Management of Fungicide Resistance by Using Computer Simulation

Chapter 18

Management of Fungicide Resistance by Using Computer Simulation

Phil A. Arneson

Downloaded by UNIV LAVAL on April 22, 2018 | https://pubs.acs.org Publication Date: February 23, 1990 | doi: 10.1021/bk-1990-0421.ch018

Department of Plant Pathology, Cornell University, Ithaca, NY 14853

Management of fungicide resistance requires some means of predicting the quantitative response of the target fungus population to various management alternatives. This can be accomplished with so-called "mechanistic" computer simulation models--models that represent the underlying biological mechanisms with sufficient fidelity that it is possible to mimic the behavior of both the fungicide-sensitive and resistant subpopulations in response to a particular spray program under a specific set of conditions. There are two major ways in which computer simulation can be used in the management of fungicide resistance--preseason planning of fungicide spray programs and day-by-day forecasting for timing of fungicide applications. Examples of two models are presented, "Resistan", a streamlined model for preseason planning, and "Sigatoka", a detailed model for day-to-day decision making. Both of these models can be used as teaching tools as well as management decision aids. Management of fungicide resistance implies purposeful manipulation not only of the frequency of fungicide resistance but also of the total population of the target fungus in a specified area. To manage fungicide resistance, both the total population of fungal propagules and the proportion of that population that is resistant must first be monitored. There must then be a way of predicting what will happen to that population when different fungicides are applied. Methods for monitoring fungicide resistance have been worked out for many of the fungal pathogens of agricultural importance (1). We now need predictive models that, given the frequency of fungicide resistance at the start of the season, will allow the manager to simulate different spray schedules with particular fungicides and to see the likely effects on frequency of resistance, disease level, and profitability at the end of the season. General models of the selection of fungicide resistance have given us overall management strategies (2-8). However, the fungi 0097-6156/90/0421-0264$06.00/0 © 1990 American Chemical Society

Green et al.; Managing Resistance to Agrochemicals ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


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Management ofFungicide Resistance by Computer Simulation 2

we attempt t o c o n t r o l w i t h f u n g i c i d e s d i f f e r w i d e l y i n t h e i r modes and r a t e s o f r e p r o d u c t i o n and i n t h e i r s e n s i t i v i t y t o d i f f e r e n t fungicides. L i k e w i s e , the f u n g i c i d e s we use t o c o n t r o l t h e s e f u n g i d i f f e r w i d e l y i n t h e i r b e h a v i o r on p l a n t s u r f a c e s and i n t h e i r f u n g i c i d a l modes o f a c t i o n . F u r t h e r m o r e , the p h y s i c a l mode o f r e s i s t a n c e , the mode o f i n h e r i t a n c e o f the r e s i s t a n c e , and the f i t n e s s o f the f u n g i c i d e - r e s i s t a n t b i o t y p e s v a r y w i d e l y w i t h b o t h the fungus and f u n g i c i d e . T h e r e f o r e , g e n e r a l models a r e n o t adequate f o r day-to-day d e c i s i o n making and may even l e a d t o a wrong d e c i s i o n i n a s p e c i f i c s i t u a t i o n . To p r e d i c t the e f f e c t s o f a p a r t i c u l a r f u n g i c i d e on a g i v e n c o m b i n a t i o n o f fungus, c r o p , s i t e , and weather c o n d i t i o n s r e q u i r e s models t h a t i n c l u d e considerable mechanistic d e t a i l . The l e v e l o f d e t a i l depends upon the o b j e c t i v e s o f the model. T h i s p a p e r c o n s i d e r s two d i f f e r e n t models t o i l l u s t r a t e two q u i t e d i f f e r e n t o b j e c t i v e s . The f i r s t model, w h i c h we c a l l " R e s i s t a n " , i s a s t r e a m l i n e d model w i t h l i m i t e d m e c h a n i s t i c d e t a i l and i s i n t e n d e d f o r p r e s e a s o n p l a n n i n g o f f u n g i c i d e s p r a y programs. The second, " S i g a t o k a " , i s a h i g h l y d e t a i l e d , m e c h a n i s t i c model t h a t responds t o h o u r l y weather c o n d i t i o n s and i s i n t e n d e d as a r e s e a r c h t o o l and f o r d a y - t o - d a y d e c i s i o n making. Both o f these models a r e s t i l l i n the e a r l y s t a g e s o f t h e i r development and w i l l need f i e l d v a l i d a t i o n b e f o r e t h e y can be u s e d i n f u n g i c i d e r e s i s t a n c e management. The

" R e s i s t a n " Model

One o b j e c t i v e o f a f u n g i c i d e management model might be t o p l a n f u n g i c i d e s p r a y s c h e d u l e s f o r the coming growing season, b a s e d upon resistance monitoring r e s u l t s . M o n i t o r i n g might be done a t the end o f the p r e v i o u s season, between seasons, o r a t the s t a r t o f the c u r r e n t season, depending on the fungus. The model would be u s e d t o p r e d i c t the r e l a t i v e e f f i c a c y o f v a r i o u s c o m b i n a t i o n s o f f u n g i c i d e s , r a t e s , and f r e q u e n c i e s o f a p p l i c a t i o n . The model would n o t n e c e s s a r i l y have t o s i m u l a t e the e f f e c t s o f weather on the b e h a v i o r o f the system, s i n c e i t i s n o t n e c e s s a r y ( o r p o s s i b l e ) t o p r e d i c t the i n c i d e n c e o r s e v e r i t y o f the d i s e a s e a t any p o i n t d u r i n g the season. I t would, however, have t o r e a l i s t i c a l l y r e p r e s e n t the r e l a t i v e e f f e c t s o f the d i f f e r e n t f u n g i c i d e s on the r e s i s t a n t and s e n s i t i v e f u n g a l s u b p o p u l a t i o n s . S i n c e the manager would l i k e l y be u s i n g a microcomputer and would want t o s i m u l a t e the whole growing s e a s o n o r perhaps even s e v e r a l growing seasons i n a few m i n u t e s , the model would have t o be somewhat s t r e a m l i n e d i n o r d e r t o execute w i t h s u f f i c i e n t speed. An example o f t h i s k i n d o f model i s " R e s i s t a n " , a m e c h a n i s t i c s i m u l a t i o n o f the p r o c e s s o f s e l e c t i o n o f f u n g i c i d e - r e s i s t a n t b i o t y p e s o f a c l o n a l l y r e p r o d u c i n g o r g a n i s m w i t h many g e n e r a t i o n s p e r s e a s o n (9.10). I n t h i s s i t u a t i o n s e l e c t i o n a l o n e i s by f a r the most i m p o r t a n t f a c t o r i n the development o f r e s i s t a n t p o p u l a t i o n s , and t h e r e f o r e i n t h i s model no attempt i s made t o s i m u l a t e g e n e t i c recombination. " R e s i s t a n " was w r i t t e n f o r the IBM-PC and PC-comp a t i b l e computers. I t has a g e n e r a l i z e d s t r u c t u r e t h a t a l l o w s the s i m u l a t i o n o f d i f f e r e n t f u n g i , c r o p s , and f u n g i c i d e s by c h a n g i n g the p a r a m e t e r s e t s . C u r r e n t l y we have a p a r a m e t e r s e t o n l y f o r one fungus, V e n t u r i a i n a e q u a l i s . and f o u r f u n g i c i d e s u s e d f o r the



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c o n t r o l o f a p p l e scab, c a p t a n , mancozeb, benomyl, and m y c l o b u t a n i l . The u s e r ' s manual (9) d e t a i l s the methods o f e s t i m a t i n g t h e s e parameters. The S t r u c t u r e o f the S i m u l a t i o n . Development o f the fungus i s simulated with three l i f e - s t a g e s (Figure 1). A population of s p o r e s , d i s p e r s e d and l a n d e d on s u s c e p t i b l e t i s s u e , g e r m i n a t e and i n f e c t , g i v i n g r i s e to a p o p u l a t i o n of l a t e n t l e s i o n s . The l a t e n t l e s i o n s d e v e l o p i n t o s p o r u l a t i n g l e s i o n s , whose s p o r e s a r e t h e n d i s p e r s e d t o complete the c y c l e . The s p o r e p o p u l a t i o n c a n be augmented by s p o r e s b l o w i n g i n from o u t s i d e the t r e a t e d a r e a . At each s t a g e o f development t h e r e a r e l o s s e s from the p o p u l a t i o n ( r e p r e s e n t e d by the c l o u d s i n F i g u r e 1 ) , r e s u l t i n g from b o t h n a t u r a l m o r t a l i t y and the e f f e c t s o f the f u n g i c i d e . The f l o w diagram i n F i g u r e 1 a c t u a l l y r e p r e s e n t s o n l y one s u b p o p u l a t i o n o f the fungus i n the model. The model, w h i c h s i m u l t a n e o u s l y s i m u l a t e s the e f f e c t s o f two f u n g i c i d e s , has f o u r such s u b p o p u l a t i o n s d e v e l o p i n g i n p a r a l l e l , one s e n s i t i v e t o b o t h f u n g i c i d e s , one r e s i s t a n t t o each o f the f u n g i c i d e s i n d i v i d u a l l y , and one r e s i s t a n t t o b o t h f u n g i c i d e s . The s u b p o p u l a t i o n s d i f f e r o n l y i n t h e i r m o r t a l i t y r a t e s , b o t h i n the p r e s e n c e o f t o x i c l e v e l s o f the f u n g i c i d e s and a l s o i n the absence o f f u n g i c i d e s . I f t h e r e i s a f i t n e s s c o s t a s s o c i a t e d w i t h f u n g i c i d e r e s i s t a n c e , the m o r t a l i t i e s o f the r e s i s t a n t s u b p o p u l a t i o n a r e s l i g h t l y h i g h e r , so w i t h o u t c o n t i n u e d s u p p r e s s i o n o f the s e n s i t i v e b i o t y p e by a p p l i c a t i o n s o f the f u n g i c i d e , the s e n s i t i v e s u b p o p u l a t i o n w i l l i n c r e a s e s l i g h t l y f a s t e r t h a n the r e s i s t a n t s u b p o p u l a t i o n , r e s u l t i n g i n a g r a d u a l r e v e r s i o n t o a low f r e q u e n c y o f r e s i s t a n c e i n the whole p o p u l a t i o n . The e f f e c t s o f the f u n g i c i d e s i n " R e s i s t a n " a r e s i m u l a t e d as d a i l y m o r t a l i t i e s t o each o f the t h r e e growth s t a g e s ( s p o r e s , l a t e n t l e s i o n s , and s p o r u l a t i n g l e s i o n s . A single probit m o r t a l i t y / l o g dose f u n c t i o n i s p a r a m e t e r i z e d f o r e a c h f u n g i c i d e , and the m o r t a l i t y ( p r o p o r t i o n ) t h a t i s c a l c u l a t e d f o r each dose i s m u l t i p l i e d by a w e i g h t i n g f a c t o r t o c a l c u l a t e the m o r t a l i t y f o r each growth s t a g e . I n t h i s way i t i s p o s s i b l e t o a p p r o x i m a t e f a i r l y s i m p l y the e f f e c t s o f f u n g i c i d e s w i t h d i f f e r e n t modes o f action. Weather v a r i a b l e s a r e n o t c o n s i d e r e d i n t h i s model. Its p a r a m e t e r s a r e e s t i m a t e d assuming optimum e n v i r o n m e n t a l c o n d i t i o n s f o r f u n g a l growth and development and r e m a i n c o n s t a n t t h r o u g h o u t the s i m u l a t i o n . " R e s i s t a n " i s a g e n e r a l i z e d model t h a t can be made t o s i m u l a t e d i f f e r e n t p o l y c y c l i c f u n g i , d i f f e r e n t c r o p s , and d i f f e r e n t f u n g i c i d e s s i m p l y by c h a n g i n g s e t s o f p a r a m e t e r s . The p a r a m e t e r s needed t o d e s c r i b e the development o f the fungus i n the model include: 1. The p r o p o r t i o n s o f the s p o r e s , l a t e n t l e s i o n s , and s p o r u l a t i n g l e s i o n s t h a t would s u r v i v e each day i n the absence o f fungicides. 2. I n f e c t i o n e f f i c i e n c y - - t h e p r o p o r t i o n o f l a n d e d s p o r e s t h a t s u c c e s s f u l l y i n f e c t p e r day i n the absence o f f u n g i c i d e s . 3. L a t e n t p e r i o d - - t h e time from i n f e c t i o n t o s p o r u l a t i o n . 4. Spores p r o d u c e d p e r l e s i o n p e r day i n the absence o f fungicides. 5. P r o p o r t i o n o f the d i s p e r s e d s p o r e s t h a t a c t u a l l y l a n d on susceptible tissue.


18. ARNESON

Management of Fungicide Resistance by Computer Simulation

BLOWIN


SPORES

INFECT

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LATENT LESIONS

DEVELOP

K

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I SPORULATING LESIONS

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DAMAGE

F i g u r e 1. Diagrammatic r e p r e s e n t a t i o n o f t h e " R e s i s t a n " s i m u l a t i o n model. R e c t a n g l e s r e p r e s e n t measurable q u a n t i t i e s t h a t change w i t h t i m e , v a l v e s r e p r e s e n t f l o w r a t e s , and c l o u d s r e p r e s e n t d i s a p p e a r a n c e from t h e system. (Reproduced w i t h p e r m i s s i o n f r o m R e f . 10. C o p y r i g h t 1988 APS P r e s s . )



268


6. I n f e c t i o u s p e r i o d - - t h e number o f days a s p o r u l a t i n g l e s i o n continues t o produce spores. 7. Upper l i m i t on t h e number o f l e s i o n s p e r a c r e . This i s to p r e v e n t u n l i m i t e d p o p u l a t i o n growth i n t h e e v e n t o f an u n c o n t r o l l e d epidemic. 8. O v e r w i n t e r i n g f a c t o r . T h i s i s a s i m p l e p r o p o r t i o n a l i t y f a c t o r t o c o n v e r t t h e f i n a l l e s i o n c o u n t i n one s e a s o n t o i n i t i a l inoculum f o r the f o l l o w i n g season (spores p e r f i n a l lesion). The f o l l o w i n g v a l u e s a r e needed t o p a r a m e t e r i z e t h e c r o p damage f u n c t i o n s and t h e c o s t a c c o u n t i n g r o u t i n e : 1. Maximum c r o p l o s s p e r day. The r e l a t i o n s h i p between number o f s p o r u l a t i n g l e s i o n s and c r o p damage i s modeled as a s a t u r a t i o n f u n c t i o n , and t h i s r e p r e s e n t s t h e p r o p o r t i o n o f the c r o p l o s s p e r day a t t h e s a t u r a t i o n l e s i o n c o u n t . 2. H a l f - s a t u r a t i o n c o n s t a n t f o r damage. T h i s p a r a m e t e r r e p r e s e n t s the l e s i o n count a t which the p r o p o r t i o n o f the c r o p l o s t p e r day i s o n e - h a l f i t s maximum. 3. Spray a p p l i c a t i o n c o s t ( d o l l a r s p e r a c r e ) . T h i s does n o t i n c l u d e the c o s t o f the f u n g i c i d e . 4. F i x e d c o s t s . These a r e t h e t o t a l c r o p p r o d u c t i o n c o s t s , e x c l u d i n g t h e f u n g i c i d e s p r a y a p p l i c a t i o n c o s t and t h e c o s t of the f u n g i c i d e s ( d o l l a r s per a c r e ) . 5. Maximum revenue. T h i s i s t h e e x p e c t e d revenue from t h e c r o p w i t h o u t any l o s s e s r e s u l t i n g from t h e d i s e a s e ( d o l l a r s p e r acre). The f o l l o w i n g p a r a m e t e r s a r e needed t o d e f i n e t h e c h a r a c t e r i s t i c s o f the f u n g i c i d e s : 1. The r a t e o f d i s a p p e a r a n c e i n micrograms p e r s q u a r e cent i m e t e r o f p l a n t s u r f a c e p e r day ( t h e exponent i n a n e g a t i v e exponential function). This represents a combination o f w e a t h e r i n g from p l a n t s u r f a c e s and m e t a b o l i s m w i t h i n p l a n t tissues. 2. The E C o f t h e f u n g i c i d e i n micrograms p e r s q u a r e c e n t i m e t e r o f l e a f s u r f a c e (depends on t h e t a r g e t f u n g u s ) . 3. The s l o p e o f t h e p r o b i t k i l l / l o g dose f u n c t i o n f o r t h e t a r g e t fungus. 4. T h r e e p a r a m e t e r s ( f a c t o r s between z e r o and one) t o r e p r e s e n t the e f f e c t s o f t h e f u n g i c i d e on s p o r e s , l a t e n t l e s i o n s , and s p o r u l a t i n g l e s i o n s . These f a c t o r s a r e m u l t i p l i e d t i m e s t h e p r o p o r t i o n k i l l o b t a i n e d from t h e p r o b i t / l o g dose f u n c t i o n t o d e t e r m i n e t h e m o r t a l i t y f a c t o r s f o r each growth s t a g e . 5. The r e s i s t a n c e l e v e l . T h i s i s u s e d as a m u l t i p l i e r times the E C o f t h e f u n g i c i d e t o d e t e r m i n e t h e dose r e s p o n s e o f the r e s i s t a n t b i o t y p e . F o r example, i f t h e r e s i s t a n t b i o t y p e r e q u i r e d 100 times t h e dose t o a c h i e v e t h e same l e v e l o f c o n t r o l as t h e s e n s i t i v e b i o t y p e , t h e r e s i s t a n c e l e v e l would be 100. 6. The r e l a t i v e f i t n e s s o f t h e r e s i s t a n t b i o t y p e compared w i t h the s e n s i t i v e b i o t y p e . T h i s a l s o i s a f a c t o r between z e r o and one t h a t i s m u l t i p l i e d times t h e n a t u r a l d a i l y s u r v i v a l at each growth s t a g e . I f t h e r e s i s t a n t and s e n s i t i v e b i o t y p e s a r e e q u a l l y f i t , t h i s f a c t o r i s one. 7. F i n a l l y , t o h e l p i n a rough b e n e f i t - c o s t a n a l y s i s a t t h e end 5 0

5 0



18. ARNESON

Management of Fungicide Resistance by Computer Simulation 2

o f the s i m u l a t i o n , the l a s t parameter i s the c o s t o f the f u n g i c i d e i n d o l l a r s p e r pound. U s i n g " R e s i s t a n " as a Management T o o l . To use " R e s i s t a n " one f i r s t e n t e r s the p a r a m e t e r s a p p r o p r i a t e f o r the fungus o f i n t e r e s t and the f u n g i c i d e s u s e d t o c o n t r o l i t . ( A l t e r n a t i v e l y , one c o u l d s i m p l y a c c e p t the d e f a u l t p a r a m e t e r s d e f i n e d i n an e x t e r n a l d a t a file.) Next one e n t e r s the l e v e l o f i n i t i a l i n o c u l u m o f the fungus and the f r e q u e n c y o f r e s i s t a n c e t o each o f i t s f u n g i c i d e s . The d e s i r e d f u n g i c i d e s a r e s e l e c t e d from the menu c h o i c e s , and the d e s i r e d s p r a y d a t e s and a p p l i c a t i o n r a t e s a r e e n t e r e d . ("Resistan" c u r r e n t l y o f f e r s a c h o i c e o f f o u r d i f f e r e n t f u n g i c i d e s , any two o f w h i c h can be a p p l i e d i n any c o m b i n a t i o n i n any g i v e n season.) The s i m u l a t i o n i s t h e n r u n f o r the d e s i g n a t e d number o f days i n the growing season. As the s i m u l a t i o n i s p r o g r e s s i n g , i t i s p o s s i b l e t o o b s e r v e day by day the numbers o f l e s i o n s and the p e r c e n t r e s i s t a n c e t o each o f the f u n g i c i d e s i n r e s p o n s e t o the s p r a y applications. A t the end o f the s i m u l a t e d s e a s o n t h e r e i s a c o s t a c c o u n t i n g t h a t can be u s e d t o compare d i f f e r e n t s p r a y s c h e d u l e s on a cost/benefit basis. The manager c o u l d t h e n r e p e a t the s i m u l a t i o n , t e s t i n g d i f f e r e n t proposed spray schedules, perhaps i n c l u d i n g tank-mixes o f f u n g i c i d e s , a l t e r n a t i n g f u n g i c i d e s p r a y s , o r some program o f r e d u c e d r a t e s o r fewer s p r a y s o f the a t - r i s k fungicide. I f one w i s h e s t o t e s t a s p r a y program o v e r a p e r i o d o f s e v e r a l growing seasons, " R e s i s t a n " w i l l s i m u l a t e the overwintering o f the i n o c u l u m and c a r r y o v e r the r e s i s t a n t p o p u l a t i o n s from one y e a r t o the n e x t . A l t h o u g h the " R e s i s t a n " model p a r a m e t e r i z e d f o r V. i n a e q u a l i s has n o t been r i g o r o u s l y v a l i d a t e d i n the f i e l d , i t s o v e r a l l behavior i s consistent with f i e l d observations of fungicide r e s i s t a n c e and a p p l e scab t o d a t e . The e f f e c t i v e n e s s o f c o n t r o l , the r a t e s o f s e l e c t i o n o f r e s i s t a n t fungus p o p u l a t i o n s , and the p e r s i s t e n c e o f the r e s i s t a n t p o p u l a t i o n s d i f f e r q u i t e m a r k e d l y f o r the d i f f e r e n t f u n g i c i d e s i n the s i m u l a t i o n , e m p h a s i z i n g the importance o f d e v e l o p i n g use s t r a t e g i e s f o r each p a r t i c u l a r one on a case-by-case b a s i s . R e d u c i n g the dose o f the " a t - r i s k " f u n g i c i d e i n the s i m u l a t i o n s o r a p p l y i n g i t i n c o m b i n a t i o n s w i t h " m u l t i - s i t e " f u n g i c i d e s , e i t h e r i n tank-mixes o r programs o f a l t e r n a t i n g s p r a y s r e d u c e s the r a t e o f s e l e c t i o n o f r e s i s t a n c e t o the " a t - r i s k " fungicide. The " b e s t " s p r a y program depends upon the s i m u l a t e d c h a r a c t e r i s t i c s o f the f u n g i c i d e . Reversion of a r e s i s t a n t p o p u l a t i o n t o a s e n s i t i v e one o c c u r s i n the s i m u l a t o r o n l y i f t h e r e i s a f i t n e s s c o s t t o the r e s i s t a n c e o r i f t h e r e i s a s i g n i f i c a n t d i l u t i o n o f the p o p u l a t i o n by s e n s i t i v e s p o r e s b l o w i n g i n from o u t s i d e the t r e a t e d a r e a . I f d i s e a s e c o n t r o l has b e e n v e r y e f f e c t i v e and the s i m u l a t e d l e v e l s o f i n o c u l u m a r e v e r y low, the s e l e c t i o n o f r e s i s t a n c e can c o n t i n u e u n d e t e c t e d f o r s e v e r a l seasons u n t i l the r e s i s t a n t p o p u l a t i o n appears t o " e x p l o d e " i n an u n c o n t r o l l a b l e epidemic. The

" S i f r a t o k a " Model

D e c i d i n g on a day-by-day b a s i s what f u n g i c i d e t o a p p l y , how much to a p p l y , and when t o a p p l y i t t o s a t i s f a c t o r i l y c o n t r o l a p l a n t d i s e a s e w h i l e a t the same time m a n i p u l a t i n g the f r e q u e n c y o f f u n g i c i d e r e s i s t a n c e r e q u i r e s d e t a i l e d knowledge o f the i n o c u l u m



270


a v a i l a b l e , the f r e q u e n c y o f r e s i s t a n c e , the c o n c e n t r a t i o n and d i s t r i b u t i o n o f f u n g i c i d e r e s i d u e s on the p l a n t s u r f a c e s , and the e n v i r o n m e n t a l c o n d i t i o n s i n the f i e l d on any g i v e n day. I t i s not p r a c t i c a l t o o b t a i n t h i s i n f o r m a t i o n s o l e l y by m o n i t o r i n g , b u t an a p p r o p r i a t e l y d e s i g n e d computer s i m u l a t i o n model might mimic r e a l i t y s u f f i c i e n t l y w e l l to s u b s t i t u t e p a r t i a l l y f o r monitoring i n d a y - t o - d a y d e c i s i o n making. U s i n g b i o l o g i c a l m o n i t o r i n g t o i n i t i a l i z e the model a t the b e g i n n i n g o f the season, the model might be d r i v e n by d a i l y e n v i r o n m e n t a l o b s e r v a t i o n s up t o the c u r r e n t d a t e . To p r e d i c t where the e p i d e m i c w i l l go i n the f u t u r e , one c o u l d use canned weather d a t a s e t s r e p r e s e n t i n g the mean o r the extreme v a l u e s o f the key weather v a r i a b l e s , o r one c o u l d even use weather v a r i a b l e s g e n e r a t e d by Monte C a r l o s i m u l a t i o n t o i n t r o d u c e r e a l i s t i c random v a r i a b i l i t y i n the weather. T h i s k i n d o f management d e c i s i o n making r e q u i r e s a c o n s i d e r a b l y more complex s i m u l a t i o n model t h a n t h a t r e p r e s e n t e d by " R e s i s t a n " . Such a model must mimic the growth and development o f the h o s t p l a n t , s p o r u l a t i o n o f the fungus, s p o r e d i s s e m i n a t i o n , i n f e c t i o n , the development o f d i s e a s e , and the e f f e c t s o f f u n g i c i d e s on the fungus, a l l i n r e s p o n s e t o a p p r o p r i a t e e n v i r o n m e n t a l v a r i a b l e s . S i n c e o n l y a few days a t a time would have t o be s i m u l a t e d t o make a d e c i s i o n about the n e x t s p r a y a p p l i c a t i o n , a slow e x e c u t i o n speed i s n o t a s e r i o u s drawback. R e p r e s e n t a t i v e o f t h i s k i n d o f model i s " S i g a t o k a " , a s i m u l a t o r o f an i m p o r t a n t f o l i a r d i s e a s e o f p l a n t a i n s and bananas ( 1 1 ) . " S i g a t o k a " c o n s i s t s o f 8 major modules: 1. a weather module t h a t s i m u l a t e s m i c r o m e t e o r o l o g i c a l varia b l e s , d r i v e n by d a i l y o b s e r v a t i o n s from a s t a n d a r d weather station, 2. a p l a n t module t h a t s i m u l a t e s l e a f development i n 15 l e a f p o s i t i o n s from the unexpanded c a n d l e l e a f t o the f i r s t expanded l e a f downward t h r o u g h the s u c c e s s i v e l y l o w e r l e a f p o s i t i o n s t o the removed l e a v e s on the ground (See F i g u r e 2), 3. a l e s i o n d i s t r i b u t i o n module t h a t moves the l a t e n t i n f e c t i o n s and s p o r u l a t i n g l e s i o n s downward as the l e a v e s develop, 4. a s p o r u l a t i o n module t h a t s i m u l a t e s the p r o d u c t i o n o f c o n i d i a and a s c o s p o r e s (See F i g u r e 3 ) , 5. a d i s p e r s a l module t h a t s i m u l a t e s the d i s p e r s a l o f c o n i d i a and a s c o s p o r e s among the 15 l e a f p o s i t i o n s , 6. an i n f e c t i o n module t h a t s i m u l a t e s the i n f e c t i o n by c o n i d i a and a s c o s p o r e s i n d e p e n d e n t l y f o r each o f the 15 l e a f positions, 7. a f u n g i c i d e w e a t h e r i n g module t h a t s i m u l a t e s the d e c r e a s e i n a v e r a g e f u n g i c i d e r e s i d u e and the r e d i s t r i b u t i o n o f the r e s i d u e s among the d i f f e r e n t l e a f p o s i t i o n s , and 8. a f u n g i c i d e e f f e c t s module t h a t s i m u l a t e s the e f f e c t s o f the f u n g i c i d e r e s i d u e s on s p o r e m o r t a l i t y , i n f e c t i o n , l e s i o n e x p a n s i o n , and s p o r u l a t i o n f o r the s u b p o p u l a t i o n s s e n s i t i v e and r e s i s t a n t t o each f u n g i c i d e . " S i g a t o k a " s i m u l a t e s the e f f e c t s o f 3 f u n g i c i d e s s i m u l t a n e o u s l y , and thus the d e v e l o p m e n t a l c y c l e i n F i g u r e 3 i s n o t o n l y e x e c u t e d f o r each o f the 15 l e a f s t r a t a b u t a l s o f o r each o f the 8 f u n g a l s u b p o p u l a t i o n s r e p r e s e n t i n g the p o s s i b l e c o m b i n a t i o n s


18. ARNESON

Management of Fungicide Resistance by Computer Simulation


CANDLE LEAF

FIRST EXPANDED LEAF

Leaf 1

SECOND EXPANDED LEAF

Leaf 2

TWELFTH EXPANDED LEAF

Leaf 12

ALL OLDER LEAVES

Leaf 13

T f

LEAVES ON THE GROUND

LEAF Leaf 14 DECOMPOSITION

F i g u r e 2. Diagrammatic r e p r e s e n t a t i o n o f t h e banana l e a f o f t h e " S i g a t o k a " s i m u l a t i o n model.

submodel


272


Infection

Infection


LATENT INFECTIONS

Lesion Development

Lesion Expansion

SPORULATING LESIONS

Sporulation

Sporulation

READY CONIDIA

READY ASCOSPORES

Dispersal

LANDED CONIDIA

Dispersal

Mortality

Mortality

LANDED ASCOSPORES

F i g u r e 3. Diagrammatic r e p r e s e n t a t i o n o f t h e fungus development submodel o f t h e " S i g a t o k a " s i m u l a t i o n model.


18. ARNESON

Management ofFungicide Resistance by Compute

o f f u n g i c i d e r e s i s t a n c e s ( s e n s i t i v e o r r e s i s t a n t t o each o f t h e 3 f u n g i c i d e s - 2 ) . Furthermore, t h e s t a t e v a r i a b l e s i n " S i g a t o k a " a r e u p d a t e d on a 2-hour t i m e - s t e p . T h i s k i n d o f b o o k k e e p i n g pushes the memory a v a i l a b l e i n t h e IBM-PC t o t h e l i m i t and makes e x e c u t i o n v e r y slow, even w i t h a math c o p r o c e s s o r (more t h a n 2 m i n u t e s p e r s i m u l a t e d day on a 8088-based s y s t e m ) . W h i l e " R e s i s t a n " has o n l y 20 p a r a m e t e r s t o be e s t i m a t e d , " S i g a t o k a " has 73 b a s i c p a r a m e t e r s , w h i c h when combined w i t h t h e v a l u e s o f t h e p a r a m e t e r s t h a t v a r y w i t h l e a f p o s i t i o n , f u n g i c i d e , and f u n g a l b i o t y p e s , make a t o t a l o f 283 p a r a m e t e r s t o be e s t i m a t e d . The f u n g i c i d e submodels i n " S i g a t o k a " a r e c o n s i d e r a b l y more d e t a i l e d t h a n i n " R e s i s t a n " . The f u n g i c i d e r e s i d u e s on l e a f s u r f a c e s a r e r e d i s t r i b u t e d downward i n r e s p o n s e t o r a i n f a l l and t o p l a n t development. Each f u n g i c i d e c a n i n d e p e n d e n t l y a f f e c t s p o r e m o r t a l i t y , i n f e c t i o n r a t e , r a t e o f l e s i o n development, and r a t e o f s p o r u l a t i o n , making i t p o s s i b l e t o mimic w i t h c o n s i d e r a b l e f i d e l i t y the d i f f e r e n t e f f e c t s o f t h e d i f f e r e n t f u n g i c i d e s on e a c h s t a g e o f development o f t h e fungus. C u r r e n t l y " S i g a t o k a " i s n o t h i n g more t h a n a l o g i c a l s t r u c t u r e r e p r e s e n t i n g o u r p r e s e n t u n d e r s t a n d i n g o f t h e b i o l o g i c a l mechanisms i m p o r t a n t i n t h e development o f t h e pathogen and i t s i n t e r a c t i o n with i t s host. None o f i t s p a r a m e t e r s has y e t been e s t i m a t e d , t h e i r c u r r e n t v a l u e s s i m p l y b a s e d upon t h e " e d u c a t e d g u e s s e s " o f i t s author. I n t h i s e a r l y s t a g e o f development, o f c o u r s e , t h e model has n o t y e t been v a l i d a t e d i n t h e f i e l d .


3

Conclusions T h e r e a r e two major ways i n which computer s i m u l a t i o n c a n be u s e d i n t h e management o f f u n g i c i d e r e s i s t a n c e , p r e s e a s o n p l a n n i n g o f f u n g i c i d e s p r a y programs and day-by-day f o r e c a s t i n g f o r t i m i n g o f fungicide applications. Each o f t h e s e u s e s r e q u i r e s a d i f f e r e n t type o f s i m u l a t i o n model, each w i t h a d i f f e r e n t s e t o f i n p u t s and a d i f f e r e n t k i n d o f outputs. " R e s i s t a n " i s an example o f a streaml i n e d , a l t h o u g h somewhat m e c h a n i s t i c , model f o r s i m u l a t i n g whole seasons o r m u l t i p l e seasons f o r use as a p r e s e a s o n management decision aid. " S i g a t o k a " , on t h e o t h e r hand, i s an example o f a d e t a i l e d m e c h a n i s t i c model, d r i v e n by h o u r l y weather, t h a t c a n g i v e day-by-day p r e d i c t i o n s o f d i s e a s e s e v e r i t y , f r e q u e n c y o f r e s i s t a n c e , and f u n g i c i d e r e s i d u e s . As n o t e d above, b o t h t h e s e models a r e s t i l l i n t h e e a r l y s t a g e s o f development as management t o o l s , and c o n s i d e r a b l y more work i s needed b e f o r e t h e y c a n be u s e d w i t h c o n f i d e n c e t o a i d i n management d e c i s i o n making. However, b o t h have a l r e a d y p r o v e n e x t r e m e l y u s e f u l as t e a c h i n g t o o l s t o i l l u s t r a t e t h e c o n c e p t s o f f i t n e s s and s e l e c t i o n t o s t u d e n t s and t o t h o s e a t t e m p t i n g t o manage f u n g i c i d e r e s i s t a n c e i n t h e f i e l d . Acknowledgments The a u t h o r w i s h e s t o acknowledge t h e programming e f f o r t s o f B a r r E. T i c k n o r i n the c r e a t i o n o f the user i n t e r f a c e f o r " R e s i s t a n " , the s o u r c e code o f w h i c h exceeds t h e number o f l i n e s i n t h e s i m u l a t i o n i t s e l f b y more t h a n 2 o r d e r s o f magnitude. Barr's c r e a t i v e t h i n k i n g and knowledge o f program d e s i g n c o n v e n t i o n s have immensely enhanced t h e u t i l i t y and " u s e r - f r i e n d l i n e s s " o f t h e program. We


273

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e x p r e s s a p p r e c i a t i o n t o Dr. Ken P. S a n d l a n f o r programming consultation. The a u t h o r g r a t e f u l l y acknowledges t h e t e c h n i c a l a s s i s t a n c e and l o g i s t i c s u p p o r t i n t h e c r e a t i o n o f " S i g a t o k a " from the C e n t r o Agrondmico T r o p i c a l de I n v e s t i g a c i 6 n y Ensefianza (CATIE) i n T u r r i a l b a , Costa Rica. T h i s r e s e a r c h was s u p p o r t e d t h r o u g h H a t c h p r o j e c t 153425, USDA.


Literature Cited 1. Delp, C. J., Ed.; Fungicide Resistance in North America; APS Press: St. Paul, 1988; Chapter 11, 16, 21, 26. 2. Delp, C. J. Plant Disease 1980, 64, 652-7. 3. Josepovits, G.; Dobrovolszky, A. Pesticide Science 1985, 16, 17-22. 4. Kable, P. F.; Jeffery, H. Phytopathology 1980, 70, 8-12. 5. Levy, Y.; Levi, R.; Cohen, Y. Phytopathology 1983, 73, 1475-80. 6. Milgroom, M. G.; Fry, W. E. Phytopathology 1988, 78, 559-70. 7. Skylakakis, G. Phytopathology 1981, 71, 1119-21. 8. Skylakakis, G. Phytopathology 1982, 72, 272-3. 9. Arneson, P. A.; Ticknor, B. E.; Sandlan, K. P. Resistan: A Mechanistic Simulation of the Selection of Fungicide Resistance; diskette and manual, Cornell University, Ithaca, NY, 1988. 10. Arneson, P. A.; Ticknor, B. E.; Sandlan, K. P. In Fungicide Resistance: Research and Management Goals and Their Implementation in North America; Delp, C. J., Ed.; APS Press, 1988; pp 107-9. 11. Arneson, P. A.; Sigatoka; diskette and manual, Centro Agronómico Tropical de Investigación y Enseñanza: Turrialba, Costa Rica, 1988. RECEIVED

October 16, 1989


Management of Fungicide Resistance by Using Computer Simulation

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