection, as domestication and modern breeding often target the two traits in opposite directions. For example, shorter and stiffer stems protect cereal crops against lodging and provide a significant yield improvement, referred as ‘Green Revolution’ in literatures (Langridge, 2014). Larger seeds for consumption might have been one of the selection goals in the domestication and breeding of grains and pulses (Milla et al., 2015). However, it is still largely unknown if the artificial selection such as domestication and intense breeding change the pattern of size scaling. Barley (Hordeum vulgare L.) is one of the most important cereal crops in Old World agriculture and has been domesticated 10,000 years ago (Badr et al., 2000). Barley has been subject to extensive genomic study with abundant genomic and phenotypic data resources available (e.g. Mascher et al., 2017; Gonzalez et al., 2018; He et al., 2019; Milner et al. 2019), which provides unprecedented opportunity to explore the genomic basis of size scaling in plants. Here we use the recently generated high-density genome-wide SNP profile for a diverse set of barley samples, and their measurements of plant height and seeds weight to identify the possible genetic mechanisms that may lead to a correlation of plant height and seeds weight to explore the genomic basis of size scaling in plants.