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II. Comparison of Yields of Mixtures and Monocultures

II. Comparison of Yields of Mixtures and Monocultures

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180



B. R. TRENBATH



TABLE I

The Distribution of Biomass Yields of Varietal or Interspecific Mixtures

Compared with Yields of Their Components’ Monocultures, Based on

Published Data of 344 Mixtures”

Below



Pz



Crop

Grasses



PftoP P t o p 1



Above



PI



3



Either grasses or leguniesc



9

1

1

9

12

1



7

38

4



1

9

2

11

10

1

8

42

5



Grasses“



5



9



11



15



Grasses

Grasses“

Grasses

Rye



2

2

1

4



2

7

4

4



1

3

5

16



1

4

7



-



-



-



-



45



92



124



83



3

1



1



Wheat

Rice

A series of nonlegumes~

Subterranean clover

Flax and linseed

Grasses“

Barley



12

1



2

3

1

4

3

1

12

a8



a



Author

Ahlgren and Aamodt

(1939)

Aberg et al. (1943)

Donald (1946)

Sakai (1953)

Sakai (1955)

Williams (1962)

Williams (1963)

Harper (1965)

England (1965)

Norrington-Davies

(1967)

Norrington-Davies

(1968)

Rhodes (1968b)

Thomson (1969)

Rhodes (1970a)

nor rington-Davies

and Hutto (1972)

= 344



62.8%

c _ _ _



39.8%

a



_T_I



60.2%



P I and PZ are the yields of the higher- and lower-yielding monocultures, respectively.



13 is the mid-monoculture yield.



” Data derived from a series of cuts.

c



Mixtures of leguminous and nonleguminous species have been omitted.



a “mixture diallel” was used. Experiments conforming to this design contain a series of genotypes grown in monoculture and all possible binary

combinations. All plots (or containers) are sown with a constant overall

density of plants, and 1 : 1 proportions are used in the mixtures. Such mixture experiments satisfy the conditions specified earlier for consideration

in this part of the review. Although replication is not specifically mentioned

by Harper (1965), it is believed that all data used in Table I were based

on replicated experiments. The data of Jacquard and Caputa (1970) were

reported as being unreplicated and are therefore not included. Taken together, the data show that mixture yields tend to lie above the mean yields



BIOMASS PRODUCTIVITY OF MIXTURES



181



of the monocultures; the difference between 60.2% and 39.8% is highly

significant ( P < 0.001 ). Presumably reflecting this difference, the reported

frequency of overyielding is significantly ( P < 0.001) greater than that

of underyielding. According to these results, apparently transgressive yielding is by no means uncommon, comprising 37% of all the mixtures considered. Although differences between overyielding mixtures and their

higher-yielding monocultures have often not been examined for statistical

significance, of those so examined, very few have reached even the 5 %

probability level.

As far as the author is aware, there are only four investigations where

overyielding has been reported as being statistically significant. The first

case (Whittington and O’Brien, 1968) concerns the “significant” overyielding by three mixtures of grasses in the third year of a field experiment.

This overyielding affected only the treatment with frequent cutting, but

there was also a tendency toward it in the less-frequent cutting treatment.

It should be noted, however, that the statistical significance of the overyielding was tested using selected data (6 out of 15 harvest periods); van

den Bergh ( 1968) has observed that apparently highly productive mixtures

in some cuts may be quite the reverse in other cuts. Since the mixtures

of Whittington and O’Brien usually yielded below PI in the first two years

of the experiment, there may have been extra reserves of nutrients in the

soil to provide the high yields of the third year. It must also be realized

that the apparent degrees of overyielding of several mixtures in a diallel

may be simultaneously affected if, owing to a chance effect, the monoculture yield of one high-yielding genotype is considerably lower (or higher)

than its potential as expressed in other plots. Since the measures of overyielding of mixtures in this diallel were not independent at any one harvest

(or between harvests), the multiple instances of overyielding reported by

Whittington and O’Brien do not provide any especially strong grounds for

believing that the overyielding was a real effect.

The second case in which overyielding achieved significance ( P << 0.01

in two independent comparisons) was reported by Rhodes ( 1968b). In

a diallel of ryegrass varieties, under two regimes of cutting (high and intermediate frequency), a particular mixture overyielded by 12% and 15%.

In the infrequent-cutting treatment, this mixture’s yield was below P. The

plots with the different cutting regimes were independent, and so there

seems to be reason to accept this result as due to a real effect. The third

case of significant overyielding was also reported by Rhodes (1970a) in

two mixtures of ryegrass genotypes grown under near-optimal soil conditions. These mixtures overyielded by 11% ( P < 0.01) and 9%

(P < 0.05) under a regime of infrequent cutting; with frequent cutting,

the same mixtures did not yield transgressively.



182



B. R. TRENBATH



A fourth instance of “significant” overyielding has been reported which,

although lacking clear statistical treatment, seems also to be due to a real

effect. Data of Khan (in Harper, 1965) and data of an independent experiment by Harper (1965) both show that mixtures of various flax and/or

linseed varieties overyielded. Khan’s data show two flax-linseed mixtures

as overyielding (significantly,” Harper, 1965, p. 471) by 13% and 14%.

Harper’s own experiment included the same two mixtures. At low density,

one overyielded by 38% while the yield of the other was nontransgressive;

at high density, neither mixture yielded transgressively. Since, at low density, only two plants were present in each pot, the experimental errors must

have been very large. Furthermore, Harper mentioned neither replication

nor significance levels, and so the value of this experiment as an independent confirmation of Khan’s results is uncertain. If Harper’s experiment

was in fact adequately replicated, the high proportion of overyielding mixtures (40% ) would suggest that his mixtures were worth further investigation. While not based on the same varieties, data of Obeid and Harper

(in Harper, 1968) again show a flax-linseed mixture (planted this time

with a range of proportions) which overyielded by a maximum of l o % ,

29%, and 31% at the three densities studied. The flax-linseed

(WEIRA-VALUTA) mixture of Khan remains, however, the only mixture

which has, to this author’s knowledge, ever been reported to overyield in

two separate experimenkl

Little consideration has been given by authors to the possibility that

mixtures may underyield. No cases of significant underyielding appear to

have been reported, although Ahlgren and Aamodt (1939) found that all

three mixtures in a incomplete diallel of grass species underyielded (nonsignificantly, by 11 % , 23 %, and 26% ) . Donald ( 1946) repeated this experiment using the same species, but none of the mixtures underyielded.

As mentioned previously, Donald (1963) and van den Bergh (1968)

have each concluded that there is no firm evidence that a mixture can have

an advantage over the higher-yielding component monoculture (mixtures

of legume and nonlegume are excepted), Also, Woodford (1 966) has expressed the same opinion. The additional evidence presented in this review

is consistent with these conclusions. However, it seems that “firm evidence”

has rarely been sought. Experiments showing transgressive yielding by mixtures have either seldom been repeated, or if they have, the results have

not been published. Until the transgressive yielding of more mixtures can

be shown to be repeatable, the addition of further data concerning once‘There are only two analogous cases in the production of grain. One is the

mixture of rice varieties (BK and 2A) of Roy (1960), and the other is a mixture

of wheat varieties (RAMONA and BAART) of Chapman ef al. (1969) and Allard and

Adams (1969).



BIOMASS PRODUCTIVITY OF MIXTURES



183



performed experiments can add little to what is already known about mixture performance.

111.



Theoretical Considerations



Let us assume that a 1 : l mixture of the seeds of two genotypes has

been sown along with monocultures of the components. If plants of each

component yield the same as they do in their respective monoculture, the

yield of the mixture will be the mid-monoculture yield ( P ) . The plants

of the components of the mixture will be said to have given their “expected

yields” (Alcock and Morgan, 1966) since they have yielded in accordance

with their genotypic potential, as expressed in monoculture. The midmonoculture yield will be the corresponding “expected yield” of the

mixture.

Writing the per-plant yield of genotype i in mixture with genotype j as

Y i j ,the average per-plant yield, M i j , of the i, j mixture will be:

Mij



=



1

-(Yij



a



+



Yji)



If per-plant yields of i and j in the mixture are the same as in their

monocultures, i.e., if Y i j = Yii and Y j i = Y j j , the mixture yield is the

“expected yield,” i.e., M =: P. In such a mixture, the average per-plant

yield would be given by

Mij



=



1



-(Yii



a



+ Y,jj)



If the density of plants is n plants per plot of unit area, then M ,P,,and

P, (the yields per unit area of the mixture and of the higher and lower



yielding monocultures, respectively) are given by



M



=



nM;,



PI = nYii (for Yii >

Pz = nYjj (for Y ; ; >



Yjj)

Yjj)



However, as many early experiments showed (e.g., Montgomery, 1912;

Tansley, 191 7; Clements and Weaver, 1924; Sukatschew, 1928), per-plant

yields of genotypes in mixture and monoculture are seldom the same. From

this springs the tendency for mixture yields to deviate from the “expected

yield.”

The biological processes responsible for the deviation of component performance from that expected are complex and varied. A general term which

has been applied to them is “interference” (Crombie, 1947; Harper,



184



B. R. TRENBATH



1961). They result in what may be called either “interference effects” or

“neighbor effects” (“Nachbarwirkungen,” Lampeter, 1960). The latter is

a more objective and neutral term and, hence, perhaps preferable (Trenbath and Harper, 1973).

The best understood, and perhaps the most important, mechanism that

can cause the biomasses of plants of a genotype to differ between mixture

and monoculture is the process of “competitionyy(Clements et al., 1929;

de Wit, 1960; Donald, 1963). Plants are conceived as “competing” for

the limited supplies of environmental resources necessary for growth. Clements (1904) showed how the anthropomorphic overtones of this concept

could be avoided when he asserted that the reaction of a plant to neighboring individuals is not a direct response to the neighbors themselves, but

to the plant’s own microenvironment insofar as it has been altered by the

presence of the neighbors. In a mixture, differences of morphology and

physiology between the mixture components cause their individuals to

experience different microenvironments and hence different resource

availabilities from those experienced by plants of the same genotype in

monoculture. As a consequence, resources are unevenly shared between the

components and per-plant mixture yields deviate from “expected yields.”

Such effects are said to be due to competition.

De Wit ( 1960) has presented a model of intergenotypic competition

based on the simple assumption that the biomass yield of each component

is strictly proportional to the share of environmental resources it can acquire, According to this model, if the sharing is uneven, plants of one genotype, say i, will be larger in mixture than in monoculture while plants of

the other component, genotype 1, will be correspondingly smaller. In such

a case, genotype i is termed the “aggressor” (Donald, 1946) and genotype

j may be termed the “subordinate.” Hence, according to this simple model

of unequal sharing of environmental resources, Yij > Yii and

Yji < Y j j .This appears to be the commonest situation in mixtures, for

of 70 results reviewed by Donald* (1963), 51 (74%) were of this type.

Among the 344 results reviewed in Section 11, there are 326 cases where

data are available of the performance of the components within the mixtures; of these 326 mixtures, 255 (78%) showed the same pattern. The

more specific predictions of the de Wit (1960) model have also been

shown to be fulfilled in many field and pot experiments using gramineous

species (de Wit, 1960; van den Bergh, 1968).

When the per-plant yield of one genotype is higher in mixture than in

monoculture and the per-plant yield of the other genotype is correspondingly lower, then the behavior of the mixture components is said to be

Of the 70 mixtures, 34 were of a grass and a legume; in 10 mixtures the density

was not closely controlled.



BIOMASS PRODUCTIVITY OF MIXTURES



185



of a “compensating” type (Aberg et al., 1943; Donald, 1963). If the plant

relative yield (PRY) (based on the per area relative yield of de Wit and

van den Bergh, 1965) of a component is defined as the ratio of the perplant yield in mixture to that in monoculture, then in such a mixture, the

PRY of the aggressor will be greater than unity; that of the subordinate

will be less than unity. Thus, if genotype i is the aggressor, Yii/Yi,i> 1

and Y i i / Y i j < 1.

The terminology of this relationship has unfortunately been confused

by Schutz and Brim (1967), who applied the term “complementary” to

mixtures in which, as above, deviations of PRY from unity are of the type

(+,-) . “Complementary” as applied to mixture components had already

been used in the botanical literature to refer to something rather different

(Salisbury, 1929; and see Section V ) . Among other terms which they introduced, Schutz and Brim used “neutral” for cases where both components

give their “expected yields,” i.e., cases of the type (0,O). Mixtures of the

type (+,O) and (-70) were described by Schutz and Brim as showing

“over-compensation” and “under-compensation,” respectively. While “neutral” and “over-compensation” and “under-compensation” seem to be useful terms, the original term “compensating” (noun “compensation”) will

here be retained for cases of the type (+,-) .

With respect to mixture productivity, the common occurrence of compensation tends to keep mixture yields between the monoculture values.

According to the de Wit (1960) model, when components in a 1 : 1 mixture

are competing for the same supplies of environmental resources, the proportional increase of per-plant yield of one component will tend to equal

the proportional decrease of per-plant yield of the other (see Fig. 1) . This

implies that the mean of the PRY’S will have a value close to unity. In

terms of the per-area relative yields of de Wit and van den Bergh ( 19651,

this value is a total which they have called the relative yield total (RYT).

The RYT is given in the present notation by



-+-



R Y T = -1 (Yii

2 Yii



G;)



Van den Bergh ( 1 968) showed that if RYT = 1, the mixture yield must

lie between the yields of the pure cultures (strictly P , 2 M 2 P 2 ) . The

general scatter of observed RYT’s around the value of unity is shown for

572 mixtures’in Table 11. These data seem to provide ample basis for expecting RYT’s to lie close to unity, and incidentally provide support for

the wide applicability of de Wit’s (1960) model. The asymmetry of the

low and the high deviations from unity (13.6% compared with 20.3%)

is significant at the 1% probability level.



186



B. R. TRENBATH



Quontity of resource acquired



/



plant



FIG. 1. Graphical interpretation of de Wit's (1960) model when components of

a 1:l mixture are competing for the same environmental resource. Compared with

the unit quantity of resource acquired in monoculture, each plant of the aggressor

gains an extra amount, F, in mixture. The quantity of resource acquired by each

plant of the subordinate is correspondingly reduced by F in mixture. The per-plant

acquisition of resource is assumed to be the s_ame in the two monocultures. M,,

is the average per-plant yield of the mixture; P/rt is the mid-monoculture yield in

per-plant terms; Y,,(open circle) and Y i , (filled circle) are per-plant yields of

genotype i in monoculture and mixture respectively; Y,,(open square) and Yji (filled

square) are corresponding per-plant yields of genotype j . Arrows by the monoculture

points lie in the direction of the points of the same genotype grown in the mixture.

The numerical values shown for biomasses indicate that in such a system, the

proportional increase of Yl, over Yii equals the proportional decrease of Y , c

below Y j , .



IV.



Types of Interaction Causing Nontransgressive Deviations



of Mixture Yields from Mid-Monoculture Values



Since the concept of relative yield total (RYT) has been introduced

in the preceding section, it can be immediately explained that the present

section treats only those mechanisms (chiefly competition) which seem

able to cause deviations of M from I' without any deviation of RYT from

unity. Such deviations of mixture yield are necessarily nontransgressive.

(Other mechanisms of interaction exist which can cause nontransgressive

deviations from I' but with RYT not equal to unity. Since these mechanisms are also potentially capable of giving rise to more extreme deviations,

they are treated in Section V.) We examine first the nature of each mecha-



187



BIOMASS PRODUCTIVITY OF MIXTURES



TABLE I1

Distribution of the Relative Yield Totals of Mixtures Based on

Published Data of Biomass of Components in 572 Mixtures

~



~~~



RYT value

0.5 to

0.7



0.7 to

0.9



1



2



Either grasses

or legumesb

Wheat

Rice

Grasses"

A series of

nonlegumesb

Subterranean

clover

Flax and

linseed

2

Grassesa

Barley



1

3



Crop

Grasses



0.9 to

1.1



1.1 to

1.3



6

5



4

9

2

26

41



11



4



8



3



1.3 to

1.5



21.7



4

1



Williams (1962)



3



5

3



Williams (1963)

9

22



5



95

10



3



7



20



9



Grasses.



3



106



4



21



26



21



4



6

6



5

18



2



3



6



-



-



3



Grasses.

Rye

-



6

1.0%



3



3



' L - 2



-



72

378

12.6% 66.1%



13.6%



Author

Ahlgen and

Aamodt (1939)

Aberg et al. (1943)

Donald (1946)

Sakai (1953)

Sakai (1955)

Lampeter (1960)



1

2

1



G rassesa



Grassesa



1.5 to

1.7



95

13

16.6% 2 . 3 %



5



0.9%



3

0.5%



Harper (1965)

England (1965)

NorringtonDavies (1967)

NorringtonDavies (1968)

van den Bergh

(1968)

Whittington and

O'Brien (1968)

Tbomson (1969)

NorringtonDnvies and

Hutto (1972)

= 572



20.3%

~~



. . . . . . . . . . . . . . . . . . . . . . . . .



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



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