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POPULATIONECOLOGY

Simulating the Dynamics of Bemisia argentifolii(Homoptera Aleyrodidae) in an Organic Cropping

System with a Spatiotemporal Model

c C BREWSTER J C ALLEN D J SCHUSTER] ANDP A STANSLy2

Entomology and Nematology Department University of Florida Gainesville FL 3261-0620

Environ Entomol 26(3) 603-616 (1997)ABSTRACT The dynamics of the whitefly Bemisia argentifolii Bellows amp Perring were stud-ied at a mixed-crop organic farm on Pine Island FL between September 1992 and January1993 Whitefly populations on tomato eggplant zucchini cucumber and pepper were mon-itored weekly by beat-pan sampling and biweekly by visual counts and parasitism was deter-mined by rearing parasitoids from whitefly infested tomato and eggplant foliage Analysis ofthe sampling data identified tomato and eggplant as the most attractive whitefly host plantsfollowed by cucumber zucchini and pepper Parasitism of whiteflies on tomato and eggplantreached 80 during the study Two peaks in population numbers were observed 011 tomatoand eggplant planted by late September whereas only 1 peak occurred when the same cropswere planted later The suitability of a spatially explicit population model as a tool for inves-tigating insect dynamics was demonstrated on whiteflies at the farm Simulation experimentsconducted to explain the trends in whitefly population numbers observed on early and latetomato indicated that these population peaks likely resulted from the interaction of plantingdate and temperature and not from the spatial heterogeneity of the crop system at the farmOther simulation experiments showed that whitefly population levels could be lowered bygrouping similar crops and maintaining barriers to whitefly movement betveen crops Theutility of this type of model for studying insect dynamics in systems where host plants varyspatially and temporally is illustrated

KEY WORDS Bemisia argentifolii Bemisia tabaci silverleaf whitefly spatial populationmodel

THE DRAMATICCHANGEin status of the sweetpo-tato whitefly Bemisia tabaci (Gennadius) in themid-1980s generated renewed interest in the bi-ology and dynamics of this insect (Byrne et aI1990 Brown et aI 1995) In Florida this changein status was accompanied by reports of an irreg-ular ripening disorder of tomato (Schuster et aI1990) and a silverleaf disorder of squash (Kring etaI 1991 Schuster et aI 1991) Crop losses fromwhitefly attacks in Florida were estimated at $141million in 1991 (Perring et aI 1993 Schuster1995) and US losses for the same year were overhaIf billion dollars (Perring et aI 1993)

A new strain of B tabaci strain B was blamedinitially for the increasing infestations (Price et aI1987 Byrne and Miller 1990) Strain B consideredto be more pestilent than the original B tabacistrain (strain A) was later described as a new spe-cies of whitefly Bemisia argentifolii Bellows amp Per-ring (Perring et aI 1993 Bellows et aI 1994) Bothwhiteflies are highly polyphagous insects that have

IGulf Coast Research and Education Center Bradenton FL34203

2SouthwestFlorida Research and Education Center Immoka-lee FL 33934

spread extensively throughout their ranges (Per-ring et aI 1992 Brown et aI 1995) however Bargentifolii exploits a greater number of host plants(Perring et aI 1992 Brown et aI 1995) has slightlydifferent oviposition preferences (Blua et aI 1995)and appears to be displacing B tabaci in manyregions (Perring et aI 1994 Brown et aI 1995) Inspite of differences between the 2 continuing de-bate among entomologists suggests that the strainspecies questions have not been resolved com-pletely (see Brown et aI 1995)

Spatial movement of these whiteflies is facilitat-ed by the existence within populations of 2 distinctdispersal morphs-a trivial flying morph and a mi-gratory morph (Byrne and Houck 1990 Blackmerand Byrne 1993a b) Evidence of the existence of2 morphs was obtained in a recent study by Byrneet al (1995) that showed the distribution of white-flies captured from a source release to be bimodalrather than random Adults whiteflies have theability to move within regionaI crop systems andtherefore their dynamics are tied closely to cropand wind patterns throughout these systems It isdifficult to study these dynamics in large spatiaIsystems with Held experiments and so simulation

0046-225X1970603~616$0200O copy 1997 EntomologicalSocietyof America

604 ENVIRONMENTAL ENTOMOLOGY Vol 26 no 3

Fig 1 Pine Island Florida

models are used Most models for whiteflies how-ever generally have been for single resource (crop)systems (von Arx et al 1983 Baumgartner et al1986 Baumgartner and Yano 1990) although re-cently a model for a regional (multicrop) systemthe Imperial Valley California was described (Wil-hoit et al 1994) There is a definite need for great-er effort in this area

The objectives of this study were 2-fold Westudied the dynamics of B argentifolii (here re-ferred to as the whitefly) in a heterogeneous crop-ping system with spatiotemporal variation in hostplants In addition we demonstrated the appro-priateness of a spatially explicit age-structuredmodel (Allen et al 1996 Brewster and Allen 1997)as a tool for studying insect dynamics in such sys-tems We emphasize that this is not a validation

exercise per se but one that serves to illustrate theutility of these models for studying insect dynamicsin temporally and spatially varying crop systems

Materials and Methods

Study Site The study was conducted at amixed-crop organic farm Pine Island Organics lo-cated on Pine Island Florida Pine Island is rela-tively isolated from the Florida mainland and is thelargest island (272 by 32 km) of its kind on thewest coast of Florida (Fig 1) The cropping areaat the farm consisted of 2 fields with 14 and 12blocks respectively Each block was planted withtomato eggplant pepper cucumber or zucchiniand was separated from other blocks by a sugar-cane windbreak To facilitate insect population

June 1997 BREWSTER ET AL WHITEFLY SPATIOTEMPORAL DYNAMICS 605

(redistributed host reproduction)

n n

Rt(l m) = L L Ky(l - u m - v)f[Y3t(u v)]=1v=1

n n

Pt(l m) = LL Kz(l - u m - v)Z3t(u v)=1v=1

(redistributed natural enemy)

Ys and Zs are now spatial density N X N matricesfor the whitefly and natural enemy respectivelyand the convolutions are solved with discrete FastFourier transforms State variables parametersand functions used in the model are outlined inTable 1

Reproductive and Attack Functions A density-dependent Ricker function (Ricker 1954)

(2)Z3t+1 = SZ2DZ2Z2t + SZ3Z3t

where

Nicholson and Bailey 1935 Hassell and Varley1969 Beddington et al 1975) or surrogates (egKot 1989) Ky and Kz are redistribution (dispersal)functions for prey and predator so that Kl - u m- v) gives the probability of individuals movingfrom point uv to point Im in the spatial systemWithin a time step in the model each K is con-volved separately with the respective interactionfunction over space creating amiddot density surface ofredistributed individuals The convolutions aresolved efficiently by taking 2-dimensional FastFourier transforms of the dispersal and interactionfunctions separately multiplying them and invert-ing the results back to the spatial domain with theinverse Fast Fourier transform This is computa-tionally more efficient than solving the integrals foreach point in the spatial system

Several modifications must be made to equation1 that would allow this model to be used to explorewhitefly dynamics at Pine Island Organics Firstfor simulating the system space is considered dis-crete and is represented by mosaic of discrete unitsor a grid Double summations therefore replacethe double integrals In addition the natural ene-my complex of the whitefly is modeled as a singlegeneric natural enemy and each population is giv-en 3 age-classes (egg immature adult) with theindividuals in each age having distinct survivalprobabilities (S) and partial development (1 - D)at each time step (Brewster and Allen 1997) Thesemodifications lead to

Ylt+1 = Rt + Sn(1 - Dn)Ylt

Y2t+1 = SnDnYlt + SY2(1 - Dy2)Y2texp(-aPt)

Y3t+1 = SY2DY2Y2teXP( -aPt) + SY3Y3t

ZI+1 = Y2t[1 - exp( -aPt)] + SZ1(1 - DZ1)Zlt

Z2t+1 = SZlDZlZlt + SZ2(1 - DZ2)Z2t

where Yt and Zt are the prey and predator in gen-eration t and f and g are their respective interac-tion functions that are general and can be any ofa number of Ni~holsonian type interactions (eg

sampling and data collection blocks were furtherdivided into several plots (Fig 2a)

Sampling and Field Data During the periodSeptember 1992 to January 1993 adult insect sam-ples were taken weekly from each plot by beat-pansampling No samples were taken from sugarcaneor areas outside the boundaries of the 2 fields Inthe beat-pan sampling method the upper foliageof 5 plants from each plot was shaken vigorouslyover a black pan containing a thin layer of vege-table oil Dislodged insects were identified andcounted Also at 2-wk intervals visual counts ofinsects were taken independently by commercialscouts on the same areas covered by the beat-pansampling

Parasitism of whiteflies was determined by tak-ing 5 leaves from tomato and eggplant plots every2 wk placing them in paper cartons in the labo-ratory and observing for emergence of whitefliesand their parasitoids Percentage of parasitism wascalculated by dividing the number of emerged par-asitoids (XlOO) by the sum of the number ofemerged parasitoids and whiteflies (McAuslane etal 1994 Simmons and Minkenberg 1994)

Spatially Explicit Population Model A spa-tially explicit population model was used to explorewhitefly dynamics at Pine Island Organics Spa-tially explicit population models combine a popu-lation model with a habitat or resource map thatdescribes the structure (composition and spatial ar-rangement) of species resources within the habitatThe details of this model are given elsewhere (Al-len et al 1996 Brewster and Allen 1997) but someof its more important characteristics are restatedhere

The model is a spatiotemporal age-structuredNicholsonian model (Nicholson and Bailey 1935)that uses integrodifference equations to simulta-neously carry out dispersal and reproduction (Kotand Schaffer 1986 Kot 1989 Murray 1989 An-dersen 1991 Hastings and Higgins 1994 Neubertet al 1995 Kot et al 1996) Unlike many previousstudies that used I-dimensional integrodifferenceequations the spatial system in this case is 2-di-mensional so that the integrodifference equationsfor a simple prey-predator system with no popu-lation age-structure are

Yt+1(l m) = If Ky(l - u m - v)v It

X f[Yt(u v) Zt(U v)] du dv

Z+1(l m) = f r Kz(l - u m - v)vJu

X g[Yt(u v) Zt(U v)] du dv (1)


N

s

W--t---E

DDC]7 IGreen Duseb8 I Pole Barn I9 Field 2 - East10 ~1112

123456

Field 1 789

101112

Field 2 - West 13 amp 14

a

b Resources amp Indiceso

01

16 Cucumber

Zucchini

14 Zucchini

Zucchini

~~(~5Yl~lil1i~1~~~

~l~ ~-~rii~~(1-1

12 Eggplant

Tomato

o Pepper

Cucumber

Tomato

Pepper

EggplantTomato

Tomato

ucumber

Resident egetation

Sugarcane

050402 03Km

01o

02

05

04

a~ 03

Fig 2 Pine Island Organics (a) Scaled map of the farm (b) Original resource map (X) used in simulations


Table 1 State variahles_ parameters and funetions in the spatiotemporal whitefly model

Variahlbull parameltrsand functions

11 Y2 Y3Sn S12SIJDnD2

fiY3)(xp(r)KlRZl 7273SJ~ Dza Q IIgt

KzP

Description

Spatial matrices of whiteAy egg immature and adult densitiesVhiteAy egg immature and adult survival probabilitiesVhiteAy egg and immature development probabilitiesWhiteAy reproductive function (density-dependent Ricker function)Reproductive egg production per female per period11iteAdispersal functionSpatial matrix of redistributed whiteAy reproductionSpatial matrices of natural enemy egg immature and adult densitiesNatural enemy age-class survival and development probabilitiesNatura] enemy searching efficiency quest constant and mutual interference constantNatural enemy dispersal functionSpatial matrix of redistributed natural enemyStandard deviation of dispersal in the It- and G-directionsSpatial matrix of whitefly resources (resource map)

Date

generic natural enemy (a) was a function of theirdensity and was given by a = QP-JII (Hassell andVarley 1969 Hassell and May 1973) The importanceof mutual interference in natural enemy interactionswas alluded to by Hassell and May (1973) who re-ported m values between 028 and 069 from labo-ratory studies and between 048 and 096 from fieldstudies These ranges were used in determining start-ing values for m in this study

Whitrfty Resource Map The spatially explicit na-ture of the model comes from the inclusion of a re-source or crop map that describes the structure ofwhitefly resources at Pine Island Organics This mapis not given explicitly in the model but is a spatial NX N matrix (X) whose entries are integers that serveas indices to rows in a lookup table containing insectparameters for each resource in the system

The resource map for the whitefly at Pine IslandOrganics was constmcted by taking measurementsof the cropping area and other related featuresand recording the spatial arrangement of resourceswithin fields This information was used to createa scaled-map of the farm (Fig 2a) onto which a128 x 128 grid was superimposed Whitefly re-sources at each location in the system were thenindexed to the respective cells in the grid The finalresource map shown as a color-coded image in Fig2b has an extent of =31 ha with each grid cell=1892 m2 (435 by 435 m)

In the assignment of resource indices to crops ar-eas that did not contain any of the 6 main resources(tomato eggplant cucumber zucchini pepper andsugarcane) were assumed to contain resident vege-tation Resource indices were assigned as follows ifa crop was planted in different blocks on the samedate the same resource index Was assigned to theseblocks and to the respective cells in the resource spa-tial matrix However if a crop Wasplanted in differ-ent blocks on different dates these were given dif-ferent resource indices The final resource maptherefore contains 16 rather than 7 resource indices(Fig 2b) Tomato for example Wasassigned resourceindices 4 5 8 and 11 because of different plantingdates Similarly eggplant was assigned resource in-

b

Phase-shifted Cycle -

(Y3t) = Y3texp[r( 1 - Y~)] (3)was chosen as the reproductive function of thewhitefly Natural enemy attack was assumed to beNicholsonian with the proportion of whiteflies thatsurvive attack equal to exp(-aP) where P is dispersedadult natural enemy The searching efficiency of the

16II-AUK 08-Sep 06-0ct OJ-Nov OI-Dec 29Dec 26-Jan

Fig 3 Forcing functions (driving variables) for modelparameters at Pine Island Organics (a) Weekly averagetemperature cycle (b) example of a crop cycle (---)and the same cycle 1800 out-of-phase and shifted slightly(----) that forces the standard deviation of dispersal


Table 2 Parameter values used for B argentifolii and tbe natural enemy complex in simulations with the model

ResourcesModel parameters

r SYI SY2 SY3 DYl DY2 Q m Szs Dzs ur10 uro

Tomato 44 090 060 030 10 060 008 035 050 050 20 10Eggplant 44 090 088 030 10 060 008 035 050 050 20 10Cucumber 38 090 050 030 10 054 008 035 050 050 20 10Zucchini 38 090 050 030 10 054 008 035 050 050 20 10Pepper 33 090 010 030 10 010 008 035 050 050 30 15RV 40 090 080 030 10 040 025 035 050 050 60 30Sugarcane 10 020 om 030 10 001 002 035 050 050 60 30

Values are based on a weekly time step and average temperature of 25degC Y and Z in parameter subscript represent whittfly andnatural enemy respectively Sources for whitefly parameters were Coudriet et al (1985) Costa et al (1991) Powell and Bellows(1992a b) Wilhoit et al (1994) Salas and Mendoza (1995) van Giessen et al (1995) Yee and Toscano (1996) Tsu and Wanl( (1996)RV resident vegetation

a Values are in units of grid cells u and Ii represent east-west and north-south directions respectively The standard deviation ofdispersal for the natural enemy was assumed to be half that of the whitefly

dices 6 and 12 cucumber 3 9 and 16 zucchini 1314 and 15 and pepper resource indices 7 and 10Sugarcane and resident vegetation were assigned re-source indices 1 and 2 respectively The matrix(map) of resources was saved in ASCII file formatand read by the simulation package MATLAB(MathWorks 1994) into the spatial resource matrixX at the start of each simulation

Ill 600Ee-lc 400~0-VIbullbull-l

0

200lt

Insect Dispersal Spatial movement of the white-fly and natural enemy was specified with dispersaldensity functions or redistribution kernels (K) Thedispersal process was accomplished by sumlIlingthe movement of individuals into each point fromall other points in the spatial system at each timestep In the case of the whitefly an integrodiffer-ence equation was used to couple dispersal with

Fig 4 Adult whiteflies collected by beat-pan sampling on various crops at Pine Island Organics Letters andnumbers in the fields crops and indices axis represent crop types and indices respectively For exunple CI6ampT iscucumber resource 16 followed by tomato E06 is eggplant resource 6 Z zucchini and P pepper


S Oct 27 Oct 17 Nov 8 Dec 31 Dec

Date

each location it is expected to be a time-varyingparameter that reaches a maximum near host plantsenescence

Model Parameters and Simulations Estimates ofparameter values for the whitefly were obtainedfrom the literature and were mainly for female lon-gevity egg production and egg and immature sur-vival and development Data on carrying capacityand spatial movement were limited and not cropspecinc Based on the sampling data and whiteflyinfestation levels observed crops were ranked andthe ranking used to derive estimates for unknownparameters Although the independently collectedvisual count data taken by commercial scouts werenot statistically independent from the other sam-pling data because both were collected during thesame periods these data were nevertheless used toassist in the derivation of estimates for natural en-emy parameters

Temperature and crop growth were the drivingor forcing variables on parameters in the modelTemperature thresholds of lOoC (lower) and322degC (upper) have been quoted for whiteflies(Butler et al 1983 Zalom et al 1985) Withinthese limits rate processes often tend to vary lin-early with temperature (Womer 1992) Becauseaverage weekly temperature at Pine Island Organ-ics for the period of study fell well within theseestablished thresholds (Fig 3a) we assumed rateswere linear with temperature

Parameters were also forced with crop growthby multiplying by a scaling factor I3t calculatedfrom a cosine wave

[27T(ST - PT)] (5)

I3t = 1 + 8 cos CP

that represented the growth cycle of the crop (Fig3b) In equation 5 8 (0 lt jjgt 1) is the amplitudeof the crop cycle ST is simulation time PT is timeat peak crop growth and CP the growth period ofthe crop Dispersal was expected to be at a maxi-mum near crop senescence and therefore thestandard deviation of dispersal was forced by a cy-cle that was =180degout-of-phase with the crop cy-cle and that was also shifted to account for any lagin response time for dispersal as crop growth be-gan to decline (Fig 3b)

Simulations ran for 25 wk on a weekly time stepInitial population densities are always difficult todetermine Because we were interested solely inthe qualitative behavior of the model and not inits ability to predict absolute whitefly densities itwas not necessary to start the simulations with ac-tual initial densities We therefore seeded each cellin the spatial grid with low (0-1) random densitiesof individuals in all whitefly age classes An exam-ination of the sampling data revealed that naturalenemy densities at the start of sampling weremuch lower than those of the whitefly We there-fore seeded each cell in the natural enemy spatialmatrices (Zl Z2 Z3) randomly as we did for the

Observed

reproduction and another integrodifference equa-tion was used to redistribute adult natural enemiesthroughout the spatial system We assumed that alldispersal was local and random and that no long-range migration occurred during the study perioaThe effects of wind on movement were thereforeignored We also assumed that spatial movementto the east or west (u-direction) was greater thanmovement to the north or south (v-direction)These assumptions were justined because of thegreater dimension of the blocks in the east-westdirection and the sugarcane barriers to movementin the north-south direction (Fig 2) A direction-biased 2-dimensional normal density function

K(l m u v)

= _1_exp[_([1 - uJ2 + [m - V]2)]27TUIIUe 2 ~ ~

UII yen- Ue (4)

was therefore chosen as the redistribution functionfor both species Because the standard deviation ofdispersal per time step U depends on the insectspecies and characteristics of the host resource at

Fig 5 Observed (----) and simulated (--) per-centage parasitism of whitefly on tomato and eggplant atPine Island Orgmucs

20

40

o

-= 100 Eggplant~cJbullbullbull 80~

~ 60

100 Tomato

80

e 60 bull

11) - 40 - - Observed11)= 20bullbullbull= 0

~ SOct 27 Oct 17 Nov 8 Dec 31 Dec


12 a 12

08 08

04 04~

-= 00 00~ 15-Sep 13-0ct 10-Nov OS-Dec 23-Sep 20-0ct 17middotmiddotNov 15-Dec

bullbullbullbullbullbull 12 12--= C

~

08 08

bullbullbullbullbullbull

IIIIIIIIC= 04 ~~ 04tS

lt~ 00 00C 03-Nov 24-Nov IS-Dec OS-Jan 23-Sep 20-0ct 17Nov IS-Dec

C 12 12fe-rIl 08 08=~

~ 04 04tS~ 00IIIIIIIIC 00~ 27-0ct 24-Nov 22-Dec 20-Jan 15-Sep 29-Sep 13-0ct 27-0ctCJ 1200 g 12 h

08 08

1 04 - - - -- - - - - - - 04

00 0023-Sep 06-0ct 20-0ct 03-Nov 06-0ct 27-0ct 17-Nov OS-Dec

Date


Fig 7 ObselVedand simulatedadultwhiteAydensitymaps at Pine Island Organicson 4 dates The 2-dimen-sional correlation coefficient for each comparisonwasgt070 Lighter areas indicatehigherwhiteAydensities

Simulated

~~----

~

m~~~

Observed

comparing whitefly dynamics on T04 with the de-clining temperature cycle given in Fig 3a andthese dynamics when a constant average temper-ature for the period of simulation was assumedAnother set of experiments compared species dy-namics in simulations that used the original white-fly resource map (Fig 2b) with those that usedexperimental resource maps in which the structureof the system was altered In one experimentalmap similar crop types were grouped within thesame blocks so that field 1 for example containedthe solanaceous crops and field 2 the cucurbits Ina variation of this map the sugarcane barriers be-tween blocks were removed In another experi-

whitefly but multiplied these densities by 010010001 times that for the whitefly respectivelyThese density matrices were saved and reused toinitialize populations at the start of simulation Inaddition we used the first 3 wk of the simulationperiod to allow the whitefly population to buildbefore the natural enemy was introduced Duringthis period we assumed that the resource mapcontained resources 1 and 2 (sugarcane and resi-dent vegetation) only and that the natural enemywas absent The full resource map and natural en-emy were introduced into the simulation after this3-wk initialization period Table 2 gives the param-eter values used to generate the simulation outputthat qualitatively matched the adult whitefly dy-namics observed from the sampling data

Comparing Model Output and Sampling DataThe sampling data were used to standardize theoutput of the model so that the model could beused to explore whitefly dynamics at Pine IslandOrganics To determine the degree to which thesampling data and simulation results agreed visualcomparisons were made by scaling each data set to(0-1) and plotting the results on the same graphCorrelation analysis were used to quantify the vi-sual comparisons and to compare simulated white-fly adult density maps with observed density mapsThese analysis were performed using the XCORRand CORR2 functions available in the signal pro-cessing and image processing toolboxes in MATLAB(MathWorks 1994) XCORR estimates the cross-correlation coefficients between 2 equal lengthdata sequences and also returns the correlation co-efficients between the 2 sequences at various lags(Krauss et al 1993 Steams and David 1996)CORR2 computes the 2-dimensional correlationcoefficient between 2 matrices (Thompson andShure 1995) In the case of 2 equal length vectorsthe output is a single value equivalent to the valuereturned by XCORR at zero lag Correlations andsignificant levels for most comparisons were veri-fied in SigmaStat (Kuo et al 1992)

Simulation Experiments A series of simulationexperiments were conducted to explore whiteflydynamics at Pine Island Organics One set of ex-periments for example was used to help explain thedifferences in whitefly population trends observedon early and late planted tomato We first deter-mined whether the trends were caused by the de-gree of heterogeneity within the crop system Wethen replaced all crops except sugarcane and res-ident vegetation with tomato resource 4 (T04) andsimulated the system We also studied the effectsof temperature on whitefly population trends by

Fig 6 Scaledbeat-pan sampledata (----)and scaledsimulationresults (--) for adultwhitefliesat Pine IslandOrganics (a) tomato resource 4 (r = 085 P lt 0001) (b) tomato resource 5 (r = 090 P lt 0001) (c) tomatoresource 11 (r = 082P lt 001) (d) eggplantresource6 (r = 092P lt 0001)(e) eggplantresource 12 (r = 089P lt 0001) (f) cucumber resource 3 (r = 088 P lt 0005) (g) zucchini resource 13 (r = 098 P lt 0001) (h)pepper resource 7 (r = 088P lt 000l)

ENVIRONMENTAL ENTOMOLOGY Vol 26 no 3

I - Whitefly------- Natural Enemy

a02

01

00=0

lt -01= OI-Sep 29-Sep 27-0ct 24-Nov 22-Dec 20-Janbull

-- Tomato amp Other Crops------- Tomato Only

t5-Sep 29-Stp 13-0ct 27-Oct to-Nov 24middotNov 08~Dec 21-Dec00

612

gt-i 12c3=iClt 080~iiicCIl 040CCIl

~I)

with

Fig 10 Relative differences (RDs) in adult densities(a) RDs between densities with the original resource mapand an experimental map with similar resources grouped(b) RDs in densities with the original resource map andan experimental map with the sugarcane barriers re-moved

r== ~a~Y Enemy I~----- bull

Date

b

OI-Sep 29-Sep 27-0ct 24-Nov 22-Dec 20-Jan

~ 05

puted using the NORM procedure in MATLAB(MathWorks 1994) Relative differences were com-puted as the differences in adult densities in sim-ulations that used the original map and those thatused the experimental map so that

RDy3 = IIOMy3II -IIEMY311RDZ3 = IIOMZ311- IIEMZ31I (6)

OM Y3 or Z3 = adult density with the original map

EM Y3 or Z3 = adult density with an experimentalmap

where 11middot11is the Frobenius norm (a measure ofdistance from zero) of the adult density matrix andY3t and Z3t are whitefly and natural enemy adultsat time t Relative differences of zero indicated nodifferences in adult densities between the mapsPositive relative differences meant that the originalmap produced relatively higher densities com-pared with the experimental map and negative rel-ative differences meant relatively lower densitiescompared with the experimental map Because theremoval of the sugarcane barriers allowed both

Date

Fig 8 Comparison of adult whitefly dynamics on to-mato resource 4 (T04) in a simulation that used a re-source map that contained T04 only and one that usedthe original resource map that contained T04 and othercrops

3008 a Tomita Only

Weekly Temperature 28 -~- bull Uc06 26 --e - bull ~ 24 =~ ~~ 04 22 ~ bullbullbull= ~

~ 20 C02 e~ 18- ~= E--0 00 16lt 15-Sep 06-0ct 27-01 17-NDv 08-0bullbull-QC 30 12 bCIl 28 -= U~ ~~ 09 26 ~

0 24 bull~ =- 06 ~~ 22 ~y bullbullbull00 ~20 C03 e18 ~

E--00 16IS-Sep O6-Oct 27-0lt1 17-Nov 08-D bullbull

DateFig 9 Comparison of adult whitefly dynamics on to-

mato resource 4 (T04) in a simulation that used a re-source map that contained T04 only (a) Simulation wasconducted under a declining temperature regime (b)simulation was conducted under an average constanttemperature regime for the period of crop growth

mental map the arrangement of the resources inthe original map was retained but the sugarcanebarriers between blocks were removed Compari-sons were made by estimating what we called therelative differences in adult densities in simulationswith these maps At each time step during simu-lations the norms of adult whiteHy density (Y3)and adult natural enemy density (Z3) were com-


species to move freely between blocks a nonnaldensity dispersal function with no directional bias

K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)

was used in these simulations as opposed to equa-tion 4

Results and Discussion

Analysis of the beat-pan sampling data taken atPine Island Organics suggested that tomato andeggplant were the most attractive whitefly hostplants followed by cucumber zucchini and pepper(Fig 4) Whitefly numbers reached 529 adults perpan sample on tomato and 317 adults per pan sam-ple on eggplant Maxima of 160 and 35 adults perpan sample were obtained on cucumber and zuc-chini respectively On pepper the highest numberof whiteflies observed was 41 adults Pepper wasconsidered a poorer host than zucchini becauseoverall whitefly numbers were lower Sugarcaneand resident vegetation were not sampled but sug-arcane was not expected to be a good whitefly hostSome resident vegetation however is known to har-bor whiteflies and natural enemies (Evans 1993)Schuster et al (1992) for example observed inwest-central Florida that although low numbers ofadult whiteflies normally were found on surround-ing weeds this resource tended to act as a reser-voir for these insects particularly after surroundingcrops had been harvested

Natural enemies were the main agent of whiteflycontrol at the farm because no conventional pes-ticides were applied Florida is renowned for itslarge fauna of whitefly natural enemies (Evans1993 Dean 1994) and under situations of limitedpesticide use (as at Pine Island Organics) parasit-ism plays a very important role in limiting whiteflypopulation increases For example in noninsecti-cide treated peanut fields in north-central Floridaup to 100 parasitism of whiteflies was observed(McAuslane et al 1993 1994) Parasitism of white-flies on tomato and eggplant at Pine Island Organ-ics reached as high as 80 during our study (Fig5)

A reasonable match was achieved between adultwhitefly population trends in the sampling dataand those generated by the simulation (Fig 6) andbetween the adult density maps (Fig 7) Each plotin Fig 6 presents the collective data (after scaling)from 1 or more blocks so that Fig 6a for exampleshows data obtained from all blocks containing re-source 4 tomato (T04) Although the matches be-tween the data sets were quite reasonable cross-correlation analysis showed that in a few casesthese data sets lagged each other by as much as 2wk (eg Fig 6 a and d) We feel this resulted fromthe manner in which crop growth was represented(equation 5 Fig 3b) It was essential to have good

agreement between the output of the model andfield data (at least qualitatively) so that the modelcould be used to examine other scenarios that werelikely to affect whitefly dynamics at the farm

The simulations were sensitive to parameters re-lated to the natural enemy In particular we foundthat the initial density of the natural enemy relativeto the whitefly the level of mutual interference (m)between natural enemy individuals and the attackparameter (Q) affected the final whitefly dynamicsin the system Simulated percentage of parasitismfor example fluctuated unlike observed parasitismalthough both showed increases (Fig 5) Differ-ences between the 2 we feel are likely caused bymany unknown aspects of parasite behavior andthe fact that one generic natural enemy was usedto represent what is actually a group of several spe-cies in the field This might be considered by someto be a significant drawback of the model How-ever at least 1 study has shown the composition ofa natural enemy complex to be less important thanthe average searching efficiency of species withinthe complex (ONeil and Stimac 1988)

Whitefly numbers on tomato planted before lateSeptember showed 2 distinct peaks (Fig 6 a andb) The 1st peak occurred in mid-October and the2nd peak occurred in mid- to late NovemberWhen tomato was planted in late October how-ever adult numbers were generally lower and only1 peak in mid- to late December was observed(Fig 6c) Whitefly populations on eggplant showedthe same general trends as those on tomato (Fig6d) In Florida Dean (1994) observed that whiteflypopulation numbers increased exponentially onspring tomatoes but fluctuated on fall tomatoes ina manner similar to that observed in this study Wetherefore suspected that population trends on earlytomato were the result of the interaction of tem-perature and planting date We tested this hypoth-esis with the model in a series of simulation ex-periments with tomato resource 4 (T04) The 1stexperiment to determine the effects of the hetero-geneity of the crop system indicated that no dif-ferences in population trends resulted when thesystem contained only T04 or when this resourcewas combined with the other resources grown atthe farm (Fig 8) It seemed unlikely therefore thatthe population peaks resulted from the presenceof the other resources in the system We also ex-plored the effects of temperature and found thatchanging from a declining temperature regime toan average constant temperature regime causedthe early population peak to disappear (Fig 9 aand b) This suggested that temperature played akey role in these trends

Environmental temperature is considered animportant determinant of whitefly population dy-namics (Zalom et al 1985 Byrne and Bellows1991 Powell and Bellows 1992a b) For examplein simulations of this pest in cotton von Arx et al(1983) found that temperature and the quality ofthe host plants were the most important factors

614 ENVIRONMENTAL ENTOMOLOCY Vol 26 no 3

controlling dynamics At Pine Island Organicswhiteflies infesting crops planted in Septemberwere exposed initially to higher average tempera-tures (Fig 3a) that most likely resulted in shortergeneration times and increased female fecundityHowever whiteflies infesting crops planted in Oc-tober were exposed to lower average temperaturesand therefore had longer generation times andlower female fecundity

The simulation experiments that examined theeffects of changes in resource structure on whiteflydynamics served to demonstrate an inherent ad-vantage of spatially explicit models as tools for rap-idly exploring alternative habitat structuresGrouping the solanaceous resources and cucurbitsin separate regions lowered the densities of boththe whitefly and natural enemy relative to the orig-inal arrangement where crop types were dispersed(relative differences were positive) (Fig lOa) Thishowever was only so when the sugarcane barriersbetween blocks were maintained in both systemsThe dispersed spatial arrangement provided thewhitefly with varying resources that were in closeproximity whereas the grouping of similar croptypes created gaps in the spatial resources at har-vest and thus tended to lower overall whitefly den-sities Removal bf the sugarcane barriers betweenblocks under any arrangement improved the abilityof the whitefly to move freely between resourcesand therefore resulted in relatively higher adultdensities compared with systems that retained thebarriers (Fig lOb)

This small study on the whitefly B argentifoliiat Pine Island Organics has served to highlightsome of the relationships between insect popula-tion dynamics and host plant spatiotemporal vari-ations in heterogeneous systems Whitefly dynam-ics are affected by the spatiotemporal arrangementof host plants and as suggested by Hirano et al(1993) such variations may be more importantthan climatic factors such as temperature in deter-mining whitefly population fluctuations Hirano etal (1993) pointed out that continuous cultivationof suitable whitefly host plants in time and spaceresults in serious damage by these insects to cropsthat are planted later and that because these lateseason crops are likely to experience heavier white-fly damage earlier in their growth they supportfewer whiteflies compared with earlier plantedcrops This could explain the lower densities ofwhiteflies on our tomato resource 11 (T11 in Fig4 and 6c) that was planted in late October com-pared with the tomato resource 4 (T04 in Fig 4and 6a) that was planted in early September Ouranalysis of whitefly dynamics with the model how-ever suggested that temperature also plays an im-portant role in these dynamics

In a relatively small system like Pine Island Or-ganics it is fairly easy to test the effects of hostplant arrangements on whitefly dynamics with fieldexperiments However spatiotemporal models likethe one used in this study open the door to sim-

ulations of crop systems of much larger extent andsuggests that we could design whole crop regionsto minimize pest populations

Acknowledgments

We thank several anonymous reviewers for their com-ments on earlier versions of the manllScript We alsothank the management at Pine Island Organics for allow-ing us to conduct this study at their farm Support forthis work was provided through grants from the NationalAgricultural Pesticide Impact Assessment Program (NA-PIAP) (92-EPIX-I-0078 93-EPIX-I-0 139and 94-EPIX-1-0156) USDA Southern Region IPl (95-34103-1583)to JCA and the Sustainable Agriculture Research andEducation (SARE)Agriculture in Concert vith the En-vironment (ACE) Project No AS92-3This is Florida Ag-ricultural Experiment Station Journal Series NoR-04965

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Bawngiirtner J and E Yano 1990 Whitefly popu-lation dynamics md modelling pp 123-146 III DGerling [ed] Whiteflies their bionomics pest statusand management Intercept Andover UK

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Beddington J R 1975 Mutual inttrference betwetnparasites or predators and its effect on searching ef-ficiencyJ Anim Ecol 44 331-340

Bellows T S T M Perring R J Gill and D HHeadrick 1994 Description of a species of Bemi-sia (Homoptera Ale)To(lidae)Ann Entomol SocAm 87 195-206

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1993b Environmental and physiologicalfactors inHu-encing phototactic Hight of Bemisia tabaci PhysiolEntomol 18 336-342

Blua M J H A Yoshida and N C Toscano 1995Oviposition preference of two Bellli~ia species (Ho-moptera Aleyrodidae)Environ Entomol 24 88-93

Brewster C C and J C Allen 1997 Spatiotem-poral model for studying insect dynamics in large-scale cropping systems Environ Entomol 26 473-482

Brown J K D R Froehlich and R C Rosell1995 The sweetpotato or silverleclfwhiteHiesBin-types of Bemisia tabaci or a species complex AnnuRev Entomol 40 511~j34

Byrne D N and T S Bellows B91 Whitefly bi-ologyAnnu Rev Entomol 36 431-57


Byrne n N and M A Houck 1990 Morphometricidentification of wing polymorphism in Bemisia tabaci(Homoptera Aleyrodidae) Ann Entomo Soc Am83 487-493

Byrne D N and W B Miller 1990 Carbohydrateand amino acid composition of phloem sap and hon-eydew produced by Bemisia tabaci J Insect Physio36 433-439

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Butler G D T J Henneberry and T E Clayton1983 Bcmisia tabaci (Homoptera Aleyrodidae) de-vdopment oviposition and longevity in relation totemperahlre Ann Entomo Soc Am 76 310-313

Costa H S J K Brown and D N Byrne 1991Life history traits of the whiteRy Bemisia tabaci (Ho-moptera Aleyrodidael on sivirus infected or healthyplant species Environ Entomo 20 1102-1107

(oudriet D L N Prabhaker A N Kishaba and DE Meyerdirk 1985 Variation in development rateon different hosts and overwintering of the sweetpo-tato whiteRy Bemisia tabaci (Homoptera Aleyrodi-dae) Environ Entomo 14 516-519

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Ha~sell M P und G C Varley 1969 New inductivepopulation model for insect parasites and its bearingon biological contro Nahlre (Lond) 223 1133-1137

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Hirano K E Budiyanto and S Winarni 1993 Bi-ological characteristics and forecasting outbreaks ofthe whiteRy Bemisia tabaci a vector of virus diseasesin soybean fields Asian Studies on the Pacific CoastFood and Fertilizer Technology Center TechnicalBull135

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Kot M and W M Schaffer 1986 Discrete-timegrowth-dispersal models Math BioSci 80 109-136

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Kraus~ T P L Shure and J N Little 1993 Signalprocessing toolbox for use with MATLAB TheMathWorks Natick MA

Kring J B D J Schuster J F Price and G WSimone 1991 Sweetpotato whitefly-vectored gem-inivirus on tomato in Florida Plant Dis 75 1186

Kuo J Eo Fox and S McDonald 1992 SigmaStatstatistical software for working scientists Users man-ua Jandel Scientific San Rafael CA

MathWorks 1994 MATLAB reference guide High-performance numeric computation and visualizationsoftware version 42c1 The MathvVorksNatick MA

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McAuslane H J F A Johnson and D A Knauft1994 Population levels and parasitism of Bellisiatabaci (Homoptera Aleyrodidae) on peanut cultivarsEnviron Entomo 23 1203-1210

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Perring T M A Cooper and D J Kazman 1992Identification of the poinsettia strain of Bemisia tahaci(Homoptera Aleyroididae) on broccoli by electropho-resis J Econ Entomo 85 1278-1284

Perring T M A D Cooper R J Rodriguez C AFarrar and T S Bellows Jr 1993 Identificationof a whitefly species by genomic and behavioral stud-ies Science (Wash DC) 259 74-77

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Powell D A and T S Bellows Jr 1992a Adultlongevity and population growth rates for Bemisia ta-baci (Genn) (Hom Aleyrodidae) on two host plantspecies J App Entomol 113 68-78

1992b Preimaginal development and survival of 131-misia tabaci on cotton and cucumber Environ En-tomo 21 359-363

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Rieker W E 1954 Stock and recruitement J FishHISBoard Can 11 559-623

Salas J and O Mendoza 1995 Biology of thesweetpotato whitefly (Hom9ptera Aleyrodadae) ontomato Fla Entomo 78 154-160

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Schuster D J T F Mueller J B Kring and D JPrice 1990 Relationship of the sweetpotato white-


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Schuster D J J B Kring and J F Price 1991Association of the sweetpotato whitefly with a silver-leaf disorder of squash HortScience 26 155-156

Schuster D J J E Polston and J F Price 1992Reservoirs of the sweetpotato whitefly for tomatoes inwest-central Florida Proc Fla State Hort Soc 105311-314

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Stearns S D and R A David 1996 Signal pro-cessing algorithms in Matlab Prentice-Hall Engle-wood Cliffs NJ

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Receivedfor publication 23 January 1996 accepted 27January 1997


Fig 1 Pine Island Florida

models are used Most models for whiteflies how-ever generally have been for single resource (crop)systems (von Arx et al 1983 Baumgartner et al1986 Baumgartner and Yano 1990) although re-cently a model for a regional (multicrop) systemthe Imperial Valley California was described (Wil-hoit et al 1994) There is a definite need for great-er effort in this area

The objectives of this study were 2-fold Westudied the dynamics of B argentifolii (here re-ferred to as the whitefly) in a heterogeneous crop-ping system with spatiotemporal variation in hostplants In addition we demonstrated the appro-priateness of a spatially explicit age-structuredmodel (Allen et al 1996 Brewster and Allen 1997)as a tool for studying insect dynamics in such sys-tems We emphasize that this is not a validation

exercise per se but one that serves to illustrate theutility of these models for studying insect dynamicsin temporally and spatially varying crop systems

Materials and Methods

Study Site The study was conducted at amixed-crop organic farm Pine Island Organics lo-cated on Pine Island Florida Pine Island is rela-tively isolated from the Florida mainland and is thelargest island (272 by 32 km) of its kind on thewest coast of Florida (Fig 1) The cropping areaat the farm consisted of 2 fields with 14 and 12blocks respectively Each block was planted withtomato eggplant pepper cucumber or zucchiniand was separated from other blocks by a sugar-cane windbreak To facilitate insect population



n n


n n






where



















N

s

W--t---E


123456

Field 1 789

101112


a


01

16 Cucumber

Zucchini

14 Zucchini

Zucchini

~~(~5Yl~lil1i~1~~~

~l~ ~-~rii~~(1-1

12 Eggplant

Tomato

o Pepper

Cucumber

Tomato

Pepper

EggplantTomato

Tomato

ucumber

Resident egetation

Sugarcane

050402 03Km

01o

02

05

04

a~ 03







KzP

Description


Date





b














0

200lt





Date





[27T(ST - PT)] (5)

I3t = 1 + 8 cos CP



Observed


K(l m u v)

= _1_exp[_([1 - uJ2 + [m - V]2)]27TUIIUe 2 ~ ~

UII yen- Ue (4)



20

40

o


~ 60

100 Tomato

80

e 60 bull




12 a 12

08 08

04 04~



~

08 08




C 12 12fe-rIl 08 08=~


08 08

1 04 - - - -- - - - - - - 04


Date



Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited




































































n n


n n






where



















N

s

W--t---E


123456

Field 1 789

101112


a


01

16 Cucumber

Zucchini

14 Zucchini

Zucchini

~~(~5Yl~lil1i~1~~~

~l~ ~-~rii~~(1-1

12 Eggplant

Tomato

o Pepper

Cucumber

Tomato

Pepper

EggplantTomato

Tomato

ucumber

Resident egetation

Sugarcane

050402 03Km

01o

02

05

04

a~ 03







KzP

Description


Date





b














0

200lt





Date





[27T(ST - PT)] (5)

I3t = 1 + 8 cos CP



Observed


K(l m u v)

= _1_exp[_([1 - uJ2 + [m - V]2)]27TUIIUe 2 ~ ~

UII yen- Ue (4)



20

40

o


~ 60

100 Tomato

80

e 60 bull




12 a 12

08 08

04 04~



~

08 08




C 12 12fe-rIl 08 08=~


08 08

1 04 - - - -- - - - - - - 04


Date



Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited



































































N

s

W--t---E


123456

Field 1 789

101112


a


01

16 Cucumber

Zucchini

14 Zucchini

Zucchini

~~(~5Yl~lil1i~1~~~

~l~ ~-~rii~~(1-1

12 Eggplant

Tomato

o Pepper

Cucumber

Tomato

Pepper

EggplantTomato

Tomato

ucumber

Resident egetation

Sugarcane

050402 03Km

01o

02

05

04

a~ 03







KzP

Description


Date





b














0

200lt





Date





[27T(ST - PT)] (5)

I3t = 1 + 8 cos CP



Observed


K(l m u v)

= _1_exp[_([1 - uJ2 + [m - V]2)]27TUIIUe 2 ~ ~

UII yen- Ue (4)



20

40

o


~ 60

100 Tomato

80

e 60 bull




12 a 12

08 08

04 04~



~

08 08




C 12 12fe-rIl 08 08=~


08 08

1 04 - - - -- - - - - - - 04


Date



Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited







































































KzP

Description


Date





b














0

200lt





Date





[27T(ST - PT)] (5)

I3t = 1 + 8 cos CP



Observed


K(l m u v)

= _1_exp[_([1 - uJ2 + [m - V]2)]27TUIIUe 2 ~ ~

UII yen- Ue (4)



20

40

o


~ 60

100 Tomato

80

e 60 bull




12 a 12

08 08

04 04~



~

08 08




C 12 12fe-rIl 08 08=~


08 08

1 04 - - - -- - - - - - - 04


Date



Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited











































































0

200lt





Date





[27T(ST - PT)] (5)

I3t = 1 + 8 cos CP



Observed


K(l m u v)

= _1_exp[_([1 - uJ2 + [m - V]2)]27TUIIUe 2 ~ ~

UII yen- Ue (4)



20

40

o


~ 60

100 Tomato

80

e 60 bull




12 a 12

08 08

04 04~



~

08 08




C 12 12fe-rIl 08 08=~


08 08

1 04 - - - -- - - - - - - 04


Date



Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited




































































Date





[27T(ST - PT)] (5)

I3t = 1 + 8 cos CP



Observed


K(l m u v)

= _1_exp[_([1 - uJ2 + [m - V]2)]27TUIIUe 2 ~ ~

UII yen- Ue (4)



20

40

o


~ 60

100 Tomato

80

e 60 bull




12 a 12

08 08

04 04~



~

08 08




C 12 12fe-rIl 08 08=~


08 08

1 04 - - - -- - - - - - - 04


Date



Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited



































































12 a 12

08 08

04 04~



~

08 08




C 12 12fe-rIl 08 08=~


08 08

1 04 - - - -- - - - - - - 04


Date



Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited




































































Simulated

~~----

~

m~~~

Observed








a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited




































































a02

01

00=0




612


~I)

with



Date

b


~ 05






Date


3008 a Tomita Only










K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited




































































K(l m U v)

= _1 e [_([1 - u]2 + [m - V]2)]27T0-2 xp 20-2 (7)
















Acknowledgments


References Cited








































































Acknowledgments


References Cited


































































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