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Analysis of the yield of two groups of tropical maize
cultivars. Varietal characteristics, yield potentials,
optimum densities
Pierre Siband, Joseph Wey, Robert Oliver, Philippe Letourmy, Hubert
Manichon
To cite this version:
Pierre Siband, Joseph Wey, Robert Oliver, Philippe Letourmy, Hubert Manichon. Analysis of the
yield of two groups of tropical maize cultivars. Varietal characteristics, yield potentials, optimum
densities. Agronomie, EDP Sciences, 1999, 19 (5), pp.379-394. �hal-00885938�
Original
article
Analysis
of the
yield
of
two
groups
of
tropical
maize
cultivars. Varietal
characteristics,
yield potentials,
optimum
densities
Pierre
Siband
a
Joseph
Wey
b
Robert
Oliver
a
Philippe
Letourmy
c
Hubert Manichon’
a
Cirad-AMIS, BP 5035, 34032 Montpellier, France b
Cirad/INERA, Station de Farako Ba, Bobo Dioulasso, Burkina-Faso
c
Cirad-CA, BP 5035, 34032 Montpellier, France
(Received 15 October 1997, revised 22 January 1999, accepted 9 March 1999)
Abstract - In order to
analyse
the results from an on-farm survey in Burkina Faso, a model forgrain
yield analysis
wascalibrated
using
data from the survey. Yield was broken down into four components, eachrepresenting
onephase
of thegrowth cycle.
In the model, the maximum value for each component (M) is definedby
the cultivar in theregion
ofstudy,
and from the values that theprevious
components have reached. These values establish thecompetition
level forresources that a
growing
componentundergoes. Competition begins beyond
a critical value (L) ofplant
density
(NP). An upperboundary
line is defined on the base of NP for each component. A maximumgrain yield
(Y
M/NP
)
is evaluatedfor each NP value. The greatest maximum
yield
(Y
GMAX
)
is considered as a varietal characteristic under thegiven
con-ditions. The model was
applied
to two varietal groups (local and selected varieties). It indicated that selected varieties hadhigher
Y
GMAX
,
mainly
due to differentcompetition
critical limit values (L) and not to varietal maxima (M). For each group of varieties, the later in thecycle
a component is determined, the lower thecompetition
limitY
M/NP
increas-es with NP up to a first
competition
limit.Subsequently, adjustments
occur between successive components,thereby
stabilizing
Y
M/NP
(=Y
GMAX
)
across levels of NP.Finally,
when the fraction of fertileplants
is limitedby
NP,Y
M/NP
decreases
against
NP. The lowest NPenabling
,
GMAX
Y
whileproviding
the greatestpotential
foradjusting yield
compo-nents,gives
the bestyields.
Thishypothesis
was verified under field conditions. The range ofpopulation
densitiesasso-ciated with
Y
GMAX
and greatestpotential
foradjustment
were also the mostfrequently
observed on farm, indicating that farmers wereprobably
familiar with the effects ofpopulation density
onyield potential.
(© Inra/Elsevier, Paris.)maize / model / maximum
yield
/density
Communicated by Jean-François Ledent (Louvain-la-Neuve, Belgium)
* Present address: Cirad-TERA, BP 5035, 34032
Montpellier, France
**
Correspondence and reprints siband @ cirad.fr
Résumé -
Analyse
du rendement de deux groupes de cultivars de maïstropical.
Caractéristiques
variétales,
ren-dements
potentiels,
densitésoptimales.
En vued’analyser
un travaild’enquête
en milieu paysan, au Burkina Faso, un modèle de rendement engrain
du maïs est calibré sur les données del’enquête.
Le rendement estdécomposé
en quatrecomposantes,
représentant
chacune unephase
ducycle
de la culture. La valeur maximalepossible
dechaque
composan-te
dépend
du cultivar dans larégion
étudiée (M), et des valeurs des composantesprécédentes.
Celles-ci déterminent le niveau decompétition
rencontré par la composante en formation. Lacompétition apparaît
àpartir
d’une valeur limite(L) de la densité de
population
deplante (NP).
Une courbeenveloppe supérieure
est ainsi définie pour la valeur dechaque
composante en fonction de NP. Elle est formée d’une droite horizontale et d’unehyperbole.
Un rendement maximalpossible
Y
M/NP
est évalué pourchaque
NP. Leplus
haut rendement maximalpossible
(Y
GMAX
)
est unecaracté-ristique
variétale dans larégion.
Le modèle estappliqué
à deux groupes variétaux(variétés
locales etsélectionnées).
Ilmontre que
Y
GMAX
des variétés sélectionnées estplus
élevé, dûprincipalement
aux valeurs des densités limites decom-pétition (L)
des différentes composantes, et non aux maxima variétaux (M). Pourchaque variété,
la limite decompéti-tion L pour une composante est d’autant
plus
basse que la composante se formeplus
tard dans lecycle.
Y
M/NP
augmenteavec NP,
jusqu’à
la limite L laplus
basse. Ilprésente
ensuite unplateau
(Y
GMAX
),
dû auxcompensations
entre compo-santes successives.Lorsque
NP limite lafréquence
deplantes fertiles,
Y
M/NP
diminue. Lesplus
faibles densitéspermet-tant d’atteindre
Y
GMAX
,
et les meilleurescapacités
decompensation
entre les valeurs des composantes du rendement,donnent les meilleures chances de rendement. Ceci est vérifié au
champ.
Lesagriculteurs
choisissent leplus
fréquem-ment ces densités. (© Inra/Elsevier, Paris.) maïs / modèle / rendement maximal / densité
List
of abbreviations
1. Institutions
Cimmyt
Centro Internacional deMejoramiento
de Maiz YTrigo
Cirad Centre de
coopération
internationale enrecherche
agronomique
pour ledéveloppement
IITA International Institute of
Tropical
Agriculture
2. Parameters
FP
frequency
of fertileplants
LCG level of
competition
betweengrains
L
FP
competition
limit at which sterileplants
begin
to appearL
NEP
competition
limit for number of ears perplant
L
NGFP
competition
limit for number ofgrains
per fertileplant
L
WG
competition
limit for unitgrain weight
NE number of ears per unitground
areaNEP number of ears per
plant
NG number of
grains
per unitground
areaNGP number of
grains
perplant
NGFP number of
grains
per fertileplant
NP number of
plants
per unitground
areaWG unit
grain weight
Y observed
grain yield
per unit areaY
M/NP
maximumgrain yield
per unit area, at agiven
NPY
GMAX
greatest maximumgrain yield
per unitarea,
given by yield
component relationsY
RAD
radiation-limitedgrain yield
per unit ofarea,
given by
a radiative model1. Introduction
A
multi-year
survey was carried out on themaize crop on small farms in the west of Burkina Faso. The
analysis
of these sitesrequired
the use ofa
diagnostic
model toorganise
the availableinfor-mation.
Maize has often been
subjected
tomodelling
(e.g.
[19, 24]).
The models are notalways
suitable for use at the fieldlevel,
or transferable without localadjustments.
Also,
they
require
information about theplant
material and environmental condi-tions which are difficult to obtain in the context ofa survey. Duncan
[11, 12]
proposed
a method forpopu-lation
density.
This modelrequires experimental
data for eachcultivar,
and is more suitable formaking
varietal than for on-farm situation compar-isons[3].
Navarro-Garza
[25]
andFleury
[14]
used a moreanalytical approach
based on theassumption
thatindividual
yield
components observed atmaturity
are indicative of the
growing
conditions at the timewere formed. This method has been used
by
sever-al researchers for various annusever-al crops
[6],
notably
cereals,
by
applying
to the identifiedcomponents
theapproach developed by
Shinozaki andKira,
citedby
Donald[9].
These authors assumed that for defined radiation and temperature conditions and agiven
cultivar,
competition
for resourceslim-its the maximum value that
yield
components
cantake.
Competition
is associated with a certain mini-mumplant density.
The maximum value of agiven
yield
componentdepends
on the value per unit areaof the
previous
component.
Forexample,
themaxi-mum value that the mean number of
grains
perplant
can takedepends
on thepopulation density
ofplants.
The maximum value acomponent
can reach is estimated from the data of thesample surveyed,
assuming
that at somesites,
the fullpotential
of the cultivar isexpressed.
The value of a
component
is assumed toprovide
information on the behaviour of the crop
during
thegrowth phase
during
which theyield
component
was established. From this
point
ofview,
thedis-tinction of
yield
components
is usefulonly
insofaras
they correspond
to well identifiedgrowth
phas-es. The number of
plants
per unit area is fixed veryearly,
anddepends largely
on the farmer’s decision[35].
The first ear is initiated about 10days
after thepanicle
is initiated.First,
its number ofgrain
rows is
established,
then the number ofspikelets
per row is determined 1 or 2 weeks before
silking
[29].
The number ofspikelets
on the ear constitutesthe limit to the number of
grains
which it can form.According
to these sameauthors,
therapid
elonga-tion of the ear can continue until 10
days
after silkemergence. The number of
grains
per ear is thusdetermined before the
beginning
of their lineargrowth
(15-18
days
afterflowering), depending
onthe function of
spikelets
fertilized,
and moreimportantly,
on the survival ofpotential grains
[31];
thegreatest
fraction of the unitgrain weight
(90 %)
is formedduring
the lineargrowth phase;
growth
ceases atmaturity
[31],
which is indicatedby
the appearance of the blacklayer
[7].
Theperi-ods of formation of the different maize
yield
com-ponents
are thusquite
distinct andsequential.
Tollenaar
[31, 32]
emphasised
thecomplexity
of the processes at work inyield
formation:competi-tion between organs
during
ear formation can leadto
sterility
of theplants
or affect the number ofgrains
per ear aroundflowering
time.Asynchronous flowering
can be associated withfailure of
fertilisation,
withoutnecessarily being
itscause.
Adjustments
occur between source and sink:on the one
hand,
the number ofgrains
isdeter-mined in relation to the reserves which are formed
in the stem after the emergence of the
flag
leaf,
and which serve as a bufferduring grain growth;
andon the other leaf senescence can be accelerated
by
insufficientfilling
of ears. These processes canincrease or reduce the
sensitivity
to theenviron-ment of
yield
components at different stages of their formation.Finally, depending
on thecombi-nation of
genotype
xenvironment,
the source orthe sink for assimilates may be
limiting
[31].
The
sensitivity
ofyield
components to a stressappears to vary in the course of their formation. The number of ears
[28]
is more affected asflow-ering approaches,
eventhough
the ears aresensi-tive to stress at a very
early
stage
[2].
The number ofgrains
is thecomponent
whichusually
reactsmost
strongly
and mostrapidly, especially
todrought
stress[4,
17,
26],
throughout
itsperiod
of determination. The unitgrain weight
isonly
sensi-tive to environmental influences after exhaustion of the stem reserves[31, 33].
It can be stated that the number of ears perplant,
the number ofgrains
perplant
and the meangrain weight
aregood
indica-tors of the
growth
of the cropduring
thepre-silk-ing,
silking
andgrain-filling periods, respectively.
Greater
plant density
iscommonly
associated with a fall in the number of ears perplant
and with alarger proportion
of sterileplants,
even in theabsence of nutrient
deficiency
ordrought
stress[13, 18, 21].
Similarly,
the number ofgrains
pergrain weight
can be unaffected if theplant
popula-tion is thinned out after anthesis
[1]. However,
in asource-limited
situation,
anegative relationship,
differing according
togrowing
conditions,
canoccur, between the number of
grains
per unit areaand the unit
grain weight
[30].
Thus,
negative
rela-tionships
between onecomponent
and thoseformed
previously
arepossible
undercompetition.
We
adopted
thishypothesis
for ourdiagnostic
model based on
yield
components.
The formulation of the
relationships
betweencomponents and their maximum values
proposed
by
Navarro[25]
andFleury
[14]
remainsqualita-tive. The
objective
of this paper is topresent
themquantitatively,
and to translate them into ananalyti-cal
framework,
which can beapplied
to determinean
adequate population density,
and enable ananalysis
of the deviations of actualyield
frompotential yield
[35].
2. Materials and methods
2.1. General conditions of the
study
and data collected
This information is detailed in another
publication
[36].
Only
informationspecific
to this paper is described here.The
study
was carried out in themaize-growing
areain the west of Burkina Faso (10°-15°N). Annual rainfall is between 800 and 1 000 mm, with a maximum in
August.
The mean temperature is 27 °C. Solar radiation ranges from 14 to 20 MJ. m-2 d-1. Radiation andtem-perature, which varied little
spatially,
areapplicable
toBobo Dioulasso; rainfall was recorded
locally using
anetwork of
raingauges representing
areas of about 300-400 km2. Soils are ultisols. The varieties grownlocally
aremostly
local,open-pollinated,
traditionaltypes, and other
open-pollinated
varieties from interna-tional selection programmes(Cimmyt, Cirad, IITA).
These cultivars are
generally
tall (3-3.5 m for localcul-tivars, 2.5-3 m for selected cultivars). The varieties will be denominated as ’local’ or ’selected’ in the text. One of them, EV422SR, is the most recent released
variety,
and was found at 145 sites. The selected varieties arespreading rapidly,
and areadopted
in a similar wayby
all kinds of farmers. Weed control is
incomplete,
and herbicides are not used; levels of fertilisation are often,but not
always,
very low,depending
on the role of maize in thefarming system
and the farmer’s means.The
study
included 456 maize fieldssurveyed
between 1989 and 1991, years withfairly
similarweath-er conditions, close to the last
10-year
mean. Cultivationpractices
andspecific
constraints (weeds, viruses,Striga,
lodging)
were recorded at the field level.Variability
within fields did not allow the use of meanvalues per field for crop condition or
yield
components. These were observed for each field on two 20-30-m2plots,
established near the middle of the field, and 15-20 m apart. On eachplot,
the number ofplants
atflowering
(NP) and the number of visible ears (earlength
over 10 cmlong)
atmaturity (NE)
were countedand
given by
unit of area. Grainyield (Y)
andgrain
moisture content were measured. The unitgrain
weight
(WG) was determined from a
representative sample
of1 000
grains
from the harvestedplot,
aftershelling.
Grainweight
wasadjusted
to 15 % moisture (Y, WG). The area-based data wereexpressed
per hectare. The number ofgrains
per hectare (NG) was obtainedby
dividing
Yby
WG. The way the survey wasorganised
did not allow a direct count of the number of sterile
plants
at harvest(plants
with no earlonger
than 10 cm). The mean number of ears perplant (NEP)
was calculat-edby dividing
NEby
NP. Therelationships
betweenparameters were studied
using
the means of the twoplots
per field.2.2. Elimination of
heterogeneous
sites and estimation ofpotential yield
components
Data were screened for
normality (section 2.2.1)
andoutliers, which were eliminated
(section
2.2.2). Thiswas
performed
for each component, eachproduct
ofsuccessive components and
yield,
and for the twogroups of cultivars (local and selected)
separately.
2.2.1. Intra-site tests:
elimination
of
unreliable valuesThe statistical
analysis
of the datarequired
that for each character studied, the differences between the tworeplicates
within fields should benormally
distributed across the entiresample.
Observations on fields wherethis difference was
largest
in absolute terms weresuc-cessively
eliminated until the condition ofnormality
was satisfied. Sixteen fields were eliminated.2.2.2 Inter-site tests: elimination
of
outliersThe statistical
analysis
alsorequired
that allpoints
statisti-cal test was
applied
fordetecting outlying
values [8]. Theproblem
is that this test isonly applicable
to asam-ple
with Gaussian(normal)
distribution, but the distribu-tion of our wholesample might
not be normal.However, as the upper limit of each component is
approached,
it may bereasonably
considered that condi-tions tend to besuboptimal,
for which the fluctuations in the value of the variable studied are the result ofdiffer-ent factors of which none is determinant. This
corre-sponds
to the condition ofnormality,
and the test can be used. It isapplied
to the tenhighest
values of eachdis-tribution, and
repeated
until no further value has to be removed. Three sites were eliminated.2.2.3. Calculation
of
radiation-limitedyield
(Y
RAD
)
For the sites which were retained, a check was made
to ensure that the
sample
included observedyields
nearthe maximum
possible
for theprevailing
radiation andtemperature conditions.
Potential
yield
can be estimatedusing
asimple
model[23, 34], already used for wheat [22] to
interpret yield
variability
betweenplots.
Thedry
matter formedduring
agiven period
is a function of the energyintercepted
by
the canopy, and of the
capacity
of the canopy to convertit to
plant
material. Yield calculated on this basis wascalled ’radiation-limited
yield’
(Y
RAD
)
where G is the incident radiation
during
thegrain-filling
period,
ecis the climaticefficiency,
ei is theinterception
efficiency
and eb is theefficiency
of conversion ofener-gy into
plant
material. This wasapplied
to theperiod
from the end of thevegetative
growth
until the end ofgrain-filling
[19, 27], whichcorresponds
to theperiod
during
whichphotosynthesis
iscontributing
most tograin-filling.
Adynamic study
ofear-filling
on cvEV8422SR at the Farako Ba station (Bobo Dioulasso)
provided
a database for this calculation [35].2.3. Model of
grain
yield
formation2.3.1.
Expression of grain yield
According
to the modelproposed by
Fleury [14]
and Navarro-Garza [25], thegrain yield
can be written as:In order to take into account the
frequent
occurrence ofbarren
plants,
afrequency
of fertileplants,
FP, can be defined. The value of FP is between 0 and 1, and wascalculated from the mean number of ears per
plant:
The mean number of
grains
per fertileplant (NGFP)
iscalculated as follows:
The
grain yield
is then:In fact, sterile and
prolific plants
can co-exist on the sameplot,
and in these cases FP would overestimate thereal
frequency
of fertileplants.
However, this type of situation is lesslikely
when NEP falls below one. In thatcase, the
probability
ofprolific
plants
decreases. Abovethat
figure,
theprobability
of sterileplants
becomes very low. It ismainly
when NEP is near one, i.e. whenthe stresses
limiting
the formation of ears are low, that there is a risk that FP overestimates thefrequency
of fertileplants.
In the absence of a more suitableindica-tor,
equation (3)
wasapplied
to estimate FP.2.3.2. Maximal value
of a
component
At low
plant density
or lowgrain
number perplant,
and thus, in the absence of
significant
competition
amongplants (or grains
within theplant),
it is assumed that the maximal values takenby
a component arechar-acteristic of the cultivar in the
region
and for the climat-ic conditions (radiation, temperature)prevailing
that year. Whencompetition exists,
the assimilates per unitarea
contributing
to the formation of a component areshared between the elements of this component
(among
plants,
amonggrains
on theplant).
The level of
competition
among these elementsdepends
on theirpopulation.
Thecompetition
exerted betweenplants
to establish their NEP, FP or NGFP is afunction of NP. For WG,
competition
is exerted at twolevels: between
plants (indicator being always NP);
and within(competition
betweengrowing
grains
for a share of the energycaptured by
thisplant
being
dependent
onNGFP). An indicator of the level of total
competition
betweengrowing grains
(LCG) is theproduct
of thesetwo terms:
LCG is the number of
grains
dividedby
the areaoccupied
by
fertileplants.
FP is thereforeregarded
as anestimator of that part of the land area which is
truly
pro-ductive.
This
approach
involves the concept ofsequential
determination ofyield
components. Indeed themaxi-mum value a component can take is determined
by
thecomponents established
previously:
FP and NGPFThe search for the
highest
value a component can reach undergiven
conditions(cultivar,
region,
year) will be describedusing
theexample
of WG, for the case ofselected varieties
(figure 1f).
WG isplotted
against
LCG. The maximalvalues
are definedby
the upperboundary
of the cloud ofpoints
representing
all fieldssurveyed.
For low values of LCG, it is assumed that the maximal value isindependent
of LCG, andmostly
determinedby
the cultivar and the radiative conditions;the relation is a horizontal line. For
high
values of LCG,the maximal value is considered to be determined
by
thequantity
of energy available for eachgrain,
in such away that LCG x WG is constant; the relation is a
hyper-bola. The
straight
horizontal line and thehyperbola
for-malise theboundary
of the distribution ofpoints.
Their intersection is defined as a limit ofcompetition
betweengrains.
It is assumed that this model is
applicable
to differentyield
components. In such a scheme, theboundary
line defines thepotential
values of the componentconsid-ered, for a
given variety
undergiven
conditions.2.4. Estimation of varietal characteristics 2.4.1.
Equations for
theboundary
linesThe
relationships
between thefollowing
pairs
of vari-ables x x y are examined on the available datasets:NP x NEP (and NP x FP, deduced from
equation
(2))(7a)
The
boundary
lines of these relations are considered toconsist of a horizontal line followed
by
ahyperbola (as
indicated above), and the
corresponding equations
are calculated afterfitting
theboundary
line to the data. The horizontal line is fittedby forcing through
thehighest
point
on the y ordinate, ymax. Thehyperbola
is forcedthrough
thepoint
for which theproduct
of theco-ordi-nates xy is maximal, xymax. After the elimination of
out-liers, these
points
are the best available estimates of theexpected
valuesμ
y
and
μ
xy
of the maximasought.
Theboundary
line is defined fromonly
two maximum val-ues. It isimportant
to evaluate the associateduncertain-ty. A
boundary
line is defined over the range ofvaria-tion observed for x,
by
the relation:σ
y
andσ
xy
are the intra-site standard errors of ymaxand
xy
max
.
i is the site index; yi. the average of the two
replication
values for the site i.
in the same way, we can write:
The
equations
were determinedseparately
for the local and selected varieties.2.4.2. Varietal group characteristics calculated
For each varietal group and for each
yield
compo-nent, a maximumcorresponding
to theintercept
for theequation
of the line (varietal maximum M =y
max
)
wasdetermined.
A
competition
limit L,which is the
point
on the abscissacorresponding
to the intersection between the line and thehyperbola.
L wascalculated
using
the set ofequations
obtained for thetwo components of the
boundary
line. It was considered necessary to determine the value μLand the varianceF
L
of L. The variables xy, x and y were not obtainedinde-pendently:
x, in the case ofequation
(7c) was obtained from y and xy; likewise y, in the case ofequations (7a)
and (7b) was obtained from x and xy. Kendall et al. [20]showed that:
and its variance:
L can be considered to be distributed
normally
if n > 30,and if
σ
xy
/μ
xy
andσ
y
/μ
y
are smaller than 0.1 [5].2.4.3. Maximum
yield
as
a function of population density
(Y
M/NP
)
The maximum value of a component is assumed to
be determined
by
the values for the components estab-lishedpreviously.
The value for the first component(NP) therefore sets the upper limit for the second, and so forth: NP determines NEP and NGFP; these variables determine LCG; and LCG determines WG. The
product
of these successive valuesgives
the maximumyield
(Y
M/NP
)
for each value of NP. The greatest maximumyield
obtained(Y
GMAX
)
across levels of NP can beregarded
as an estimate of the radiation-limitedyield
Y
RAD
. Its
standard error can be estimated from theprod-uct xymaxfor
equation (7c).
In fact, underoptimal
condi-tions one can assume FP = 1, and therefore fromequa-tion (6) that LCG = NG, and from
equations (5)
and (6)that LCG x WG
equals
theyield.
2.4.4.
Comparisons of the
mean valuesof the
characteristics calculatedVarietal groups can be
compared
for greatest maxi-mumyield
(Y
GMAX
),
maximum level ofyield
compo-nents (M), and
competition
limits (L, expressed asplant
densities) and calculated for individual varietal group. The mean values
(μ
1
,
μ
2
)
for varietal group parameters(M, L,
Y
GMAX
)
arecompared
using
the usual Student’st-test:
The test
requires
that the variancesσ
1
2
andσ
2
2
are notdifferent. In the present case, the
degrees
of freedom v1 and v2 arelarger
than 100, and t can be considered asnormally
distributed.3.
Results and discussion
3.1. Observed
yield
(Y)
3.1.1. Yield distributionThe observed
yields
fell within a very widerange of variation: from 0.3 to 7.3
t·ha
-1
for local varieties with a mode between 1 and 2t·ha
-1
,
and from 0.4 to 9.5t·ha
-1
for selectedvarieties,
with amode between 3 and 4
t·ha
-1
.
Yield
maxima werethus very
high,
andpresented
anexceptional
rangeof variation
compared
with othercurrently
avail-able datasets:they
are among the best recorded inlow altitude
tropical
Africa,
judging
from the meanestimates
published by
the national statisticalser-vices for Burkina Faso
(1-2
t·ha
-1
)
or inneigh-bouring
countries such as Bénin(0.9-1.4
t·ha
-1
[37])
andTogo
(1.03
t·ha
-1
[15]).
3.1.2. Radiation-limited
yield
(Y
RAD
)
From the datasets for cv
EV8422SR,
theperiod
from
silking
to the end ofgrain-filling
was estimat-ed at 47days,
with a meandaily
temperature of24 °C. Mean radiation was 17
MJ·m
-2
·d
-1
.
Taking
values of 2.49 for
e
b
[16],
0.48 fore
c
,
[34]
and Ifor
e
i
,
a value forY
RAD
of 9.6t·ha
-1
is obtained.The
3-year
survey showsquite
similar climatic characteristics across the years[35].
Thetempera-tures
during
the months with the least sunshinewere also the
lowest,
which shouldprolong
theperiod
ofgrain-filling
and have acompensatory
effect.
Therefore,
Y
RAD
probably
varied little amongsowing
dates or among years.Finally,
however inaccurateY
RAD
evaluationmight
be,
it was in the same order ofmagnitude
asthe
greatest
observedyields
Y for this cultivar.Therefore,
it is reasonable to suppose that:-
the range of situations encountered includes
most of those which are
likely
to occur in theregion;
- all
of the sites included in the survey were
sub-ject
tocomparable
conditions of radiation and tem-perature;- the
graphical representation
of therelation-ships
between components included situations withyields
close toY
RAD
,
and enabled us toaccurately
position
theboundary
lines for the clouds ofpoints.
We assume that this is valid for both groups of
varieties.
3.2. Yield
components
3.2.1.
Relationships
amongyield
components
On the scattergrams forpairs
ofyield
compo-nents
(figure
1),
it ispossible
to locate the two parts of theboundary
line,
calculate theirequations
and find theposition
of thecompetition
limitsL
NEP
,
L
NGFP
andL
WG
,
and of the limitL
FP
.
In figure
1bshowing
the localvarieties,
it appears thatcompetition
amonggrowing
grains
as
expressed
by
theproduct
NP x NGFP(= LCG)
was constant
beyond
40 000plants·ha
-1
:
according
to the
model,
LCG cannot exceed this value ifplant density
increases further. A maximum also appears to exist for LCG for the selected varietiesmaxi-mum mean WG
(within
theboundary
lines)
variedbetween 260 and 390 mg
(local varieties)
and between 306 and 420 mg(selected varieties),
depending
on NP.From these
relationships,
others can be derived that describe therelationship
ofcompetition
withNP. The
relationship
of LCG with NP infigure
2a is derived fromfigure
1b. For anygiven
value ofNP,
there is asingle
corresponding
maximum valuefor LCG. On the basis of
this,
therelationship
of thecompetition
limitL
WG
with NP can becalculat-ed. The value of LCG at which
L
WG
is reached is indicatedin figure
1c;
the value of NPcorrespond-ing
to this value of LCG is calculatedfrom figure
2a.Thus,
the limit ofcompetition
betweengrains
L
WG
may beexpressed
notonly
as a function ofLCG but also as a function of
NP,
as thisapplies
toL
NEP
,
L
FP
andL
NGFP
.
Therelationship
of WG withNP may be found in the same way.
3.2.2. Varietal characteristics
(tables
I andII)
3.2.2.1. Varietal maximaAccording
to the calculated values of the varietalcharacteristics,
the two groups of cultivars are notvery
prolific,
and are not distinctaccording
to NEP(table I).
The traditional varieties havesignificant,
butslightly
maximumhigher
NGFP andslightly
lower maximum WG than the selected varieties. The maximumgrain weight
perplant
is notdiffer-ent for the two groups.
3.2.2.2.
Density
limits tocompetition
In
interpreting
theresults,
the extent ofcompeti-tion will be considered to
depend
on the ratio between assimilate and demand:competition
increases withincreasing
NP or whenplants
are moredemanding (e.g.
tall varieties have ahigher
demand);
orconversely,
when the availableresources per unit area are more limited
(low
sup-ply).
It is observable that the low
population
level(27
100-35 200plants·ha
-1
,
depending
on thevari-etal
group)
at whichcompetition
that affects WG within a standbegins
to appear(table I)
agreeswell with tall
tropical
maizevarieties,
which maydisplay
acompetition
effect at lower densities thantemperate
ones[10].
Thedensity
limit seemshigh-er for the establishment of the number of ears per
plant
(L
NEP
)
than for the number ofgrains
perplant
(L
NGFP
)
(table
II),
implying
a lowercompetitive
pressure for NEP. This may be related to the
growth
stage at which the two components devel-op: NEP is determined between ear initiation andflowering,
whenvegetative
growth
isincomplete
and the canopy is stillclosing.
NGFP appears afterthe gaps in the canopy are
closed,
and at a timewhen the
plant’s
demand for external resources ishigh.
Thecompetition
limit for meangrain weight
(L
WG
)
was evenlower,
indicating
more intensecompetition.
Thismight
be due to theprogressive
senescence of the
foliage,
which reduces the utili-sationefficiency
for theintercepted
radiation. This would cause an increasedcompetition
forassimi-lates between
grains, through supply
limitation. The selected varieties seem to toleratesignifi-cantly higher density
limits tocompetition
than the local varieties(table I):
20 %higher
for the firstcomponents to be
established,
and 30 %higher
for WG. This is related to a smaller individualplant
size.
3.2.2.3. Greatest maximum
yield
(Y
GMAX
)
The
greatest
maximumgrain yield
(Y
GMAX
,
tableI)
may be calculated if theplant
density
reaches the lowestcompetition density
limit(L
WG
).
For the selected varieties it was about 30 %higher
than for local varieties. The difference was
directly
related to the increase in the
competition density
limit.With
regards
to theplant
type,
the selection of maize cultivars in theregion
ofstudy
seems tohave been based
essentially
on the size of theplants,
whileretaining
their individualproduction
potential.
This agreescompletely
with data from the literature(e.g.
[10]).
Examination of varietal characteristics
(potential
values foryield
components,density
limits for theirexpression,
differences betweentropical
vari-etalgroups) highlights
several consistent traits:i)
the values of the limits for variousyield
compo-nents reflect the
dynamics
of the system:competi-tion sets in at lower densities as the season
advances,
i.e. as theplants
getlarger
(before
flow-ering)
or as thefoliage
gets older and less efficient(after
flowering);
ii)
similarly,
the classification ofvarieties agrees with
expectation,
the tallest vari-etiesexhibiting competition
at a lowerpopulation.
This was true at each
competition
limit.3.3.
Population density
and calculated maximumyield
(Y
M/NP
)
The
equations
established and the parameters calculated can be used to describe the maximumgrain
yield
as a function ofpopulation density
foreach varietal group. This curve is shown
in figure 3
for the
example
of the local varieties andin figure
4 for the two groups:
- below
L
WG
,
there is nocompetition
amongplants,
which can all form ears. The number ofgrains
perplant
(NGP
=NGFP)
and their unitweight
(WG)
areindependent
ofplant density,
towhich
yield
islinearly
related;
- between
L
WG
andL
NGFP
,
the number of earsper
plant
(NEP)
and the number ofgrains
per fer-tileplant
(NGFP)
remain constant, such that the number ofgrains
per square meter(NG)
and the level ofcompetition
betweengrains
(LCG)
increase withdensity,
whereas unitgrain weight
(WG)
falls:Y
M/NP
(=
NG xWG)
nolonger
increas-es; -
beyond
L
NGFP
,
NGFP decreases as NPincreas-es,
thereby
stabilising
LCG(and
consequently
WG)
and NG. Aslong
as all theplants produce
grain,
Y is constant;-
beyond
L
NEP
,
prolificacy
declines,
but without effect onY
M/NP
untilL
FP
.
The increase in NPcom-pensates for the decrease in NGFP.
Across these three parts of the curve
(from
L
WG
the curve is reached. The
plateau corresponds
toY
GMAX
,
whichtheoretically equals
Y
RAD
:
- if NP if
larger
thanL
FP
,
sterileplants
appear. LCG and WG remain constant.But,
as FPdecreas-es, NG
(=
LCG xFP)
also decreases. As aresult,
the
potential yield
at agiven population
Y
M/NP
decreases.
The model of
Y
M/NP
as a function ofdensity
has threecomponents
(increase,
plateau
anddecrease).
In all the
relationships
established,
the twoarea-based components are associated with
possible
compensatory
effects:NP,
the variation of whichcauses variation in
NGFP;
andLCG,
to which WG is related.The
proposed
relationship
between maximumgrain yield
andpopulation
density,
with aY
M/NP
plateau
betweenL
WG
andL
FP
,
is not consistent with the modelproposed by
Duncan[11,
12],
and usedby
various authors[3, 32].
Theplateau
is dif-ficult toverify experimentally,
as the absence of alimiting
factor other thanprevailing light
and tem-perature is a necessary condition.Also,
severalpopulation
densities are neededcovering
the range betweenL
WG
andL
FP
,
in order to demonstrate that variation indensity
iscompensated
forby grain
yield
perplant.
These limits arespecific
to cultivartype. To our
knowledge,
such situations have notbeen
reported
in the literature.However,
yields
per unit area arefrequently
constant acrossplant
densi-ties: this
applies
to two sets of data with two[13,
30],
or even three densities[18].
The modeldevel-oped
here canexplain
thisphenomenon.
It is true,
however,
that a direct consideration ofthe observation
points
does notclearly
show this evolution withplant density
(see,
forexample,
fig-ure
4),
and that the trend of the calculated maxi-mumyield
isstrongly dependent
on the model cho-sen to be fitted to thedata,
and on the method offitting.
3.4. Observed
plant
population
densities andyields
3.4.1. Distribution
of population
densities usedby
thefarmers
The lowestpopulation density
recorded was16 000
plants·ha
-1
.
Table
III shows the distribution of sitesby
density,
recordedseparately
for each varietal group: most of the densities recorded werelower than 50 000
plants·ha
-1
.
Compared
to localvarieties,
the selected varieties occurred much lessfrequently
below 30 000plants·ha
-1
,
and muchplant
densities weremostly
below thoselocally
recommended for selected varieties
(50
000plants·ha
-1
for lowinput
conditions and 62 500 forhigh input).
Grouping
casesaccording
toplant
densities rela-tive to thevariety-specific competition
limits(table
IV)
virtually
eliminated the differences between varietal groups. More than half of thepopulation
of each group had densities situated betweenL
WG
andL
NGFP
.
Densitiesgreater
thanL
NEP
were rare(8 %),
and cases with densities
exceeding
L
FP
wereexcep-tional.
In summary, it appears that:
- varieties differed
strongly
in NP in absolute terms, but not in terms of thecompetition
levelresulting
from NP. Insofar asplant
densities resultfrom farmers’
decisions,
rather than from variableseedling
emergence, farmers seem to have aper-ception
of varietal behaviour with respect tocom-petition
limits;
-
the densities of selected varieties were
mostly
found between the two first
competition
limits(L
WG
andL
NGFP
);
- the farmers’ choices differ from the
recom-mendations.
At a
population
density
belowL
WG
(table V),
local varieties were
virtually
theonly
onesrepre-sented. Above this
value,
the selectedvarieties,
although
still lessfrequent
than the localvarieties,
increased 8-fold.
3.4.2. Distribution
of observed
yields
(Y)
The curves calculated for
Y
M/NP
frompopulation
density
werecompared
with observedyield (figure
4).
The cloud of data was subdivided into sectorsaccording
toyield
reduction relative to themaxi-mum
(<
1.0,
<0.8,
< 0.6 ofY
M/NP
)
andcompeti-tion limits
(critical
population
densities).
The
variability
ofyield
within each varietal group will beanalysed
in aseparate report
[36].
Inboth the varietal groups, the
greatest
yields
wereobserved for densities close to
L
NGFP
.
These densi-ties wereslightly
greater
than thepopulation
rangefound most often
(table III).
At NP values above and belowL
NGFP
,
observedyields
weregenerally
inferior to
Y
M/NP
:
the value of 0.8Y
M/NP
wasonly
exceeded between
L
WG
andL
NEP
,
and the 0.6level,
with threeexceptions,
wasonly
reached betweenL
WG
andL
FP
.
At NP >
L
NGFP
,
thecapacity
forcompensation
with
respect
to the unitgrain
weight
is maximal(figure
3e):
beyond
thislimit,
the farmer has the bestprobability
ofachieving
Y
M/NP
.
Thus,
in addition to varietalconsiderations,
other
parameters
werepossibly
associated withsowing
density,
and may have contributed to the farmer’s choice of the low densities observed.- An increase in