S U P P L . 1 2 SOUTHWESTERN ENTOMOLOGI ST F E B . 1 9 8 9

CONSIRVATIoN AND AUGI'{ENTATTON OI' It{IcRoPLITIs cRocErPEs 1/FOR CON TROLLI NG H E LI O TTiSJ--dP'.

_Z

Keith R. Hopper V

Southern Field Crop Insect Managernent LaboratoryARS, USDA, Stonevi l le, MississiPPi

ABSTRACT

Var ious approaches are ava i lab le fo r conserva t ion andaugmenta t ion o f Mi -c rop l i t i s c roce ipes (Cresson) to cont ro lo f H e l i o t h i s z e a ( B o d d i e ) a n d H e l i o t h i s v i r e s c e n s ( F . ) .S i r n u l a t i o n s o f a u g m e n t a t i o n w i t h s e v e r a l m o d e l s o f h o s t -parasitoid populat ion dynanics showed that such models couldr e v e a l i m p o r t a n t p a r a m e t e r s t o m e a s u r e a n d c o u l d h e l p i nd e s i g n o f a u g m e n t a t i o n p r o g r a m s . I n a m o d e l w i t h n od i s p e r s a l b e t w e e n s u b p o p u l a t i o n s , s i m u l a t e d L 0 - f o 1 daugmentation of M. croceipes density in spring suppressed H-v i rescens dens i ty th roughout the season. Add j ,ng dens i ty -independent d ispersa l be tween subpopu la t ions to th is mode ld e c r e a s e d t h e i m p a c t o f a u g m e n t a t i o n . I n c o r p o r a t i n gp a r a s i t o i d a g g r e g a t i o n i n r e s p o n s e t o h o s t d e n s i t y c a u s e dthe behav io r o f the mode l w i th d ispersa l to re tu rn to tha twith no dispersal. Adding density-dependent nortal i- ty fromc a u s e s o t h e r t h a n p a r a s i t i z a t i o n h a d l i t t l e a f f e c t o ns i rnu la ted t ra jec to r ies when such mor ta l i t y occur red be foreparasit izat ion, but adding density-dependent nortal i ty afterp a r a s i t i z a t i o n r e d u c e d p a r a s i t o i d i r n p a c t . A l t h o u g h I w a su n a b l e t o d r a w o n n a n y d a t a f o r s e v e r a l p r o c e s s e s a n dparameters, the sinulat ions suggest that augmentation of l{ .croceipes for control of Heliothis spp. would be technical lyfeas ib le .

INTRODUCTION

To prac t ice ra t iona l conserva t ion or augmenta t ion wen e e d e x p l i c i t p r e d i c t i o n s o f n a t u r a l e n e m y i m p a c t . F o re x a m p l e , t o d e c i d e w h e n , w h e r e , a n d i n w h a t n u m b e r s t ore lease paras i to ids in an inocu la t i ve re lease program' oneneeds to predict what effect date/tfune, p1ace, and density ofre lease have on reduc t j .on in hos t dens i ty in the genera t iono f r e l e a s e a n d i n s u b s e q u e n t g e n e r a t i o n s . T o g e t s u c hp r e d i c t i o n s o n e c a n u s e e i t h e r r e g r e s s i o n m o d e l s o rmechanistj-c rnodels. To develop a regression model , one trouldr e l e a s e v t a s p s u n d e r v a r i o u s c o n d i t i o n s a n d t h e n r e g r e s sparasit ism on numbers released, host density, t i rne of season'

V Hvmenoptera: Braconidae

!, t epiaoftera: Noctuidael/ Current address: EuropeanL3-15 rue de la Masse, 789L0

Parasite Laboratory, ARs. USDA,Orgerus-Behoust, France

9 5

t e m p e r a t u r e a n d o t h e r b i o t i c a n d a b i o t i c f a c t o r s . T h i sapproach can be very expensive because of the many variablesi n v o l v e d a n d b e c a u s e o f t h e l a r g e a r e a s n e e d e d f o re x p e r i m e n t s w i t h h i g h l y n o b i l e h o s t s a n d p a r a s i t o i d s .F u r t h e r m o r e , o n e c a n n o t s a f e l y e x t r a p o l a t e r e g r e s s i o ne q u a t i o n s t o c o n d i t i o n s b e y o n d t h o s e o f t h e e x p e r i m e n t a lre leases .

Mechanistic rnodels, rirhich are based on understanding ofthe causa l in te rac t ions be tween dependent and independentvariables, provide an alternative to regression models. Hereone has to rneasure the paraneters of the component processesa f f e c t i n g d a n a g e a n d p o p u l a t i o n d y n a m i c s , e . g . f e e d i n g ,s e a r c h , d e v e l o p m e n t , d i s p e r s a l , n a t a l i t y , a n d n o r t a l i t y .A l though these measurements a re expens ive , they are o f tenless expens ive than the la rge sca le exper inents needed fo rregress ion mode ls . Fur thernore , i f rnechan is t i c node ls a redesigned well , they can apply to a wide range of condit ions.

I n t h i s p a p e r , I r e v i e w t h e f o r m s c o n s e r v a t i o n a n da u g m e n t a t i o n c o u l d t a k e w i t h M i c r o p l i t i s c r o c e i p e s(c resson) (Hyrnenoptera : Bracon idae) aga ins t He l io th is zea( B o d d i e ) a n d H e l i o t h i s v i r e s c e n s ( F . ) ( L e p i d o p t e r a :N o c t u i d a e ) . I t h e n d e s c r i b e s i r n u l a t i o n s w i t h s e v e r a lmechanist ic models of host-parasitoid populat ion dynarnics anddraw in fe rences about impor tan t paraneters to measure anda b o u t t h e p r o s p e c t s f o r a u g m e n t a t i o n . H . z e a a n d H .v i r e s c e n s a r e m a j o r i n s e c t p e s t s i n t h e U n i t e d s t a t e s( S c h w a r t z 1 9 8 4 , H e a d 1 9 8 4 ) , a n d H e l i o t h i s s p p . a r e m a j o rpes ts nor ldwide (Nevrson 19?2, Anonymous 1981) . M. c roce ipesis often the most abundant parasitoid of the larvae of thesemoths in f ie ld surveys (Lewis and Brazze l L968, Mue l le r andP h i l l i p s l - 9 8 3 , S t a d e l b a c h e r e t a l . 1 9 8 4 , K i n g e t a l . l - 9 8 5 ) ,and as this paper r{r i l l shovr, i t is a promising candidate forcontrol of these pests.

CONSERVATTON

s e v e r a l f o r r n s o f c o n s e r v a t i o n a r e p o s s i b l e f o r M .c r o c e i p e s : ( 1 ) u s i n g c u l t u r a l p r a c t i c e s , e s p e c i a l l y w e e dcont roL , w i th min inum impact on l , { . c roce ipes , (2 ) app ly ingi n s e c t i c i d e s l e a s t t o x i c t o M . c r o c e i p e s , ( 3 ) a p p l y i n ginsec t ic ides on ly s rhen sampled Eg! jg ! -b ; !s - spp . dens i tyexceeds the econorn ic th resho ld , and (4 ) us ing [ . c roce ipesdensity and potential inpact of i t and other natural enemiesi n d e c i d i n g h r h e t h e r t o a p p l y a n i n s e c t i c i d e . C o n c e r n i n gc u l t u r a l p r a c t i c e s , s t a d e l b a c h e r ( 1 9 8 L ) h a s r e c o m m e n d e ddestruction of non-crop hosts plants in the spring to reduceH e l i o t h i s s p p . n u m b e r s i n c r o p s l a t e r i n t h e s e a s o n .Ho l tever , th is p rac t ice cou ld a lso reduce the dens i ty o f U .c r o c e i p e s a n d o t h e r n a t u r a l e n e n i e s . w h e t h e r t h e i n p a c ton Heliothis spp. of noncrop host plant destruction is vtorththe loss o f na tura l enemies depends on the re la t i ve inpac ton Heliot,his spp. and natural enerny populations in subsequentgenerations and on the irnportance of Heliothis spp. rnortal i tyfron natural enemies.

A s w i t h s o m e o t h e r p r e d a t o r s a n d p a r a s i t o i d s , M .c r o c e i p e s i s r e l a t i v e l y t o l e r a n t o f p y r e t h r o i d s a n dcarbamates and in to le ran t o f o rganophosphates (Powel l andScott 1986), rrhich suggests use of pyrethroids and carbamatesr a t h e r t h a n o r g a n o p h o s p a t e s t o c o n s e r v e t h i s a n d o t h e r

9 6

n a t u r a l e n e m i e s . H o n e v e r , u s i n g p y r e t h o i d s c o u l d m e a n aconf l i c t w i th res is tance management : sorne researchers a ren o w r e c o m n e n d i n g u s e o f o r g a n o p h o s p h a t e s i n e a r l y s e a s o nand reduced use o f pyre thro ids to p revent deve lopment o fpyrethroid resistance in Heliothis spp.

S o m e g r o w e r s a n d c o n s u l t a n t s a l r e a d y s a m p l e p e s td e n s i t i e s a n d u s e e c o n o n i c t h r e s h o l d s . F u r t h e r m o r e ,H a r t s t a c k e t a l . ( 1 9 7 6 ' ) , B r o w n e t a l . ( 1 9 8 3 ) , a n d H o p p e rand Stark (1987) deve loped mode ls fo r use in He l io th is spp.m a n a g e m e n t t h a t i n c l u d e t h e i n p a c t o f n a t u r a l e n e m i e s .H o w e v e r , a g r e a t p r o b l e m w i t h a n y e x p l i c j - t u s e o f M .croceipes in decisions about Heliothis spp. management l ieswith the dif f iculty of sarnpl ing parasitoid density. Rearingh o s t l a r v a e u n t i l p a r a s i t o i d s e m e r g e t a k e s t o o l o n g f o rshor t - te rm dec is ions t d issec t ion is too labor in tens ive andr e q u i r e s t o o n u c h e x p e r t i s e ; a n d a d u l t s a r e d i f f i c u l t t os a m p l e w i t h c o n v e n t i o n a l t e c h n i q u e s ( e . 9 . w h o l e p l a n texaminat ions , suc t ion co l lec to rs ) . Beyond us ing re la t i ve lynon- tox ic insec t ic ides and economic th resho lds , improvedconservation of M. croceipes for control of Heliothis spp.at this point does not look prornising.

AT'GII{ENTATION

T h r e e f o r m s o f a u g r n e n t a t i o n a r e l i k e l y f o r M .c r o c e i p e s : i n u n d a t i v e r e l e a s e s , i n o c u l a t i v e r e l e a s e s , a n dnursery crops.

I n u n d a t i v e r e l e a s e s . N o p a r a s i t o j " d r e p r o d u c t i o n i sa s s u m e d f o r i n u n d a t i v e r e l e a s e s . T h u s t h e y a r e l i k eapp l ica t ions o f se lec t j . ve insec t ic ides and are assoc ia tedmore w i th reduc ing danage by the hos t popu la t ion presentat release than with suppressing host density in subseguentg e n e r a t i o n s . l t . c r o c e i p e s r e d u c e s d a m a g e t o c o t t o n b yr e d u c i n g t h e f e e d i n g r a t e o f p a r a s i t i z e d H e l i o t h i s s p p .l a r v a e , a l t h o u g h p a r a s i t i z a t i o n d o e s n o t r e d u c e t h e t i r n etha t hos t la rvae spend on the hos t p lan t (Hopper and K ingL 9 8 4 b ) . I t i s u n k n o w n w h e t h e r p a r a s i t i z e d l a r v a e s u f f e rh igher o r lower nor ta l i t y than unparas i t i zed la rvae in thef i e l d , b u t C h r v s o p e r l a c a r n e a ( S t e p h e n s ) d o e s n o t p r e f e re i t h e r t y p e o f l - a r v a i n f i e l d c a g e e x p e r i m e n t s o n c o t t o n(Stark and Hopper 1988) .

I n t r a g e n e r a t i o n m o d e l s c a n b e u s e d t o p r e d i c t t h eirnpact of inundatj.ve releases. Applying data frorn field cagee x p e r i m e n t s o n h o s t i n s t a r p r e f e r e n c e s , H o p p e r a n d K i n g( 1984a) descr ibed a s imp le node l o f the re la t ion be th teent h e d e n s i t y o f f e n a l e p a r a s i t o i d s , h o s t i n s t a r , a n d t h ep r o p o r t i o n o f h o s t s p a r a s i t i z e d . T h e y u s e d a m o d i f i e dversion of the search model proposed by Nicholson and Bailey( L 9 3 5 ) i

jx i /ni : 1 - exP (-P. : a1T1) ( 1 ) ,

where l f l i s t he dens i t y o f pa ras i t i zed hos ts , 8 .1 i s t hedensi ty 'o f unparasi t ized hosts, P is the densi ty of feura leparasi to ids, a{ is the search rate (area/ t ine) per femaleparasitoid for host larvae in instar l, and T1 is developnentL ine for host instar i . An inpor tant assu:mpt ion of th is

9 7

model i s tha t the propor t ion o f hos ts paras i t i zed per fe rna lep a r a s i t o i d i s i n d e p e n d e n t o f h o s t d e n s i t y , a n d H o p p e r a n dK i n g ( l - 9 8 6 ) d e m o n s t r a t e d t h i s i n d e p e n d e n c e i n f i e l d c a g ee x p e r i m e n t s ( F i g . l - ) . T h i s m o d e l p r e d i c t s e t e l l t h ep r o p o r t i o n o f h o s t s p a r a s i t i z e d v s . h o s t i n s t a r , g i v e n a ne s t i m a t e o f f e m a l e p a r a s i t o i d d e n s i t y ( F i g . 2 , H o p p e r a n dK i n g L 9 8 4 a ) .

l 0

=d 8a

tL!')<

ri-- 1

GLrlm z2=z.

z I 6 I t 0

NUMBER AVAILABLE ( /SO. M)

F I G . 1 . D e n s i t y o f H . z e a a n d H . v i r e s c e n s l a r v a ep a r a s i t i z e d b y M . c r o c e i p e s v e r s u s d e n s i t y o f l a r v a ea v a i l a b l e . E a c h p o i n t r e p r e s e n t s a t l e a s t o n e c a g e dp o p u l a t i o n . L i n e i s l e a s t - s q u a r e s r e g r e s s i o n ( f r o r n H o p p e ra n d K i n g 1 9 8 6 ) .

w i th th is mode l , one can pred ic t the i rnpac t o f var iousdens i t ies o f M. c roce ipes on the propor t ion o f He l io th is spp.l a r v a e p a r a s i t i z e d a t e a c h i n s t a r ( F i g . 3 , H o p p e r a n d K i n g1 9 8 4 a ) . T h i s p r e d i c t i o n c a n b e c o n b i n e d w i t h d a t a o n t h eef fec t o f paras i t i za t ion on feed ing to p red ic t the darnage toa c rop :

6 6D =

. X D p i N i + . : D , ' 1 ( H 1 - N 1 )i= f i= l

( 2 ) ,

w h e r e D i s t o t a l d a m a g e r a t e ( n u m b e r o r b i c - m a s s o f f r u i td a m a g e d p e r u n i t t i r n e ) , D ^ { i s t h e d a m a g e b y p a r a s i t i z e dh o s t s i n i n s t a r i , N i i s t h - e - d e n s i t y o f p a r a s i t i z e d h o s t s ,P u i i = t h e d a m a g e b y - u n p a r a s i t i z e d h o s t i n i n s t a r i , a n d H 1i s t h e d e n s i t y o f h o s t s i n i n s t a r i . H o p p e r a n l S t a r k ( l - 9 8 7 tused these components in a dec is ion mode l fo r He l io th is spp.nanagement, in cotton.

A prob le rn w i th th is fo rmula t ion o f M. c roce ipes i rnpac ton He l io th is spp. i s tha t the paras i to id and hos t a re assurnedt o b e r a n d o n l y d i s t r i b u t e d i n t h e f i e l d . I n f i e l d

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0 . 6

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H O S T I N S T A R

f I G . 2 . M . c r o c e i p e s p a r a s i t i z a t i o ni n s t a r ( I i n e ) p r e d i c t e d u s i n g e q u a t i o nd a t a ( b a r s ) r e p o r t e d b y M u e l l e r a n dHopper and K ing L984a) .

versus He l io th is spp.l" compared with f ield

P h i I I i p s ( 1 9 8 3 ) ( f r o m

0 . 8

3

H O S T I N S T A R

F I G . 3 . P r e d i c t e d p a r a s i t i z a t i o n b y M . c r o c e i p e s v e r s u sHel io th is spp. ins ta r fo r var ious dens i t ies o f fena le nasps(number /ha) ( f ron Hopper and K ing 1984a) .

T

z

o 0 . 6utN

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t o .oIL

zotr5 o . ,otr(L

o

9 9

exper iments w i th f ree- rang ing \ tasps female ' M- ' .g roce lpesagjregated in areas of high

-host aeniity, although the search

-' iL" -p"r

female parasitold was independent of host density

lunpu ' f t i shed da ia ) . The nex t s tep in - deve- Io -p ] t9 . t mode l

i o r ' i n u n d a t i v e , i n t r a g e n e r a t i o n c o n t r o l o f H e l i g t h i s s p p '

ly U.. croceipes hrould 6e to incorporate spatial distributiono i nos t ana paras i to id . Be low, I descr ibe one apProach to

i n c o r p o r a t l n g s p a t i a l d i s t r i b u t i o n i n a m o d e l f o r

inocul i t ive, in€ergLneration control of Heliothis spp. by M'croceipes.

lnocu la t i ve re leases and Nurserv Crops . A f requentprobleur with biotogical control of insect pests is that pestpopulat ions often increase to high densit ies before naturale n L r n y d e n s i t i e s r e a c h s u f f i c i e n t l e v e I s f o r c o n t r o l .tnocu la t i ve re leases , h lh ich un l i ke inundat ive re leases doassume parasitoid reproduction in the f ield, are intended tosolve this probfern by start ing parasitoid populat ions r^Ihenand where needed in suff icient numbers to keep up with hostpopu la t ions . such re leases are assoc ia ted more o f ten w i thluppress ing the hos t popu la t ion in subsequent genera t ionsthan with reducing damage by the host population in the fielda t the t ime o f re lease. Th is tac t i c i s c lose ly re la ted tot h e u s e o f n u r s e r y h o s t p l a n t s t o p r o v i d e r e s e r v o i r s o fparasitoids: nursery plants provide an insectary in the f ieldfrom which parasitoids can disperse to attack host larvae.

Intergeneration models are needed to predict the irnpacto f b o t h i n o c u l a t i v e r e l e a s e s a n d n u r s e r y c r o p s . H e r e , Idescribe simulat ions of augnentation with several nodels ofin te rgenera t ion dynamics o f E . v i rescens and U. c roce ipes( T h e n o d e l s a l s o a p p l y t o H . z e a . , I d i s c u s s ( 1 ) a n o d e lhr i thout d i .spersa l be tween subpopu la t ions , (2 ) node ls v i thv a r i o u s L e v e l s o f d e n s i t y - i n d e p e n d e n t d i s p e r s a l b e t w e e ns u b p o p u l a t i o n s , ( 3 ) a m o d e l w i t h d i s p e r s a l b e t w e e nsubpopuJ-ations in which parasitoid dispersal depends on hostd e n s i t y , a n d ( 4 ) a m o d e l w i t h d i s p e r s a l b e t w e e nsubpopulat ions, density-dependent parasitoid dispersal, andd e n s i t y - d e p e n d e n t h o s t m o r t a l i t y f r o m o t h e r c a u s e s . T h ep e r i o d s i r n u l a t e d r / a s o n e s e a s o n , r t h i c h i s f i v e H e l i o t h i sspp. genera t ions in Miss iss ipp i .

T h e g o a l s w e r e t o e x p l o r e t h e p o s s i b l e r e s u l t s o finoculative releases and to find where further research hrouldmost inprove such releases. I report simulated trajectorieso f h o s t d e n s i t y a n d p r o p o r t i o n o f h o s t l a r v a e p a r a s i t i z e db e c a u s e t h e s e a r e f r e q u e n t l y r n e a s u r e d a n d m o s t r e a d i l ycompared with experi-ence.

Mode l w i th No D ispersa l be tween Subpopu la t ions . Theequations for dynamics of host and parasitoid were:

-aPtHte ( 3 ) ,

( 4 ) ,

( s ) ,

( 6 ) ,

Ht+t7z =

-aPtPt+t1z = sHt( l -e )

-aP

Ht+L = r1t+t12e t+L/2

-aPE+r/2Pt+l - = sHg*r72(1-e )

1 0 0

yhefe Hg is . the dens i ty o f hos t la rvae a t the beg inn ing o fnosE genera t lon t , .E iL+L/2 is the dens i ty o f hos t la rvae a tthe nidpoint of host lef i6iat ion t, pe is Lhe densitv of adultf e m a l e p a r a s i t o i d s . a t t h e b e g i n n i r i g o f h o s t g e n & a t i o n t ,P l + t / , 1 s t h e d e n s i t y o f a d u l t f e m a l e p a r a s i t o i d s a t t h enrqp 'o rn t o f hos t genera t ion t . a i s the area searched perfernale. parasitoid during her l i fet ime, s is the proport io; ofp a r a s i t i z e d l a r v a e t h a t p r o d u c e a d u l t f e r n a l e p a ' r a s i t o i d s( thus i t combines surv iva l and sex ra t io ) , and r i s the hos trate of increase per generation in the absence of parasit ismby ! ! . . c roce ipes . The te r rn e rp( -ap+) i s the prop-or t ion o fhos ts escap ing paras i t i sm, and the te rm t -exp1-an* ) i s thepropor t ion o f hos ts paras i t i zed a t reas t once-1 i l t i ch81son andB a i r e y l - 9 3 5 , R o y a r n a 1 - 9 7 1 ) . r n t h e r e s u r t s o i s i m u l a t i o n sr e p o r t e d h e r e , t h e h o s t d e n s i t i e s a r e E + d r t d H + r r l , f r o mequat ions 3 and 5 and the propor t ions o f hos ts p?- . ' J r ' i t i " "dare 1--exp1-aPg) and l-ex-p(-apg.a172) from equationJ a and 6.. t l . c rocerpes c teve lops th r iCe as fas t as He l io th is spp.(Nadgauda and P i t re l_983, Jones and Lewis t -SZf , nopper anaK 1 . S 1 9 8 4 a ) , a n d a s y n c h r o n y o f H e l i o t h i s s p p . d e v i l o p r n e n twithin a generation means ttrat M. steqeipesi idutts ern6rgingfrom a generation of host larvae-can atEEEk-that generationlT h e r e f o r e , I a s s u m e d t w o p a r a s i t o i d g e n e r a t i o n J p e r h o s tgeneration. I used host generation as the t ime unit.

The search . ra te p .e r fena le M.^ c roce ipes measured inf ie ld cage exper i rnents i s about f rnZZaaV tUopper and K ingL986) , and the nea.n longev i ty o f adu l t fe rna le -M. c roce ipe iin the laboratory is 28 days lnopper r.986). assuninl fernaleil i v e a b o u t L / 3 X o L / 2 a s 1 o n 9 i n t h e f i e l d a s i n t h eIabora tory , I used. a search area (a ) o f 10 n2 ( : t fn27aay11fO9 . y " 1 ) . M . c r o c e i p e s f e r n a l e s p r e f e r t o p a r a s i t i i e t h i r a linstar larvae (Hopper and King l_-984a), and Hogg and Nordhefun( l -983) found tha t about 60A o f He l io t .h is spp. Ia rvae wh ichreached the end of the third instar survived to sixth instari n t h e f i e l d ( i . e . e s s e n t i a l l y t o p u p a t i _ o n ) . I a s s u m e dthat M. c roce ipes la rvae in H. v i rescens la rvae surv ive a tthis rate. Pupal survival for l t . SlgSgipeg in laboratorye x p e r i n e n t s v l r i e s b e t w e e n O . S s a n a l l g F a e p e n d i n g o n t h eh o s t i n s t a r p a r a s i t i z e d ( H o p p e r 1 9 8 6 ) . T h e s e x r i t i o h . =b e e n 1 : L i n t h e c o l o n i e s a t S t o n e v i l l e a n d i n f i e l dcol lect ions of parasit ized rarvae. putt ing these paramet,erst o g e t h e r , I u s e d s = 0 . 2 ( = t 0 . 5 1 t O . 7 5 l t O . 5 l )

The rate of increase of the H. virescens populat ior int h e , a b s e n c e o f M . c r o c e i p e s ( r ) i s t h e r n o s t

- a i t f i c u l t t o

e s t i m a t e o f t h e s e p a r a r n e t e r s . ' f t d e p e n d s o n n a t a l i t y a n dnortal i ty of Helipthis spp. in the f ield, which are l ike1y tobe h igh ly var iab le and fo r wh ich there are few es t ina tes .He l io th is spp. na ta l i t y var ies w i th spec ies , agef d ie t , andternperature (Lukefahr and Mart in 1954, Frostrotd 6t 'al . Lgt2,N a d g a u d a a n d p i t r e L 9 8 3 , T o l l e f s o n a n d W a t s o n 1 9 8 1 - l .However, 10O eggslday appears an adequate approximation fort h e m o d e l s p r e s e n t e d h e r e . S n o h r e t a t . ( l - 9 5 9 ) r e p o r Enor ta r i t y o f adur t no ths tha t ind ica tes a su iv iva i ra te o fO.5 /Aay . , assuming cons tan t rnor ta l i t y . Las ter e t a I . ( j .gg- i )r e p o r t a d u l t n a l e s u r v i v a t r J t e s i n t h e f i e l d o ; "0 . 8 3 - 0 . 8 7 / d a y . w i t h t h e s e v a l u e s , e a c h f e m a r e n o t h w o u r dl a y . a l . a v e r a g e o f 2 0 0 - 7 6 9 e g g s o v e r h e r l i f e t i r n e . I fn o r t a l i t y d u r i n g t h e p e r i o d f r o m o v i p o s i l i ; ; - ; ; a d u l t

1 0 1

ec los ion were 95 -99 t and the sex ra t i o \ t e re 1 : l - ' t he ra te

o f i nc rease wou ld be 5 - fo ld pe r gene ra t i on ' These va lues

for juveni re nor tar i ty . t " 1 i : , 'o t labre g iven,egg-.ar :d rarvalmort -a l i ty observed i . i t t re f ie ld (4oSS an-d Nordhein 1983) '

Therefore-, I used r=5 in the sinulations below'Heliothis tp;. i;;ai a"n"it i"" ringe f r9n p Eo 4o/m2

on sprT6f-I-o"t f,r i" i, in rhe detta region o-f..Mississippi

lsta-aefUicher rg-at and stadelbacher et .aI-'^ 199a)-: -Holtlever'most of ten densi t ies 1 ie between o.a and Lo/mz so I used an

in i t i a l hos t dens i t y o f 5 l a r vae /n2 . Las te r e t a1 . (1987 )

found tha t 5 .7 t ; i 43 o r " t r i n te r i ng H ' v i r escens .ene rgedpe r ha o f l and a rea . I f 160 hos t l a r vae /ha su rv i ved the

ii"t.t, ="* i i t i" for IrI . croceipes \tere .l-:L' -and about half

in" - o.tit,ointering hosf larvae ltere. parasitized,, ld"lt fernale

p"t""i i" iJ dlnsitf would be loo/ha in sprirrg, which is what I

irsed for the ini€ial parasitoid density'In the del ta r :egion of u iss iss ippi , host p lant area

increases greatly irot-the first neliothis spp' -ge-neration'r-ni.tt- i" oi spriirq tron"rop pfants, to tne second Heliothis;n; . : gen" iat ion, which i i

-on summer crop p lants ' thus the

nirirber-ot insects per unit area of suitable habitat decreases

d ra rna t i ca l l y ( s t ; de lbache r e t a1 . L984 ) ' I . assumed hos t

;i;;t n"-u-ilii ].ncreasea 20-fo1d between the firsr and secondffeliothis sPP. generations.

Sufpo@ese paraneter est imates, in i t ia lA;eIEGns, and equat ions 3-6, s imulat ion of 5 H' v i rescens

; ; ; ; ; ; t i ; t i " y i " rd"d the sol id-r ine t ra jector ies for hostdensity and p-roportion of hosts parasitized in Fig' 4' Thei i i j " 6 t " r y o f h o s t d e n s i t y m i m i c s r e a s o n a b l y w e L l t h edyni rn ics of H. v i rescens i -n t t re f ie ld. The precip i touse;;i i ;" rrornJirs-I-E6 second generation resul-ted fron theincrease in host ptant habita€, not fro4 para-s-i^t. isn' The

i ; " ; i h gene ra t i on dens i t y o f . 4 l a r vae /m2 (40 ,000 /ha ) f a l l s

in the iange found in t f re f ie ld, a l though- i t considerablyexceeds 5odo/ha, a f requent ly used econonic threshold for

ieiiotnis spi. l-n cott6n. rne decline from fourth to fifthg"ndatio" i isufiea from the high level of parasitisn (Fig'

ifj.- S""tt declines are sometirneJ observed, but they probablyrarely result from parasitisrn alone.

Aug rnen t i ng p -a ras i t o i d dens i t i es t o 1o0o fena les /ha(P (0 ) =

-o . r ) gav i t he do t ted - l i ne t r a j ec to - r i e -1 i n F ig - ' 4 '

i n ' t f r i s s i n i u l a t i on , f i r s t gene ra t i on f ema le M . c roce ipesparlsit ized such a high proportion of f irst generation hosts

i;;;-f;; E. -ysesssE.-

poprtration did not exceed the economic

threshold inFo€Ton-to.s inz1 by the end of the season' Thepa ras i t o i d popu la t i on a l so ' f a i l ea t o recove r , as shon tn by

the Iow l eve l s o i pa ias i t i s rn a f t e r t he f i r s t gene ra t i on .

n i in""eh th is resr i l t is encouraging qqr the prospects .ofiulrnentlt ion, this model tends to-let the parasitoids drive

t h e h o s t t o v e i y 1 o w l e v e l s t h r o u g h h i g h l e v e l s o fparasitism. This inay fe because the rnodel is overty sinple;i o p i .C i "u la r , 11 r i c r s d i spe r . sa r and dens i t y -dependen tp r o c e s s e s , s u c h a s p a r l a s i t o i d a g g r e g a t - i o n a n d

Sensity-aepenaeni-nottirity from other causes' Berow r rr'irl

add each of tnese f'tr"nor"tri to test the effects on simulated

augrentation. I n s . Ioccuredassumea that the popufat ions of host and

L U L

1 . 5

P ( 0 ) - 0 . 0 1

P ( D - 0 . 1

2 ? 1 5 -

HOST GENERATION

3 1.:6 3 .s

3

= z.sUI

A zoF 1 . 5UIA r-,

0 . 5

E

H 0 . 8F

6f o .E(L

zg 0 . 1FaEL

P o-2L

FIG. 4. Sinru lated host densi ty (A) and proport ion of hostsparasitizgd (B) versus host gener'ation as-sunlng no dispersalo r . d ^ e n s i t y d e p e n d e n c e . p ( b 1 = 9 . 0 1 a n d p ( O ) = O . t i n d i c a t ein i t ia l parasi to id densi t ies of O.OI/m2 and 6. t /m2

103

in a 4ox4o km area, divided into subpopulat ions in cel ls L krn

on a siae, and tnat interactions be€ween host and parasitoid

occured within each subpopulat ion according to equations 3-6'

This system size ana sfadial subdivision are reasonable given

a i " p " . ! " f d i s t a n c e s o - t t t e l i o t h i s s p p ' ( ! 1 o n e t a I ' L 9 6 9 '

H e n ' d r i c k s e t a l . L g 7 3 , I { a i l e e t a 1 ' r g z s , S p a r k s e t a I '

L g 7 5 , s p a r k s L g 7 9 , H a r t s t a c k a n d W i t z L 9 8 1 ) a n d a n d M '

croceipes (unPublished data)--Dr=pdr=ir bethreen subpopulations can be rnodeled in rnany

vrays. fo'r sirnpl ici ty ' I aslumed that rnoths disperse between

; ; ; ; " p n r . t i o i t . o n c e p e r g e n e r a t i o n a n d o v i p o s i t a f t e r

ai=p^Lrl i"g and that r.=^ps disperse twice per host_generation

i"-a-pir"" i t ize after ais^persi irq. T\to extrenes of dispersal

; ; ; ' p " s s i b r e

u n d e r t h e s e a s s u r n p t i o n s : . s t e p p i n g - s t o n e

d ispe- rsa l where d ispersers can on l t move to ad jacent ce l l s '

an-a- isr"na aispeisai lrhere disperseis can move to any cerl in

i ; ; ; t J " ; w i€n equar p robab i l i t y , no ma. t te r .h .ow f a r f rom

i n e l - r s t a r t i n g c e i t . - B e l o w ,

I i e p o r t s i n u l a t i o n s o f f o u r

' " a " r s o f d i s - p e r s a l i n v o l v i n g v a r i o u s c o m b i n a t i o n s o f.t"ppi-t tg-stone and island disperslt , but f i rst I describe how

tneie forrns of dispersal were represented'ro i s tepp in i -s tone, dens i ty - indep.endent d ispersa l o f

host and p...si toi ls ' I used these equations for novernent:

H ( x , y ) = t H ( x - L , y ) + H ( x + L ' y ) + H ( x ' y - L ) + H ( x , y + 1 ) ) / 4 ( 7 ) '

P ( x , y ) = [ P ( x - 1 , y ) + P ( x + ] - ' y ) + P ( x ' y - 1 ) + P ( x , y + L ) l / 4 ( 8 ) '

where H(xrY) and P(xry ) a re the dens i ty o f hos t la rvae

and adult fernale'paiasitoid!-, respectively, in subpopulat ion

;;t " i iat dispers^al. Host and pJrasitoids dispersing beyond

tn-e foraers oi the system were considered lost'For dens i ty - in lependent , i s land d ispersa l o f hos ts and

parasitoids, I uied these equations for movement:

H ( x , y ) : R ( x , Y )

P ( x , y ) = R ( x ' Y )

K I: ti j

k 1t ti j

H ( i , i ) / n

P ( i , 1 ) / n

( 9 ) ,

( 1 0 ) '

l r h e r e R ( x r Y ) i s a r a n d o m n u m b e r b e t w e e n 0 a n d 2 c h o s e n

inaepena"ntiy for each subpopulation (with the condition that

[n" ir"^ler of dispersers is- l irnited to the number availableto d i spe rse ) ; r 1 i a61 and I (=40 ) a re t he d inens ions o f t he

"v" i " . ; and n is ' the number of subpopulat ions in the systen

( = 1 6 o 0 ) .6 i r n u l a t i o n s w i t h M o d e l s w i t h D i s p e r s a l - b e t v r e e n

sulpoiu lEt ions. r used the same paralet .e-rs and the same

mern init ial densities of host and parasitoid as in the model

without dispersaitJt"".t subpopul;t ions' r distributed the

i i .= l - i "a pa^rasi - to ids across subpoputat ions at the star t o f

; ; ; h ; i t . i t a t i on -u ; i n t

r andon i a i ues d rawn f rom a un i ro rm

d :s t r i bu t i on f e twee -n -o

ana tw i ce t he mean dens i t y ' S ince

island dispersal nade the rnodel stochastic' I repeatedly ran

; ; ; ; ; t d ; i w i t h i ; i ; " d d i spe rsa ' r t o t es t f o r d i f f e rences

between runs ' Th;h; ; ' d t "Si tv for the whore svstem ( i 'e '

1 0 4

averaged across subpopulat ions) dif fered l i t t le between runs( F i S . 5 ) . T h e r e f o r e , b e l o w I r e p o r t t h e r e s u l t s o f o n erepresentative run for each simulat ion.

When the in i t ia l paras i to id dens i ty was o .oL /nz , thet r a j e c t o r i e s f o r h o s t d e n s i t y ( a v e r a g e d a c r o s ssubpopulat ions) with island dispersal for host and parasitoidd id no t d i f fe r much f ro rn those w i thout d ispersa l (cornpareF i g . 4 a a n d 5 a ) . H o \ d e v e r , w h e n p a r a s i t o i d d e n s i t y - w a saugrnented to 0 .L /m2, the behav io r was very d i f fe ren t f romthat without dispersal (cornpare Fig. 4a and 5b).

F i g . 5 s h o w s s i m u l a t e d t r a j e c t o r i e s o f h o s t d e n s i t ya n d p r o p o r t i o n o f h o s t s p a r a s i t i z e d ( b o t h a v e r a g e d a c r o s ssubpopu la t ions) fo r augrnented paras i to id dens i ty (p (o) :0 .1 )w i th (1 - ) no d ispersa l , (2 ) s tepp ing-s tone d ispersa l fo r hos tand paras i to id , (3 ) i s land d ispersa l fo r hos t and s tepp ing-s tone d ispersa l fo r paras i to id , and (4 ) i s land d ispersa l fo rbo th spec ies . The increase in hos t dens i ty f ro rn t ra jec to ry1 to 4 in the fourth and f i f th host generation indicate thata d d i n g d i s p e r s a l t o t h e m o d e l d e c r e a s e d t h e i r n p a c t o f M .c r o c e i p e s o n H . v i r e s c e n s . F u r t h e r m o r e , t h e g r e a t e r t h ed i s p e r s a l , w h e t h e r i t w a s o f h o s t o r p a r a s i t o i d , t h e l e s sthe parasitoid inpact on host dynarnics. Host density exceedseconon ic th resho ld in genera t ion f i ve w i th s tepp ing-s tonedispersal for one or both species and in generation four withi s l a n d d i s p e r s a l f o r b o t h s p e c i e s . T h e r e a s o n f o r t h i se f fec t o f d ispersa l was tha t augmenta t ion succeeded in themodel without dispersal by driving host density so low thati t did not recover by the end of the season. In models withdensity- independent dispersal, the host had refuges with 1owor zero parasitoid density frorn which moths could recolonizeareas where the parasitoids had driven thern to low density.

S i n c e b o t h h o s t s a n d p a r a s i t o i d s d i s p e r s e di n d e p e n d e n t t y i n t h e s e m o d e l s , t h e p a r a s i t o i d s c o u l d n o td i f f e r e n t i a l l y e x p l o i t a r e a s v r h e r e h o s t d e n s i t y w a s h i g h .However , as po in ted ou t above, f ie ld exper iments show tha tM . c r o c e i p e s a g g r e q a t e s i n a r e a s o f h i g h h o s t d e n s i t y .There fore , I added paras i to id aggregat ion to a node l w i thi s l a n d d i s p e r s a l t o t e s t v r h e t h e r s u c h a g g r e g a t i o nc o u l d c o u n t e r a c t t h e e f f e c t s o f d i s p e r s a l .

M o d e l w i t h D e n s i t v - D e p e n d e n t P a r a s i t o i d D i s p e r s a l .In this model-, parasi-toids dispersed into a subpopulat ion inp r o p o r t i o n t o t h e r e l a t i v e h o s t d e n s i t y i n t h a tsubpopulat ion. Thus parasitoid abundance after dispersal wasg iven by :

P ( x , y ) P ( i , j ) I H ( x , y ) / H ( i , i ) ( 1 1 ) ,k 1t ti j

k l= [ : t

i j

t there the var iab les are as descr ibed above. Such a per fec tresponse to hos t dens i ty i s un l i ke ly g iven tha t paras i to idsw o u l - d n o t h a v e c o m p l e t e k n o w l e d g e o f h o s t d i s t r i b u t i o n .H o w e v e r , w i t h o u t a f i r r n e r u n d e r s t a n d i n g o f p a r a s i t o i da g g r e g a t i o n , t h i s n o d e l s e r v e s a s a l i m i t i n g c a s e . I u s e dis land d ispersa l fo r the hos t and equat ions 3-6 to descr ibeinteractj .ons within a subpopulat ion.

Simulation with Model with Densitv-Dependent ParasitoidDispersa l . Aga in , I used the sane parameters and the samemean init ial densit ies of host and parasitoid as in the model

1 0 5

-c i 1It

F

tnz.l J 2t:t

F(.rI

E r

-d 1U'

F

UIz.ttJ 2u

F1n

? ,

I z ? {HOST GENERATION

F I G . 5 . R e p e a t e d s i m u l a t i o n s o f h o s t d e n s i t y v e r s u s h o s tg e n e r a t i o n a s s u m i n g i s l a n d d i s p e r s a l . b u t n o d e n . s i t yd e p e n d e n c e . ( A ) i n i t i a l p a r a s i t o i d d e n s i t y = o . o 1 , / n z a n d(B) in i t ia l paras i to id dens i ty = o -L /mz-

1.06

5

{ . 5

{

3 . 5

3

? . 5

2

1 . 5

I

0 . 5

0

I

0 . 8

0 . 8

0 . f

0 . 2

0

3 f

HOST GENERATION

F I G . 6 . S i r n u l a t e d h o s t d e n s i t y ( A ) a n d p r o p o r t i o n o f h o s t sp a r a s i t i z e d ( B ) v e r s u s h o s t g e n e r a t i - o n f o r v a r i o u sa s s u m p t i o n s c o n c e r i n g d i s p e r s a l : ( L ) n o d i s p e r s a l , ( 2 )s tepp ing-s tone d ispersa l fo r hos t and paras i to id , (3 ) i s landd i s p e r s a l f o r h o s t a n d s t e p p i n g - s t o n e d i s p e r s a l f o rp a r a s i t o i d , ( 4 ) i s l a n d d i s p e r s a l f o r h o s t a n d p a r a s i t o i d .In i t ia l paras i to id dens i ty = 0 .L /mz.

-C]LT'

F

tnz.tr.loFU'Cf

cltrlN

F

UI

(ro-z.ctF(Ecl(Lo&.o-

L O 7

w i t h o u t d i s p e r s a l b e t w e e n s u b p o p u l a t i o n s ' A g a i n , I

d i s t r i b u t e a t n e h o s t a n d p a r a s i t o i d s a c r o s s

subpopulat ions at the start of each simulat ion using random

valuet drawn from a uniform distribution between 0 and twice

the mean density.si-mulated trajectories of host density and proport ion

of hosts parasit ize-a l lottr averaged across subpopulat ions)w i t h t h i J m o d e l ( F i 9 . 7 ) r e s e m b l e d t r a j e c t o r i e s f r o r n t h emodel with no dispersl l (Fig. 4). The refuge from parasit isnf o u n d w i t h d e n s i t y - i n a e p e n d e n t , i s l a n d d i s p e r s a l w a s n oI o n g e r a v a i l a b l e , s o t h e p a r a s i t o i d s a g a i n . r e d u c e d h o s tdens i t ies to 10w leve ls . There r i re re two na in d i f fe rencesb e t w e e n t h e s i r n u l a t i o n s w i t h n o d e l s w i t h n o p a r a s i t o i d

d ispersa l and w i th dens i ty -dependent paras i to id d ispersa l 'r i r s t , d e n s i t y - d e p e n d e n t d i s p e r s a l p r e v e n t e d t h e h o s tpopulation frorn incieasing so rapidty when parasitoid densityw a s l o w , i . e . t h e p a r a s i t o i d s h r e r e m o r e e f f i c i e n t a tp revent ing an ou tbre lk . Second, d ispersa l -p revented h ighd e n s i t y p a r a s i t o i d p o p u l a t i o n s f r o m d r i v i n g t h e h o s tpopu la t ion to such low leve ls tha t i t cou ld no t recover a ta l I b e f o r e t h e e n d o f t h e s e a s o n .

Model with Densitv-Dependent Host Mortalitv fron otherC a u s e s . A s W a n g a n d G u t i e r r e z ( L 9 8 0 ) , M a y e t a l . ( l - 9 8 L ) ,laay ana Hassell (L988) have pointed out, the relat ive t imingo f d e n s i t y - d e p e n d e n t p r o c e s s e s i n a n i n s e c t r s l i f e - c y c 1 ecan greatly af iect the irnpact of a natural enemy. To testwhether density-dependent mortal i ty frorn causes other thanp a r a s i t i z a t i o n b y M . c r o c e i D e s a f f e c t e d s i m u l a t e da u g m e n t a t i o n . I I n o d i f i e d e q u a t i o n s 3 - 5 . F o r h o s tsubpopu la t ion dynarn ics w i th dens i ty -dependent nor ta l i t ybefore parasit izat ion, I used the fol lowing equations:

-aPtHt+tyz : Ht(1-Ht,/c)e

-aPt+L/zHr+j . = G/ (L-L/c))Ht+t /ze

\ there c i s the nax imum nunber o f hos t la rvae tha t can besupported per unit area of host p1ant. The other variablesand parameters were as described previously. The equationsfor parasitoid dynarnics remained unchanged with this rnodel.

F o r d y n a m i c s o f h o s t a n d p a r a s i t o i d w i t h n o r t a l i t yafter parasit izat ion, I used the fol lowing equations:

-aPt -aPtH t + t y z = H g ( l - H g [ 1 + ( l - e ) ) / c ) e

-lP+ -aP+

P t + r 1 z - = H r ( L - H g t L + ( L - e -

) l / c ) ( 1 - e - )

- -aPt+ t12 . - . -aPt+ t /z

na*1: G/ Q-L/ c, I Ht+t/ zQ-tra:r17 21 1+ ( l-e ) I / e) e

Ht+yz l1+(1- - iP t+1 /2 ) l / c ) ( r . ;aPt+L/2 ,

where the parameters and variables were as described above.

(12) ,

( 1 3 ) '

ToU'

3

FHU'zr ! 2

FU'o

I

IUNHFHa

zoH

F.

oo

o

1 . 0

0 . 8

0 . 6

0 . 4

o . 2

0

A

P ( 0 ) - 0 . 0 1

P ( o ) - o . L , , '

B

P ( o ) - o . o l

P ( o ) - 0 . 1

HOST GENEFATION

F I G . ? . S i m u l a t e d h o s t d e n s i t y v e r s u s h o s t g e n e r a t i o na s s u m i n g i s l a n d d i s p e r s a l a n d p a r a s i t o i d a g g r e g a t i o n -P ( O ) = s . 0 1 ^ a n d P ( O ) : q . L i n d i c a t e i n i t i a l p a r a s i t o i d d e n s i t i e so f O . O L / m z a n d o . I / m z .

1 0 9

T h e m a x i r n u m h o s t d e n s i t y ( c ) i n t h e s e m o d e l s c o u l dresult either from cornpeti t ion between host larvae or fromp r e d a t i o n b y n a t u r a l e n e - m i e s o t h e r t h a n M . c r o c e i p e s . Il s s u m e d a = L 0 l a r v a e / r n 2 , w h i c h h t a s d o u b l e t h e i n i t i a ldens i ty in spr ing . For bo th node ls , I used equat ions 7 and1 L f o r h o s t a n d p a r a s i t o i d d i s p e r s a l , r e s p e c t i v e l y , i . € .island dispersal hri th parasitoid aggregation.

Morta l i tv f rom other causes. Densi ty-dependent nor ta l i tyb e f o r e p a r a s i t o i d a t t a c k h a d l i t t l e a f f e c t o n s i m u l a t e dtrajectories of host density and proport ion parasit ized bothw i t h n o r n a l p a r a s i t o i d d e n s i t y ( F i S . 8 ) a n d a u g f t e n t e dp a r a s i t o i d d e n s i t y ( l ' i q . 9 ) . T h i s i s n o t s u r p r i s i n g s i n c es u c h m o r t a l i t y o n l y l i n i t s t h e g r o w t h r a t e o f t h e h o s tpopulat ion. On the other hand, density-dependent nortal i tya f t e r p a r a s i t o i d a t t a c k r e d u c e d t h e i m p a c t o f n o r m a lp a r a s i t o i d d e n s i t y ( F i S . 8 ) a n d o f a u g m e n t e d p a r a s i t o i dd e n s i t y ( F i g . 9 ) . E v e n w i t h a u g n e n t a t i o n , t h e h o s tpopu la t ion exceeded the economic th resho ld in co t ton by thefour th genera t ion when dens i ty -dependent nor ta l i t y occuredafter parasitoid attack.

ST'MMARY AND CONCLUSIONS

M. croceipes can be conserved by using insecticj .des towhich i t is relat ively tolerant and by applying insecticideso n l y w h e n H e l i o t h i s s p p . p o p u l a t i o n s e x c e e d e c o n o m i cthreshold. The dif f iculty of measuring M. croceipes densityprevents expl ici t use of parasitoid density data in decidinglthether to spray insecticides.

S i r n u l a t i o n s w i t h s e v e r a l m o d e l s o f t h e p o p u l a t i o nd y n a m i c s o f I { . c r o c e i p e s a n d H e l i o t h i s s p p . s h o h r e d t h a taugmenta t ive cont ro l nay be techn ica l l y feas ib le . w i th amode l incorpora t ing hos t d ispersa l and dens i ty -dependentparas i to id d ispersa l , Lo- fo ld augtnenta t ion o f M. c roce ipesdensity in spring suppressed H. virescens below the economicthreshold in cotton.

S i r n u l a t i o n s a l s o s h o h r e d t h a t t h e g r e a t e r t h e l e v e lo f dens i ty - independent d ispersa l o f hos t and paras i to id theless the i rnpac t o f augmenta t ive re leases on hos t dens i ty .However , dependence o f paras i to id d ispersa l on hos t dens i tyi n c r e a s e d p a r a s i t o i d i r n p a c t o n h o s t p o p u l a t i o n d y n a r n i c s .Furthermore, the t ining of other density-dependent processesw a s c r u c i a l : d e n s i t y - d e p e n d e n t h o s t r n o r t a l i t y b e f o r eparas i t i sn had l i t t le e f fec t on hos t dynamics , bu t dens i ty -d e p e n d e n t m o r t a l i t y a f t e r p a r a s i t i s n g r e a t l y r e d u c e dparasitoid irnpact on host dynarnics.

Eventua l l y , mode ls such as those descr ibed here cou ldpredict where, when, and how many M. croceipes to release tocontrol Heliothis spp.

ACKNOWIEEEI{ENT

E . c . K i n g p r o v i d e d I n u c h s u p p o r t a n d c o n t i n u o u se n c o u r a g e m e n t d u r i n g n y t i n e i n S t o n e v i l l e , M i s s i s s i p p i .T h i s r e s e a r c h w a s s u p p o r t e d i n p a r t b y g r a n t s 8 5 - C R C R - 1 -u 1 7 1 5 a n d 8 ? - C R C R - 1 " - 2 4 7 3 f r o m t h e U s D A C o r n p e t i t i v e G r a n t sProgram.

1 1 0

5 . 5

- 4 . sat n L

3 . 5

F ?

az . 2 .5UJc r zFa 1 . 5o- l

0 . 5

oH o . gF

u't& 0 . 6(L

z.c l 0 . 4

Fu.o(Lq o . 2Eo-

. - - - - - \/ ir.ror, /, ' A T T A c x

t

I

AFTER ATTACK

3 4

HOST GENERATION

FIG. 8 . S i rnu la ted hos t dens i ty (A) and propor t ion o f hos tsp a r a s i t i z e d ( B ) v e r s u s h o s t g e n e r a t i o n a s s u m i n g i s l a n dd i s p e r s a l a n d p a r a s i t o i d a g g r e g a t i o n . N o N E i n d i c a t e s n odensity-dependent nortal i ty. from other causesi BEFoRE ATTACKind ica tes dens i ty -depende i t nor ta l i t y be fore paras i t j -za t ion ;A F T E R A T T A C K i n d i c a t e s d e n s i t y - d e p e n d e n t m o r t a l i t y a f t e rparas i t i za t ion . In i t ia l paras i to id dens i ty : o .OL/m' -

1 1 1

4 . 5

3 1

6 3 .s

3

5 z . sa

6 2o. t . 5lnO r-

0 . 5

oH o . BF

UI

f 0 .6(L

z.a o . {F(xoTL9 o . 2ETL

3 4

H O S T G E N E R A T I O N

F I G . 9 . S i m u l a t e d h o s t d e n s i t y ( A ) a n d p r o p o r t i o n o f h o s t sp a r a s i t i z e d ( B ) v e r s u s h o s t g e n e r a t i o n a s s u m i n g i s l a n dd i s p e r s a l a n d p a r a s i t o i d a g g r e g a t i o n . N O N E i n d i c a t e s n odensity-dependent rnortal i ty frorn other causes; BEFORE ATTACKind ica t .es dens i ty -dependent nor ta l i t y be fore paras i t i za t ion ;A F T E R A T T A C K i n d i c a t e s d e n s i t y - d e p e n d e n t n o r t a l i t y a f t e rparas i t i za t ion . In i t ia l paras i to id dens i ty = o . I /m2.

\AFTEn rrncx /

1/ \

/ aeroneATTACX

I . - - -

J y' NBNE

t t 2

LITERATURE CITED

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1 1 5