RESEARCH ARTICLE Modelling cacao pod growth ......Cacao pod growth G.MartijntenHoopenetal. Fruit...

Annals of Applied Biology ISSN 0003-4746

R E S E A R C H A R T I C L E

Modelling cacao pod growth: implications for disease controlG. Martijn ten Hoopen1,2,3, P. Deberdt1,2,3,4, M. Mbenoun3 & C. Cilas1,2

1 CIRAD, UPR Bioagresseurs analyse et maıtrise du risque, Yaounde, Cameroon

2 CIRAD, UPR Bioagresseurs analyse et maıtrise du risque, F-34398, Montpellier, France

3 Phytopathology Laboratory, IRAD, BP2067, Yaounde, Cameroon

4 Present address: CIRAD, UPR HortSys, F-97285, Le Lamentin, Martinique, France

KeywordsBeta growth; Gompertz; Logistic; pod;

Richards; sigmoid; Theobroma cacao.

CorrespondenceG. Martijn ten Hoopen, CIRAD, BP 2572,

Yaounde, Cameroon.

Email: [email protected]

Received: 27 October 2011; revised version

accepted: 3 February 2012.

doi:10.1111/j.1744-7348.2012.00539.x

Abstract

Cacao trees are affected by diseases that attack either their vegetative parts,their fruits or both. In cacao pod diseases, several factors are involved in diseasesusceptibility, such as the fruiting cycle, fruit size, age, position on the tree andcacao genotype. To gain a clearer understanding of how these characteristicsinfluence cacao pod diseases, four models describing pod growth in severalcacao genotypes were evaluated. Three models used to estimate pod volume orsurface area were also compared. Observed pod growth was of a sigmoid formand fitted best to the Richards model, well to the Logistic and Beta growthmodels, and least to the Gompertz model. Pod volume and probably pod surfacearea were best estimated using a prolate spheroid model. Pod growth modelscan help improve pod disease management and thereby cacao production.They can help to predict yield, as well as provide information for the timingand frequency of control operations. Information on pod size, surface areaand susceptibility will help to improve dose transfer and spray deposit studiesintended to optimise control efficiency.

Introduction

Millions of people have acquired a taste for chocolateand its derivatives in its many forms. It is estimatedthat around 6 000 000 tonnes of chocolate-basedconfectionery are consumed worldwide each year (Lass,2004). The global trade in cacao beans, the primaryingredient of chocolate, is currently worth some $9 billiondollars (ICCO, 2010; P. Bastide, personal communication)and a significant revenue earner for developing countries.Cacao (Theobroma cacao L.) is therefore one of the mostimportant perennial crops in the world.

At the same time, it is estimated that over 40% ofall cacao production is lost annually to just five diseases:black pod disease, frosty pod rot, witches’ broom disease,cacao swollen shoot disease and vascular streak dieback.Additional losses are inflicted by insect and vertebratepests (Flood et al., 2004). Phytophthora spp., causing blackpod disease, are the single greatest cause of global yieldlosses. The most serious species is Phytophthora palmivora

(Butl.) Butl., causing global yield losses estimated at20−30% and causing tree deaths of up to 10% annually

(Flood et al., 2004). However, Phytophthora megakarya

Brasier & Griffin, which is currently restricted to West and

Central Africa, is much more aggressive than P. palmivora

(Nyasse et al., 1999; Appiah et al., 2004). P. megakarya

reached Ivory Coast probably sometime in the late 1990s

(N’Goran et al., 2006) and is now well on its way to

becoming the single most important cacao disease in the

world’s two largest cacao producing countries, Ghana

and Ivory Coast. Frosty pod rot, caused by Moniliophthora

roreri (Cif) Evans, is considered to be the most dangerous

cacao disease, and is the most important pathogen in

the countries where it is present. Thankfully, this disease

is, as yet, restricted to Mexico, and Central and South

America (Ploetz, 2007). Although both the vegetative

parts, as well as cacao pods, are affected by numerous

diseases, both P. megakarya and M. roreri only attack cacao

pods.

Several studies have shown that the developmental

age of pods can influence their susceptibility to infection

and the severity of the symptoms produced. Although

P. megakarya can infect cacao pods at all developmental

260 Ann Appl Biol 160 (2012) 260–272 © 2012 The AuthorsAnnals of Applied Biology © 2012 Association of Applied Biologists

G. Martijn ten Hoopen et al. Cacao pod growth

stages, a study from Cameroon by Efombagn et al. (2004)showed that 2- to 3-month-old cacao pods are the mostsusceptible development stage for a cacao clone withvery high susceptibility to P. megakarya. Susceptibility toblack pod is probably also influenced by the length ofthe fruiting cycle. Clones with a short pod cycle seemto be less susceptible in the field when compared withartificial pod inoculations, since the pathogenic exposureof such pods is shorter (Berry & Cilas, 1994). Datafrom a 3-year field study in Cameroon by Deberdt etal. (2008) showed a significant correlation between podrot incidence and development stage; immature pods,aged between 10 and 20 weeks (2.3 and 4.6 months)had the highest disease incidence levels. In the caseof M. roreri, it was shown that cacao pods graduallybecome less susceptible beyond the age of 3 months(Phillips-Mora et al., 2005 and references therein). Recentwork actually shows that under field conditions M. rorerionly infects cacao pods in the first 2 months after theirappearance (Leandro Munoz, 2011; J. Avelino, personalcommunication) Since M. roreri only infects meristematictissue (Krauss et al., 2006), which means that undernatural conditions only actively growing cacao pods areinfected, this could explain why only young pods areinfected by M. roreri. Thus, cacao pod development seemsclosely linked to disease susceptibility.

To gain a clearer understanding of how thesecharacteristics influence cacao pod diseases, it would beuseful to have a model describing cacao pod growthfor several genotypes. Although certain authors havedescribed pod growth (Waters & Hunter, 1928; McKelvie,1956; Daymond & Hadley, 2008), to our knowledge, nodetailed comparison of cacao pod growth functions isavailable.

In cacao production, the most common diseasecontrol method consists in spraying systemic or copper-based contact fungicides. Numerous authors have oftenreported the negative externalities of chemical control inorder to advocate alternative control methods (Tondje etal., 2006, 2007; Deberdt et al., 2008). However, it is afact that fungicide spraying in cacao is often cost-effective(Akrofi et al., 2003; Bateman et al., 2005; Gockowski etal., 2010) and for the time being, a necessity for ensuringefficient disease control. With the current interest inreducing pesticide dependency and its negative impactson human and environmental health, it is surprisingthat only a few studies have focused on better timingof applications and improving dose transfer and spraydeposition in cacao (Hidalgo et al., 2003; Bateman, 2004;Bateman et al., 2005; Jessop et al., 2010). Such anapproach would reduce costs for farmers while, at thesame time, reducing some of the negative externalitiesassociated with fungicide spraying. The analysis of dose

transfer and spray deposition in cacao is linked to cacaopod surface area. An accurate estimate of cacao podsurface area is therefore important. Since cacao poddevelopment and disease susceptibility are closely linked,the timing of fungicide applications is also linked to poddevelopment. Moreover, the fast expansion of cacao podshas been identified as a limiting factor for chemical diseasecontrol (Evans et al., 1977).

The growth cycle of a plant organ such as a cacao podcan usually be divided into three sub-phases: an earlyaccelerating/cell division phase, a linear/cell enlargementphase and a saturation phase for ripening/maturation(Goudriaan & van Laar, 1994; Fig. 1). Thus, growthpatterns often follow sigmoid curves (Fig. 1). Thereare numerous growth functions that have been usedto describe the growth of plants or their organs.Some of the best known classic growth curves arethe Logistic (Verhulst, 1838), Richards (Richards, 1959)and Gompertz (Gompertz, 1825) functions. The Logisticfunction is symmetrical around the point of inflexion,whereas both Richards and Gompertz are asymmetrical.Other, less well-known asymmetrical growth functionsexist, such as the Beta growth function (Yin et al., 1995,2003).

Detailed descriptions of growth stages in plants providethe basis for a comparison of epidemiological disease stud-ies and of genetically clone-specific parameters helpfulfor developing management practices and experiments(Niemenak et al., 2010) The objective of this studywas therefore to describe cacao pod growth, compar-ing four sigmoid growth functions, and to compare threedifferent ways of calculating pod surface area. This infor-mation will help shed light on cacao pod susceptibilityto diseases and will therefore be useful in determin-ing the optimum period for applying protective treat-ments, while at the same time allowing for dose transferoptimisation.

Materials and methods

Study site

A site (03◦51′40.0′′N, 011◦27′19.3′′E) was selected nearthe headquarters of the Institut de Recherche Agricole pour le

Developpement (IRAD) in Nkolbisson, Cameroon. The areawas planted in 2001 with four replicates of 10 trees of 25genotypes. Nineteen of these were derived from a 6 × 6complete diallel design (without the selfs), with IMC 67,ICS 84, ICS 95, SNK 10 SNK 413 and UPA 134 as parents,and selected according to their yield and Phytophthora

resistance using a selection index (Ndoumbe et al., 2001).Each replicate also contained the local clones SNK 10,SNK 12, SNK 620, SNK 630, and the international clones

Ann Appl Biol 160 (2012) 260–272 © 2012 The Authors 261Annals of Applied Biology © 2012 Association of Applied Biologists

Cacao pod growth G. Martijn ten Hoopen et al.

Fruit growth curve

Time (days)

Fru

it w

eigh

t/vol

ume/

leng

th

0 20 40 60 80 100 120 140 1600

40

80

120

160

200

Cell division Maturation Cell enlargement

Stage I Stage III Stage II

First division zygote and first wilt peak

Pod and ovule growth slow down at the

expense of embryo growth

Endosperm consumed by embryo Second wilt peak

Figure 1 Sigmoid growth curve with specific cacao pod development periods as described by McKelvie (1956) and generalised fruit development

stages.

UPA 134 and SCA 6. This site was selected because of itsproximity to the research station and, most importantly,because no pod rot due to P. megakarya was observedsince its installation.

Cacao pod growth, volume and surface area

Cacao pods from the cacao accessions SCA 6, SNK 10,BBK 1606, BBK 1016, BBK 887, BBK 726, BBK 693,and BBK 62 were used to monitor pod development.Since only one replicate contained 10 trees for eachaccession or clone, pod growth was only measured inthat replicate. Open pollinated pods (with a maximumof 10 per tree) were marked when approximately 1- to2-weeks old and the length and diameter (in mm) of thepod were subsequently measured weekly. Pod losses overthe observation period were attributed to either cherellewilt, feeding damage by insects or rodents or losses due toother reasons. Observations started on 18 May and lasteduntil 18 December 2007.

Ripe pods were harvested and taken to the laboratory.Pods were weighed and their volume was determinedby measuring water displacement. Measurements asindicated in Fig. 2 were taken on each pod in orderto estimate pod surface area and pod volume.

D1 D2

L1

L2r

Hemisphere Cylinder Cone

Figure 2 Pod model used to estimate pod surface area and pod volume,

consisting of a hemisphere with radius D1/2, a cylinder with a radius of (D1

+ D2)/4 and length L1 and a cone with radius D2/2 and length L2.

Data analysis – pod growth curves

A preliminary analysis of the cacao pod growth curveswas undertaken using CurveExpert (version 1.3, Hyams,2010). Since the Richards, Logistic, and Gompertz growthequations were the most recurrent equations, bestdescribing longitudinal as well as lateral pod growth, theywere selected for data analyses. Furthermore, as Maisin& Lamin (2006) introduced the Beta growth functionto describe cacao pod growth, this function was alsoincorporated.



Longitudinal and diametrical pod growth curves wereanalysed using the PROC NLIN procedure in SAS(SAS Institute Inc., 2007). For all individual pods, thegrowth parameters of each of the four growth functionswere obtained through iterative nonlinear least squareregression using the Marquardt method (Marquardt,1963).

The only symmetrical sigmoid curve was the Logisticfunction (Verhulst, 1838):

L = Lmax

1 + be−ct

where L is the length (or width) of a cacao pod andt is the pod age, Lmax is the upper limit to the growthof the variable L, b is a measure of kurtosis, c controlsgrowth rate and tmax = ln(b)/c gives the day on whichthe growth rate reached its maximum value and at whichtime L = Lmax/2.

The following three non-symmetrical growth curveswere used:

First, the Richards function (Richards, 1959):

L = Lmax(1 + eb−ct

)1/d

where Lmax is the upper limit of the length or diameterof the pod, b controls growth rate and c the timeof maximum growth, whereas d affects near whichasymptote maximum growth occurs. The day on whichmaximum growth occurred is given by:

tmax = (b − ln d) /c

Second, the Gompertz function (Gompertz, 1825):

L = Lmaxe−eb−cx

where Lmax is again the upper asymptote and b and care the function coefficients, the day on which maximumgrowth occurred is given by tmax = b/c while the lengthat this time is given by Lmax/e

Third, the Beta growth curve (Yin et al., 1995, 2003)

L = Lmax

(1 + te − x

te − tm

) (x

te

) tete−tm

with 0 ≤ tm < te

where Lmax is not the asymptote but the maximumvalue of L, which is reached at time te, and tm thepod age at which the maximum pod growth rate isachieved.

For each parameter of each growth curve, a box plotwas traced and outliers were identified. The cacao podsthat were thus identified, having at least one outliergrowth parameter irrespective of growth function, wereexcluded from further analyses. The R2 value of the linear

regression between observed and predicted longitudinaland lateral pod growth and the mean absolute predictivediscrepancy (MD) were used to indicate goodness of fit(as per Yin et al., 2003).

Data analysis – pod surface area and volume

Pod surface area was estimated using a slightly modifiedversion of the model described by Bateman (2004).Our model was based on a hemisphere (pedicel end= 2π(D1/2)2), a cylinder and cone 2π(D1 + D2/4)L1

and π(D2/2)√

((D2/2)2 + L22) (Fig. 2). The outcome of

this model was used to calculate pod volume which wascompared to actual pod volume.

Waters & Hunter (1928) determined a relationshipbetween pod volume V (mL) and pod length (L) anddiameter (D) for the West African Amelonados:

V = L(πD)2

22

Jessop et al. (2010) used a prolate spheroid model tocalculate the surface area of cacao pods. This model alsoallows the calculation of volume, which can be comparedto measured volume. The prolate spheroid model surfacearea (A) is given by:

A = 2π

(a2 + abα

sin(α)

)

and volume (V) is given by:

V = 4

3πa2b

where α = arccos(

ab

), b is the polar radius and a is the

equatorial radius.Butler (1980) determined a relationship between pod

surface area and weight. The relationship between podsurface area, A (cm2), calculated as an obloid spheroid,and weight Wp(g) was determined by regression usingdata from 60 pods:

A = 4.22W0.71p

Estimated pod volumes of each method were comparedwith actual measured volumes using the appropriategeneralised linear model in SAS (SAS Institute Inc.,2007). Estimated pod surface areas were also comparedwith each other using a one-way ANOVA. The sameanalyses were carried out for pods of individualclones.



Results

In all, 305 pods were monitored over the course of the2007 production season. A total of 163 pods reachedmaturity. The rest were lost due to either cherelle wilt,insect or mammal damage or due to other reasons(Table 1). Of the 163 pods that reached maturity, 36had one or more parameter values that were consideredoutliers and thus were eliminated from all furtheranalyses. Of the 127 pods that remained, 126 were usedin the pod surface area/volume study.

Pod growth curves

Parameter values for the different growth curves fittedto the longitudinal and lateral growth data for cacaopods of the eight different cacao genotypes are given inTables 2 and 3, respectively. All four functions accuratelydescribed longitudinal and lateral pod growth as revealedby R2 values > 0.98. The Richards function was thegrowth function that described both growth curves withthe highest accuracy as shown by the R2-values > 0.99.

All four equations have one common parameter,namely Lmax. A significant (P < 0.0001, df 4) growthfunction effect was observed for the estimation of Lmax.All growth functions overestimated Lmax values whencompared with real pod length (Table 3; Fig. 3). Similarlyfor lateral pod growth, a significant (P < 0.0001, df 4)growth function effect was found for Lmax estimates.Again, all growth functions overestimated Lmax (Table 3).

If individual cacao genotypes were considered, all fourequations overestimated pod length, but there was onlya significant effect for SCA 6 (P = 0.026, df 4; Fig. 3).For lateral growth, again all four equations overestimatedmax width. There were significant effects for all cacaogenotypes except BBK 62. For BBK 693, BBK 726, BBK887 and BBK 1606 (P < 0.003, df 4) the Gompertzfunction clearly overestimated maximum pod width. ForSCA 6, BBK 1016 and SNK 10 (P < 0.0001, df 4), theGompertz, and to a lesser extent, the Logistic functionclearly overestimated maximum pod width.

Pod length ranged from 14.2 for SCA 6 to 18.3 cm forBBK 62 and was 16.2 cm on average (Table 1). As can beseen from the data in Tables 2 and 3, the Beta growthfunction parameter te clearly showed that maximumpod length was obtained approximately 6 days beforemaximum pod width. Taking individual genotypes, thisdifference varied from approximately 4 days for SNK 10,BBK 62 and BBK 1606 to almost 13 days for BBK 693.The average time taken to reach maturity was 157 days;for individual genotypes this period varied from 151 daysfor SCA 6 to 163 days for SNK 10 (Table 1).

The time at which maximum pod length or widthincrease took place was 71.9 and 87.0 days on average, Ta

ble

1C

acao

germ

pla

smus

ed,i

tsor

igin

,the

num

ber

ofp

ods

stud

ied

,the

num

ber

ofp

ods

used

inth

esu

rfac

ear

ea/v

olum

est

udy,

pod

loss

reas

ons,

day

sat

whi

chm

axim

umle

ngth

orw

idth

incr

ease

was

mea

sure

dan

dm

ean

pod

leng

than

dw

idth

inm

m,a

ndd

ays

until

mat

urat

ion

(SE

inb

rack

ets)

Pod

Loss

Rea

son

Day

ofM

axP

odG

row

thM

ean

Pod

Clo

neO

rigi

nP

ods

Mar

ked

Pod

sus

edin

Surf

ace

Are

a/V

olum

eSt

udy

Che

relle

Wilt

Eate

nO

ther

sLe

ngth

(day

s)W

idth

(day

s)Le

ngth

(mm

)W

idth

(mm

)D

ays

toP

odM

atur

ity

SCA

645

264

17

71.7

(2.4

)87

.8(2

.3)

142.

2(3

.1)

76.9

(1.1

)15

1.3

(1.1

)SN

K10

369

40

1369

.5(7

.0)

81.8

(2.7

)17

0.6

(5.8

)89

.6(1

.9)

163.

2(2

.5)

BB

K62

UP

A13

4×

IMC

6725

97

18

67.7

(6.8

)83

.3(6

.0)

182.

6(1

0.3)

79.9

(3.4

)15

5.3

(2.7

)B

BK

693

UP

A13

4×

SNK

413

2716

50

666

.7(4

.1)

80.9

(2.2

)16

1.4

(5.2

)78

.6(1

.4)

152.

9(2

.2)

BB

K72

6IM

C67

×U

PA

134

4527

101

566

.0(3

.3)

82.6

(1.7

)15

4.0

(5.1

)72

.5(1

.4)

159.

8(2

.2)

BB

K88

7U

PA

134

×SN

K41

348

2113

012

77.4

(3.5

)91

.6(1

.8)

170.

2(5

.4)

81.6

(1.6

)15

7.6

(1.4

)B

BK

1016

UP

A13

4×

SNK

413

345

140

777

.9(3

.9)

88.9

(5.3

)17

6.5

(5.5

)78

.4(1

.0)

156.

8(4

.2)

BB

K16

06U

PA

134

×SN

K41

345

1312

012

79.1

(5.0

)97

.3(2

.0)

169.

2(5

.3)

77.3

(2.1

)15

9.4

(2.0

)

Tota

l/mea

n30

512

669

370

71.9

(1.5

)87

.0(1

.1)

162.

0(2

.1)

78.8

(0.7

)15

6.6

(0.8

)



Tab

le2

Estim

ated

pod

grow

thp

aram

eter

sof

four

grow

thfu

nctio

ns(L

ogis

tics,

Ric

hard

s,G

omp

ertz

and

Bet

aG

row

th)fi

tted

tolo

ngitu

din

alca

cao

pod

grow

thof

eigh

tcac

aoge

noty

pes

(SE

inb

rack

ets)

a

Cac

aoC

lone

Func

tion

Par

a-m

eter

bSC

A6

SNK

10B

BK

62B

BK

693

BB

K72

6B

BK

887

BB

K10

16B

BK

1606

Mea

nA

llP

ods

Uni

t

Logi

stic

L max

148.

762

(3.1

69)

172.

667

(6.0

61)

190.

738

(11.

909)

167.

652

(5.6

14)

157.

597

(4.9

73)

175.

836

(5.8

80)

184.

355

(6.1

74)

174.

839

(5.9

43)

167.

548

(2.2

50)

mm

b10

.793

(0.5

28)

14.3

97(1

.173

)10

.168

(0.6

75)

13.4

48(0

.669

)10

.613

(0.5

56)

13.6

20(0

.763

)14

.432

(1.7

05)

11.1

63(0

.607

)12

.188

(0.3

14)

mm

−1

c0.

043

(0.0

00)

0.05

1(0

.001

)0.

043

(0.0

01)

0.05

1(0

.001

)0.

050

(0.0

01)

0.04

7(0

.001

)0.

044

(0.0

01)

0.04

3(0

.001

)0.

046

(0.0

00)

mm

day

−1

t m54

.986

(0.9

45)

51.2

79(1

.826

)53

.270

(1.8

82)

50.7

90(1

.203

)46

.562

(1.0

12)

55.4

33(1

.270

)59

.624

(2.6

37)

56.2

39(1

.588

)53

.320

(0.5

92)

day

R2

0.99

40.

996

0.99

30.

995

0.99

40.

995

0.99

60.

995

0.99

5

MD

3.36

02.

946

4.51

13.

429

3.31

73.

696

3.28

83.

405

3.44

0m

m

Ric

hard

sL m

ax14

3.91

6(3

.094

)17

0.74

7(6

.026

)18

8.09

4(1

0.80

4)16

6.00

5(5

.344

)15

5.91

4(4

.946

)17

2.51

1(5

.718

)18

2.03

6(6

.136

)17

3.70

4(5

.588

)16

4.85

8(2

.228

)m

m

b5.

750

(0.2

60)

4.71

3(0

.446

)3.

505

(0.7

55)

3.76

2(0

.270

)4.

067

(0.2

52)

4.81

1(0

.322

)3.

836

(0.4

22)

2.94

4(0

.327

)4.

395

(0.1

43)

day

c0.

072

(0.0

02)

0.07

0(0

.004

)0.

054

(0.0

05)

0.06

1(0

.002

)0.

066

(0.0

03)

0.06

6(0

.003

)0.

055

(0.0

05)

0.04

7(0

.002

)0.

064

(0.0

01)

day

−1

d2.

725

(0.1

34)

2.44

8(0

.272

)1.

636

(0.3

14)

1.54

3(0

.123

)1.

872

(0.1

31)

2.03

5(0

.138

)1.

558

(0.1

75)

1.28

0(0

.138

)1.

947

(0.0

69)

–

t m65

.496

(1.0

65)

57.4

84(2

.254

)57

.359

(3.9

53)

54.5

40(1

.471

)52

.396

(1.0

47)

62.2

14(1

.677

)63

.383

(2.4

53)

58.2

33(2

.290

)59

.392

(0.7

38)

day

R2

0.99

60.

997

0.99

40.

995

0.99

50.

996

0.99

60.

995

0.99

6

MD

2.50

12.

392

4.20

13.

218

2.99

53.

170

3.03

63.

291

2.99

2m

m

Gom

per

tzL m

ax15

8.55

9(3

.471

)17

8.95

9(6

.543

)20

1.11

6(1

3.02

6)17

4.81

1(6

.052

)16

2.64

8(5

.235

)18

5.05

7(6

.374

)19

6.48

1(6

.691

)18

5.08

5(6

.995

)17

6.14

2(2

.441

)m

m

b1.

094

(0.0

25)

1.28

5(0

.050

)1.

089

(0.0

33)

1.25

4(0

.029

)1.

129

(0.0

29)

1.23

8(0

.030

)1.

248

(0.0

57)

1.13

7(0

.029

)1.

177

(0.0

13)

mm

c0.

026

(0.0

00)

0.03

3(0

.001

)0.

027

(0.0

01)

0.03

2(0

.000

)0.

033

(0.0

01)

0.02

9(0

.000

)0.

027

(0.0

01)

0.02

7(0

.001

)0.

029

(0.0

00)

mm

day

−1

t m42

.130

(0.9

46)

39.3

42(1

.792

)40

.205

(1.7

65)

39.0

36(1

.193

)34

.430

(0.9

25)

42.9

73(1

.255

)47

.096

(2.5

48)

43.1

18(1

.583

)40

.842

(0.5

70)

day

R2

0.98

80.

990

0.98

90.

991

0.99

00.

990

0.99

20.

992

0.99

0

MD

4.54

74.

917

5.31

14.

664

4.53

05.

256

4.63

84.

158

4.72

0m

m

Bet

aL m

ax14

4.58

9(3

.058

)17

4.72

5(5

.973

)18

6.72

1(1

1.27

0)16

7.79

8(5

.519

)15

8.81

4(4

.923

)17

4.37

1(5

.810

)18

0.78

2(6

.020

)17

1.45

8(5

.467

)16

5.91

3(2

.213

)m

m

t e13

7.26

4(0

.967

)13

4.43

1(1

.755

)13

7.88

0(1

.829

)12

8.44

0(1

.338

)13

0.76

3(1

.784

)13

6.07

9(1

.104

)14

1.14

1(3

.914

)14

2.45

8(1

.540

)13

5.73

8(0

.696

)d

ay

t m32

.536

(2.3

63)

30.9

47(4

.331

)28

.695

(3.8

91)

33.5

28(2

.738

)20

.417

(2.1

68)

38.1

20(2

.623

)43

.221

(4.5

82)

33.3

86(3

.339

)32

.231

(1.1

93)

day

R2

0.98

90.

990

0.99

10.

994

0.99

10.

993

0.99

40.

994

0.99

2

MD

4.57

65.

018

5.27

14.

055

4.39

14.

676

4.16

84.

082

4.50

6m

m

aD

ata

pre

sen

tati

on

base

do

nth

efo

rmat

use

dby

Yin

etal

.,2

00

3.

bP

aram

eter

so

fth

ed

iffe

ren

tgr

ow

thcu

rves

.L

max

ism

axim

um

po

dle

ngt

h,

t mgi

ves

the

po

int

of

infl

exio

n(i

nd

ays)

,t e

isth

en

um

ber

of

day

saf

ter

wh

ich

max

imu

msi

zeis

obt

ain

edan

db,

can

dd

are

coef

fici

ents

of

the

dif

fere

nt

gro

wth

fun

ctio

ns.

Th

eir

sign

ifica

nce

vari

esac

cord

ing

togr

ow

thfu

nct

ion

and

isex

pla

ined

inS

ecti

on

‘Mat

eria

lsan

dm

eth

od

s’.

MD

isth

em

ean

abso

lute

dis

crep

ancy

betw

een

mea

sure

dan

des

tim

ated

po

dle

ngt

h.



Tab

le3

Estim

ated

pod

grow

thp

aram

eter

sof

four

grow

thfu

nctio

ns(L

ogis

tics,

Ric

hard

s,G

omp

ertz

and

Bet

aG

row

th)fi

tted

tola

tera

lcac

aop

odgr

owth

ofei

ghtc

acao

geno

typ

es(S

Ein

bra

cket

s)

Cac

aoC

lone

Func

tion

Par

a-m

eter

bSC

A6

SNK

10B

BK

62B

BK

693

BB

K72

6B

BK

887

BB

K10

16B

BK

1606

Mea

nA

llP

ods

Uni

t

Logi

stic

L max

84.0

64(1

.303

)92

.212

(1.9

33)

84.7

52(3

.642

)83

.563

(1.4

79)

75.9

69(1

.399

)86

.732

(1.6

89)

84.2

53(1

.201

)83

.602

(2.1

06)

83.9

97(0

.709

)m

m

b19

.968

(0.9

60)

25.3

49(1

.871

)14

.814

(1.1

16)

24.1

04(1

.313

)19

.428

(0.8

21)

27.1

69(1

.317

)21

.635

(2.0

24)

21.5

14(1

.565

)22

.014

(0.5

47)

mm

−1

c0.

041

(0.0

00)

0.05

0(0

.001

)0.

042

(0.0

00)

0.04

5(0

.001

)0.

047

(0.0

01)

0.04

5(0

.001

)0.

042

(0.0

01)

0.04

1(0

.000

)0.

044

(0.0

00)

mm

day

−1

t m72

.466

(0.9

68)

63.4

97(1

.646

)64

.096

(1.5

32)

70.6

92(1

.234

)62

.441

(0.7

45)

72.4

29(1

.171

)73

.507

(2.8

19)

74.6

70(1

.507

)69

.574

(0.6

22)

day

R2

0.99

00.

995

0.99

20.

995

0.99

10.

993

0.99

00.

991

0.99

2

MD

2.36

31.

987

1.98

11.

747

2.09

62.

393

1.95

42.

211

2.14

2m

m

Ric

hard

sL m

ax77

.752

(1.1

86)

89.5

75(1

.805

)80

.705

(3.3

10)

79.3

35(1

.435

)72

.809

(1.3

32)

81.9

63(1

.576

)80

.084

(0.9

44)

78.0

18(1

.871

)79

.439

(0.6

76)

mm

b11

.286

(0.5

03)

8.42

2(0

.701

)8.

202

(1.1

15)

7.76

1(0

.398

)11

.246

(0.6

20)

11.0

75(0

.659

)7.

333

(0.8

20)

11.9

44(1

.078

)10

.101

(0.2

86)

day

c0.

113

(0.0

05)

0.09

8(0

.007

)0.

090

(0.0

10)

0.08

4(0

.004

)0.

124

(0.0

06)

0.11

3(0

.006

)0.

077

(0.0

07)

0.11

5(0

.009

)0.

105

(0.0

03)

day

−1

d4.

637

(0.2

09)

3.19

4(0

.280

)3.

556

(0.4

98)

2.90

8(0

.172

)4.

707

(0.2

60)

4.18

1(0

.250

)2.

831

(0.3

37)

4.80

3(0

.403

)4.

032

(0.1

20)

–

t m86

.633

(0.8

73)

74.1

63(1

.881

)76

.444

(2.5

93)

80.1

12(1

.154

)77

.703

(1.1

97)

85.3

93(1

.246

)82

.351

(3.4

61)

89.6

12(2

.017

)82

.352

(0.7

06)

day

R2

0.99

60.

998

0.99

60.

997

0.99

70.

998

0.99

20.

997

0.99

7

MD

1.28

11.

088

1.40

01.

196

1.05

51.

181

1.53

41.

234

1.22

4m

m

Gom

per

tzL m

ax96

.153

(1.5

51)

97.2

33(2

.193

)92

.341

(4.0

14)

93.3

16(2

.525

)80

.873

(1.5

72)

95.8

13(2

.133

)94

.495

(1.8

25)

93.9

90(2

.613

)92

.869

(0.8

81)

mm

b1.

347

(0.0

23)

1.57

8(0

.047

)1.

243

(0.0

37)

1.49

3(0

.034

)1.

406

(0.0

26)

1.54

9(0

.030

)1.

423

(0.0

43)

1.39

8(0

.033

)1.

433

(0.0

14)

mm

c0.

022

(0.0

00)

0.03

1(0

.001

)0.

024

(0.0

00)

0.02

5(0

.001

)0.

028

(0.0

00)

0.02

5(0

.001

)0.

023

(0.0

01)

0.02

2(0

.000

)0.

025

(0.0

00)

mm

day

−1

t m62

.336

(1.0

39)

51.7

77(1

.743

)51

.748

(1.5

01)

60.3

32(1

.869

)50

.224

(0.7

11)

61.5

97(1

.524

)62

.664

(2.9

21)

63.5

03(1

.640

)58

.501

(0.7

07◦

day

R2

0.98

10.

987

0.98

60.

988

0.98

20.

983

0.98

40.

982

0.98

4

MD

3.40

33.

428

2.87

72.

803

3.21

63.

669

2.82

73.

258

3.25

4m

m

Bet

aL m

ax78

.883

(1.2

11)

92.5

90(2

.010

)81

.607

(3.5

26)

80.6

44(1

.499

)75

.199

(1.3

58)

84.0

75(1

.787

)80

.107

(1.0

62)

79.2

30(1

.977

)81

.033

(0.7

20)

mm

t e14

2.12

2(1

.263

)13

8.77

9(1

.759

)14

1.88

6(1

.919

)14

1.04

1(1

.694

)13

7.10

2(1

.386

)14

1.27

1(1

.233

)14

6.47

1(3

.447

)14

6.28

3(1

.319

)14

1.55

7(0

.630

)d

ay

t m65

.648

(1.5

80)

57.1

37(2

.864

)51

.065

(3.3

77)

66.3

84(1

.740

)54

.455

(1.3

38)

69.9

08(1

.570

)66

.989

(3.8

77)

68.9

28(2

.535

)63

.325

(0.9

24)

day

R2

0.98

60.

989

0.98

90.

992

0.98

70.

990

0.98

70.

988

0.98

8

MD

3.21

23.

049

2.81

72.

473

2.83

13.

076

2.56

02.

909

2.91

8m

m

aP

aram

eter

so

fth

ed

iffe

ren

tgr

ow

thcu

rves

.L

max

ism

axim

um

po

dw

idth

,t m

give

sth

ep

oin

to

fin

flex

ion

(in

day

s),

t eis

the

nu

mbe

ro

fd

ays

afte

rw

hic

hm

axim

um

size

iso

btai

ned

and

b,c,

and

dar

eco

effi

cien

tso

fth

ed

iffe

ren

tgr

ow

thfu

nct

ion

s.T

hei

rsi

gnifi

can

ceva

ries

acco

rdin

gto

gro

wth

fun

ctio

nan

dis

exp

lain

edin

Sec

tio

n‘M

ater

ials

and

met

ho

ds’

.M

Dis

the

mea

nab

solu

ted

iscr

epan

cybe

twee

nm

easu

red

and

esti

mat

edp

od

wid

th.



Clone Model 627KBB 01 KNS 6 ACS

Richards

Pod

leng

th o

r w

idth

(cm

)

0

50

100

150

200

0 50 100 150 2000

50

100

150

200

0 50 100 150 200

0

50

100

150

200

0 50 100 150 200

Logistic

0

50

100

150

200

0 50 100 150 200

0

50

100

150

200

0 50 100 150 200

0

50

100

150

200

0 50 100 150 200

Beta

growth

0

50

100

150

200

0 50 100 150 200

0

50

100

150

200

0 50 100 150 200

0

50

100

150

200

0 50 100 150 200

Gompertz

0

50

100

150

200

0 50 100 150 2000

50

100

150

200

0 50 100 150 200

0

50

100

150

200

0 50 100 150 200

Time (days) 05-18 till 10-12 2007 06-21 till 11-31 2007 05-18 till 10-26 2007

Model prediction

Measured values

Length

Width

Figure 3 Goodness of fit of the four models used to describe longitudinal pod growth for three different cacao genotypes.



respectively. In the case of individual clones, it variedfrom 66.0 (BBK 726) to 79.1 (BBK 1606) days for podlength, and it varied from 80.9 (BBK 693) to 97.3 (SNK10) days for pod width (Table 1). The point of inflexion,the point in time at which maximum growth speed wasestimated, varied largely between the different growthmodels. For longitudinal growth it varied from 59.4 daysfor the Richards function to only 32.3 days for the Betagrowth function (Table 2). For lateral growth it rangedfrom 83.4 days as estimated by the Richards function to58.5 for the Gompertz function (Table 3).

Pod surface area and volume

The calculated pod surface area and actual as well asestimated pod volume values are given in Table 4.Estimated pod surface areas varied from ±100 to 610cm2, with a mean of approximately 330 cm2. A significantdifference (P = 0.001, df 2) was observed betweenmethods. The method used by Jessop et al. (2010),with an estimated mean pod surface area of ±355 cm2,overestimated the pod surface area compared with theother two methods, which both had an estimated meanpod surface area of approximately 320 cm2. A comparisonof the cacao clone data showed that a significant (P =0.04, df 2) difference between methods was only observedfor clone BBK 1016. The method used by Jessop et al.(2010) had the highest pod surface area estimates, whencompared to the other methods. No significant differenceswere observed between the three methods for any otherclones (0.087 ≤ P ≤ 0.634, df 2).

Actual pod volumes varied from 100 to 1040 mLand the mean was over 500 mL. Large differences wereobserved between clones: the mean pod volume for SNK10 (823.9 mL) was more than twice the mean pod volumefor BBK 726 (347.8 mL). A significant effect (P = 0.001, df

= 3) was found when comparing estimated pod volumesand measured pod volumes. Compared to the actual podvolumes, the method used by Waters and Hunter tendedto underestimate pod volume. Similarly, but to a lesserextent, the Bateman method also underestimated actualpod volume (Table 4). In contrast, the method proposedby Jessop et al. (2010) tended to slightly overestimatepod volume. When individual clones were considered,no differences were observed between the three methodsand actual pod volume (0.217 ≤ P ≤ 0.803, df 3).

Discussion

The four growth functions used in this study were ableto describe cacao pod growth relatively accurately, yetseveral differences were observed. The Richards functionseems to be the growth function that best adapts to

cacao pod growth data as indicated by the highest R2

and the lowest MD values. Moreover, the time at whichmaximum pod growth occurred (tm) was best estimatedby the Richards function. The Richards function is flexiblebut at the cost of an extra parameter compared to theother three growth functions. However, as mentionedby Zeide (1993), the shape parameter of the Richardsfunction has no obvious biological interpretation andis very unstable. The Gompertz function systematicallyoverestimated Lmax, which seems to be a commonproblem for this growth curve (Yin et al., 2003), probablydue to its intrinsic inflexibility. Of the two remaininggrowth functions, the Logistic function, as indicated bythe R2 and MD values, adjusted slightly better to thecacao pod growth data than the Beta growth function.The Logistic function is symmetrical around tm (the timeat which maximum growth occurs) and its parameters canhave a biological interpretation, making it an informativeand easy-to-use growth function. Maisin & Lamin (2006)also found that pod growth of four cacao clones (COCA3370-5, KKM 22, PBC 123 and BR 25) fitted closely tothe Beta growth function; however, they did not compareresults from different growth functions. The Beta growthfunction can provide a range of asymmetrical growthcurves. It has three biologically interpretable parameters,the day on which maximum growth occurs, the day onwhich maximum size is achieved, as well as maximumsize itself, and these parameters may even be roughlyestimated from a visual inspection of the data (Yin et

al., 2003). The Beta growth function does accuratelydetermine the time at which maximum pod size isreached. Interestingly, the value of te corresponds wellwith the point in time at which the jelly-like endospermin the ovule is rapidly consumed by the embryo(approximately 140 days after pollination according toMcKelvie, 1956; Fig. 1). At that time, embryo growthceases, there is no further resumption of pod growth andripening begins.

To conclude, the Richards function appears to bethe most accurate function for describing pod growth,but it raises problems with regard to the biologicalinterpretation of the parameters. The Logistic and Betagrowth functions also appear to be very useful fordescribing cacao pod growth, but we favour the Betagrowth function, since it is easy to use and in all casesprovides biologically interpretable parameters. However,the choice of which function to use will have to depend onthe underlying research questions. Moreover, since thisstudy was limited to four growth functions, two cacaoclones (SCA 6 and SNK 10), five cacao accessions of asingle bi-parental family and one other cacao genotype(Table 1), certain caution is called for in generalising these



Tab

le4

Pod

volu

me

estim

atio

nsan

des

timat

edca

cao

pod

surf

ace

area

sfo

rei

ghtc

acao

geno

typ

es(S

Ein

bra

cket

s)

Cac

aoC

lone

s

Mod

elP

aram

eter

SCA

6SN

K10

BB

K62

BB

K69

3B

BK

726

BB

K88

7B

BK

1016

BB

K16

06M

ean

All

Pod

s

Act

ualm

easu

rem

ents

Mea

nw

eigh

t(g)

[min

–m

ax]

399.

5(2

2.8)

[190

.2–

540.

7]

702.

2(6

1.1)

[428

.3–

990.

5]

572.

3(8

0.3)

[268

.8–

868.

0]

435.

0(8

0.3)

[279

.4–

549.

4]

325.

7(2

7.7)

[92.

2–

592.

4]

480.

1(2

9.6)

[273

.0–

723.

5]

504.

7(2

7.9)

[394

.6–

542.

9]

512.

6(3

5.7)

[369

.6–

742.

4]

450.

9(1

5.0)

[92.

2–

990.

5]

Mea

nvo

lum

e(m

L)

[min

–m

ax]

438.

4(2

4.5)

[180

–60

0]

823.

9(6

0.4)

[490

–10

40]

617.

5(8

5.7)

[280

–90

0]

479.

4(2

6.8)

[300

–64

0]

347.

8(2

9.8)

[100

–70

0]

555.

2(3

6.5)

[310

–80

0]

577.

0(4

5.7)

[420

–70

0]

580.

8(3

9.0)

[400

–85

0]

503.

8(1

7.4)

[100

–10

40]

Pod

volu

me

acco

rdin

gto

Wat

ers

&H

unte

r(1

928)

Vol

ume

(mL)

[min

–m

ax]

397.

2(2

2.0)

[164

.9–

577.

3]

656.

4(4

9.0)

[414

.2–

823.

7]

620.

5(9

0.0)

[284

.3–

937.

1]

430.

2(2

3.1)

[290

.4–

566.

6]

326.

9(2

6.7)

[99.

5–

602.

7]

483.

6(2

7.8)

[266

.5–

698.

7]

512.

6(3

6.5)

[383

.6–

588.

6]

507.

5(2

6.5)

[365

.1–

702.

5]

450.

2(1

4.5)

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findings. For a more detailed revision of growth equationsand their usefulness we refer to Zeide (1993).

In our study, in accordance with previous studies(Berry & Cilas, 1994; Daymond & Hadley, 2008), wefound that cacao genotypes differed in their pod growthcharacteristics and overall maturation time. These factorsdetermine cropping patterns and, thus, have practicalsignificance. Indeed, they have an impact on yield,on susceptibility to diseases, especially those attackingpods, and on disease management strategies. The riskof infection, or pod susceptibility, depends on numerousfactors such as disease incidence the year before, actualpod presence/density, climate, pod position and thegenetic makeup of the cacao tree itself, which determinesfor example pod size, growth duration and inherentresistance, hence tissue susceptibility. Pod size alsoindirectly affects disease susceptibility. Pod size influencespod wetness duration due to dew. Prolonged wetness willincrease the chances of pathogen propagules, presenton the cacao pod, to germinate and subsequently infectthe pod (Butler, 1980). Thus, pod development stageand disease resistance are linked. In cacao breedingprogrammes for resistance to Phytophthora spp., pod testsare used to determine whether a cacao clone is susceptibleor resistant. If cacao pod susceptibility to Phytophthora isalso a function of pod age, the practical implication ofthis work would be that pod tests should be performedon pods with the same relative age, not necessarily podsof the same size.

Growth curves may also help in understanding aphenomenon such as cherelle wilt. Cherelle wilt, whichcan cause considerable fruit losses (Niemenak et al.,2010), is a fruit thinning mechanism, a physiologicaldisorder whose definition is often linked to pod size/age.According to McKelvie (1956), the incidence of cherellewilt increases from pollination to a peak at about 50days, then diminishes and rises to a second peak after 70days. After 95−100 days, no further wilting takes place.According to the pod growth curve data presented here,it seems that the maximum wilt periods coincide withmaximum pod growth (Tables 2 and 3). Since it is thoughtthat this mechanism is brought about by competition forcarbohydrates (Daymond & Hadley, 2008 and referencestherein), this could explain why maximum wilting occursat maximum pod growth.

Knowledge of growth dynamics can also be used inplant simulation modelling to predict ultimate yield. Astudy by Jeuffroy & Chabanet (1994) showed that theseed number per pea pod is correlated with early podelongation and a model was proposed for predicting theseed number per pod from early elongation rates. Whilesuch modelling approaches may be useful for certainfruits, the relationship between cacao pod size and cacao

bean numbers and size seems to be less straightforward.A recent study by Daymond & Hadley (2008) showedthat final fruit size (Lmax) was a positive function of beannumber in five different cacao clones. However, the R2

values for the linear regression models were R2 = 0.21,0.23, 0.29, 0.4 and 0.76 for an Amelonado genotype andthe cacao clones UF 676, AMAZ 15/15, SPEC 54/1 andSCA 6, respectively.

Zuidema et al. (2005) created a physiological andproduction model for cacao based on the SUCROS-familyof physiological crop growth models (van Ittersum et al.,2003) and adjusted the base model to allow for modellingof perennial growth and typical aspects of fruit ripening.However, they did not take into account production lossesdue to pests, diseases or wilt. In accurately modellingcacao production, losses due to cherelle wilt and diseases(linked to disease susceptibility) are important factors.Increasing our knowledge of cacao pod development andits link to cherelle wilt and disease susceptibility willthus be beneficial to the development of more accurateproduction models.

To ensure sufficient yield, farmers usually protecttheir cacao pods from diseases and pests by applyingpesticides. In order to reduce the amount of pesticideused on cacao, it is thus necessary to accurately timespraying operations, improve the dose transfer processand examine spray deposition on cacao pods. To that end,such studies require reliable estimates of cacao growthrates; for example, spray intervals could vary in relationto growth rates, with shorter intervals between sprayingrounds when growth rate is at its maximum (around tm),when pod surface area increases rapidly. Although it isdifficult to relate ‘ideal’ deposits with biological effect,it is relatively easy to demonstrate that large amountsof pesticides are lost through run-off from the crop intothe soil (Bateman, 2004). Large droplets easily bounce-off plant surfaces, whereas very small droplets can bedisplaced by the wind.

The three methods used in our study to estimate cacaopod surface area led to surface estimates that were gener-ally not different from each other. These three methodsthus have a similar potential. However, two of them, theBateman and Jessop methods, have the advantage of alsoallowing the calculation of pod volume. Here, the Bate-man method underestimated, whereas the Jessop methodoverestimated pod volume. Yet, no significant differenceswere detected between these methods and the actual podvolume for individual cacao clones. However, since a largevariety of pod shapes exists, different models may be bet-ter suited for certain cacao varieties. According to Jessopet al. (2010), their method was more appropriate for thecacao pod varieties grown in Ghana than the method usedby Bateman (2004) to estimate cacao pod surface areas



for Costa Rican cacao varieties. While the calculation ofpod volume provides an indication of the accuracy of podsurface area estimations, the method used by Jessop et

al. (2010) appeared better suited to the cacao genotypesstudied here. We therefore conclude that the cacao podvolume and probably pod surface area are best estimatedusing the prolate spheroid model of Jessop et al. (2010).

There are several ways in which knowledge ofcacao pod growth can help improve cacao productionand pod disease management. It can help to predictyield, as well as provide information for improving thetiming and frequency of pesticide applications, since, forexample, ripening time and fruit size are linked to diseasesusceptibility. Information on pod size and susceptibilityin turn will help to improve dose transfer and spraydeposit studies intended to optimise control efficiencywhile minimising costs and the negative externalitieslinked to fungicide spraying. Consequently, growersshould be able to maximise returns on investment andensure sustainable cacao production.

Acknowledgements

This work was funded by the United States Departmentof Agriculture (USDA) and CIRAD. Joyce GninghayeFongang, Zacharie Techou, Prosper Innocent Badjeckand Amougou Fidele Nsouga provided technical andadministrative assistance. We thank Laurence Dedieu andPeter Biggins for their revision of the manuscript and useof the English language. We also thank the reviewers fortheir comments and suggestions that helped improve themanuscript.

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