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IV. Types of Interaction Causing Nontransgressive Deviations of Mixture Yields from Mid-Monoculture Values
BIOMASS PRODUCTIVITY OF MIXTURES
Distribution of the Relative Yield Totals of Mixtures Based on
Published Data of Biomass of Components in 572 Mixtures
A series of
' L - 2
Aberg et al. (1943)
16.6% 2 . 3 %
van den Bergh
. . . . . . . . . . . . . . . . . . . . . . . . .
Data derived from a series of cuts.
Mixtures of leguminous and nonleguminous species have been omitted.
nism and then consider how it may influence the relationship between the
yield of a mixture and the yields of its component monocultures.
The environmental resources for which plants compete are principally
the light, water, and soil-nutrient supplies necessary for growth (Clements
et al., 1929; Harper, 1961; Donald, 1963; Risser, 1969; Rhodes, 1970b).
Although carbon dioxide is required for shoot photosynthesis and oxygen
B. R. TRENBATH
is needed for the respiration of the roots, competition for these seems normally unlikely to occur. Competition for C02 is probably absent because
the air within the canopy is generally well mixed (Monteith, 1963; Impens
et al., 1967) ; all leaves are surrounded by air of approximately the same
CO, concentration. Similarly, except in almost waterlogged soils, the diffusion of oxygen in soil is usually fast enough to maintain adequate supplies
to all roots (Greenwood, 1969).
Apart from the relatively small number of instances where chemical secretions by one species are thought to have influenced the growth of
another, it seems that most investigators who have reported results of mixture experiments in English-language journals appear satisfied that the
neighbor effects which they observed were due to competition for light,
water, or one of the major nutrients (nitrogen, phosphate, and potassium),
or a combination of these factors. Since it is relatively easy to measure
and explain the unevenness of the sharing of light between the foliage of
two components in a mixture, the studies involving competition for light
have generally been the most conclusive.
Clements and many others have related differences in success in mixture
to differences in height between the leaves of the components of mixtures,
simply inferring that leaves of the shorter component must be experiencing
some degree of harmful shading. More recent analytical approaches have
been based on methods suggested by Monsi and Saeki (1953). Working
with natural communities, Monsi and Saeki introduced techniques for the
measurement of profiles of light intensity and leaf area index (LAI) . Since
then, these techniques have been used very successfully in experimental
mixtures to relate the differences in growth rates of the two components
to differences in the proportions of the total incident light intercepted by
leaves of the two components (Black, 1958; Iwaki, 1959; Stern and
Donald, 1962a,b; Williams, 1963). The general conclusion from all experiments involving competition for light is that the component with its leaf
area higher in the canopy is at an advantage. It is also likely (Stern and
Donald, 1962a) that, if the leaves are horizontal, the advantage is greater
than if they are erect (this is because horizontal leaves intercept more of
the total downward light flux per unit area of leaf than do erect leaves).
If the taller component has a greater leaf area, its advantage is again correspondingly greater (Iwaki, 1959).
In most of the experiments cited above, the investigators have attempted
to exclude the possibility of competition for soil factors. By providing optimal soil conditions or by separating the roots of the mixture components,
it was intended that neighbor effects would be interpretable in terms of
competition only for light. In most agricultural environments, however,
soil conditions are suboptimal and since root systems usually interpenetrate
BIOMASS PRODUCTIVITY OF MIXTURES
each other freely, there is a possibility of competition for water and/or
nutrients. Where the soil is very infertile and the density of planting low,
competition between root systems for soil factors is likely to decide which
component becomes the aggressor because the leaf area produced may
never become great enough to lead to significant competition for light. Indeed, large neighbor effects have been reported in cases where shading
was claimed to have been absent (Pavlychenko and Harrington, 1935;
Myers and Lipsett, 1958). In experiments in containers where competition
for light has been prevented by partitions, competition for soil factors has
similarly been shown to produce large effects (Donald, 1958; Aspinall,
1960; Rhodes, 1 9 6 8 ~Snaydon,
1971; Eagles, 1972).
The principles involved in competition between root systems have not
been as well worked out as in the case of competition between shoots,
but Bray (1954) has outlined a general theoretical approach. In contrast
with supplies of light, nutrient supplies are usually not greatly added to
after the beginning of growth of an annual crop although subsequent rainfali or irrigation normally supplements the initial store of soil water.
Whereas success of a species in competition for light depends on it having
a large absorptive area closer to the light source than the leaves of the
other component, the variable and complex geometry of root systems and
the sources of water and nutrients makes it less easy to define the plant
characteristics likely to confer competitive success.
Bray (1954) noted that competition between root systems for nitrogen
is likely to start at lower root densities, i.e. earlier in growth, than competition for phosphorus or potassium. This is because nitrogen is much more
mobile in soil than phosphorus and potassium. Zones of nitrogen depletion
round individual roots will therefore begin to overlap relatively early. To
test this proposition, Andrews and Newman (1970) grew pure and mixed
communities of young wheat plants in soil deficient in nitrogen and phosphorus with root densities between 1.2 and 8 cm/cm3; their resuIts showed
that whereas competition for nitrogen was intense, competition for phosphorus was indeed slight. Since the mobilities of nitrogen and water in
soil are similar (Fried and Broeshart, 1967), the soil resources most likely
to be subject to competition are nitrogen and/or water.
If Bray’s propositions are correct, they allow the identification of the
characteristics that will determine the relative aggressiveness of the components of a crop mixture growing on infertile soil. For one component to
gain an advantage over the other in the early competition for nitrogen and
water, a faster growing root system (i.e., generally a greater length of root)
is required. The limited evidence so far available does indeed suggest a
possible correlation between seedling competitive ability and early root production (see review in Rhodes, 1970b). However, it also seems clear that
B. R. TRENBATH
if root lengths are similar, the genotype having the more widely spreading,
less-branched root system will be at an advantage. Theoretical considerations suggest that there will probably also be an advantage in having roots
as thin as possible, thus allowing the available root material to be present
as the maximum length of root (Olsen et al., 1962). Abundant, long root
hairs (see Olsen and Kemper, 1968) and a high root “demand” factor
(Drew et al., 1969) are also likely to contribute to competitive success.
This theoretical consideration of competition for soil factors has treated
competition between root systems (root competition) as independent of
competition for light between shoots (shoot competition). However,
Donald (1958) has suggested that in well developed agricultural crops of
uniform genotype, both shoot and root competition are usually occurring.
The relative importance and time of onset of root and shoot competition
will depend on environmental conditions (Aspinall, 1960) ; the nature of
the genotypes involved will also have an effect. To compare, for a particular set of conditions and genotypes, the contributions of the effects of root
and shoot competition with the overall effect of being grown in mixture,
pot experiments have been designed in which partitions separated either
roots or shoots, or both, or none (Donald, 1958; Griimmer, 1958; Aspinall,
1960; Rhodes, 1968c; Snaydon, 1971; Eagles, 1972).
Of the results of these experiments, those of Snaydon (1971 ) are the
easiest to interpret, for in his experiment alone were there constant
numbers of partitions per treatment and plants per compartment. Using
ecotypes of white clover, Snaydon confirmed the results of the other investigators who had shown that root competition had a greater effect (and probably began earlier) than shoot competition. Although this finding suggests
that dominance-suppression relationships in crop mixtures may depend
more on root characters than on shoot characters, the concentration of
roots at the surfaces of the containers in such experiments must have
hastened the overlapping of zones of depletion around individual roots,
and hence led to an overestimation of the agronomic effect of competition
for soil factors.
Considering a possible interaction between the two types of Competition,
Donald (1958) showed that the proportional reduction in the subordinate’s
yield due to shoot competition was greater when root competition was occurring than when it was absent. Similarly, the proportional reduction due
to root competition was greater when shoots were competing for light than
when they were separated. Donald suggested that the failure of, say, the
root to acquire sufficient nitrogen caused leaf development to suffer. This
in turn reduced the supplies of assimilate to the roots which grew less and
so were less able to compete for nitrogen. Donald proposed a similar set
of causes and effects for a component of a mixture which was unsuccessful
BIOMASS PRODUCTIVITY OF MIXTURES
in competition for light. The important conclusion was that the effects of
Competition, once initiated, tend to be magnified by a system of positive
feedbacks if simultaneous shoot and root competition are occurring.
Milthorpe (1961) has discussed the effects of the onset of competition
for soil factors in a mixture where competition for light has already caused
some depression of the growth of one component. Arguing from the depressive effect of shading on root:shoot ratio (e.g., Brouwer, 1966), Milthorpe
considered that any deficiency of soil water or nutrients would cause the
accelerated suppression of the subordinate if any previous shading had reduced its root’s uptake capacity relative to the size of its shoot. Similarly,
the writer has presented results (Trenbath and Harper, 1973) which suggest that the development of a slight deficiency of soil factors where competition for light was already occurring caused an approximately 4-fold increase in the depression shown by a series of subordinates.
While competition for resources has usually seemed able to explain observed differences between per-plant yields in mixture and monoculture,
a number of workers believe that these differences (neighbor effects) are
sometimes caused by other processes. This belief has been expressed by
workers well acquainted with the mechanisms of competition (Warne,
1953), has been implied by other investigators (Sakai, 1955), and has
been used as a convenient explanation of unexpected results by others
(Ahlgren and Aamodt, 1939; Went, 1942).
As an alternative explanation of neighbor effects, allelopathy (Grummer,
1955) has been frequently proposed. The type of allelopathy most likely
to occur in a field crop is that described by Winter ( 1961), where one
or more biologically active substances are liberated from the root or shoot
of a plant, enter a neighboring plant, and there cause a depression of that
plant’s growth. T o allow for cases of stimulation of growth in the affected
plant, the general term “allelochemical” effect (Anonymous, 1971 ) has been
introduced to include both positive and negative effects on growth. Since,
however, the term “allelopathy” is both more convenient and more familiar, in what follows it will be used in a general sense, i.e., allowing the
possibility of either positive or negative effects.
Allelopathy in plant communities has been studied most actively in the
Soviet Union and Germany; the rapidly expanding literature has been reviewed by Griimmer (1955), Rademacher (1959), Grodzinsky (1965,
1971), and Borner (1971). On the other hand, in some other European
countries and in the United States, research on allelopathy has had an uneven history. Several instances of apparent allelopathy have been shown
(sometimes by the original investigators) either to be due to other causes
(Went, 1942; Gray and Bonner, 1948; but see Muller, 1953; Grummer,
1958; but see de Wit, 1960; Sandfaer, 1968; but see Sandfaer, 1970a,b)
B. R. TRENBATH
or to be explained by alternative mechanisms (Muller, 1966, but see Bartholomew, 1970). These cases have tended to make investigators cautious
of suggesting allelopathy as the cause of neighbor effects, indeed, they have
inclined the present author to agree with Harper’s (1965) opinion that
research into the role of allelopathic substances in mixtures is beset with extreme technical difficulties. To avoid greatly extending this review no detailed
discussion will be attempted, but three general comments will be made.
First, as Borner (1960) pointed out, although many investigators have
demonstrated allelopathic effects between plants growing in solution culture
or sand culture, instances where the same effects have been conclusively
proved to be significant under field conditions are rather few. Among such
cases reported in English-language and western European literature, the
most convincing seem to be the existence of inhibitory effects on associated
plants due to walnut (Massey, 1925; Bode, 1958) and to Arctostaphylos
species (Hanawalt, 1971) . Also, the demonstration of autotoxicity among
individuals of Grevillea robusta (Webb et al., 1967) grown in both the
field and glasshouse seems conclusive. It should be noted that although
Bonner (1946) demonstrated the autotoxic activity of root exudates of
guayule plants in gravel culture, the active substance was degraded so fast
in field soil that no autotoxic effect was likely under normal agricultural
conditions. A rather different case is that of Hirano and Kira (1965), who
demonstrated apparent autotoxicity among densely planted peach saplings
in an experiment planted in field soil (clay loam) under glass; this result
accorded well with expectations (Hirano and Morioka, 1964; Proebsting
and Gilmore, 1940). However, a similar experiment carried out on a sandy
soil in the open gave no indication of an autotoxicity effect (Hirano and
Second, since crops are normally grown at densities high enough for
competition between neighbors for resources to be intense (Donald, 1963) ,
any allelopathic effect would be either exaggerated (or reversed) through
competition. To emphasize the importance of taking into account both aspects of the total interaction, we may consider an hypothetical example
of a crop mixture growing on a soil poor in nitrogen. If the suppression
of one of two otherwise evenly-matched components was initiated through
some slight allelopathic inhibition of its nitrogen uptake, later competition
for nutrients might result in plants of this component being nitrogen deficient and heavily suppressed. The agronomist would “prove” the suppression to be due to competition for nitrogen since he would find, in an experiment with separated shoot systems, that neighbor effects were strongest
on soils with the lowest nitrogen level; in the meanwhile, the specialized
investigator of allelopathic effects might have discounted some slight inhibitory effect as insignificant in view of the great intensity of the suppression
in the field. Through the lack of an integrated approach, both workers
BIOMASS PRODUCTIVITY OF MIXTURES
would have drawn false conclusions. The experimental separation of the
effects of competition and allelopathy is thus an important objective, although it is certain to be difficult to achieve (Welbank, 196l ) .
Third, providing (a) that an allelopathic inhibition takes effect early
enough in the life of the crop for compensatory growth to occur in the
other component (see Section V ) , and (b) that the inhibition reduces the
uptake of growth factors rather than the efficiency with which they are
used, the total quantity of environmental resources intercepted by the mixture may not be much affected. Consequently, the yield may scarcely be
less than that of another mixture with the same values of P, and P , in
which a similar degree of suppression has been brought about by competition acting alone. Where, however, the allelopathic effect reduces the efficiency with which growth factors are used in dry-matter production, the
RYT will probably be lowered and the mixture could underyield (see Section V) .
Whether caused by competition alone or by a combination of competition and allelopathic effect, the unequal sharing of resources between components generally affects the yields of mixtures. If the higher-yielding component in monoculture is the aggressor, then with RYT = 1 the mixture
yield will lie between f' and P I . The greater the depression of the loweryielding component, the closer the approach of M to P,; with its complete
suppression, M = PI. Similarly, if the lower-yielding component in monoculture is the aggressor in the mixture (the so-called Montgomery effect,
Gustaffson, 1951), then M lies between P and P,. With complete suppression of the subordinate, M = P,.
The tendency for mixture yields to lie above P (Table I) combined with
the closeness of RYT's to unity (Table 11) suggests that there is a positive
correlation between aggressiveness in mixtures and biomass production in
pure stands. The association is not strong, however, for the value of the
correlation coefficient has been estimated from published data to be only
about 0.3 (Trenbath, 1972). The existence of a positive correlation is
nevertheless in agreement with the ideas discussed earlier, namely, that
a large leaf area displayed at a sufficient height gives an advantage in competition for light (e.g., Donald, 1961) ; the close dependence of productiv;
ity in monoculture on LA1 is well established (Watson, 1952).
A possible reason for the looseness of the correlation between aggressiveness and monoculture yield is found in a suggestion by Iwaki (1959).
Iwaki postulated that a species would be aggressive in mixture if it diverted
a particularly large share of photosynthetic product into building tall stems.
Associated species would be shaded and suppressed. In monoculture, however, the tall species would grow relatively slowly because of the low proportion of its dry matter invested in productive leaves. A negative correlation between aggressiveness and monoculture grain yield in rice (Jennings
B. R. TRENBATH
and Aquino, 1968) was similarly related to the tallness of the stems of
one type of rice, but in this case the low monoculture yield of the tall
type was mainly the result of its tendency to lodge. The bending over of
the tips of long grass leaves (“flagging”) will also lead to greater aggressiveness (see above) and lower growth rates in monoculture (Alberda,
The aggressiveness of a species is well known to depend on environmental conditions and such a dependence will affect the relative values
of M ,P I , and P,. The dominance-suppression relationship between genotypes has been reversed by changing the temperature regime (Eagles,
1972) and by aItering the soil conditions (van Dobben, 1955; Sakai and
Iyama, 1959; Stern and Donald, 1962a; van den Bergh and Elberse, 1962;
Snaydon, 1971). Aggressiveness often depends on the stage of growth of
the plants (e.g., de Wit and van den Bergh, 1965; van deli Bergh, 1968;
Rhodes, 1968a; Nguyen Van, 1968), but in field experiments, the concurrent changes in developmental stage and in meteorological factors usually
make it difficult to identify the factor responsible for any change of aggressiveness with time. The hard-to-define differences between growing seasons
have marked effects on aggressiveness at least where the index used to
measure it is based on seed yields (Laude and Swanson, 1942; Sakai and
Oka, 1955; Allard and Workman, 1963; Workman and Allard, 1964; Lin
and Torrie, 1968). Allard et al. (in Edwards and Allard, 1963) showed
from the data of Suneson (1949) that taking the value of ATLAS as 100,
the selective advantage of VAUGHN ranged from 40 to 173 in 13 seasons.
Transfer from the field to the greenhouse may also cause reversals of dominance (Aberg e f al., 1943; Syme and Bremner, 1968).
If aggressiveness is so sensitive to environmental conditions, it might
be asked how this sensitivity affects mixture yields over a series of sites
or seasons. Unfortunately, although diallel experiments have been carried
out using a range of environments or treatments (Harper, 1965; England;
1965; Whitehouse et al., 1967; Bell et al., 1968; Norrington-Davies, 1968;
Sandfaer, 1970b; Schutz and Brim, 1971), no systematic attempt has yet
been made to study the effect of associated changes of aggressiveness on
mixture yields. Presumably connected in some way with such changes, a
greater stability of seed yields has often been found in varietal mixtures
of cereals and soybeans grown over a range of environments [Allard, 1961;
Simmonds, 1962; Pfahler, 1965; Frey and Maldonado, 1967; Byth and
Weber, 1968; Qualset and Granger, 1970; Schutz and Brim, 1971; but
see Rasmusson (1968) and Clay and AIIard (1969)l. Taking together
the results of three reports (Allard, 1961; Pfahler, 1965; Qualset and
Granger, 1970) in which an index of yield stability was given for each
mixture and monoculture, 5 out of a total of 12 binary mixtures were more
BIOMASS PRODUCTIVITY OF MIXTURES
stable than their more stable component monoculture; the remaining mixtures showed stabilities between those of their component monocultures.
In a comprehensive study involving 16 environments, Schutz and Brim
(1971) calculated, for each type of stand, indices of stability with respect
to several types of environmental variation (seasons, locations, replicates,
etc.) . The lack of agreement between the several stability indices of individual types of stand suggests a complex situation with no clear-cut stability
advantage for mixtures. To add to difficulties of interpretation, stability
parameters are much less accurately estimated than parameters related directly to yield (Allard, 1961;Marshall and Brown, 1973) .
With reference to biomass rather than to seed yield, very few data are
available that allow the comparison of any index of yield stability of individual mixtures with those of their component monocultures. While two
studies (England, 1968; Sechler and Chapman, 1967) suggested that mixture yields were collectively more stable than monoculture yields, data of
individual mixtures from two other studies (Pfahler, 1965; Thomson,
1969) showed stabilities to be intermediate between those of the monocultures in 9 out of a total of 10 cases. These limited data seem to indicate
that the stability of mixture yields is, like yield itself, usually nontransgressive, and that in seed yield, but not in biomass yield, there is a tendency
for mixture stability to be close to that of the more stable component.
In a theoretical study of mixture stability, Marshall and Brown (1973)
suggested that varietal mixtures were most likely to show agronomically
useful stability in highly variable environments to which the available genotypes were not individually well adapted. Perhaps it is partly the lack of
crop species with sufficiently wide adaptation that has led to the extensive
culture of multispecific mixtures in India (Aiyer, 1949). The markedly
differing adaptation characteristics of the components of such mixtures ensure that even in the worst season there will be something to harvest.
The principal conclusions from this and the previous sections may now
be summarized. In field-crop mixtures, competition for both light and soil
resources will usually be occurring; allelopathic effects (if present) will
operate in conjunction with this competition; competition for resources
and/or allelopathy will usually cause per-plant yields of each genotype in
mixture to differ from that in monoculture; the differences of per-plant
yields are usually of a compensating type; if RYT = 1, M will lie between
PIand P,;any positive correlation between aggressiveness and monoculture
yield will produce a tendency for M > P; there are some indications that
the biomass yield of a mixture having sufficiently different components is
likely to be more stable than that of the more stable of its components
in monoculture. We continue now by turning to the more varied and subtle
forms of interaction that may lead to transgressive yielding.
B. R. TRENBATH
Mechanisms Capable of Causing Transgressive Yielding by Mixtures
The results reviewed in Section I1 show that mixtures have often been
recorded as apparently yielding transgressively. Furthermore, the data indicate that records of mixtures overyielding are significantly more frequent
than records of underyielding. Two contrasting interpretations of this situation could be proposed.
1 . It might be suggested that if RYT could be measured without experimental error, its value might always be close to unity; the observed skewness of its distribution (Table 11) could be a consequence of basing RYT
on two ratios of random normal variables (Fieller, 1932). Since there is
a weak, positive correlation between aggressiveness and monoculture yield
(Section IV) , the preponderance of mixture yields greater than P could
be the result of this correlation. If this were the case, theoretical error-free
experiments would show mixture yields lying usually between P, and p,
less frequently between P and P,, and never outside the range P, to P2.
The experimental error found in actual experiments would be expected
to disperse the observed results about their “true” values, so that overyielding mixtures would be recorded more frequently than underyielding ones.
This view implies that observed cases of transgressive yielding are due only
to experimental error.
2. An alternative interpretation might be that at least some of the observed cases of transgressive yielding do represent real effects. If the correlation between aggressiveness and monoculture yield were discounted as
being too weak to have appreciable effect, the tendency for mixture yields
to exceed P could be attributed to apparent mutual stimulation of the mixture components, as indicated by the preponderance of RYT’s greater than
unity (Table 11).
These two interpretations are only preliminary attempts to explain the
observations; they represent extreme, but not necessarily incompatible, approaches. Having discussed in Section I1 the evidence in favor of transgressive yielding being a real phenomenon, we consider here the mechanisms
that could lead to transgressive yielding. If they appear likely to operate
under the conditions normally used for mixture experiments, this would add
credibility to the second interpretation given above.
In connection with overyielding, the findings and theory of animal
ecology may be relevant since they help to define conditions that might
lead to this kind of transgressive yielding. Gause (1934) quoted Formozov’s observations of natural mixed populations of tern in which four species coexisted, apparently because they exploited the environment in different ways. In such a case, it seems likely that a mixed population would
BIOMASS PRODUCTIVITY OF MIXTURES
be more productive than any monospecific population. Gause (1934)
summed up his own experimental results in the principle that species of
very similar requirements tend not to coexist. Using this principle, Harper
(1967) and others argued that the species diversity found in natural communities implies that the component species occupy differing niches. Together, therefore, they must exploit the environment more completely than
a community of few species. Providing support for this view, Beardmore
et ul. (1960) and Seaton and Antonovics (1967) reported overyielding
of mixtures of Drosophilu strains in controlled environments. Seaton and
Antonovics suggested that in their mixtures the two genotypes were avoiding competition by occupying different niches.
In the botanical literature, genotypes believed to be avoiding competition
while they share a habitat are said to be “complementary” (Woodhead,
in Salisbury, 1929). Woodhead first used the term in connection with natural woodlands where, by the sharing of environmental resources in either
time or space, the various types of species seem to escape, at least partially,
the effects of competition. His concept of the complementary use of resources would seem to be applicable to crop mixtures; the possible ways
in which resources may be used in such a manner will now be considered.
Van den Bergh and de Wit (1960) reported an example where temporal
sharing of the environment may have been responsible for a case of apparent mutual stimulation in mixture. In a mixture of two grass species which
differed markedly in time of development, plants of both components had
more tillers (53% and 3 6 % ) than did plants in the corresponding monocultures; although biomasses were not reported, it may be noted that the
RYT based on tiller number was 1.49. Syme and Bremner ( 1968) reported
a series of experiments involving oats and barley varieties chosen to differ
in flowering time; the results of an experiment performed under glass (data
given in Syme, 1963) showed that in all four oats-barley mixtures, both
components showed higher per-plant shoot weights than in monoculture.
While overyielding of dry matter did not occur, the RYT based on shoot
weights averaged over the four (replicated) mixtures and two densities
was 1.12. Such an RYT value in a mixture of which the two monoculture
yields were very similar would be associated with the mixture outyielding
the monocultures by 12%. Sechler and Chapman (1967) also reported
an experiment with cereal genotypes (oats) which differed greatly in
flowering date. Again no mixture overyielded. Unfortunately, the data
given were insufficient to allow the calculation of RYT’s and so no detailed
comparison is possible with the experiment of Syme and Bremner ( 1968).
In corn-rice mixtures in the Philippines, the corn flowers and matures
before the rice begins to flower; this phenological difference probably explains the reported overyielding of grain by such a mixture (International