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ABSTRACTMora-Aguilera, G., Nieto-Angel, D., Tliz, D., and Campbell, C. L. 1993. Development of a predictionmodel for papaya ringspot in Veracruz, Mexico. Plant Dis. 77:1205-1211.

A model to predict incidence of papaya ringspot was developed and validated from 5 yr of fieldobservations in central Veracruz, Mexico. The model was developed from 1 yr of data collected from

papaya (Carica papaya) plantations in two different locations in Veracruz during 1985-1986. Incidenceof papaya ringspot was evaluated every 15 days, and viral infection was confirmed by ELISA. Aphidectors (Myzus persicae, Aphis gossypii, A. nerii, A. citricola, andMacrosiphum euphorbiae) of papaya

ringspot virus were collected every 3 days from Moericke yellow pan traps placed at each location. Theprediction model was obtained from an examination of the matrix of Pearsons correlation coefficientsand by simple and multiple regression analysis. Model selection was based on Mallows C p statistic,

proportion of variance explained, variance inflation factor, analysis of structure, and predictive capacity.The largest amount of variation in the data was accounted for by modely=1.45 + 0.42ANS-f 0.00016

PW+ 0.116AG5

0.0058AN52

0.0057MP52

, in whichywas the incremental increase of disease (ytyt.)at any given time (/);AN5, AG5, andMP5

2were the numbers of the alate aphid speciesA. nerii, A.gossypii, and Myzus persicae , respectively. PWwas an interaction variable defined as the product ofprecipitation (P)and speed and duration of wind from the north (W).Values for independent variableswere accumulated during a 4-wk period that ended 3 wk before the calculated incremental increase ofdisease. The equation accounted for 78% (R2> 0.78) of the total variation of the change of diseaseincidence (ytyt.)in the original data set. Validity of this model was tested with data obtained from 60epidemics in papaya plantations established from 1987 to 1989 to represent different dates, plantdensities, and plantation sites. The model predicted the relative rate of disease increase in 38% of theepidemics (23 of 60, R2> 0.60). Three other models that accounted for less variance explained in theoriginal data set than the first model (R

2 < 0.78) were also validated. One model predicted the

incremental increase in disease incidence of 40% of the papaya ringspot epidemics (24 of 60) with R2>0.60. In this model, the disease incidence change was explained by the independent variablesAN5, AG5,andPW.

Plant Disease/December 1993 1205

Development of a Prediction Model for Papaya Ringspot in Veracruz, Mexico

GUSTAVO MORA-AGUILERA, Former Graduate Assistant, DANIEL NIETO-ANGEL, Graduate Assistant, andDANIEL TLIZ, Professor, Centro de Fitopatologa, Colegio de Postgraduados, 56230 Montecillo, Mxico; and C. LEE

CAMPBELL, Professor, Department of Plant Pathology, North Carolina State Univesity, Raleigh 27695- 7616

Papaya ringspot virus (PRV) disease isthe most limiting factor in papaya{Caricapapaya L.) production in Mexico

(1,2,28,29). In some regions of southeasternMexico, 90% of plants die from this diseasein less than 1 yr and the normal productivelife of a plantation may be reduced fromseveral years to 1 yr. Cross-protection with amild strain of PRV from Hawaii, differenttypes of reflective material barriers, andapplication of vegetable oils (e.g., corn oil)have not provided satisfactory control ofPRV on papaya in Mexico (2,28,29).

Accepted for publication 24 August 1993.

1993 The American Phytopathological Society

Studies relating vector numbers, weatherconditions, and other factors to the spread ofseveral diseases of plants caused by

semipersistently and/or persistently(8,12,14,17,22,31) and nonper- sistently(16,23,25,30) transmitted virus have beenattempted. In some of these studies,forecasting systems were developed thatresulted in partially (12) and very successful(22) aphicide application programs. Fornonpersistenly transmitted viruses, such as

papaya ringspot virus, least squaresregression can be useful for identifying andselecting climatic and biological variablesthat explain the variability in diseaseincidence (16,23). Papaya ringspot has beenstudied with respect to several temporal andspatial epidemiological aspects (19).

However, the biological and climatologicalfactors

related to the spread of PRV on papaya havenot been studied extensively.

The objective of this work was to developand validate a prediction model of papayaringspot incidence based on counts of eachaphid vector species and climatic factors byusing data acquired during 1985-1989 atVeracruz, Mexico. Such models could

provide an understanding of the mostimportant biological and climatologicalfactors involved in the spread of papayaringspot epidemics. This information could

be used as a guide to further studies and as a

basis for future management strategies.Portions of this research have been reported(18,20,21).

MATERIALS AND METHODSEstablishment of field plantings for

model development. Two plots of papayawere established at the Research Center forthe Development of the Humid Tropics atPaso San Juan, Veracruz (19 10' N, 98 16'W). Site A (70 X 40 m) was nearly level andthe soil was a clay loam. Site B (40 X 45 m),approximately 3 km from site A, also had aclay loam soil and was located on a hill witha slope of 3-4%. Fields at both sites had beencropped previously to maize. Seedbeds (30

X 1 m) were sown in June 1985 with papayacv. Cera, the predominant cultivar grown inVeracruz. From sowing until transplanting, acheesecloth cover was placed over theseedbeds to protect seedlings from aphids. InAugust 1985, virus-free seedlings weretransplanted in each field with 3-m spacings

between plants and rows. A total of 286plants (22 X 13) and 168 plants (12 X 14)were transplanted to sites A and B, respec-tively.

Establishment of field plantings formodel validation. Seventy-two additional

plots of papaya cv. Cera were established inthree fields also at the Research Center for

the Development of the Humid Tropics atPaso San Juan, Veracruz. The field at site Cwas nearly level, the


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1206 Plant Disease/Vol. 77 No. 12

field at site D was located on a hill with aslope of 3-4% approximately 3 km from siteC, and the field at site E was nearly level andwas located about 2 km from site C and D.Each of the three sites had clay loam soil,and maize was the previous crop.

A total of 2,000 papaya seedlings weregrown from October 1987 through March1988 in black plastic containers (18 X 15cm) prior to planting. Papaya plantationswere established at each site on six

transplanting dates (beginning December1987, then every 2 mo thereafter) withdensities of 135, 84, 51, and 42 plants per

plot (6.6 m X 40 m), to give an equivalent of4,444, 2,500, 1,600, and 1,111 plants perhectare, respectively. Twenty-four plotswere established per site. Standard cultural

practices were used in all plots. Twelveplots, corresponding to the first three trans-planting dates at site E, were damaged andlost due to heavy rain and strong winds.

Disease assessment. Each plant wasobserved once every 2 wk from trans-

planting in August 1985 until December1986 (for plots used in model development)and from December 1987 until August 1989(for plots used in model validation) forsymptoms typical of PRV infections.Typical symptoms included a

leaf mosaic and shoestring, watery spots onstem and leaf petioles and ring spots on fruit.The location of each individual diseased

plant was recorded for each plot andevaluation date. Progress in time of virus

incidence at each plot was considered as anepidemic. Two and 60 epidemics wereassessed to generate and validate the model,respectively. Presence of PRV in about 30symptomatic plants was verified by ELISA(27) each month from transplanting inAugust 1985 to August 1986 in the two

plantations used for model development.Collection of weather data. A mete-

orological station was located within 2 km ofeach of the five sites where disease

assessments were made. Data on relativehumidity, precipitation, and maximum andminimum temperatures were collected dailyduring 1985-1989. Wind speed and directionwere calculated by the Gulf Foresight Centerfrom data collected within 20 km of eachexperimental site. Land area between wherewind measurements were made and theexperimental area is a level coast withoutgeographic barriers.

Aphid monitoring. Alate aphids werecaptured in Moericke yellow pan traps (30 X55 X 13 cm) from August 1985 untilDecember 1986 (for fields used in modeldevelopment) and December 1987 untilAugust 1989 (for fields used in model

validation). One trap was placed midwayalong each edge of each field at all sites.Four traps were placed per field. Trap heightwas initially set at 0.30 m above the ground,then was adjusted up to 1.30 m as the cropgrew to approximately 2 m. Aphids wereremoved from each trap every 3 days, placedin 70% ethyl alcohol in glass vials, andreturned to the laboratory for counting andidentification.

Selection of independent variables.Counts of each aphid vector species of PRVin Veracruz (10) (Myzus persicae, Aphis

gossypii, A. nerii, A. citricola, andMacrosiphum euphorbiae)were utilized as

independent biological variables. Only thenumber of alate members of these aphidspecies was used as estimator of PRVincidence because papaya plants are notcolonized by migratory aphid species (19).The proportion of viruli- ferous aphids invector populations was not determined.

Independent meteorological variableswere mean rain (mm) and temperature (C)and mean wind velocity (m/ sec) when froma north azimuth (regionally, the

phenomenon is known as norte).Only northwinds were included in model development

because numbers of aphids trapped wascorrelated with frequency of north winds. Ina previous analysis (G. Mora, unpublished)

we concluded that the best representation ofthe wind variable is the product of norteduration (number of days) and mean windvelocity (m/sec). Single variables, products,and square values of meteorologicalvariables were included in the analysis(Table 1). The period of time frominoculation with the five vectors found inVeracruz to first symptoms of papayaringspot ranged from 6 to 38 days (mean of25 days) and was dependent on vectorspecies (10). Therefore, values of each

biological variable were accumulated overintervals of 3 and 4 wk that ended 1, 2, or 3wk before the reference time when predic-

tions of the dependent variable (diseaseincidence) were made. Because biologicalvariables were of paramount interest and toavoid reduction in residual degrees offreedom (due to high number of independentvariables), the weather variables wereaccumulated only for a 4-wk period thatended 3 wk before the disease incidenceassessments. These a priori constraints wereset to identify the explanatory capacity ofeach independent variable. Independent

variables used in this study included twoclasses of variables corresponding toenvironment and vectors (Table 1).

Selection of dependent variables. De-pendent variables were incremental changesin percent disease incidence and the naturallog (In) transformation of incrementalchange in disease per unit time (Table 1).

Model development, selection, andvalidation. Multiple regression analysis wasused to examine the influence of en-vironment and aphid vector numbers (asindependent variables) on dependent var-iables. Model development comprised threestages: 1) selection of the dependent variableand reduction of the number of independent

variables, 2) selection of a set of potentialpredictive models, and 3) validation of thosemodels with independent data. Becauseindependent variables had differentmagnitudes and units of measurement (e.g.,mm, C,) they were standardized to zeromean and unit variance to permitcomparison of effects (9). Also, becauseincremental change of disease incidence (Yt Yt.h Table 1) was expressed as apercentage and thus had a discretedistribution, it was transformed to a squareroot to approximate a normal distribution. Instages one and two of model development,the stepwise procedure of SAS was used

(9,24).The proportion of variance accounted forby the model, Mallows Cp statistic, theanalysis of structure using eigenvalues, andvariance inflation factor (VIF) were used ascriteria to select regression models in stagetwo of model development. The proportionof variance accounted for [(total meansquareresidual mean square)/(total meansquare)] takes into account the number ofindependent variables in the model.Mallows Cpwas used as a criterion for thegoodness-of-fit of regression equations withdifferent numbers of independent variables.A model is less subject to bias when the Cpvalue is close to the

Table 1. Independent and dependent variablesused to analyze the relationship between thechange of disease incidence and environmentaland biological variables for papaya ringspot incentral Veracruz, Mexico

Variables SymbolIndependent

Vector

Aphis gossypii AG(1-5)A. nerii AN(1-5)A. citricola AC(1-5)Myzus persicae MP(1-5)

Macrosiphumeuphorbiae MF(1-5)

EnvironmentalbMean minimumtemperature (C) T

Accumulatedprecipitation (mm)P

Northern wind(days/m/sec) W

Interaction and TP, TW, PW,square values T2P2and W2

DependentcDisease increment Yt~ Yt.jRate of disease increase ln (T,Y.O/At

3Numbers (1-5) represent accumulated num-

ber of aphids trapped during a 3-wk period ending1 (1) and 2 (2) wk before the date of diseaseassessment and accumulated number of aphidstrapped during a 4-wk period ending 1 (3), 2 (4),and 3 (5) wk before the date of diseaseassessment. bVariables were accumulated (PandW)or averaged (T)during a 4-wk period ending 3wk before the date of disease assessment; W =the

product of northern winds duration (days) andthe mean of wind velocity (m/ sec). cY =diseaseincidence (%);At =number of days between timeinterval tand t-1.


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Time (weeks)Fig. 1. Observed and predicted increment of papaya ringspot incidence (YtYt.)in papaya, using themodel y, = - 1.45 + 0.42 ANj + 0.00016PW +0.116 AGS- 0.0058 ANS

2~ 0.0057MP,and actualnumber of the aphid vectors of papaya ringspot virus Aphis gossypii, A. nerii, A. citric ola, Myzus

ersicae, and Macrosiphum euphorbiaeand accumulated number of individuals of A. gossypii (AG5)andA. nerii(AN5) during a 4-wk period that ended 3 wk before the date of disease assessment in site A,Veracruz, Mexico, 1985-1986.

number of parameters (p) in the model(9,24). Draper and Smith (7) suggest that aregression model should have a Cp valueabout equal to the number of parameters.The VIF and analysis of structure measuredthe effect of multi- collinearity amongindependent variables on the variances ofestimated coefficients and, thereby,

provided additional measures of modelstability (9). If VIF is larger than 5, theassociated coefficients may be poorly

estimated (7,9). The analysis of structureusing eigenvalues can be used to identifyvariables involved in linear dependence (9).With this methodology, relatively largevalues of variance proportions associatedwith small eigenvalues (close to 0) indicatethat the independent variables are highlycorrelated (9). The coefficient of determi-nation adjusted for degrees of freedom (Ra

2)evaluated the relative merit of including aspecific independent variable within a model(9,14). The selected models were validatedin the third stage by programming in SASthe equations, imputing data from 60 PRVepidemics monitored during 1987-1989, andregressing predicted and observed values.

The target value for model reliability was setat r2 > 0.60 (p > 0.05). None of these 60epidemics was used to develop the initial

prediction models.Disease progress in time. The linearized

forms of the monomolecular, Gom- pertz,and logistic models were evaluated forgoodness-of-fit to data from the 60epidemics by simple linear regression an-alysis (4,24). Goodness-of-fit was evaluated

by examination of r2values. The objective ofthis analysis was to estimate the average rateof progress of each epidemic (4) (i.e., rL =logistic, rG = Gom- pertz, or rM monomolecular) and use this information to

characterize epidemics that were and werenot predicted in the validation process.

RESULTSPreliminary selection of independent

and dependent variables. Models to pre-dict changes in disease incidence (Figs. 1and 2) were developed in several stages. Inthe first stage, each dependent variable wasregressed on 60 biological variables and nineenvironmental variables for each site (A andB) and for pooled data. The R2of the bestequations indicated the level of precisionobtainable for any given dependent variable.TheR2values ranged from 0.40 to 0.43, 0.70to 0.98, and 0.60 to 0.66 for pooled, site B,

and site A data, respectively. Models withincrement of disease development (YtYt.j)as the dependent variable had the highestR2values. Square root transformation of thisvariable did not improve R2 estimates, soonly models with untransformed incrementsas dependent variable were evaluatedfurther. Variables regularly selected in thestepwise procedure wereAN5, AG5,andPW,

where symbols and subscripts are thosegiven in Table 1.

Model development and selection. Inthe second stage of model development,

pooled data from sites A and B were usedwith the independent variables AN5, AG5,

AN52, PW, and MP5

2, which had beenselected in the first stage. The in-tercorrelation among independent anddependent variables was examined using thecorrelation matrix. The objective was to

contrast these results with those usingfurther stepwise procedure (9). All inde-pendent variables, exceptPWandMP5

2 werecorrelated significantly with increment ofdisease incidence (i.e., YtYt.j)(Table 2).Regression models of

combinations of three-, four-, and five-variable regression variables were obtainedwith the stepwise procedure of SAS. The

best model was selected based on statisticsshown in Table 3. There were no one- ortwo-variable models with proportion ofvariance accounted for (JR2) greater than0.50 and Cp 0.59) andsignificantly estimated parameters (p

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