In plant breeding, heritability is often calculated (i) as a measure of precision of trials and/or (ii) to compute the response to selection. It is usually estimated on an entry-mean basis, since the phenotype is usually an aggregated value, as genotypes are replicated in trials, which stands in contrast with animal breeding and human genetics. When this was first proposed, assumptions such as balanced data and independent genotypic effects were made that are often violated in modern plant breeding trials/analyses. Due to this, multiple alternative methods have been proposed, aiming to generalize heritability on an entry-mean basis. In this study, we propose an extension of the concept for heritability on an entry-mean to an entry-difference basis, which allows for more detailed insight and is more meaningful in the context of selection in plant breeding, because the correlation among entry means can be accounted for. We show that under certain circumstances our method reduces to other popular generalized methods for heritability estimation on an entry-mean basis. The approach is exemplified via four examples that show different levels of complexity, where we compare six methods for heritability estimation on an entry-mean basis to our approach (example codes: https://github.com/PaulSchmidtGit/Heritability). Results suggest that heritability on an entry-difference basis is a well-suited alternative for obtaining an overall heritability estimate, and in addition provides one heritability per genotype as well as one per difference between genotypes.

The cultivation of perennial wild plant mixtures (WPMs) in biogas cropping systems dominated by maize (Zea mays L.) restores numerous ecosystem functions and improves both spatial and temporal agrobiodiversity. In addition, the colorful appearance of WPM can help enhance landscape beauty. However, their methane yield per hectare (MYH) varies greatly and amounts to only about 50% that of maize. This study aimed at decreasing MYH variability and increasing accumulated MYH of WPM by optimizing the establishment method. A field trial was established in southwest Germany in 2014, and is still running. It tested the effects of three WPM establishment procedures (E1: alone [without maize, in May], E2: undersown in cover crop maize [in May], E3: WPM sown after whole‐crop harvest of spring barley [Hordeum vulgare L.] in June) on both MYH and species diversity of two WPMs [S1, S2]). Mono‐cropped maize and cup plant (Silphium perfoliatum L.) were used as reference crops. Of the WPM treatments tested, S2E2 achieved the highest (19,296 normalmnormalN3/ha, 60.5% of maize) and S1E1 the lowest accumulated MYH (8,156 normalmnormalN3/ha, 25.6% of maize) in the years 2014–2018. Cup plant yielded slightly higher than S2E2 (19,968 normalmnormalN3/ha, 62.6% of maize). In 2014, the WPM sown under maize did not significantly affect the cover crop performance. From 2015 onward, E1 and E2 had comparable average annual MYH and average annual number of WPM species. With a similar accumulated MYH but significantly higher number of species (3.5–10.2), WPM S2E2 outperformed cup plant. Overall, the long‐term MYH performance of WPM cultivation for biogas production can be significantly improved by undersowing with maize as cover crop. This improved establishment method could help facilitate the implementation of WPM cultivation for biogas production and thus reduce the trade‐off between bioenergy and biodiversity.

The genetics underlying heterosis, the difference in performance of crosses compared with midparents, is hypothesized to vary with relatedness between parents. We established a unique germplasm comprising three hybrid wheat sets differing in the degree of divergence between parents and devised a genetic distance measure giving weight to heterotic loci. Heterosis increased steadily with heterotic genetic distance for all 1903 hybrids. Midparent heterosis, however, was significantly lower in the hybrids including crosses between elite and exotic lines than in crosses among elite lines. The analysis of the genetic architecture of heterosis revealed this to be caused by a higher portion of negative dominance and dominance-by-dominance epistatic effects. Collectively, these results expand our understanding of heterosis in crops, an important pillar toward global food security.

525RESEARCH I n plant breeding programs and cultivar evaluation trials, cultivars (genotypes) of interest are often grown and tested at multiple locations across several years. Such a series of trials is called a multienvironment trial (MET), where a year-location combination is referred to as an environment. To quantify and eventually compare the precision of METs, plant breeders often calculate narrow-sense heritability (h 2 ) or broad-sense heritability (H 2 ) on a genotype-mean basis. The latter is defined as the proportion of phenotypic variance that is attributable to an overall variance for the genotype, thus including additive, dominance, and epistatic variance (Holland et al., 2003;Falconer and Mackay, 2005). Moreover, there are usually additional interpretations associated with H 2 : (i) it is equivalent to the coefficient of determination of a linear regression of the unobservable genotypic value on the observed phenotype, (ii) it is also the squared correlation between predicted phenotypic value and genotypic value, and (iii) it represents the proportion of the selection differential (S) that can be realized as the response to selection (R) (Falconer and Mackay, 2005). It is important to note that the necessity to estimate H 2 on a genotype-mean basis results from the fact that in plant breeding, genotypes are often tested across a wide range of environments in designed, replicated experiments. ABSTRACTBroad-sense heritability is defined as the proportion of phenotypic variance that is attributable to an overall variance for the genotype. It is often calculated as a measure (i) to quantify and eventually compare the precision of agricultural cultivar trials, and/or (ii) to estimate the response to selection in plant breeding trials. In practice, most such trials are conducted at multiple environments (i.e., year-location combinations) resulting in a multienvironment trial (MET) with unbalanced data, as, for example, not all cultivars are tested at each environment. However, the standard method for estimating heritability implicitly assumes balanced data, independent genotype effects, and homogeneous variances. Therefore, we compared the estimates for broad-sense heritability computed via the standard method to those obtained via six alternative estimation methods (example codes:https://github.com/PaulSchmidtGit/ Heritability). We did so by analyzing four cultivar METs, which all displayed a typically unbalanced data structure but differed in the genetic frameworks of their cultivars. Results indicate that the standard method may overestimate heritability for all datasets, whereas alternative methods show similar estimates per dataset and thus seem better able to handle this kind of unbalanced data. Finally, we show that to compare heritability estimates between different METs, genetic variance component estimates should be fixed to common values for both datasets.

The medicinal use of cannabinoids renewed the interest in industrial hemp (Cannabis sativa L.). The aim of this study was to evaluate the impact of growth stage and biomass fractions of seven industrial hemp genotypes. The study focused on biomass yield, content of cannabidiolic acid/cannabidiol (CBDA/CBD), cannabigerolic acid/cannabigerol (CBGA/CBG), and tetrahydrocannabinolic acid (THCA). The experiment was conducted in 2017 and 2018. The biomass samples were taken at the vegetative (S1), bud (S2), full-flowering (S3) and seed maturity stage (S4). Plants were fractionated into inflorescence, upper and lower leaves. The average inflorescence dry yield of genotypes Futura75, Fédora17, Félina32 and Ferimon ranged between 257.28 g m−2 to 442.00 g m−2, resulting in a maximum yield of CBDA at S4, with 4568.26 mg m−2, 6011.20 mg m−2, 4975.60 mg m−2 and 1929.60 mg m−2, respectively. CBGA was exclusively found in genotype Santhica27, with a maximum CBGA yield of 5721.77 mg m−2 in inflorescence at growth stage S4 and a dry weight yield of 408.99 g m−2. Although these industrial hemp genotypes are mainly cultivated for fibre and seed production, however, cannabinoids offer an additional value. For an optimized harvest result, yield of extractable material and overall yield of cannabinoids must be considered.