ExplAgric. (1980), volume 16, pp. 117-125
Printed in Great Britain
A COMPETITIVE RATIO FOR QU ANTIFYING
COMPETITION BETWEEN IN TERCRO PSf
By R. W. WILLEY and M. R. RAO
International Crops Research Institute for the Semi-Arid Tropics (ICRISAT),
ICRISAT Patancheru PO 502 324, AP, India
(Accepted 31 July 1979)
SUMMARY
A simple competitive ratio (CR) is proposed as a measure of intercrop competition, to indicate
the number of times by which one component crop is more competitive than the other. Inter
cropping data show that this CR term could be useful in (i) comparing the competitive ability
o f different crops, (ii) measuring competitive changes within a given combination, (iii) identi
fying which plant characters are associated with competitive ability, and (iv) determining what
competitive balance between components is most likely to give maximum yield advantages.
Although intercropping research has greatly increased during recent years there
has been little attempt to produce any simple and meaningful measure of the
competition which occurs between component crops. The broad effects of
competition are of course frequently examined by comparing intercropping
with sole crop yields, and this can be particularly useful if yields of the different
crops are put on a valid comparable basis by using some relative measure such
as the Land Equivalent Ratio (LER - e.g. Rao and Willey, 1980). But these
general comparisons have not produced any measure which can be used to
define quantitatively the exact degrees of competition in any given situation.
Some quantitative measures o f competition have in the past been suggested
in ecological or pasture research, but they have usually been proposed for limi
ted situations, and there have been problems in interpreting what a given mea
sure of competition actually means in practice. This paper examines the prob
lems of some of these competition functions and develops the concept of a
simple competitive ratio (CR), as well as suggesting preliminary ways in which
this ratio might be useful.
THE CONCEPT OF A COM PETITIVE RATIO
The competition function which has been most widely used in ecological
research is the relative crowding coefficient proposed by de Wit (1960). In its
original form this compared, for any given species, the actual yield per plant in
a mixture with an ‘expected’ yield per plant, which was the yield which would
be achieved if the species experienced the same degree of competition in mix
ture as in pure stand. Because it was based on yield per plant, however, popu
lation pressure had to be constant across mixtures and pure stands and it was
f ICRISAT Journal Article No. 104.
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118
R. W. WILLEY AND M. R. RAO
thus proposed only for use with ‘replacement’ mixtures (i.e. mixtures which
are formed by ‘replacing’ a proportion of one crop with an equivalent propor
tion of another). As originally proposed, therefore, it can only be of limited
use in intercropping because it cannot be applied to the many ‘additive’ situa
tions where the total population in intercropping is greater than that o f either
sole-cmp^-Yetlh^s.eJadditive.’-situations can be extremely important because of
the evidence that, at least for some combinations, the required optimum
populations may be higher in intercropping than sole cropping (Willey, 1979).
It is possible to broaden the use of the relative crowding coefficient simply
by basing it on yield per unit area, calculating ‘expected’ yields on the basis of
how much o f the area is initially allocated to each crop. Thus for an ‘additive’
alternate row situation of constant row width the ‘expected’ yield for either
crop would be 50% of its sole crop yield. On this yield per unit area basis, the
coefficient can be written:
, __ Yab Zba
k ab ~ y X —- (1 )
1 aa — 1 ab /--ab
where kab = relative crowding coefficient of crop a intercropped with crop b,
Yab = yield per unit area of crop a intercropped with crop & (expressed
over.the area occupied by both crops),
Yaa = yield per unit area of sole crop a,
Zab = proportion of intercropped area initially allocated to crop a, and
Zba = proportion o f intercropped area initially allocated to crop b.
For a given crop, this coefficient will be greater than, equal to, or less than
unity, respectively, if its intercrop yield is greater than, equal to, or less than
its ‘expected’ yield. Moreover, if the product (usually designated K) of the
coefficients of each crop is greater than, equal to, or less than unity it indicates
that there is a yield advantage, ‘no effect’, or yield disadvantage for inter
cropping respectively.
In situations where there is ‘no effect’ of intercropping (i.e. where K = 1 and,
of course, LER = 1) an individual coefficient of greater than, equal to, or less
than unity means that the given crop is more, equally, or less competitive than
its associated crop. However, if there is a yield advantage of intercropping (i.e.
if both K and LER are greater than unity), which is after all the situation of
most interest, this relationship breaks down because both crops can exceed
their ‘expected’ yield and thus have coefficients greater than unity. As an
example of the importance of this aspect, a paper presented elsewhere in this
journal (Rao and Willey) cites 13 of 21 pigeonpea combinations and 8 of 21
sorghum combinations that produced yields where both coefficients were
greater than unity/‘‘In‘‘such‘ situations the more competitive crop can still be
identified as the one with the higher coefficient, but this highlights a major
limitation of these coefficients, which is that a given value for one crop can
mean quite different things depending on the coefficient value of the other.
Quantifying competition between intercrops 119
This is because each crop’s coefficient indicates the degree of intercrop com
petition relative to sole cropping and does not really indicate the between, or
intercrop competition. Even comparison of the coefficients for each crop can
not give a quantitative measure of this intercrop competition but can only indi
cate that a given crop is ‘more' or less' competitive.
A function which has attempted to measure the intercrop competition, by
relating the yield changes of both component crops, is the aggressivity pro
posed by McGilchrist (1965), originally for replacement situations, though it
can be generalized in the yield-per-unit-area form given earlier:
Aggressivity o f crop a with b -A ab
Actual yield of a when intercropped -
‘Expected’ yield of a when intercropped
Actual yield o f b when intercropped
‘Expected’ yield of b when intercropped
= Yab
________
Yba /o')
YaaXZab Ybb X Zba * ' K ]
Thus this term indicates the simple difference between the extent to which
crops a and b vary from their respective ‘expected’ yields. However, because it
is based on a simple difference, there may be difficulties in interpreting it
meaningfully when comparing intercropping situations that give different levels
of yield advantage. Consider, for example, a range of situations sown with an
initial area allocation of 50:50, and achieving relative yields (or LER values) of
0.6:0.4, 0.7:0.5, 0.8:0.6 etc. These would all give the same aggressivity value for
the first crop o f 0.4. And yet it is difficult to argue that the competitive ability
of the first crop, relative to the second crop, is constant across all these situa
tions.
It is therefore suggested that, although aggressivity has the merit o f trying
to relate the yield changes of both crops, it might be more meaningful to calcu
late the ratio o f the two terms in Equation 2 (i.e. the competitive ratio, or CR):
CRa = - ^ r - + ¥ I ^ r • • ■(3)
•» aa ' ' ^ab *■bb ~ba
The merit of doing this is more readily seen if the relation is rewritten:
CRa= ( ^ - ^ ) x | ^ = ( L E R a/LER6)X ^ -a . . (4)
\*aa *bb 1 4ab ^ab
The CR term is therefore simply the ratio of the individual LERs of the two
component crops, but correcting for the proportions in which the crops were
initially sown. For example, a situation sown at 50:50, which achieved LERs
of 0.8:0.4, would give a CR value for the first crop of 2. Since this indicates
120
R. W. WILLEY AND M. R. RAO
that the first crop produced relatively twice as much yield, it can be logically
taken to mean that the first crop was twice as competitive. In other words the
CR value gives the exact degree of competition by indicating the number of
times one crop is more competitive than the other. Moreover, in contrast to the
problems experienced with the two methods above, this relationship will hold
'•trae~wha-tever--leve-l-©f—yield-ad-vantage is being achie-ved--by intercropping (i.e.
for any total LER value). Since the CR values of the two crops will in fact be
the reciprocals of each other, it will often be sufficient to consider the values
of only one of the crops. The following sections examine some intercropping
data to illustrate ways in which this CR term might be useful.
SOME POSSIBLE USES OF THE C OM PETITIVE RAT IO
The competitive-abilities of-different crops
An earlier paper (Rao and Willey) described experiments in which various
‘intercrops’ were grown in alternate row combinations with a ‘base’ crop of
long-season pigeonpea or short-season sorghum. Competitive effects were dis
cussed in general terms, but could be examined more precisely using CR values.
Thus in Fig. 1, for example, the CR values of the intercrops clearly show that
2.0 -? a. Intercrops in pigeonpea
1.5 -
1.5 -
£ 1.0
0.5 -
b. Intercrops in sorghum
(D
>-
o
CO
o
Fig. 1. Competitive ratios o f different intercrops grown with a base crop of long-season
pigeonpea or short-season sorghum (after Rao and Willey, 1980).
Quantifying competition between intercrops
121
legume intercrops grown with a pigeonpea base crop were less competitive than
cereal intercrops, whereas all intercrops were less competitive when grown with
a sorghum base crop than with pigeonpea. The most striking feature, however,
was that the ranking of competitive abilities for the legume and cereal inter
crops was exactly the same with both base crops though this had not been
apparent in the earlier examination. The differences in competitive ability of
castor, depending on the base crop with which it was grown, were sufficiently
large to have been clearly observed earlier, but even here the CR term would
be helpful in providing a quantitative measure of these effects.
Competitive changes within a given combination
Many workers haye observed changes in competitive abilities of components
because o f changes in such factors as plant population and spatial arrangement.
Such effects might be appropriately examined using CR values, e.g. Fig. 2a and
b shows data from Makerere University, Uganda, where either maize or sorghum
Safflower population (plants/m2)
Fig. 2. Competitive ratios indicating changes in competitive abilities under different plant populations and
row arrangements (2a after Willey and Osiru, 1972; 2b after Osiru. and Willey, 1972; 2c - ICRISAT
unpublished data).
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