Fruiting efficiency: an alternative trait to further rise wheat yield

Wheat is critical for food security, as it is the crop most widely grown and is the primary source of protein for the world population (Chand 2009 ; Braun et al. 2010 ). Genetic gains in wheat yield have been outstanding during the second half of the 20th century (Calderini et al. 1999 ; Foulkes and Reynolds 2015 ; and references quoted therein). This success has been instrumental for, roughly contributing 50% (Slafer and Andrade 1991 ) to the increases in ORIGINAL RESEARCH

production, more than matching the increased demand produced by an unprecedented growth in world population (more than doubling in just half-century the population built up in the previous 2000 centuries, since the beginning of our species). Thus genetic gains were critical for the improved levels of food security in the last half century.
The population is still growing fast and, in addition, there is an on-going change in diet habits, both factors determining that the demand will further increase over the next decades. This time, the satisfaction of the increased demand must mainly come from yield improvement as the amount of land for agriculture will not increase, and may even decline (Albajes et al. 2013 ). It may be required that yield of wheat (and other major crops) be increased by at least 50% in the next few decades (Reynolds et al. 2009 ), which will depend on improving yield potential (Fischer and Edmeades 2010 ;Hall and Richards 2012 ). As crop management should be environmentally more sustainable in the future (Godfray 2011 ;Tilman et al. 2011 ), the contribution from genetic gains should be similar to that of the few decades following the Green Revolution. But, in the last 2 decades wheat yield grew less than the demand and in several regions showed signs of stagnation (Calderini and Slafer 1998 ;Brisson et al. 2010 ;Ray et al. 2012 ). Likewise, genetic gains reported for different countries for the last decades also seem to have been increasing less than required (Shearman et al. 2005 ;Acreche et al. 2008 ;Sadras and Lawson 2011 ;Lopes et al. 2012 ).

How was yield improved in the past?
It seems reasonable to speculate that a better understanding of crop yield physiology would help to increase the current rates of genetic gains (Slafer 2003 ;Araus et al. 2008 ;Reynolds et al. 2012 ). Based on the model proposed long time ago by Fischer ( 1984 ), and well developed in a recent review (Fischer 2011 ), the diagram in Figure 1 shows that: • Wheat yield is most commonly sink-limited during grain fi lling; which means that the amount of available assimilates (current photosynthesis plus remobilization of preanthesis reserves) are in excess to the demand of the growing grains (Borras et al. 2004 ;González et al. 2014 ), not only under high-yielding but also across a wide range of conditions (Pedro et al. 2011 ;Serrago et al. 2013 ). Thus, genotypic differences in yield are frequently strongly related to those in grain number (Garcia et al. 2013 ;Slafer et al. 2014 ), as it is more plastic than grain weight (Sadras and Slafer 2012 ). But for a particular number of grains there is variation in grain size which does also affect yield though not as primarily (in most conditions) as grain number . In fact, genetic gains in wheat yield have been more related to improvements in the number than in the size of the grains (e.g., Canevara et al. 1994 ;Calderini et al. 1995 ;Sayre et al. 1997 ;Shearman et al. 2005 ;Acreche et al. 2008 ). • Grain number, in turn, is strongly related to spike dry weight at anthesis; which is quite reasonable as: (1) wheat is a cleistogamous plant and therefore most fertile florets set grains and consequently grain number is related to the number of fertile florets; (2) final number of fertile florets depends on the developmental process of floret generation/degeneration; (3) this developmental process occurs in the growing spike before anthesis; and (4) is related to the availability of resources (González et al. 2011a ;Ferrante et al. 2013b ;Dreccer et al. 2014 ). Therefore, the final number of grains is source-limited during preanthesis and depends mechanistically on the growth of the juvenile spikes in which floret primordia are developing  ) and, for particular levels of spike dry weight, on the efficiency with which the resources are used to set grains or fruiting efficiency 1 (González et al. 2011b ;Ferrante et al. 2012 ;García et al. 2014 ). Therefore, breeding through the Green Revolution improved spike growth (and consequently spike dry weight at anthesis) bringing about a reduced rate of fl oret mortality increasing the number of fertile fl orets (e.g., Miralles et al. 1998 ). • Spike growth during the prefl owering period is the result of crop growth during that period and the proportion of that growth partitioned to the spikes. Virtually all papers analyzing these aspects in breeding during the second half of the 20th century agreed in that there were not trends to systematically and consistently modify growth of the crop whilst there was a consistent trend to increase partitioning of biomass to the reproductive organs (e.g., Siddique et al. 1989b ;Slafer and Andrade 1993 ).
When considering how wheat breeding has successfully achieved large gains in the second half of the 20th century, it seems quite straightforward. The tremendous success of the Green Revolution was achieved through relatively simple (seen retrospectively) interventions in yield physiology ( Fig. 1 , open arrows on left panels and panels on the right). Although exceptional cases could eventually be found, the vast majority of studies of physiological attributes explaining genetic gains in wheat yield coincides in that breeding during the second half of the last century: • Did not systematically affect biomass production of the crop (Austin et al. 1980(Austin et al. , 1989Perry and D`Antuono 1989 ;Siddique et al. 1989a ;Slafer and Andrade 1991 ;Sayre et al. 1997 ;Calderini et al. 1999 ), but increased the partitioning toward the developing juvenile spike due to genetic restrictions to stem growth (Siddique et al. 1989a , b ;Slafer and Andrade 1993 ), so that during the stem elongation phase, the stem requirements for extension were reduced and partitioning to the spikes favoured, • Consequently, even with no trends to improve crop growth, spike dry weight at anthesis consistently increased whilst stem length was reduced from traditional to semidwarf plant statures; and the increased growth of the juvenile spikes brought about improvements in fl oret development increasing spike fertility (Miralles et al. 1998 ), • As spike fertility increased, the number of grains set by the crop in modern cultivars improved compared to their predecessors and the increased postanthesis sink strength resulted in concomitant increases in yield (Sayre et al. 1997 ;Abbate et al. 1998 ;Calderini et al. 1999 ).
Consequently, when comparing cultivars released at different times from before to after the Green Revolution, or when comparing isogenic lines for dwarfi sm (Rht lines), it can be seen that modern cultivars (or semidwarfi ng lines) out-yield the older ones (or the tall lines) due to having more grains associated with higher spike dry weight at anthesis (e.g., Fischer and Stockman 1980 ;Brooking and Kirby 1981 ;Siddique et al. 1989b ;Slafer and Andrade 1993 ;Miralles et al. 1998 ;Acreche et al. 2008 ).

The problem that fruiting effi ciency could help to solve
Past breeding during the Green Revolution and the few decades following it was extremely successful. In the process plant type was modifi ed optimizing its height and consequently current high-yielding cultivars possess a height that is within the optimum range to maximize yield (c. 0.7-1.0 m: Richards 1992 ; Slafer 1995a , 1997 ;Flintham et al. 1997 ). This means that the main trait genetically manipulated to obtain remarkable genetic gains in yield cannot be further deployed: taller plants would have penalties due to poor partitioning, and higher risk of lodging; shorter plants would result in lower crop growth as radiation use effi ciency would be reduced due to poor radiation distribution within the canopy (Miralles and Slafer 1995a ). For future genetic gains to recover the pace that characterized breeding in the recent Figure 1 . Simplifi ed conceptual model of the physiological components of yield in wheat (Fischer 1984(Fischer , 2011Slafer et al. 2005 ). On the left the most common relationships considering wide ranges in yield produced by genotypic or environmental factors are shown. The open arrows point out the main pathways used by breeding to produce genetic gains in yield during the second half of the 20th century. Panels on the right exemplify relationships most commonly found when the source of variation has been cultivars released at different years during the 20th century (when the abscissa is "time" it refers to the time from the onset of stem elongation to anthesis, and in these cases the solid and dashed lines stand for cultivars released before or after the Green Revolution, respectively). For more detail see Calderini et al. ( 1999 ) and Foulkes and Reynolds ( 2015 ).
past, alternative traits putatively related with grain number and yield, must be identifi ed and exploited. One avenue would be identifying sources of variation to increase crop photosynthesis, so that higher biomass at anthesis would result in more spike dry weight at anthesis bringing about more grains set and higher yields (Parry et al. 2011 ;Reynolds et al. 2012 ). Another alternative, not mutually exclusive with the previous one, could be to lengthen the duration of the spike growth period (or more broadly the duration of the stem elongation phase) so that for a constant rate of growth and level of partitioning, the longer the phase the higher the spike dry weight at anthesis Miralles and Slafer 2007 ;González et al. 2011b ). Scaling up one step in Figure 1 , there is another alternative which is to increase fruiting effi ciency; that is the number of grains produced per unit of spike dry weight at anthesis. In other words, the effi ciency with which the resources allocated to the spikes are used to produce a certain number of grains (Abbate et al. 1998(Abbate et al. , 2013González et al. 2011b ;Ferrante et al. 2012 ;Garcia et al. 2014 ).

Objective
The aim of this paper is to review the state-of-the-art in wheat fruiting effi ciency. For that purpose we (1) described the trait and its physiological bases, (2) revised to what degree fruiting effi ciency has been deployed in past breeding, (3) reviewed the literature to quantify the degree of variation available for the trait, particularly within elite material including modern cultivars, and finally (4) considered potential drawbacks that must be taken into account to avoid increases in fruiting effi ciency not resulting in yield gains by being compensated by other traits.

Pathways to Increase Fruiting Effi ciency
As indicated above, fruiting effi ciency is estimated as the ratio between grain number (determined after grain set, normally at maturity) and spike dry weight at anthesis. It refl ects the overall effi ciency with which a certain amount of resources, allocated to the juvenile spike growing before anthesis, are used to set grains. Grains are the product of pollinated fertile fl orets, which in turn are the result of fl oret primordia development; which occurs within the spike (within the spikelets of the spike) precisely during the period when the juvenile spike grows before anthesis (Kirby 1988 ;González et al. 2011a ;Slafer et al. 2015 ). It has been many times shown that fl oret primordia development is rather responsive to the availability of assimilates.
Studying the dynamics of fl oret development for contrasting availability of resources can illustrate the responsiveness of this developmental process. For instance, one of the treatments imposed by Ferrante et al. ( 2013a ) consisted in detillering plants during stem elongation. Then, the fate of fl oret primordia in the main-shoot spikes of plants tillering freely (and then growing under competition with other spikes) was compared with the ones being detillered permanently (and then growing in the absence of the competition from other spikes). Detillering the plants did not affect the developmental patterns of the most proximal fl orets (which do develop to produce fertile fl orets in virtually any condition), but more vulnerable fl orets in less proximal positions within the spikelets (those that develop to produce fertile fl orets or die in the process, depending on the conditions; for example, fl orets 3, 4, and 5 from the rachis) developed more in the spikes of the detillered plants than in the spikes of the plants with free tillering (Fig. 2 ). This increased survival of the distal fl orets was associated with increased assimilate availability to the growth of the main stem spike in the detillered plants (Ferrante et al. 2013a ). This is the main reason why it has been widely documented that the number of grains is drastically sensitive to spike growth immediately before anthesis, and therefore it decreases sharply in response to shading during the period when spike growth takes place (Fischer 1985 ;Savin and Slafer 1991 ;Slafer et al. 1994 ;Abbate et al. 1997 ;Demotes-Mainard et al. 1999 ;Demotes-Mainard and Jeuffroy 2004 ), as well as to changes in duration of the spike growth phase as affected by manipulation of day-length in sensitive cultivars (Miralles et al. 2000 ;González et al. 2003González et al. , 2005bFischer 2007 ;Serrago et al. 2008 ). These responses are mostly related to the positive relationship between grain number and spike dry weight at anthesis, that also explains for instance grain number (and yield) responsiveness to nitrogen fertilization (Fischer 1993 ;Abbate et al. 1995 ;Demotes-Mainard et al. 1999 ;Demotes-Mainard and Jeuffroy 2001 ;Prystupa et al. 2004 ;Ferrante et al. 2010Ferrante et al. , 2012Ferrante et al. , 2013a or to general environmental changes affecting yield (Marti and Slafer 2014 ), as well as to improvements in biomass partitioning to the juvenile spikes (as discussed above, explaining the main physiological reason for the Green Revolution). More recently, it has been also shown the mortality of fl oret primordia (the main component explaining the fi nal number of fertile fl orets and grains) seems to be clearly dependent upon the availability of assimilates (González et al. 2011a ;Ferrante et al. 2013b ).
Fruiting effi ciency is the fi nal outcome of fl oret developmental rates (determining the number of fl oret primordia that reach the stage of fertile fl orets at anthesis) and the proportion of grain set per fertile fl oret (the opposite to grain abortion), per unit of spike weight (i.e., more effi cient genotypes would show a higher survival of fl oret primordia, and/or a reduced level of grain abortion). As modern wheat cultivars show low grain abortion (Siddique et al. 1989a , b ;González et al. 2003González et al. , 2005a, differences in fruiting effi ciency in modern cultivars maybe likely related to higher survival of fl oret primordia. Therefore, there are two alternative physiological pathways ( Fig. 3 ) to improve fruiting effi ciency, by allowing a normal development of most vulnerable fl oret primordia (those in more distal positions of the spikelets), through maintaining cell division in these fl orets and avoiding the initiation of autophagy 2 (Ghiglione et al. 2008). These are: • An increased allocation of assimilates for the fl orets developing during spike growth before anthesis (for a particular level of spike growth). This would result in less investments in the structural pieces of the spike (rachis, glumes) in favour of an increased allocation to the growth of the fl orets, or • A reduced demand of the fl orets for maintaining their normal development. If fl orets constitutively demand less assimilates for normal development, the proximal fl orets would leave more resources available for more distal fl orets which would maintain their growth and development normally for longer. Then, the intermediate fl orets would increase their likelihood to become fertile fl orets at anthesis (and to produce a grain). The most likely consequence of this would be that fertile fl orets at anthesis would be smaller in the genotype with higher fruiting effi ciency.
As in some studies differences in fruiting effi ciency seemed associated with dry matter partitioning within the spike at anthesis (Slafer and Andrade 1993 ;Abbate et al. 1997 ), whilst in others such relationship was not identifi ed (Abbate et al. 1998 ;Fischer 2007 ), both alternatives may be possible. It might be critical to recognize which of them is the actual cause of differences in fruiting effi ciency as the potential trade-offs with grain weight are quite different (see later discussion on Potential drawbacks ). One inconvenience of fruiting effi ciency is that it is a trait requiring the sampling and processing of samples at two different stages: spike dry weight must be determined at anthesis 3 and grain number when it has been fi xed, at least 2-3 weeks later, most normally at maturity. To make this simpler, sometimes the dry weight of the chaff at maturity (structural parts of the spike after removing the grains) is used to provide an estimate of the dry weight of the spikes at anthesis (e.g., Abbate et al. 2013 ;Marti and Slafer 2014 ). For this to be accurate there should be  no growth in the nongrain parts of the spikes during grain fi lling. Although to the best of our knowledge reasons have not been understood, there are clear indications that chaff weight at maturity is consistently higher than spike dry weight at anthesis (or than the nongrain spike dry weight a week after anthesis). Fischer ( 2011 ) estimated this difference to be neither minor nor constant (chaff weight can be 20-50% greater), based on relatively old studies (Wall 1979 ;Fischer and Stockman 1980 ;Stockman et al. 1983 ) in which the focus was not genotypic variation in fruiting effi ciency. Not many studies analyzed (or at least reported) genetic variation in spike dry weight at anthesis and chaff weight at maturity within high-yielding modern cultivars. The two of which we are aware of showed data that broadly confi rmed that the estimated difference reported by Fischer ( 2011 ) was not an exception. In the papers by González et al. ( 2011b ) and Abbate et al. ( 2013 ) chaff weight at maturity was, without a single exception, greater than spike dry weight at anthesis (averaging across genotypes and experiments a difference of 32 and 43%, respectively), with a substantial variation due to genotypes within each of the experiments; and there was a consistent trend to increase the magnitude of the underestimation with increases in fruiting effi ciency as the slope was substantially lower than 1 (Fig. 4 ). Expanding further the analysis, when the variation was not restricted to modern cultivars but to a much larger population of double haploid lines (Garcia et al. 2014 ) , the general pattern that using chaff at maturity does consistently underestimate fruiting effi ciency (and the higher the effi ciency the greater the magnitude of the overestimation) is further emphasized (Fig. 4 ). Thus, even though there was a signifi cant positive relationship between both estimates, it seems clear that using chaff at maturity could provide only a rough proxy to fruiting effi ciency.
In some cases it has been preferred to determine spike dry weight few days after anthesis to consider the period of grain set (during the lag-phase of grain fi lling; Loss et al., 1989) as well. Although this is rather sensible, it has two major inconveniences. Firstly a huge amount of extra work is required to remove the tiny grains that might have already started to grow (otherwise the spike dry weight would be strongly overestimated and the overestimation would vary between genotypes (and environments) depending on the number of grains set and the potential size of the grains. Secondly, the estimated spike dry weight would include any eventual growth occurring during that extra week, which is naturally positive, but would exclude the weight contributed by the fertile fl orets to the spike dry weight at anthesis, which would be a drawback. All in all, we believe that it would be convenient to standardize the determination of fruiting effi ciency using spike dry weight at anthesis.

Contributions of Fruiting Effi ciency to Wheat Breeding
Was fruiting effi ciency improved during past breeding?
Due to the dominating effect of reducing stem growth (semi-dwarfi sm), favoring the growth of the juvenile spike bringing about improvements in spike fertility and yield (see above), there have been only limited attempts to quantify the impact of past breeding on fruiting effi ciency. In this section we revisited the very few cases in which this trait was analyzed in experiments comparing sideby-side cultivars released at different times (covering at least 20 years of breeding) under fi eld conditions (Table 1 ).
Within the few cases available, there were no consistent trends: no increases in fruiting effi ciency were observed at all in Argentina, there seemed to have been a clear positive trend in Spain; and the relationship was not signifi cant but a positive trend might be inferred in the UK (Fig. 5 ). Grain number was increased in all the three countries analyzed, in Argentina the improvement in grain number was exclusively due to parallel increases in spike growth before anthesis (Slafer and Andrade 1993 ;González et al. 2003 ), while in Spain it was associated with spike growth before anthesis as well but also with fruiting effi ciency of the cultivars (Acreche et al. 2008 ). In the UK (Shearman et al. 2005 ) increases in grain number were also consequence of increased In addition, we added data adapted from Garcia et al. ( 2014 ) who analyzed variation among a mapping population with a much larger degree of variation than modern cultivars that broadly fall within the same cloud of data-points but with an even smaller slope; data from the study in which spike dry weight was measured at anthesis and values at chaff were unpublished).
spike dry weight, although again there was a nonsignificant positive trend between grain number and fruiting effi ciency for the cultivars released during the last three decades of the 20th century. In a much shorter period of analysis, Abbate et al. ( 1998 ) reported for cultivars released from 1984 to 1994 in Argentina that improvement of grain number was mostly associated with differences in fruiting effi ciency.

Potential usefulness of fruiting effi ciency in future breeding
In the past, fruiting effi ciency was not even considered as a possibility because huge gains could be obtained relatively simply by selecting for reduced height (increasing partitioning to the spikes before anthesis and gaining in sink strength and yield, see above). In the future, it may be more relevant as a trait to consider, at least for identifying prospective parents for a cross designed to increase further yield potential. Selecting for fruiting effi ciency would be much more diffi cult, unless trustworthy molecular markers are identifi ed or high throughput tools could be developed. Abbate et al. ( 2013 ) have shown that selecting few individual spikes at maturity from a crop may produce sensible results reducing enormously the amount of work required for a more refi ned determination of fruiting effi ciency. However, even measuring fruiting effi ciency in few spikes would be a diffi cult task in realistic Table 1 . Description of studies in which breeding impact on fruiting effi ciency was estimated (or the data are available for the estimation). All experiments carried out under high-yielding conditions.

Location
Cultivar Year of release Grain number 1 (10 −3 m −2 )  breeding programs selecting thousands of plots per season. In any case, there is an indication that if it were possible to identify proper markers (or to develop a high throughput screening method) it could be effective to select for fruiting effi ciency. Pedro et al. ( 2012 ) have conducted an experimental selection procedure (selecting divergently for higher or lower fruiting effi ciency) on segregating mutants (Fig. 6 ). These mutants were a TILLING population of durum wheat generated by Martin Parry′s group at Rothamsted Research (RRes), UK  ). As determination of fruiting effi ciency is destructive it would be impracticable in early generations when segregation is high and, therefore, the authors used the number of grains per unit stem length as a close proxy (see Pedro et al. 2012 ). The process started with a selection made on the M2 generation at RRes under glasshouse conditions and then continued for three further generations (M3, M4, and M5) under fi eld conditions at the University of Lleida (UdL), although the M5 generation was grown and selected at RRes under glasshouse conditions as well. Finally the selected lines, already largely stabilized M6 populations, were grown in fi eld plots at normal plant density at the UdL. Selection was systematically applied through successive generations (M2 to M5).
There was a positive response to selection through the entire process. At any single selecting generation the number of grains of the selected offspring evidenced response to the divergent selection, being the difference between the offspring selected for high or low fruiting effi ciency enlarged throughout the generations (Fig. 6 ). In addition, these results were consistent, disregarding whether the performance of the offspring were analyzed under greenhouse or fi eld conditions (Fig. 6 , grain number in M5 plants). Finally in the M6 generation it was clear not only that lines selected for high fruiting effi ciency produced more grains and higher yield than the sister lines selected for low fruiting effi ciency, but also that the best lines from the population selected for high fruiting effi ciency out-yielded (because they produced a higher number of grains) the controls in the fi eld plot experiment (Fig. 6 ). Thus, selecting for a proxy of fruiting effi ciency produced individual plants with enhanced reproductive output which did translate into the performance at the crop level of organization.

Genetic Variation in Fruiting Effi ciency Within elite Germplasm
It was shown (above) that when considering the physiological bases for yield gains in past breeding, fruiting effi ciency was not consistently relevant: although there was genetic variation between cultivars released at different times, fruiting effi ciency was not regularly improved across studies (Fig. 5 ) during a period when improving partitioning of dry matter to the growing spikes was dominant (Calderini et al. 1999 ;Foulkes and Reynolds 2015 ). More relevant for future breeding is to count with genetic variation for this trait among modern, high-yielding genotypes (which are the elite material in most breeding programmes from which breeders attempt further pyramiding genes contributing to yield).

Genetic variation among modern cultivars or advanced lines
Again the number of studies reporting on fruiting efficiency for elite genotypes is rather scarce but the few published papers that we found showed a wide range of variability (Table 2 ). Differences among studies are expected as the actual values may depend on particular methodological details (e.g., how and when spike dry weight was measured). But what is really relevant is the consistently large degree of genotypic variation found within particular studies. It is clear that fruiting effi ciency varies largely and, whenever different cultivars are compared a wide range of variation can be evidenced (Table 2 ).
In a paper that was just published, Mirabella et al. (2015) reported new results confi rming wide variation in fruiting effi ciency among modern cultivars and revealing that this variation was consistently larger than GxE interaction.
As genotypes within particular studies do differ in many other traits that may affect spike dry weight at anthesis, and then grain number determination, it would not be necessarily expected a strong correlation between grain number and fruiting effi ciency in every single case. However, in the studies analyzed comparing modern cultivars or high-yielding lines there was in general a positive relationship: considering only the cases in which there were more than 10 genotypes compared (to have at least 8 degrees of freedom for the regression analysis) the relationship between grain number and fruiting effi ciency was signifi cantly positive in the studies published by Abbate et al. ( 2013 ); González et al. ( 2011b ); Garcia et al. ( 2014 ) in the experiment carried out in Argentina; and Foulkes et al. ( 2011 ). The unique exception was the experiment conducted in Mexico by Garcia et al. ( 2014 ) in which a nonsignifi cant positive relationship was found.
Thus, in the cases analyzed not only was there substantial genetic variation among modern cultivars but also, unlike what occurs when comparing modern versus old cultivars, the differences among them in grain number tended to be due to their differences in fruiting effi ciency; emphasizing the potential value of the trait for future breeding.

Relevance of fruiting effi ciency in a population designed to increase grain number and yield
Beyond the degree of variation available in elite germplasm, further variation can be expected if the trait shows transgressive segregation (observation of extreme individual phenotypes which exceed parental phenotypic values in either a positive or negative direction; Rieseberg et al. 1999 ). Transgressive phenotypes can be produced when alleles at multiple loci present in parental lines (some of them reducing and others increasing the parental phenotypic value) recombine in the segregating progeny (Bell and Travis 2005 ).
Phenotyping of wheat elite population, that is, population obtained by the cross of well-adapted and high-yielding parental lines, have reported positive transgressive segregation in traits related to phenology and tillering dynamics (Borràs Gelonch et al. 2012 ) , in drought-adaptive traits (Olivares-Villegas et al. 2007 ), or in reserves and yield numerical components (Rebetzke et al. 2008 ;Rattey et al. 2009 ). Regarding fruiting effi ciency, it has been recently phenotyped a doubled-haploid population derived from a cross between two high-yielding wheat cultivars with similar phenology but consistently differing in yield components: Bacanora (possessing high grain number) and Weebil (possessing heavy grains), under two different evaluation environments (Garcia et al. 2014 ) . It was reported that 20-34% (depending on the experiment) of the DH lines exhibited higher values of fruiting effi ciency than Bacanora (the parent characterized by having high fruiting effi ciency; Garcia et al. 2014 ). Furthermore, focusing on top DH lines, simulating the selection carried out in a breeding program aimed to improve grain number, transgressive segregation was also evident (i.e., lines with grain number increased by 25% over the parental mean had also higher fruiting effi ciency, consistently across experiments; Garcia et al. 2014 ). This suggests that crossing parents from the elite germplasm of high-yielding lines of a breeding programme may be a valuable strategy to further increase grain number through the expression of transgressive variation in fruiting effi ciency. In a paper that just became available, Martino et al. (2015) also found that fruiting effi ciency exhibited transgressive segregation and would be reasonably heritable.

Potential Drawbacks
As with any other potentially valuable trait, when considering the usefulness of fruiting effi ciency to achieve yield gains through increasing grain number it must be considered whether it may cause important trade-offs with other yield determining components. The two most obvious trade-offs that must be analyzed are (1) that increases Table 2 . Genotypic variation (ranges) reported in the literature for grain number and fruiting effi ciency in experiments in which different genotypes were compared side by side. Information is presented on whether fruiting effi ciency was estimated with spike dry weight (including when and how) or chaff weight at maturity. Plant material type, number of genotypes, years of release (when it was mentioned) of these genotypes, country of evaluation, level of input in the experiment were also included. in fruiting effi ciency be not constitutively related to decreases in spike dry weight at anthesis (the other major determinant of grain number), resulting fruiting effi ciency irrelevant to bring about actual increases in grain number; and (2) that increases in grain number produced by higher fruiting effi ciency is not constitutively related to decreases in grain weight (the other major yield component), resulting fruiting effi ciency irrelevant to bring about actual increases in yield.

Does high fruiting effi ciency require low spike dry weights?
The conceptual model proposed by Fischer ( 1984 ) includes the idea that fruiting effi ciency and spike dry weight at anthesis are, at least partially, independent. The strong relationship between grain number and spike dry weight at anthesis when the variations were imposed either by genetic factors like introgressing semi-dwarfi ng genes (e.g., Fischer and Stockman 1980 ;Brooking and Kirby 1981 ;Miralles et al. 1998 ), management factors like nitrogen fertilization (e.g., Fischer 1993 ;Prystupa et al. 2004 ;Ferrante 2012 ), or artifi cial manipulations of the growing conditions like extending the photoperiod or shading the crops during stem elongation (e.g., Stockman et al. 1983 ;Savin and Slafer 1991 ;González et al. 2003González et al. , 2005aSerrago et al. 2008 ) seem to support the idea that there would be no major trade-offs between these two components of grain number. However, studies directly analyzing trade-offs between fruiting effi ciency and spike dry weight at anthesis are, once again, rather scarce. From the few direct evidences reported in the literature, there are no evidences for a consistent conclusion. There are studies reporting negative relationship between these traits, supporting the idea of a likely trade-off Ferrante et al. 2012 ;Lázaro and Abbate 2012 ) ; while in other cases there were no signifi cant relationships, supporting the idea of independence (González et al. 2011b ;Bustos et al. 2013 ;Garcia et al. 2014 ). Thus, there are no evidences for postulating a constitutive, and therefore inexorable, trade-off between fruiting effi ciency and spike dry weight at anthesis; and even in the cases in which such trade-off emerged, the cause is uncertain and the interpretation not possible at this stage of knowledge on the trait (Foulkes and Reynolds 2015 ).
Therefore, it is reinforced the idea that it may be possible to select for fruiting effi ciency not necessarily expecting any trade-off in spike dry weight at anthesis. For instance, in the work by Garcia et al. ( 2014 ) it was shown that high yield was associated with grain number due to higher fruiting effi ciency, not compensated by reductions in spike dry weight, when the top yielding lines (which represent those that would have been selected in a breeding program) were analyzed. Similarly, Pedro et al. ( 2012 ) showed that selecting divergently for (a proxy to) fruiting effi ciency, after fi ve generations there were two clear populations of either lower yielding with fewer grains or higher yielding with more grains than commercial controls used in the study.

Does high fruiting effi ciency constitutively reduce the size of the grains?
Increasing grain number via fruiting efficiency would result in low yield advantages if average grain weight is highly reduced due to a trade-off between fruiting efficiency and average grain weight. It seems likely to expect a negative relationship between the average weight of the grains and fruiting efficiency (Ferrante et al. 2012 ) although it is not necessarily so always  ). However, a negative relationship does not always represent a true compensation; this would depend upon the nature of the causes behind the negative relationship. For this analysis we will assume that the basis for the negative relationship would hardly be the increased competition for resources to maximize grain size as the availability of assimilates during the effective period of grain filling is most frequently enough to fill the grains (see above in section How was yield improved in the past? ).
In this context, there are two alternative hypothetical causes for the negative relationship between average grain weight and fruiting effi ciency, one representing a clear trade-off while in the other the trade-off is only apparent (Fig. 7 ). The mechanism behind the true trade-off would be that the cause of the increased fruiting effi ciency would be a reduced demand of individual fl orets to develop normally and consequently the fi nal size of the fertile fl orets would be smaller (i.e., the same amount of resources may sustain the normal growth or more, though smaller, fl orets). As fi nal grain weight would be related, albeit not necessarily linearly, to the size of the fl orets (Calderini et al. 2001 ;Hasan et al. 2011 ) increasing fruiting effi ciency would concomitantly reduce the size of all grains and consequently the average grain weight (Fig. 7 , left side). Should this hypothesis refl ect the reality, increasing fruiting effi ciency would increase number of grains which would be of smaller potential size and consequently would not necessarily produce any yield gain. But the trade-off could be only apparent if the reason behind the increased fruiting effi ciency would be independent of the size of the fl orets (and then potential size of the grains); which may require an improved partitioning of the resources within the juvenile spike toward the fl orets at the expense of the more-structural parts. Should this hypothesis be true, increasing fruiting effi ciency would not affect the potential size of individual grains, but as it would reduce the mortality of more distal fl orets and these fl orets have lower size potential than the proximal ones, it would increase the proportion of fl orets of smaller size potential (Miralles and Slafer 1995b ;Acreche and Slafer 2006 ) and consequently the average size would be reduced but yield gains would be certain (Fig. 7 , right side). In this case, fruiting effi ciency could be used as a trustworthy selection criterion to further increase yield, if molecular markers were identifi ed or high throughput tools were developed for making this possible in practice.
As far as we are aware there is only one paper reporting the relationship between potential grain weight (obtained after 50% trimming of the spike at the onset of grain fi lling) and fruiting effi ciency for cultivars differing in this last trait , in which it was not found a general negative relationship between potential grain weight and fruiting effi ciency. Furthermore, in a rather comprehensive study comparing two cultivars contrasting in fruiting effi ciency and average grain weight under 8 different environmental conditions (Ferrante et al. 2015 ), it was evident that the cultivar with consistently higher fruiting effi ciency and lower average grain weight had grains at particular positions within the spike of very similar weight to those of the cultivar with consistently lower fruiting effi ciency and higher average grain weight. It was clear in that case that the negative relationship would not be constitutive and there Figure 7 . Schematic representation of the two alternative hypotheses to explain the negative relationship between average grain weight and fruiting effi ciency. Left: a constitutive reduction in fl oret size bringing about a trade-off between weight of each of the grains (not just the average weight of all grains) and fruiting effi ciency resulting in no yield gain from increased fruiting effi ciency. Right: a nonconstitutive alternative hypothesis in which the size of individual grains are not affected but the proportion of grains of smaller size potential is increased and then increasing fruiting effi ciency does produce yield gain, even when the average grain weight is reduced. Adapted from Ferrante et al. ( 2015 ) would be an apparent, not real, trade-off produced by the increased proportion of distal grains in the cultivar with high fruiting effi ciency (Ferrante et al. 2015 ).

Concluding Remarks
Alternative ways to further increase yield by breeding are urgently required to maintain current levels of food security. Fruiting effi ciency is among the traits which could be exploited to achieve the needed gains in wheat yield. It has not been exploited consistently in past breeding and shows a wealth of genetic variation, particularly within the elite germplasm for breeding programmes. An empiric divergent selection exercise evidenced that it is likely to obtain yield gains through selecting for (a proxy to) fruiting effi ciency. With the current understanding of the physiology of fruiting effi ciency we can only characterize elite germplasm for breeders to be able to choose prospective parents when deciding their strategic crosses (in which case the characterization must consider the nature of the high fruiting effi ciency to discard trade-offs). However, to be able to select for this trait in realistic breeding programmes molecular markers must be identifi ed or high throughput phenotyping systems must be developed.
Finally, we focused this paper on wheat as it has been in this crop where this trait has been treated more explicitly. However, the concept is equally applicable to other cereals (and likely to any grain crop), as fruiting effi ciency is an integral component to understand grain number determination through the general physiological model that establishing that grain number is related to growth during the "critical period for grain number determination" (e.g., for barley: Miralles et al. 2000 ;Prystupa et al. 2004 ;Arisnabarreta and Miralles 2010 ;maize: Otegui and Bonhomme 1998 ;Vega et al. 2001 ;Rattalino Edreira and Otegui 2012 ;and soybean: Jiang and Egli 1995 ;Slafer 2001 , 2005 ;Egli 2010 ;Kantolic et al. 2013 ). Briefl y, in all grain crops, due to evolutionary and breeding reasons, grain number is far more relevant than grain weight in determining yield (Sadras 2007 ) and grain number is far more dependent on fl oret survival than on fl oret initiation processes (Sadras and Slafer 2012 ). Therefore, in all grain crops grain number is related to growth in that critical period and genotypic differences in the effi ciency of transforming that growth into grain number would likely be expected. Thus, what we exemplifi ed in this paper for wheat is simply a general process linking reproductive biology and agronomic performance of crops that could likely be manipulated to further increase yield. However, comparisons among different species should be avoided as in this case differences in fruiting effi ciency may be tightly related to constitutive differences in grain size among crops as shown by Gambín and Borrás ( 2010 ) for a comprehensive comparison among widely different species; and by Marti and Slafer ( 2014 ) for a constitutive difference between durum and bread wheat.

Acknowledgments
The work on fruiting effi ciency has been funded by grants from the "National Plan" of Research in Spain, grants AGL2009-11964 and AGL2012-35300 at the Crop Physiology Lab of the University of Lleida; National Agency of Scientifi c and Technical Promotion (PICT-2008(PICT- -1039 and INTA (PNCER-1336) at CONICET and INTA Lab, and PICT RAICES 1368 and UBACyT G-076 competitive grants at the University of Buenos Aires.

Confl ict of Interest
None declared.

Notes
1 This trait has been also termed "spike fertility index" (e.g. Fischer 2011 ;Foulkes et al. 2011 ; and references therein) but the term index in crop physiology usually refers to ratios of variables with similar units (like harvest index or leaf area index), while the term effi ciency is used to refl ect the translation of certain amount of resources into variables of agronomic interest (e.g. water or nitrogen use effi ciency). Thus, the term fruiting effi ciency has been increasingly employed to describe the effi ciency with which resources allocated to the spikes translate to the generation of a certain number of grains (e.g. González et al. 2011a ;Pedro et al. 2011 ;Ferrante et al. 2012 ;Reynolds et al. 2012 ;Bustos et al. 2013 ;González et al. 2014 ;Marti and Slafer 2014 ;Garcia et al. 2014 ;Foulkes and Reynolds 2015 ;Sadras and Calderini, 2015). 2 a massive decrease in the expression of genes involved in cell proliferation, a decrease in soluble carbohydrate levels, and an increase in the expression of genes involved in programmed cell death; Ghiglione et al. 2008 ). 3 In some cases it has been preferred to determine spike dry weight few days after anthesis to consider the period of grain set (during the lag-phase of grain fi lling; Loss et al., 1989) as well. This is rather sensible but it has two major inconveniences. Firstly a huge amount of extra work is required to remove the tiny grains that might have already started to grow (otherwise the spike dry weight would be strongly overestimated and the overestimation would vary between genotypes (and environments) depending on the number of grains set and the potential size of the grains. Secondly, the estimated spike dry weight would include any eventual growth occurring during that extra week, which is naturally positive, but would exclude the weight contributed by the fertile fl orets -as the small grains would have been removed-to the spike dry weight at anthesis, which would be a drawback. All in all, we believe that it would be convenient to standardize the determination of fruiting effi ciency using spike dry weight at anthesis.