Table 1.

A summary of genetic effects contributing to variation within the various links (trait×trait) of the WD

Trait–trait	Reference	Main finding in relation to WD	Gene(s)	Chromosome	Validation
Grain set×yield	Sakuma et al. (2019)	This gene is an HD-Zip I transcription factor which is expressed most abundantly in the most distal floret primordia where the authors suggest it inhibits growth. Reduced function mutants produce more fertile florets.	GN1-1A	2A	Tilling, RNAi
	Peng et al. (1999)	Rht-D1b dwarfing alleles increase grain number.	Rht-1	4B and 4D	NIL, transgenic
	Muqaddasi et al. (2019); Kuzay et al. (2019, 2022)	Both studies showed that the wheat homologue of the rice gene Aberrant panicle organization 1 (APO-1) controls spikelet number in bread wheat.	TaAPO-A1/WAPO1	7A	GWAS
	Griffiths et al. (2009)	Meta QTL analysis identified a number of Earliness per se QTLs, some of which were later shown to also effect grain number.	QTL	Multiple	Meta QTL
	Sukumaran et al. (2016)	This work showed that a major Earliness per se gene (EPS-D1) identified in the UK was also important in CIMMYT germplasm and these phenology effects were later shown to influence grain number.	Eps-D1/ TaELF3D1	1D	GWAS
	Alvarez et al. (2016); Zikhali et al. (2016)	These studies showed that EPS-D1 corresponded to ELF3 which is a component of the circadian clock.	EpsD1/TaELF3D and EpsAm1	1D and 1A	NIL, fine map
	Martinez et al. (2021)	A yield QTL identified in the Avalon×Cadenza population and validated using NILs was mapped at higher genetic resolution and shown to co-locate with heading date effects for which the best gene candidate was TaFT2.	TaFTA2 (candidate)	3A	NIL, fine map
	Shaw et al. (2019)	This work supports an important role for FT2 in grain number determination, with transgenic manipulation of the gene producing changes in various fertility traits.	TaFT2	Group 3	Transgenic
	Glenn et al. (2022)	A single amino acid substitution was associated with significant increases in grain number per spike in bread and pasta wheat.	TaFT2	3A	NIL and population
Grain size×yield	Snape et al. (2007)	The identification of a major QTL for grain size underwent intensive subsequent study.	QTL	6A	NIL (later studies)
	Farre et al. (2016)	Grain size QTL validated in the Avalon×Cadenza NIL library.	NIL effects	2A, 5A, 6A	NIL
	Huang et al. (2015)	A robust set of QTLs identified in Chinese germplasm for grain size were validated in NILs showing that marker-assisted selection for this trait is effective and relatively facile.	QTL	2D, 4B, 5A	NIL
	Guan et al. (2019)	As above.	QTL	4A	NIL
	Calderini et al. (2021)	Overexpression of an α-expansin in early developing wheat seeds leads to a significant increase in grain size without a negative effect on grain number, resulting in a yield boost under field conditions.	Expansin		Transgenic
	Simmonds et al. (2014)	Probably the most intensively studied grain size QTL in wheat.	TaGW2-A1	6A	NIL, tilling
Crop growth×duration of TS–An	Borras-Gelonch et al. (2012)	Independent genetic control of phenology stages shows that, if it is beneficial to allocate more time to the TS–An phase, the genetic variation to do this is available.	QTL	Multiple QTLs	None
	Guo et al. (2016)	Detailed glasshouse study using GWAS to map genes controlling phenology phases.	MTA	Multiple	None
Internode length and dry matter partitioning×spike partition index	Peng et al. (1999)	Rht-1 was cloned and shown to be a DELLA domain growth inhibitor. The wild-type protein (full length) is degraded when GA levels increase so that growth is no longer supressed. This sensitivity is removed in the semi-dwarf plants so that growth repression (stem extension) is constitutively expressed so more assimilate can be directed towards the spike.	Rht-1	Homoeologous loci on group 4 chromosomes. Semi-dwarfing alleles reported on 4B and 4D.	NIL, transgenic
Spike partition×spike growth	Abeledo et al. (2019)	This study shows that when the trouble is taken to collect these phenotypes, QTLs are detected, in this case for spike dry weight at anthesis.	QTL		None
	Rebetzke et al. (2011)	Rht13 is an NBS-LRR class of gene with the Rht13b allele autoactivated to reduce height to a similar extent to Rht1 semi-dwarfing alleles and, like those alleles, can also act to increase grain yield through grain number.	Rht13	7B	NIL, tilling
	Cui et al. (2011); Zhang et al. (2017); Abeledo et al. (2019)	Physiological studies show that even when optimal height is achieved in wheat, further fine-tuning is possible by reducing the length of specific internodes. These studies show that QTLs can be identified for internode specific length variation.	QTL	Multiple QTLs	NIL
	Miralles and Slafer (1995); Flintham et al. (1997)	Both studies use NILs in very diverse backgrounds to show that genetic variation at the Rht1 locus reduces height, increases harvest index, and increases grain yield by increasing grain number.	Rht-1	See above	NIL
	Tang et al. (2021)	This work shows that Rht18 can confer the same advantages as Rht-1 without some of the negative effects such as reduced coleoptile length. Ford et al., (2018) showed that Rht18 is associated with increased expression of GA2ox-A9, which encodes a GA-inactivating enzyme that reduces bioactive GA levels.	Rht18 (major gene not cloned)
Fruiting efficiency×grain set	Pretini et al. (2020b)	In a doubled haploid population (Baguette 19×BIOINTA 2002) increasing alleles for a fertile floret efficiency QTL acted through increased grain set.	QTL	5A	F2
Floret development×fruiting efficiency	Prieto et al. (2020)	This shows how Earliness per se genes alter seed number by influencing floret survival, but the direction of effect is temperature dependent, so maximizing grain number via phenology is a genetic balancing act that depends on environmental factors.	ELF3 and FT2 (candidates)	1D and 3A	NIL
Time of anthesis×fruiting efficiency	Giunta et al. (2018)	Fruiting efficiency QTLs were identified and their relationship to phenology dissected.	QTL	Multiple	None
Duration of TS–An×floret development	Basavaraddi et al. (2021b, c)	Both QTLs affected the spike fertility by altering the rate of floret development and mortality.	QTL	2B and 7D	NIL
Spike vascular architecture×floret development	Sang et al. (2010)	No publications could be found for QTLs for variation in spike vasculature, but Sang et al. did find QTLs for small and large vascular bundles of the peduncle.	QTL	Multiple	None
Ovary size×grain weight potential	Brinton et al. (2017)	A robust QTL controlling a 7% increase in grain weight shown to be due to increased pericarp cell length.	QTL	5A	NIL
Grain weight potential×grain weight realization	Chapman et al. (2021)	Independent EMS-induced mutants expressing delayed senescence and increased grain yield by extended grain fill were shown to have undergone amino acid changes in subdomain 4 of the NAC domain of NAM1.	NAM-A1 and NAM-D1	6A and 6D	Major gene, tilling, NIL
Endosperm cell number/maximum water content of grain×grain weight potential	Bednarek et al. (2012)	Cell number has been shown to underlie single gene effects on grain size, as in this study.	TaGW2	Group 6	RNAi
Spike hormones–grain weight potential	Guo et al. (2022)	TaCYP78A5 participates in auxin synthesis pathway and promotes auxin accumulation and cell wall remodelling in ovary. Localized overexpression of TaCYP78A5 in ovary results in delayed flowering and prolonged proliferation of maternal integument cells, which promote grain enlargement.	TaCYP78A5		Transgenic
Sink strength×source strength	Mason et al. (2013)	Source and sink strength are captured in many studies as biomass components at harvest. Here a Halberd×Karl92 population was used to show the co-localization of grain yield and biomass QTL.	QTL	3B	None
Protein/starch synbthesis×grain weight realization	Uauy et al. (2006)	Grain yield and protein concentration are negatively correlated but yield can be increased without decreasing protein if genes controlling grain protein difference (GPD) are exploited. In this work it was shown that NAM-B1 variants can increase grain protein without decreasing grain yield.	NAM-B1/Gpc-B1	6B	NIL, transgenic
Duration of grain fill×grain weight realization	Chapman et al. (2021)	Independent EMS-induced mutants expressing delayed senescence and increased grain yield by extended grain fill were shown to have undergone amino acid changes in subdomain 4 of the NAC domain of NAM1.	NAM-A1 and NAM-D1	6A and 6D	Major gene, tilling, NIL
Source strength×grain weight realization	Chapman et al. (2021)	Source strength was increased through delayed senescence.	NAM-A1 and NAM-D1	6A and 6D	Major gene, tilling, NIL
Source strength×protein/starch synthesis	Uauy et al. (2006)	This study showed that a NAC transcription factor was a major regulator of senescence in wheat.	NAM-B1	6B	NIL, fine map, transgenic
	Chapman et al. (2021)	Independent EMS-induced mutants expressing delayed senescence and increased grain yield by extended grain fill were shown to have undergone amino acid changes in subdomain 4 of the NAC domain of NAM1.	NAM-A1 and NAM-D1	6A and 6D	Major gene, tilling, NIL
Carbohydrate storage and remobilization×starch synthesis	Yang et al. (2007)	Several studies had identified QTLs for stem soluble carbohydrate reserves and, as in this case, the remobilization efficiency of those reserves (RESWC) and effect on yield.	QTL	1A, 3B, 7A	None
Protein synthesis×starch synthesis	Numerous	The strong negative correlation between yield and protein content means that almost all yield QTLs correspond to an opposite effect for protein.

For well-studied traits with high heritability, studies in which causative genes have been identified are prioritized. When most evidence is at the level of QTL studies or genome-wide association studies (GWAS), the support of independent validation using unrelated populations and/or NILs is used to help prioritize studies for inclusion. In several cases, the only level of genetic evidence (if any) is based on QTL studies without further validation. Priority is also given to studies in which the wider deployment of beneficial alleles is most likely to lead to progress in modern breeding programmes. In cases where no publications were found in spite of best efforts, this is stated. In all but a few cases, these studies are based on yield measured in field experiments with wheat grown in replicated plots