Discussion
The offspring size at independence has been shown to be correlated with adult size across plant species (Moles et al., 2004) and animals (McMahon & Bonner, 1983; Rollinson et al., 2019). Here we show that the size scaling law holds within domesticated crop species when examining the plant height and seeds weights within 12,828 globally collected barley samples. The observed correlation across species between adult size and offspring size at independence (seeds weight in the case of the plant) has been hypothesized as the result of evolutionary coordination between the two traits (Moles et al., 2005; Rees & Venable, 2007, 2009; Westoby et al., 2009), though Grubb et al. (2005) argued for a biomechanically constrained mechanism shaping size scaling. Despite the mechanisms underlying size scaling remain debated from a theoretical perspective (Niklas, 2004), the size components – plant height and seeds weight – are undoubtedly under natural selection or artificially selection in the case of crop plants (Gross & Beckage, 2012). It is a logical hypothesis that the correlation between the two traits has a genetic basis. Using a large dataset with high-density genome-wide SNP map and phenotypes for barley, we demonstrated that two genetic mechanisms might be involved in shaping the plant height and seeds weight scaling. Both plant height and seeds weight are complex traits and are influenced by multiple genes. Multiple genes with significance in plant growth and development assert pleiotropic effects on both plant height and seeds weight contribute to the positive correlation of the two traits. Meanwhile, many of the genes influencing either plant height or seeds weight are closely linked in the chromosome, leading to co-inheritance of the two traits, also contributing to the trait correlation in barley. Together, our results provide direct empirical evidence to the hypothesis that the size scaling in plant has a genetic basis and it may be the result of shared genetic factors controlling both traits.
The plant height and seeds weight scaling hold for the domesticated barley, in both landraces and cultivars, despite thousands of years of domestication and breeding targeting the two traits in opposite directions. Barley breeding tends to select varieties with shorter and stiffer for protection against lodging and benefit of yield improvement (Langridge, 2014). Indeed, we observed an average shorter plant in landrace and cultivar than in wild barley. On the other hand, larger and plump barley grains are favoured as plump kernels could produce more beer from a given weight of malts (Gupta et al., 2010). Larger seeds would also be a selection goal as they could contribute to yield improvement. However, we observed averagely smaller seeds in both landrace and cultivars than in the wild barley. It seems that plant height and seed weight scaling is genetically constrained and less influenced by direct artificial selection.
The evolution of seeds weight (size) in domestication has been hypothesised be affected by both artificial and natural selection (Milla et al., 2015). However, a comparative study (Kluyver et al., 2013) failed to support the natural selection mechanism that proposes larger seeds were selected in agricultural habitats to allow more effective germination and larger vigorous seedlings with greater fitness (Turnbull & Rees, 1999; Purugganan, 2019). Our results of shared genetic factors controlling the two traits open an alternative hypothesis that the evolution of seed weight in domestication may have been constrained by the selection in plant height (size). Except for major cereal crops, domestication tended to increase aboveground plant size in many crops (Milla et al., 2017), likely as a consequence of selecting larger vegetative part for human consumption. Therefore, larger seeds may have been selected indirectly as the consequence of selecting for larger non-seed part as the two traits are genetically correlated. For cereal crops such as barley, rice and wheat, shorter plant with stiffer stem is advantageous as it resists lodging and increases the relative proportion of photosynthesis product allocating to seeds output. With cereal varieties having shorter plant is selected for improving grain yield, seeds adversely become smaller because of the genetic constrains.
Despite current researches believe that genetic architecture of size scaling and more broadly trait correlations, in general, are polygenic (Saltz et al., 2017). Gardner & Latta (2007) reviewed genetic correlations among  quantitative traits and found that an average of only two QTLs (quantitative trait locus) were shared between two correlated traits. The traditional method identifying causal QTLs for a trait, such as GWAS, may have limits because those methods usually rely on linkage decay among causal and non-causal variants to detect associations, and therefore cannot directly establish the number of causal variants (Gianola et al., 2015), which consequently underestimate the pleiotropic genetic variants underlying trait correlations (Saltz et al., 2017). Indeed, using regular GWAS analysis, we identified eight SNPs in two clusters (two QTLs) possibly have pleiotropic effects on plant height and seeds weight in barley. The advanced method in deciphering the genetic architecture of trait correlation, e.g. common factor analysis within the genomic SEM framework, allow us to identify SNPs that may be pleiotropic on influencing plant height and seeds weight, highlighting the power of advancement of analytical methodology.
At least three genes have been revealed to likely play an important role in structuring plant height and seeds weight scaling in barley, an expansins gene, an elongation factor G gene, and an Hsp90 organizing protein gene. It is known that these genes have a function for diverse traits related to plant growth and development. In barley, transcripts of these genes could be found in both grain and shoot (https://ics.hutton.ac.uk/barleyrtd/index.html). Expansins enable the local sliding of wall polymers by reducing adhesion between adjacent wall polysaccharides, and has an important role in cell wall re-modelling after cytokinesis. Expansins are required in plant physiological development aspects from germination to fruiting. It is known that expansins influence seed development and seed size, also increase plant height, root mass, number and size of leaves in plants (Chen et al., 2001; Ma et al., 2013; Bae et al., 2014). Elongation factor (EF ) G protein  promotes tRNA translocation on the ribosome (Stark, 2000). Liu et al. (2016) reported that overexpressed an EF gene (MaEF1A ) greatly enhanced plant height, root length, and both rachis and silique length by promoting cell expansion and elongation. Hsp90 organizing protein mediates nuclear-encoded chloroplast preproteins binding to HSP90 prior to chloroplast sorting (Odunuga et al., 2004). Hsp90 is extensively involved in plant growth and development and has a function for diverse traits such as hypocotyl elongation, leaf size, seed mass (Sangster et al., 2008; Delker & Quint 2011). These previous molecular biology studies suggest that the plant height and seed weight scaling may be co-ordinated through multi-functioning genes involved in plant growth and development.
The extensive research into crop genetic improvement has led to the accumulation of extensive data resources from genomics to phenotypes, which offers unprecedented opportunity to explore fundamental biological questions at the molecular and cellular level. Our results on the genomic mechanism underlying size scaling demonstrated the promise of using crop plants as a model organism in the research of plant biology. On the other hand, allometric relationships between traits can constrain phenotypic variation (Vasseur et al., 2018), which opens promising avenues for crop species with a perspective of targeting optimal crosses based on allometric relationships in parental lines (Garnier & Navas., 2012). For example, a pleiotropic genetic variant with desirable effects on two correlated traits would have direct benefit in plant breeding (Gross & Beckage 2012). In conclusion, plant height and seeds weight scaling could be formed through pleiotropic effect of many genes conferring an effect on both traits, and by the genetic linkage of genes with multiple functions in plant growth and development. Plant height and seed weight scaling is genetically constrained and less influenced by direct artificial selection, which could pose a serious challenge in crop breeding when targeting correlated traits in opposite direction. Though we here only examined plant height and seeds weight scaling within a species, it could be speculated that similar genomic basis may exist to explain the often observed allometric scaling across diverse species. The recent advances at cellular to molecular levels of organization, genomic analysis and large scale phenotyping, and research into heritability and genetic basis of size scaling could open a new venue for a grand unifying theory on allometric scaling in plants.