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UBC Theses and Dissertations

Pollen transfer : processes and consequences Lertzman, Kenneth P. 1981

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POLLEN TRANSFER: PROCESSES AND CONSEQUENCES by KENNETH P. LERTZMAN B.Sc. ( h o n o u r s ) , U n i v e r s i t y Of M a n i t o b a , Winnipeg, 1978 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE, UNIVERSITY OF BRITISH COLUMBIA i n THE FACULTY OF GRADUATE STUDIES (Department of Zoology) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA 10 J u l y 1981 © Kenneth P. } Lertzman, 1981 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It i s understood that copying or pu b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 rate Qeffr/tl  i ABSTRACT The c e n t r a l theme of t h i s t h e s i s i s the p r o c e s s e s and p a t t e r n s of p o l l e n d i s p e r s a l by. hummingbirds. The main q u e s t i o n s a r e : "To how many f l o w e r s p a s t i t s s o u r c e i s p o l l e n d e p o s i t e d ? " , and "What are the p r o c e s s e s t h a t i n f l u e n c e the t r a n s f e r and and d e p o s i t i o n of p o l l e n ? " . U s i n g powdered dyes as p o l l e n mimics, I conducted l a b o r a t o r y e x p e r i m e n t s w i t h r u f o u s hummingbirds ( S e l a s p h o r u s  r u f u s ) and I n d i a n p a i n t b r u s h ( C a s t i l l e j a m i n i a t a ) which showed t h a t dye (and presumably p o l l e n ) i s c a r r i e d t o many f l o w e r s p a s t i t s source f l o w e r . The p a t t e r n of p o l l e n d e p o s i t i o n was complex and was r e l a t e d t o v a r i a t i o n i n f l o r a l morphology. I h y p o t h e s i z e d t h a t v a r i a t i o n i n f l o r a l morphology has a s t r o n g i n f l u e n c e on p a t t e r n s of p o l l e n t r a n s f e r . The l a b o r a t o r y e x p e r i m e n t s a l s o s u p p o r t e d the h y p o t h e s i s t h a t p o l l e n i s d e p o s i t e d i n p a r t i a l l y o v e r l a p p i n g l a y e r s on the p o l l i n a t o r . A s e r i e s of models showed t h a t d i f f e r e n t s e t s of assumptions about p o l l e n t r a n s f e r c o u l d produce q u a l i t a t i v e l y s i m i l a r p a t t e r n s of p o l l e n d e p o s i t i o n , and t h a t v a r i a b i l i t y i n d e p o s i t i o n i n c r e a s e d w i t h the s t r u c t u r a l c o m p l e x i t y of the model. In the model based on the l a b o r a t o r y e x p e r i m e n t s , v a r i a t i o n i n f l o r a l morphology ( d e f i n e d i n terms of the l o c a t i o n s where stigma s and a n t h e r s c o n t a c t the p o l l e n p o o l on the p o l l i n a t o r ) had a s i g n i f i c a n t i n f l u e n c e on both p o l l e n p o o l s t r u c t u r e ( l a y e r i n g ) and on p o l l e n c a r r y o v e r . In f i e l d e x p e r i m e n t s on o p t i m a l o u t c r o s s i n g and p o l l e n d i s p e r s a l i n C a s t i l l e j a m i n i a t a , I found o n l y v e r y t e n t a t i v e i i s u p p o r t f o r a w i t h i n p o p u l a t i o n o p t i m a l o u t c r o s s i n g d i s t a n c e . V a r i a t i o n between y e a r s was g r e a t : one y e a r ' s experiment showed a peak of seed p r o d u c t i o n a t i n t e r m e d i a t e o u t c r o s s i n g d i s t a n c e s , the the o t h e r y e a r s d a t a showed almost no e f f e c t of o u t c r o s s i n g d i s t a n c e . P o l l e n d i s p e r s a l (as i n d i c a t e d by dye d i s p e r s a l ) i s p r o b a b l y not l i m i t e d by hummingbird t e r r i t o r i a l b o u n d a r i e s i n t h i s system, i n the d i s t a n c e or d i r e c t i o n of i t s movement. I d i s c u s s the gap between knowledge of p r o c e s s e s a t the l e v e l of i n d i v i d u a l f l o w e r s and p a t t e r n s a t the l e v e l of p o p u l a t i o n s of f l o w e r s , and suggest some e x p e r i m e n t s o r i e n t e d towards t r y i n g t o b r i d g e t h a t gap. i i i TABLE OF CONTENTS ABSTRACT i i LIST OF TABLES v LIST OF FIGURES v i ACKNOWLEDGEMENTS v i i i G e n e r a l I n t r o d u c t i o n 1 G e n e r a l System I n t r o d u c t i o n 3 L a b o r a t o r y E x periments On P o l l e n T r a n s f e r : P o l l e n T r a n s f e r K i n e t i c s 8 I n t r o d u c t i o n 8 M a t e r i a l s and Methods 11 R e s u l t s 17 D i s c u s s i o n 35 S i n g l e Source E x p e r i m e n t s 35 M u l t i p l e Source Experiment 38 P l a n t - P l a n t T r a n s f e r 40 Bumblebee-Hummingbird Comparison 41 Male V e r s u s Female F u n c t i o n 42 C o n c l u s i o n s 43 A l t e r n a t i v e models of p o l l e n t r a n s f e r 45 I n t r o d u c t i o n 45 On B u i l d i n g Models Of P o l l i n a t i o n 48 A l t e r n a t i v e Models 49 Model 1: Co n s t a n t P r o p o r t i o n Of P o l l e n G r a i n s D e p o s i t e d : E x p o n e n t i a l Decay 53 i v Model 2: Constant P r o p o r t i o n Of P o l l e n G r a i n s D e p o s i t e d : E x p o n e n t i a l Decay W i t h B l a n k s 59 Model 3: Constant Number of P o l l e n G r a i n s Dropped O f f : L i m i t e d S t i g m a l C a p a c i t y 68 Model 4: 3-Dimensional P o l l e n P o o l With L a y e r i n g and F l o r a l V a r i a b i l i t y 78 D i s c u s s i o n 105 I m p l i c a t i o n s For Mechanisms 105 I m p l i c a t i o n s For P l a n t P o p u l a t i o n s 107 C o n c l u s i o n s 109 O p t i m a l O u t c r o s s i n g and P o l l e n D i s p e r s a l i n C a s t i l l e j a m i n i a t a 111 I n t r o d u c t i o n 111 M a t e r i a l s and Methods 114 R e s u l t s 119 O p t i m a l O u t c r o s s i n g 119 Dye D i s p e r s a l 122 D i s c u s s i o n 129 O p t i m a l O u t c r o s s i n g D i s t a n c e : V a r i a b i l i t y i n F i t n e s s 129 Dye D i s p e r s a l D i s t a n c e : I s P o l l e n D i s p e r s e d O p t i m a l l y ? 132 Dye D i s p e r s a l D i r e c t i o n : Do T e r r i t o r i a l B o u n d a r i e s R e s t r i c t P o l l e n Movement? 133 C o n c l u s i o n s 135 G e n e r a l D i s c u s s i o n 137 R e f e r e n c e s 145 V LIST OF TABLES T a b l e I . Means and extremes of dye c a r r y o v e r from l a b o r a t o r y e x p e r i m e n t s 24 Ta b l e I I . L i n e a r r e g r e s i o n s of dye d e p o s i t e d on f l o w e r p r e s e n t a t i o n sequence 27 Ta b l e I I I . T e s t s of dye d e p o s i t i o n on d i f f e r e n t f l o r a l morphology c l a s s e s 28 Ta b l e IV. Comparison of s i n g l e and m u l t i p l e source t r i a l s - p r o p o r t i o n d e p o s i t e d 34 Ta b l e V. Comparison of s i n g l e and m u l t i p l e source t r i a l s -mean and maximum c a r r y o v e r 35 Ta b l e V I . G e n e r a l c h a r a c t e r i s t i c s of the models 50 Ta b l e V I I . C a r r y o v e r s t a t i s t i c s from models 2, 3, and 4 .. 67 Ta b l e V I I I . R e g r e s s i o n s t a t i s t i c s f o r c a r r y o v e r on f l o r a l v a r i a b i l i t y 103 Ta b l e IX. Degree of s a t u r a t i o n of l o c a l f l o w e r s by dye from d i f f e r e n t . s o u r c e s 125 T a b l e X. D i r e c t i o n a l s t a t i s t i c R* 128 Ta b l e X I . T e r r i t o r y and meadow s t a t i s t i c s f o r the dye d i s p e r s a l experiment 129 LIST OF FIGURES v i a F i g u r e 1. F l o w e r i n g s t a g e s i n C a s t i l i e j a , and d r a w i n g of a hummingbird f e e d i n g from C a s t i l l e j a 5 F i g u r e 2. Dye d e p o s i t i o n on stigmas from the s i n g l e source e x p e r i m e n t s 18 F i g u r e 3. Dye d e p o s i t i o n on a n t h e r s from the s i n g l e source e x p e r i m e n t s 20 F i g u r e 4. Dye d e p o s i t i o n on stigmas and a n t h e r s of d i f f e r e n t m o r p h o l o g i c a l c l a s s e s 22 F i g u r e 5. Dye d e p o s i t i o n on stigmas and a n t h e r s of d i f f e r e n t m o r p h o l o g i c a l c l a s s e s - p o o l e d d a t a •••• 25 F i g u r e 6. Dye d e p o s i t e d on f l o w e r s of d i f f e r e n t l e n g t h s , dye from one sourc 29 F i g u r e 7. The p r o p o r t i o n of dye d e p o s i t e d pn a d j a c e n t groups of 10 f l o w e r s 32 F i g u r e 8. P o l l e n d e p o s i t i o n c u r v e s from model 1 55 F i g u r e 9. P o l l e n d e p o s i t i o n c u r v e s from model 2 a t d i f f e r e n t per cent d e p o s i t i o n 61 F i g u r e 10. Frequency d i s t r i b u t i o n s of mean and maximum c a r r y o v e r from models 2,3 and 4 63 F i g u r e 11. Mean and maximum p o l l e n d e p o s i t i o n from model 2 65 F i g u r e 12. P o l l e n c a r r y o v e r c u r v e s from model 3 70 F i g u r e 13. C a r r y o v e r from model 3 w i t h v a r y i n g s t i g m a l c a p a c i t y • 72 v i i F i g u r e 14. V a r i a n c e i n mean and maximum p o l l e n c a r r y o v e r vs g r a i n s d e p o s i t e d per st i g m a - from model 3 75 F i g u r e 15. Hummingbird w i t h p o l l e n p o o l from model 4 80 F i g u r e 16. P o l l e n c a r r y o v e r c u r v e s from model 4 83 F i g u r e 17. P o l l e n g r a i n s p i c k e d up v s . f l o r a l v a r i a b i l i t y 90 F i g u r e 18. P o l l e n g r a i n s d e p o s i t e d v s . f l o r a l v a r i a b i l i t y 92 F i g u r e 19. P r o p o r t i o n of p o o l o c c u p i e d v s . f l o r a l v a r i a b i l i t y 94 F i g u r e 20. Mean l a y e r i n g v s . f l o r a l v a r i a b i l i t y 96 F i g u r e 21. P o l l e n c a r r y o v e r v s . f l o r a l v a r i a b i l i t y 99 F i g u r e 22. P r o p o r t i o n of z e r o d e p o s i t i o n v s . f l o r a l v a r i a b i l i t y 101 F i g u r e 23. Seed p r o d u c t i o n under d i f f e r e n t p o l l i n a t i o n t r e a t m e n t s 120 F i g u r e 24. P r o p o r t i o n of dye d i s p e r s e d t o d i f f e r e n t d i s t a n c e s away from the dye sour c e 1,23 F i g u r e 25. The p r o p o r t i o n of ob s e r v e d f l o w e r s w i t h dye a t d i f f e r e n t d i s p e r s a l d i s t a n c e s 126 v i i i ACKNOWLEDGEMENTS I would l i k e t o thank Lee Gass f o r h i s committment over the l a s t t h r e e y e a r s . . He has c o n t r i b u t e d t o t h i s t h e s i s i n many ways, both t a n g i b l e and i n t a n g i b l e , and f o r much of the time he has been more of a p a r t n e r than a s u p e r v i s o r . I was s u p p o r t e d f i n a n c i a l l y by an N.S.E.R.C. P o s t g r a d u a t e S c h o l a r s h i p , by a U.B.C. Graduate F e l l o w s h i p , and by N.S.E.R.C. O p e r a t i n g g r a n t 67-9876 t o C.L. Gass. Many people have h e l p e d w i t h the f i e l d work. I would p a r t i c u l a r l y l i k e t o thank my a s s i s t a n t s P e t e r N o r t h c o t e , Dianne Goodwin, and P e t e r Thompson f o r a u n i f o r m l y h i g h s t a n d a r d of work and f o r f r e e l y f l o w i n g c r i t i c i s m . Other people who h e l p e d a t v a r i o u s t i m e s i n f i e l d work or w i t h f i e l d l o g i s t i c s were: Glenn S u t h e r l a n d , Joan S u t h e r l a n d , Gay L e w i s , L o w e l l C l a r d y , E l i z a b e t h B u e l n a , Ann B r i n i t z e r , M a r i l y n n F r i l e y , John Markov, Dave Marmorek, B e t t y Bronson, and M a r i l y n n Thurmeier. F o r e s t Gass and G e r a l d Gass deserve s p e c i a l r e c o g n i t i o n f o r many t h i n g s . F i e l d seasons w i t h o u t them would have been much l e s s p l e a s a n t a t b e s t , and c e r t a i n l y much more d i f f i c u l t . The members of my r e s e a r c h committee have been h e l p f u l and ap p r o a c h a b l e f o r a l l my q u e s t i o n s . They a r e : Judy Myers, N e i l G i l b e r t , and B i l l N e i l l . Other p e o p l e who have h e l p e d w i t h i d e a s or a n a l y s i s a r e C h a r l i e K r e b s , Ray H i l b o r n , L a r r y D i l l , Dave Marmorek, Steve O b e r s k i , and Tim Webb. N i c k Waser has g i v e n v a l u a b l e support and c r i t i c i s m of th e s e s t u d i e s from t h e i r i n c e p t i o n and de s e r v e s p a r t i a l c r e d i t i x f o r much of the c o n c e p t u a l b a s i s of t h e s e s t u d i e s . People who c r i t i q u e d e a r l i e r d r a f t s of p o r t i o n s of t h i s t h e s i s a r e Glenn S u t h e r l a n d , N i c k Waser Mary P r i c e , S c o t t C a r l e y , A l e x B r e t t , and the members of my committee. I would l i k e t o acknowledge a g e n e r a l , deep, g r a t i t u d e t o Dave Marmorek, A l e x B r e t t and my p a r e n t s who have h e l p e d me get th r o u g h many t r i a l s . " . . . w i t h a l i t t l e h e l p from my f r i e n d s . " "Thus s c i e n c e i s much c l o s e r t o myth than a s c i e n t i f i c p h i l o s o p h y i s p r e p a r e d t o admi t . I t i s one of the many forms of thought t h a t have been d e v e l o p e d by man, and not n e c e s s a r i l y the b e s t . I t i s c o n s p i c u o u s , n o i s y , and impudent, but i t i s i n h e r e n t l y s u p e r i o r o n l y f o r those who have a l r e a d y d e c i d e d i n f a v o r of a c e r t a i n i d e o l o g y , or who have a c c e p t e d i t w i t h o u t h a v i n g ever examined i t s advantages and i t s l i m i t s . " Feyerabend (1975) "Be f o r e I s t u d i e d Zen, mountains were j u s t mountains and r i v e r s j u s t r i v e r s . W h i l e I s t u d i e d Zen, mountains were no l o n g e r mountains and r i v e r s no l o n g e r r i v e r s . But once I a c h i e v e d e n l i g h t e n m e n t , mountains were once a g a i n j u s t mountains, and r i v e r s once a g a i n j u s t r i v e r s . " Zen S a y i n g 1 GENERAL INTRODUCTION P l a n t - p o l l i n a t o r systems p r o v i d e o p p o r t u n i t i e s f o r s t u d y i n g the p r o d u c t s of c o - e v o l u t i o n of d i f f e r e n t groups of organisms. T h i s i s e x p r e s s e d i n many dimensions f o r both the p l a n t s and the a n i m a l s ( F a e g r i and van der P i j l 1979; Grant and Grant 1968; P r o c t o r and Yeo 1972). E a r l y s t u d i e s f o c u s s e d on the s t r u c t u r a l a s p e c t s of the s e systems - the " f i t " between p o l l i n a t o r and f l o w e r m o r p h o l o g i e s , and how t h i s r e s u l t e d i n the p o l l i n a t i o n of the p l a n t s (summarized by F a e g r i and van der P i j l 1979; P r o c t o r and Yeo 1972). There has been a g r a d u a l s h i f t i n emphasis t o the more dynamic a s p e c t s of these systems e.g. p o l l i n a t o r b e h a v i o u r (Gass e t a l . 1976; Gass 1979; H e i n r i c h et a l . 1977; Kodr i c - B r o w n and Brown 1978; Waddington and Holden 1979; Zimmerman 1979), p a t t e r n s of n e c t a r p r o d u c t i o n and f l o r a l d i s p l a y (Cruden 1976; Corbet 1978a; 1978b; F e i n s i n g e r 1978; W i l l s o n 1979; W i l l s o n and Rathcke 1974; Augspurger 1980), and the s t r u c t u r e of n e c t a r i v o r e communities (e.g. C o l w e l l 1973; F e i n s i n g e r 1976; C a r p e n t e r 1978; F e i n s i n g e r and C o l w e l l 1978; Pimm 1978; Wolf 1978; Montgomerie 1979). I was i n i t i a l l y i n t e r e s t e d i n problems a t the l e v e l of p l a n t p o p u l a t i o n s ; gene f l o w , d i f f e r e n t i a t i o n , and o p t i m a l o u t c r o s s i n g . However, I r e a l i z e d t h a t t o st u d y t h e s e p o p u l a t i o n problems i n a p r e d i c t i v e way, I would have t o make p o o r l y s u p p o r t e d a s s u m p t i o n s about p o l l e n t r a n s f e r p r o c e s s e s a t the l e v e l of i n d i v i d u a l f l o w e r s . These were 2 the same assumptions t h a t I had found f r u s t r a t i n g i n the l i t e r a t u r e . For i n s t a n c e , i t i s commonly assumed t h a t p o l l e n p i c k e d up by a p o l l i n a t o r i s d e p o s i t e d a t o n l y a few f l o w e r s a f t e r the one from which i t i s p i c k e d up ( L e v i n e_t a l . 1971; F r a n k i e e t a l . 1976; F e i n s i n g e r 1978; R i c h a r d s and I b r a h i m 1979; Augspurger 1980; S c h m i t t 1980). The main f o c u s of t h i s t h e s i s i s on p a t t e r n s and p r o c e s s e s of p o l l e n d i s p e r s a l a t the l e v e l of i n d i v i d u a l f l o w e r s . My g o a l was t o a s s e s s the v a l i d i t y of some commonly made assumptions and some a l t e r n a t i v e s t o them. I d i d t h i s f i r s t t h r o u g h l a b o r a t o r y e x p e r i m e n t s ( c h a p t e r 3) and then through a s e r i e s of s i m u l a t i o n models t h a t i n c o r p o r a t e d i n f o r m a t i o n from the e x p e r i m e n t a l s t u d i e s ( c h a p t e r 4 ) . In c h a p t e r 5 I ask q u e s t i o n s about mate q u a l i t y and p o l l e n d i s p e r s a l a t the p o p u l a t i o n l e v e l . S p e c i f i c a l l y , I t e s t the p r e d i c t i o n s t h a t r e p r o d u c t i v e s u c c e s s w i l l be maximized a t an i n t e r m e d i a t e l e v e l of o u t c r o s s i n g , and t h a t hummingbird t e r r i t o r i a l b o u n d a r i e s r e s t r i c t the p o o l of p o t e n t i a l mates a v a i l a b l e t o the p l a n t s c o n t a i n e d i n the t e r r i t o r y . In the g e n e r a l d i s c u s s i o n I a s s e s s whether my s t u d i e s a t the i n d i v i d u a l l e v e l w i l l h e l p i n c o n d u c t i n g r e s e a r c h on p o p u l a t i o n l e v e l p a t t e r n s such as a r e d i s c u s s e d i n c h a p t e r 5. I c o n c l u d e w i t h a d i s c u s s i o n of the most p r o f i t a b l e ways to f o l l o w up t h i s work. 3 GENERAL SYSTEM INTRODUCTION The S e l a s p h o r u s r u f u s - C a s t i l i e j a m i n i a t a system i s good f o r s t u d y i n g p l a n t - p o l l i n a t o r i n t e r a c t i o n s . I t i s s i m p l e - one s p e c i e s of p o l l i n a t o r w i t h two main foo d p l a n t s - and t h e r e had been n e a r l y 10 y e a r s of e c o l o g i c a l r e s e a r c h on the system p r i o r t o the s t a r t of t h i s s t u d y . Thus t h e r e i s a c o n t e x t f o r s t u d y i n g hummingbird-plant i n t e r a c t i o n s i n which i m p o r t a n t e c o l o g i c a l b a s e l i n e i n f o r m a t i o n i s a l r e a d y known. Rufous hummingbirds ( S e l a s p h o r u s r u f u s ) breed from s o u t h e r n Oregon t o A l a s k a and defend temporary f e e d i n g t e r r i t o r i e s i n the s u b a l p i n e meadows of n o r t h e r n C a l i f o r n i a d u r i n g t h e i r southward p o s t - b r e e d i n g m i g r a t i o n (Gass 1974; Gass e t a_l. 1976; Gass 1979). These s t u d i e s were conducted a t G r i z z l y Lake i n the S a l m o n - T r i n i t y A l p s P r i m i t i v e Area i n n o r t h w e s t e r n C a l i f o r n i a . Here r u f o u s hummingbirds ( p r i m a r i l y a d u l t females and immatures) defend t e r r i t o r i e s i n d e n s e l y f l o w e r i n g s u b a l p i n e meadows from snowmelt i n e a r l y J u l y , u n t i l l a t e August (Gass 1974; 1979; Gass et a l . 1976). T h e i r main s o u r c e s of n e c t a r a r e I n d i a n p a i n t b r u s h ( C a s t i l l e j a m i n i a t a ) and columbine ( A q u i l e g i a f o r m o s a ) . Other f l o w e r s a r e f e d on i r r e g u l a r l y when thes e a r e not a v a i l a b l e or are r a r e . The number of f l o w e r s defended by i n d i v i d u a l hummingbirds i s r e g u l a t e d t o p r o v i d e t h e i r 24 hour energy needs (Gass e t a l . 1976; Gass 1979; Kodric-Brown and Brown 1978). Thus s i n c e A q u i l e g i a produces n e c t a r a t r o u g h l y 4 4 t i m e s the r a t e of C a s t i l l e j a (per n e c t a r y ) , t e r r i t o r i e s h e l d i n C a s t i l l e j a have many more f l o w e r s i n them than t e r r i t o r i e s h e l d i n A q u i l e g i a (Gass et_ a_l. 1976). E x c l u d i n g d u r a t i o n s of l e s s than one day, average t e n u r e of hummingbirds i n the s e meadows i s 5.86 days, though one i n d i v i d u a l has been observed t o s t a y f o r 21 days (Gass 1979). My work f o c u s s e s on i n t e r a c t i o n s between S'elasphorus  r u f u s and C a s t i l l e j a m i n i a t a . C a s t i l l e j a i s a p e r e n n i a l h e r b t h a t s e t s l i t t l e seed when s e l f e d ( P e r k i n s 1977, and c h a p t e r 5 on o p t i m a l o u t c r o s s i n g ) , or when hummingbirds are e x c l u d e d ( C a r p e n t e r 1981). F l o w e r i n g i s i n d e t e r m i n a t e and o l d e r f l o w e r s a r e lower on the i n f l o r e s c e n c e . New f l o w e r s emerge a t the t o p - o f the i n f l o r e s c e n c e w h i l e the seeds are m a t u r i n g below. F l o w e r s a r e h e r m a p h r o d i t e s , and though t h e r e i s weak e v i d e n c e f o r p r o t y g y n y , a n t h e r s and s t i g m a s appear t o mature a t about the same time ( P e r k i n s 1977). F i g u r e 1 diagrams C a s t i l l e j a f l o w e r s i n v a r i o u s s t a g e s and shows the geometry of hummingbird f e e d i n g and p o l l i n a t i o n . One p l a n t may have many i n f l o r e s c e n c e s , w i t h an average of 4.1 + 0.45 f l o w e r s per i n f l o r e s c e n c e i n the middl e of the season. There are 0 t o about 23 f l o w e r s per i n f l o r e s c e n c e , w i t h an average of 4.9 + 0.54 i n the m i d d l e of the season ( e x c l u d i n g p l a n t s and i n f l o r e s c e n c e s w i t h 0 i n f l o r e s c e n c e s or f l o w e r s , P e r k i n s 1977). Non-hummingbird p o l l i n a t o r s r a r e l y v i s i t C a s t i l l e j a a t G r i z z l y Lake ( P e r k i n s 1977, p e r s . o b s . ) . 5 F i g u r e 1. F l o w e r i n g s t a g e s i n C a s t i l i e j a and drawing of a hummingbird f e e d i n g from C a s t i l i e j a . N e c t a r i s p r e s e n t and hummingbirds fe e d from s t a g e s 3-5. A n t h e r s b e g i n to d e h i s c e a t stage 4 and stigmas a r e r e c e p t i v e by stage-4. F l o w e r i n g s t a g e s re-drawn from P e r k i n s (1977). The h a t c h e d a r e a on the hummingbird's f o r e h e a d i s , i n a d d i t i o n t o the p r o x i m a t e p o r t i o n of the beak, the a r e a c o n t a c t e d by the r e p r o d u c t i v e p a r t s of the f l o w e r s - the a r e a o c c u p i e d by the p o l l e n p o o l , a = stigma b = a n t h e r s 6 7 D e t a i l s of the methods are p a r t i c u l a r t o each s e c t i o n and w i l l be d e s c r i b e d where they a r e used. 8 LABORATORY EXPERIMENTS ON POLLEN TRANSFER: POLLEN TRANSFER KINETICS I n t r o d u c t i o n In the C a s t i l i e j a - S e l a s p h o r u s system, p o l l i n a t i o n i n v o l v e s the p i c k u p of p o l l e n by a hummingbird w h i l e i t i s f e e d i n g on the n e c t a r i n a f l o w e r , the t r a n s p o r t of p o l l e n i n a p o o l on the hummingbird's f o r e h e a d , and the d e p o s i t i o n of the p o l l e n on some of the f l o w e r s the hummingbird s u b s e q u e n t l y feeds from. The number of f l o w e r s past i t s s o u r c e t o which p o l l e n i s c a r r i e d i s r e f e r r e d t o as p o l l e n  c a r r y o v e r . P o l l e n c a r r y o v e r i s i m p o r t a n t because i t d e t e r m i n e s whether a p o l l i n a t i o n event w i l l r e s u l t i n o u t c r o s s i n g or s e l f i n g . The k i n e t i c s of p o l l e n c a r r y o v e r a r e the shapes of p o l l e n c a r r y o v e r or p o l l e n d e p o s i t i o n c u r v e s and the p r o c e s s e s t h a t g i v e them t h e i r forms. Does p o l l e n d e p o s i t i o n decay e x p o n e n t i a l l y ? Does i t d e c r e a s e l i n e a r l y ? What u n d e r l y i n g mechanisms are r e s p o n s i b l e f o r t h e s e p a t t e r n s ? H e r e t o f o r e , most r e f e r e n c e s t o t h e s e p r o c e s s e s have been i m p l i c i t , and c a r r y o v e r has been assumed t o be v e r y s h o r t ( L e v i n and K e r s t e r 1967; 1968; I969a,b; L e v i n and Berube 1972; F r a n k i e et a l . 1976; F e i n s i n g e r 1978; R i c h a r d s and I b r a h i m 1979; Augspurger 1980; S c h m i t t 1980). L e v i n and Berube (1972) found t h a t c a r r y o v e r of h e t e r o s p e c i f i c p o l l e n 9 by C o l i a s b u t t e r f l i e s f e e d i n g on P h l o x d e c l i n e d s t e e p l y and e x p o n e n t i a l l y , w i t h l i t t l e c a r r y o v e r p a s t the f o u r t h f l o w e r i n a f i v e f l o w e r sequence. Assuming l i t t l e f l o w e r - f l o w e r c a r r y o v e r , and a l a r g e number of f l o w e r s f e d on per p l a n t , L e v i n and K e r s t e r (1969a) argued t h a t t h e r e would be l i t t l e c a r r y o v e r from one p l a n t t o another p a s t the f i r s t few f l o w e r s . T h i s r e s u l t of s t e e p e x p o n e n t i a l decay has been g e n e r a l i z e d t o o t h e r systems, e.g. F e i n s i n g e r (1978) f o r a t r o p i c a l hummingbird-plant community, Augspurger (1980) f o r a t r o p i c a l , mass f l o w e r i n g , i n s e c t p o l l i n a t e d shrub, and F r a n k i e e_t a_l. (1976) f o r a t r o p i c a l , mass f l o w e r i n g , bee p o l l i n a t e d t r e e . An i n f e r e n c e of s h o r t gene d i s p e r s a l d i s t a n c e s i s a consequence of these a s s u m p t i o n s . To the e x t e n t t h a t c a r r y o v e r does exceed th e s e a s s u m p t i o n s , the i n f e r e n c e of r e s t r i c t e d gene f l o w w i l l be i n a c c u r a t e . Recent e v i d e n c e s u g g e s t s t h a t t h i s i s an o v e r s i m p l i f i e d and i n a c c u r a t e d e s c r i p t i o n of p o l l e n c a r r y o v e r k i n e t i c s i n g e n e r a l . In c o n t r a s t t o L e v i n and Berube's (1972) r e s u l t , P e r k i n s (1977), w o r k i ng w i t h r u f o u s hummingbirds and emasculated F u s c h i a f l o w e r s , found c a r r y o v e r t o the end of her 20 f l o w e r sequences. C a r r y o v e r was not smooth but was e r r a t i c . Thomson and P l o w r i g h t (1980) found s i m i l a r r e s u l t s f o r bumblebees (Bombus and P s i t h r y u s ) f e e d i n g from E r y t h r o n i u m , C l i n t o n i a , and D i e r v i 1 1 a . P o l l e n d e p o s i t i o n d e c l i n e d r o u g h l y e x p o n e n t i a l l y , but t h e r e was much v a r i a t i o n i n d e p o s i t i o n , and c a r r y o v e r was common t o 18 f l o w e r s (but 10 i n one case p o l l e n was d e p o s i t e d 54 f l o w e r s p a s t the p o l l e n s o u r c e ) . U s i n g powdered dyes as p o l l e n mimics, Waser and P r i c e (1981) found i r r e g u l a r d e p o s i t i o n t o 20 f l o w e r s p a s t the dye s o u r c e s ( f o r Bombus f e e d i n g from D e l p h i n i u m and S e l a s p h o r u s p l a t y c e r c u s f e e d i n g from Ipomopis a g g r e g a t a . The f i r s t q u e s t i o n t h i s c h a p t e r a d d r e s s e s i s : What i s the shape of the p o l l e n c a r r y o v e r c u r v e f o r S e l a s p h o r u s  r u f u s f e e d i n g from C a s t i l l e j a m i n i a t a ? The n u l l h y p o t h e s i s i s s t e e p , smooth, e x p o n e n t i a l decay. Three q u a l i t a t i v e p r e d i c t i o n s of t h i s h y p o t h e s i s a r e : 1) each f l o w e r v i s i t e d has p o l l e n d e p o s i t e d on i t , 2) the amount of p o l l e n d e p o s i t e d i s a c o n s t a n t p r o p o r t i o n of the p o l l e n p r e s e n t on the b i r d ( t h u s the amount d e p o s i t e d d e c r e a s e s w i t h each f l o w e r v i s i t e d ) , and 3) the c o n s t a n t p r o p o r t i o n d e p o s i t e d i s a s u b s t a n t i a l ( i . e . > 0.2) p r o p o r t i o n of what i s p r e s e n t -c a r r y o v e r i s t o o n l y a few f l o w e r s beyond the p o l l e n s o u r c e . The second q u e s t i o n i s : What f a c t o r s a r e r e s p o n s i b l e f o r the form of t h i s r e l a t i o n s h i p ? Two g e n e r a l components t h a t c o u l d be examined a r e the e f f e c t s of hummingbird f o r a g i n g b e h a v i o u r ( i . e . p o s t u r e w h i l e f e e d i n g , response t o n e c t a r s t a n d i n g c r op) and the c h a r a c t e r i s t i c s of f l o r a l d i s p l a y . T h i s s e c t i o n f o c u s s e s on how v a r i a b i l i t y i n f l o r a l morphology i n f l u e n c e s p o l l e n c a r r y o v e r by a f f e c t i n g the geometry of b i r d - f l o w e r c o n t a c t . The f i n a l q u e s t i o n of t h i s s e c t i o n i s : t o what e x t e n t i s p o l l e n from d i f f e r e n t f l o w e r s d e p o s i t e d on hummingbirds' foreheads i n o v e r l a p p i n g l a y e r s - can the p o l l e n from one f l o w e r c o v e r up p o l l e n from a n o t h e r ? A l t h o u g h no one has ad d r e s s e d t h i s q u e s t i o n d i r e c t l y , the i m p l i c i t assumption has been t h a t l a y e r i n g of p o l l e n does not occur (e.g. Waser 1978). C a r r y o v e r i s o f t e n thought of i n terms of p o l l e n d e p o s i t i o n from independent i n d i v i d u a l f l o w e r s . However, p o l l e n can p o t e n t i a l l y be both added t o and removed from the p o o l of p o l l e n on the hummingbird a t each f l o w e r v i s i t e d . I s the p o l l e n i n the p o o l from d i f f e r e n t f l o w e r s removed i n d e p e n d e n t l y , or does the p o l l e n from d i f f e r e n t f l o w e r s i n t e r a c t i n some way t h a t a f f e c t s the p r o b a b i l i t y of i t s d e p o s i t i o n ? I f p o l l e n d e p o s i t e d by l a t e r f l o w e r s i n a sequence of v i s i t s c o v e r e d up p o l l e n from e a r l i e r f l o w e r s , i t would make t h a t p o l l e n u n a v a i l a b l e t o subsequent s t i g m a s . P o l l e n c a r r y o v e r c u r v e s g e n e r a t e d under c o n d i t i o n s where such l a y e r i n g can occur s h o u l d decay f a s t e r than under c o n d i t i o n s where l a y e r i n g does not o c c u r . Note however, t h a t i f p o l l e n was b u r i e d and s u b s e q u e n t l y uncovered, v e r y l o n g c a r r y o v e r c o u l d r e s u l t . M a t e r i a l s and Methods In J u l y of 1979 and 1980, two r u f o u s hummingbirds were caught i n the meadows around G r i z z l y Lake and kept i n h o l d i n g cages made of 3/4 i n c h mesh n y l o n s e i n e n e t t i n g . A s o l u t i o n of sugar, p r o t e i n , and v i t a m i n supplements was p r o v i d e d ad l i b i t u m from f e e d e r s . In o r d e r t o conduct e x p e r i m e n t s , the hummingbirds were t r a i n e d t o fee d from C a s t i l i e j a f l o w e r s p r e s e n t e d i n t e s t 1 2 t u b e s . I t e s t e d d i f f e r e n t methods of p r e s e n t i n g f l o w e r s . P r e s e n t i n g one i n f l o r e s c e n c e ( s e v e r a l f l o w e r s ) per t e s t tube m a i n t a i n e d the most r e a l i s t i c f l o w e r p o s i t i o n , but made i t d i f f i c u l t t o s c o r e sequences of v i s i t s . For the f o l l o w i n g e x p e r i m e n t s , f l o w e r s were p r e s e n t e d one per t e s t tube, u s u a l l y f i v e tubes at a t i m e , 5 cm. a p a r t i n a l i n e a r a r r a y . B e f o r e each e x p e r i m e n t , f l o w e r s were d r a i n e d w i t h a m i c r o -p i p e t t e and a c o n s t a n t amount (5 or 10 m i c r o - l i t e r s ) of i m i t a t i o n n e c t a r added t o each one (32% su c r o s e s o l u t i o n , the mean c o n c e n t r a t i o n of C a s t i l l e j a n e c t a r , L. Gass unpub. d a t a ) . In 1979 I used m i c r o n i z e d , f l u o r e s c e n t , powdered dyes as p o l l e n mimics (R-103-G-111, g r e e n ; R-103-G-112, orange-y e l l o w ; R-103-G-119,.blue; R-103-G-115, r e d ; R a d i a n t C o l o r , 2800 R a d i a n t ave., Richmond, C a l i f o r n i a , see a l s o F r a n k i e 1973, Stockhouse. 1976, P r i c e and Waser 1979; Waser and P r i c e 1981; L i n h a r t and F e i n s i n g e r 1980). Thus these e x p e r i m e n t s s t u d i e d dye c a r r y o v e r r a t h e r than p o l l e n c a r r y o v e r . F l o w e r s f o r use i n ex p e r i m e n t s were chosen from the meadows a t random w i t h the c o n s t r a i n t t h a t they were w i t h i n the range of v a r i a t i o n i n shape and age t h a t we had o b s e r v e d hummingbirds f e e d i n g from i n the w i l d . For the dye c a r r y o v e r e x p e r i m e n t s , a l a r g e , mature ( d e h i s c i n g a n t h e r s , exposed stigma) f l o w e r was chosen from those c o l l e c t e d , and i n j e c t e d w i t h t w i c e the amount of n e c t a r t h a t the dye r e c i p i e n t s had. The stigma and a n t h e r s of the source f l o w e r were c o a t e d w i t h dye, and the 13 hummingbird a l l o w e d t o f e e d u n t i l a spot of dye was v i s i b l e on i t s f o r e h e a d . T h i s sometimes took s e v e r a l v i s i t s . Then the r e m a i n i n g f l o w e r s were p r e s e n t e d t o the hummingbird. T r a i n e d hummingbirds almost always v i s i t e d f l o w e r s i n a l i n e a r sequence w i t h o u t r e v i s i t s . Hummingbirds were f r i g h t e n e d away i f they a t t e m p t e d t o r e v i s i t f l o w e r s . A f t e r the hummingbirds had f e d , f l o w e r s were s c o r e d f o r s t i g m a and a n t h e r p o s i t i o n , and f o r the amount of dye on the s t i g m a s and the a n t h e r s (dye on e i t h e r s t i g m a s or a n t h e r s i n d i c a t e s r e p r o d u c t i v e l y s i g n i f i c a n t b i r d - f l o w e r c o n t a c t ) . Stigma and a n t h e r p o s i t i o n c l a s s e s were d i s t r i b u t e d randomly i n the p r e s e n t a t i o n sequences (p<0.00l; c h i s q u a r e ) . F l o w e r s were u s u a l l y s c o r e d w i t h i n a few hours of c o n d u c t i n g the e x p e r i m e n t , but f l o w e r s from the m u l t i p l e source experiment were s c o r e d over a p e r i o d of s e v e r a l days. The hummingbird's f o r e h e a d was not c l e a n e d between t r i a l s because c l e a n i n g had s t r o n g a d v e r s e e f f e c t s on the hummingbird's subsequent b e h a v i o u r . Dye was r a r e l y v i s i b l e from p r e v i o u s t r i a l s and between t r i a l c a r r y o v e r was m i n i m a l . Dye c o l o r was changed from one t r i a l t o the next t o m i n i m i z e between t r i a l e f f e c t s . For s c o r i n g the amount of dye d e p o s i t e d , I used an index based on the ease of s e e i n g any dye t h a t was p r e s e n t : v i s i b l e by eye under d a y l i g h t (8), v i s i b l e w i t h a t e n power hand l e n s under d a y l i g h t (4), v i s i b l e by eye under u l t r a v i o l e t l i g h t (2), v i s i b l e w i t h t h e hand l e n s under u l t r a v i o l e t l i g h t (1), no dye v i s i b l e under any c o n d i t i o n s 1 4 ( 0 ) . The magnitudes of the numbers a r e my own s u b j e c t i v e i m p r e s s i o n of the magnitude of the d i f f e r e n c e between the l e v e l s , and do not a f f e c t the c o n c l u s i o n s : the t e s t s I a p p l y r e q u i r e a t l e a s t o r d i n a l but not r a t i o measures, and the g e n e r a l q u a l i t a t i v e c o n c l u s i o n s a r e not dependent on the a b s o l u t e v a l u e s of the numbers, but o n l y on t h e i r r e l a t i v e v a l u e s . For the b a s i c d y e / p o l l e n c a r r y o v e r e x p e r i m e n t s t h e r e was o n l y one d y e / p o l l e n s o u r c e . To t e s t the h y p o t h e s i s of l a y e r i n g of p o l l e n or dye from d i f f e r e n t s o u r c e s , I c o n ducted an experiment w i t h m u l t i p l e dye s o u r c e s . B e f o r e the f i r s t , and a f t e r every t e n t h dye r e c i p i e n t f l o w e r i n a sequence, I p r e s e n t e d a d i f f e r e n t dye source t o the b i r d . Three c o l o r s of dye were used and t h e r e were thus 30 r e c i p i e n t f l o w e r s between dye s o u r c e s of the same c o l o r . There were t h r e e c y c l e s of 30 f l o w e r s g i v i n g 9 r e p l i c a t e s , t h r e e f o r each c o l o u r of dye. T h i s experiment was conducted on 16 Aug. 1979. I p r e d i c t e d t h a t i f dye were d e p o s i t e d i n o v e r l a p p i n g l a y e r s , then c a r r y o v e r c u r v e s of i n d i v i d u a l f l o w e r s under m u l t i p l e source c o n d i t i o n s would be s t e e p e r and s h o r t e r than the c u r v e s from the s i n g l e s o u r c e t r i a l s . I f t h e r e i s no l a y e r i n g , s p o t s of dye from d i f f e r e n t s o u r c e s a r e i n d ependent, and the m u l t i p l e s o u r c e c a r r y o v e r c u r v e s s h o u l d be the same as s i n g l e source c u r v e s . Because the amount of dye d e p o s i t e d a t one f l o w e r i s not independent of the dye d e p o s i t e d a t o t h e r f l o w e r s , the 15 use of r e g r e s s i o n i s not a p p r o p r i a t e f o r a n a l y z i n g t h e s e r e s u l t s . I n s t e a d , I c a l c u l a t e d the p r o p o r t i o n of the t o t a l index s c o r e s ( f o r a run of 30 f l o w e r s ) of dye d e p o s i t e d onto the f i r s t t e n , the second t e n , and the t h i r d t e n f l o w e r s . Comparing th e s e p r o p o r t i o n s c o n t r o l s f o r v a r i a t i o n i n the amount of dye d e p o s i t e d on the hummingbird. I f l a y e r i n g o c c u r s i n the m u l t i p l e s o u r c e e x p e r i m e n t , I would expect t o see a g r e a t e r d i f f e r e n c e i n the p r o p o r t i o n of dye d e p o s i t e d t o s e q u e n t i a l groups of t e n f l o w e r s when compared t o the s i n g l e s o u r c e c a r r y o v e r c u r v e s . T h i s i s the same as e x p e c t i n g c u r v e s w i t h s t e e p e r s l o p e s from the m u l t i p l e source e x p e r i m e n t . I m p l i c i t i n t h i s i s the assumption t h a t dye i s not uncovered t o a g r e a t e x t e n t once o t h e r dye has co v e r e d i t up. Two of the s i n g l e s o u r c e c u r v e s have l e s s than 30 f l o w e r s . T h i s w i l l b i a s t h e s e t e s t s towards the n u l l h y p o t h e s i s of no d i f f e r e n c e : e s t i m a t e s of c a r r y o v e r would be dec r e a s e d r e l a t i v e t o what they would have been had t h e r e been 30 f l o w e r s . T h i s w i l l d e c r e a s e the p e r c e i v e d d i f f e r e n c e between the m u l t i p l e source and s i n g l e source v a l u e s i f the n u l l h y p o t h e s i s i s indeed f a l s e . I s i t j u s t i f i e d t o assume t h a t powdered dyes a r e good p o l l e n mimics? T h i s s t u d y f o c u s s e s on q u a l i t a t i v e p r o p e r t i e s of p o l l e n c a r r y o v e r ( e . g . every f l o w e r r e c e i v e s dye, e x p o n e n t i a l decay, e t c . ) , and the s e p r o p e r t i e s s h o u l d be consequences p r i m a r i l y of the geometry of b i r d - f l o w e r c o n t a c t . Any s m a l l powdery substance s h o u l d mimic the g r o s s 16 b e h a v i o u r of p o l l e n , o t h e r t h i n g s ( e . g . s t i c k i n e s s ) b e i n g e q u a l . However, q u a n t i t a t i v e r e s u l t s s h o u l d be i n t e r p r e t e d c o n s e r v a t i v e l y . J . Thomson ( p e r s . comm.) has found t h a t w h i l e dyes s l i g h t l y o v e r e s t i m a t e d p o l l e n c a r r y o v e r ( f o r Bombus f e e d i n g on E r y t h r o n i u m ) , they d i d show the same q u a l i t a t i v e b e h a v i o u r as h i s t r i a l s w i t h p o l l e n . T h i s r e s u l t seems r e a s o n a b l e t o g e n e r a l i z e t o the S e l a s p h o r u s - C a s t i l l e j a system. In 1980 I conducted s e v e r a l t e s t s u s i n g a C a s t i l i e j a p o l l e n source ( v i r g i n s t igma and a n t h e r s ) , and em a s c u l a t e d r e c i p i e n t s ( v i r g i n s t i g m a s ) . I a l s o ran t r i a l s u s i n g d i f f e r e n t c o l o r and s i z e morphs of t u l i p p o l l e n . Though C a s t i l l e j a and t u l i p p o l l e n t r i a l s d i f f e r e d q u a n t i t a t i v e l y from each o t h e r and from the dye e x p e r i m e n t s , they were q u a l i t a t i v e l y s i m i l a r . T h i s l e n d s credence t o the use of dyes f o r p r e l i m i n a r y e x p l o r a t i o n s . The t u l i p and C a s t i l l e j a p o l l e n c a r r y o v e r e x p e r i m e n t s were not c o n t i n u e d because of l o g i s t i c a l problems. In August 1980, 203 f l o w e r s were randomly chosen and photographed. T h e i r r e p r o d u c t i v e s t a t e and m o r p h o l o g i c a l c l a s s e s were r e c o r d e d and the s e d a t a were used t o t e s t f o r • the independence of f l o r a l morphology and r e p r o d u c t i v e s t a t e . By p r o j e c t i n g the photgraphs onto an A p p l e microcomputer g r a p h i c s t a b l e t , I was a b l e t o ta k e measurements of f l o r a l v a r i a b i l i t y t h a t were used i n the m o d e l l i n g c h a p t e r . 17 R e s u l t s In g e n e r a l , c a r r y o v e r was l o n g and i r r e g u l a r . Some f l o w e r s r e c e i v e d no dye a t a l l w h i l e o t h e r s f o l l o w i n g them r e c e i v e d a g r e a t d e a l . The r e s u l t s of the b a s i c dye c a r r y o v e r e x p e r i m e n t s a r e shown i n f i g u r e s 2 and 3. They are c h a r a c t e r i z e d by h i g h v a r i a b i l i t y i n the amount of dye d e p o s i t e d , i r r e g u l a r l y spaced " b l a n k s " where no dye i s d e p o s i t e d , and r e l a t i v e l y l o n g c a r r y o v e r . We can thus r e j e c t t h e n u l l h y p o t h e s i s of smooth, s t e e p , e x p o n e n t i a l decay. T a b l e I shows the means and extremes f o r dye c a r r y o v e r f o r the t o t a l number of f l o w e r s i n the r u n , and f o r the run t r u n c a t e d t o 23 f l o w e r s (the l e n g t h of the s h o r t e s t r u n ) . N o t i c e t h a t the mean dye c a r r y o v e r d i s t a n c e i s dependent on run s i z e . A l i n e a r r e g r e s s i o n on the combined d a t a from these runs has an x i n t e r c e p t a t 36 f l o w e r s f o r dye d e p o s i t e d on s t i g m a s , and 45 f l o w e r s f o r dye d e p o s i t e d on a n t h e r s ( T a b l e I I ) . L i n e a r r e g r e s s i o n s h o u l d u n d e r e s t i m a t e dye c a r r y o v e r i f c a r r y o v e r does decay e x p o n e n t i a l l y . These e q u a t i o n s a r e i n c l u d e d f o r comparison w i t h o t h e r p u b l i s h e d v a l u e s and w i l l not be used i n my a n a l y s i s . What r o l e does f l o w e r v a r i a b i l i t y p l a y i n the v a r i a b i l i t y i n dye d r o p o f f ? F i g u r e 4 shows an example of the mean amount of dye d e p o s i t e d on stigmas and a n t h e r s of d i f f e r e n t m o r p h o l o g i c a l c l a s s e s i n one run (dye d e p o s i t e d from the spot of dye from one s o u r c e ) . Some c l a s s e s r e c e i v e a d i s p r o p o r t i o n a t e amount of dye. Even when the r e s u l t s of gure 2. Dye d e p o s i t i o n c u r v e s e x p e r i m e n t s - dye d e p o s i t e d e x p l a n a t i o n of the index of from the 4 s i n g l e source on s t i g m a s . See t e x t f o r the amount of dye d e p o s i t e d . 19 if) CTj E 8 U) V - > oo c 4 | O 21 r O X 4 (D C 2 11 n= 23 L i n = 42 1 n =24 n = 41 M M 10 20 30 40 10 20 30 4 0 f l o w e r presentat ion sequence 20 F i g u r e 3. Dye d e p o s i t i o n c u r v e s e x p e r i m e n t s - dye d e p o s i t e d e x p l a n a t i o n of the index of from the 4 s i n g l e source on a n t h e r s . See t e x t f o r the amount of dye d e p o s i t e d . 10 2 0 3 0 4 0 10 2 0 3 0 4 0 f l owe r p resenta t ion sequence gure 4 . Dye d e p o s i t i o n on s t i g m a s and a n t h e r s of d i f f e r e n t m o r p h o l o g i c a l c l a s s e s . Data from 1 f l o w e r sequence, i . e . dye o r i g i n a t e d from one s o u r c e . Though f l o r a l morphology i s r e l a t e d t o f l o r a l age, the sequence of m o r p h o l o g i c a l c l a s s e s p r e s e n t e d here does not r e p r e s e n t an a g i n g sequence, i . e . c l a s s 8 s t i g m a s a r e not n e c c e s s a r i l y o l d e r than c l a s s 7 s t i g m a s . an t he r c lass 24 T a b l e I . Means and extremes of dye c a r r y o v e r from the l a b o r a t o r y e x p e r i m e n t s . s i n g l e source t r u n c a t e d t o 23 f l o w e r s whole run s t igmas a n t h e r s s t i g m a s a n t h e r s mean ext mean ext mean ext mean ext 8.9 23 14.1 22 8.9 23 14. 1 22 n 7.5 22 8.9 23 7.5 22 8.9 23 n 11.4 21 7.5 22 17.6 32 11.5 41 n 15.7 22 9.5 20 19.4 40 19.3 41 n m u l t i p l e s o u r c e s 11.8 15 10.7 19 8.0 18 6.6 1 2 9.1 22 4.8 7 2.0 2 4.3 9 7.3 21 6.8 18 5.1 10 4.6 10 9.5 18 9.0 15 6.5 9 5.9 18 ex t = extreme a l l runs a r e combined ( F i g . 5 ) , c e r t a i n c l a s s e s r e c e i v e more dye than o t h e r s . T able I I I summarizes t e s t s of the independence of dye d e p o s i t i o n and st i g m a and a n t h e r c l a s s e s . S i x out of 7 t e s t s showed s i g n i f i c a n t l y non-random d e p o s i t i o n of dye among the s e morphology c l a s s e s . 25 F i g u r e 5. Dye d e p o s i t i o n on s t i g m a s and a n t h e r s of d i f f e r e n t m o r p h o l o g i c a l c l a s s e s . Combined d a t a from 4 r u n s , i . e . dye o r i g i n a t e d from s e v e r a l s o u r c e s . mean amount of dye o R) k b> oo 5 r- 1 1 • • — i r i • • .27 T a b l e I I . P r e d i c t i v e l i n e a r r e g r e s s i o n e q u a t i o n s ( f o r p o o l e d s i n g l e s o u r c e and p o o l e d m u l t i p l e source data) of dye d e p o s i t e d on f l o w e r p r e s e n t a t i o n sequence. E n t i r e runs used, see T a b l e I f o r l e n g t h s s i n g l e s o u r c e dye on a n t h e r s dye on stigmas y = 1.16 - 0.03x x i n t e r c e p t = 36 r = 0.24 n = 1 30 y = 2.78 - 0.06x x i n t e r c e p t = 45 r = 0.30 n = 1 30 m u l t i p l e source dye on stigmas dye on a n t h e r s y = 0.72 - 0.03x x i n t e r c e p t = 28 r = 0.26 n = 260 y = 1.30 - 0.05x x i n t e r c e p t = 28 r = 0.33 n = 260 Based on the f i e l d measures of 1980, the s e stigma and a n t h e r c l a s s e s based on morphology are not independent of stigma and a n t h e r c l a s s e s based on r e p r o d u c t i v e s t a t e . The p r o b a b i l i t y t h a t shape c l a s s e s and age c l a s s e s a r e independent i s < 0.001 f o r both st i g m a s and a n t h e r s . The c o n t i n g e n c y c o e f f i c i e n t C i s 0.40 f o r the r e l a t i o n between st i g m a shape and stigma age c l a s s e s and i s 0.52 f o r a n t h e r shape and a n t h e r r e p r o d u c t i v e s t a t e c l a s s e s (see S i e g e l 1956 f o r d e s c r i p t i o n of the c o n t i n g e n c y c o e f f i c i e n t ) . Thus 28 T a b l e I I I . Summary of Chi Squared t e s t s f o r the independence of dye d e p o s i t i o n on d i f f e r e n t s t i g m a and a n t h e r c l a s s e s . ( d a t a a r e from s i n g l e source e x p e r i m e n t s ) stigma c l a s s e s t r i a l s i g n i f i c a n c e 1 p = 0.001 2 ac c e p t Ho 3 e x p e c t e d v a l u e s too low f o r t e s t 4 p = 0.05 an t h e r c l a s s e s t r i a l s i g n i f i c a n c e 1 p = 0.001 2 p = 0.02 3 p = 0.05 4 p = 0.001 f l o w e r s of d i f f e r e n t r e p r o d u c t i v e s t a t e have d i f f e r e n t l i k e l i h o o d s of r e c e i v i n g dye. Some of t h i s i s l i k e l y t o be s t r i c t l y due t o g e o m e t r i c f a c t o r s , and some due t o f a c t o r s such as the g r e a t e r s t i c k i n e s s of r e c e p t i v e s t i g m a s . S i m i l a r l y , i n the one run f o r which t h e r e are a p p r o p r i a t e d a t a , dye was not d e p o s i t e d randomly w i t h r e s p e c t t o f l o w e r l e n g t h (p = 0.02; c h i square, F i g . 6 ) . These r e s u l t s suggest t h a t dye (or p o l l e n ) t r a n s f e r from one f l o w e r t o another depends on congruence i n the 29 F i g u r e 6. Dye d e p o s i t i o n on f l o w e r s of d i f f e r e n t l e n g t h s . Data from 1 f l o w e r sequence, i . e . dye o r i g i n a t e d from 1 s o u r c e . Data a r e dye d e p o s i t e d on a n t h e r s . 3 © 1.0r T3 .8 .6 c o .4 o .2 o 12-14 14-16 16-18 18-20 20-22 22-24 coro l l a length c l a s s e s (mm) 31 l o c a t i o n s where the two f l o w e r s c o n t a c t the hummingbird, which i s dependent on s i m i l a r i t y i n t h e i r m o r p h o l o g i e s . Thus a s h o r t f l o w e r w i t h i t s c o r o l l a tube bent t o the r i g h t i s u n l i k e l y t o p o l l i n a t e a l o n g , s t r a i g h t f l o w e r w i t h an e r e c t s t i g m a . Because of s t o c h a s t i c f a c t o r s such as the wind b l o w i n g the f l o w e r s w h i l e the b i r d i s f e e d i n g , and v a r i a t i o n i n the b i r d ' s b e h a v i o u r ( e.g. i n t r u d e r s f e e d much d i f f e r e n t l y than t e r r i t o r i a l r e s i d e n t s ; p e r . o b s . ) , t h i s i s not a s i m p l e d e t e r m i n i s t i c c o r r e s p o n d e n c e , and f l o w e r s do o c c a s i o n a l l y have t h e i r p o l l e n d e p o s i t e d on d i s s i m i l a r t y p e s . I compared the s i n g l e s o u r c e data w i t h the m u l t i p l e s o u r c e data i n t h r e e ways: comparing the d i f f e r e n c e i n the p r o p o r t i o n of the dye t h a t was d e p o s i t e d on s e q u e n t i a l groups of ten f l o w e r s , the f l o w e r t o which the mean index u n i t of dye was c a r r i e d , and the l a s t f l o w e r i n the run t o r e c e i v e dye. In g e n e r a l , the data s u p p o r t the l a y e r i n g h y p o t h e s i s , ( f o r d a t a see F i g . 7, f o r t e s t r e s u l t s see T a b l e I V ) . The comparisons of the p r o p o r t i o n of dye d e p o s i t e d on a d j a c e n t groups of ten f l o w e r s were e q u i v o c a l : they showed s i g n i f i c a n t d e c r e a s e s i n d r o p o f f f o r dye d e p o s i t e d on m u l t i p l e source s t i g m a s , but not f o r dye d e p o s i t e d on a n t h e r s . However, when the d i f f e r e n c e s between f l o w e r s 1-10 and 21-30 were compared, the d i f f e r e n c e s between the m u l t i p l e source v a l u e s were s i g n i f i c a n t l y g r e a t e r f o r both -st i g m a s and a n t h e r s . 32 F i g u r e 7. The p r o p o r t i o n of t o t a l dye d e p o s i t e d t h a t was d e p o s i t e d on the f i r s t , second, and t h i r d group of 10 f l o w e r s . d y e on s t i gmas dye on an the r s 1-1Q 11-20 21-30 1-10 11-20 21-30 f l o w e r presentat ion sequence .34 T a b l e IV. Comparison of d i f f e r e n c e s i n the p r o p o r t i o n of t o t a l dye d e p o s i t e d , s i n g l e source v s . m u l t i p l e s o u r c e e x p e r i m e n t s (Mann-Whitney U t e s t s ) . 1) comparing the p r o p o r t i o n d e p o s i t e d on f l o w e r s 1-10 w i t h f l o w e r s 11-20: dye on stigmas dye on a n t h e r s p=0.055 p=0.230 ms > ss ms = ss 2) comparing the p r o p o r t i o n d e p o s i t e d on f l o w e r s 11-20 w i t h f l o w e r s 21-30: dye on stigmas dye on a n t h e r s p=0.036 + p=0.285 ms > ss ms = ss 3) comparing the p r o p o r t i o n d e p o s i t e d on f l o w e r s 1-10 w i t h f l o w e r s 21-30: dye on stigmas dye on a n t h e r s p=0.024 p=0.055 ms > ss ms > ss + = approximate v a l u e because of t i e s . T a b l e V compares the means and extremes of p o l l e n c a r r y o v e r f o r s i n g l e and m u l t i p l e s o u r c e d a t a . S i n g l e and m u l t i p l e s o u r c e c u r v e s d i d not d i f f e r i n the mean c a r r y o v e r f o r s t i g m a s , but d i f f e r e d s i g n i f i c a n t l y f o r a n t h e r s , c a r r y o v e r b e i n g l o n g e r f o r s i n g l e s o u r c e c u r v e s . The l a s t f l o w e r i n the sequence t o r e c e i v e dye was s i g n i f i c a n t l y f a r t h e r i n the sequence f o r s i n g l e s o u r c e runs f o r both st i g m a s and a n t h e r s . 35 T a b l e V. Summary of t e s t s of mean and maximum dye c a r r y o v e r comparing s i n g l e and m u l t i p l e source t r i a l s (Mann-Whitney U t e s t ) . comparing means: s i n g l e source ( s s ) v s . m u l t i p l e source (ms) sti g m a s a n t h e r s p = 0.107 p = 0.036 ss = ms ss > ms comparing extremes: s i n g l e s t igmas p = 0.021 ss > ms source vs m u l t i p l e source a n t h e r s p = 0.003 ss > ms D u r i n g the c o u r s e of the experiment we were a b l e t o observe dye of d i f f e r e n t c o l o r s (and t h e r e f o r e from d i f f e r e n t s o u r c e s ) o v e r l a p p i n g on the hummingbird's f o r e h e a d , p r o v i d i n g d i r e c t support f o r the l a y e r i n g h y p o t h e s i s . D i s c u s s i o n S i n g l e Source Experiments Dye d e p o s i t i o n , and by i n f e r e n c e p o l l e n d e p o s i t i o n , does not f o l l o w a s i m p l e e x p o n e n t i a l decay model, but de c r e a s e s as a complex f u n c t i o n of f l o w e r morphology, p r o b a b l y v a r i a b i l i t y i n hummingbird b e h a v i o u r , and s t o c h a s t i c f a c t o r s , such as the weather. T h i s r e s u l t s i n many f l o w e r s b e i n g " b l a n k s " which do not i n t e r a c t w i t h the 3 6 p o o l of p o l l e n on the b i r d , and thus extends the number of f l o w e r s t o which p o l l e n i s c a r r i e d . Note t h a t w h i l e a g i v e n f l o w e r may not r e c e i v e any of the p o l l e n t h a t the hummingbird p i c k e d up from any o t h e r g i v e n f l o w e r , and thus c o n s t i t u t e s a b l a n k i n t h a t sequence, i t may r e c e i v e p o l l e n t h a t the hummingbird p i c k e d up from o t h e r f l o w e r s , and does not n e c c e s s a r i l y r e c e i v e not p o l l e n a t a l l . I n c r e a s e s i n c a r r y o v e r may be v e r y i m p o r t a n t t o the p l a n t s . O b l i g a t e l y o u t c r o s s i n g p l a n t s t h a t produce l a r g e numbers of f l o w e r s commonly have o n l y a s m a l l p r o p o r t i o n of t h e i r o v u l e s s e t t i n g seed, p u r p o r t e d l y due t o a f l o o d i n g of the p o l l e n p o o l w i t h s e l f e d p o l l e n (see d i s c u s s i o n below, and see Bawa 1974; F r a n k i e et a l . 1976; Schemske 1980). Because C a s t i l l e j a i s s e l f i n c o m p a t i b l e and produces many f l o w e r s , and s h o r t between-flower f l i g h t s by hummingbirds predominate i n t h i s system ( P e r k i n s 1977), i n c r e a s e s i n c a r r y o v e r w i l l i n c r e a s e the l i k e l i h o o d of o u t c r o s s i n g , and t h u s i n c r e a s e p l a n t f i t n e s s . The p r o p o r t i o n of f l o w e r s t h a t a r e b l a n k s may be an i m p o r t a n t way t h a t the p l a n t s are a b l e t o i n f l u e n c e mate i d e n t i t y ( i . e . s e l f v s . non - s e l f ) . T h i s does not imply group s e l e c t i o n . One p l a n t may have many f l o w e r s r e p r o d u c t i v e a t a s i n g l e t i m e , and may r e p r e s e n t a s i g n i f i c a n t subset of t h e p o p u l a t i o n of f l o w e r s t h a t a hummingbird v i s i t s . I f an i n d i v i d u a l p l a n t ' s c h a r a c t e r s can i n c r e a s e i t s f i t n e s s by m a n i p u l a t i n g the p r o p o r t i o n of b l a n k s i t s p o l l e n e x p e r i e n c e s , then those i n d i v i d u a l s w i l l be s e l e c t e d f o r . 37 The p r o p o r t i o n of b l a n k s w i l l p r o b a b l y change t h r o u g h a season s i n c e f l o w e r morphology c l a s s e s a r e r e l a t e d t o f l o w e r age c l a s s e s , and the d i s t r i b u t i o n of f l o w e r age c l a s s e s changes as the season p r o g r e s s e s (note though t h a t the p r o p o r t i o n of b l a n k s i s a f u n c t i o n of the v a r i a n c e i n f l o w e r morphology, and not morphology per se. T h i s v a r i a n c e w i l l p r o b a b l y i n c r e a s e t o the peak of f l o w e r i n g and then d e c r e a s e . ) . F lower d e n s i t y , the number of t e r r i t o r i e s i n a meadow, t e r r i t o r y s i z e s , and the number of p l a n t s r e p r e s e n t e d i n a g i v e n t e r r i t o r y change t h r o u g h the season a l s o (Gass 1979), and i t w i l l be i m p o r t a n t t o i n t e g r a t e a l l t h e s e s e a s o n a l changes i n terms of t h e i r consequences f o r p o l l e n f l o w between p l a n t s . Does a p l a n t ' s o p t i m a l s t r a t e g y of f l o r a l d i s p l a y change t h r o u g h the season, e m p h a s i z i n g maleness a t one p e r i o d and femaleness at a n o t h e r ? I f so, do p l a n t ' s . a c t u a l f l o r a l d i s p l a y s r e f l e c t t h i s ? Thomson and P l o w r i g h t (1980) observed much v a r i a t i o n i n p o l l e n d e p o s i t i o n by bumblebees, i n c l u d i n g some f l o w e r s t h a t had no p o l l e n d e p o s i t e d on them a t a l l . They a l s o a t t r i b u t e d t h i s t o v a r i a t i o n i n f l o r a l geometry and ' p o l l i n a t o r p o s t u r e , but s u g g e s t e d t h a t such "haphazard" d e p o s i t i o n i s m a l a d a p t i v e because i t might d e c r e a s e the p r o b a b i l i t y of s u c c e s s f u l t r a n s f e r . T h i s c o u l d be v a l i d when a few (<30 or so) f l o w e r s are f e d on. Patchy placement of p o l l e n w i l l d ecrease the l i k e l i h o o d of t r a n s f e r s i n c e any g i v e n f l o w e r would be l e s s l i k e l y t o c o n t a c t the a n i m a l i n a l o c a t i o n where p o l l e n had been p r e v i o u s l y d e p o s i t e d . 38 However, i f many f l o w e r s a r e v i s i t e d (the u s u a l s i t u a t i o n f o r b o th hummingbirds and b e e s ) , the p o l l e n p o o l as a whole becomes l e s s patchy s p a t i a l l y , w h i l e r e t a i n i n g i t s h e t e r o g e n e i t y i n terms of p o l l e n s o u r c e i d e n t i t y . Thus the s i t u a t i o n where patchy d e p o s i t i o n of p o l l e n i s m a l a d a p t i v e i s l i k e l y t o be an uncommon s p e c i a l c a s e . C a s t i l l e j a e x h i b i t s both p r e c i s i o n i n p o l l e n placement, and v a r i a b i l i t y between placements (compared t o , f o r i n s t a n c e , A q u i l e g i a , a s e l f - c o m p a t i b l e s p e c i e s ) . Both of these w i l l be l e s s i m p o r t a n t f o r s e l f - c o m p a t i b l e s p e c i e s . I f s e l f i n g i s not d e t r i m e n t a l , then broad d e p o s i t i o n of p o l l e n and o v e r l a p p i n g a r e a s of f l o r a l c o n t a c t on the b i r d w i l l i n c r e a s e the p r o b a b i l i t y of p o l l e n t r a n s f e r w i t h no r e s u l t i n g l o s s i n f i t n e s s when o n l y a few f l o w e r s a r e v i s i t e d . M u l t i p l e Source Experiment The h y p o t h e s i s t h a t p o l l e n may be d e p o s i t e d i n p a r t i a l l y or t o t a l l y o v e r l a p p i n g l a y e r s i s t e n t a t i v e l y s u p p o r t e d . What a r e the consequences of l a y e r i n g on p o l l e n c a r r y o v e r ? I t has the o p p o s i t e e f f e c t t o f l o w e r v a r i a b i l i t y i n t h a t i t d e c r e a s e s c a r r y o v e r on the s h o r t term. However, on a l o n g e r time s c a l e , i t may l e a d t o ve r y l o n g c a r r y o v e r s i n c e p o l l e n t h a t i s c o v e r e d up may be exposed s u b s e q u e n t l y by p r e e n i n g , or the s l o u g h i n g o f f or d e p o s i t i o n of upper l a y e r s (see d i s c u s s i o n i n next c h a p t e r ) . T h i s c o u l d l e a d t o e x t e n s i v e c a r r y o v e r between f o r a g i n g f l i g h t s . 39 P e r k i n s (1977) c o n c l u d e d t h a t between f o r a g i n g f l i g h t c a r r y o v e r i s p r o b a b l y t h e most i m p o r t a n t component i n between genome p o l l e n t r a n s f e r . The l e n g t h of time t h a t p o l l e n i s v i a b l e once removed from the a n t h e r s may s e t l i m i t s t o the b e n e f i t s a c c r u i n g from t h i s u n c o v e r i n g p r o c e s s ( p o l l e n v i a b i l i t y i s s e n s i t i v e t o u l t r a v i o l e t r a d i a t i o n ( P e r c i v a l 1965), r e l a t i v e h u m i d i t y , and temperature ( S t a n l e y and L i n s k e n s ( 1 9 7 4 ) ) . F r a n k i e e t §_1. (1976) have suggested t h a t c a r r y o v e r of r e s i d u a l p o l l e n from day t o day may be i m p o r t a n t f o r o u t c r o s s i n g . In t h e i r system, day o l d p o l l e n i s v i a b l e and the s e l f - i n c o m p a t i b l e t r e e s they were s t u d y i n g s e t more seed than c o u l d be e x p l a i n e d by t h e i r assumption of almost no c a r r y o v e r . P r e l i m i n a r y e v i d e n c e suggests t h a t l a y e r i n g o c c u r s on bumblebees as w e l l ( J . Thomson, p e r s . comm.). I have been r e f e r r i n g t o the p o o l of p o l l e n on the hummingbird as i f i t were neat and h i g h l y s t r u c t u r e d . I t p r o b a b l y i s not. But i t i s d i s t i n c t l y t h r e e d i m e n s i o n a l , and i s p r o b a b l y heterogeneous w i t h r e s p e c t t o p o l l e n i d e n t i t y i n a l l t h r e e d i m e n s i o n s . When I examined p o l l e n p o o l s on both c a p t i v e and w i l d b i r d s , they were i r r e g u l a r and o f t e n d i s c o n t i n u o u s , and they p e n e t r a t e d the t h r e e d i m e n s i o n a l s t r u c t u r e of the f e a t h e r s . I t took s e v e r a l a p p l i c a t i o n s of tape t o the same p l a c e on a p o l l e n p o o l i n a b i r d ' s f e a t h e r s t o remove a l l the p o l l e n . 40 P l a n t - P l a n t T r a n s f e r T a k i n g i n t o account l a y e r i n g , and the p r o b a b l e o v e r e s t i m a t i o n of p o l l e n c a r r y o v e r by dye c a r r y o v e r (see methods), we can assume, f o r s p e c u l a t i v e p u r p o s e s , t h a t a c a r r y o v e r l i m i t of 15 t o 20 f l o w e r s p a s t the source i s common i n t h i s system. In the average bout of f o r a g i n g , a hummingbird w i l l v i s i t 21 f l o w e r s on 3-10 p l a n t s ( P e r k i n s 1977). Thus c a r r y o v e r t o 2-9 p l a n t s p a s t the sour c e s h o u l d be common, and f o r l a t e r p l a n t s i n a f l i g h t , between bout c a r r y o v e r s h o u l d be s i g n i f i c a n t . Any c a r r y o v e r due t o u n c o v e r i n g of b u r i e d p o l l e n w i l l be i n a d d i t i o n t o t h i s . T h i s c o n c l u s i o n i s i n c o n t r a s t t o t h a t of L e v i n and K e r s t e r (1969 a) who c o n c l u d e d t h a t c a r r y o v e r t o 3-10 p l a n t s was a " g r o s s o v e r e s t i m a t e " i n a b e e - p l a n t system. Thomson and P l o w r i g h t ' s (1980, and Thomson p e r s . comm.) e s t i m a t e s of bee c a r r y o v e r a r e between L e v i n and K e r s t e r ' s (1969a) assumption f o r bees, L e v i n and Berube's (1972) f i n d i n g s f o r C o l i a s b u t t e r f l i e s , and my own v a l u e s f o r hummingbirds. Waser and P r i c e (1981) r e p o r t p o l l e n c a r r y o v e r v a l u e s f o r bumblebees (Bombus) t h a t a r e comparable t o Thomson and P l o w r i g h t ' s . They found h i g h e r c a r r y o v e r f o r hummingbirds (S. p l a t y c e r c u s ) than f o r bees, but not as h i g h as I found f o r S. r u f o u s . 41 Bumblebee-Humminqbird Comparison Many e x p e r i m e n t a l s t u d i e s of p o l l i n a t o r - p l a n t systems have i n v o l v e d bumblebees or hummingbirds (e.g. Pyke 1978; P r i c e and Waser 1979; Thomson and P l o w r i g h t 1980; P l e a s a n t s and Zimmerman 1980; Waser and P r i c e 1981). There a r e im p o r t a n t d i f f e r e n c e s between th e s e two c l a s s e s of p o l l i n a t o r s t h a t have consequences f o r p o l l e n t r a n s f e r k i n e t i c s . Bumblebees o f t e n f o r a g e f o r p o l l e n , hummingbirds do n o t , and bumblebees r e g u l a r l y remove p o l l e n from i t s d e p o s i t i o n s i t e s on t h e i r b o d i e s w h i l e grooming, and thus change the c h a r a c t e r of the p o l l e n p o o l subsequent t o the d e p o s i t i o n of p o l l e n (Thomson and P l o w r i g h t 1980). While p r e e n i n g by hummingbirds may have the same e f f e c t as grooming by bumblebees, i t i s p r o b a b l y not as common w h i l e f o r a g i n g , or as e x t e n s i v e . Waser and P r i c e (1981) r e p o r t a s t r o n g e r r e l a t i o n s h i p between dye d r o p o f f and f l o w e r v i s i t a t i o n sequence f o r bumblebees than f o r hummingbirds (r=-0.44 vs -0.23, compare w i t h T able I I ) . Grooming by the bumblebees may reduce the e f f e c t s of f l o r a l and b e h a v i o u r a l v a r i a b i l i t y on p o l l e n c a r r y o v e r , l e a d i n g t o a s t r o n g e r e f f e c t of f l o w e r sequence, and fewer " b l a n k s " . T h i s c o u l d a l s o e x p l a i n the s h o r t e r , s t e e p e r , c a r r y o v e r c u r v e s t h a t have been found f o r bumblebees. Because of th e s e d i f f e r e n c e s , the tendency t o g e n e r a l i z e q u a n t i t a t i v e l y between t h e s e systems must be c a r e f u l l y r e a p p r a i s e d . 42 Male V e r s u s Female F u n c t i o n A s e l f - i n c o m p a t i b l e p l a n t s h o u l d m i n i m i z e the t r a n s f e r of p o l l e n between i t s own f l o w e r s . One l o g i c a l extreme of t h i s c o u l d be a c c o m p l i s h e d by h a v i n g o n l y one f l o w e r mature at a t i m e . T h i s would maximize t h a t f l o w e r ' s r e p r o d u c t i v e s u c c e s s t h r o u g h female f u n c t i o n , but would p r o b a b l y not maximize the b e n e f i t t o the p l a n t as a whole. The more f l o w e r s a p l a n t p r e s e n t s , the h i g h e r i t s s u c c e s s t h rough male f u n c t i o n - i t w i l l f l o o d the p o l l e n p o o l and s h o u l d p o l l i n a t e many o t h e r f l o w e r s . However, the more f l o w e r s a p l a n t has s i m u l t a n e o u s l y , the more l i k e l y i t w i l l be s e l f e d . Augspurger (1980) d e s c r i b e s a s i m i l a r s i t u a t i o n f o r a t r o p i c a l m a s s - f l o w e r i n g s h r u b , where much s e l f i n g i s e x p e c t e d due t o " f l o o d i n g " of the p o l l i n a t o r s by p o l l e n from the l a r g e number of f l o w e r s a s i n g l e p l a n t p r e s e n t s (see a l s o Schemske 1980). Freeman et_ a l . (1980) suggest t h a t i n p a t c h y environments p l a n t s w i l l b e n e f i t from l a b i l e s e x u a l e x p r e s s i o n , and t h a t e n v i r o n m e n t a l d e t e r m i n a t i o n of s e x u a l e x p r e s s i o n i s much more common than has g e n e r a l l y been assumed. I suggest t h a t i n a d d i t i o n t o the p r o d u c t i o n of s t r i c t l y male or female f l o w e r s , p l a n t s c o u l d a c h i e v e t h i s k i n d of s e x u a l t r a c k i n g of t h e i r environment by s u b t l e t u n i n g of t h e i r f l o r a l d i s p l a y . C h a r a c t e r s such as the number of f l o w e r s produced, v a r i a t i o n i n f l o r a l morphology, n e c t a r p r o d u c t i o n r a t e , n e c t a r c o n c e n t r a t i o n , and the time c o u r s e s of a n t h e r d e h i s c e n c e and s t i g m a l r e c e p t i v i t y c o u l d 43 a c t t o g e t h e r t o make an apparent hermaphrodite f u n c t i o n a l l y o n l y one sex. When w i l l i t pay t o ensure s u c c e s s t h r o u g h male f u n c t i o n a t the expense of su c c e s s t h rough female f u n c t i o n ? When w i l l i t pay t o compromise a t bo t h and r i s k not d o i n g w e l l a t e i t h e r ? How th e s e d i f f e r e n t components of f l o r a l d i s p l a y i n t e r a c t w i t h each o t h e r and w i t h p o l l i n a t o r b e h a v i o u r t o r e s u l t i n p a t t e r n s of p o l l i n a t i o n and f i t n e s s i s the key problem f a c i n g p o l l i n a t i o n e c o l o g y i n the near f u t u r e . C o n c l u s i o n s Past a n a l y s e s have tended t o i g n o r e v a r i a b i l i t y i n p o l l e n t r a n s f e r . V a r i a b i l i t y i n f l o r a l morphology appears t o p l a y a c r u c i a l r o l e i n d e t e r m i n i n g not o n l y the l e n g t h of p o l l e n c a r r y o v e r , but t o which i n d i v i d u a l s p o l l e n i s c a r r i e d . In the f u t u r e , v a r i a b i l i t y s h o u l d be c o n s i d e r e d as an i m p o r t a n t f a c t o r i n i t s e l f , and not averaged out i n the a n a l y s i s . T h i s i s most t r u e f o r s p e c i e s i n which v a r i a t i o n i n p o l l i n a t o r - f l o w e r geometry i s g r e a t , e i t h e r due t o c h a r a c t e r s of the p o l l i n a t o r , o r of the p l a n t . R e s e a r c h e r s study l o n g e r sequences of f l o w e r s than has been the norm i n the p a s t . U s i n g s h o r t sequences b i a s e s the r e s u l t towards s h o r t c a r r y o v e r . I f l o n g c a r r y o v e r i s o c c u r r i n g , i t w i l l not be d e t e c t e d i n s h o r t f l o w e r sequences. These r e s u l t s a r e not c o n c l u s i v e , but suggest r e a l i s t i c a l t e r n a t i v e hypotheses f o r the shapes of p o l l e n c a r r y o v e r c u r v e s and the p r o c e s s e s t h a t g e n e r a t e them. 45 ALTERNATIVE MODELS OF POLLEN TRANSFER "... even when we have c o r r e c t p r e m i s e s , i t may be v e r y d i f f i c u l t t o d i s c o v e r what they i m p l y . A l l c o r r e c t r e a s o n i n g i s a grand system of t a u t o l o g i e s , but o n l y God can make d i r e c t use of t h a t f a c t . The r e s t of us must p a i n s t a k i n g l y and f a l l i b l y t e a s e out the consequences of our a s s u m p t i o n s . " Simon (1981) . I n t r o d u c t i o n T r a n s f e r of p o l l e n among f l o w e r s i s a fundamental component of gene f l o w i n many p l a n t s p e c i e s . I n the l i t e r a t u r e , p o l l e n d i s p e r s a l i s o f t e n d e s c r i b e d by t h r e e components: p o l l i n a t o r f l i g h t d i s t a n c e s , p o l l i n a t o r d i r e c t i o n a l i t y , and p o l l e n c a r r y o v e r . P o l l i n a t o r f l i g h t d i s t a n c e s have r e c e i v e d much a t t e n t i o n as e s t i m a t o r s of p o l l e n d i s p e r s a l ( L e v i n and K e r s t e r 1969a,b; L e v i n e_t a l . 1971; B e a t t i e 1978; B e a t t i e and C u l v e r 1979; S c h m i t t 1980; Waser and P r i c e 1981), and v a r i o u s a s p e c t s of p o l l i n a t o r b e h a v i o u r , i n c l u d i n g i n t e r - f l i g h t d i r e c t i o n a l i t y of p o l l i n a t o r s , have been s t u d i e d by those i n t e r e s t e d i n f o r a g i n g (e.g. Pyke 1978; H e i n r i c h 1979; Zimmerman 1979; Gass and Montgomerie 1981). However, l i t t l e i s known about 46 c a r r y o v e r , and assumptions about c a r r y o v e r a r e weak l i n k s i n the c h a i n of r e a s o n i n g about gene f l o w . For t h i s d i s c u s s i o n (as above) I w i l l d e f i n e p o l l e n c a r r y o v e r as the number of subsequent f l o w e r s t o which the p o l l e n of one f l o w e r i s c a r r i e d . C a r r y o v e r c o u l d a l s o be d e f i n e d i n terms of numbers of p l a n t s . I f p o l l e n from one f l o w e r i s c a r r i e d over and d e p o s i t e d a t more f l o w e r s than j u s t the next one the p o l l i n a t o r v i s i t s , then p o l l i n a t o r f l i g h t d i s t a n c e s w i l l u n d e r e s t i m a t e p o l l e n t r a n s f e r d i s t a n c e s . Many t i m e s r e s e a r c h e r s have made r e l a t i v e l y u n supported assumptions about the e x t e n t of p o l l e n c a r r y o v e r ( L e v i n e t a_l. 1971; F r a n k i e et §_1. 1976; F e i n s i n g e r 1978; R i c h a r d s and I b r a h i m 1979; Augspurger 1980; S c h m i t t 1980). Many c u r r e n t i d e a s about p o l l e n d i s p e r s a l and the f a c t o r s a f f e c t i n g i t stem from the work of L e v i n and h i s c o l l e a g u e s ( L e v i n and K e r s t e r 1967; 1968; 1969 a,b; L e v i n and Berube 1972; L e v i n et. a_l. 1971; K e r s t e r and L e v i n 1968). In g e n e r a l , they observed t h a t p o l l i n a t o r f l i g h t d i s t a n c e s a r e l e p t o k u r t i c and c l o s e l y r e l a t e d t o p l a n t s p a c i n g d i s t a n c e s , and i n f e r r e d or assumed low p o l l e n c a r r y o v e r . Some of thes e r e s u l t s appear t o be g e n e r a l ; f o r i n s t a n c e a l e p t o k u r t i c d i s t r i b u t i o n of p o l l i n a t o r f l i g h t d i s t a n c e s i s common i n hummingbirds, bumblebees, hawkmoths, and b u t t e r f l i e s (e.g. P e r k i n s 1977; P r i c e and Waser 1979; Waser and P r i c e 1981; B e a t t i e 1978; S c h m i t t 1980; Gass and Montgomerie 1981), a l t h o u g h t h e r e may be s i g n i f i c a n t d i f f e r e n c e s i n the degree of l e p t o k u r t o s i s between d i f f e r e n t 47 p o l l i n a t o r s ( S c h m i t t 1980). Recent work on hummingbirds ( P e r k i n s 1977; L ertzman, t h i s t h e s i s ; Waser and P r i c e 1981) and bumblebees (Thomson and P l o w r i g h t 1980; Waser and P r i c e 1981) s u g g e s t s t h a t p o l l e n c a r r y o v e r i s l o n g e r and more v a r i a b l e than was p r e v i o u s l y i n d i c a t e d . T h i s may be due t o v a r i a t i o n i n both f l o r a l morphology (Lertzman, see l a s t c h a p t e r ) and p o l l i n a t o r b e h a v i o u r (Thomson and P l o w r i g h t 1980). I f nuances of f l o r a l morphology or p o l l i n a t o r b e h a v i o u r do s t r o n g l y a f f e c t whether p o l l e n i s p i c k e d up by or dropped o f f from p o l l i n a t o r s a t any g i v e n f l o w e r , then l i t t l e g e n e r a l i z a t i o n between systems may be p o s s i b l e w i t h o u t t a k i n g t h e s e f a c t o r s i n t o a c c o u n t . T h i s c h a p t e r w i l l d e s c r i b e a l t e r n a t i v e s e t s of a ssumptions about the p r o c e s s e s i n v o l v e d i n p o l l e n t r a n s f e r and w i l l d i s c u s s t h e i r consequences i n terms of p o l l e n c a r r y o v e r . There are t h r e e o b j e c t i v e s : t o o r g a n i z e and s t a t e e x p l i c i t l y the common assumptions about p o l l e n c a r r y o v e r , t o a s s e s s the v a l i d i t y of t h e s e a s s u m p t i o n s , and t o suggest some a l t e r n a t i v e s . T h i s d i s c u s s i o n i s based on a s e r i e s of s i m u l a t i o n m o d e l l i n g e x e r c i s e s . B e f o r e d i s c u s s i n g s p e c i f i c models i n d e t a i l , i t i s i m p o r t a n t t o d i s c u s s the approach t o modeling i n g e n e r a l . The f o l l o w i n g s e c t i o n does t h i s , and a l s o i n t r o d u c e s the s t r u c t u r a l framework of the models. 48 On B u i l d i n g Models Of P o l l i n a t i o n Models are u s e f u l as e x p l i c i t s t a t ements of hy p o t h e s e s . They a l l o w f o r m a l e v a l u a t i o n of the consequences of g i v e n s e t s of of ass u m p t i o n s , and a r e thus p o w e r f u l d e d u c t i v e t o o l s . I d i s t i n g u i s h between p a t t e r n - o r i e n t e d and s t a t i s t i c a l models, and p r o c e s s - o r i e n t e d models. P a t t e r n - o r i e n t e d models p r o v i d e u s e f u l d e s c r i p t i o n s of broad r e l a t i o n s h i p s e x p e c t e d from t h e o r y or ob s e r v e d i n n a t u r e , and t o the e x t e n t t h a t the p a t t e r n s they g e n e r a t e a r e a c c u r a t e , may be u s e f u l a i d s t o u n d e r s t a n d i n g h i g h e r level.phenomena. For example, models t h a t g e n e r a t e p a t t e r n s of p o l l e n d i s t r i b u t i o n can be used t o examine the i m p l i c a t i o n s of these p a t t e r n s f o r the neighbourhood s t r u c t u r e of p l a n t p o p u l a t i o n s ( L e v i n and K e r s t e r 1969; L e v i n e_t a_l. 1971; S c h m i t t 1980). In my view, however, models can p r o v i d e o n l y l i m i t e d i n s i g h t i n t o how p a t t e r n s a r e g e n e r a t e d u n l e s s they embody r e a l i s t i c b i o l o g i c a l p r o c e s s e s . That i s , the u s e f u l n e s s of models i n c r e a s e s when they g e n e r a t e r e a l i s t i c b i o l o g i c a l p a t t e r n s a t one l e v e l t h r o u g h the s i m u l a t i o n of r e a l i s t i c b i o l o g i c a l p r o c e s s e s a t a more d e t a i l e d l e v e l ( C l a r k and H o l l i n g 1979). Such h i e r a r c h i c a l l y s t r u c t u r e d models a r e doubly v u l n e r a b l e t o l o g i c a l or e x p e r i m e n t a l i n v a l i d a t i o n , and t h e r e f o r e d o u b l y p o w e r f u l as h e u r i s t i c t o o l s . Not o n l y can t h e i r o utput f a i l t o show r e a s o n a b l e p a t t e r n s , but t h e i r e x p l i c i t a s s u m p t i o n s about the u n d e r l y i n g mechanisms can be shown t o be wrong. There a r e t h r e e e s s e n t i a l components t o p r o c e s s models 49 of p o l l i n a t i o n : p i c k u p of p o l l e n by a p o l l i n a t o r from the a n t h e r s of f l o w e r s , t r a n s p o r t of p o l l e n i n a p o o l of p o l l e n on the p o l l i n a t o r , and d e p o s i t i o n of p o l l e n on the stigmas (or a n t h e r s ! ) of o t h e r f l o w e r s . A l t e r n a t i v e models may be d i s t i n g u i s h e d by the number of sub-components i n t o which t h e s e b a s i c t h r e e a re d i s a g g r e g a t e d , by the assumptions t h a t a r e made about those sub-components, and by the ways i n which i n t e r a c t i o n s between t h e s e components a r e o r g a n i z e d . The c e n t r a l f e a t u r e of each model i s a v i s i t by a p o l l i n a t o r t o a s i n g l e f l o w e r : the " u n i t i n t e r a c t i o n " . P o p u l a t i o n - l e v e l consequences of assumptions about the u n i t i n t e r a c t i o n a r e ge n e r a t e d by i t e r a t i n g t h r ough i t many times and c o l l e c t i n g i n f o r m a t i o n from each i t e r a t i o n about p o l l e n p i c k e d up or d e p o s i t e d , or about the s t r u c t u r e of the p o l l e n p o o l . By a l l o w i n g v a r i a t i o n i n the f a c t o r s t h a t a f f e c t the components of t h i s i n t e r a c t i o n , f o r i n s t a n c e v a r i a t i o n i n f l o r a l morphology, we a r e a b l e t o study how the d i s t r i b u t i o n of t r a i t s i n p o p u l a t i o n s of f l o w e r s i s r e f l e c t e d i n p o p u l a t i o n - l e v e l p a t t e r n s of p o l l e n d i s p e r s a l . A l t e r n a t i v e Models Models 1 through 3 were programmed i n BASIC on Apple m i c r o c o m p u t e r s . Model 4 was w r i t t e n i n "C" and run on a D i g i t a l PDP-11/45. C o p i e s of a l l programs are a v a i l a b l e on r e q u e s t . The models a r e a r r a n g e d i n o r d e r of i n c r e a s i n g r e a l i s m of both p r o c e s s and p a t t e r n and i n c r e a s i n g s t r u c t u r a l 50 c o m p l e x i t y ( T a b l e V I ) . Model 1 i s p a t t e r n o r i e n t e d , w i t h T a b l e V I . G e n e r a l c h a r a c t e r i s t i c s of the models. c h a r a c t e r model 1 model 2 model 3 model 4 s t i g m a l capac i t y u n l i m i t e d u n l i m i t e d l i m i t e d 1 i m i t e d a n t h e r capac i t y l i m i t e d l i m i t e d l i m i t e d l i m i t e d p o l l e n p i c k e d up from every f l o w e r yes no yes no p o l l e n from each-source d e p o s i t e d a t every f l o w e r yes no no no number of p o l l e n g r a i n s p i c k e d up, c o n s t a n t c o n s t a n t c o n s t a n t v a r i a b l e when not 0 number of p o l l e n g r a i n s d e p o s i t e d , when not 0 c o n s t a n t p r o p o r t i o n of the p o l l e n r e m a i n i n g from each sou r c e c o n s t a n t number randomly chosen from the p o l l e n p o o l v a r i a b l e : f u n c t i o n of number and d i s t r i b u t i o n of p o l l e n r e m a i n i n g from each source l i t t l e u n d e r l y i n g r e a l i s m . I t i s s i m p l e , h i s t o r i c a l l y s i g n i f i c a n t , and r e p r e s e n t s commonly h e l d a s s u m p t i o n s . I t r e a t i t as an i n i t i a l n u l l h y p o t h e s i s f o r comparison w i t h o t h e r models and e x p e r i m e n t a l d a t a . Model 2 i s a s i m p l e 51 m o d i f i c a t i o n of model 1 t h a t produces more r e a s o n a b l e p a t t e r n s of p o l l e n d i s p e r s a l , but s t i l l l a c k s a r e a l i s t i c mechanism. Models 3 and 4 make more e x p l i c i t s t a t e m e n t s about p o l l e n p o o l s t r u c t u r e and how i t a f f e c t s p o l l e n d e p o s i t i o n . Model 4 i n c o r p o r a t e s s t o c h a s t i c v a r i a t i o n i n f l o r a l morphology t h a t d e t e r m i n e s from where i n the p o l l e n p o o l p o l l e n w i l l be d e p o s i t e d or p i c k e d up. These models assume t h a t the p o l l i n a t o r d e p o s i t s p o l l e n on a f l o w e r ' s s tigma p r i o r t o p i c k i n g up p o l l e n from i t s a n t h e r s . Though t h i s r e f e r s t o the temporal sequence of the mechanics of p o l l e n t r a n s f e r , i t i m p l i e s an assumption about p l a n t b r e e d i n g systems. Thus the models w i l l a p p l y most d i r e c t l y t o systems where f l o w e r s r a r e l y i f ever r e c e i v e t h e i r own p o l l e n . S p a t i a l s t r u c t u r e i s absent from these models. F l o w e r s are u n i q u e , and are v i s i t e d o n l y once. They have no p r e -d e f i n e d a s s o c i a t i o n as p l a n t s . S u p e r p o s i t i o n of s p a t i a l f a c t o r s and p o l l i n a t o r movement on t o p of t h e s e models i s the next s t e p i n the m o d e l l i n g of p o l l e n t r a n s f e r , but i t i s not c o v e r e d h e r e . The p o l l i n a t o r s t a r t s out a t the b e g i n n i n g of a model run w i t h no p o l l e n on i t - an empty p o l l e n p o o l . As i t f e e d s , p o l l e n i s added t o and t aken away from the p o o l a c c o r d i n g t o the r u l e s f o r t h a t model. To measure p o l l e n c a r r y o v e r , one f l o w e r i s chosen from each run and the d e p o s i t i o n of i t ' s p o l l e n is- f o l l o w e d . In models 1 and 2 t h e r e i s no e f f e c t of p o o l s i z e on the p r o b a b i l i t y of 52 d e p o s i t i o n of i n d i v i d u a l p o l l e n g r a i n s , and I s t u d i e d c a r r y o v e r from the f i r s t f l o w e r of the sequence. In models 3 and 4, d e p o s i t i o n p r o b a b i l i t i e s v a r y w i t h p o o l s i z e , so I s t u d i e d c a r r y o v e r from the 11th and 20th f l o w e r s i n each sequence r e s p e c t i v e l y . I used 50 f l o w e r sequences ( i . e . c h e c k i n g 50 f l o w e r s p a s t the source f o r p o s s i b l e p o l l e n d e p o s i t i o n ) t o g e n e r a t e the output f o r comparison between a l l f o u r models. Data p r e s e n t e d a r e from up t o 60 runs of a model i n o r d e r t o ge n e r a t e a d i s t r i b u t i o n of p o s s i b l e outcomes from a g i v e n s e t of a s s u m p t i o n s . The r e s t r i c t i o n t o a maximum of 50 f l o w e r s per run was s e t by space l i m i t a t i o n s on the Apple microcomputers. Model 4 i s a l s o d i s c u s s e d w i t h more f l o w e r s per run f o r the more d e t a i l e d a n a l y s i s of i t s b e h a v i o u r . The output v a r i a b l e s a re mean and maxmimum c a r r y o v e r . Mean c a r r y o v e r i s c a l c u l a t e d by summing the sequence numbers of the f l o w e r s t h a t r e c e i v e p o l l e n and d i v i d i n g t h a t number by the number of f l o w e r s t h a t r e c e i v e d p o l l e n . For i n s t a n c e , a sequence i n which p o l l e n was d e p o s i t e d on the 5 t h , 16th, and 24th f l o w e r s p a s t the sour c e would have a mean c a r r y o v e r o f : 5 + 1'6 + 24 / 3 = 15 f l o w e r s . The maxmimum c a r r y o v e r i s the sequence number of the l a s t f l o w e r i n a sequence t o r e c e i v e p o l l e n . U n l e s s s p e c i f i e d o t h e r w i s e , " c a r r y o v e r " r e f e r s t o both of t h e s e s t a t i s t i c s . Grand means and mean maxima are the means of these v a l u e s f o r a number of sequences. 53 Model j _ : C onstant P r o p o r t i o n Of P o l l e n G r a i n s D e p o s i t e d : E x p o n e n t i a l Decay To study gene f l o w or t o make i n f e r e n c e s about the g e n e t i c s t r u c t u r e of p l a n t p o p u l a t i o n s o f t e n r e q u i r e s a knowledge of p o l l e n d i s p e r s a l d i s t a n c e s ( i . e . L e v i n and K e r s t e r 1968; 1969 a,b; R i c h a r d s and I b r a h i m 1978; S c h m i t t 1980; Waser and P r i c e 1981). Because t h i s i s d i f f i c u l t t o measure, observed p o l l i n a t o r movement d i s t a n c e s a r e o f t e n used t o e s t i m a t e p o l l e n t r a n s f e r d i s t a n c e s ( e . g . B e a t t i e and C u l v e r 1979). T h i s c o r r e s p o n d e n c e i s p e r f e c t i f t h e r e i s no p o l l e n c a r r y o v e r . L e v i n and K e r s t e r (1969a) used e x p o n e n t i a l decay t o model c a r r y o v e r t o produce a c o r r e c t i o n f a c t o r f o r p o l l i n a t o r f l i g h t d i s t a n c e s so as t o b e t t e r e s t i m a t e p o l l e n t r a n s f e r d i s t a n c e s . They found t h a t , g i v e n the assumption of e x p o n e n t i a l decay, t h e i r e s t i m a t e s of p o l l e n t r a n s f e r d i s t a n c e s were i n s e n s i t i v e t o t h e i r a s s u mptions about c a r r y o v e r ( i . e . the v a l u e s of the parameters of the model). S i n c e e x p o n e n t i a l decay c h a r a c t e r i z e s much of the l i t e r a t u r e , I w i l l s t a r t w i t h i t as the i n i t i a l n u l l h y p o t h e s i s f o r p o l l e n t r a n s f e r . E x p o n e n t i a l decay i s produced i f a p o l l e n p o o l i s decremented by a c o n s t a n t p r o p o r t i o n of i t s c u r r e n t s i z e a t each f l o w e r v i s i t e d . When t h i s p r o p o r t i o n i s l a r g e , the decay c u r v e i s s t e e p . Thus, i n t h i s model, a c o n s t a n t number of p o l l e n g r a i n s i s p i c k e d up a t each f l o w e r v i s i t e d by the p o l l i n a t o r , and a c o n s t a n t p r o p o r t i o n of the p o l l e n r e m a i n i n g from each p r e v i o u s l y v i s i t e d source i s d e p o s i t e d 54 a t each subsequent f l o w e r . P o l l e n from d i f f e r e n t s o u r c e s i s assumed not t o i n t e r a c t i n the p o l l e n p o o l on the p o l l i n a t o r , and i s e q u a l l y a v a i l a b l e f o r d e p o s i t i o n . There i s no l i m i t t o the number of g r a i n s t h a t can be d e p o s i t e d on s t i g m a s . The amount of p o l l e n d e p o s i t e d d e c l i n e s r a p i d l y w i t h the number of f l o w e r s a f t e r the p o l l e n source ( F i g . 8 ) . When the p r o p o r t i o n of the r e m a i n i n g p o l l e n d e p o s i t e d from each s o u r c e i s h i g h ( 0 . 4 ) , no p o l l e n i s d e p o s i t e d a f t e r 11 f l o w e r s . When the p r o p o r t i o n i s v e r y low (0. 0 5 ) , s m a l l amounts of p o l l e n a re d e p o s i t e d up t o 46 f l o w e r s p a s t i t s s o u r c e . There a re t h r e e key q u a l i t a t i v e a t t r i b u t e s of t h i s model t h a t we can compare w i t h d a t a : 1) a l l f l o w e r s r e c e i v e p o l l e n and the curve i s thus smooth. 2) a c o n s t a n t p r o p o r t i o n of the r e m a i n i n g p o l l e n i s d e p o s i t e d a t each f l o w e r , so t h a t we s h o u l d observe d e p o s i t i o n as a d e c r e a s i n g f u n c t i o n of the f l o w e r v i s i t a t i o n sequence, and 3) i f the p r o p o r t i o n d e p o s i t e d i s l a r g e , the c u r v e drops s t e e p l y . Based on e x p e r i m e n t a l r e s u l t s from bumblebees (Thomson and P l o w r i g h t 1980; Waser and P r i c e 1981), and hummingbirds ( P e r k i n s 1977; Lertzman, t h i s t h e s i s ) , each of the s e p o i n t s can be r e j e c t e d . In each of the s e e x p e r i m e n t s p o l l e n d e p o s i t i o n was v a r i a b l e ; some f l o w e r s r e c e i v e d no p o l l e n , and l a t e r f l o w e r s i n a sequence o f t e n r e c e i v e d more p o l l e n t h a n e a r l i e r f l o w e r s . However, some of these r e s u l t s must be a c c e p t e d c a u t i o u s l y and q u a l i t a t i v e l y . Lertzman ( t h i s 55 F i g u r e 8. P o l l e n d e p o s i t i o n c u r v e s from model 1: c o n s t a n t p r o p o r t i o n d e p o s i t e d , s i m p l e e x p o n e n t i a l decay. Each c u r v e i n d i c a t e s the p a t t e r n of p o l l e n d e p o s i t i o n from ' s o u r c e f l o w e r s e x p e c t e d under model 1 i f 40%, 20%, 10%, or 5% of the p o l l e n from each s o u r c e r e m a i n i n g on the p o l l i n a t o r were d e p o s i t e d on each f l o w e r v i s i t e d . The o r d i n a t e s c a l e i s a r b i t r a r y , i n d i c a t i n g t h a t 100 g r a i n s were p i c k e d up from the source f l o w e r . P O L L E N G R A I N S D E P O S I T E D 57 t h e s i s ) and Waser and P r i c e (1981) used f l o u r e s c e n t powders as p o l l e n m i m i c s , and they assumed t h a t t h e dyes mimic p o l l e n a t l e a s t q u a l i t a t i v e l y . However the c orrespondence between p o l l e n c a r r y o v e r and dye c a r r y o v e r i s not w e l l e s t a b l i s h e d (see d i s c u s s i o n i n c h a p t e r on l a b o r a t o r y e x p e r i m e n t s ) . W h i l e t h i s model may seem something of a straw man, i t i s i m p l i c i t i n much c u r r e n t t h i n k i n g about p o l l e n c a r r y o v e r . I t i s c o r r o b o r a t e d by L e v i n and Berube's (1972) d a t a on P h l o x and C o l i a s b u t t e r f l i e s , but t h e i r r e s u l t s are p r o b a b l y not g e n e r a l . F o r i n s t a n c e , L e v i n et_ aj-. (1971) c a u t i o n e d t h a t systems i n which p o l l e n i s t r a n s p o r t e d on a p r o b o s c i s w i l l show lower c a r r y o v e r than those i n which p o l l e n i s c a r r i e d on the body of the p o l l i n a t o r because p r o b o s c i a r e more e f f i c i e n t a t d e p o s i t i n g p o l l e n . The paper by L e v i n and Berube (1972) has had a l a r g e impact on a s s u m p t i o n s about p o l l e n c a r r y o v e r , and p o l l e n f l o w i s p r o b a b l y s e n s i t i v e t o these a s sumptions (even though L e v i n and K e r s t e r (1969 a) showed t h a t p o l l e n f l o w was i n s e n s i t i v e t o parameter changes g i v e n the e x p o n e n t i a l decay model, t h i s does not n e c e s s a r i l y h o l d f o r the assumptions about the u n d e r l y i n g model i t s e l f ) . I t i s t h e r e f o r e v a l u a b l e t o d i s c u s s t h e i r r e s u l t s i n d e t a i l . One f a c t o r t h a t may have l e d t o the view of v e r y e f f i c i e n t p o l l e n d e p o s i t i o n from p r o b o s c i i s t h a t L e v i n and Berube (1972) e x p e r i m e n t a l l y p r e v e n t e d the b u t t e r f l i e s i n t h e i r e x p e r i m e n t s from r e t r a c t i n g t h e i r p r o b o s c i between f l o w e r s . 58 Normal c o i l i n g and u n c o i l i n g c o u l d d i s p l a c e p o l l e n from i t s s i t e s of i n i t i a l d e p o s i t i o n , which would l e a d t o a more patchy d i s t r i b u t i o n of p o l l e n . A s p a t i a l l y p a t c h y d i s t r i b u t i o n of p o l l e n on the p o l l i n a t o r p r o b a b l y r e s u l t s i n l o n g e r c a r r y o v e r than a u n i f o r m and c o n t i g u o u s d i s t r i b u t i o n (Thomson and P l o w r i g h t - 1980; Lertzman, t h i s t h e s i s ) . A d d i t i o n a l l y , L e v i n and Berube (1972) used s h o r t (5 f l o w e r ) sequences i n t h e i r e x p e r i m e n t s ; t h e r e f o r e they c o u l d not have o b s e r v e d l o n g c a r r y o v e r even had i t o c c u r r e d . Observed c a r r y o v e r i s v e r y s e n s i t i v e t o the l e n g t h of the sequence of f l o w e r s t h a t i s used t o measure i t . For i n s t a n c e , when we i n c r e a s e d the number of f l o w e r s i n a sequence from 30 t o 100 ( i n model 4 ) , the p r o p o r t i o n of the t o t a l p o l l e n t r a n s f e r r e d t h a t was d e p o s i t e d more than 19 f l o w e r s p a s t the source i n c r e a s e d from about 10% t o about 30%. The e f f e c t of sequence l e n g t h on observed c a r r y o v e r seems an o b v i o u s p o i n t , but t h e r e a r e no e x p e r i m e n t a l measures of c a r r y o v e r w i t h r e a l i s t i c a l l y l a r g e numbers of f l o w e r s . In the w i l d , some hummingbirds need t o f e e d from an average of 3700 f l o w e r s per day (Gass et a l . 1976), and we have no i d e a whether s h o r t t o moderate (e.g. 30 f l o w e r s ) e x p e r i m e n t a l sequences ( e . g . Thomson and P l o w r i g h t 1980; Waser and P r i c e 1981; L e r t z man, t h i s t h e s i s ) g i v e any where near a r e a l i s t i c p i c t u r e of p o l l e n t r a n s f e r when such l a r g e numbers of f l o w e r s are i n v o l v e d . What can be i n f e r r e d about c a r r y o v e r from the p o l l e n l o a d s on s t i g m a s o b s e r v e d i n n a t u r e ? Based on the h i g h l y 59 v a r i a b l e p o l l e n l o a d s found on the stigmas of a d j a c e n t f l o w e r s and p l a n t s , Levin, and K e r s t e r (1967; 1968) i n f e r r e d low c a r r y o v e r . A l t e r n a t i v e l y , t h e s e v a r i a b l e p o l l e n l o a d s c o u l d have r e s u l t e d from l o n g e r but more v a r i a b l e p a t t e r n s of p o l l e n d e p o s i t i o n . In t h i s c a s e , a d j a c e n t f l o w e r s would not n e c e s s a r i l y r e c e i v e s i m i l a r p o l l e n l o a d s . How c o u l d t h i s v a r i a b i l i t y o r i g i n a t e ? The f o l l o w i n g models examine some' p o s s i b i l i t i e s . Model 2: C o n stant P r o p o r t i o n Of P o l l e n G r a i n s D e p o s i t e d ; E x p o n e n t i a l Decay W i t h B l a n k s W ithout e x p l i c i t l y m o d e l l i n g the p r o c e s s e s t h a t g e n e r a t e v a r i a b i l i t y , the e x p o n e n t i a l decay model can be made t o produce somewhat more r e a l i s t i c r e s u l t s by assuming t h a t some f l o w e r s do not i n t e r a c t w i t h the p o o l of p o l l e n on the p o l l i n a t o r (Lertzman, t h i s t h e s i s ) : no p o l l e n i s p i c k e d up from t h e i r a n t h e r s and/or none i s dropped o f f t o t h e i r s t i g m a s . In n a t u r e , t h i s c o u l d be produced by v a r i a t i o n i n f l o r a l morphology, i n the r e p r o d u c t i v e s t a t e of the a n t h e r s and s t i g m a s , and i n p o l l i n a t o r b e h a v i o u r (e.g. the o r i e n t a t i o n of r e l e v a n t p a r t s of the body w h i l e c o n t a c t i n g the f l o w e r s ) . These f a c t o r s c o u l d a c t i n e i t h e r or b oth of two ways. They c o u l d i n f l u e n c e the p r o b a b i l i t y t h a t f l o w e r s w i l l c o n t a c t the p o l l i n a t o r , or they c o u l d i n f l u e n c e the p r o b a b i l i t y of s u c c e s s f u l p o l l e n t r a n s f e r i f t h a t c o n t a c t i s made. I w i l l r e f e r t o t h e s e f l o w e r s t h a t c r e a t e gaps i n p o l l e n d e p o s i t i o n sequences as " b l a n k s " (see c h a p t e r on 60 l a b o r a t o r y e x p e r i m e n t s ) . Model 2 has two k i n d s of b l a n k s ; a n t h e r s t h a t don't d e p o s i t any p o l l e n on the p o l l i n a t o r , and st i g m a s t h a t r e c e i v e no p o l l e n from the p o l l i n a t o r . M i s s e d stigmas i n c r e a s e the c a r r y o v e r of p r e v i o u s l y d e p o s i t e d p o l l e n (compare F i g s . 8 and 9 ) . M i s s e d a n t h e r s d e c r e a s e the obs e r v e d mean c a r r y o v e r because z e r o v a l u e s from "non-p a r t i c i p a t i n g " a n t h e r s a r e i n c l u d e d i n the p o p u l a t i o n s t a t i s t i c s ( F i g . 10; T a b l e V I I ) . As e x p e c t e d , b oth mean and maximum c a r r y o v e r d e c r e a s e as the p r o p o r t i o n of the r e m a i n i n g p o l l e n d e p o s i t e d a t each f l o w e r i n c r e a s e s ( F i g . 11). For comparison of t h i s model w i t h the f o l l o w i n g two models (Table V I I and F i g . 10) I use a p r o p o r t i o n of 0.3 as r e p r e s e n t a t i v e . T h i s model assumes t h a t t h e r e i s no i n t e r a c t i o n between p o l l e n from d i f f e r e n t s o u r c e s , and t h a t s t i g m a s have u n l i m i t e d c a p a c i t y f o r p o l l e n . A l t h o u g h the d e p o s i t i o n of p o l l e n i s s t i l l a d e c r e a s i n g f u n c t i o n of the number of f l o w e r s v i s i t e d p r e v i o u s l y , the number of g r a i n s stigmas r e c e i v e i s v a r i a b l e because not a l l p r e v i o u s l y v i s i t e d f l o w e r s c o n t r i b u t e p o l l e n t o the c u r r e n t f l o w e r . T h i s model of e x p o n e n t i a l decay w i t h b l a n k s i s p r i m a r i l y of v a l u e as a more r e a s o n a b l e n u l l h y p o t h e s i s than s i m p l e e x p o n e n t i a l decay; i t mimics the v a r i a b i l i t y of the r e a l w o r l d w i t h o u t s p e c i f y i n g c a u s a l mechanisms. Thus i t p r o v i d e s a b a s i s f o r comparison w i t h the f o l l o w i n g models, which make e x p l i c i t s t a t e m e n t s about the p r o c e s s e s t h a t 61 F i g u r e 9. P o l l e n d e p o s i t i o n c u r v e s from model 2: c o n s t a n t p r o p o r t i o n d e p o s i t e d , e x p o n e n t i a l decay w i t h b l a n k s . Symbols and s c a l e s are as i n F i g u r e 1, except t h a t the a b s c i s s a extends t o 50 f l o w e r s p a s t the source f l o w e r . Based on f i e l d measurements of r e p r o d u c t i v e s t a t e i n C a s t i l l e j a m i n i a t a 26% of the s t i g m a s , and 27.5% of the a n t h e r s , randomly chosen, d i d not i n t e r a c t w i t h the p o l l e n p o o l on the p o l l i n a t o r i . e . were b l a n k s . POLLEN GRAINS DEPOSITED O g o i rn 73 co C O C O O c 73 O m CO o •M o O 7 cn o o O O o o ro O - 1 M U ^ o o o o o 63 F i g u r e 10. Frequency d i s t r i b u t i o n s of mean and maximum p o l l e n c a r r y o v e r from models 2, 3, and 4. Sample s i z e s '(number of runs of the model) a r e g i v e n i n Table 2. Data from model 2 w i t h 0.3 of the r e m a i n i n g p o l l e n d e p o s i t e d a t each f l o w e r , d a t a from model 3 w i t h 10 p o l l e n g r a i n s p i c k e d up and 3 g r a i n s d e p o s i t e d a t each f l o w e r . means m a x i m a 40 30 20 >- 10 u z UJ a ^20] " l 5 i u DC UJ Q_ 10 50-20' 15 ID-S' a JL a — a n t L d 10 20 30 40 50 10 20 30 FLOWERS PAST SOURCE 40 50 o CL 3 O CL o_ OJ 3 o CL (P_ 4\ n n I n l gure 11. Mean and maximum p o l l e n d e p o s i t i o n from model 2 C l o s e d c i r c l e s and s o l i d l i n e s i n d i c a t e means of 30 r u n s . Open c i r c l e s and broken l i n e s i n d i c a t e the 25 those runs i n which some p o l l e n was dropped o f f ( i . e . e x c l u d i n g z e r o d e p o s i t i o n v a l u e s ) . V e r t i c a l l i n e s • i n d i c a t e 95% c o n f i d e n c e i n t e r v a l s . Table V I I . C a r r y o v e r s t a t i s t i c s f o r models 2, 3 and 4. model 2 model 3 model 4 w i t h z e r o depos. w i t h o u t z e r o depos. w i t h z e r o depos. wi thout z e r o depos. grand mean c a r r y o v e r 7 9 1 6 5 14 median mean, c a r r y o v e r 9 9 15 0 14 v a r i a n c e 14.2 1 .2 43.3 85.5 98.2 mean extreme c a r r y o v e r 1 4 1 7 32 7 17 median extreme c a r r y o v e r 1 7 18 35 0 16 var i a n c e 49 4.5 116.4 1 45.4 135.4 n 30 25 30 60 40 z e r o depos. = z e r o d e p o s i t i o n generate v a r i a b i l i t y i n p o l l e n d e p o s i t i o n . 68 Model 3_: C o n stant Number of P o l l e n G r a i n s Dropped O f f : L i m i t e d St igmal Capac i t y In h i s models of c o m p e t i t i o n between p l a n t s f o r p o l l i n a t i o n , Waser (1978) assumed t h a t a c o n s t a n t number of p o l l e n g r a i n s was p i c k e d up from each f l o w e r v i s i t e d , and t h a t a c o n s t a n t number of g r a i n s , randomly chosen from the p o o l , was d e p o s i t e d a t each f l o w e r . Each f l o w e r had a l i m i t e d number of g r a i n s on i t s a n t h e r s , and a l i m i t e d amount of space a v a i l a b l e on i t s s t i g m a . Model 3, based on Waser's a s s u m p t i o n s , assumes t h a t p o l l e n g r a i n s from e a r l y f l o w e r s i n v i s i t a t i o n sequences a r e j u s t as l i k e l y t o be chosen f o r d e p o s i t i o n as p o l l e n from more r e c e n t l y v i s i t e d f l o w e r s . Thus t h e r e i s a g a i n no i n t e r a c t i o n between p o l l e n from d i f f e r e n t source f l o w e r s ( i n c o n t r a s t , model 4 e x p l i c i t l y models i n t e r a c t i o n s among p o l l e n g r a i n s i n the p o l l e n p o o l ) . F o l l o w i n g Waser (1978), i n model 3 the p o l l i n a t o r d e p o s i t s 3 randomly chosen p o l l e n g r a i n s on the stigma of each f l o w e r and p i c k s up 1 0 ' p o l l e n g r a i n s from the a n t h e r s of each f l o w e r . G r a i n s a r e drawn i n d e p e n d e n t l y and w i t h o u t replacement from the p o o l of p o l l e n on the p o l l i n a t o r . There are two d i f f e r e n c e s between t h i s model and Waser's (1978). Whereas he s i m u l a t e d a p o l l i n a t o r moving through an a r r a y of f l o w e r s , and f l o w e r s c o u l d be r e v i s i t e d , i n t h i s model f l o w e r s have no s p a t i a l i d e n t i t y and are o n l y v i s i t e d once. S i m i l a r l y , , w h i l e a t o t a l of 3 g r a i n s was d e p o s i t e d per f l o w e r per v i s i t , t h e s e were counted towards a' 69 t o t a l of 5 per f l o w e r as a maximum s t i g m a l c a p a c i t y . In model 3, s i n c e r e v i s i t s do not o c c u r , the 3 g r a i n s d e p o s i t e d on one v i s i t a r e e q u i v a l e n t t o the s t i g m a l c a p a c i t y . The d i f f e r e n c e between 3 and 5 g r a i n s might be i m p o r t a n t i f I was a l s o d i r e c t l y m o d e l l i n g gene f l o w , but s i n c e here I am p r i m a r i l y i n t e r e s t e d i n the consequences of the p o l l e n d e p o s i t i o n r u l e s , the d i s t i n c t i o n i s not i m p o r t a n t . Model 3 produces l o n g and i r r e g u l a r c a r r y o v e r ( F i g . 10, F i g . 12, and Ta b l e V I I ) t h a t i s s i m i l a r t o some e x p e r i m e n t a l r e s u l t s (Thomson and P l o w r i g h t 1980; Lertzman, t h i s t h e s i s ) . T h i s v a r i a b i l i t y most l i k e l y r e s u l t s from the l i m i t e d s t i g m a l c a p a c i t y . S t i g m a l c a p a c i t y i s l e s s than the number of g r a i n s a v a i l a b l e f o r d e p o s i t i o n . Thus even though each stigma i s s a t u r a t e d , o n l y a s m a l l p r o p o r t i o n of the p o l l e n g r a i n s a v a i l a b l e can be d e p o s i t e d on any 'given s t i g m a . For a g i v e n p o l l e n s o u r c e , many b l a n k s e x i s t . When the model i s d r i v e n w i t h i n c r e a s i n g s t i g m a l c a p a c i t y , mean c a r r y o v e r d e c r e a s e s and maximum c a r r y o v e r shows a peak between 3 and 5 g r a i n s per stigma ( F i g . 13). T h i s peak of maximum c a r r y o v e r o c c u r s i n the range of p o l l e n p i c k u p t o d e p o s i t i o n r a t i o s commonly observed i n r e a l systems (Waser 1978). The s h o r t e r c a r r y o v e r a t the two extremes of s t i g m a l c a p a c i t y r e s u l t s from d i f f e r e n t c a u s e s . The o n l y s i t u a t i o n i n which z e r o d e p o s i t i o n v a l u e s o c c u r r e d ( i . e . when a l l p o l l e n from a p a r t i c u l a r s o u r c e remained on the p o l l i n a t o r and was never d e p o s i t e d ) was when o n l y one g r a i n was d e p o s i t e d per s t i g m a . Thus a t the lowe s t s t i g m a l c a p a c i t y , 70 F i g u r e 12. Three r e p r e s e n t a t i v e p o l l e n d e p o s i t i o n c u r v e s from model 3: c o n s t a n t number of g r a i n s d e p o s i t e d . 1, 2, or 3 p o l l e n g r a i n s c o u l d be d e p o s i t e d per s t i g m a . POLLEN GRAINS DEPOSITED ro , — i — i ro i i ro 1 , I o 1 1 1 1 ~n J 20 -OWERS ZD 1 1 PAST 30 ' SOURCE 1 O Ui O • _ l 72 F i g u r e 13. Mean ( c l o s e d c i r c l e s and s o l i d l i n e s ) and maximum (open c i r c l e s and broken l i n e s ) p o l l e n c a r r y o v e r from 30 runs of model 3 a t each of s e v e r a l l e v e l s of s t i g m a l c a p a c i t y . V e r t i c a l l i n e s i n d i c a t e 95% c o n f i d e n c e i n t e r v a l s . S3 L U 4 0 i LL 2 4 6 8 10 GRAINS PER STIGMA 74 c a r r y o v e r was lowered because p o l l e n s t a y e d on the p o l l i n a t o r and was not d e p o s i t e d . The p r o b a b i l i t y t h a t a g i v e n p o l l e n g r a i n w i l l be d e p o s i t e d i s s e n s i t i v e t o the c u r r e n t s i z e of the p o l l e n p o o l on the p o l l i n a t o r . A f t e r many f l o w e r s have c o n t r i b u t e d p o l l e n t o the p o o l the p r o b a b i l i t y t h a t p o l l e n from any g i v e n f l o w e r w i l l be chosen i s q u i t e s m a l l : p = 1 / (10N - N), where N i s the number of f l o w e r s f e d on p r e v i o u s l y . The reason t h a t c a r r y o v e r d e c r e a s e s a t h i g h r a t i o s of d e p o s i t i o n t o p i c k u p i s t h a t as the number of p o l l e n g r a i n s d e p o s i t e d per stigma approaches 10, p o l l e n i s b e i n g d e p o s i t e d from the p o l l i n a t o r a l m o s t as f a s t as i t i s b e i n g p i c k e d up. When 10 g r a i n s were d e p o s i t e d by a n t h e r s and 10 p i c k e d up by stigmas c a r r y o v e r was t o one f l o w e r past the s o u r c e . C a r r y o v e r (grand means and mean maxima) i s both l o n g e r and more v a r i a b l e i n model 3 than i n r e s u l t s from model 2 (T a b l e V I I , F i g . 10). C a r r y o v e r i n model 2 c o u l d be made l o n g e r by h a v i n g a h i g h e r p r o p o r t i o n of " b l a n k " s t i g m a s , but I s u s p e c t t h a t the v a r i a n c e would not i n c r e a s e . I t i s im p o r t a n t t o note t h a t t h i s i s v a r i a n c e not o n l y i n p o l l e n d e p o s i t i o n i n i n d i v i d u a l sequences of f l o w e r s ( i . e . F i g . 12), but i n the p o p u l a t i o n parameters a s s o c i a t e d w i t h the d i s t r i b u t i o n of t h a t v a r i a b i l i t y ( i . e . T a b l e V I I , F i g . 10). V a r i a b i l i t y i n model 3 output i s h i g h e s t a t low r a t i o s of d e p o s i t i o n t o st i g m a s t o p i c k u p from a n t h e r s ( F i g . 14). T h i s i s c o n s i s t e n t w i t h the d e c r e a s e d p r o b a b i l i t y t h a t a g i v e n p o l l e n g r a i n w i l l be d e p o s i t e d 75 F i g u r e 14. V a r i a n c e s of mean ( c l o s e d c i r c l e s and s o l i d l i n e s ) and maximum (open c i r c l e s and broken l i n e s ) F i g u r e . P o l l e n d e p o s i t i o n d i s t a n c e s from the same runs of model 3 as F i g u r e 6. 77 under t h e s e c o n d i t i o n s . The p o l l e n p o o l i t s e l f i s assumed t o be a randomly o r g a n i z e d b i n of p o l l e n g r a i n s : s e l e c t i o n of p o l l e n f o r t r a n s f e r t o stigmas i s random, w i t h o u t r e g a r d f o r e i t h e r the c h a r a c t e r i s t i c s of the c u r r e n t f l o w e r or the sequence i n which p o l l e n was d e p o s i t e d i n the p o o l . T h i s i s d i f f i c u l t t o imagine i n terms of u n d e r l y i n g b i o l o g i c a l p r o c e s s e s . A l t h o u g h grooming by bumblebees or p r e e n i n g by hummingbirds' c o u l d c o n c e i v a b l y randomize p o l l e n i n the p o o l w i t h r e s p e c t to v i s i t a t i o n sequence (or o b l i t e r a t e i t a l t o g e t h e r ) , I would s t i l l e xpect some non-random p o l l e n p o o l s t r u c t u r e . In o t h e r words, I would expect precedence f o r d e p o s i t i o n from th e p o l l i n a t o r - based on the time s i n c e l a s t grooming or p r e e n i n g . An a l t e r n a t i v e model might r e t a i n l i m i t e d s t i g m a l c a p a c i t y but i n c o r p o r a t e precedence f o r d e p o s i t i o n based on v i s i t a t i o n sequence. For i n s t a n c e , the p r o b a b i l i t y t h a t p o l l e n w i l l be d e p o s i t e d c o u l d be made dependent on the number of g r a i n s r e m a i n i n g from a f l o w e r and the number of f l o w e r s v i s i t e d s i n c e they were p i c k e d up. T h i s p r o b a b i l i t y c o u l d be c a l c u l a t e d u s i n g a r b i t r a r y s c a l i n g f a c t o r s t o produce r e a s o n a b l e p a t t e r n s , but I chose i n s t e a d t o model a h y p o t h e t i c a l c a u s a l mechanism. The next s t e p , t h e n , i s t o e x p l i c i t l y model p o l l e n p o o l s t r u c t u r e and i t s i n p u t / o u t p u t p r o c e s s e s . When comparing model 4 w i t h model 3, the q u e s t i o n t h a t s h o u l d be asked i s "How much u n d e r s t a n d i n g i s g a i n e d by a d d i n g th e s e a d d i t i o n a l components and t h e i r a t t e n d a n t c o m p l e x i t y , and a t what c o s t ? " Model 4: 3-Dimensional P o l l e n P o o l W i t h L a y e r i n g and F l o r a l V a r i a b i l i t y Other than l i m i t e d s t i g m a l s u r f a c e a r e a , what f a c t o r s c o u l d r e s u l t i n the " b l a n k s " of model 2? Thomson and P l o w r i g h t (1980) and Lertzman ( t h i s t h e s i s ) suggested t h a t v a r i a t i o n i n the o r i e n t a t i o n of p o l l i n a t o r and the f l o w e r d u r i n g c o n t a c t r e s u l t s i n p a t c h y d i s t r i b u t i o n of p o l l e n i n the p o l l e n p o o l . A p o s s i b l e mechanism f o r t h i s i s t h a t v a r i a t i o n i n f l o r a l morphology, f o r i n s t a n c e i n f l o w e r l e n g t h or l a t e r a l d i s p l a c e m e n t of s t i g m a s and a n t h e r s , would r e s u l t i n p o l l e n from d i f f e r e n t f l o w e r s b e i n g d e p o s i t e d i n d i f f e r e n t l o c a t i o n s i n the p o l l e n p o o l . F l o w e r s of d i f f e r e n t l e n g t h s would c o n t a c t p o l l i n a t o r s i n d i f f e r e n t p l a c e s , and hence p o l l e n t r a n s f e r between them would be u n l i k e l y . T h i s model r e s t s on the f o l l o w i n g a s s u m p t i o n s : 1. P o l l i n a t o r - f l o w e r geometry d u r i n g c o n t a c t d e t e r m i n e s where p o l l e n w i l l be d e p o s i t e d on p o l l i n a t o r s . 2. P o l l i n a t o r - f l o w e r geometry i s d r i v e n by v a r i a b i l i t y i n f l o r a l morphology (one of s e v e r a l p o s s i b l e mechanisms). 79 3. I f d i f f e r e n t f l o w e r s d e p o s i t p o l l e n i n the same p l a c e on the p o l l i n a t o r , i t w i l l be d e p o s i t e d i n l a y e r s , or l a s t - i n - f i r s t - o u t s t a c k s . These i d e a s a r e based on l a b o r a t o r y e x p e r i m e n t s w i t h r u f o u s hummingbirds ( S e l a s p h o r u s r u f u s ) and I n d i a n p a i n t b r u s h ( C a s t i l l e j a m i n i a t a ) f l o w e r s (Lertzman, t h i s t h e s i s ) , and p r o b a b l y a p p l y most d i r e c t l y t o hummingbird-plant systems. In t h i s model, the p o l l e n p o o l i s a 3 - d i m e n s i o n a l a r r a y 14 u n i t s i n w i d t h by 36 u n i t s i n l e n g t h ( F i g . 15). The di m e n s i o n s are based on measurements of p o l l e n l o a d s on f r e s h l y n e t t e d w i l d S e l a s p h o r u s r u f u s t h a t h e l d t e r r i t o r i e s i n C a s t i l l e j a m i n i a t a meadows, and on l a b o r a t o r y b i r d s t h a t had f e d from known numbers of f l o w e r s . The t h i r d d i m e n s i o n , d e p t h , i s a l l o c a t e d d y n a m i c a l l y as space i s needed ( F i g . 15). Whether model a n t h e r s and stigmas c o n t a c t t h i s p o o l or n o t , and where they c o n t a c t i t , i f they do, depends on t h e i r l e n g t h and l a t e r a l d i s p l a c e m e n t from the m i d l i n e of the f l o w e r . Both a n t h e r s and stigmas a r e c o n s t a n t i n s i z e , but a n t h e r s have a r e a s 6 ti m e s l a r g e r than stigmas ( 4 x 6 v s . 2 x 2 p o l l e n p o o l map u n i t s , based on measurements of C a s t i l l e j a m i n i a t a ) . I assume t h a t v a r i a t i o n i n two f l o r a l c h a r a c t e r s , l a t e r a l d i s p l a c e m e n t and c o r o l l a tube l e n g t h , i s n o r m a l l y d i s t r i b u t e d ( F i g . 15). R e a l C a s t i l l e j a m i n i a t a f l o w e r l e n g t h s d e v i a t e s i g n i f i c a n t l y from n o r m a l i t y ( t h e y a r e both skewed and l e p t o k u r t i c ) , but the l a t e r a l d i s p l a c e m e n t of 80 F i g u r e 15. Drawing of an immature male r u f o u s hummingbird ( t r a c e d from a photograph) showing the h y p o t h e t i c a l b i v a r i a t e normal d i s t r i b u t i o n of c o n t a c t between the p o l l i n a t o r and f l o r a l r e p r o d u c t i v e o r g a n s . The two dark r e c t a n g l e s i n d i c a t e the r e l a t i v e s i z e s of C a s t i l i e j a m i n i a t a s t i g m a s ( s m a l l ) and a n t h e r s ( l a r g e ) B i v a r i a t e normal d i s t r i b u t i o n from S o k a l and R o h l f (1969; F i g . 15.1, p. 501). 81 82, stigmas and a n t h e r s does not d e v i a t e s i g n i f i c a n t l y from n o r m a l i t y ( d a t a a re from the measurements of photographs d e s c r i b e d i n the s e c t i o n on l a b o r a t o r y e x p e r i m e n t s ) . In u n i t i n t e r a c t i o n s between p o l l i n a t o r s and f l o w e r s , a n t h e r s and stigmas a re chosen randomly from normal d i s t r i b u t i o n s of a g i v e n mean and v a r i a n c e . F l o w e r s a re thus most l i k e l y t o c o n t a c t the c e n t e r of the p o o l r a t h e r than the edges. F l o w e r s i n the t a i l s of the d i s t r i b u t i o n s a re l i k e l y t o c o n t a c t the p o o l o n l y p a r t i a l l y i f a t a l l , and w i l l have l e s s s u r f a c e a r e a a v a i l a b l e f o r p o l l e n t r a n s f e r . I f t h e r e i s no p o l l e n a t a l o c a t i o n i n the p o o l when a stigma c o n t a c t s i t , then no p o l l e n i s d e p o s i t e d on t h a t s t i g m a . Stigmas r e c e i v e p o l l e n from the top l a y e r of the p o o l o n l y , and once the t o p l a y e r a t a l o c a t i o n i s removed, the r e m a i n i n g l a y e r s a r e pushed up one s t e p c l o s e r t o the s u r f a c e . They a r e pushed back down i f p o l l e n i s added on to p of them. T h i s model produces h i g h l y v a r i a b l e c a r r y o v e r ( F i g . 16, Table V I I ) . Many f l o w e r s r e c e i v e no p o l l e n , and those t h a t do r e c e i v e v a r i a b l e amounts. In t h e s e 5 0 - f l o w e r r u n s , t h e r e are many c a s e s where no p o l l e n from a f l o w e r i s d e p o s i t e d on o t h e r f l o w e r s . The fr e q u e n c y d i s t r i b u t i o n s of mean and maximum c a r r y o v e r show a h i g h p r o p o r t i o n of z e r o d e p o s i t i o n v a l u e s and have l o n g t a i l s r e p r e s e n t i n g l e s s f r e q u e n t l o n g c a r r y o v e r ( F i g . 10). Zero d e p o s i t i o n c o u l d r e s u l t e i t h e r from p o l l e n b e i n g b u r i e d by o t h e r p o l l e n and never b e i n g uncovered, or from 83 F i g u r e 16. Three r e p r e s e n t a t i v e p o l l e n d e p o s i t i o n c u r v e s from modeler: 3 - d i m e n s i o n a l p o l l e n p o o l . 0, 1, 2, 3, or 4 p o l l e n g r a i n s c o u l d be d e p o s i t e d per s t i g m a . POLLEN GRAINS DEPOSITED ro ro ro Oi o m ° CO 5 C O h 73 o m oi cn I O 85 p o l l e n b e i n g d e p o s i t e d a t l o c a t i o n s where o t h e r f l o w e r s a r e u n l i k e l y t o c o n t a c t i t ( i t c o u l d a l s o r e s u l t from no p o l l e n b e i n g p i c k e d up by the p o l l i n a t o r from t h a t f l o w e r , see b e l o w ) . Because I assume the p o l l e n p o o l i s r e c t a n g u l a r , and t h a t f l o w e r v a r i a b i l i t y f o l l o w s a b i v a r i a t e normal d i s t r i b u t i o n , the c o r n e r s of the p o l l e n p o o l have a low l i k e l i h o o d of c o n t a c t i n g f l o w e r s . I f a u n i f o r m d i s t r i b u t i o n of f l o w e r v a r i a b i l i t y i s assumed, and z e r o d e p o s i t i o n v a l u e s a r e s t i l l p r e s e n t , then z e r o d e p o s i t i o n i s not a r e s u l t of the d i s t r i b u t i o n of f l o w e r v a r i a t i o n , but more l i k e l y a r e s u l t of the c o v e r i n g up of p o l l e n . T h i s appears t o be the c a s e ; when I run model 4 assuming u n i f o r m l y d i s t r i b u t e d v a r i a t i o n i n f l o r a l morphology, many z e r o v a l u e s s t i l l o c c u r . I f the runs had been l o n g e r , say 120 f l o w e r s , p o l l e n from these s o u r c e s may e v e n t u a l l y have been d e p o s i t e d , but I have not obser v e d t h i s . Two k i n d s of m o d i f i c a t i o n s t o model 4 would make i t more l i k e l y t h a t b u r i e d p o l l e n would r e s u r f a c e : 1 . The " c o a l scoop" h y p o t h e s i s s u g g e s t s t h a t s t i g m a s are dragged t h r o u g h the p o l l e n p o o l , r a t h e r than t o u c h i n g on i t s s u r f a c e as we have assumed so f a r . T h i s has two new consequences: p o l l e n from more than the s u r f a c e l a y e r i s a v a i l a b l e f o r d e p o s i t i o n on s t i g m a s , and u n i t i n t e r a c t i o n s c r e a t e 3-d i m e n s i o n a l grooves t h r o u g h the p o l l e n p o o l r a t h e r than s i m p l y l i f t i n g t he t o p l a y e r of p o l l e n from 86 an a r e a of t h e i r own s i z e . Both of thes e consequences would make i t much more l i k e l y t h a t s t i g m a s c o n t a c t p o l l e n i n a p a t c h y or s p a r s e l y f i l l e d p o o l , and t h a t b u r i e d p o l l e n would r e s u r f a c e . T h i s would d e c r e a s e the i n c i d e n c e of z e r o d e p o s i t i o n and i n c r e a s e mean c a r r y o v e r . 2. In n a t u r e , d i f f e r e n t i a l s t i c k i n e s s of p o l l e n t o o t h e r p o l l e n , t o s t i g m a s , and t o a n t h e r s may keep p o l l e n p o o l s from b u i l d i n g up as much as i n t h i s model. A d d i t i o n a l l y , p e r i o d i c s l o u g h i n g of pa t c h e s of p o l l e n , i n d u c e d by r a i n , grooming or p r e e n i n g by the p o l l i n a t o r , wind r e s i s t a n c e d u r i n g f l i g h t , or weak b i n d i n g of p o l l e n i n the p o o l may " r e s e t " the p o o l and expose d e e p l y b u r i e d p o l l e n . There i s e v i d e n c e t h a t i n many anemophilous s p e c i e s of p l a n t s , p o l l e n commonly o c c u r s i n clumps of 2 - 9 g r a i n s (Anderson 1970, i n S t a n l e y and L i n s k e n s 1974). P o l l e n - p o l l e n b i n d i n g of t h i s s o r t would f a c i l i t a t e the s l o u g h i n g o f f of l a r g e r masses of p o l l e n , both onto s t i g m a s and d u r i n g p r e e n i n g . O v e r a l l mean c a r r y o v e r f o r model 4 i s much l e s s than f o r model 3 (T a b l e V I I ) , and the i n c i d e n c e of z e r o d e p o s i t i o n i s much g r e a t e r ( F i g . 10). However, i f mean c a r r y o v e r i s c a l c u l a t e d e x c l u d i n g the z e r d d e p o s i t i o n v a l u e s ( i . e . i f we o n l y c o n s i d e r c a r r y o v e r of p o l l e n t h a t was 87 d e p o s i t e d on s t i g m a s ) , then c a r r y o v e r i n model 4 i n c r e a s e s s u b s t a n t i a l l y . Both mean and maximum c a r r y o v e r i n model 4 have g r e a t e r v a r i a n c e s than i n model 3. T h i s d i f f e r e n c e i s m a i n t a i n e d even when z e r o d e p o s i t i o n v a l u e s a r e e x c l u d e d . Thus models 3 and 4 both show r e g u l a r l o n g c a r r y o v e r ( F i g . 10), but model 4 has a h i g h e r v a r i a n c e a s s o c i a t e d w i t h c a r r y o v e r and a much h i g h e r f r e q u e n c y of z e r o d e p o s i t i o n . When I d e c r e a s e d the r a t i o of s t i g m a l p i c k u p t o a n t h e r d e p o s i t i o n i n model 3 from 3:10 toward 1:10 ( F i g s . 13 and 14), model 3's beh a v i o u r approached t h a t of model 4. However, i t remained i n t e r m e d i a t e and d i d not rea c h the l e v e l of model 4. For i n s t a n c e , model 3 produced 13% z e r o d e p o s i t i o n when 1 g r a i n was d e p o s i t e d per s t i g m a , compared t o 65% i n model 4. Model 4 has p o t e n t i a l l y a much s m a l l e r s t i g m a : a n t h e r c a p a c i t y r a t i o and the r e m a i n i n g d i f f e r e n c e between model 3 and model 4 c o u l d be due t o t h i s . However I sus p e c t t h a t i t i s due t o a c o m b i n a t i o n of the l a r g e number of g r a i n s i n the p o l l e n p o o l r e l a t i v e t o s t i g m a l c a p a c i t y and the l i k e l i h o o d t h a t many of those g r a i n s w i l l be permanently c o v e r e d by o t h e r p o l l e n . As l o n g as the r a t e of c o v e r i n g i s g r e a t e r than the r a t e of u n c o v e r i n g , the p o s s i b i l i t y of l a y e r i n g w i l l enhance the e f f e c t of l i m i t e d s t i g m a l c a p a c i t y r e l a t i v e t o a n t h e r d e p o s i t i o n and produce t h i s e f f e c t of many z e r o d e p o s i t i o n v a l u e s . Though t h e r e i s some e x p e r i m e n t a l e v i d e n c e s u g g e s t i n g l a y e r i n g of p o l l e n on hummingbirds, (Lertzman, t h i s t h e s i s ) , i t i s f a r from c o n c l u s i v e . Because of the p o t e n t i a l t h a t 88 l a y e r i n g p r o f o u n d l y a f f e c t s c a r r y o v e r by i n c r e a s i n g the l i k e l i h o o d of z e r o d e p o s i t i o n (which may j u s t be v e r y l o n g c a r r y o v e r ) , i t i s i m p o r t a n t t o a s s e s s the o c c u r r e n c e of l a y e r i n g i n r e a l systems. The r o l e of v a r i a t i o n i n f l o r a l geometry was one of the main r e s u l t s of the l a b o r a t o r y e x p e r i m e n t s , and i s the prime d i s t i n g u i s h i n g f e a t u r e of model 4. What a r e the e f f e c t s of i n c r e a s i n g or d e c r e a s i n g the amount of v a r i a b i l i t y i n f l o r a l c h a r a c t e r s ? I a c c o m p l i s h e d t h i s by v a r y i n g the c o e f f i c i e n t s of v a r i a t i o n f o r f l o r a l c o n t a c t i n both the x and y d i m e n s i o n s . In the p r e v i o u s d i s c u s s i o n of model 4 r e s u l t s , f l o r a l v a r i a b i l i t y was n o r m a l l y d i s t r i b u t e d i n the x and y d i m e n s i o n s of the p o l l e n p o o l w i t h a c o e f f i c i e n t of v a r i a t i o n of 1. In the f o l l o w i n g d i s c u s s i o n t h e s e c o e f f i c i e n t s of v a r i a t i o n v a r y from 0.2 t o 4.0. T h i s i s analogous t o an experiment where a p o l l i n a t o r f e d from p o p u l a t i o n s of f l o w e r s t h a t v a r i e d from b e i n g h i g h l y s t e r e o t y p e d i n form t o b e i n g h i g h l y v a r i a b l e . F l o r a l c h a r a c t e r s measured i n the f i e l d had c o e f f i c i e n t s of v a r i a t i o n from about 0.2 t o 2.0. For i n s t a n c e two measures of f l o w e r l e n g t h had c o e f f i c i e n t s of v a r i a t i o n of 0.291 and 0.345, and two measures of l a t e r a l d i s p l a c e m e n t (of stigmas and a n t h e r s ) had c o e f f i c i e n t s of v a r i a t i o n of 1.29 and 1.80. There are t h r e e t y p e s of o u t p u t v a r i a b l e s w i t h which I w i l l examine the e f f e c t s of d r i v i n g model 4 w i t h the amount of f l o r a l v a r i a b i l i t y : 1) t o t a l p o l l e n p o o l i n p u t and 89 o u t p u t ; the t o t a l number of p o l l e n g r a i n s p i c k e d up and d e p o s i t e d by the p o l l i n a t o r , 2) p o l l e n p o o l s t r u c t u r e a t the end of an 85 f l o w e r r u n ; the p r o p o r t i o n of the p o o l o c c u p i e d i n the x,y d i m e n s i o n s , and the mean depth of the l a y e r s i n the p o o l , and 3) the p o l l e n c a r r y o v e r s t a t i s t i c s , mean and maximum c a r r y o v e r . P o l l e n p i c k u p d e c r e a s e s w i t h i n c r e a s i n g f l o r a l v a r i a b i l i t y ( F i g . 17). As f l o w e r s a re more and more v a r i a b l e , a g r e a t e r p r o p o r t i o n of them oc c u r i n the t a i l s of the d i s t r i b u t i o n t h a t e x t e n d over the edge of the p o l l e n p o o l . The p o l l i n a t o r r e c e i v e s no p o l l e n from t h e s e f l o w e r s . T h i s e x p l a i n s many of the z e r o d e p o s i t i o n v a l u e s ( a c t u a l l y z e r o p i c k u p v a l u e s ) t h a t occur a t h i g h f l o r a l v a r i a b i l i t y . However, even a t the l o w e s t l e v e l of f l o r a l v a r i a b i l i t y , when z e r o p i c k u p i s v e r y u n l i k e l y , t h e r e was 20% z e r o d e p o s i t i o n . The t o t a l number of p o l l e n g r a i n s d e p o s i t e d f i r s t i n c r e a s e s s l i g h t l y and then d e c r e a s e s w i t h i n c r e a s i n g f l o r a l v a r i a b i l i t y ( F i g . 18). Why i s l e s s p o l l e n d e p o s i t e d a t v e r y low f l o r a l v a r i a b i l i t y than a t s l i g h t l y h i g h e r l e v e l s of v a r i a b i l i t y ? At ve r y low v a r i a b i l i t y , o n l y a s m a l l p r o p o r t i o n of the area of the p o o l i s o c c u p i e d ( F i g . 19), and most of the p o l l e n i s c o n c e n t r a t e d i n a h i g h l y l a y e r e d c e n t r a l a r e a ( F i g . 2 0 ) . A l l f l o w e r s a r e c o n t a c t i n g the p o o l i n almost e x a c t l y the same l o c a t i o n , and s i n c e more p o l l e n i s put i n t o the p o o l w i t h each f l o w e r than i s taken o u t , p o l l e n i s o n l y exposed on the s u r f a c e and a v a i l a b l e f o r gure 17. T o t a l number of p o l l e n g r a i n s p i c k e d up by the p o l l i n a t o r w h i l e f e e d i n g from 85 f l o w e r s , o utput from model 4 d r i v e n w i t h c h a n g i n g f l o r a l v a r i a b i l i t y . C o e f f i c i e n t s of v a r i a t i o n i n both the x and y d i m e n s i o n s were stepped from 0.2 t o 4.0 i n i n c r e m e n t s of 0.2. There were 20 runs of t h e model ( i . e . 20 sequences of 85 f l o w e r s ) a t each l e v e l of f l o r a l v a r i a b i l i t y . n H ±, q < i—i NLM3ER OF POLLEN GRAINS PICKED UP a 68 o c 01 6 PJ4-6 IU. I in uij,. o H—I—I—I—I—H H—r—I—I 1 1 IIIIIIIH--*H»H -HHH-H-I1IBIIH-r HIS IB I inn in ms HI 4S'SHh HWfH~ -ttfflH Jji JjflttSL. , TUTTBI O 92 F i g u r e 18. T o t a l number of p o l l e n g r a i n s d e p o s i t e d from the p o l l e n p o o l w h i l e the p o l l i n a t o r feeds from 85 f l o w e r s , o u t p u t from model 4 d r i v e n w i t h , c h a n g i n g f l o r a l v a r i a b i l i t y . The method f o r g e n e r a t i n g t h e s e r e s u l t s was as d e s c r i b e d f o r F i g . 17. T O T . A L N U M B E R F C L L E N G R A I N S C E P C B I T E D 9 B I 6 9 8 8 I ?-) 1 1 1 i 1 1—rH-° ni iiiim II MHI ui -im un i l U n i i u i *T-- turn HI ^ • aa tit i n f I B HI I If -IIIIIIIH II tin I HUB r IH1WHII ° it mm i gure 19. The p r o p o r t i o n of the p o l l e n p o o l o c c u p i e d i n the x and y ( s u r f a c e ) d i m e n s i o n s a t the end of runs of 85 f l o w e r s , o utput from model 4 d r i v e n w i t h c hanging f l o r a l v a r i a b i l i t y . The methods f o r g e n e r a t i n g t h e s e r e s u l t was as d e s c r i b e d f o r F i g . 17. PRCPCRTIQN OF POQ_ OCCUPIED IN X Y r 3 t-n M •t-H >; M g a a P . 6 P J -6 ru. i V-b U J . • h o h1 a QJ o Ul o H 1 1 h I 111! II! ib 6 H 1 4 f-»+f l a t a HI 1 RIB, - H I H I U 1 4 1 1 1 B BI HII I I r I I "ITrntnl i +H- II i IIIII T Tn l l 1 JIT) ] i i ++-W-+Hfr4 + 444-H- -H+ -frf+ 4 11 II 1 11 I L H 1 I 11 T T T I tr i I B I T ii in t Bfll 1 II 1 I il 4_ -ft- 4 I 81 II I -K- 4 4 11 n i i; an i ii II L l l if Tr i 111 III Ii r + IIIII HI II -ff 4 96 F i g u r e 20. Mean l a y e r i n g i n the p o l l e n p o o l a t the end of runs of 85 f l o w e r s , output from model 4 d r i v e n w i t h c h a n g i n g f l o r a l v a r i a b i l i t y . The method f o r g e n e r a t i n g t h e s e r e s u l t s was as d e s c r i b e d f o r F i g . 17. MEAN LAYERING a -t • PJ K 9 1 j j 1 j tin i i i im •+ -W-K-II StB~ -MH-I BC] t B* Tr IB Hill TIE II +J8+-• -Htt-- f l f -- H B --Mr 4 -m--w--w--J--BH-98 d e p o s i t i o n f o r a few f l o w e r s b e f o r e i t i s c o v e r e d up. Hence the h i g h degree of l a y e r i n g . There a r e two reasons why t o t a l p o l l e n d e p o s i t e d d e c r e a s e s a t h i g h e r f l o r a l v a r i a b i l i t y . F i r s t , because l e s s p o l l e n i s p i c k e d up t o b e g i n w i t h ( F i g . 17), t h e r e i s l e s s a v a i l a b l e t o be d e p o s i t e d . Second, the p o l l e n p o o l i s much s p a r s e r a t h i g h l e v e l s of f l o r a l v a r i a b i l i t y and i t i s l e s s l i k e l y t h a t any g i v e n f l o w e r ' s stigma w i l l c o n t a c t the p o o l a t a l o c a t i o n where p o l l e n has been p r e v i o u s l y d e p o s i t e d . F i g u r e 19 shows t h a t the p r o p o r t i o n of the p o o l o c c u p i e d i s low a t both low and h i g h v a r i a b i l i t y . However, a t low f l o r a l v a r i a b i l i t y , f l o r a l c o n t a c t i s g e n e r a l l y r e s t r i c t e d t o t h a t s m a l l a r e a , w h i l e a t h i g h v a r i a b i l i t y , c o n t a c t i s spre a d throughout the p o l l e n p o o l . R e g r e s s i o n s of mean and maximum p o l l e n c a r r y o v e r on f l o r a l v a r i a b i l i t y have a s i g n i f i c a n t n e g a t i v e s l o p e (Table V I I I and F i g . 21), i . e . t h e r e i s a p p a r e n t l y l o n g e r c a r r y o v e r w i t h lower f l o r a l v a r i a b i l i t y . However, i f the z e r o c a r r y o v e r v a l u e s a re removed, the r e g r e s s i o n of mean c a r r y o v e r on f l o r a l v a r i a b i l i t y has a s i g n i f i c a n t p o s i t i v e r e l a t i o n s h i p , and t h a t f o r maximum c a r r y o v e r has no s i g n i f i c a n t r e l a t i o n s h i p (note however, t h a t i n a l l c a s e s the r squared i s q u i t e s m a l l ) . The p r o p o r t i o n of z e r o d e p o s i t i o n v a l u e s i n c r e a s e s w i t h f l o r a l v a r i a b i l i t y ( F i g . 22). T h i s a c c o u n t s f o r the n e g a t i v e s l o p e of the r e g r e s s i o n of c a r r y o v e r on v a r i a b i l i t y when z e r o v a l u e s a re i n c l u d e d . Thus a t h i g h l e v e l s of f l o r a l v a r i a b i l i t y , 99 F i g u r e 21. Means and 95% c o n f i d e n c e i n t e r v a l s f o r mean and maximum c a r r y o v e r of p o l l e n when model 4 i s d r i v e n w i t h c h a n g i n g f l o r a l v a r i a b i l i t y . The method f o r g e n e r a t i n g t h e s e r e s u l t s was as d e s c r i b e d f o r F i g . 17. 100 181 > 0.6 1.2 1.8 2 .4 3 . 0 coefficient of variation 101 F i g u r e 22. The p r o p o r t i o n of z e r o d e p o s i t i o n when model 4 i s d r i v e n w i t h c hanging f l o r a l v a r i a b i l i t y . Zero d e p o s i t i o n c o u l d have r e s u l t e d from e i t h e r no p o l l e n b e i n g p i c k e d up or no p o l l e n b e i n g d e p o s i t e d . The method f o r g e n e r a t i n g t h e s e r e s u l t s was as d e s c r i b e d f o r F i g . 17. 0.4 0.8 1.2 1.6 2.0 2.4 2 .8 coe f f i c i e n t of v a r i a t i on 103 T a b l e V I I I . R e g r e s s i o n s t a t i s t i c s f o r mean and maximum c a r r y o v e r on f l o r a l v a r i a b i l i t y , w i t h and w i t h o u t z e r o d e p o s i t i o n v a l u e s . r e g r e s s i o n e q u a t i o n P s l o p e = 0 r squared n mean c a r r y o v e r w i t h y=11.8-3.1x P < 0.001 0.088 400 z e r o ' s maximum c a r r y o v e r w i t h y=l7.8-5.1x P < 0.001 0.13 400 z e r o ' s mean c a r r y o v e r w i t h o u t y=12.9+6.9x P < 0.001 0.119 103 z e r o ' s maximum c a r r y o v e r w i t h o u t y=24.7+2.39x P = 1.0 0.0073 1 04 z e r o ' s c a r r y o v e r i s l i k e l y t o be l o n g , i f any p o l l e n i s d e p o s i t e d a t a l l . But t h e r e i s an i n c r e a s e d l i k e l i h o o d t h a t no p o l l e n w i l l be p i c k e d up, and t h a t i f any p o l l e n i s p i c k e d up, none w i l l be d e p o s i t e d . At low l e v e l s of f l o r a l v a r i a b i l i t y , c a r r y o v e r i s s h o r t e r , but i t i s much more l i k e l y t h a t some p o l l e n w i l l be d e p o s i t e d . The h i g h i n c i d e n c e of z e r o d e p o s i t i o n a t h i g h f l o r a l v a r i a b i l i t y i s p r o b a b l y due t o the d e c r e a s e d p i c k u p of p o l l e n by the p o l l i n a t o r under those c o n d i t i o n s . The optimum l e v e l of f l o r a l v a r i a b i l i t y i n terms of p o l l e n c a r r y o v e r i s thus i n t e r m e d i a t e . I t i s the r e s u l t of 104 a b a l a n c e between d e c r e a s e d c a r r y o v e r a t low f l o r a l v a r i a b i l i t y and the i n c r e a s e d i n c i d e n c e of z e r o p i c k u p and d e p o s i t i o n a t h i g h f l o r a l v a r i a b i l i t y . D r i v i n g model 4 w i t h f l o r a l v a r i a b i l i t y i s u s e f u l i n 2 ways. F i r s t , i t shows that, both p o l l e n p o o l s t r u c t u r e and p o l l e n c a r r y o v e r are s e n s i t i v e t o the amount of f l o r a l v a r i a b i l i t y , g i v e n the model's a s s u m p t i o n s . I t thus p r o v i d e s an o p p o r t u n i t y , i n a model system, f o r e x p l o r i n g how f l o r a l c h a r a c t e r s can d r i v e p o l l e n p o o l s t r u c t u r e , and how p o l l e n c a r r y o v e r i s r e l a t e d t o p o l l e n p o o l s t r u c t u r e . Second, i t p r o v i d e s t e s t a b l e p r e d i c t i o n s of model 4. I would be s u r p r i s e d i f the d e t a i l e d p r e d i c t i o n s of model 4 a c c u r a t e l y r e f l e c t r e a l w o r l d phenomona. While model 4 does r e p r e s e n t an educated guess at the p r o c e s s e s of p o l l e n t r a n s f e r , t h e r e i s much t h a t i t l e a v e s out ( e . g . movement of stigmas and a n t h e r s through the p o l l e n p o o l , s l o u g h i n g o f f of p o l l e n , e t c . ) . I t i s a f i r s t a p p r o x i m a t i o n a t m o d e l l i n g p o l l e n p o o l s t r u c t u r e , and as such i s more u s e f u l than the p r e v i o u s models. However, i t s main p o i n t i s t o s t i m u l a t e i d e a s and suggest e x p e r i m e n t s . I t i s more a statement about i d e a s than a c o n c l u s i o n about the r e a l w o r l d . 105 D i s c u s s i o n I m p l i c a t i o n s For Mechanisms Much p o l l i n a t i o n r e s e a r c h has attempted t o study broad p o p u l a t i o n l e v e l p a t t e r n s of p o l l e n and gene f l o w , but has been l i m i t e d by i n c o m p l e t e knowledge of p o l l e n t r a n s f e r p r o c e s s e s a t the i n d i v i d u a l l e v e l . H i s t o r i c a l l y , as i n t h i s d i s c u s s i o n , the f o c u s has moved from d e s c r i p t i o n of p a t t e r n s toward the c o n s i d e r a t i o n of p r o c e s s e s , w i t h some accompanying i n c r e a s e i n u n d e r s t a n d i n g of how the p a t t e r n s are g e n e r a t e d . Each a l t e r n a t i v e model I have d i s c u s s e d added components t o the d e t e r m i n a t i o n of p o l l e n t r a n s f e r : " b l a n k s " , l i m i t e d s t i g m a l s u r f a c e a r e a , v a r i a b i l i t y i n f l o w e r morphology p r o d u c i n g a s p a t i a l l y s t r u c t u r e d p o l l e n p o o l , and the t h i r d d i m e n s i o n of the p o l l e n p o o l - d epth. These a d d i t i o n a l components and the ways t h a t they i n t e r a c t s h o u l d p r o f o u n d l y a f f e c t the c o n c e p t u a l c o n t e x t i n which p o l l i n a t i o n r e s e a r c h i s c o n d u c t e d , but we need c r i t i c a l e x p e r i m e n t s t o a s s e s s t h e i r importance and g e n e r a l i t y . The most i m p o r t a n t and g e n e r a l c o n c l u s i o n t o be drawn from t h e s e model r e s u l t s i s t h a t s i m p l e and o f t e n i m p l i c i t a s sumptions about p o l l e n p o o l s t r u c t u r e and the r u l e s f o r p i c k u p and d e p o s i t i o n of p o l l e n can have major consequences i n terms of p o l l e n c a r r y o v e r . One example of t h i s i s the complex p a t t e r n of p o l l e n d e p o s i t i o n t h a t r e s u l t e d from assuming random s e l e c t i o n of p o l l e n g r a i n s and l i m i t e d s t i g m a l c a p a c i t y i n model 3. T h i s k i n d of r e s u l t 1 06 i l l u s t r a t e s and r e i n f o r c e s the importance of making assumptions about c a r r y o v e r as e x p l i c i t as p o s s i b l e . Models 3 and 4, which make e x p l i c i t s t a t e m e n t s about the p r o c e s s e s t h a t g e n e r a t e v a r i a b i l i t y i n p o l l e n d e p o s i t i o n , p r e d i c t l o n g e r and more v a r i a b l e c a r r y o v e r than has o f t e n been assumed. I f c a r r y o v e r i s much lower (or h i g h e r ) than suggested h e r e , e i t h e r the p r o c e s s e s m o d e l l e d are i n v a l i d , or t h e r e a r e o t h e r p r o c e s s e s a c t i n g which i n f l u e n c e c a r r y o v e r . Some p o s s i b l e f a c t o r s a r e : 1) p o l l e n g r a i n s s t i c k t o g e t h e r and come o f f i n l a r g e clumps, 2) the f l o w e r s and the p o l l i n a t o r s c o n t a c t each o t h e r i n more s t e r e o t y p e d ways than we assumed, or 3) s t i g m a l c a p a c i t y i s h i g h r e l a t i v e t o the amount o f - p o l l e n p i c k e d up by the p o l l i n a t o r . Any of these c o u l d lower f l o w e r t o f l o w e r c a r r y o v e r , even i f the p r o c e s s e s d e s c r i b e d by the s e models were i n o p e r a t i o n . Note t h a t the f i r s t p o s s i b i l i t y r e f l e c t s a s t r u c t u r a l c h a r a c t e r i s t i c of the n a t u r a l system and would r e q u i r e a s t r u c t u r a l change i n the model, whereas the o t h e r s are merely q u a n t i t a t i v e ( t h a t i s , they would be m o d e l l e d s i m p l y by changing parameter v a l u e s i n the model). I n c r e a s i n g the c o m p l e x i t y of model s t r u c t u r e r e s u l t e d i n an i n c r e a s i n g l y complex p a t t e r n of model o u t p u t . While t h i s has g r e a t h e u r i s t i c v a l u e i n terms of u n d e r s t a n d i n g the consequences of a s s u m p t i o n s , i n c r e a s i n g c o m p l e x i t y does not n e c e s s a r i l y imply i n c r e a s i n g r e a l i s m . We need more knowledge of r e a l systems t o a s s e s s b o t h the h y p o t h e t i c a l mechanisms on which the models a r e based and the p a t t e r n s 1 07 they g e n e r a t e . These models w i l l be w o r t h w h i l e i f t h e i r v r e s u l t s can be used t o f o c u s f u t u r e r e s e a r c h . I m p l i c a t i o n s For P l a n t P o p u l a t i o n s Based on an average of about 5 f l o w e r s v i s i t e d per p l a n t by hummingbirds on s i n g l e bouts of f o r a g i n g ( P e r k i n s 1977), mean and maximum p o l l e n c a r r y o v e r v a l u e s of b oth models 3 and 4 would l e a d t o p l a n t t o p l a n t c a r r y o v e r i n the range suggested by L e v i n and K e r s t e r (1969a) and L e v i n e t a l . (1971) - about 3 t o 10 p l a n t s , depending on the number of f l o w e r s v i s i t e d per p l a n t . However, the s e models suggest t h a t w h i l e much of the p o l l e n w i l l be d e p o s i t e d near i t s s o u r c e p l a n t , a s m a l l e r but s u b s t a n t i a l p r o p o r t i o n w i l l be c a r r i e d many f l o w e r s past i t s s o u r c e . The t a i l of the d i s t r i b u t i o n of c a r r y o v e r d i s t a n c e s i s l o n g ; b oth models 3 and 4 show i n f r e q u e n t , but r e g u l a r d e p o s i t i o n of p o l l e n 40 t o 50 f l o w e r s p a s t the s o u r c e . To the e x t e n t t h a t the p r o c e s s e s d e s c r i b e d i n t h e s e models r e p r e s e n t r e a l systems, we need t o be a s k i n g about the importance of such r a r e e v e n t s i n n a t u r e . I f , a f t e r p o l l i n a t i o n , r e a l p o l l e n g r a i n s from d i f f e r e n t s o u r c e s compete f o r a l i m i t e d number of o v u l e s , or i f r e p r o d u c t i v e s u c c e s s of o v u l e s ( i . e . seed number, seed q u a l i t y , or s e e d l i n g q u a l i t y ) v a r i e s w i t h p o l l e n d i s p e r s a l d i s t a n c e i n the manner su g g e s t e d by P r i c e and Waser (1979), Waser and P r i c e (1981) and the f o l l o w i n g c h a p t e r , then a s m a l l p r o p o r t i o n of the p o l l e n t r a n s f e r s c o u l d c o n t r i b u t e 108 d i s p r o p o r t i o n a t e l y t o r e p r o d u c t i v e s u c c e s s . T h i s p o s s i b i l i t y can o n l y be a s s e s s e d w i t h r e f e r e n c e t o the p o l l e n t r a n s f e r mechanisms and o p t i m a l o u t c r o s s i n g d i s t a n c e s of p a r t i c u l a r systems, so i t would be premature t o c o n c l u d e t h a t l o n g d i s t a n c e p o l l e n t r a n s f e r s do g e n e r a l l y have d i s p r o p o r t i o n a t e f i t n e s s consequences. However, I can c o n c l u d e t h a t mean v a l u e s of p o l l e n c a r r y o v e r a r e not s u f f i c i e n t f o r a s s e s s i n g the importance of r a r e e v e n t s . In f a c t , i t i s l o g i c a l l y i m p o s s i b l e i n g e n e r a l t o u n d e r s t a n d a n y t h i n g about the importance of r a r e e v e n t s by examining measures of c e n t r a l tendency. These a n a l y s e s have been o r i e n t e d towards male f u n c t i o n ; the p r i m a r y f o c u s has been on how many f l o w e r s beyond i t s source p o l l e n i s d e p o s i t e d . The complementary a n a l y s i s would a l s o be w o r t h w h i l e , a s k i n g : "what i s the d i s t r i b u t i o n of i d e n t i t i e s of p o l l e n g r a i n s r e c e i v e d by a s t i g m a ? " . C e r t a i n l y , f o r any u n d e r s t a n d i n g of how s e l e c t i o n a c t s on f a c t o r s i n f l u e n c i n g c a r r y o v e r we w i l l have t o be a b l e t o i n t e g r a t e consequences of p o l l e n d i s p e r s a l e v e n t s i n terms of both male and female f u n c t i o n . For example, the f i n d i n g t h a t seed s e t i s maximized a t a p a r t i c u l a r p o l l e n d i s p e r s a l d i s t a n c e (female f u n c t i o n ; P r i c e and Waser 1979; next c h a p t e r ) must be i n t e r p r e t e d i n terms of the f a c t o r s t h a t d e t e r m i n e the a c t u a l d i s t a n c e s t o which p o l l e n i s c a r r i e d (male f u n c t i o n ; t h i s s t u d y ) . These two k i n d s of f a c t o r s c l e a r l y a r e not independent. For i n s t a n c e , f l o o d i n g a p o l l e n p o o l w i t h one's own p o l l e n s h o u l d i n c r e a s e s u c c e s s 109 as a male, but decrease s u c c e s s as a female (Schemske 1980; Lertzman, p r e v i o u s c h a p t e r ) . There i s a growing l i t e r a t u r e on the t r a d e o f f s and c o n s t r a i n t s i n v o l v e d i n male v s . female e x p r e s s i o n and the t a c t i c s a p p r o p r i a t e f o r each (e.g. W i l l s o n and Rathcke 1974; W i l l s o n 1979; Charnov et a l . 1976; Charnov and B u l l 1977; Janzen 1975; Hancock and B r i n g h u r s t 1980; Lertzman, p r e v i o u s c h a p t e r ) . I t w i l l be most i m p o r t a n t i n the f u t u r e t o t i g h t e n the l i n k between our i n t e r e s t i n such f i t n e s s consequences of d i f f e r e n t p a t t e r n s of p o l l e n d i s p e r s a l and our knowledge of the p r o c e s s e s t h a t a c t i n p r o d u c i n g t h e s e p a t t e r n s . C o n c l u s i o n s P r o c e s s - o r i e n t e d models t h a t i n c l u d e the d i s t r i b u t i o n of i n d i v i d u a l v a r i a b i l i t y a r e more l i k e l y t o be u s e f u l i n u n d e r s t a n d i n g p o l l i n a t i o n systems than d e t e r m i n i s t i c p a t t e r n - o r i e n t e d models t h a t a re p r i m a r i l y s e n s i t i v e t o mean v a l u e s . As components of p o l l e n t r a n s f e r a r e m o d e l l e d more e x p l i c i t l y , p o l l e n t r a n s f e r i s l e s s p r e d i c t a b l e from f l o w e r v i s i t a t i o n sequences a l o n e and p o l l e n i s c a r r i e d f a r t h e r and more v a r i a b l y beyond i t s s o u r c e . D e t a i l e d a n a l y s i s of a model based on the l a b o r a t o r y 110 e x p e r i m e n t s of the p r e v i o u s c h a p t e r showed t h a t both p o l l e n p o o l s t r u c t u r e and p o l l e n c a r r y o v e r a r e s e n s i t i v e t o the amount of . - f l o r a l v a r i a b i l i t y , g i v e n the models a s s u m p t i o n s . Comparison of th e s e models s u g g e s t s t h a t i n c r e a s i n g s t r u c t u r a l c o m p l e x i t y can p r o v i d e i n c r e a s i n g h e u r i s t i c power, but I c a u t i o n a g a i n s t making the c o n c l u s i o n t h a t t h i s a l s o i m p l i e s i n c r e a s i n g r e a l i s m . C r i t i c a l e x p e r i m e n t s i n n a t u r a l systems a r e needed t o a s s e s s the c o n t r i b u t i o n of r a r e e v e n t s ( i . e . p o l l e n t r a n s f e r r e d i n t h e t a i l s of the d i s p e r s a l d i s t r i b u t i o n ) t o p l a n t r e p r o d u c t i v e s u c c e s s . 111 OPTIMAL OUTCROSSING AND POLLEN DISPERSAL IN CASTILLEJA MINIATA I n t r o d u c t i o n I t i s a commonplace t h a t an a n i m a l ' s f i t n e s s i s r e l a t e d t o the q u a l i t y of i t s mate (e.g. Coulson 1966; 1968; Coulson and White 1958; O r i a n s 1969; Downhower and A r m i t a g e 1971; Cox and LeBoeuf 1977; Weatherhead and Robertson 1977). R e c e n t l y , s i m i l a r i d e a s of mate s e l e c t i o n and mate q u a l i t y have been a p p l i e d t o p l a n t s (e.g. Janzen 1975; W i l l s o n 1979; Charnov 1979). Two t y p e s of f a c t o r s l e a d t o d i f f e r e n t i a l mate q u a l i t y ; p h e n o t y p i c c h a r a c t e r s such as c o m p e t i t i v e or f o r a g i n g a b i l i t y and t e r r i t o r i a l a g g r e s s i v e n e s s , and more d i r e c t l y g e n o t y p i c c h a r a c t e r s such as g e n e t i c s i m i l a r i t y (Waser and P r i c e 1981). In p l a n t s , p o l l e n i s the o n l y r e p r e s e n t a t i o n of the male t h a t i s a v a i l a b l e f o r assessment by the female. A s s e s s i n g m a t e , q u a l i t y based on p h e n o t y p i c c h a r a c t e r s r e q u i r e s t h a t genes f a v o r i n g the s p o r o p h y t e are e i t h e r e x p r e s s e d i n or c o r r e l a t e d w i t h t r a i t s of the gametophyte (Waser and P r i c e 1981). Though t h i s has been documented (Mulcahy 1971), i t i s l e s s p l a u s i b l e than d i f f e r e n t i a l mate q u a l i t y based on g e n e t i c s i m i l a r i t y as a f a c t o r of g e n e r a l importance f o r p l a n t s . G e n e t i c s i m i l a r i t y of mates i s o f t e n d i c h o t o m i z e d as i n b r e e d i n g v e r s u s o u t b r e e d i n g . W h i l e the d e p r e s s i o n of r e p r o d u c t i v e output due t o i n b r e e d i n g i s common ( F a l c o n e r 1960; Wright 1977), d e c r e a s e d r e p r o d u c t i v e s u c c e s s due t o 1 12 o u t b r e e d i n g d e p r e s s i o n i s l e s s w e l l known ( F a l c o n e r 1960). The p r o d u c t s of i n t e r p o p u l a t i o n c r o s s e s f i r s t show h e t e r o s i s and then i n c r e a s i n g i n c o m p a t i b i l i t y as the d i s t a n c e (or time) s e p a r a t i n g the p o p u l a t i o n s i n c r e a s e s ( K r u c k e b e r g 1957; O l i v e r 1971; Hughes and V i c k e r y 1974; V i c k e r y 1978). Hughes and V i c k e r y (1974) suggested t h a t t h e maximum h e t e r o z y g o s i t y t h a t w i l l r e s u l t i n h e t e r o s i s i s t h e same as the l e v e l a t which p a r t i a l c r o s s i n g b a r r i e r s s t a r t t o o c c u r . ' Presumably, the mating of more d i s t a n t i n d i v i d u a l s , . a d a p t e d t o d i f f e r e n t m i c r o h a b i t a t s , l e a d s t o the m i x i n g or breakdown of gene complexes f a v o r a b l e t o one or the o t h e r s i t e s and thus a lower f i t n e s s of the o f f s p r i n g i n e i t h e r s i t e . Thus, at an i n t e r - p o p u l a t i o n s p a t i a l s c a l e , an i n t e r m e d i a t e l e v e l of o u t c r o s s i n g s h o u l d r e s u l t i n the h i g h e s t r e p r o d u c t i v e s u c c e s s . R e c e n t l y i t has been proposed t h a t s i m i l a r p r o c e s s e s occur w i t h i n p o p u l a t i o n s . P r i c e and Waser (1979) and Waser and P r i c e (1981) suggested t h a t r e p r o d u c t i v e s u c c e s s w i l l be maximized a t i n t e r m e d i a t e o u t c r o s s i n g d i s t a n c e s t h a t may be q u i t e s m a l l (e.g. 1 - 10 m f o r D e l p h i n i u m n e l s o n i and Ipomopis a g g r e g a t a ) . T h i s assumes a s t r o n g i n v e r s e c o r r e l a t i o n of r e l a t e d n e s s and d i s t a n c e , and t h u s r e q u i r e s e x t e n s i v e g e n e t i c d i f f e r e n t i a t i o n of p l a n t p o p u l a t i o n s on a s m a l l s p a t i a l s c a l e . Such d i f f e r e n t i a t i o n c o u l d r e s u l t from e i t h e r s t r o n g s e l e c t i o n , h i g h l y r e s t r i c t e d gene f l o w , or b o t h . E h r l i c h and Raven (1969) s u g g e s t e d t h a t l o c a l d i f f e r e n t i a t i o n might be much more common than had 1 13 p r e v i o u s l y been b e l i e v e d , and t h a t s e l e c t i o n might overcome the homogenizing e f f e c t s of gene f l o w i n t h e s e p o p u l a t i o n s . S i n c e then i t has been shown t h a t g e n e t i c d i f f e r e n t i a t i o n of p o p u l a t i o n s can occur q u i t e l o c a l l y , and t h a t i n some ca s e s i t can be m a i n t a i n e d by s e l e c t i o n even i n the presence of e x t e n s i v e gene f l o w ( A n t o n o v i c s 1971; E n d l e r 1973; 1977; S c h a a l 1975; Adams 1977; K e e l e r 1978; S i l a n d e r 1979). In t h i s study I ask whether C a s t i l l e j a m i n i a t a , an o u t b r e e d i n g p e r e n n i a l h e r m a p h r o d i t i c herb, e x h i b i t s a w i t h i n p o p u l a t i o n i n t e r m e d i a t e o p t i m a l o u t c r o s s i n g d i s t a n c e . I then compare t h i s i n f o r m a t i o n t o e s t i m a t e s of a c t u a l o u t c r o s s i n g d i s t a n c e s based on the d i s p e r s a l of dye by i t s hummingbird p o l l i n a t o r s . T h i s system i s s i m i l a r i n many ways t o the o n l y o t h e r systems f o r which t h e r e i s i n f o r m a t i o n of t h i s type (Waser and P r i c e 1981). I t d i f f e r s i n t h a t C a s t i l l e j a m i n i a t a appears t o be more s p e c i a l i z e d on hummingbirds as p o l l i n a t o r s than e i t h e r of the o t h e r p l a n t s p e c i e s s t u d i e d so f a r ( D e l p h i n i u m n e l s o n i and Ipomopis  a g g r e g a t a ) . T h i s C a s t i l l e j a - S e l a s p h o r u s r u f u s system has a l s o been the s u b j e c t of a s t u d y of the i n f l u e n c e of hummingbird t e r r i t o r i a l i t y on p o l l e n f l o w ( P e r k i n s 1977). I use the dye d i s p e r s a l d a t a t o a d dress the q u e s t i o n of the i n f l u e n c e of hummingbird t e r r i t o r i a l i t y on the p a t t e r n of p o l l e n movement i n a meadow. L i n h a r t (1973) c o n c l u d e d t h a t because most of the f o r a g i n g f l i g h t s of a t e r r i t o r i a l p o l l i n a t o r a r e w i t h i n i t s t e r r i t o r y , p l a n t s w i t h i n the t e r r i t o r y w i l l have a p o o l of p o t e n t i a l p o l l e n donors and 1 14 r e c i p i e n t s t h a t i s m o s t l y r e s t r i c t e d t o o t h e r p l a n t s i n the t e r r i t o r y . However, P e r k i n s (1977) c o n c l u d e d t h a t though t h i s may be t r u e on the s h o r t term, on the l o n g term ( i . e . t h r o u g h a f l o w e r i n g season)., t h i s e f f e c t i s swamped. Because t e r r i t o r i a l b o u n d a r i e s f l u c t u a t e i n t i m e , p l a n t s have a much l a r g e r p o o l of p o t e n t i a l mates than those s h a r i n g the same t e r r i t o r y a t any one p o i n t i n t i m e . I ask whether t e r r i t o r i a l b o u n d a r i e s r e s t r i c t p o l l e n movement on the s h o r t term, and whether they a f f e c t the d i r e c t i o n of p o l l e n d i s p e r s a l from p l a n t s near the b o u n d a r i e s . M a t e r i a l s and Methods A l l e x p e r i m e n t s were c a r r i e d out i n meadow 2 of the G r i z z l y Lake study area (Gass e_t a l . 1976). C a s t i l l e j a  m i n i a t a i s the predominant hummingbird p o l l i n a t e d f l o w e r i n t h i s meadow. Only a few A q u i l e g i a formosa a re p r e s e n t , and. they a r e o n l y t h e r e e a r l y i n the season. Meadow 2 i s bounded on the south by a t a l u s s l o p e , on the n o r t h by c o n i f e r o u s f o r e s t , and on the t o p and bottom by s h o r t c l i f f s (about 5-15 m). I t has a s l o p e of 35-40 degrees and an e a s t e r n e x p o s u r e . Of the 3 main study meadows a t G r i z z l y Lake, meadow 2 i s the most homogeneous i n terms of the d i s t r i b u t i o n of f l o w e r s . The one major d i s c o n t i n u i t y i s a s m a l l d r a i n a g e r u n n i n g from the t o p t o the bottom t h a t o n l y c a r r i e s water e a r l y i n the season ( j u s t a f t e r snowmelt) b e f o r e much C a s t i l l e j a i s i n bloom. Though m i c r o -e n v i r o n m e n t a l f e a t u r e s ^ have not been measured, t h e r e appears 115 t o be a s u b s t a n t i a l g r a d i e n t of m o i s t u r e from the w e t t e r a r e a s below the c l i f f s a t the t o p of the meadow t o the d r i e r exposed a r e a s a t the bottom of the meadow. T h i s i s based on d i r e c t o b s e r v a t i o n of s o i l m o i s t u r e , and of the o t h e r v e g e t a t i o n growing i n the meadow. To a s s e s s the r e p r o d u c t i v e v a l u e of p o l l e n from d i f f e r e n t d i s t a n c e s , I hand p o l l i n a t e d f l o w e r s w i t h p o l l e n t h a t o r i g i n a t e d from v a r i o u s p r e - d e t e r m i n e d d i s t a n c e s away ( a f t e r P r i c e and Waser 1979). In 1979 the hand p o l l i n a t i o n t r e a t m e n t s were: s e l f i n g , and p o l l e n from 0.5, 2, 10, and 30 m away from the e x p e r i m e n t a l p l a n t . In 1980 the t r e a t m e n t s were s e l f i n g , and 0.5, 1, 5, 10, and 30 m. P o l l e n r e c i p i e n t s ( e x p e r i m e n t a l p l a n t s ) were l o c a t e d t h roughout the meadow, and t r e a t m e n t s were a s s i g n e d t o them randomly. To o b t a i n p o l l e n , the tr e a t m e n t d i s t a n c e was measured away from the e x p e r i m e n t a l p l a n t and f l o w e r s were se a r c h e d a t t h a t d i s t a n c e u n t i l enough p o l l e n c o u l d be o b t a i n e d on a wooden t o o t h p i c k (a new t o o t h p i c k f o r each p o l l e n t r e a t m e n t ) . T h i s sometimes r e q u i r e d s e v e r a l f l o w e r s on more than one p l a n t . T h i s p o l l e n was then c a r r i e d t o the e x p e r i m e n t a l p l a n t and a p p l i e d t o a l l r e c e p t i v e s t i g m a s but one. The l e n g t h of time i n t r a n s i t was s t a n d a r d i z e d f o r p o l l e n from a l l d i s t a n c e s t o c o n t r o l f o r l o s s of v i a b i l i t y . A l l e x p e r i m e n t a l s t i g m a s were c o a t e d w i t h p o l l e n as c o m p l e t e l y as p o s s i b l e . F l o w e r s were then c o v e r e d i n mesh bags t h a t were f i n e enough t o e x c l u d e hummingbirds and bumblebees. A l o n g l e p i d o p t e r a n p r o b o s c i s ( e.g. of 116 hawkmoths) c o u l d p r o b a b l y f i t through the mesh, but i t would have been d i f f i c u l t f o r the i n s e c t t o r e a c h the n e c t a r and I have not obser v e d l e p i d o p t e r a n s f e e d i n g from C a s t i l l e j a a t G r i z z l y Lake. The f l o w e r s i n each bag (each i n f l o r e s c e n c e ) l e f t u n p o l l i n a t e d were c o n t r o l s f o r n o n - e x p e r i m e n t a l p o l l i n a t i o n . I f these f l o w e r s s e t seed above the mean f o r s e l f e d f l o w e r s , then d a t a from t h a t bag was d i s c a r d e d . Seeds were c o l l e c t e d when the pods were near d e h i s c e n c e , and the "normal" seeds per pod ( i n s i z e and appearance) were co u n t e d under a d i s s e c t i n g m i c r o s c o p e . Treatments have unequal sample s i z e s because a h i g h i n c i d e n c e of seed p r e d a t i o n by i n s e c t l a r v a e reduced sample s i z e s u n e q u a l l y . To e s t i m a t e p o l l e n d i s p e r s a l , I used the same f l u o r e s c e n t powders d e s c r i b e d i n the l a b o r a t o r y e x p e r i m e n t s on p o l l e n c a r r y o v e r . Four dye source p l a n t s were chosen i n a s i n g l e t e r r i t o r y , the b o u n d a r i e s of which were m o n i t o r e d b e f o r e and d u r i n g the e x p e r i m e n t . The t e r r i t o r i a l b o u n d a r i e s approached the bottom edge of the meadow ( e a s t s i d e ) , and f o l l o w e d the meadow boundary at the t a l u s on the sou t h s i d e . The b o u n d a r i e s extended i n t o the c e n t e r of the meadow a t both the t o p (west) end of the t e r r i t o r y and the n o r t h s i d e of the t e r r i t o r y . The t e r r i t o r y o v e r l a p p e d much of the ar e a t h a t was o c c u p i e d by the f o c a l i n d i v i d u a l d e s c r i b e d by Gass (1979). One dyed p l a n t was a t the edge of the t e r r i t o r y and a t the edge of the meadow ( o r a n g e ) , one p l a n t was a t the edge of the t e r r i t o r y and a t the c e n t e r of 1 17 the meadow ( g r e e n ) , and two p l a n t s were i n the c e n t e r of the t e r r i t o r y near the c e n t e r of the meadow ( r e d and b l u e , see F i g . 2 6 ) . Four f l o w e r s were chosen on each of f o u r i n f l o r e s c e n c e s on each of t h e s e p l a n t s and had dye a p p l i e d t o them. An exce s s of dye was a p p l i e d by d i p p i n g the sti g m a s and a n t h e r s i n t o a t e s t tube c o n t a i n i n g dye. A d i f f e r e n t c o l o u r of dye was a p p l i e d t o each p l a n t . Dye was a p p l i e d on the e v e n i n g of 26 J u l y . On the n i g h t of the t h i r d day f o l l o w i n g (29 J u l y ) , t he green and re d p l a n t s were censused. On the f o l l o w i n g n i g h t (30 J u l y ) , the b l u e and red p l a n t s were censused. I t would have been p r e f e r a b l e t o do a l l the p l a n t s on the same n i g h t , but i t took the f u l l n i g h t t o do the f i r s t two p l a n t s . We censused f l o w e r s by e x t e n d i n g a tape measure a g i v e n d i s t a n c e out from the p l a n t , and w a l k i n g a c i r c l e w i t h a r a d i u s of t h a t d i s t a n c e . A l l f l o w e r s of a l l p l a n t s t h a t c o n t a c t e d t h a t c i r c l e were examined by eye under u l t r a v i o l e t l i g h t f o r dye p a r t i c l e s . Only dye a c t u a l l y on s t i g m a s , a n t h e r s , or i n the c o r o l l a tube near the a n t h e r s were counted as h a v i n g dye, i . e . dye on n o n - r e p r o d u c t i v e s t r u c t u r e s was i g n o r e d . Some p r e c i s i o n was l o s t by u s i n g presence/absence s a m p l i n g as opposed t o p i c k i n g f l o w e r s and examining them l a t e r under a d i s s e c t i n g m i c r o s c o p e where dye g r a i n s c o u l d be co u n t e d (e.g. P r i c e and Waser 1979; Waser and P r i c e 1981). However, t h i s would have caused a major p e r t u r b a t i o n t o the meadow - removal of about one f o u r t h of the f l o w e r s -t h a t I was not w i l l i n g t o make. A l s o , presence/absence 118 measures make l e s s r i g i d assumptions about how w e l l the dyes mimic the be h a v i o u r of p o l l e n than a c t u a l c o u n t s of dye g r a i n s . I d i v i d e d the ar e a around each e x p e r i m e n t a l p l a n t i n t o e i g h t e q u a l p i e s e c t i o n s and r e c o r d e d the d i r e c t i o n from the source f o r each f l o w e r censused. Thus dye d i s p e r s a l i n f o r m a t i o n i s two d i m e n s i o n a l ; presence/absence a t a g i v e n d i s t a n c e and i n a g i v e n d i r e c t i o n . For each d i s t a n c e and d i r e c t i o n (number of d i s t a n c e s = 5, number of d i r e c t i o n s = 8 ) , I c a l c u l a t e d the per cen t of the t o t a l number of f l o w e r s w i t h dye on them t h a t o c c u r r e d t h e r e , and d i v i d e d t h a t number by the number of f l o w e r s t h a t o c c u r r e d t h e r e . T h i s p r o v i d e s a s t a t i s t i c t h a t i s c o r r e c t e d f o r the g r e a t e r number of f l o w e r s sampled i n c i r c l e s of l a r g e r r a d i u s . T h i s i s the s t a t i s t i c used i n the t e s t d e s c r i b e d below. However, the u n c o r r e c t e d p r o p o r t i o n of dye a t each d i s t a n c e i s p r e s e n t e d i n f i g u r e 24 because the p r o p o r t i o n s make more i n t u i t i v e sense. I f t e r r i t o r i a l b o u n d a r i e s do r e s t r i c t p o l l e n movement on a day-to-day b a s i s , then p l a n t s near t e r r i t o r i a l b o u n d a r i e s s h o u l d show a net movement of p o l l e n or dye i n toward the c e n t e r of the t e r r i t o r y . P l a n t s i n the c e n t e r of the t e r r i t o r y s h o u l d show a more homogeneous d i s p e r s i o n of p o l l e n i n a l l d i r e c t i o n s . To t e s t the n u l l h y p o t h e s i s t h a t p o l l e n was d i s t r i b u t e d u n i f o r m l y from each p l a n t (as opposed t o d i r e c t i o n a l l y ) , I used a m o d i f i c a t i o n of the R a y l e i g h t e s t t h a t t a k e s i n t o account the magnitudes of the v e c t o r s 119 i n each d i r e c t i o n (Moore 1980). T h i s t e s t makes the assumption t h a t any d e p a r t u r e from u n i f o r m i t y w i l l be u n i m o d a l , and thus may g i v e m i s l e a d i n g r e s u l t s i f the d a t a a r e m u l t i - m o d a l l y d i s t r i b u t e d ( B a t s c h e l e t 1965). T h i s a ssumption seems r e a s o n a b l e i n t h a t t h e r e are no a p r i o r i r e asons t o expect m u l t i m o d a l d i s t r i b u t i o n s of p o l l e n d i s p e r s a l v e c t o r s i n t h i s system i f they r e p r e s e n t a l a r g e number of f l i g h t s . S i n c e t h i s t e r r i t o r y c o n t a i n e d an average of 856 f l o w e r s d u r i n g t h i s e x p e r i m e n t , and a l l or most had t o be v i s i t e d by the hummingbird each day (Gass et a l . 1976; Gass 1979), the assumption t h a t t h e s e d i s t r i b u t i o n s r e p r e s e n t a l a r g e number of f l i g h t s i s j u s t i f i e d . R e s u l t s O p t i m a l O u t c r o s s i n g The r e s u l t s show much v a r i a b i l i t y both w i t h i n and between t r e a t m e n t s and between y e a r s ( F i g . 2 3 ) . W h i l e i n 1979 t h e r e was a peak i n seed p r o d u c t i o n a t the 2.0 m t r e a t m e n t , t h e r e was no such t r e n d i n 1980, when the mean seeds per pod were almost i d e n t i c a l between t r e a t m e n t s . In b o t h y e a r s s e l f e d f l o w e r s s e t almost no seed. I f the 1979 d a t a are grouped i n t o s e l f e d , c l o s e (0.5 and 2.0 m), and d i s t a n t (10.0 and 30.0 m) t r e a t m e n t s , the c l o s e group s e t s s i g n i f i c a n t l y h i g h e r numbers of seeds than e i t h e r the s e l f e d or d i s t a n t groups (Mann-Whitney U t e s t ; p 120 F i g u r e 23. Seeds produced under d i f f e r e n t hand p o l l i n a t i o n t r e a t m e n t s , means and 95% c o n f i d e n c e i n t e r v a l s . 3 6 12C* O .5 1 2 5 10 3 0 pollination treatment (meters) 122 = 0.002 f o r c l o s e v s . s e l f e d , p = 0.001 f o r c l o s e v s . d i s t a n t ) . When 1979 and 1980 d a t a a r e combined ( F i g . 23), t h i s t r e n d i s m a i n t a i n e d ; w h i l e (except f o r s e l f i n g ) a d j a c e n t t r e a t m e n t s do not d i f f e r s i g n i f i c a n t l y , the 2 m sample i s s i g n i f i c a n t l y h i g h e r than e i t h e r the s e l f e d or the 30 m samples (p < 0.001, p < 0.25 r e s p e c t i v e l y , Mann-Whitney U t e s t ) . Dye D i s p e r s a l In g e n e r a l , much of the dye was d e p o s i t e d on or near the source p l a n t s , w i t h s m a l l e r p r o p o r t i o n s b e i n g c a r r i e d l o n g e r d i s t a n c e s ( F i g s . 24 and 25). However, w i t h i n t h i s p a t t e r n t h e r e was a g r e a t d e a l of v a r i a b i l i t y between p l a n t s . For example, 41% of the f l o w e r s o b s e r v e d w i t h dye from the r e d p l a n t were 2 m away from the dye source p l a n t , but o n l y 9% of the f l o w e r s w i t h dye from the green dye p l a n t were 2 m away ( F i g . 2 4 ) . W ith such a s m a l l sample i t i s d i f f i c u l t t o make a c o n c l u s i o n about the e f f e c t s of t e r r i t o r i a l and meadow edges on the d i s t a n c e t h a t dye i s t r a n s f e r r e d . However t h e r e appear t o be no c o n s i s t e n t d i f f e r e n c e s between the edge and c e n t e r p l a n t s i n dye d i s p e r s a l d i s t a n c e . The comparison of dye d i s p e r s a l d i s t a n c e s f o r t h e s e p l a n t s i s confounded by v a r i a t i o n i n p l a n t d e n s i t y (Table I X ) . The edge of the meadow was the l e a s t dense a r e a , and a l s o , because the orange p l a n t l a y a t the meadow edge, much 123 F i g u r e 24. The p r o p o r t i o n of the t o t a l observed dye t h a t was d i s p e r s e d t o v a r i o u s d i s t a n c e s away from the s o u r c e p l a n t . There was no 10 m sample f o r the green dye p l a n t . dispersal distance (m) 125 T a b l e IX. Degree of s a t u r a t i o n of l o c a l f l o w e r s by dye from d i f f e r e n t s o u r c e s . source # f l o w e r s 0 - 5 m # f l o w e r s w i t h dye % f l o w e r s w i t h dye green 280 33 11.8 r e d 1 92 48 25.0 b l u e 191 52 27.2 orange 73 23 31.5 of the a r e a sampled was a c t u a l l y o u t s i d e the meadow and t h e r e f o r e c o n t a i n e d no p l a n t s . The r e s u l t t h a t dye (or p o l l e n ) from p l a n t s i n a r e a s of lower d e n s i t y i s c a r r i e d l o n g e r d i s t a n c e s (Table IX) i s i n agreement w i t h p r e v i o u s f i n d i n g s of d e n s i t y dependent p o l l i n a t o r f l i g h t d i s t a n c e s and p o l l e n d i s p e r s a l d i s t a n c e s ( L e v i n and K e r s t e r 1969 a,b; B e a t t i e 1976). Even though the l o w e s t d e n s i t y p l a n t had the h i g h e s t per c e n t s a t u r a t i o n of l o c a l f l o w e r s w i t h dye (Table I X ) , fewer f l o w e r s w i t h i n 10 m a c t u a l l y r e c e i v e d dye. The d i r e c t i o n a l t r e n d s of dye movement are i l l u s t r a t e d i n F i g u r e 25. Though i t appears t h a t the edge p l a n t s have a d i s t r i b u t i o n more skewed d i r e c t i o n a l l y than the c e n t e r p l a n t s , none of the p l a n t s d e v i a t e d s i g n i f i c a n t l y from a u n i f o r m c i r c u l a r d i s t r i b u t i o n ( T a ble X ) . However, w h i l e they d i d not re a c h s t a t i s t i c a l s i g n i f i c a n c e ( i . e . a l p h a = 0.05), the edge p l a n t s have h i g h e r (more s i g n i f i c a n t ) v a l u e s 126 F i g u r e 25. The d i r e c t i o n a l v e c t o r s of dye d i s p e r s a l and t e r r i t o r i a l b o u n d a r i e s on the day b e f o r e the b e g i n n i n g of the dye d i s p e r s a l e x p e r i m e n t . The l e n g t h of the l i n e s f o r each d i r e c t i o n i n d i c a t e the amount of dye t h a t was d i s p e r s e d i n t h a t d i r e c t i o n and do not i n d i c a t e d i s t a n c e . I ^ t e r r i t o r y b ounda r y edge of m e a d o w 1 28 T a b l e X. D i r e c t i o n a l s t a t i s t i c R* f o r each p l a n t i n the dye d i s p e r s a l e x p e r i m e n t . p l a n t orange green red b l u e R* P 0.40 >0.5 0.41 >0.5 0.16 >0.9 0.23 >0.5 n 8 8 8 8 of R* than do the c e n t e r p l a n t s ( T able X ) . Thus t h i s r e s u l t i s s u g g e s t i v e , but f a r from c o n c l u s i v e . The t e r r i t o r i a l b o u n d a r i e s f l u c t u a t e d a g r e a t d e a l d u r i n g the c o u r s e of the dye d i s p e r s a l experiment (Table X I ) . In the 6 days from the f i r s t census t o the f i n a l one the a r e a c o n t a i n e d w i t h i n the b o u n d a r i e s i n c r e a s e d and then d e c r e a s e d t o l e s s than the o r i g i n a l v a l u e . The number of f l o w e r s c o n t a i n e d i n the t e r r i t o r y doubled and then d e c r e a s e d t o l e s s than the o r i g i n a l v a l u e . T h i s f o l l o w e d the p a t t e r n of f l o w e r s i n the meadow as a whole. 129 T a b l e X I . T e r r i t o r y and meadow s t a t i s t i c s f o r the dye d i s p e r s a l e x p e r i m e n t . d a t e 25 J u l y 28 J u l y 31 J u l y a r e a of f o c a l t e r r i t o r y 491 764 350 p e r i m e t e r of f o c a l t e r r i t o r y 101 1 24 81 # C a s t , i n t e r r i t o r y 675 1 295 590 # Aqu. i n t e r r i t o r y - 4 4 # C a s t . i n meadow 3324 4133 2346 # Aqu. i n meadow 41 36 5 # t e r r i t o r i e s i n meadow 6 5 4 C a s t . = C a s t i l l e j a m i n i a t a Aqu. = A q u i l e g i ' a formosa D i s c u s s i o n O p t i m a l O u t c r o s s i n g D i s t a n c e : V a r i a b i l i t y i n F i t n e s s The o p t i m a l o u t c r o s s i n g experiment was f a i r l y i n c o n c l u s i v e . T h i s p o p u l a t i o n of C a s t i l l e j a m i n i a t a may have an i n t e r m e d i a t e o p t i m a l o u t c r o s s i n g d i s t a n c e of between 1 and 10 m ( t e n t a t i v e l y around 2 m), but i f i t does, i t s 130 e x p r e s s i o n i s q u i t e v a r i a b l e . A l l a r d and Workman (1963) found sharp s e a s o n a l changes i n the a d a p t i v e v a l u e s of d i f f e r e n t genotypes i n e x p e r i m e n t a l l i m a bean p o p u l a t i o n s grown i n a c o n t r o l l e d environment. I t i s l i k e l y t h a t i n s e a s o n a l l y v a r i a b l e a l p i n e environments the s e l e c t i v e s i g n i f i c a n c e of g i v e n genotype c o m b i n a t i o n s would change from year t o year even more than i n such s t u d i e s under c o n t r o l l e d c o n d i t i o n s . Weather i n the two y e a r s of t h i s s t u d y d i f f e r e d g r e a t l y . In 1979 the snow me l t e d o f f of the meadows e a r l y , and the i c e was gone from G r i z z l y Lake b e f o r e 8 J u l y . The date we f i r s t o b s e r v e d t e r r i t o r i a l b e h a v i o u r by hummingbirds i n the meadow was 16 J u l y , and i t r a i n e d 18% of the days between 8 J u l y and 1 Sept. In 1980, the snow d i d not melt from the meadows t i l l q u i t e l a t e , and the i c e was not gone from G r i z z l y Lake t i l l the t h i r d week i n J u l y . The date of f i r s t o b s e r v e d t e r r i t o r i a l i t y was 31 J u l y and i t d i d not r a i n a t a l l between 9 J u l y and 28 Aug. In a l o n g l i v e d p e r e n n i a l p l a n t i t i s h a r d t o imagine t h a t the g e n e t i c s t r u c t u r e of the p o p u l a t i o n would respond t o such changes on a season t o season b a s i s ( u n l e s s many p l a n t s were k i l l e d by c a t a s t r o p h i c e v e n t s ; e.g. Gass and Lertzman 1980), but i t i s easy t o p i c t u r e d r a s t i c f l u c t u a t i o n s i n the a d a p t i v e v a l u e of g i v e n t r a i t s , and thus i n the v a l u e as a mate of the i n d i v i d u a l s t h a t c a r r y those t r a i t s . In such p l a n t s the p o p u l a t i o n s t r u c t u r e p r o b a b l y r e f l e c t s l o n g term t r e n d s or i n v a r i a n t s i n the environment. 131 However, measurements i n a g i v e n year may be s t r o n g l y dependent on s h o r t term f l u c t u a t i o n s t h a t have l i t t l e t o do w i t h the u l t i m a t e f i t n e s s of these i n d i v i d u a l s . In t h e i r s t udy of a l l e l e f r e q u e n c i e s i n e x p e r i m e n t a l l i m a bean p o p u l a t i o n s , A l l a r d and Workman (1963) c o u l d not p r e d i c t from any p a i r of g e n e r a t i o n s e i t h e r the mean s e l e c t i v e - v a l u e of any a l l e l e or i t s v a r i a n c e over 1 1 g e n e r a t i o n s . T h i s r e i n f o r c e s the importance of l o n g term s t u d i e s of p o p u l a t i o n dynamics and g e n e t i c s i n a known e c o l o g i c a l c o n t e x t . I t would be v a l u a b l e t o f o l l o w m i c r o h a b i t a t changes, changes i n o p t i m a l o u t c r o s s i n g d i s t a n c e , changes i n r e c r u i t m e n t , and changes i n g e n e t i c s t r u c t u r e over s e v e r a l seasons r e p r e s e n t i n g the range of s e a s o n a l v a r i a b i l i t y . Such a l o n g term s t u d y would be d i f f i c u l t and l a b o r i n t e n s i v e , but s h o u l d y i e l d v ery v a l u a b l e i n f o r m a t i o n . V a r i a b i l i t y i n o p t i m a l o u t c r o s s i n g r e s u l t s b o t h w i t h i n and between y e a r s c o u l d be an a r t i f a c t of hand p o l l i n a t i o n methods. I t seems l i k e l y t h a t t h i s i s a t l e a s t p a r t i a l l y t r u e f o r the w i t h i n y e a r , w i t h i n t r e a t m e n t v a r i a t i o n . I t i s l e s s l i k e l y to be the cause of the changes i n p a t t e r n between y e a r s , i . e . I expect q u a n t i t a t i v e , but not q u a l i t a t i v e e r r o r s . S i m i l a r between year v a r i a t i o n has been found i n o t h e r s t u d i e s ( P r i c e and Waser 1979; Waser and P r i c e 1 9 8 1 ; N. Waser and M. P r i c e p e r s . comm.). I n c r e a s e d sample s i z e s and improved methods of hand p o l l i n a t i o n w i l l i n c r e a s e the c o n f i d e n c e t h a t can be p l a c e d i n r e s u l t s such as t h e s e . 132 Another reason f o r the l a c k of a c l e a r p a t t e r n may be t h a t I o n l y measured seed p r o d u c t i o n , and have i g n o r e d p o s s i b l e e f f e c t s of o u t c r o s s i n g d i s t a n c e on seed q u a l i t y . T h i s i s c l e a r l y i m p o r t a n t and needs t o be s t u d i e d b e f o r e f i r m c o n c l u s i o n s about o p t i m a l o u t c r o s s i n g i n t h i s system can be reached. Dye D i s p e r s a l D i s t a n c e : I s P o l l e n D i s p e r s e d O p t i m a l l y ? How do a c h e i v e d p o l l e n d i s p e r s a l d i s t a n c e s compare w i t h a p o s s i b l e o p t i m a l d i s p e r s a l d i s t a n c e of about 2 m? The dye d i s p e r s a l experiment suggests a f a i r l y good c o r r e s p o n d e n c e . A h i g h e r p r o p o r t i o n of dye was t r a n s p o r t e d t o the o p t i m a l d i s t a n c e (1-2 m) i n t h i s system than has been found f o r D e l p h i n i u m or Ipomopis ( P r i c e and Waser 1979; Waser and P r i c e 1981). However, these comparisons a r e confounded by v a r i a t i o n i n p l a n t d e n s i t y . D i f f e r e n c e s i n the d e n s i t y of f l o w e r s w i l l be r e f l e c t e d i n dye d i s p e r s a l d i s t a n c e s ( L e v i n and K e r s t e r 1969 a,b; B e a t t i e 1976), and between p o p u l a t i o n comparisons must take t h i s i n t o a c c o u n t . We s h o u l d not n e c e s s a r i l y e xpect c l o s e c orrespondence between a c t u a l and optimum p o l l e n d i s p e r s a l d i s t a n c e s ( P r i c e and Waser 1979; Waser and P r i c e 1981). . I have d e f i n e d optima i n terms of the p l a n t ' s needs a l o n e , and r e a l i z e d p o l l e n d i s p e r s a l r e s u l t s from i n t e r a c t i o n s between p l a n t s and p o l l i n a t o r s . C o - e v o l u t i o n does not imply c o - o p e r a t i o n . I t i s not known ye t t o what e x t e n t p l a n t c h a r a c t e r s are a b l e t o m a n i p u l a t e p o l l i n a t o r b e h a v i o u r . W h i l e P r i c e and 133 Waser (1979) suggest t h a t p l a n t s c o u l d o n l y e x e r t minor e f f e c t s on p o l l i n a t i o n i n t h i s manner, Thomson and P l o w r i g h t (1980) found a s i g n i f i c a n t r e l a t i o n s h i p between p o l l e n d e p o s i t i o n and n e c t a r s t a n d i n g c r o p . T h i s s u g g e s t s t h a t p l a n t s may be a b l e t o e x e r t a g r e a t d e a l of i n f l u e n c e on p o l l i n a t i o n through t h e i r i n f l u e n c e on p o l l i n a t o r b e h a v i o u r . Dye D i s p e r ' s a l D i r e c t i o n : Do T e r r i t o r i a l B o u n d a r i e s R e s t r i c t  P o l l e n Movement? Though none of the f o u r p l a n t s showed a s t a t i s t i c a l l y s i g n i f i c a n t d e v i a t i o n from a u n i f o r m d i r e c t i o n a l d i s t r i b u t i o n of p o l l e n , the t e r r i t o r y edge p l a n t s showed more d i r e c t i o n a l movement of p o l l e n than the t e r r i t o r y c e n t e r p l a n t s . T h i s d i f f e r e n c e may be r e a l , and o n l y a l a r g e r sample or b e t t e r r e s o l u t i o n of t e r r i t o r i a l b o u n d a r i e s and b e t t e r c h o i c e of p l a n t s i s needed f o r s t a t i s t i c a l s i g n i f i c a n c e . A l t e r n a t i v e l y , t e r r i t o r i a l b o u n d a r i e s may have have l i t t l e r e s t r i c t i v e i n f l u e n c e on the p o l l e n d i s p e r s a l of most p l a n t s even on the s h o r t term. I f t e r r i t o r i a l b o u n d a r i e s a r e o n l y v a g u e l y d e f i n e d or s h i f t on a s h o r t time s c a l e ( i . e . such as the p e r i o d of t h i s s t udy) then they may have l i t t l e meaning f o r p o l l e n d i s p e r s a l . The major changes i n both the a r e a o c c u p i e d by the f o c a l t e r r i t o r y , and the number of f l o w e r s i t c o n t a i n e d combined w i t h the l a c k of s i g n i f i c a n t d i r e c t i o n a l i t y i n the dye d i s p e r s a l from t e r r i t o r y edge p l a n t s l e n d s s u pport t o t h i s h y p o t h e s i s . A p l a n t t h a t one day i s on the edge of a 134 t e r r i t o r y and might have d i r e c t i o n a l l y skewed d i s p e r s a l of i t s p o l l e n , c o u l d be s e v e r a l meters i n s i d e the t e r r i t o r y t h e f o l l o w i n g day. A p l a n t t h a t i s o u t s i d e the t e r r i t o r y on one day and t h e r e f o r e p o t e n t i a l l y e x c l u d e d from the p l a n t s i n t h a t t e r r i t o r y as a mate, may be i n s i d e the t e r r i t o r y the f o l l o w i n g day (see P e r k i n s 1977). Thus t h i s system c o n t r a s t s s t r o n g l y w i t h the one s t u d i e d by L i n h a r t (1973) which i s a p p a r e n t l y more t e m p o r a l l y s t a b l e t o know whether o t h e r systems w i l l be more s i m i l a r t o one or the o t h e r of t h e s e examples w i l l r e q u i r e a knowledge of the dynamics of t e r r i t o r i a l i t y i n those p a r t i c u l a r systems. Do p l a n t s at l o o s e l y d e f i n e d b o u n d a r i e s r e c e i v e enhanced p o l l e n d i s p e r s a l by v i s i t s from both a d j a c e n t r e s i d e n t hummingbirds? The o p p o s i t e may be happening: p l a n t s a t d i s p u t e d b o u n d a r i e s p r o b a b l y r e c e i v e fewer v i s i t s than o t h e r p l a n t s . The green dye p l a n t , i n the most dense a r e a s t u d i e d , had p o l l e n d e p o s i t e d on fewer f l o w e r s than e i t h e r of the c e n t e r t e r r i t o r y p l a n t s , and of the f l o w e r s w i t h i n 5 m, the p e r c e n t a g e w i t h dye was l e s s than h a l f of the v a l u e f o r the two c e n t e r t e r r i t o r y p l a n t s . The t e r r i t o r y boundary next t o the green dye p l a n t changed the most of any boundary i n the s t u d y ; from 1 m away from the green dye p l a n t on the day b e f o r e dye was i n t r o d u c e d t o 5 m away 2 days f o l l o w i n g , t o 4 m away on the day b e f o r e the f i n a l c e n s u s . I f p l a n t s i n such d i s p u t e d a r e a s a r e v i s i t e d l e s s f r e q u e n t l y , but by b oth t e r r i t o r i a l r e s i d e n t s , then a n o n - d i r e c t i o n a l p a t t e r n of dye d i s p e r s a l such as I o b s e r v e d 135 would r e s u l t . I n d i s t i n c t t e r r i t o r i a l b o u n d a r i e s a r e l i k e l y t o occur o n l y i n a r e l a t i v e l y homogeneous meadow such as meadow 2. In a much more heterogeneous meadow (e.g. much of meadow 3) where t e r r i t o r i e s may be s e p a r a t e d by a r e a s w i t h o u t f l o w e r s , t e r r i t o r i a l b o u n d a r i e s w i l l be much more d i s t i n c t and may a c t more l i k e r e f l e c t i n g b o u n d a r i e s f o r p o l l e n d i s p e r s a l . T h i s p r e d i c t i o n of a low v i s i t a t i o n f r e q u e n c y t o p l a n t s on d i s p u t e d t e r r i t o r i a l b o u n d a r i e s s h o u l d be e a s i l y t e s t a b l e . C o n c l u s i o n s C a s t i l l e j a m i n i a t a may have an i n t e r m e d i a t e o p t i m a l o u t c r o s s i n g d i s t a n c e on the o r d e r of 2 m. But i f so, i t i s v a r i a b l y e x p r e s s e d from year t o y e a r . T h i s v a r i a t i o n may be r e l a t e d t o c l i m a t i c and m i c r o h a b i t a t changes. Dye d i s p e r s a l d i s t a n c e s show much v a r i a b i l i t y between p l a n t s , but i n g e n e r a l , a p p roximate o p t i m a l o u t c r o s s i n g d i s t a n c e s f a i r l y w e l l . A h i g h e r p e r c e n t a g e of dye was t r a n s p o r t e d t o the p u r p o r t e d o p t i m a l d i s t a n c e than i n o t h e r s t u d i e s . I suggest t h a t t h i s might be due t o C a s t i l i e j a  m i n i a t a s p e c i a l i z i n g on hummingbird p o l l i n a t o r s w h i l e D e l p h i n i u m n e l s o n i i s p o l l i n a t e d e x t e n s i v e l y by both hummingbirds and bumblebees. Dye d i s p e r s a l d i r e c t i o n s do not d e v i a t e s i g n i f i c a n t l y from a u n i f o r m c i r c u l a r d i s t r i b u t i o n f o r both t e r r i t o r y c e n t e r and t e r r i t o r y edge p l a n t s . T h i s i s p r o b a b l y r e l a t e d t o changes i n t e r r i t o r y b o u n d a r i e s over the c o u r s e of the 136 s t u d y . T h i s s u p p o r t s P e r k i n s ' (1977) c o n c l u s i o n t h a t t e r r i t o r y b o u n d a r i e s i n t h i s system do not r e s t r i c t gene f l o w . Both the o p t i m a l o u t c r o s s i n g experiment and the dye d i s p e r s a l experiment s u f f e r e d from s m a l l sample s i z e s . The c o n c l u s i o n s a r e t e n t a t i v e a t b e s t . 137 GENERAL DISCUSSION The l a b o r a t o r y s t u d i e s showed t h a t p o l l e n c a r r y o v e r i s c o m p l e x l y p a t t e r n e d , and suggested t h a t these p a t t e r n s are r e l a t e d t o m o r p h o l o g i c a l c h a r a c t e r s of f l o w e r s . V a r i a t i o n i n f l o r a l morphology was i m p l i c a t e d as a key f a c t o r i n f l u e n c i n g c a r r y o v e r because of i t s i n f l u e n c e on t h e number of " b l a n k " f l o w e r s i n a sequence, and on l a y e r i n g of p o l l e n i n the p o o l on the p o l l i n a t o r . M o d e l l i n g e x e r c i s e s showed t h a t such p a t t e r n s can be produced by d i f f e r e n t s e t s of a s s u m p t i o n s . In e x p l o r i n g one s e t of assumptions i n d e t a i l (model 4 ) , I found t h a t both p o l l e n p o o l s t r u c t u r e and p o l l e n c a r r y o v e r were s e n s i t i v e t o the amount of v a r i a t i o n i n f l o w e r morphology. The two f i e l d e x p e r i m e n t s gave i n t e r e s t i n g r e s u l t s but are not w e l l l i n k e d t o the l a b o r a t o r y and m o d e l l i n g s t u d i e s . C a s t i l l e j a m i n i a t a p r o b a b l y has a w i t h i n p o p u l a t i o n o p t i m a l o u t c r o s s i n g d i s t a n c e t h a t may or may not be e x p r e s s e d i n any g i v e n y e a r . A s i g n i f i c a n t p r o p o r t i o n of the p o l l e n p r o b a b l y r eaches t h i s d i s t a n c e , and hummingbird t e r r i t o r i a l i t y p r o b a b l y does not r e s t r i c t p o l l e n d i s p e r s a l s i g n i f i c a n t l y . The m i s s i n g l i n k between the l a b o r a t o r y and m o d e l l i n g s t u d i e s and the f i e l d s t u d i e s i n v o l v e s how p r o c e s s e s a t i n d i v i d u a l f l o w e r s are d i s t r i b u t e d over space by the i n t e r a c t i o n between hummingbird movement r u l e s and the s p a t i a l d i s t r i b u t i o n of energy ( n e c t a r ) . A s t a t i s t i c a l r e l a t i o n between p l a n t d i s p e r s i o n and p o l l i n a t o r movement, and gene f l o w has been known s i n c e 1969 ( L e v i n and K e r s t e r 138 1969 a , b ) , but a c a u s a l r e l a t i o n i s s t i l l vague, d e s p i t e the r e c e n t p r o f u s i o n of r e s e a r c h on p o l l i n a t o r b e h a v i o u r . I s i t v a l u a b l e t o expend e f f o r t t o make t h i s mechanismal c o n n e c t i o n between the l e v e l of i n d i v i d u a l f l o w e r s and p o p u l a t i o n s of f l o w e r s ? For some purposes one can a d e q u a t e l y d e s c r i b e p o l l e n d i s p e r s a l , w i t h o u t knowing i t s u n d e r l y i n g mechanisms. Given s t a t i s t i c a l e x p e c t a t i o n s of c a r r y o v e r ( i n numbers of f l o w e r s ) , f l o w e r s per p l a n t , the d i s t r i b u t i o n of p l a n t s i n space, and p o l l i n a t o r movement, we can make a p r e d i c t i o n f o r mean p o l l e n d i s p e r s a l d i s t a n c e s . For i n s t a n c e , i f one's g o a l i s t o e s t i m a t e p l a n t p o p u l a t i o n neighborhood s i z e s (e.g. L e v i n and K e r s t e r 1971; Augspurger 1980), then t h i s i n f o r m a t i o n i s p r o b a b l y adequate - u n l e s s r a r e e v e nts p l a y an impo r t a n t r o l e i n the system under s t u d y . However, i f i t i s s p e c i f i c a l l y the dynamics of a p o l l i n a t o r - p l a n t r e l a t i o n s h i p t h a t one i s i n t e r e s t e d i n , , the s t a t i s t i c a l d e s c r i p t i o n i s i n a d e q u a t e . Dynamics r e f e r t o changes i n time i n which the c h a r a c t e r s of the system's s t a t e a t one p o i n t i n time feedback t o i n f l u e n c e i t s f u t u r e s t a t e s . The study of dynamics n e c e s s a r i l y i n v o l v e s an u n d e r s t a n d i n g of the feedback mechanisms - not j u s t a d e s c r i p t i o n of t h e i r r e s u l t s . J u s t as knowing the numbers of c l o u d s i n the sky does not l e a d t o a p r e d i c t i v e t h e o r y of weather ( C l a r k and H o l l i n g 1979), knowing the l o c a t i o n s and i d e n t i t i e s of p o l l e n g r a i n s i s inadequate f o r p r e d i c t i n g e i t h e r how they got t h e r e or what k i n d s of f i t n e s s consequences they w i l l 139 have i n t h o s e l o c a t i o n s . Whether or not d e t a i l e d p r o c e s s e s s t u d i e s a r e w o r t h w h i l e depends on ones u l t i m a t e r e s e a r c h g o a l s . I f i t i s i m p o r t a n t t o f i n d the c a u s a l r e l a t i o n s h i p s i n p o l l e n d i s p e r s a l , what a r e the b e s t ways t o go about i t ? The prime f o c u s s h o u l d be p r o c e s s o r i e n t e d e x p e r i m e n t s -w i t h a t l e a s t as much emphasis on f i e l d e x p e r i m e n t s as i n the l a b o r a t o r y . Models a r e u s e f u l f o r e x p l o r i n g i d e a s g e n e r a t e d by e x p e r i m e n t s (as i n t h i s t h e s i s ) , but the e m p i r i c a l base i s too weak a t t h i s p o i n t t o s u pport l a r g e , p r e d i c t i v e , dynamic models (e.g. G i l b e r t et a_l. 1975; C l a r k and H o l l i n g 1979). S i m i l a r l y we don't know enough ye t to b u i l d t h e o r y w i t h a sound e m p i r i c a l base. What ex p e r i m e n t s s h o u l d be done next? The f o c u s i s on c h a r a c t e r s of the p l a n t s t h a t i n f l u e n c e p o l l i n a t o r b e h a v i o u r t o produce p a t t e r n s of p o l l i n a t i o n , and on the f i t n e s s consequences of these p a t t e r n s f o r the p l a n t s . 1. L a b o r a t o r y and F i e l d E x p e r i m e n t s on P o l l e n C a r r y o v e r a) How does p o l l e n c a r r y o v e r v a r y w i t h the amount of f l o r a l v a r i a b i l i t y ? The r o l e of f l o r a l v a r i a b i l i t y was a key i s s u e i n both the l a b o r a t o r y and m o d e l l i n g s t u d i e s . An experiment s h o u l d be performed t h a t s t u d i e s how c h a n g i n g the amount of v a r i a b i l i t y i n a p o p u l a t i o n of f l o w e r s i n f l u e n c e s p o l l e n c a r r y o v e r . T h i s p a r a l l e l s the s e n s i t i v i t y 140 a n a l y s i s of model 4 t o f l o r a l v a r i a b i l i t y , t h i s experiment r e q u i r e s a l a b system where both c a r r y o v e r and f l o r a l v a r i a b i l i t y can be measured e a s i l y . I attempted t h i s l a s t summer but c o u l d not complete i t due t o l o g i s t i c a l problems. T h i s experiment i s i m p o r t a n t b o t h as the l o g i c a l f o l l o w up of the p r e v i o u s l a b o r a t o r y e x p e r i m e n t s , and as a t e s t of the p r e d i c t i o n s of model 4. b) How does p o l l e n c a r r y o v e r v a r y w i t h the amount of n e c t a r per f l o w e r ? N e c t a r p r o d u c t i o n r a t e (and the c o n c e n t r a t i o n of sugar i n the n e c t a r ) i s one of the most obvious ways t h a t p l a n t s might i n f l u e n c e p o l l i n a t o r b e h a v i o u r ( H e i n r i c h and Raven 1972), and i s a t l e a s t p a r t i a l l y h e r i t a b l e i n some s p e c i e s ( S h u e l 1952; Walker et a l . 1974). The amount of time t h a t a p o l l i n a t o r spends at a f l o w e r i s s e n s i t i v e t o the amount of n e c t a r i n the f l o w e r , and Thomson and P l o w r i g h t (1980) found t h a t f l o w e r s w i t h more n e c t a r r e c e i v e d more p o l l e n . T h i s experiment needs t o be r e p e a t e d i n o t h e r systems and i n more d e t a i l . N e c t a r s t a n d i n g c r o p s and n e c t a r p r o d u c t i o n r a t e s a r e t y p i c a l l y h i g h l y v a r i a b l e (Cruden 1976; Corbet 1978; F e i n s i n g e r 1978; P l e a s a n t s and Zimmerman 1979; Montgomerie et a l . i n p r e p ) , and p o l l i n a t o r s appear t o be s e n s i t i v e t o the amount of v a r i a t i o n 141 i n n e c t a r i n t h e i r food s o u r c e s (Caraco et a l . 1980). What i s the i n f l u e n c e of t h i s v a r i a b i l i t y i n n e c t a r on p o l l e n c a r r y o v e r ? c) How do these l a b o r a t o r y s t u d i e s r e l a t e t o the r e a l w orld? The l a b o r a t o r y e x p e r i m e n t s s h o u l d be done i n p a r a l l e l w i t h f i e l d e x p e r i m e n t s on the same q u e s t i o n s . T h i s w i l l be d i f f i c u l t and l a b o r i n t e n s i v e , but w o r t h w h i l e . For i n s t a n c e n e c t a r per f l o w e r , p l a n t d e n s i t y , and f l o w e r s per p l a n t c o u l d be e a s i l y m a n i p u l a t e d . The e f f e c t of the s e v a r i a b l e s on p o l l e n c a r r y o v e r and d i s p e r s a l d i s t a n c e i s b a s e l i n e i n f o r m a t i o n f o r u n d e r s t a n d i n g the c o n n e c t i o n between p l a n t p h e n o t y p i c c h a r a c t e r s and p l a n t f i t n e s s . 2. L a b o r a t o r y and F i e l d S t u d i e s of P o l l e n P o o l S t r u c t u r e A l l the above e x p e r i m e n t s f o c u s on p o l l e n t r a n s f e r from i n d i v i d u a l s o u r c e s . I t i s i m p o r t a n t t o study the c o n t e x t i n which p o l l e n t r a n s f e r o c c u r s ; i . e . the p o l l e n p o o l . How many f l o w e r s have p o l l e n r e p r e s e n t e d i n the p o l l e n p o o l s t h a t a r e observe d on b i r d s i n the f i e l d ? Does a p o l l e n p o o l r e a c h a stea d y s t a t e of i n p u t s and o u t p u t s a f t e r some number of f l o w e r s ? I s c a r r y o v e r d i f f e r e n t from a p o l l e n p o o l i n the b u i l d u p 1 42 p r o c e s s than from a p o o l a t s t e a d y s t a t e ? I performed p i l o t s t u d i e s on t h e s e q u e s t i o n s l a s t summer. These q u e s t i o n s c o u l d be answered by a c o m b i n a t i o n of l a b o r a t o r y s t u d i e s where p o l l e n p o o l s t r u c t u r e i s measured a f t e r the p o l l i n a t o r has f e d from v a r i o u s numbers of f l o w e r s , and measures of p o l l e n p o o l s t r u c t u r e from w i l d b i r d s . 3. F i e l d E x p eriments on P l a n t R e p r o d u c t i v e Success The purpose of t h e s e e x p e r i m e n t s i s t o c o r r e l a t e the r e s u l t s of the f i e l d e x p e r i m e n t s on p o l l e n c a r r y o v e r and d i s p e r s a l d i s t a n c e w i t h consequences i n terms of p l a n t f i t n e s s . The same m a n i p u l a t i o n s of n e c t a r s t a n d i n g c r o p , p l a n t d e n s i t y , and f l o w e r s per p l a n t t h a t I suggested f o r s t u d y i n g p o l l e n c a r r y o v e r c o u l d be c o n t i n u e d t h r o u g h the season and the subsequent seed p r o d u c t i o n measured. The c o n n e c t i o n between p r o x i m a t e " b e h a v i o u r a l " p a t t e r n s and r e p r o d u c t i v e o u t p u t i s weak i n most s t u d i e s of f o r a g i n g or r e p r o d u c t i v e t a c t i c s . These e x p e r i m e n t s p r o v i d e an o p p o r t u n i t y t o make a s t r o n g c o n n e c t i o n . 4. L a b o r a t o r y E x p e r i m e n t s On P o l l i n a t o r B e h a v i o u r The key q u e s t i o n s here are how the p o l l i n a t o r s respond t o d i f f e r e n t d i s t r i b u t i o n s of energy i n 143 space - i n p a r t i c u l a r how they d e a l w i t h s p a t i a l and t e m p o r a l v a r i a b i l i t y . D e t a i l e d l a b o r a t o r y s t u d i e s a r e needed t o u n d e r s t a n d how the p o l l i n a t o r s end up p e r f o r m i n g i n a c e r t a i n way. I t would a l s o be v a l u a b l e t o monitor p o l l i n a t o r b e h a v i o u r i n c o n j u n c t i o n w i t h the f i e l d m a n i p u l a t i o n s d i s c u s s e d above. Thus I am s u g g e s t i n g an i n t e g r a t e d s e r i e s of s t u d i e s where, w i t h the same s e t of m a n i p u l a t i o n s of f l o r a l c h a r a c t e r s , one would l o o k a t p o l l i n a t o r b e h a v i o u r , p o l l e n c a r r y o v e r and d i s p e r s a l d i s t a n c e , and p l a n t r e p r o d u c t i v e s u c c e s s . 5. H e r i t a b i l i t y Any e v o l u t i o n a r y i n t e r p r e t a t i o n of the r e s u l t s of these e x p e r i m e n t s would r e q u i r e e i t h e r knowledge or assumption of the h e r i t a b i l i t i e s of the p l a n t c h a r a c t e r s under c o n s i d e r a t i o n . C u r r e n t knowledge i s r u d i m e n t a r y (e.g. n e c t a r p r o d u c t i o n r a t e i s t o some degree h e r i t a b l e ; S h u e l 1952; Walker e_t a l . 1974). T h i s q u e s t i o n t a k e s on major s i g n i f i c a n c e i n the l i g h t of the b u r g e o n i n g l i t e r a t u r e on how p l a n t c h a r a c t e r s i n f l u e n c e p o l l i n a t o r b e h a v i o u r . P o l l i n a t o r - p l a n t systems a r e dynamic, i n both a p r o x i m a t e and an e v o l u t i o n a r y s ense. To u n d e r s t a n d them r e q u i r e s a r e s e a r c h program t h a t i n t e g r a t e s c h a r a c t e r s of both the p l a n t s and the p o l l i n a t o r s , and the p r o c e s s e s 144 t h r o u g h which they i n t e r a c t . I t h i n k t h i s i n t e g r a t i o n i s p o s s i b l e , but o n l y t h rough much work w i t h r e a l systems, and a r e - o r i e n t a t i o n of r e s e a r c h away from t e s t i n g o p t i m a l i t y t h e o r y towards b u i l d i n g up some more e m p i r i c a l l y based t h e o r y . 145 REFERENCES Adams, R.P. 1977. 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