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V. Mechanisms Capable of Causing Transgressive Yielding by Mixtures

V. Mechanisms Capable of Causing Transgressive Yielding by Mixtures

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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



Rice Research Institute, 1974). Flax and linseed differ in maturity date

and their overyielding of biomass in several mixtures was attributed to this

by Obeid ( 1965) (see Section 11).

Differing temporal patterns of growth or development sometimes result

in a reversal of dominance during the growth of a mixture (Harper and

Clatworthy, 1963; England, 1965). Even if the biomass increments of the

mixture over the periods before and after the reversal are not transgressive

compared with the increments in the monocultures over the same intervals,

the biomass accumulated by the mixture over the whole growing season

may yet be transgressive. Van den Bergh (1968) gave a hypothetical example of this in which the more aggressive component in each phase was

the component with the greater biomass-increment in its monoculture during that phase. In this example, the total accumulation of biomass over

the two phases was the same in each component monoculture; the association of greater aggressiveness and faster biomass accumulation within each

phase resulted in overyielding by the mixture at the final harvest. If the

direction of this association had been reversed, the result would have been

an underyielding mixture. Examples of such effects have not yet been

found, and too few suitable sets of data exist to judge their plausibility.

Van den Bergh (1968), failing to find this kind of effect in the data of

England ( 1965), suggested that the originally suppressed species had been

unable to take advantage of the sharp reduction in the vigor of the other

component of the mixture.

The components of a mixture may be complementary in a spatial sense

by exploiting different layers of the soil with their root systems. Although

Gustaffson’s ( 1954) discussion and vague reference to such a case cannot

be taken as more than an indication, he claims the possibility of increased

grain yields in cereal mixtures through the stratification of root systems.

Cable (1969) found that desert plants were affected least by the proximity

of plants of other species when the root systems of these neighbors did

not overlap the depth of their own. Mutual avoidance^' by adjacent root

systems (Raper and Barber, 1970; Baldwin and Tinker, 1972) could lead

to a late-developing root system occupying deeper soil horizons in mixture

than in monoculture. The significant overyielding of grass mixtures reported by Whittington and O’Brien (1968) was accompanied by phosphorus uptake from greater depths in the mixtures than in the monoculture

(O’BrienBet al., 1967) and so might be due to such an effect. However,

the different pattern of uptake in mixture could also have been the result

rather than the cause of enhanced growth. The writer (Trenbath, 1970),

measuring panicle weights in a field experiment involving 5 mixtures of oat

species, found in one replicate that 5 out of 5 mixtures overyielded; in

the succeeding two replicates in a linear sequence of three, the numbers



of overyielding mixtures were, respectively, 2 and 1 out of 5. The reality

of this trend was supported by the significance (P < 0.01) of the regression of panicle-weight RYT’s of the 5 mixtures on the position of the replicate in the linear sequence across the field. The trend in mixture yields

was tentatively related to an observed soil-depth gradient. It was suggested

that stratification of root systems had occurred on the deep soil, leading

to high RYT’s and overyielding, but that this stratification had been prevented on the shallow soil. The two species making up the mixture with

the highest RYT were suspected to differ the most in depth of rooting.

Ellern et al. (1970) showed that indeed these two species had rooting

depths significantly different; the other species were unfortunately not


Components of a mixture may complement each other nutritionally; one

component may require much of an element of which the other component

needs little (see Kolb, 1962; Davies and Snaydon, 1973). Considering a

particular element, one component may be able to utilize a form that is unavailable to the other. Although mixtures of leguminous and nonleguminous species are not formally treated in this review, it is such mixtures

which provide the most striking and repeatable examples of overyielding

due to nutritional complementation. Since the roots of the components are

drawing on different supplies of nitrogen (soil and atmospheric sources),

on nitrogen-deficient soils, RYT values regularly exceed unity and overyielding is often recorded (e.g., de Wit et af.,1966; Ennik, 1969). When

nodulation is prevented, the species compete for the same supply of nitrogen, the RYT falls to unity, and overyielding does not occur (de Wit et

a!., 1966). Since phosphorus is present in the soil in several forms of differing availability to different species (Richardson et al., 1931; Schander,

1941 ) , nutritional complementation with respect to phosphorus could also

occur but has not yet been reported.

Overyielding by mixtures has in some instances been attributed to a more

efficient utilization of light by their canopies. The use of mathematical

models has suggested that the highest photosynthetic rate might be obtained

from a canopy in which the steepness of the inclination of the leaves decreases with depth (Warren Wilson, 1960; Verhagen et al., 1963; Duncan

et al., 1967; Nilson, 1968). This “ideal” leaf arrangement could be approached by a mixture of a tall erect-leaved genotype and a short, prostrateleaved one. A mixture of such components might possibly overyield. In

addition, Verhagen et al. (1963) have used a simple model to show theoretically that to maximize photosynthetic production, as the leaf area of

a crop increases, the average inclination of the leaves should also increase.

I n the “leaf-inclination” mixture just described, the shorter, prostrateleaved form would tend to be progressively suppressed through shading by



the taller form, and hence the average inclination of leaves in the canopy

as a whole would indeed increase.

To examine further the possibility of mixtures overyielding due to favorable canopy configurations, the author (Trenbath, 1972) used a computer

model based on that of Duncan et al. (1967) to simulate daily gross photosynthesis of mixtures and monocultures of wheat varieties with contrasting

leaf inclinations. In 3 of the 4 sets of conditions used, mixture advantages

in photosynthetic rate were predicted to appear between LA1 2 and 7

(approximately) ; such advantages depended on the latitude, cloud cover,

and planting time being such that most of the incident light arrived from

relatively high elevations. In a mixture with LA1 4, given the radiation

conditions of latitude Oo at the equinox (sunny, with a solar elevation at

noon of 9 0 ” ) , the RYT based on simulated daily photosynthesis was 1.087.

This RYT corresponded to the unreal, but extremely favorable, situation

of a mixture of nonoverlapping, stemless canopies, the upper canopy with

a leaf inclination of 75O and the lower with an inclination of 1 5 O . The

introduction of stems and the inclusion of a moderate degree of overlapping

of the canopies reduced the RYT considerably. If the components were

to have less extremely erectophile and planophile leaf canopies, the RYT

would be reduced still further and any predicted mixture advantage in

photosynthesis would be very small.

Rhodes (1968b) reported the yield of grass in a mixture whose canopy

structure approached Warren Wilson’s ( 1960) “ideal” configuration mentioned above. The mixture overyielded significantly in two treatments with

frequent cutting, but not in the treatment where plots were left to grow

until their canopies intercepted 95% of the incident light. It is unlikely

that this overyielding was due to any similarity between the mixture canopy

and Warren Wilson’s (1960) ideal type since, as already mentioned, theoretical experiments (Trenbath, 1972) suggest that the advantage of a “leaf

inclination” mixture (erect-leaved canopy above a prostrate-leaved

canopy) will be greatest in stands with LAI’s between 2 and 7. In a similar

way to Rhodes, van den Bergh (1968) and Alcock and Morgan (1966)

found (nonsignificant) overyielding in grass mixtures where repeated cutting probably prevented the LA1 from exceeding 2 for any extended period.

Although van den Bergh appealed to possibilities of better use of light by

the sods of such mixtures, he gave no measurements or theoretical basis

for such an explanation.

Of extreme interest is Rhodes’ (1970a) finding that two mixtures, of

which the components had contrasting leaf inclinations, overyielded significantly (see Section 11) under infrequent cutting, whereas under frequent

cutting they yielded between PI and P,. Such observations accord much

better with theory than do Rhodes’ (1968b) results, but it should be noted


20 1

( a ) that canopy structures were not actually measured in any of these

studies, and ( b ) that other mixtures which contained apparently similar

combinations of tall-erect with short-prostrate forms (two in Rhodes’

1970a experiment and three in his 1968b experiment) did not overyield.

If yields of individual components had been measured in Rhodes’ studies,

it would have been possible to use RYT values to detect and quantify

positive interactions between components in a manner independent of overall yields. It is possible that positive interactions occurred in all Rhodes’

“leaf-inclination” mixtures, but that differences of monoculture yields were

sufficient to prevent their expression as overyielding.

Before leaving the topic of light utilization, it is pertinent to point out

that Duncan et al. (1967) simulated the photosynthesis of a canopy of

which the leaves were horizontal above, becoming more inclined with

depth. According to their result, it can be expected that a mixture of a

tall, prostrate-leaved form and a short, erect-leaved form might underyield.

No detailed models of competition for water appear to have been published and hence there are no quantitative predictions of the effect of water

shortage on mixture yields. Nevertheless, considering the growth of mesophytic crops under conditions of high radiation and water shortage, Aiyer

(1949) has emphasized the beneficial effect of shade trees or other tallergrowing mixture components; also, Baldy (1963) has argued that the

many-layered mixed communities traditionally grown in desert oases (e.g.,

date palm

apricot vegetables) may use applied water more efficiently

in biomass production than pure stands. In such oasis communities, the

shading- and windbreak-effect of the upper layer(s) creates a favorable

microclimate for the layer below; the component chosen for each successively lower layer is more mesophytic and less light-demanding than the

one above. The shortest component (the vegetable crop) escapes suppression possibly because soil cultivations tend to prevent intermingling of the

root systems. Where the shorter component grows better under shade than

in the open (Aiyer, 1949) and where the taller component benefits from

the presence of the shorter one (Baldy, 1963, p. 339), water-use efficiency

may be superior in the mixture and overyielding of biomass may occur.

To the author’s knowledge, this possibility has not been rigorously tested.

Allelopathic effects can theoretically cause transgressive yielding. If an

allelopathic substance produced by one component affects the growth rate

of the other component by changing only the rate of uptake of some limiting growth factor, the apparent relative competitive abilities of the mixture

components will change but the total quantity of the factor taken up may

not be much different from that in the absence of allelopathy. If this is

so, RYT will be close to unity (Section IV). If, however, the substance

changes the efficiency with which the growth factor is utilized, RYT will





deviate from unity and transgressive yielding is possible. Roy (1960) discovered a binary mixture of rice varieties which overyielded in grain weight

in several independent trials. By manipulating the cultural conditions, he

found that the growth stimulation appeared to be caused by some agent

carried between components in the irrigation water. Although the importance of this result ought to have led to an immediate repetition of the

work, no further reports appear to have been published. Allelopathic stimulation has not so far been invoked as an explanation of overyielding in

experiments where the yield was dry matter.

Another way in which allelopathy could lead to overyielding is suggested

by the experience of foresters in New South Wales and Queensland. Webb

et al. (1967) have reported that six rain-forest trees which do not form

natural pure stands show unexpectedly poor growth in commercial monocultures. Detailed experimentation using one of the species (Grevillea robustu) indicated that the growth of young individuals was inhibited by a

water-soluble substance apparently produced by the roots of adjacent G .

robusta plants. If the same mechanism is causing the autoinhibition of the

other five species, mixtures of them might overyield. It is to be hoped that

experiments will soon be undertaken to confirm and clarify these and other

possible effects of allelopathy on mixture yields.

Mechanical factors could, again theoretically, lead to transgressive yielding by a mixture. For example, let us suppose first that the component

with the potentially higher yield in monoculture is susceptible to lodging,

and second that the other component resists lodging strongly enough to

cause the mixture to stand while the susceptible monoculture lodges. If

the lodged monoculture yields less than the unlodged mixture, the mixture

is expected to overyield. Such a situation is not unlikely since lodging in

mixtures commonly follows the behavior of the more resistant component

(Atkinson, 1900; Tsedik-Tomashevich, 195 1 ; StringEeld, 1959; de Wit,

1960; B. R. Trenbath, unpublished data; but see Probst, 1957; Qualset

and Granger, 1970).

Although very few critical experiments appear to have been performed

to test the point, a consensus of opinion is developing which maintains

that mixtures have a generally greater tolerance of disease and pest attack

(Schwerdtfeger, 1954; Borlaug, 1959; Simmonds, 1962; Browning and

Frey, 1969; Adams et al., 1971; Cherrett et a]., 1971). When a stand

of susceptible plants is “diluted” with resistant plants, the level of infestation or damage of individual susceptible plants may be reduced. (Suneson,

1960; Browning, 1966). Since the foliage of the resistant plants acts as

a spore trap, the growth rate of rust in an epidemic is reduced (Browning,

1966; Leonard, 1969). Similarly, resistant plants can act as a barrier to

the transmission of a virus among plants of a susceptible component in a



mixture (Broadbent, 1957; Sandfaer, 1970b). The effects of admixed nonhost plants on insect infestations may however be more subtle. The nonhost

plants may interfere with the visual cues by which the insect finds its

host (International Rice Research Institute, 1974), or with the olfactory

cues for host finding (Tahvanainen and Root, 1972); the nonhost plants

may interfere with feeding behavior (Tahvanainen and Root, 1972), may

attract predators (International Rice Research Institute, 1974), or

provide a more favorable biotic environment for the growth of predator

populations (Muller, in Lampeter, 1960).

If, as in some mixtures of cotton genotypes grown in India (Simmonds,

1962), each of the two components is attacked simultaneously by a disease

to which the other is resistant, theory suggests that pathogen escape in

the mixture may result in the mixture overyielding (Chilvers and Brittain,

1972). If only one component is affected, the mixture is more likely to

yield intermediate between the monocultures. Whether the mixture

yields close to PI (as in Suneson, 1960), or closer to P (as in Klages,

1936) is decided by several factors such as time of onset of the disease,

the degree of pathogen escape due to the dilution effect mentioned above,

and whether the affected component is the aggressor or the subordinate

(de Wit, 1960; Sibma et al., 1964).

Although the above discussion suggests that the growing of appropriate

mixtures will help to minimize the effects of pathogens, it should be pointed

out that mixtures have no automatic advantage in this respect. After a

long series of elegant experiments, Sandfaer (1968, 1970a,b) concluded

that the low RYT values (based on grain yield) in a series of varietal

mixtures of barley were due to barley stripe mosaic virus being transmitted

from a certain variety, a symptomless carrier, to the other, sensitive components of the mixtures. The virus caused sterility in the sensitive varieties,

an effect that occurred too late in growth for the carrier variety to show

a compensating increase of grain growth. In this context, an earlier study

of van den Bergh and Elberse (1962) may be mentioned. Here, low values

of dry-matter RYT in a series of grass mixtures were attributed to an exactly similar situation; the evidence for the involvement of the virus was,

however, only circumstantial. In connection with diseases caused by fungi,

Butler and Jones (1949) stated that, in general, more active carbon assimilation (due for instance to increased light levels) increases susceptibility to

obligate parasites of the green parts of plants (e.g., rusts). According to

Gaumann (1950), however, reduced light levels lead to increased susceptibility to “eusymbiotic” parasites (e.g., Fusarium spp.). With this in mind,

it is not difficult to imagine a crop mixture in which, owing to neighbor

effects, each of the components was more susceptible than in monoculture

to a parasitic fungus which was attacking it. However, so far only single



components have been reported to be worse infected in mixture, e.g., alfalfa by Rhizoctonia solani when mixed with a grass (Chamblee, 1958)

and rice by blast when mixed with corn (International Rice Research Institute, 1974).

Before passing to the final conclusions, the points discussed in this section may be summarized by means of Table 111. When considering the

implications of an observed deviation of RYT from unity unaccompanied

by transgressive yielding, or of a report of transgressive yielding without

the data needed to calculate an RYT, it should be remembered that overyielding implies RYT > 1 and underyielding implies RYT < 1 but that

the converses are true only if the monoculture yields are sufficiently similar.


Summary of the Evidence Discussed in Section V Concerning Deviations of

Relative Yield Totals (RYT) from Unity and Transgressive Yielding.





Mechanism that might lead to RYT




Differing growth rhythms

Differing rooting depths

Nutritional complementation

Enhanced light-use efficiency

Enhanced water-use efficiency


Lodging escape

Pathogen escape

Mechanism that might lead t o R Y T


Lowered light-use efficiency


Induced lodgingd

Disease expression through infection of a susceptible


RYT < 1










A cross shows that a t least one report exists t o substantiate the operation of the

given mechanism to produce the given result. I f , for lack of data o n biomass, n report

concerning grain yield has been cited, the cross is shown in parentheses.

Unreplicated, but 5 out of the 6 mixtures grown overyielded.


Only in mixtures of legume

If lodging in the mixture were to follow the pattern in the more susceptible







The main findings of this review are now listed:

1. Most binary mixtures have been recorded as yielding at a level between the yields of the components’ monocultures (see Table I ) . This

“nontransgressive” yielding is what might be predicted on the assumption

of competition between components for the same resources. Such competition would be expected, as a first approximation, to lead to equal proportional increases and decreases of plant biomass compared with per-plant

performance of the components in monocultures. This implies that the relative yield totals (RYT’s) of mixtures would have values close to unity. This

is found in practice (see Table 11).

2. A minority of binary mixtures has been recorded as yielding transgressively, that is to say outside the range defined by the yields of the components grown in monoculture. This suggests that the above proportional

model may not always apply, but the frequent lack of repetition of experiments and the small margins by which the mixture yields transgressed the

range between the monoculture yields usually make it impossible to say

whether a given case of transgressive yielding was due to experimental error

or to a real effect. Since a series of mechanisms can be suggested that

could plausibly lead to mutually beneficial effects between mixture components, it seems likely, or at least possible, that some of the observed cases

of overyielding are due to such mechanisms. The frequent absence of conclusive experimental evidence in favor of the operation of the hypothetical

mechanisms may be due in part to the lack of sustained investigations of

specific cases of overyielding and in part to their extreme sensitivity to

variations of environmental conditions. Also, few informed attempts have

yet been made to increase the likelihood of overyielding by a conscious

choice of conditions and genotypes. Similar remarks apply to underyielding

by mixtures, although rather fewer mechanisms have been suggested to account for it.

3. The operation of mechanisms resulting in the stimulation or inhibition of the growth of mixture components beyond expectations based on

the proportional model give transgressive yields only if the monocultures

are sufficiently similar. A convenient measure of such stimulation or inhibition, and thus of the mechanisms underlying them, is the relative yield

total. This index takes account of the monoculture yields in such a way

as to detect the operation of these mechanisms even in mixtures which do

not yield transgressively.

Owing to the complexity and unpredictability of many agricultural PCOsystems, the control over them which man claims he has is often only nomi-



nal. Given a sound theoretical framework, however, he can hope for fruitful

research into ways of improving this control. This survey of literature attempts to point to areas of ignorance and to suggest means of strengthening

our research so that we may seek to proceed towards more effective exploitation of mixed crops.


I am grateful to Professor C. M. Donald and Dr. I. Valentine for their critical

reading and discussion of drafts of the manuscript.


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Butterworth, London.

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V. Mechanisms Capable of Causing Transgressive Yielding by Mixtures

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