PRESENCE-ABSENCE SAMPLINO DECISION RLJLES
FOR PIE DAMAGE CAUSED DV PIE COFFEE LEAF MINER (LEUCOPTERA COFFEELLA (GUÊRIN - MENÊVILLE, 18421) 1
AMADOR VILLACORTA2 and ANDREW PAUL GUTIERREZ3
ABSTRACT - An accurate bul simple presence-absence sampling rnethod is proposed for estimating densities of lesions on leaves, caused by lhe coffee leaf miner (Leucoptera coffedlla (Guérin - Menévifle, 1842). This sampling method enables 1PM Scouts to quickly detennine whether lhe infestation has reached lhe action threshold of one leaf miner lesion per leaL The acduracy of lhe sample size can also be
determined.
Index terma: binomial sampling, Poisson disiribution.
REGRAS DE DECISÂO NA AMOSTRAGEM PRESENÇA-AUSÊNCIA
DO DANO CAUSADO PELO BICHO-MINEIRO (LEUCOPTERA COFFEELL4 GUÉRIN-MENÉVILLE, 1842) RESUMO - Um método preciso e simples de amosagem da presença-ausência de lesóes causadas pelo bicho-mineiro (Leucoptera coffeella (Gudrin-Menéville, 1842) é proposto para estimar a densidade destas lesões. Este método de monitoração permite aos especialistas do MIP determinar rapidamente se a inleslaflo alcançou o limiar de ação de uma lesão por tolha. A precisão do Iarnanho da axnosn pode também ser
determinada.
Termos para Indexação: amosagem binomial, disbibuição Poisson. INTRODUCTION
Coffee (Coffea arabica L.) is an important export cornmodity in Brazil and many other tropical and subtropical countries. One of its principal pest throughout Latin America is the coffee leaf miner (Leucoptera coffeella) (Guérin-Menéville, 1842) (= CLM). Siivestri (1943) proposed the generic name F'erÜeucoptera for L. coffeella, a name adopted only in Brazil. CLM mines the leaf reducing the photosynthetic area of the canopy when coffee berry growth rales are aI their maximum (Villacorta 1980). Mean densities below 1 lesion per leaf ( m*) appear not to cause economic damage, and leveis above two lesions per leaf cause increasing leveis of defoliation (Villacorta 1984). Dry season stress compounds the effects of CLM damage. Additionai work is required across a wider range of CLM lesion densities lo more accurately estimate lhe economic threshold (m*).
CLM popuiations grow mosi rapidly during dry periods of suminer, as rainfall cause high mortality CLM larvae. Rainfall occurs throughout lhe year in
Accepted for publication on August 26, 1988.
2 Eng. - Agr., Ph.D., Entomologist, inst. Agron. do Paraná (IAPAR), Caixa Postal 1331, CEP 86001, Londrina, PR, Brazil.
' Entomologist, Professor, Division of Biological Control, University of California, Berkeley, CÁ., USA.
Paraná, but is more abundant during the summer period. During some years, the CLM damage reaches economic leveis during December-March. Natural enemies are thought not to be sufficiently effective in regulating CLM densities below m*, and insecticides are lhe primary method of controi. However, to malce Sound recommendations for pest control, it is important lo determine when the number of lesions is likely lo exceed the current econonüc levei. This paper describes an easy to use method for assessing this problem.
A sequential sampiing plan based upon the negative binomial distribution was developed for CLM by Villacorta & Tornero (1982), bul unfortunately lhe method proved too difficult for fleld workers to understand and use. For this reason, a simplified sampling method is developed here lo fiji this important need. In this work we use the methodology for estimating lhe accuracy of a saxnple size deveioped by Ruesínk (1980) and Wilson & Room (1982, 1983). These methods are based upon Karandinos' (1976) formula [1] for estimating lhe accuracy of a sample size for different leveis of accuracy (D) as a fraction of lhe mean (m) (equation [1]).
n = 12 D 2 S 21m 2 [1]
n iii [1] is lhe number of samples required to reach a levei o! precision D. 1 = ta/2 is the standard normal Pesq, agropec. bra»., Brasília, 24(5):5 17-525, maio 1989.
518 A. VILLACORTA e A.P. GUTIERREZ deviate (t = 1.282 for a = 0.2 or 0.1 on each tail of
the distribution) and S 2 is the sample variance. Taylor (1961, 1984) proposed that lhe variance and lhe mean was deseribed by [2]
= amb, [21
where lhe coefficients a and b are quickly estimated by regressing log S 2 on log m. The coefficient a is a sampling factor and b is an index of aggregation characteristic of a species. Ruesink (1980) and later Wilson & Room (1982) substituted 12] for S 2 ia [11 facilitating lhe deveiopnsent of rales for deterrnining lhe number of samples required to meet a predetermined levei of accuracy.
a = 12 D2 b.2 [3]
Counting lhe number of coffee ieaf miner iesions on a 100 leaf sampie is cumbersome is lhe fieid; however, estinmting lhe proportion of icaves wilh lesions is quite easy. Wilson & Room (1982, 1983) proposed presence-absence sampling mies (Le., binomial sampling mies) also based upon Karandinos' work [4].
a =
12
D 2pq [4]ia [4], p is lhe proportion of infested leaves and q = 1-p. However, lhe accuracy of lhe sampie is aoL lhe sarne across alI vaiues of m, hence lo
maintain lhe sarne levei of accuracy Q = (D, rn) and not a constant as in [4] (Wilson & Room 1983). Tbis probiern may be illustrated by plotting lhe proportion of infested sampling units (P1 = p) against lhe inean number of organisms per sarnpie unit, and based upon estimates of lhe coefficient bis [2], one of lhe four models proposed by Wilson & Room (1983) is fitted to lhe data. If b < 1 lhe population is under díspersed, if b = 1, lhe popuiaüon is randomiy dispersed, and if b> 1 lhe population is aggregated or ciurnped. The four modeis have lhe general forrn
P1 = 1.- e1'(m). [5]
This rnodei was used to determine lhe reiationsbip between lhe proportion of leaves having CLM iesions and lhe mean number of lesions per leaf. It is this reiationship ([5]) upon which our treat-no treat decision rale for CLM is based. 1-lowever, predicting ai from estimates of P1
produces different error lirnit for m. This can be seen by projecting varions band P1 ± 1 P1 to lhe ai axis and computing lhe error limits for Use predicted rn. In general these error lirnits increase in ai for
over lhe range of P1, and hence [4] must be corrected for this (Le., [6], Wilson & Room (1983).
= t2 Q(D,rn) 2 pq [6]
MATERIAL AND METHODS
The samples ia this study were taken ia a commerciai coffee plantation located ia IbiporA, Paran& Brazil, oa the cofies variety "Mundo Novo" during August 1979 througli July 1981. The experimental arca consisted of three blocks each with 120 "covas" (= 2 plants per sito). Oae biock na lhe untreated control and the othcr two blocks were treated respectively with Pcrmetluine (at lhe rata of iOO mi/ha of lhe cominercial product followed by one application ei sulphur WP 2 kg/ba to confrol mitos induced by Use insecticide), and Temik(i.e.,aldicarb, logofcommercialpercova).
In lhe field study, lhe action threshold for applying lhe insecicide was sol between 1.2 lo 1.5 le,sions per leal. 100
leal samples were taken at random at monthly interval ia each of 10 random selected cofies "covas". Cofies rust
Wanileia wistawiv Ber. & Brj ia Use plots was controlled
with copper base fungicidca. Strickly speaking, lhe variance of lhe data lias two componenz that due lo between cova variatioa and Use other between leaves. Here we ignore lhe between cova variafion because lhe data are not available.
'fie ieaf samples (mm lhe check were taken te laboratory and lhe leaf and CLM lesion arcas measured using an arca meter model AAD400 (Hayashi Denkoh, Go. Ltd. Japan). Average temperawre and rainfali were obtained from lhe weather station maintained by lhe Instituto Agronômico do Paraná (LAPAR), at lbiporL
RESULTS
The phenoiogy of CLM iesions per leaf and the average percentage of lhe leal' arca with lesions ia lhe untreated controi biock is shown ia Fig. 1. The two trends are correlated (Fig. 2, p < 0.05) but lhe predictive vaiue of lhe regression equation is iow (r2 = 0.45). The two dips ia lhe trends occur during periods of prolonged raias when high mortality of CLM iarvae occurred. CLM populations were above lhe economic lhreshold for a considerable period of time.
Lesions do not aiways contain live CLM Me stages, and ieaves wilh lesions tend to accumulate over time until lhey abscise. ilence, lhe observed nurnber of iesions is greater lhan lhe number of Iarvae per leaf. The reduction ia photosynlhetic potential of lhe piant is, however, due te lhe loas of 1cM arca caused by lhe CLM lesions. Thus iesion density and not lhe deasity of CLM Me atages is a Peaq. agropeo. bras., Brasilia, 24(5):517-525, maio 1989.
PRESENCE-ABSENCE SAMPLJNG 519 zø w 44 o- Lii 1- z E E II Li. 4 -J O o') -I o, z O o, -J = 1- 4 4 5 O N D J F M AM J J A SONO J F M AM J J 1979 1980 1981
FIG. 1. Phenology af CLM lesions per leaf and their average percenlage ei leal area in the conoI biock. Also shown are me daily maximun and minimum temperatures and rainfali.
520 A. VJLLACORTA e A.P. GUTIERREZ better indicator of damage. This is fortunate, as
lesion density is much easier to assess in the field. Estimating the Taylor coefficients
The coefficients a and b estimated by regressing log S2 on iog M are presented in Tabie 1. Note that a in Taylor's modei ([2]) a equals ea, where a' is the intercept of the regression equation. The data from aU bioeks and the regression limes are shown in Fig. 3. The siopes for lhe control, Permethrine, aldicarb and lhe pooied data were not significantiy different from naity or each other. The aidicarb treatment had a few divergent points which lowered r2 and affected the siope. The anaiysis suggests that the lesions are randomiy distributed among leaves.
The regression coefficients for the pooied data were used in [3, 4, 61 to determine lhe number of samples required to estimate the mean number of lesions per leaf m with leveis of accuracy 1) = 0.1 and 0.2. Using equation [31 at a levei of precision D = 0.2, the one hundred ieaf sampie estimates m = 1 with a better than 20% accuracy (Fig. 4A).
1-lowever, lo achieve a 10% levei of accuracy aI m = 1, a sample of approximately 220 leaves is required.
Figure 413 shows the binomial sampling rules using [4] assuming a constant value for D. The observed vaiues of p (Le. lhe data) are shown in relation to the predicted funetion n(m) (i.e. lhe solid lines). In general, lhe predictions over the range of observed m are reasonabiy ciose. The predictions of n assuming D = (1) = .2,m) (i.e. [6]) are shown as lhe dashed Une suggesting that a is higher over the entire range of m, and is at odds with lhe data.
Presence absence sampling decision rule for CLM
The proportion of infested leaves is plotted in Fig. 5 showing that lhe range of observed P1 is below 0.8. The parameter b in [2] for the different data seta (rabie 1) suggest that Poisson distribution model [7] would be appropriate.
P1 = 1 _em [7] .8- Y =-t.68 +0.65x o - r2=0.45 1.6- - O 1.4- o o 1.2- O o 1- o
-
o
0.8- Oo
O 0.6- O O OA- 0.2- 0.5 1.5 2.5 3.5 4.5MEAN PERCENT LEAF AREA DAMAGED
FIG. 2. Regression ai mean percentage ai leal area with CLM leslans on Ve mean leslons per leal. Pesq. agropec. bras., Brasilia, 24(5):517-525, maio 1989.
LI- Isi —J 0
=
o 0 u1 -J=
4 tuPRESENCE-ABSENCE SAMPLINO 521
TABLE 1. Linear regression statisties for S2 on m and Iog S2 mi Iog m for the CLM lesion data.
S2onm log S2onlogm
Treanent a b r2 a' b r2 n ConoI 0.071 1.491 0.76 0.422 1.012 0.66 92 Pem,ethrjne 0.108 1.436 0.86 0.245 1.078 0.91 76 Aldicarb 0.167 1.074 0.61 0.182 0.793 0.73 76 Ali dala 0.452 1.345 0.73 0.292 0.946 0.81 244 2 - - - - PERMETHRINE 1.5- ______ DCONTROL • -. - . ALDICARB n ALI. DATA 1- o o O.5
H
LII o a -j 4 E «o
0
t > -J .Ø5 o x 'o •15 / , 25 -1.5 -0.5 0.5 LN MEAN LESIONS/LEAFFIO. 3. Regression of log varianco of baiona por leal on Iog rnean besions por leaf for ali treanents.
522 o w o -J • •l < 2 o -J si 5 SG 'si o -.5 u. b o e D 2
A. VJLLACORTA e A.P. GUTIERREZ
2.6 2.8- NUMERICAL 2.4 - 2.2 2.0-1.8 1-6 1.4 1.2 OS- fi O 0.4 0.8 12 1.6 2 2.4
MEAN LESIONS PER LEAF
1
o .0 BINOMIAL .91
b
o 16- ocX D(m,Oi) 0 0 4. O .3- 0% ! - -. — -- 1 — .2- o 0 0:0.1 O O 9 • D 0.2 o o ' 00 0 0 O ct o 0- nt 1' is In 2.4 25MEAN LESIONS PER LEAF
FIG. 4. Number of leaves requirecj at ditterent CLM lesion densities required lo meet predetemiined leveis ol sampling preci-sion (O = 0.1 and 0.2): (A) numericai sampiing and(S) binomial samphng (i.e., presence-absence) with constant levei of precision (sohd hnes) and with lhe levei ot precision which varies with rnean lesions per leaf (Q = (m. 0.1). see text).
PRESENCE-ABSENCE SAMPLINO 523 The term em is [5] is the zero term of the Poisson
distribution (i.e., Lhe proportion of non-infested leaves (P(0)), and P1 = 1 - em is Lhe proportion of leaves having 1 or more lesions. This une is shown is Fig. 5 as Lhe dashed Une. This model tends to systematically over estimate P1, hence a modified Poisson model was fit to Lhe data (solid Une, modei 4 of Wilson & Room, 1982; [8])
P1= 1_e-em [8]
If 220 leaves are sampled to estimate P1, then m at a 10% levei of accuracy is predicted projecting Lhe P1 value to Lhe function (Lhe solid Une) and then projecting from that poist to Lhe m- axis lo estimate Lhe mean lesions per leaf (m). Because lhe error is not equal on both the P1 and m ais, Lhe number of sampies required to meet Lhe 10% levei must is theory be increased with higher values of P1 (Wilson & Room 1983). All this means is lhat as Lhe proportion of leaves approacbes unity, it becomes increasingly difficult lo estimate m unless ao increasing sample Se is taken. Given the limitation
of not including Lhe between cova variance is our aiialysis, Lhe model is quite adequate for estimating CLM densities near or above ao action threshold of one lesion per leaL
The une perpendicular Lo the m axis (± the 10% error limits) separates Lhe treatino treat areas. If Lhe predicted number of lesions per leaf falIs within this error limit, a field seouL must use judgement as lo whether ao insecticide application is warranted. This mie is conservative, but used it is likely to reduce Lhe excessive pesticides currently used is Lhe absence of any scientifically based decision mie. Viflacorta & Sánchez-Rodrigues (1984) showed that a sisgle insecticide applications timed aL the leveI m = 1 is sufficient for season long control of CLM.
Steps to follow to use the binomial sampling niethod.
The method proposed here similar to Lhe methods used to gather Lhe data used is Lhe analysis.
1. Divide Lhe area lo sampled is sampling areas no more than one lia, and map Lhe coffee piantation givisg a number to each sampling unit area.
1.uu. 0.75 0 > Lii 0.55- DECISION 0.53 ZONE 0.50- '4- o z
o
R o 0.25- 1 it.r
NO II TREATMENT "1 ZONE - — — Pi = 1 /D=o.1 fo TREATMENT ZONE MEAN LESIONS/LEAFFIG. S. Propoilion of infested leaves (P1) on mean lesions por leaf. The dashed une is Via Poisson model, and the solid une is
tho modiliod Poisson model fit to Via data and used for dia treat-no beat docision rule (soe taxt).
524 A. VILLACORTA e A.P. CIUTIERREZ 2. Waik across Lhe sampling unit area and from
nine random Lrs (cova) make visual observations on the presence or absence of CLM lesions on 25 random middle aged leaves per tree. Avoid sampling new leaves from Lhe first two pair of leaves from Lhe branch.
3. Calculate Lhe proportion of infested leaves and use this va!ue in Pig. 5 Lo estimate the mean lesions perleaf.
4. If lhe proportion of infested !eaves (i.e., P1) is less than 0.50, Lhe predicted lesions (i.e., m) fail within the NO-TREATMENT ZONE. If P1 is between 0.50 and 0.58, m falis in Lhe DECISION ZONE. In this case, eilher take another round of sampies or samp!e 15 days later. If P1 is greater than .58, Lhe predicted m falls is the TREATMENT ZONE.
5. Sampling shou!d begin at the time of flower initiation and continue at monthiy intervals until coffee berry growth ceases. There are two periods during summer: the less critical four to five month period from Lhe time of fiower iniliation until the coffee berries begin rapid growffi, and the critical period of rapid berry growth. Ii general, leveis of CLM infestation higher than 1 lesion per leaf do not cause economic damage during Lhe first period as Lhe high raLes of leaf production enable Lhe piant Lo compensate. However, when berry growth rates are aL maximum, and densities of 1 CLM lesion per leaf rnay cause economie damage. Hence, if a short dry period oecurs, the time between samples must be reduced to 15 days.
The data presented here relates specifically to the CLM phenoiogy as modified by Lhe weather pattern common Lo Paraná. With additional data, Lhe sarne model could be applied to other areas.
DISCUSSION
The presence-absence sampling decision rule for CLM presented here is designed for practical utilization
is
Lhe fieid by 1PM scouts. For this reason, Lhe formulae were kept Lo a minimum and easy to understand explanations were offered. The ride was related to theory, but ia lhe fmal analysis a least squares El to lhe proportion infested data proved the most accurate predictor of mean lesions per !eaf.Natural enemies are known from CLM, but Lhey do nol appear to be effective. (Viliacorta 1980). Hence, while we might wish for natural contro! of CLM, pesticide applications are required ou
occasions, but at frequencies far !ess than is Lhe current pracúce. In Lhe final analysis, farmers wish to rnaximize profit, hence ki!ling pests is merely na necessary inconvenience is that endeavor. Putting more resources than necessary isto pest control reduces profits, and hence is contrary Lo farmer objectives. The use of Lhis binomial sampling ru!e could greatly reduce the number of pesticide application against CLM is coffee, and over time enable farmer Lo !earn Lo detect the zone of frequent infestation on their farras further increasing the efficiency of their pest control efforts.
ACKNOWLEDGMENTS
We wish to Lhank W.S. Oliveira, E.T. de Lima, I. Maretto from Lhe area of Entomology and A.F. Megumi from Lhe area of biometrics for lhe able technica! assistance.
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