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Oblique swimming in characoid fishes with special reference to the genus Nannostomus Gunther 1872 Chondoma, Emmanuel C. 1979

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OBLIQUE SWIMMING IN CHABACOID FISHES WITH SPECIAL BEFEBENCE TO THE GENUS NANNOSTOMUS GUNTHEB 1872 by EMMANUEL C. CHONDOMA B,Sc. (Hons.) , U n i v e r s i t y o f Dar-es-Salaam, 197<i k THESIS SUBMITTED IN PASTIAL FULFILLMENT OF THE BEQUIBEMENTS FOB THE DEGREE OF MASTEB OF SCIENCE | j i n THE FACULTY OF GRADUATE STUDIES (Department of Zoology) He a c c e p t t h i s t h e s i s as conforming to the r e q u i r e d s t a n d a r d THE UNIVEBSITY OF BRITISH COLUMBIA May, 1979 © Emmanuel Chumira Chondoma, 1979 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department nf Z ^ D LOcS Y The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date ABSTRACT The hydrodynamics and mechanics of obliquely swimming characoid species Chilodus punetatus, Nannostomus ejues, Nannostomus unifasciatus, Thayeria. boehlkei and Thayeria obliqua are investigated. In Chilodus punctatug, Nannostomus eques and Nannostomus unifasciatus the: position of the centre of mass r e l a t i v e to the centre of buoyancy i s the reverse of what would be expected from t h e i r pitch. Tha:centre of mass i s infront of the centre of buoyancy in the two Nannostomus species which swim with a positive pitch and vice versa in Chilodus £ U n e t a t u s which swims with negative pitch. The r e l a t i v e positions of these two centres are i n such a way that they help to brinq t h e . f i s h horizontal durinq fa s t swimminq. Pitch i n these species i s maintained by the action of the pectoral and caudal f i n s . In the two Thayeria species the centre of mass i s behind the centre of buoyancy and t h e i r separation i s responsible f o r the posit i v e pitch. The f i n s are used to correct for t h i s pitch to the desirable l e v e l . The enlarged lower lobe of the: caudal f i n i n Nannostomus species has an epibatic e f f e c t and does not contribute.to the forces responsible for the pitch i n hovering as previously proposed. Relative vertebrae size i n Nannostomus eg_u.es and Nannostomus unifasciatus when compared to Nannostomus beefordi and Nannostomus t r i f a s c i a t u s which swim horizontally show adaptations towards a strategy of rapid s t a r t from rest. i i i TABLE OF CONTENTS Abstrac t i i Table of Contents i i i L i s t o f Ta b l e s • v L i s t o f F i g u r e s v i Acknowledgement v i i i INTRODUCTION 1 1..HYDROMECHANICAL ANALYSIS 9 General Methods and M a t e r i a l s 9 A. Angle of o r i e n t a t i o n 12 Method ..... 12 R e s u l t s ....... ,14 B. E f f e c t s o f f i n removal 20 Method , 20 R e s u l t s : P e c t o r a l f i n removal ...21 Resul t s : Caudal f i n removal .22 C. Swimbladder a n a l y s i s 26 X-ray method 27 Transmitted l i g h t method 28 D i s s e c t i o n 28 Re s u l t s -••>• 28 D. Density d e t e r m i n a t i o n ................................ 29 E. Centres of Buoyancy and Mass 34 I. Centre of buoyancy 34 I I . Centre of mass 35 R e s u l t s 36 i v F. E q u i l i b r i u m O r i e n t a t i o n 37 Method .37 EesuIts 37 Swimming Modes - 4 0 S p a t i a l d i s t r i b u t i o n and Feeding h a b i t s 53 E f f e c t s of l i g h t ........................................ 56 2. MORPHOLOGICAL AND ANTOMICAL ANALYSIS ................... 58 T h e o r e t i c a l a n a l y s i s .59 M a t e r i a l s and Methods ................................... 64 A x i a l System 65 V e r t e b r a l number and s i z e 66 Caudal F i n 74 Terminology 75 Nannostomus 77 T h a y e r i a p b l i q u a 80 C h i l o d u s guntatus and Leporinus maculatus 81 Abramistes microcephalus 82 GENERAL DISCUSSION 88 CONCLUSIONS . . . . ........... ........ 105 LITERATURE CITED 108 V LIST OF TABLES TABLE 1. Angles of o r i e n t a t i o n by s i z e 18 2. E f f e c t o f ca u d a l f i n removal on o r i e n t a t i o n .......... 25 3. Caudal f i n removal and p e c t o r a l f i n frequency 25 4. Vertebrae Number and Siz e In Nannostomus spp. 68 v i LIST OF FIGURES FIGURE 1. F r o n t view of Photographing Tank .................... 16 2.. Sign n o t a t i o n f o r angles of o r i e n t a t i o n .............17 3. V a r i a t i o n of o r i e n t a t i o n with s i z e .................. 19 4. Swimbladder i n Nanngstumus s p e c i e s 31 5. Swimbladder i n C. punctatus and L. maculatus ........ 32 6. D e n s i t i e s and 5% Confidence I n t e r v a l s ., 33 7. E q u i l i b r i u m O r i e n t a t i o n 39 8. Swimminq Movements i n C h i l o d u s punctatus ............ 51 9.. Caudal F i n Movements i n C. punctatus ................,52 10. Vertebra Size-Standard Lenqth Reqression of Nannostomus u n i f a s c i a t u s 70 11. Vertebra Size-Standard Lenqth Reqression of Nannostomus e<_ues ............... , 71 12. Vertebra Size-Standard Lenqth Reqression of Nannostomus b e c k f p r d i ,...,,......72 13. Vertebra Size-Standard Lenqth Regression of Nannostomus t r i f a s c i a t u s ,. .,,....,,,,.73 14. Caudal s k e l e t o n of Nannostomus spp. 83 15. Caudal f i n of Nannostomus egues ..................... 84 16. Caudal s k e l e t o n of T h a y e r i a o b l i q u a 85 17.. Caudal s k e l e t o n o f C. punctatus and L. maculatus .... 86 18. Caudal s k e l e t o n of Abramistes microcephalus ..,87 Rear view of Caudal f i n i n Transverse motion v i i i Acknowledgement I thank Prof. Norman J . Wilimovsky f o r i n t r o d u c i n g me to the problem of swimming i n f i s h e s and f o r s u p e r v i s i n g me.in t h i s study. I a l s o thank my t h e s i s committee. Prof. , N.R. L i l e y , P r o f . J.D. MacPhail and P r o f . W.S. Wel l i n g t o n f o r t h e i r v a l u a b l e a s s i s t a n c e . d u r i n g the.study and p r e p a r a t i o n of t h i s t h e s i s . I would l i k e to thank Mr..Ronald P r e c i o u s of the Department of Theatre, U B C , f o r a l l o w i n g me to use cinematographic equipment under h i s care and together with Ms. Koula Rapanos f o r t h e i r t e c h n i c a l a s s i s t a n c e i n f i l m i n g and use of the cinematographic equipment i n the l a b o r a t o r y . I would a l s o l i k e to thank Mrs. May Wong, owner of the Main Aquariums, Vancouver f o r har e f f o r t s t o o b t a i n some w i l d c h a r a c o i d specimens from Peru used i n t h i s study. L a s t l y I would l i k e to thank my w i f 8 . M a t s e l i s o f o r her encouragement throughout t h i s study and her help i n t y p i n g the t h e s i s . . T h i s work was p a r t l y supported by a N a t i o n a l Research C o u n c i l Grant t o Dr. Norman J. Wilimovsky. 1 INTRODUCTION In the e v o l u t i o n of swimming modes i n f i s h n a t u r a l s e l e c t i o n f a v o u r s mechanisms t h a t i n c r e a s e e f f i c i e n c y of swimming (Alexander, 1967). Increased swimming e f f i c i e n c y may e n t a i l more e f f i c i e n t use of energy, thus making more energy a v a i l a b l e f o r growth and r e p r o d u c t i o n . In energy l i m i t i n g s i t u a t i o n s t h i s may be very important. Increased swimming e f f i c i e n c y a l s o i n v o l v e i n c r e a s e d a c c e l e r a t i o n (high l u n g i n g a b i l i t y ) and ma n e u v e r a b i l i t y . Both t r a i t s are b e n e f i c i a l to predators and prey. For a predator t h i s t r a n s l a t e s i n t o an i n c r e a s e i n the a b i l i t y to catch prey and f o r a prey an i n c r e a s e i n the chances of outperforming a predator. F i s h design and behaviour have besn shaped through e v o l u t i o n t o optimize combinations of these mechanisms depending upon the f i s h ' s e c o l o g i c a l requirements. I t would be best i f a f i s h shape c o u l d optimize the s t r a t e g i e s f o r a c c e l e r a t i o n , m a n e u v e r a b i l i t y and high c r u i s i n g speeds. However, t h i s i s not p o s s i b l e because some of these s t r a t e g i e s r e q u i r e body designs which are m o r p h o l o g i c a l l y mutually e x c l u s i v e . For example to have a high lunging a b i l i t y a f i s h r e q u i r e s a f a i r l y l a r g e t a i l f i n area. T h i s enlargement of the caudal f i n area gives the necessary t h r u s t r e q u i r e d f o r quick a c c e l e r a t i o n (Weihs, 1973). Such a t a i l c o n f i g u r a t i o n would be u n s u i t a b l e f o r continuous high swimming speeds because of i t s e f f e c t s i n i n c r e a s i n g drag. Under such c o n d i t i o n s a f i n with s m a l l area and l a r g e aspect r a t i o (lunate t a i l ) as seen i n tunas and tuna l i k e . f i s h e s proves to be o p t i m a l ( L i g h t h i l l , 1969, 1970; Chopra, 1974, 1976). To understand the d i f f e r e n t f i s h shapes and t h e i r swimming 2 behaviour i t i s necessary t o i n v e s t i g a t e the hydrodynamic f e a t u r e s which govern t h e i r p r o p u l s i o n as well as t h e i r modes o f l i f e . Some progress has been made r e g a r d i n g hydrodynamic t h e o r i e s of f i s h p r o p u l s i o n and a n a l y s i s of t h e i r e f f i c i e n c i e s . L i g h t h i l l (1960, 1969, 1970) and Wu (1971b, c, d) analysed the hydrodynamics of constant v e l o c i t y swimming by s l e n d e r f i s h . Chopra (1974, 1976) f u r t h e r developed L i g h t h i l l ' s (1970) a n a l y s i s of lunate f i n p r o p u l s i o n . L i g h t h i l l (1971) extended h i s s l e n d e r body theory i n a g e n e r a l form to i n c l u d e l a r g e amplitude displacements at r i g h t angles to the d i r e c t i o n of motion. , T h i s theory was f u r t h e r expanded by Weihs (1972, 1973) to i n c l u d e the e f f e c t s of f i n s on t u r n i n g motions and a n a l y s i s of unsteady motions during r a p i d s t a r t . A l l the above s t u d i e s c oncentrated on f i s h which use the caudal f i n as a major source.of p r o p u l s i v e f o r c e . Breder (1926), H a r r i s (1936, 1938, 1953), Breder and Edgerton (1942), Webb (1973) and Blake (1976, 1977, 1978) give d e t a i l e d k i n e m a t i c a n a l y s i s of the use of other f i n s i n . f i s h p r o p u l s i o n . These s t u d i e s are u s e f u l to comparative.morphologists and e c o l o g i s t s i n t h a t they c o n t r i b u t e to the understanding of how d i f f e r e n t f i s h shapes are r e l a t e d to the d i f f e r e n c e s i n swimming c a p a b i l i t i e s r e q u i r e d by d i f f e r e n t modes of l i f e and a l s o i n understanding optimum f i s h shapes f o r d i f f e r e n t swimminq s t r a t e g i e s as i n r a p i d s t a r t from r e s t , t u r n i n g and c o n s t a n t high c r u i s i n g speeds. The present study i s a hydromechanical a n a l y s i s of an 3 i n t e r e s t i n g group of f i s h which swim with t h e i r l o n g a x i s at an angle t o the h o r i z o n t a l . U s u a l l y a l l f i s h at one.time.or another swim o b l i q u e l y or even with ths long a x i s v e r t i c a l e s p e c i a l l y when a v o i d i n g o b s t a c l e s , f e e d i n g , or as i n some s p e c i e s d u r i n g b e h a v i o u r a l and spawning r i t u a l s . These d e v i a t i o n s from the h o r i z o n t a l are temporary r a t h e r than a us u a l mode of swimming or hovering. However, t h e r e are some groups of f i s h i n which one or more s p e c i e s normally swim or hover o b l i q u e l y t o the h o r i z o n t a l , and swim h o r i z o n t a l l y only when d i s t u r b e d or escaping from enemies ( P f e i f f e r , 1968). T h i s swimming mode i s common among the freshwater c h a r a c o i d f i s h e s to which t h i s study i s c o n f i n e d . These f i s h when hovering, n i b b l i n g or swimming s l o w l y o r i e n t themselves at an angle to the h o r i z o n t a l a x i s . The angle v a r i e s from a smal l i n c l i n a t i o n i n some s p e c i e s to almost v e r t i c a l i n o t h e r s . Some s p e c i e s swim with t h e i r heads p o i n t i n g up ( p o s i t i v e p i t c h ) ; f o r example tube mouthed p e n c i l f i s h , Nannostomus egues Steindachner, 1876 (family L e b i a s i n i d a e ) and others swim with t h e i r heads p o i n t i n g down (negative p i t c h ) ; f o r example s p o t t e d headstander, C h i l o d u s punctatus Muller and T r o s c h e l , 1845 (family C h i l o d o n t i d a e ) and s h r i m p f i s h , A e o l i s c u s s t r i g a t u s (Gunther, 1860), (family C e n t r i s c i d a e ) . The purpose of t h i s study i s to analyse the. hydromechanics (kinematics and dynamics) i n v o l v e d i n t h i s behaviour of o b l i q u e swimminq, and the s t r u c t u r a l and morphological a d a p t a t i o n s shown by these o b l i q u e l y swimming s p e c i e s when compared to t h e i r c l o s e l y r e l a t e d s p e c i e s . The s t r u c t u r a l - m o r p h o l o g i c a l a d a p t a t i o n s are analysed i n terms of the hydromechanical t h e o r i e s of swimming and the behavior of these f i s h observed i n 4 the l a b o r a t o r y with notes on t h e i r n a t u r a l behavior. In t h i s study I have i n v e s t i g a t e d two components which may play a r o l e i n producing the p i t c h r e s p o n s i b l e f o r the o b l i q u e swimming. These are the nature and p o s i t i o n of the swimbladder and other buoyant m a t e r i a l s i n r e l a t i o n to the centre of mass and the kinematics of f i n movements. Harder (1976) doubted whether f i s h c o u l d use p o s i t i o n i n g o f the swimbladder i n r e l a t i o n to the c e n t r e of mass to c r e a t e s u f f i c i e n t p i t c h i n g moment to d e v i a t e the body's long a x i s from the h o r i z o n t a l a x i s . There are only suggestions t h a t the p o s i t i o n of centre of buoyancy i n r e l a t i o n t o c e n t r e of mass may cause p i t c h i n g moments. Examples i n c l u d e Alexander (1966) on c a t f i s h C r y p t o _ 3 t e r u s b i c i r r h i s , Klauewitz (1964) on s h r i m p f i s h A e o l i s c u s s t r i q a t u s . P o l l (1969) on s e v e r a l s p e c i e s and Willoughby (1976) on upsidedown c a t f i s h genus Synodgntis. Of s p e c i a l i n t e r e s t to t h i s study i s the work of Hoedeman on p e n c i l f i s h e s . Hoedman (1950) e r e c t e d a new genus Nannobry_cgn w i t h i n nannostomine f i s h f o r the o b l i q u e l y swimminq s p e c i e s Nannobrycon egues. Weitzman (1966) showed t h a t Hoedeman's Nannobrycon egues was i n f a c t made up of two s p e c i e s Po § £ i I o b r y_con Nannobrycon - egues and £°§2il2brycon Nannobrycon u n i f a s c a i t u g . L a t e r Weitzman and Cobb (1975) presented an o p i n i o n that a l l members of the t r i b e Nannostomini should be i n one qenus Nannostomus Eiqenmann, 1909. In t h i s r e p o r t n o m e n c l a t o r i a l names w i l l f o l l o w Weitzman and Cobb (1975), see Weitzman (1966) f o r f u l l synonyms.. Hoedeman (1950) i n s e p a r a t i n q Nannostomus- egues and Nannostomus u n i f a s c i a t u s i n t o h i s new qenus Nannobrycon from the 5 r e s t of nannostomone f i s h e s used three c h a r a c t e r s as f o l l o w s : 1. The lower lobe of the c a u d a l f i n i s l a r g e r than the upper l o b e , whereas the two lobes are equal i n ot hers 2. The swimbladder i s c a r r o t - s h a p e d and narrows s h a r p l y p o s t e r i o r l y , whereas i t i s c y l i n d r i c a l and ending b l u n t l y i n o t h e r s 3. They normally swim i n a s l a n t i n g p o s i t i o n with head up, whereas others normally swim h o r i z o n t a l l y . Hoedeman (1971) used the nature of the swimbladder and the enlarged lower lobe of the caudal f i n t o e x p l a i n the hydromechanics i n v o l v e d i n m a i n t a i n i n g the s l a n t i n g swimming i n Nannostomus egues and Nannostomus u n i f a s c i a t u s . According t o Hoedeman, the sharp narrowing of the p o s t e r i o r end o f Nannostpmus egues and Nannostomus u n i f a s c i a t u s compared to the other Nannostomus s p e c i e s g i v e s l e s s upward pressure and thus accounts f o r the head-up s l a n t of these two s p e c i e s . Weitzman (1966) doubts t h i s i n t e r p r e t a t i o n due to incomplete a n a l y s i s by Hoedeman's study. P e t e r s (1951) used a s i m i l a r l i n e of argument to e x p l a i n posture maintenance and o r i e n t a t i o n i n the sea horse, Hippocampus b r e v i r o s t r i s . Using X-ray p i c t u r e s showing the swimbladder, he observed that the sea horse c o u l d c o n t r o l the gas volume i n the two chambers of the swimbladder. Increase i n volume of the p o s t e r i o r chamber l i f t s the t a i l and i n c r e a s e to the a n t e r i o r chamber l i f t s the head. The r e l a t i v e volumes of the two chambers are c o n t r o l l e d by the swimbladder w a l l muscles and 6 the s p h i n c t e r muscles s e p a r a t i n g the two chambers. From the laws of h y d r o s t a t i c s , i f the p o s i t i o n of the centre of mass i s separated by a s u f f i c i e n t h o r i z o n t a l d i s t a n c e from the p o s i t i o n of the ce n t r e of buoyancy the s e p a r a t i o n can cause a p i t c h i n g moment. I f a f i s h i s to swim h o r i z o n t a l l y and be i n e q u i l i b r i u m i t has t o use the f i n s t o c o u n t e r a c t t h i s moment. I f the centre of mass i s behind the centre of buoyancy then t h i s w i l l produce a p o s i t i v e p i t c h . A negative p i t c h i s produced i f the centre of mass i s i n f r o n t of the c e n t r e o f buoyancy.. Some f i s h swimming or hovering with p o s i t i v e or n e g a t i v e p i t c h u t i l i z e t h i s moment due to the s e p a r a t i o n of c e n t r e s o f mass and buoyancy. Alexander (1966) r e p o r t s an a n a l y s i s on the c a t f i s h C r y p t o p t e r u s b i c i r r h i s which has the. c e n t r e of mass behind the centre of buoyancy and hovers with a p o s i t i v e p i t c h of about 45°. The moment produced i s coun t e r a c t e d by a d o r s a l f i n and probably a l s o the caudal f i n when the f i s h swims h o r i z o n t a l l y . P i t c h i n g moments can a l s o be produced a c t i v e l y by the a c t i o n of the f i n s r e g a r d l e s s of the r e l a t i v e p o s i t i o n s of the centre of mass and the centre o f buoyancy. Osing the f i n s to produce such a p i t c h i n g moment may seem to be e n e r g e t i c a l l y more expensive than passive moments produced by the s e p a r a t i o n of the ce n t r e s o f mass and buoyancy; however, a system using f i n s to produce these movements has an advantage of being f a s t e r i n a c t i o n and more f l e x i b l e and maneuverable. In the pre v i o u s s t u d i e s concerning o b l i q u e l y swimminq f i s h t h e r e i s none which dea l s i n any d e t a i l with the hydromechanics 7 and a d a p t a t i o n s o f t h e s e f i s h t o t h e mode o f o b l i q u e s wimminq. T h e r e f o r e , i n t h i s s t u d y I have s o u q h t a n s w e r s t o f o u r b a s i c q u e s t i o n s c o n c e r n i n q f i s h w h i c h swim o b l i q u e l y . T h e s e q u e s t i o n s a r e : 1 . What m e c h a n i s m s do t h e s e o b l i q u e l y swimminq f i s h u s e t o m a i n t a i n t h e p i t c h ? 2. How do t h e s e f i s h p r o p e l t h e m s e l v e s ? 3 . A r e t h e r e any m o r p h o l o q i c a l and a n a t o m i c a l m o d i f i c a t i o n s i n t h e p r o p u l s i v e s y s t e m a s s o c i a t e d w i t h t h i s swimminq o r i e n t a t i o n ? 4. What i s t h e f u n c t i o n o f o b l i q u e swimminq i n t h e s e f i s h ? A n s w e r s t o q u e s t i o n s one t o t h r e e a r e i n v e s t i q a t e d e x p e r i m e n t a l l y i n d e t a i l . The l a s t q u e s t i o n i s d i s c u s s e d l a r q e l y i n t e r m s o f t h e weak, c o n c e p t o f f u n c t i o n i n t h e s e n s e o f H i n d e ( 1 9 7 5 ) . I n t e r p r e t a t i o n o f t h e s t r o n q f u n c t i o n o f o b l i q u e swimminq b e h a v i o r w o u l d r e q u i r e more e x p e r i m e n t a t i o n a n d o b s e r v a t i o n s , e s p e c i a l l y i n t h e i r n a t u r a l e n v i r o n m e n t . F o r q u e s t i o n s one and t w o , a r e s e a r c h h y p o t h e s i s t h a t 'The n a t u r e and p o s i t i o n o f t h e s w i m b l a d d e r and o t h e r b u o y a n t m a t e r i a l s i n c o n j u n c t i o n w i t h t h e p o s i t i o n and movement o f t h e f i n s a r e r e s p o n s i b l e . f o r m a i n t a i n i n q t h e o b l i q u e ; o r i e n t a t i o n ' was f o r m u l a t e d t o i n v e s t i q a t e t h e m e c h a n i s m s i n v o l v e d . From p r e v i o u s s t u d i e s r e p o r t e d above i t was t h o u q h t t h a t t h o s e . f i s h w h i c h swim and h o v e r w i t h a p o s i t i v e . p i t c h w o u l d h a v e t h e c e n t r e o f mass b e h i n d t h e c e n t r e o f b u o y a n c y p r o d u c i n q a p o s i t i v e p i t c h and v i c e v e r s a f o r t h o s e w h i c h swim and h o v e r w i t h a n e q a t i v e p i t c h . 8 P r e l i m i n a r y d i s s e c t i o n s o f t h e v i s c e r a o f t h e . s p e c i e s s t u d i e d h e r e r e v e a l e d v e r y l i m i t e d d i f f e r e n t i a l f a t d e p o s i t i o n . T h e r e f o r e , t h e c e n t r e o f b u o y a n c y was i n v e s t i g a t e d o n l y i n t e r m s o f t h e s w i m b l a d d e r . T h u s t h e a b o v e h y p o t h e s i s w a s f o r m u l a t e d i n t e r m s o f a t e s t a b l e n u l l h y p o t h e s i s a n d i t s a l t e r n a t i v e : H c : T h e n a t u r e a n d p o s i t i o n o f t h e s w i m b l a d d e r i n r e l a t i o n t o t h e c e n t r e o f g r a v i t y h a v e no e f f e c t i n t h e d i r e c t i o n ( h e a d - u p o r h e a d - d o w n ) o f t h e b o d y t i l t Hj : T h e n a t u r e a n d p o s i t i o n o f s w i m b l a d d e r i n r e l a t i o n t o t h e c e n t r e o f g r a v i t y d e t e r m i n e s t h e d i r e c t i o n ( h e a d - u p o r h e a d - d o w n ) o f t h e b o d y t i l t The r o l e o f f i n s i n m a i n t a i n i n g t h e o b l i q u e o r i e n t a t i o n a n d i n s w i m m i n g m o v e m e n t s w e r e i n v e s t i g a t e d b y u s i n g c i n e m a t o g r a p h i c m e t h o d s f o r t h e f i n k i n e m a t i c s a n d v e c t o r a n a l y s i s , b y i m m o b i l i z a t i o n o f f i n a c t i o n u s i n g MS 222, a n d by f i n a m p u t a t i o n s . F o r c o n v e n i e n c e o f p r e s e n t a t i o n , t h i s s t u d y i s d i v i d e d i n t o t w o p a r t s , h y d r o m e c h a n i c a l a n a l y s i s a n d s t r u c t u r a l - m o r p h o l o g i c a l a n a l y s i s . Q u e s t i o n t h r e e w i l l b e i n v e s t i g a t e d i n t h e l a t t e r p a r t a n d t h e w o r k i n g h y p o t h e s e s w i l l be i n t r o d u c e d i n t h a t s e c t i o n a f t e r t h e p r e s e n t a t i o n o f t h e t h e o r e t i c a l a n a l y s i s o f s w i m m i n g . 9 1. HYDROMECHANICAL ANALYSIS GENERAL METHODS AND - MATERIALS B a s i c a n a l y s i s f o r those f i s h which swim with a p o s i t i v e p i t c h was done on p e n c i l f i s h of the genus Nannostomus, Gunther, 1872 (family Lesbianidae) . Two s p e c i e s Nannostomus egues, Steindachner, 1876, and Nannostomus u n i f a s c i a t u s , Steindachner, 1876, which swim o b l i g u e l y with a p o s i t i v e p i t c h were used as t e s t s p e c i e s . Two other s p e c i e s Nannostomus b e e f o r d i , Gunther, 1872, and Nannostomus t r i f a s c i a t u s , Eigenmann, 1909, which swim normally ( h o r i z o n t a l l y ) were, used as c o n t r o l s f o r comparative purposes. Less d e t a i l e d o b s e r v a t i o n s were a l s o ' made: on penguin or hockey s t i c k f i s h , T h a y e r i a b o e h l k e i , Weitzman, 1957, and Thayeria o b l i g u a , Eigenmann, 1908, (f a m i l y Characidae) which swim with a p o s i t i v e , p i t c h . To compare hydromechanics i n v o l v e d i n maint a i n i n g the p o s i t i v e and negative p i t c h , s i m i l a r a n a l y ses were: c a r r i e d out on f i s h which swim with a negative p i t c h . C h i l o d u s punctatus, Muller and T r o s c h e l , 1845, (family Chilodontidae) which swims with a negative p i t c h was used as a t e s t s p e c i e s , and a c l o s e l y r e l a t e d s p e c i e s Leporinus maculatus (f a m i l y Anostomidae) which swims h o r i z o n t a l l y was used as a c o n t o l f o r comparative purposes. , See Roberts (1969, 1973) f o r the d i s c u s s i o n of the r e l a t e d n e s s of these two f a m i l i e s which were p r e v i o u s l y t r e a t e d as one f a m i l y Anostomidae, before being s p l i t i n t o two by Greenwood e t . a l . (1967) . Less d e t a i l e d o b s e r v a t i o n s were a l s o made on marbled 10 headstander, Abramistes l i £ E o e e g h a l u s , Norman, 1926, an anostomid s p e c i e s which swims with a negative p i t c h . A l l the s p e c i e s used i n t h i s study were purchased from aquarium d e a l e r s . Only those w i l d specimens with known i n f o r m a t i o n on the area of o r i g i n were used i n a c t u a l experiments. T h i s was a p r e c a u t i o n a g a i n s t v a r i a b i l i t y i n behaviour and morphological c h a r a c t e r s a s s o c i a t e d with mass breeding i n aguarium f i s h . However, some gen e r a l o b s e r v a t i o n a l notes were made on specimens without i n f o r m a t i o n on area o f o r i g i n . The experimental f i s h were kept i n the l a b o r a t o r y i n th r e e s i z e d tanks of varying l e n g t h , width, and depth dimensions as f o l l o w s : A. 75cm X 45cm X 50cm = 168,750cm3 OK 168.75 l i t r e s B. 75cm X 45cm X 30cm = 101,250cm3 OR 101.25 l i t r e s C. 50cm X 25cm X 30cm = 37,500cm3 OR 37.50 l i t r e s These tanks were used f o r d i f f e r e n t o b s e r v a t i o n s and w i l l be r e f e r r e d to as tanks A, B, and C r e s p e c t i v e l y . The tanks were f i t t e d with an e x t e r n a l f i l t r a t i o n system d r i v e n by a s m a l l e l e c t r i c motor, c o n t i n o u s l y c i r c u l a t i n g water maintained at 25 ± 2°C. Swimming modes and f i n kinematics were s t u d i e d with a 16mm E c l a i r c i n e camera with m u l t i p l e speed c o n t r o l , and used Ectachrome VNF 7240 r e v e r s i b l e f i l m . Swimming f i s h were.filmed 11 at two r a t e s , 50 and 75 frames/second.. F i n movements were s t u d i e d and analysed u s i n g a Steenbeck e d i t i n g and p r o j e c t i o n t a b l e . The p r o j e c t i o n machine had two speeds a normal speed o f 24, and a slow speed of 4 frames/second. P e c t o r a l f i n b e a t i n g f r e g u e n c i e s were counted at the slow speed. During f i l m i n g i t takes a few m i l l i s e c o n d s f o r the camera motor t o a c c e l e r a t e from zero to the steady s e l e c t e d speed. T h e r e f o r e , s i x to seven frames were l e f t at the beginning of each f i l m s e c t i o n when counting the number of frames to c a l c u l a t e the f i n b e a t i n g f r e q u e n c i e s . The number of frames to be excluded c o u l d e a s i l y be i d e n t i f i e d by the change i n l i g h t i n g ; the l i g h t i s b r i q h t e r when the camera motor a c c e l e r a t e s . S t i l l camera p i c t u r e s were used i n the measurements of the anqles of o r i e n t a t i o n i n i n t a c t f i s h , i n f i s h with f i n s removed i n v a r i o u s combinations, and i n f i s h a n a e s t h e t i z e d i n MS 222 and l e f t t o f a l l f r e e l y i n a water column. Most of these p i c t u r e s were taken i n a s p e c i a l photoqraphing tank d e s c r i b e d below. Photographing tank The tank was gridded on the r e a r s i d e and the bottom with graph paper. The v e r t i c a l l i n e s of the graph paper on the r e a r s i d e were s e t p a r a l l e l t o a plumbline so t h a t they were i n the d i r e c t i o n of the a c t i o n of g r a v i t y . The graph paper at the bottom was l a i d i n such a way that i t s l i n e s were continous and at r i g h t angles to t h e . v e r t i c a l l i n e s o f the graph paper on the r e a r s i d e . The whole arrangement i n three dimensions was t h a t o f two gridded p l a n e s , XY and XZ, a t r i g h t angles to each o t h e r (Figure 1) . A. b i g m i r r o r was then put at 45° to the h o r i z o n t a l on the 12 r e a r s i d e of the tank, with a p o r t i o n p r o j e c t i n g above the tank. With t h i s arrangement both the s i d e and d o r s a l views of the f i s h c o u l d be seen simultaneously when viewed from the f r o n t , the d o r s a l view being a v i r t u a l image from the mirror. Both these views have graph paper g r i d s on t h e i r background. T h i s set-up made i t p o s s i b l e to get accurate measurements of the angle of o r i e n t a t i o n with r e s p e c t to t h e . h o r i z o n t a l a x i s subtended by the f i s h i n space. Only those p i c t u r e s i n which the s a g i t t a l o r median plane of the f i s h was p a r a l l e l t o the XY plane of the tank were used. These p i c t u r e s c o u l d e a s i l y be i d e n t i f i e d when both s i d e , and d o r s a l views were looked at s i m u l t a n e o u s l y . In these p i c t u r e s the l o n g i t u d i n a l a x i s of the f i s h i s p a r a l l e l t o the X-axis of the bottom graph paper. Thus e r r o r s i n the angle due to the r o t a t i o n of the f i s h i n water were minimized. A. THE ANGLE OF ORIENTATION Breamer and Breamer (1958) found t h a t the s l a n t i n g angle i n Nannostomus egues changed with s i z e , with the s m a l l Nannostomus egues adopting g r e a t e r angles. Franke (1972) a l s o r e p o r t s s i m i l a r o b s e r v a t i o n s f o r C h i l o d u s punctatus, where.small s i z e s adopt g r e a t e r angles. In t h i s study t e s t s were made to see how much the s l a n t i n g i s a f u n c t i o n of s i z e , and what d i f f e r e n c e s might e x i s t between s l a n t i n g s p e c i e s and t h e i r normally swimming r e l a t i v e s . Method The v a r i a t i o n of the angle of o r i e n t a t i o n with s i z e i n these f i s h made i t necessary to use s t a t i s t i c a l t e s t s on 13 specimens of same s i z e or n e a r l y so. A l l the experiments d e s c r i b e d below i n v o l v i n g angle measurement were designed i n such a way that angles were measured before and a f t e r treatments on the same i n d i v i d u a l s w i t h i n a very s m a l l s i z e range. However, the measurements were not p a i r e d . The e f f e c t of s i z e put a l i m i t a t i o n on the number of specimens t h a t c o u l d be o b t a i n e d w i t h i n a very s m a l l s i z e range. As a r e s u l t most of the experiments were done on s m a l l sample s i z e s v a r y i n g from 12-20 9 f i s h . Four s i z e c a t e g o r i e s were used f o r Nannostomus egues and three f o r Chilodus punctatus. Since l i m i t e d s i z e range was a v a i l a b l e , s i z e c a t e g o r i e s were chosen around those s i z e s where enough specimens were a v a i l a b l e . For T h a y e r i a o b l i g u a only two s i z e groups were used r e p r e s e n t i n g the extremes of the s i z e range s t u d i e d . Therefore the d e s i g n a t i o n s m a l l and l a r g e i n Table 1 i s r e l a t i v e . To a v o i d overcrowding the f i s h were i n t r o d u c e d i n t o the photographing tank a few at a time. Each set c o n t a i n e d at l e a s t one i n d i v i d u a l from a d i f f e r e n t s i z e group. T h i s arrangement allowed the i n d i v i d u a l specimens i n each s e t to be matched with t h e i r p i c t u r e s a f t e r p r i n t i n g . In some cases i n d i v i d u a l specimens were photographed alone i f they d i s t u r b e d o t hers i n a group. The f i s h were a c c l i m a t i z e d to the photographing tank f o r a day before p i c t u r e s were taken. Six t o e i g h t p i c t u r e s were taken from the f r o n t to b r i n g i n t o view both the d o r s a l and s i d e views of the f i s h . The p i c t u r e s were taken a t a r e l a t i v e l y c onstant i n t e r v a l of 10 minutes. However, d e l a y s were sometimes necessary i f most of the f i s h d i d not have t h e i r s a g i t t a l planes 14 p a r a l l e l t o the XY plane of the tank. The whole procedure was repeated f o r other f i s h , each time e n s u r i n g t h a t the l i g h t i n g c o n d i t i o n s were the same. The s i z e c a t e g o r i e s of each s p e c i e s were kept i n separate tanks a f t e r t h i s experiment. These specimens were l a t e r used to study the e f f e c t of removing v a r i o u s f i n s r e p o r t e d below i n c o n j u n c t i o n with the cinematographic method. The angle of o r i e n t a t i o n was measured from those specimens with both s i d e and d o r s a l views i n the same p i c t u r e . However, t h e r e were some p i c t u r e s which had only the si d e view. For these only those specimens with t h e i r s a g i t t a l plane p a r a l l e l t o the XY plane of the tank were used. I t was easy to i d e n t i f y such specimens a f t e r g a i n i n g experience with those having d o r s a l and s i d e views t o g e t her. The angle was measured as the angle between the m i d l i n e along the f i s h ' s long a x i s and the X-axis ( h o r i z o n t a l axis) u s i n g the background graph paper (XY plane of the tank) i n the d i r e c t i o n of the head. T h i s angle takes a p o s i t i v e value above and a negative value below the X-axis when the c e n t r e of the f i s h i s taken to be at the p o i n t of o r i g i n of the C a r t e s i a n c o o r d i n a t e s as shown i n F i g u r e 2a and b. T h i s n o t a t i o n i s based on the s i g n of the p i t c h i n g moments, as i n aerodynamics ( M i l n e -Thomson, 1 966) . R e s u l t s Although 6-8 p i c t u r e s were taken of each specimen, the s u i t a b l e p i c t u r e s f o r angle measurements v a r i e d from 2 t o 5. Therefore, the mean angle f o r each specimen was f i r s t c a l c u l a t e d 15 from i t s s u i t a b l e p i c t u r e s , then these mean angles f o r each i n d i v i d u a l were used as independent values t o c a l c u l a t e the mean and other s t a t i s t i c s f o r the s i z e c a t e g o r i e s . In comparing s i z e c a t e g o r i e s i t was assumed t h a t the ranges of s i z e s i n each category were.small enough f o r a l l the f i s h t o be t r e a t e d together. The r e s u l t s are given i n Table 1, and f o r Nannostomus egues and C h i l o d u s punctatus the r e s u l t s are a l s o shown g r a p h i c a l l y with 5% confidence l i m i t s i n F i g u r e 3. The v a l u e s f o r f o r k l e n g t h on the X-axis are the mid p o i n t s of each s i z e range. Fork length was used because i t was f a s t e r to measure i n l i v e f i s h a n a e s t h e t i z e d i n MS 222 with minimum h a n d l i n g . The r e s u l t s show that the angle of o r i e n t a t i o n decreases with d e c r e a s i n g s i z e i n both Nannostomus egues and C h i l o d u s eunctatus, and i n c r e a s e s with i n c r e a s i n g s i z e . i n T h a y e r i a o b l i q u a . T e s t s of s i g n i f i c a n c e using Student's t - t e s t f o r the extreme s i z e c a t e g o r i e s showed s i g n i f i c a n t d i f f e r e n c e s at a l e v e l of P(0.05) f o r Nannostomus egues Ch i l o d u s punctatus and Thayeria o b l i q u a . The angular values are only good f o r comparative purposes under the same c o n d i t i o n s , e s p e c i a l l y with regard to l i g h t . For example Nannostomus egues i s known to vary i t s angle with l i g h t i n g c o n d i t i o n s , e s p e c i a l l y with day and n i g h t (Braemer and Braemer, 1958). T h e r e f o r e , they are not of value i n d e s c r i b i n g the expected angles without r e f e r e n c e to t h e . c o n d i t i o n s under which they were measured. 16 F i g u r e 1. D i a g r a m a t i c p r e s e n t a t i o n of the f r o n t veiw of the photographing tank showing the g r i d e d X Y and X Z p l a n e s . 17 18 Table 1. Angles of o r i e n t a t i o n by s i z e i n C h i l o d u s punctatus, Nannostomus-egues and T h a y e r i a o b l i q u a . Sample s i z e used are enc l o s e d i n p a r e n t h e s i s • • i SHALL | LARGE • | SPECIES r 1 | SIZE 1 (MM) |MEAN ANGLE AND| |5% CONF LIMIT |SIZE | MEAN ANGLE AND |5% CONF LIMIT - — i — + -PR0B| -1 INannostomus j egues 120-23 |50 ± 3.0 (15) |38-40 134 ± 2.0 (11) |0 .000| IChilodus I panetatug |22-26 I-59 ± 2 . 5 (15)|42-46 |-48 ± 2.0 (15) |0 .0001 IThayeria I b p e h l k e i |16-20 | 18 ± 2.0 (14) |28-31 |23 ± 2.5 {14) |0 J .006| 19 F i g u r e 3. O r i e n t a t i o n by s i z e i n C h i l o d u s j g u n c t a t u s , and Napnostoipus egues showing .the v a r i a t i o n of t h e a n g l e w i t h s i z e mi£NLvricN I N N B W . r>tnjmus F U M T T A T L E B Y s r z E -40' T - 4 3 . . . - 4 5 . . . - 4 8 - . . - 5 0 . . . - 5 3 . . . - 5 5 - . . - 5 9 . . . -GO. . . - 6 3 - . . - G 5 1 5 I S is : : • i 1 j 1 i 1 1 1 4 2 0 - 0 2 3 ^ 0 E S - O e a - O 3 2 - 0 3 5 - 0 3 3 - 0 4 1 - 0 4 4 - 0 4 7 - 0 5 0 - 0 FCFoA L E N G T H I N ORIENT A T I E N IN K B W . N A N S C B T C K t f i EXLE5 BY SIZE BO- _ 5 S » . . 5 2 - . . 43^  . . AA- . . AO- . . M s -7B-ZA-5 0 -1 5 1 7 14 1 ± H L I I ' ' ' A, ' _ - a O - 2 3 - 3 5 . 3 0 - 3 3 - 3 5 - 3 3 - «3- < 3 - < S - 43-50-FURS. L E N G T H I N 20 B. EFFECTS OF FIN REMOVAL Method The specimens used here are those which were a l s o used t o study the ang l e s of o r i e n t a t i o n i n a normal f i s h d e s c r i b e d above. T h i s design enabled s t a t i s t i c a l comparison of the changes i n the angle of o r i e n t a t i o n before and a f t e r f i n removal i n each s i z e category. In these experiments i t was hypothesized t h a t i f the c a u d a l and p e c t o r a l f i n s play a r o l e i n maintaining the angle o f d e v i a t i o n from the h o r i z o n t a l , the removal of these f i n s should decrease the s i z e of t h i s angle. Therefore the experiments below are designed to use a, o n e - t a i l Student 1 s t - t e s t with the n u l l s t a t e d as: Ho : mean angle before f i n removal = mean a f t e r f i n removal Hj : mean angle before f i n removal > mean a f t e r f i n removal A l l the t e s t s i n v o l v e the d i f f e r e n c e s of two sample means. As use of Student's t - t e s t f o r t h i s type of a n a l y s i s assumes e q u a l i t y of v a r i a n c e s between the two samples, F - t e s t s were done to a s c e r t a i n t h a t t h i s requirement was f u l f i l l e d . However, i n a l l cases where the e q u a l i t y of varia n c e was d o u b t f u l , the d i f f e r e n c e s between the two sample means were t e s t e d by us i n g sample v a r i a n c e s i n s t e a d of assuming e g u a l i t y of v a r i a n c e s , and c a l c u l a t i n g the new degrees of freedom f o r the.new d i s t r i b u t i o n (Hoel, 1971) . The experimental specimens were a n a e s t h e t i z e d i n 80mg/L MS 21 222 before removing the f i n s . In Nannostomus egues, p e c t o r a l f i n s were removed from group 2 specimens (27-30mm) , i n C h i l o d u s punctatus from group 2 specimens (30-33mm), and i n T h a y e r i a pblig.ua from group 1 specimens (16-20mm) . In Nannostomus egues the caudal f i n was removed i n t h r e e d i f f e r e n t p a t t e r n s . In the f i r s t , only the lower lobe was removed. In the second, only the upper lobe was removed, whereas i n the l a s t p a t t e r n the whole caudal f i n was removed. The whole c a u d a l f i n was a l s o removed from specimens of group 3 (33-35mm), t h i s group was used f o r s t a t i s t i c a l a n a l y s i s . In C h i l o d u s punctatus, the caudal f i n was removed from group 3 (42-46mm) , and from group 2 (28-31mm) of Thayeria b o e h l k e i . In a l l these cases of f i n amputations only the f i n r a y s were removed, and i n most cases the f i s h regenerated the f i n s w i t h i n t h r e e weeks (except f o r the p e c t o r a l f i n amputations i n Nannostomus egues, which caused 100% m o r t a l i t y a f t e r about a week). In each case the f i s h were l e f t i n the tank f o r 12 hours t o recover from the amputation trauma before the angles of o r i e n t a t i o n were measured. The.angles were measured i n the same way as d e s c r i b e d above f o r normal f i s h . In a d d i t i o n , cinematographs were taken to analyse the e f f e c t of caudal f i n removal i n Nannostomus egues by counting p e c t o r a l f i n - b e a t frequency before and a f t e r c audal f i n removal. R e s u l t s of p e c t o r a l f i n removal In Nannostomus egues the f i s h r e s t e d h o r i z o n t a l l y with a s l i g h t negative p i t c h (mean angle of -13°). The stumps of the p e c t o r a l s were s t i l l b e a t i n g r h y t h m i c a l l y , and the other f i n s 22 beat i n the.normal manner f o r hovering. When swimming s l o w l y forward the f i s h used small-amplitude l a t e r a l f l e x u r e s of the caudal f i n . During t h i s movement the f i s h tended to bend the caudal p a r t of the body j u s t i n f r o n t of the ca u d a l peduncle to compensate f o r the negative p i t c h . According t o A f f l e c k (1950) t h i s tendency to upturn the caud a l p a r t of the body at the caudal peduncle would produce a downward d i r e c t e d f o r c e behind the c e n t r e of mass and t h e r e f o r e would lower t h e . t a i l and r a i s e the head. When the f i s h were d i s t u r b e d , and s t a r t e d r a p i d l y from r e s t o r e l s e swam f a s t i n carangiform motion with. l a r g e - a m p l i t u d e l a t e r a l f l e x u r e s of the caudal f i n , the ne g a t i v e p i t c h i n c r e a s e d . For T h a y e r i a b o e h l k e i the f i s h s t i l l r e s t e d with a p o s i t i v e p i t c h which d i d not change s i g n i f i c a n t l y from t h a t before the removal of p e c t o r a l s . Removal o f p e c t o r a l s from the normally swimming Nannostomus b e e f o r d i and Nannostomus t r i f a s c i a t u s had no e f f e c t on the p i t c h when the f i s h swam slowly, although sometimes Nannostomus b e c f o r d i showed a tendency t o have a s l i g h t p o s i t i v e p i t c h . A l l these s p e c i e s when swimming f a s t or a c c e l e r a t i n g had problems i n stopp i n g , sometimes h i t t i n g the tank w a l l . In C h i l o d u s punctatus, i n d i v i d u a l s s t i l l swam with a negative p i t c h as before, although the f i s h showed i n s t a b i l i t y with r e s p e c t to yaw and bra k i n g . R e s u l t s of caudal f i n removal In Nannostomus egues, independent removals of the lower or 23 upper l o b e , or of the complete caudal f i n l e f t the f i s h s t i l l s l a n t i n g with a p o s i t i v e p i t c h , so t h a t s u p e r f i c i a l l y i t appeared t h a t the removal of the caudal f i n had no e f f e c t . One-t a i l Student's t - t e s t a n a l y s i s f o r the angles before and a f t e r the removal of the whole caudal f i n show t h a t there i s no s i g n i f i c a n t d i f f e r e n c e at the l e v e l of P(0.05); i . e., a p r o b a b i l i t y P < 0.025 (Table 2), 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 i s accepted. However, i f the component of l i f t due to the caudal f i n i s compensated by an i n c r e a s e d a c t i v i t y of the p e c t o r a l f i n , then t h i s s t a t i s t i c a l r e s u l t may be m i s l e a d i n g . To t e s t f o r t h i s p o s s i b i l i t y , the f o l l o w i n g n u l l and a l t e r n a t i v e hypotheses were formulated: H o Mean p e c t o r a l f i n f r e g u e n c y Mean p e c t o r a l f i n f r e g e n c y b e f o r e c a u d a l f i n removal a f t e r c a u d a l f i n removal Mean p e c t o r a l f i n freguency Mean p e c t o r a l f i n frequency before c a u d a l f i n removal a f t e r caudal f i n removal P e c t o r a l f i n b e a t i n q f r e q u e n c i e s were counted before and a f t e r the removal of the caudal f i n i n the qroup t h r e e specimens (33-35mm). A o n e - t a i l Student's t - t e s t showed that the i n c r e a s e i n the mean p e c t o r a l f i n - b e a t frequency from 465 to 496 beats per minute was s i q n i f i c a n t at a l e v e l of P(0.05). Table 3 summarizes these r e s u l t s . ( With the removal o f the lower lobe of the caudal f i n , the f i s h could not achieve a h o r i z o n t a l p o s i t i o n when s t a r t i n q r a p i d l y from r e s t . There was always some p o s i t i v e p i t c h t h a t p o i n t e d the head upwards. The removal of the upper lobe alone 2 4 d i d not have t h i s e f f e c t , so t h a t the f i s h c o u l d achieve a h o r i z o n t a l p o s i t i o n when s t a r t i n g r a p i d l y from r e s t . I t appears that i n Nannostomus egues, the enla r g e d lower lobe of the cau d a l f i n makes the r e s u l t a n t o f t h i s f i n pass upwards and behind the centre of mass, when the f i s h s t a r t s r a p i d l y from r e s t with l a r g e - a m p l i t u d e caudal f i n movements. T h i s point w i l l be f u r t h e r e l a b o r a t e d under the d i s c u s s i o n . 25 Table 2. E f f e c t of caudal f i n removal on the angle o f o r i e n t a t i o n i n C h i l o d u s p u n c t a t u s and Nannostomus S3y.es. Sample s i z e s a re e n c l o s e d i n p a r e n t h e s i s 1 i | SIZE r |MEAN ANGLES AND 5% CONF.LIMIT r I SPECIES 1 (MM) i | BEFORE j AFTER | PROB 1Nannostomus ! ! !. | egues |27-30 141.5 ± 3 (17) J41 ± 3 (14) | 0.9744 1Chilodus 1 I ! I punctatus 142-46 1-48 ± 2.0 (15) |-45 t 2.5 (14) | 0.0168 • • i Table 3. E f f e c t of caudal f i n removal on the p e c t o r a l f i n -\ beat freguency i n Nannostomus egues. Sample s i z e s are e n c l o s e d i n p a r e n t h e s i s Mean p e c t o r a l f i n frequency {._with 5% c o n f i d e n c e l i m i t Prob Before caudal f i n removal A f t e r c a u d a l f i n removal 0.0051 465 ± 13.5 (19) 496 ± 8.5 (17) 26 Caudal f i n removal i n Thayeria o b l i g u a had an e f f e c t on the angle of o r i e n t a t i o n . The t a i l r e g i o n tended to drop and the head r e g i o n rose whenever the f i s h stopped swimming. The c a u d a l s t r o k e s which the f i s h u s u a l l y uses d u r i n g normal hov e r i n g d i d not r a i s e . t h e t a i l r e g i o n . Thus much of the time the f i s h were swimming u s i n g the caudal region i n carangiform mode with l a r g e r amplitudes than normal, (that i s , as Gray (1933) observed i n whiting, Gadus merlangus). This mode of swimming brought the f i s h t o about the same p i t c h and sometimes even l e s s than tha-t at which they normally hover. Whenever they stopped swimming the angle i n c r e a s e d again. Because of such e f f e c t s i t was not p o s s i b l e to measure the angles f o r comparison with those obtained before the caudal f i n was removed. Caudal f i n removal i n C h i l o d u s punctatus d i d not e l i m i n a t e the n e g a t i v e p i t c h . The f i s h s t i l l swam with the head down. However, th e r e was a s i g n i f i c a n t decrease i n the mean angle o f o r i e n t a t i o n i n group 3 specimens a f t e r removal of the caudal f i n . These r e s u l t s are summarized i n Table 2. U n f o r t u n a t e l y no p e c t o r a l f i n f r e q u e n c i e s were obtained f o r these f i s h so t h a t changes c o u l d not be assessed. In Nannostomus b e e f o r d i , Nanngstomus t r i f a s c i a t u s and Leporinus maculatus, removal of the caud a l f i n d i d not s i g n i f i c a n t l y a f f e c t the angle, of o r i e n t a t i o n . These f i s h s t i l l swam h o r i z o n t a l l y . chambered physostomus n e c e s s a r i l y the same C. . SWIMBLADDER ANALYSIS Characoid f i s h e s have two swimbladders. The two chambers are not 27 (Rowntree, 1903; Nelson, 1961). Hoedeman (1974) suggested t h a t narrowing of the p o s t e r i o r chamber of the swimbladder i n Nannostomus egues and Nannostomus u n i f a s c i a t u s reduced the upward pressure i n the hind p a r t , t h e r e f o r e , was r e s p o n s i b l e f o r the s l a n t i n g o r i e n t a t i o n . In t h i s s e c t i o n the p o s i t i o n and nature of the swimbladder i s i n v e s t i g a t e d i n the s l a n t i n g s p e c i e s and t h e i r h o r i z o n t a l r e l a t i v e s t o see i f there i s any d i f f e r e n c e . I t i s expected t h a t those s p e c i e s with n e g a t i v e p i t c h may have c a u d a l p r o l o n g a t i o n of swimbladder and/or narrowing of the a n t e r i o r chamber o f the swimbladder, and those with p o s i t i v e p i t c h to have f o r e p r o l o n g a t i o n and/or narrowing of the p o s t e r i o r chamber of the swimbladder. The p o s i t i o n and nature of the swimbladder were determined by three d i f f e r e n t methods: d i r e c t d i s s e c t i o n , X - r a y i n g , and t r a n s m i t t e d l i g h t . X-ray. X-ray p i c t u r e s to show the form of the swimbladder i n r e l a t i o n t o the r e s t of the.body were taken using the UBC F i s h Museum X-ray machine. The f i s h specimens to be X-rayed were immobilized by a n e s t h e t i z i n g them i n 80mg/L MS 222. They were kept moist by c o v e r i n g them with cheese c l o t h . A f t e r . s e v e r a l p r e l i m i n a r y exposures with Kodak X-ray paper M21 processed i n Kodak X-ray f i x e r and developer, a time of 50 seconds was found s u i t a b l e f o r f i s h i n s i z e range 10mm-50mm. The f i s h were put d i r e c t l y on top of the. unexposed X-ray paper i n the centre of the X-ray cone. Since the exposed p i c t u r e and the a c t u a l specimens were the.same s i z e , i t was easy t o compare the r e l a t i v e s i z e s of the swimbladder and the whole 28 body. Transmitted l i g h t The swimbladder ( p a r t i c u l a r l y the p o s t e r i o r chamber) o f l i v e swimming specimens of a l l s p e c i e s of Nannostomus and Chilodus punctatus (smaller than 40mm) could e a s i l y be seen i n strong back l i g h t i n g . The f i s h were allowed to swim or hover f r e e l y i n s m a l l g l a s s c o n t a i n e r s 6.0 X 2.0 X 4.0cm..When they assumed t h e i r n a t u r a l o r i e n t a t i o n , they were viewed a g a i n s t a strong back-l i g h t i n a dark room-. D i f f e r e n c e s i n the tran s m i t t a n c e of l i g h t through t i s s u e s and the gas chamber i n the swimbladder, made the swimbladder c l e a r l y v i s i b l e . Observations were made on Nannostomus egues d u r i n g the day and the n i g h t because t h i s s p e c i e s r e s t s almost h o r i z o n t a l l y at n i g h t . D i s s e c t i o n Specimens a n a e s t h e t i z e d i n 80mg/L MS 222 were d i s s e c t e d under a d i s s e c t i n g scope to measure the swimbladder with gases i n i t . L i v e specimens were d i s s e c t e d i n MS 222 t o minimize gas l o s s from the swimbladder, as a r e s u l t the measurements c l o s e l y approximated those f o r swimming f i s h . R e s u l t s Swimbladder form and r e l a t i v e p o s i t i o n w i t h i n the body are shown i n F i g u r e s 4 and 5. There was no r e m a r k a b l e . d i f f e r e n c e i n the nature and p o s i t i o n of the two chambers of the swimbladder between the s l a n t i n g s p e c i e s and t h e i r h o r i z o n t a l r e l a t i v e s . 29 There i s some d i f f e r e n c e i n the angle the swimbladder makes with the s p i n a l column i n C h i l o d u s punctatus and Lep o r i n u s maculatus. I t i s l a r g e r i n C h i l o d u s punctatus than Leporinus maculatus (Figure 5 ) . This e f f e c t can not be r e s p o n s i b l e f o r r a i s i n g the hind p a r t . However once the f i s h i s s l a n t i n g the swimbladder becomes almost h o r i z o n t a l and may help i n m a i n t a i n i n g the s l a n t . There was no observable day-night d i f f e r e n c e i n terms of the r e l a t i v e s i z e s o f the two lobes i n Nannostomus egues. During d i s s e c t i o n , swimbladders were checked f o r any abnormal v a s c u l a r i z a t i o n , which would i n d i c a t e u t i l i z a t i o n o f atmospheric a i r . None of these s p e c i e s showed any such v a s c u l a r i z a t i o n . D. DENSITY DETERBINftTION F i s h d e n s i t y was determined to r e l a t e the buoyancy and s i n k i n g f a c t o r to the swimming l e v e l s and p i t c h . . I f the f i s h i s more dense than water then i t would r e g u i r e more f o r c e to maintain the p i t c h than when i t i s n e u t r a l l y buoyant. Method The f i s h were put i n tank A and a c c l i m a t i z e d to t h e i r swimming l e v e l s f o r s e v e r a l weeks (see under s p a t i a l d i s t r i b u t i o n ) . The f i s h were then removed one at a time and immediately put i n a strong s o l u t i o n of MS 222 of 150mg/L f o r one minute which deeply n a r c o t i z e d them. The. n a r c o t i z a t i o n process was very r a p i d , which minimized the l o s s of gas from the swimbladder. A f t e r t h i s the f i s h were immobile showing no s i g n of f i n r e f l e x e s or body movements. The f i s h were then b l o t t e d dry and weighed on an e l e c t r i c 30 balance to an accuracy of a hundredth of a gram. The volume of a f i s h was then determined i n a 100ml volumetric f l a s k , i n which the f i s h d i s p l a c e d i t s own volume. The water which e g u a l l e d the volume of the f i s h was then p i p e t t e d out and blown i n t o a b u r r e t t e with d i v i s i o n s of 0.0 5mls. The b u r r e t t e was g e n t l y shaken t o l e t a l l the drops s e t t l e b efore reading the volume. Densit y was then c a l c u l a t e d from the normal formula: mass o f the f i s h Density = volume of the f i s h R e s u l t s M l the s p e c i e s are e i t h e r n e u t r a l l y buoyant or are s l i g h t l y denser than water. Nannostomus egues was l e s s dense than Nannostomus b e e f o r d i and Nannostomus t r i f a s c i a t u s , and C h i l o d u s punctatus and Lepprinus maculatus were more dense than the Nannostomus s p e c i e s . T h i s r e s u l t i s to be expected from the s p a t i a l d i s t r i b u t i o n of these s p e c i e s i n the. water column. C h i l o d u s punctatus and Leporinus maculatus occupies lower l e v e l s than Nannostomus s p e c i e s . F i g u r e 6 summarizes the r e s u l t s . 31 F i g u r e 4. Swimbaldder i n Nannostomus s p e c i e s . 4a. Nannostomus egues and 4b. Nannostomus b e e f o r d i 32 # C e n t r e o f mass O C e n t r e o f buoyance F i g u r e 6 . D e n s i t i e s and 556 c o n f i d e n c e i n t e r v a l s D E N S I T Y I N G R A K G P E R C U B I C C E N T I M E T E R O O •» H •» H • • • • • • § § § § § § * 1 1 1 1 h N a n n o s t o m u s e g u e s - I x ifc N a n n o s t o m u s b e c k f o r d i . • ' * *Q N a n n o s t o m u s t r i f a s c i a t u s , x : C h i l o d u s p u n c t a t u s • I x « Q L e p o r i n u s m a c u l a t u s " H x ~ ~ — ' G : 3 4 E. THE CENTERS OF BUOYANCY AND MASS Separation of the cen t r e s o f buoyancy and mass may cause s t a t i c p i t c h i n g moments which could be used t o maintain p i t c h (Alexander, 1966). T h e r e f o r e ; i t i s hypothesized t h a t t h o s e : f i s h which hover with a p o s i t i v e p i t c h have the centre of mass behind the c e n t r e : o f buoyancy, and those with a negative p i t c h have the cen t r e of mass i n f r o n t of the c e n t r e of buoyancy. Methods I. Centre o f buoyancy The f i s h were X-rayed as d e s c r i b e d above t o show both the swimbladder and the . r e s t of body outline,. Then the X-ray f i l m was p r o j e c t e d and magnified 10 times on a smooth hard paper. The magnified image of the swimbladder was t r a c e d on the hard paper and i t s o u t l i n e c u t out. Thus the paper model had a s i m i l a r shape as the swimbladder, ten times l a r g e r . Assuming t h a t the gases i n the swimbladder are uniform, then the ce n t r e of buoyancy o f the swimbladder would be a t the same point as the c e n t r e of g r a v i t y of the paper model of the swimbladder. The c e n t r e o f g r a v i t y of the paper model was determined by a plumbline as f o r a polygon. F i v e : f i n e pin holes were : bored along the edges on d i f f e r e n t s i d e s of the paper model. When the paper model was suspended on a pin through each of these h o l e s , i t s own weight caused the.model to r o t a t e smoothly around the p i n . Then the plumbline, a weighted th r e a d t i e d at the p i n , was dropped and i t s l i n e drawn on the paper model. T h i s was repeated with the p i n i n the other h o l e s , and 3 5 the poi n t at which these l i n e s i n t e r s e c t e d was taken as the centre of g r a v i t y . To check the c o n s i s t e n c y and accuracy of the r e s u l t s , paper models of f i v e specimens were l a t e r balanced on a pin head at t h e i r i n t e r c e c t i o n p o i n t s . The p o i n t of balance was c o n s i s t e n t l y found to be.at the p o i n t of i n t e r s e c t i o n . By the use of r e l a t i v e measurements from the magnified models, t h i s p o i n t of balance was marked i n the o r i g i n a l x-ray p i c t u r e . I I . Centre.of mass The c e n t r e of mass was determined from the same i n d i v i d u a l s t h a t had p r e v i o u s l y been used f o r the centre of buoyancy determinations. These, i n d i v i d u a l s were k i l l e d and t h e i r c e n t r e of mass determined w i t h i n an hour a f t e r being x-rayed. The centre of mass was a l s o determined by the plumbline method d e s c r i b e d above with f i n e pin holes bored a t f o u r p o i n t s : through the eyes; a t the base of the d o r s a l f i n ; at the upper end of cau d a l peduncle; and at the base of the a n a l f i n . When suspended the f i s h r o t a t e d smoothly around the p i n i n each of these holes by nature of i t s own weight. As be f o r e plumblines were, dropped and drawn on t h e . f i s h . T h e i r point of i n t e r s e c t i o n was taken as the c e n t r e of mass of the whole f i s h . By l a y i n g the o u t l i n e of the f i s h d i r e c t l y above the t r a c e of the x-ray p i c t u r e of the same f i s h , the point of the c e n t r e of mass of the f i s h was t r a n s f e r r e d and marked on the o r i g i n a l X-ray p i c t u r e t o be compared with the c e n t r e of buoyancy. In t a k i n g the centre of buoyancy of the swimbladder as the centre of buoyancy of the whole f i s h body, the e f f e c t of other bouyant substances such as v i s c e r a l f a t s has been n e g l e c t e d . 36 This i s a reasonable s i m p l i f i c a t i o n , as d i s s e c t i o n s of these f i s h showed very l i t t l e f a t d i p o s i t i o n . T h e i r c o n t r i b u t i o n to buoyancy t h e r e f o r e i s n e g l i g i b l e compared with t h a t of the gases i n the swimbladder. R e s u l t s The r e l a t i v e p o s i t i o n s of the c e n t r e s of mass and buoyancy are shown i n F i g u r e s 4 and 5. For both Nannostomus egues and Chilodus punctatus the r e s u l t s were c o n t r a r y to what was expected from the d i r e c t i o n o f the hypothesis. In Nannostomus egues the c e n t r e of mass i s i n f r o n t of the centre of buoyancy. This s i t u a t i o n would cause a p a s s i v e n e g a t i v e : p i t c h i n g moment which must be counteracted by the a c t i o n of the f i n s i f the f i s h i s t o swim and hover with a p o s i t i v e p i t c h . In C h i l o d u s punctatus the c e n t r e of mass i s behind the c e n t r e of buoyancy, which would mean t h a t there i s a p o s i t i v e p i t c h i n g moment i n c o n t r a s t to the observed negative p i t c h i n g moment when the f i s h swims sl o w l y or hovers. In T h a y e r i a b o e h l k e i and Thayeria o b l i g u a the r e s u l t s are as expected from the h y p o t h e s i s . The centre of mass i s behind the c e n t r e of buoyancy which would t h e o r e t i c a l l y give a s t a t i c p o s i t i v e p i t c h . For both Nannpstpmus b e e f o r d i and Leporinus- maculatus the centre of mass and centre of buoyancy are approximately on the same v e r t i c a l l i n e . In Nannostomus b e e f o r d i they are s c a r c e l y separated, but i n Leporinus maculatus the c e n t r e of buoyancy i s s l i g h t l y below the c e n t r e of mass. 37 F. EQUILIBRIUM IN IMMOBILE LIVE FISH The above r e s u l t s were, checked by observing the s t a t i c e q u i l i b r i u m of l i v e f i s h . Method L i v e f i s h were put i n a 150mq/L s o l u t i o n of MS 222 f o r 45 seconds to one minute during which time the f i s h . were deeply n a r c o t i z e d and showed no r e f l e x e s with regard to the movements of t h e i r f i n s . The high c o n c e n t r a t i o n of MS 222 with very s h o r t a n a e s t h e t i z i n g time was chosen because i t e l i m i n a t e d s t r u g g l i n g before the f i s h were deeply narcotized..Thus the f i s h d i d not lo s e any swimbladder gas which would otherwise have a f f e c t e d the e q u i l i b r i u m o r i e n t a t i o n . The n a r c o t i s e d f i s h were.put i n the photographing tank and l e f t t o si n k f r e e l y , as a l l the s p e c i e s s t u d i e d were h e a v i e r than water or n e u t r a l l y buoyant (see d e n s i t y measurements). During t h e i r f r e e f a l l p i c t u r e s were taken as d e s c r i b e d above to determine the mean angle of o r i e n t a t i o n with r e s p e c t to the h o r i z o n t a l a x i s . Results Both Nannostomus egues and Nanngstomus u n i f a s c i a t u s sank slowly t o the bottom upside down with the head p o i n t i n g down at a mean angle of -23° from the h o r i z o n t a l . T h i s e g u i l i b r i u m was very s t a b l e and r e s t o r e d i t s e l f a f t e r v a r i o u s displacement moments were a p p l i e d . At the bottom the f i s h s t i l l r e s t e d with the head to u c h i n g the f l o o r and the t a i l p art r a i s e d . T h a y e r i a b o e h l k e i e i t h e r sank very slowly t o the bottom or remained suspended i n midwater. In e i t h e r case the s t a b l e e g u i l i b r i u m was with the head p o i n t i n g up. The angle v a r i e d from 38 28° i n s m a l l specimens group (15-19mm) up t o almost v e r t i c a l i n l a r g e specimens. In those specimens with the a n g l e . l e s s than 90° the p o s i t i o n was upside down with the b e l l y f a c i n g up. C h i l o d u s punctatus a l s o sank to the f l o o r upside down as wel l but with the t a i l f i r s t at a mean angle of +48° with the h o r i z o n t a l f o r specimens of 30-33mm. T h i s e g u i l i b r i u m was a l s o very s t a b l e j u s t as i n Nannostomus egues and Nannostomus u n i f a s c i a t u s . C h i l o d u s punctatus r e s t e d on the f l o o r with the head r a i s e d . The e g u i l i b r i u m o r i e n t a t i o n of Nannostomus egues, T h a y e r i a b o e h l k e i , and Ch i l o d u s punctatus a f t e r i m m o b i l i z a t i o n o f the f i n s c o n f i r m s the expected p i t c h i n g moment caused by the s e p a r a t i o n of the centre of mass and the centre of buoyancy. As the centre of buoyancy i s s l i g h t l y below the ce n t r e of mass i n these f i s h they sank upside down (Figure 7) . That these e g u i l i b r i u m o r i e n t a t i o n s are not simply a r e f l e c t i o n of the str e a m l i n e e f f e c t o f t h e i r shapes i s a l s o confirmed by the f a c t that these o r i e n t a t i o n s are very s t a b l e with r e s p e c t t o displacements i n a l l d i r e c t i o n s , and they r e s t i n the same o r i e n t a t i o n at the bottom and are e g u a l l y s t a b l e . Nannostomus b e e f o r d i , Nannostomus t r i f a s c i a t u s , and Leporinus maculatus, a l l sank upside down and almost h o r i z o n t a l with only minor d e v i a t i o n s . However, Nannostomus b e e f o r d i and Leporinus maculatus were u n s t a b l e , sometimes s i n k i n g sideways, but were s t a b l e when d i s p l a c e d along the XY plane. The e g u i l i b r i u m o r i e n t a t i o n s of these c o n t r o l s p e c i e s during f r e e f a l l are a l s o t o be expected from the r e l a t i v e p o s i t i o n s of t h e i r c e n t r e s o f mass and buoyancy. . 3 9 F i g u r e 7. E q u i l i b r i u m o r i e n t a t i o n of immobile l i v e C h i l o d u s punctatus. 1 ( T 40 QUALITATIVE DESCRIPTION OF S WIMIM MODES The d e s c r i p t i o n s of the swimming modes are based on the a n a l y s i s of the cinematographic' f i l m and o b s e r v a t i o n of the f r e e l y swimming f i s h i n the tanks. In a d d i t i o n , f i s h were put i n a s m a l l g l a s s c o n t a i n e r 6.0 X 2.0 X 4.0cm and a drop of red dye was i n t r o d u c e d near the f i n with a f i n e bent hypodermic needle. Then the movement of the dye c o u l d be observed as i t was c a r r i e d by the c u r r e n t s generated by f i n movements. Nannostomus egues and Nannostomus u n i f a s c i a t u s These two s p e c i e s are the l e a s t a c t i v e swimmers among the Nannostomini. They show three b a s i c swimming modes, h o v e r i n g , slow forward and rearward movements and f a s t forward movement. Hovering T h i s i s t h e i r common method of m a i n t a i n i n g p o s i t i o n i n the water column. A f i s h maintains i t s e l f i n a r e l a t i v e l y s t a t i o n a r y p o s i t i o n u s u a l l y near the s u r f a c e with i t long a x i s making an angle with t h e . h o r i z o n t a l i n a head up o r i e n t a t i o n . The p e c t o r a l f i n s beat a l t e r n a t e l y . They are completely out of phase, when the l e f t one i s f u l l y abducted, the r i g h t one i s f u l l y adducted. T h i s movement i s very c l e a r when viewed from above. The phase d i f f e r e n c e between the p e c t o r a l f i n r a y s i s s m a l l conseguently the p e c t o r a l f i n s move as s i n g l e planes. In each beat t h e r e i s a f a s t forward stroke, and a slow backward s t r o k e . During abduction, the f i n r o t a t e s around i t s base making the forward stroke e f f e c t i v e downward and forwards so that the r e a c t i o n of the water i s upwards and backwards..The 41 r e s u l t a n t of t h i s movement g i v e s the l i f t t o the f r o n t part of the body. ' During adduction the s t r o k e i s slower than i n abduction, the v e n t r a l p a r t s t a r t d u r i n g the r e t u r n s t r o k e but the whole. f i n r o t a t e s again at i t s base and the d o r s a l p a r t c a t c h up b e f o r e the f i n i s f u l l y adducted. The out of phase a l t e r n a t e b e a t i n g of the two s i d e s may be a mechanism of c a n c e l l i n g the h o r i z o n t a l component i n hovering (Magnan and Sainte-Lague, 1929). The phase d i f f e r e n c e i s s m a l l e r i n other s p e c i e s of Nannostomus s t u d i e d here than i n Nannostomus- egues and Nannostomus u n i f a s c i a t u s , and i t a l s o decreases when Nannostomus egues and Nannostomus u n i f a s c i a t u s swims forward s l o w l y , a necessary change f o r i m p a r t i n g a f o r w a r d - p r o p e l l i n g component to the f i n movement. The d o r s a l f i n i s f u l l y s t r e t c h e d and makes a s e r i e s of continous waves from the top f r e e end to the base of the f i n . A s i m i l a r s e r i e s of waves i s produced by the d o r s a l lobe of the caudal f i n which d r i v e s a c u r r e n t of water down along the margin of the f i n . During t h i s metachronal movement of the r a y s of the upper lobe of the d o r s a l f i n there i s a l s o a s e r i e s of waves moving along the l e n g t h of the r a y s , a t an angle to the h o r i z o n t a l a x i s of the body. T h i s movement generates a f o r c e d i r e c t e d downwards and forwards which a c t s t o depress the c a u d a l f i n . The l a r g e r lower lobe of the c a u d a l f i n i s normally f u l l y s t r e t c h e d and remains s t a t i o n a r y . The p e l v i c f i n s are s t r e t c h e d out from the body w a l l . Slow forward and rearward movements Short forward and rearward swimming movements are i n t e r s p a c e d between long p e r i o d s of hovering p o s i t i o n s . U s u a l l y these movements occur while the f i s h n i b b l e at p l a n t s u r f a c e s or feed on or i n s p e c t p a r t i c l e s suspended i n water. When the r e are many f i s h i n a tank, they move slowly forward together i n a l o o s e ' s c h o o l 1 , harmonizing stops and t u r n s . During the slow forward movements the p e c t o r a l f i n s beat c o n t i n o u s l y j u s t as i n hovering but the phase d i f f e r e n c e between the two s i d e s i s reduced. The d o r s a l lobe of the caudal f i n a l s o produces a v e r t i c a l s e r i e s of waves as i n hovering but the lower lobe of the caudal f i n i s not f u l l y s t r e t c h e d . Instead i t i s f o l d e d and compressed, reducing the c a u d a l - f i n a r e a . Decrease i n c a u d a l - f i n area reduces drag. There i s no l a t e r a l movement of the t a i l r e g i o n i n t h i s mode. The f i s h moves forward s l o w l y with the use of the p e c t o r a l f i n s and maintains the head-up p o s i t i o n . During slow rearward movement the p e c t o r a l f i n movements are r e v e r s e d . Otherwise a l l other f i n movements remain the same as i n slow forward movement. l a s t forward movement Nannostomus egues and Nannostomus u n i f a s c i a t u s r a r e l y e x h i b i t t h i s movement. They swim forward f a s t only when there i s a d i s t u r b a n c e i n t h e i r v i c i n i t y or when f e e d i n g on l i v e organisms, such as Daphnia, or when atta c k e d by another f i s h ; e.g. Abramistes mierocephalus or Leporinus maculatus, both o f which are t a i l b i t e r s . At the beginning of f a s t movement the lower lobe of the caudal f i n i s f u l l y s t r e t c h e d . Then the whole of the caudal f i n i s thrown i n t o a s e r i e s of l a t e r a l movements with the waves 43 s t a r t i n g about h a l f way al o n g the trunk, i n a t y p i c a l carangiform motion. A f t e r a few l a t e r a l movements of the c a u d a l f i n , the lower lobe i s f o l d e d and compressed as i n slow forward movement. The l a t e r a l movements then continue f o r a few more c y c l e s a f t e r which the f i s h g l i d e s t o a stop. During the l a t e r a l movements of the caudal f i n , the d o r s a l and v e n t r a l margins of the f i n l e a d the:middle p a r t . The whole f i n thus forms a cu r v a t u r e of a very l a r g e r a d i u s ; i . e . , t h e r e i s a s m a l l l a g i n the.middle p a r t . When the lower lobe i s f u l l y s t r e t c h e d and h e l d r i g i d l y as i t i s j u s t before a r a p i d s t a r t or durin g c o r r e c t i o n a l movements, the whole f i n moves as a u n i t . In f a s t forward movement the p e c t o r a l f i n s a re f o l d e d and held a g a i n s t the body and the e l e v a t i o n of the . d o r s a l f i n i s a l s o reduced c o n s i d e r a b l y , which reduces t h e i r drag. There i s a p o s i t i v e l i f t on the caudal area l o w e r i n g the a n t e r i o r r e g i o n . T h i s p o s i t i v e . l i f t i n the caudal r e g i o n during the a c c e l e r a t i o n was a l s o e v i d e n t i n the experiments of f i n removal. The l i f t on the caudal area and the conseguent lowering o f the f r o n t r e g i o n b r i n g s the body to a h o r i z o n t a l p o s i t i o n or even to a ne g a t i v e p i t c h , depending on the s t a r t i n g a c c e l e r a t i o n . The. higher the a c c e l e r a t i o n the g r e a t e r the negative p i t c h . This e f f e c t i m p l i e s t h a t the lower lobe may l a g behind the d o r s a l lobe f o r p a r t of the c y c l e when i t i s f u l l y s t r e t c h e d and r i g i d during l a t e r a l movement. But t h i s l a g was not c l e a r i n the f i l m s . S h i f t i n g t o a h o r i z o n t a l p o s i t i o n during r a p i d swimming i s i n accordance with e f f i c i e n t swimming as p r e d i c t e d by hydrodynamic models ( L i g h t h i l l 1969, 1970; Weihs, 1973) as the 44 e f f i c i e n c y of the p r o p u l s i v e f o r c e i s highest when the f o r c e i s i n the d i r e c t i o n of motion and passes through the c e n t r e o f mass. Turning Nannostomus-egues and Nannostomus u n i f a s c i a t u s show two p a t t e r n s of t u r n i n g movements, one i n slow o b l i g u e swimming and the other d u r i n g f a s t t u r n s . When hovering o b l i g u e l y or swimming slowly forward, these f i s h t u r n p r i m a r i l y with the p e c t o r a l f i n s . F i r s t , t h e . p e c t o r a l f i n away from the d i r e c t i o n of t u r n i n g s t a r t s to beat f a s t e r than the i n n e r one. Then the f i s h s l o w l y t u r n s , m a i n t a i n i n g the o b l i g u e p o s i t i o n . During the whole t u r n i n g movement a l l other f i n s move i n the normal f a s h i o n f o r hovering or slow forward movement. The other t u r n i n g p a t t e r n depends p r i m a r i l y on the c a u d a l f i n f o r r a p i d t u r n i n g . In t h i s p a t t e r n the lower lobe of the caudal f i n i s f i r s t f u l l y s t r e t c h e d as a t the onset of f a s t forward movement. Then the caudal f i n i s thrown i n t o a l a r g e -amplitude l a t e r a l f l e x u r e i n the d i r e c t i o n opposite to t h a t i n which the f i s h w i l l e v e n t u a l l y t u r n . The head i s bent i n the d i r e c t i o n of the t u r n . These changes are f o l l o w e d by two c y c l e s of complete l a t e r a l movements of the c a u d a l f i n which complete the t u r n . During r a p i d t u r n s the caudal r e g i o n i s r a i s e d and the f i s h becomes momentarily h o r i z o n t a l . I f the t u r n i n g i s part of an escape response, then the l a r g e amplitude l a t e r a l f l e x u r e s o f the caudal f i n c o n t i n u e s as d e s c r i b e d f o r t h e . f a s t forward movement. 45 Nannostomus beefordi and -Nannostomus t r i f a s c i a t u s Unlike Nannostomus egues and Nannostomus unifasciatus which are slow swimmers that use pectoral f i n s for most of the i r swimming a c t i v i t i e s , Nannostomus beefordi and Nannostomus t r i f a s c i a t u s are active f i s h that move constantly by caudal f i n propulsion i n the. subcarangiform pattern t y p i c a l of other p e n c i l f i s h e s . Active f i s h dart forward for a short distance, stop suddenly, hover f o r a very short period and then dart forward again. This cycle i s repeated frequently. When there i s an unusual object i n the water or when the f i s h i s near plant leaves, the sudden stop and hovering may be followed by a b r i e f rearward movement. Hovering Hovering periods are r e l a t i v e l y short. Gravid females of Nannostomus beefordi tend to hover longer than the males or Nannostomus t r i f a s c i a t u s . They usually hover hori z o n t a l l y but when feeding, or slowly ascending or descending, they may hover obliguely with head-up or head-down orientation. The action of the f i n s during these movements i s s i m i l a r to that described for Nannostomus egues and Nannostomus unifasciatus except f o r the following: During the forward stroke of the pectorals these f i n s are not rotated as much as i n Nannostomus egues. The pectorals are s t i l l out of phase i n t h e i r strokes, but the phase:difference i s smaller than that observed i n Nannostomus egues and Nannostomus unifasciatus, e.g., when one f i n i s f u l l y abducted the other i s 46 only two t h i r d s adducted. Forward movements During forward d a r t i n g the f i s h uses caudal f i n p r o p u l s i o n i n the subcarangiform p a t t e r n . The p e c t o r a l and p e l v i c f i n s are f o l d e d and held a g a i n s t the body. The h e i g h t s of the d o r s a l and anal f i n s are reduced. The same f i n movements take place d u r i n g f a s t forward p r o p u l s i o n when the f i s h i s d i s t u r b e d , attacked by another f i s h or a g g r e s s i v e chases, but the amplitude of the l a t e r a l movements of the caudal f i n i s i n c r e a s e d , and there are more f l e x u r e c y c l e s b e f o r e the f i s h stops. Rearward movement Slow rearward movements are not so common as i n Nannostomus egues or Nannostomus u n i f a s c i a t u s . They are performed with p e c t o r a l f i n s as d e s c r i b e d f o r Nannostomus egues and Nannostomus u n i f a s c i a t u s . Thayeria b o e h l k e i and T h a y e r i a o b l i q u a These, s p e c i e s swim with a p o s i t i v e p i t c h l i k e Nannostomus egues and Nannostomus u n i f a s c i a t u s , but they are more a c t i v e than these o b l i g u e l y swimming nannostomine s p e c i e s . The angle v a r i e s from 16-25° with l a r g e f i s h s l a n t i n g a t g r e a t e r angles than s m a l l f i s h . In the l a r g e community tank (tank A) they occupy the upper s u r f a c e waters l i k e Nannostomus u n i f a s c i a t u s and Nannostomus egues. 4 7 Hovering During hovering these species do not maintain a s t r i c t l y stationary position but tend to move s l i g h t l y forward with each stroke. They maintain position by rhythmic strokes of the pectoral f i n s and the caudal f i n beating i n unison. Between strokes there i s a tendency of the posterior part of the body to drop, thus increasing the.positive p i t c h . The caudal f i n strokes involving a low-amplitude l a t e r a l cycle act as a compensating mechanism to raise the.posterior part and bring the body to the desired angle. The f i s h appears to constantly experience a positive pitching moment around i t s centre of mass fo r which i t compensates with these f i n movements. With each pectoral and caudal f i n stroke the f i s h also gains a small forward displaceme nt. The dorsal lobe of the caudal f i n does not display the series of waves moving down i t s margin that i s t y p i c a l of the nannostomine species. Fast forward movement -During a fast foward movement both species use the caudal f i n i n a carangiform motion. The caudal f i n i s r i g i d l y held open swinging from side to side with large amplitude. The caudal region i s raised and the f i s h swims almost horizontally with a very s l i g h t positive pitch. The swimming pattern i s l i k e that of Nannostomus egues involving a burst phase of a few caudal f i n strokes followed by a g l i d i n g phase. 48 C h i l o d u s punctatus T h i s s p e c i e s swims and hovers with a negative p i t c h with the angle normally v a r y i n g from -45° to -70°. The small f i s h s l a n t a t g r e a t e r angles than the l a r g e f i s h (Table 1), In c o n t r a s t t o Nannostomus egues and Nannostomus u n i f a s c i a t u s they maintain t h i s s l a n t i n g p o s i t i o n day and n i g h t . They are a c t i v e f i s h c o n t i n o u s l y n i b b l i n g at the bottom and on p l a n t stems and l e a v e s . They can move forwards, backwards and v e r t i c a l l y upwards or downward (Figure 8 ) . Hovering These f i s h do not maintain one p o s i t i o n i n the water column f o r a l o n g time as does Nanngstomus egues.' They u s u a l l y move slowly forward or v e r t i c a l l y downward or upward..During h o v e r i n g t h e r e are a c t i v e movements i n a l l the f i n s except the p e l v i c s which show only s l i g h t movement. With each s t r o k e . of the p e c t o r a l , the f i n i s abducted outward and downward. During the s t r o k e s the phase d i f f e r e n c e between su c c e s s i v e rays i s l a r g e and a t y p i c a l u n d u l a t i o n i s seen with c r e s t s p a s s i n g from the upper ( a n t e r i o r ) margin to the lower ( p o s t e r i o r ) margin. During each s t r o k e the upper ( a n t e r i o r ) rays l e a d the lower rays.. The s t r o k e , s t a r t s slowly on the.upper rays but i t i s immediately f o l l o w e d by a f a s t whip as the wave progresses to the lower r a y s . During adduction the lower r a y s r e t u r n f a s t e r and the whole f i n r e t u r n s to the s i d e o f the f i s h at about the same time. The movement i s c l o s e to the b a s i c t e l e o s t type d e s c r i b e d by H a r r i s (1937), the d i f f e r e n c e s being due to the o r i e n t a t i o n of the f i s h . The c a u d a l f i n a l s o makes some i n t e r m i t t e n t movements with the two l o b e s a c t i n g independently.. The upper lobe i s more a c t i v e during hovering, beating from s i d e to s i d e but not i n a r e g u l a r seguence. For example, i t may make 2-3 s t r o k e s to one s i d e before i t beats to the other. .The outer edge l e a d s the c e n t r a l p a r t i n each of these l a t e r a l s t r o k e s from c e n t r a l p o s i t i o n outward. The f i n whips r a p i d l y outward then r e t u r n s very s l o w l y to i t s c e n t r a l p o s i t i o n . The lower l o b e sometimes d i s p l a y s s i m i l a r movements but i t s s t r o k e s are much slower with longer waves than the d o r s a l l o b e . The d o r s a l lobe of the caudal f i n thus moves l i k e an i n c l i n e d plane on each of i t s e f f e c t i v e l a t e r a l s t r o k e . Since the r e t u r n i s slower and t h e r e f o r e l e s s e f f e c t i v e , the r e a c t i o n from t h e . water g i v e s the f i n an upward l i f t . T h i s sequence o f movement i n the d o r s a l lobe of the caudal f i n i s given i n F i g u r e 9, which shows t h a t the outward s t r o k e i s f a s t e r , t a k i n g fewer frames than the r e t u r n s t r o k e . The upper o u t e r margin which l e a d s these movements i s shown as a t h i c k e r l i n e than the t r a i l i n g margin. The d o r s a l f i n a l s o has a s e r i e s of waves from the outer margin down to the base. The f o r c e components here are downward and backward. Chilodus-punctatus uses the. r e a c t i o n t o these components mainly f o r c o n t r o l l i n g r o l l . I n d i v i d u a l s always i n c l i n e t h e i r d o r s a l f i n s opposite to the d i r e c t i o n of r o l l i n g and removal of t h i s f i n makes them very unstable t o r o l l . Slow movements During slow movements forward, backwards or v e r t i c a l l y upward or downward, Chilodus punctatus p r i m a r i l y uses p e c t o r a l 50 f i n s . These f i n s have a s m a l l base and are very f l e x i b l e . Fast forward movement Th i s i s not a common mode of p r o p u l s i o n i n C h i l o d u s punctatus.. During t h i s movement the caudal f i n beats i n a t y p i c a l subcarangiform mode and i f the movement i s f a s t enough, p i t c h i s reduced and the head i s r a i s e d . T h i s change towards the h o r i z o n t a l i s seen when the f i s h are swimming f a s t as when aggr e s s i v e males compete f o r a female or chase her d u r i n g spawning. 52 53 SPATIAL DISTRIBUTION AND FEEDING HABIT S e v e r a l members of the f a m i l y L e b i a s i n i d a e , i n p a r t i c u l a r some s p e c i e s of the genera P y r r h u l i n a , Copeina and Nannostomus tend t o swim i n the upper waters and f r e g u e n t l y f e e d on food p a r t i c l e s near the s u r f a c e . In t h e i r n a t u r a l environment i n the f o r e s t - s h a d e d streams and r i v e r s of t r o p i c a l South America, the s u r f a c e waters are.very r i c h i n food r e s o u r c e s (Roberts, 1972). The s u r f a c e zone i s e n r i c h e d with s m a l l organisms the m a j o r i t y of which are of t e r r e s t r i a l o r i g i n . The l e b i a s i n i d s and many other c h a r a c o i d s which e x p l o i t t h i s zone show i n t e r e s t i n g anatomical and morphological a d a p t a t i o n s . These a d a p t a t i o n s can be g e n e r a l i z e d i n t o two c a t e g o r i e s . F i r s t are those i n v o l v i n g the snout which have s h i f t e d the jaws forward and upward. When these f i s h swims h o r i z o n t a l l y the upturned mouth i s d i r e c t e d to the s u r f a c e ; f o r example the f l y i n g c h a r a c i n s genera C a r n e g i e l l a Eigenmann, 1909, Thoracocharax Fowler, 1906 and Gasteropelegus S c o p o l i , 1777. In these genera, t h e i r d e n t i t i o n with heavy sharp t e e t h i s a l s o adapted f o r c u t t i n g s m a l l hard i n s e c t s caught at the s u r f a c e (Weitzman, 1954). The second category i n v o l v e s t h e . s t r u c t u r e s of p r o p u l s i o n and hydrodynamic e g u i l i b r i u m ( f i n s ) and the body form. In these f i s h the body u s u a l l y makes an acute angle, with i the s u r f a c e so t h a t the mouth and the eyes are a l l d i r e c t e d towards the s u r f a c e ; f o r example, Nannostomus egues. Many s p e c i a l i z e d s u r f a c e f e e d e r s show morphological a d a p t a t i o n s o f t h i s second type. When swimming and f e e d i n g near t h e . s u r f a c e the body a x i s makes an acute angle ( u s u a l l y l e s s than 45°) with the s u r f a c e ( M a r s h a l l , 1971), Included here are the three l e b i s i a n i d 54 genera. I have observed f i v e s p e c i e s of p e n c i l f i s h , genus Nannostomus: Nannostomus b e e f o r d i , Nannostomus t r i f a s c i a t u s , Nannostomus Marginatus, Nannostomus egues, and Nannostomus u n i f a s c i a t u s i n aquarium tank A. The.tank was f u l l y p l a n t e d a t the bottom and other p l a n t s were l e f t to f l o a t a t and near the s u r f a c e . T h i s tank was l a r q e enouqh to make ob s e r v a t i o n s on the swimming p a t t e r n s , f e e d i n g h a b i t s and s p a t i a l d i s t r i b u t i o n w i t h i n the v e r t i c a l column. There was a s p e c i f i c v e r t i c a l d i s t r i b u t i o n of the f i v e s p e c i e s d u r i n g the day ( l i g h t h o u r s ) , but a t n i g h t (dark hours) the p a t t e r n disappeared with most s p e c i e s coming very c l o s e t o i the s u r f a c e and h i d i n g below the f l o a t i n g p l a n t s . Even when the f l o a t i n g p l a n t s were removed, a l l f i v e s p e c i e s s t i l l came to the s u r f a c e at n i g h t . Nannostomus egues-and Nannostomus u n i f a s c i a t u s always occupied the top-most zone, hovering o b l i g u e l y with t h e i r heads up a few centimetres below the s u r f a c e . There appeared to be a tendency f o r the two sp e c i e s t o segregate, but t h i s c o u l d not be g u a n t i f i e d . Both s p e c i e s made slow forward and v e r t i c a l movements, n i b b l i n g at the f l o a t i n g p l a n t s and then r e t r e a t i n g a short d i s t a n c e backward. S i m i l a r movement p a t t e r n s were observed when dry food f l a k e s were dropped on the s u r f a c e . However, when the f i s h were f e d l i v e Daphnia, t h e i r movements became j e r k y , sometimes almost b r i n g i n g the body to the h o r i z o n t a l p o s i t i o n . They a l s o tended to f o l l o w the swimming Daphnia t o lower l e v e l s , whereas they would r a r e l y f o l l o w the dry food as i t sank. Below the l e v e l of Nannostomus egues and Nannostomus 5 5 u n i f a s c i a t u s there was a mixed group of Nannostomus b e e f o r d i and Nannostomus t r i f a s c i a t u s . Nannostomus b e e f o r d i had a g r e a t e r tendency than Nannostomus t r i f a s c i a t u s t o swim at an angle t o the h o r i z o n t a l and i n d i v i d u a l s sometimes swam near the s u r f a c e to n i b b l e f l o a t i n g p l a n t s . Normally these two s p e c i e s swim a c t i v e l y a t middle l e v e l s n i b b l i n g at growing p l a n t s and suspended matter. They may come to the s u r f a c e when fed dry food but f o l l o w i t back t o lower l e v e l s as i t s i n k s and feed on i t t h e r e . When fed l i v e Daphnia they feed i n the same jerky p a t t e r n as Nannostomus egues and Nannostomus u n i f a s c i a t u s but they are somewhat more a g i l e i n t h e i r forward movements; e.g., they stop almost i n s t a n t l y a f t e r c a t c h i n g a Daphnia. Nannostomus marginatus occupied the lowest l e v e l , but f r e g u e n t l y moved to mid l e v e l s and mixed with Nannostomus t r i f a s c i a t u s . I t s fee d i n g p a t t e r n i s very s i m i l a r to t h a t of Nannostomus t r i f a s c i a t u s . Of a l l the Nannostomini s p e c i e s , Nannostomus egues and Nannostomus u n i f a s c i a t u s have the: most s p e c i a l i z e d swimming h a b i t f o r s u r f a c e f e e d i n g . T h e i r heads-up o r i e n t a t i o n and h a b i t of swimming near the s u r f a c e make i t easy f o r these s p e c i e s t o e x p l o i t the s u r f a c e food resource. I t would be of i n t e r e s t to know t h e i r s p a t i a l d i s t r i b u t i o n i n nature i n p l a c e s where they occur .together with other Nannostomus s p e c i e s and see .whether there i s any resource p a r t i t i o n i n g . At present the only i n f o r m a t i o n on t h i s matter comes from,aguarium s t u d i e s (Weiss, 1971) . Feeding near the s u r f a c e exposes the f i s h t o many pr e d a t o r s from below. Conseguently extreme s p e c i a l i z a t i o n f o r s u r f a c e 56 f e e d i n g i s u s u a l l y coupled with a d a p t a t i o n s f o r escaping p r e d a t o r s from below. For example, i n the c h a r a c i d genera, Carnegie11a, Gasteropelecus and Thoracoeharax, the p e c t o r a l f i n and g i r d l e are adapted f o r f l y i n g (Weitzman, 1954; Gery, 1969; Brousseau, 1976) e n a b l i n g the f i s h t o stay i n the a i r f o r d i s t a n c e s up to t h r e e meters. Some members of the f a m i l y Exocoetidae s k i t t e r at the s u r f a c e and some a c t u a l l y take o f f i n t o the a i r i n the same response. I t i s suggested below t h a t the enlarged lower lobe i n Nannostomus egues- and Nannostomus u n i f a s c i a t u s may a l s o have a s i m i l a r f u n c t i o n when these f i s h respond to predators a t t a c k i n g from below. E f f e c t s of l i g h t The most important e f f e c t here i s the d i f f e r e n c e between day and n i g h t r a t h e r than the i n t e n s i t y of l i g h t . Onder normal c o n d i t i o n s of l i g h t Nannostomus egues and Nannostomus u n i f a s c i a t u s swim o b l i g u e l y d u r i n g the day and r e s t almost h o r i z o n t a l at n i g h t . T h i s change i n o r i e n t a t i o n has been a t t r i b u t e d to two components ( l i g h t and g r a v i t y ) determining t h e i r angle of o r i e n t a t i o n ( M i t t e l s t a d t , 1964, 1971). A l l the other s p e c i e s observed here swim i n n e a r l y h o r i z o n t a l plane day and n i g h t . A l l the s p e c i e s of the genus Nannostomus develop s p e c i f i c c o l o u r p a t t e r n s at n i g h t (see Hoedeman, 1950, 1974; S t e r b a , 1962; and Weitzman, 1966 f o r d e t a i l e d d e s c r i p t i o n of these c o l o u r p a t t e r n s ) . There i s a c i r c a d i a n rhythm i n these c o l o r changes between day and n i g h t . Nannogtomus b e e f o r d i has a 12-hour c y c l e with regard to l i g h t . I f the l i g h t s are not turned 5 7 o f f a f t e r 12 hours, the f i s h s t i l l develop t h e i r n o r c t u r n a l c o l o u r s , although they may not be so pronounced as they are i n the dark., However, i f the l i g h t s are not turned on i n the morning, the f i s h w i l l maintain t h e i r n o c t u r n a l c o l o u r s u n t i l the l i g h t i s switched on. I n f a c t , Nannostomus b e e f o r d i once kept i t s n o c t u r n a l p a t t e r n s f o r 36 hours i n c o n t i n o u s darkness. Nannostomus t r i f a s c i a t u s has the same rhythm as Nannostomus b e e f o r d i but the n o r c t u r n a l c o l o u r s were f a i n t l y developed i f the l i g h t s were not turned o f f a f t e r 12 hours of d a y l i g h t . Nannostomus egues and Nannostomus u n i f a s c i a t u s developed n o r c t u r n a l c o l o u r s o n l y i n darkness and d i d not show the 12 hour c y c l e with regard to l i g h t . During the day these f i s h w i l l develop t h e i r n o r c t u r n a l c o l o u r p a t t e r n s whenever the l i g h t i s turned o f f and at n i g h t they w i l l l o se c o l o u r whenever the l i g h t i s switched on. These changeovers take l e s s than 30 minutes. These c o l o u r s a l s o develop when the f i s h are under s t r e s s . Reed (1968) and Reed et a l . (1969) have given a model i n v o l v i n g melatonin i n the c i r c a d i a n c o n t r o l of these c o l o u r p a t t e r n s , but no one has produced an adeguate e x p l a n a t i o n of the f u n c t i o n of n o c t u r n a l c o l o u r s i n these f i s h . 58 2. MORPHOLOGICAL AND AN&TOMIGAL ANALYSIS In the mechanics of subcarangiform and carangiform swimming caudal p r o p u l s i o n i s of prime importance. ; Caudal p r o p u l s i o n depends on th r e e i n t e r a c t i n g systems: the a x i a l s k e l e t o n , a x i a l and caudal musculature, and the caudal f i n . Depending on the gene r a l b i o l o g y of the f i s h , the th r e e systems are l i k e l y t o show d i f f e r e n t a d a p t a t i o n s ; e.g., i n c r e a s e d caudal f i n s u r f a c e i n c r e a s e s a c c e l e r a t i o n and t h e r e f o r e l u n g i n g a b i l i t y . The s p e c i e s of Nannostomus are of i n t e r e s t s i n c e they show two d i s t i n c t swimming p a t t e r n s . Nannostomus eaijes and Nannostomus u n i f a s c i a t u s hover much of the time and use t h e i r p e c t o r a l f i n s f o r t h i s mode of swimming, however, they t u r n to subcarangiform motion when a c c e l e r a t i n g or when swimming f a s t and i n t h i s mode they use the caudal f i n . The remaining s p e c i e s use subcarangiform motion f o r most of t h e i r swimming a c t i v i t i e s . T h e r e f o r e , some.species of the genus Nannostomus have been used to analyse the p r e d i c t i o n s expected from the t h e o r e t i c a l a n a l y s i s o f f i s h swimming by L i g h t h i l l ' s models ( L i g h t h i l l , 1969, 1970, 1971) and with the improvements made on these models by Weihs (1972, 1973). S p e c i a l emphasis has been placed on the hydrodynamics of r a p i d s t a r t from r e s t . A more complete survey of f i s h swimming and the t h e o r e t i c a l c o n s i d e r a t i o n s i n v o l v e d are given i n L i g h t h i l l (1973, 1975) and Webb (1974).. 59 THEORETICAL ANALYSIS The purpose of t h i s s e c t i o n i s to b r i e f l y i n t r o d u c e and analyse L i g h t h i l l ' s (1971) la r g e - a m p l i t u d e elongate-body theory of f i s h locomotion and show the t h e o r e t i c a l r e l a t i o n s h i p between the t h r u s t generated by the caudal f i n , and i t s l a t e r a l bending (amplitude) and l a t e r a l v e l o c i t y . Then proceed to show the dependence.of amplitude and l a t e r a l v e l o c i t y on the v e r t e b r a l s i z e and number. The v e r t e b r a l s i z e and number of the two s l a n t i n g s p e c i e s Nannostomus egues and Nannostomus u n i f a s c i a t u s are compared to those of other Nannostomus s p e c i e s . I t i s expected t h a t the v e r t e b r a l s i z e and number of Nannostomus egues and Nannostomus u n i f a s c i a t u s w i l l show a d a p t a t i o n s of r a p i d s t a r t from r e s t as seen i n t h e i r g e n e r a l behaviour. Symbols In the f o l l o w i n g a n a l y s i s the f i s h w i l l be assumed to be swimming i n the p o s i t i v e x d i r e c t i o n i n a h o r i z o n t a l x, z plane. a Lagrangian c o o r d i n a t e along the f i s h ' s s p i n a l column which takes values 0 to L, o r i g i n a t i n g from the p o s t e r i o r end m V i r t u a l mass per u n i t l e n g t h xyz C a r t e s i a n c o o r d i n a t e s , x, z at r i g h t angles t o each other and forming a h o r i z o n t a l plane at y = 0 u H o r i z o n t a l v e l o c i t y component t a n g e n t i a l to the v e r t e b r a l column 60 w H o r i z o n t a l v e l o c i t y component p e r p e n d i c u l a r to the v e r t e b r a l column L i g h t h i l l ' s l a r ge-amplitude elongate-body theory of f i s h locomotion ( L i g h t h i l l , 1971) i s b a s i c a l l y a r e a c t i v e t h e o r y emphasizing the r e a c t i v e f o r c e s due to i n e r t i a between a s m a l l volume of water and the p a r t s o f the f i s h ' s s u r f a c e i n c o n t a c t with i t . I t can be used t o analyse l a r g e amplitude displacements of s l e n d e r c a u d a l f i n s (lobe angle l e s s than 30°) at r i g h t angles to the d i r e c t i o n of motion as i n v o l v e d i n r a p i d a c c e l e r a t i o n and t u r n i n g . The f o r c e s are con s i d e r e d from the r a t e . o f change of momentum and only the momentum changes produced by motions p e r p e n d i c u l a r t o the v e r t e b r a l column are considered and those. produced by t a n g e n t i a l motions are ne g l e c t e d . T h i s i s so because the v i r t u a l mass, m per u n i t l e n g t h i n r e s p e c t to motions p e r p e n d i c u l a r t o the v e r t e b r a l column i s l a r g e and the v i r t u a l mass due t o t a n g e n t i a l motions i s n e g l i g i b l e . The theory i s based on three p r i n c i p l e s : 1. Water momentum near a s e c t i o n of a f i s h i s i n a d i r e c t i o n p e r p e n d i c u l a r to the v e r t e b r a l column and has a magnitude mw. 2. Thrust i s obtained by c o n s i d e r i n g the r a t e of change of momentum wi t h i n a volume V e n c l o s i n g the f i s h whose boundary at each i n s t a n t i n c l u d e s a f l a t s u r f a c e S p e r p e n d i c u l a r to the caudal f i n through i t s p o s t e r i o r end. 3. In b a l a n c i n g the momentum, t r a n s f e r of momentum of the r e s u l t a n t 0.5mwz of the pressures generated by 61 motions w i t h i n the plane S are taken i n t o account. L i g h t h i l l (1971) obtained r T | | *b Z <)x| 1 ^ X C T - Z J l-mwul- --,--| + -mwz --,--| - (T, Q) | | Ca oa| 2 o a da| I L J | L J a=o _ 1 Where the l e f t hand s i d e i s the r a t e of change of the momentum i n V of the motions p e r p e n d i c u l a r t o v e r t e b r a l column (w motions) and on the r i g h t hand sid e are t h r e e components c o n t r i b u t i n g t o t h i s r a t e o f change. The f i r s t term i s the r a t e of change o f t h i s momentum out of V a c r o s s the. plane S, and repr e s e n t s a l o s s . The second term i s the r a t e of change of t h i s momentum due to the pressure f o r c e a c t i n g a c r o s s S, and re p r e s e n t s a gai n . The t h i r d term i s the in s t a n t e n e o u s r e a c t i v e f o r c e (T f Q) with which the water a c t s on the f i s h , where T i s the component i n the d i r e c t i o n of movement (x); i . e . , t h r u s t and Q s i d e f o r c e s . From eguation 1 I ^ z 1 £>x| T = |mwu— + -mw2--| + | 6 t 2 o a | L J A=0 I fcz bx| mw | - — , — |da = | ba ba\ L J 62 I t can be shown that t h i s e x p r e s s i o n can be s i m p l i f i e d to r i | ^z 1 ^x| T = | mw— - -mw2—| + | ^ t 2 ba| J a=0 From t h i s e x p r e s s i o n of t h r u s t two important c o n c l u s i o n s about the magnitude:of t h r u s t can be made which are of i n t e r e s t to the present a n a l y s i s . For the t h r u s t (T) to be l a r g e 1. bz/bt must be as l a r g e . a s p o s s i b l e . In p r a c t i c e t h i s would r e g u i r e the f i s h t o move i t s caudal f i n as f a r away as p o s s i b l e from the d i r e c t i o n of motion and a t as a high speed as p o s s i b l e . Thus, f o r the t h r u s t to be l a r g e , l a t e r a l amplitude must be l a r g e 2. w must be s m a l l because the p o s i t i v e terms i n eguation 3 ( f i r s t and t h i r d terms), are o n l y l i n e a r l y dependent on w, whereas the negative term depends on the square of w. T h i s means t h a t the t a i l should be moving r a p i d l y at a s m a l l p o s i t i v e angle with i t s o r i e n t a t i o n . Under these c o n d i t i o n s bx/ba. i s a l s o very s m a l l , f u r t h e r reducing the second term. Before l o o k i n g at the experimental m a t e r i a l another i n t e r e s t i n g t h e o r e t i c a l work must be i n t r o d u c e d , Spouge and L a r k i n (1979) used elongate-body theory of L i g h t h i l l (1970) i n an attempt to e x p l a i n pleomerism. Although t h i s theory does not take i n t o c o n s i d e r a t i o n l a r g e p e r t u r b a t i o n s i n v o l v e d i n f a s t s t a r t i n g , some of t h e i r c o n c l u s i o n s and c o r o l l a r i e s are s t i l l d dt * z mw—da ba 63 r e l e v a n t t o t h i s study. They showed t h a t the formulae f o r time-averaged t h r u s t f o r a n g u i l l i f o r m and carangiform motions are approximately the same. Secondly, they demonstrated that the maximal l a t e r a l v e l o c i t y of the t a i l and t h e r e f o r e the t h r u s t depends on the r e l a t i v e number of locomotor v e r t e b r a e and the s i z e of the caudalmost v e r t e b r a . L a s t l y , i n f i s h of same shape swimming under the same c o n d i t i o n s , the speed i n c r e a s e s i f more of the f i s h ' s l e n g t h i s devoted to locomotor vertebrae. We have seen above the c o n d i t i o n s which i n c r e a s e t h r u s t . Now I w i l l c o n s i d e r l a t e r a l bending of the caudal f i n (amplitude) and i t s l a t e r a l v e l o c i t y . In a t y p i c a l f i s h both amplitude and maximum l a t e r a l v e l o c i t y of the caudal f i n i n c r e a s e d u r i n g r a p i d s t a r t from r e s t (Bainbridge, 1958, 1963; Weihs, 1973). Maximum l a t e r a l v e l o c i t y w i l l depend on the muscle p u l l on the caudalmost v e r t e b r a (see Spouge and L a r k i n , 1979 f o r d e t a i l e d a n a l y s i s ) and the amplitude w i l l depend on the f l e x i b i l i t y of the body musculature and v e r t e b r a l column i n f r o n t of the caudalmost v e r t e b r a . During a r a p i d s t a r t from r e s t the. f i s h makes l a r g e l a t e r a l bends t h a t make the caudal r e g i o n almost L-shaped so the caudal v e r t e b r a e which support the u r a l fan must a c t as one u n i t . . T h e r e f o r e the s i z e of the caudalmost v e r t e b r a given below i s the mean s i z e of the l a s t t h r e e vertebrae which support the u r a l fan i n Nannostomus s p e c i e s . I f we assume the muscle d i s t r i b u t i o n i n the caudal r e g i o n of the s p e c i e s of Nannostomus s t u d i e d here i s s i m i l a r , then f l e x i b i l i t y o f the caudal r e g i o n i n f r o n t of the caudalmost v e r t e b r a w i l l depend on the number and s i z e of locomotor 64 v e r t e b r a e . The v e r t e b r a l column may be viewed as a segmented beam around which the muscles are organised i n m u s c l e - f i b r e t r a j e c t o r i e s i n the sense o f Alexander (1969); i . e . , the e f f e c t of a muscle f i b r e i s continued a c r o s s the myoseptum by t h e : f i b r e d i r e c t l y o p p o s i t e i t and so on f o r some d i s t a n c e , so t h a t these f i b r e s a c t as u n i t s i n bending s e v e r a l vertebrae (Laerm, 1976). I t can be seen then from such a biomechanical model t h a t i n c r e a s i n g the v e r t e b r a l number w i l l a l s o i n c r e a s e the r a d i u s o f c u r v a t u r e of the body waves as w e l l as t h e i r amplitude, i f they i n v o l v e long a b s o l u t e zones as i n e e l s (Willemse, 1975, 1977). In bends t h a t i n v o l v e s h o r t absolute zones, the amplitude may be i n c r e a s e d by decreasing the v e r t e b r a l s i z e and/or i n c r e a s i n g i n t e r v e r t e b r a l c h o r d a l t i s s u e , willemse (1977) g i v e s a d e t a i l e d a n a l y s i s f o r the bending of the t a i l o f Mexican a x o l o t l , Siredon mexicanum (Shaw). In t h i s study anatomical and morphological a n a l y s e s of the a x i a l and caudal systems were done to r e l a t e these s t r u c t u r e s to the i n t e r p r e t a t i o n s of these models of swimming. S p e c i a l emphasis has been placed on the t o t a l number of v e r t e b r a e , number and s i z e of locomotor vertebae and how they r e l a t e t o l a t e r a l bending of the caudal f i n and t h e ; s t r u c t u r e of the caudal f i n i t s e l f . F u r t h e r emphasis has been placed on r a p i d s t a r t from r e s t which on a small s c a l e seem to be a major s t r a t e g y of Nannostomus egues and Nannostomus u n i f a s c i a t u s compared with other nannostomines. M a t e r i a l s and Methods Nannostomus s p e c i e s used i n the anatomical s t u d i e s came 6 5 from the P e r u v i a n Amazon. The f i s h were c l e a r e d and s t a i n e d i n a l i z a r i n r e d a c c o r d i n g to the method of T a y l o r (1967). The v e r t e b r a e and caudal f i n elements were a l l counted on c l e a r e d and s t a i n e d specimens using b i n o c u l a r d i s s e c t i n g microscope. The v e r t e b r a l s i z e s were measured with an o c u l a r s c a l e i n the d i s s e c t i n g microscope and a standard c a l i b r a t e d stage s l i d e . The measurement of each v e r t e b r a excluded the, i n t e r v e r t e b r a l r e g i o n . Although the i n t e r v e r t e b r a l r e g i o ns play an important r o l e i n the l a t e r a l bending of the v e r t e b r a l column (Ford, 1937; Laerm, 1976; Willemse, 1977), they were too s m a l l to be measured a c c u r a t e l y . AXIAL SYSTEM S t r u c t u r a l l y three regions can be d i s t i n g u i s h e d i n the v e r t e b r a l column of c h a r a c o i d f i s h e s , the Weberian apparatus vertebrae, precaudal vertebrae, and caudal v e r t e b r a e . The Weberian apparatus vertebrae are c o n s t a n t l y f o u r i n a l l the s p e c i e s s t u d i e d here, which i s a t y p i c a l c h a r a c o i d c h a r a c t e r (Weitzman, 1962; Rosen and Greenwood, 1970; Roberts, 1969, 1973). The precaudal vertebrae are those without a hemal sp i n e and u s u a l l y with p l e u r a l r i b s , and c a u d a l vertebrae are those i n which the hemal spine i s present with a hemal c a n a l at the base through which the blood v e s s e l s pass. The t r a n s i t i o n from precaudal t o caudal v e r t e b r a e i s not abrupt. There i s an i n t e r m e d i a t e t r a n s i t i o n a l r e g i o n i n which the hemal c a n a l i s present but the hemal spine i s not. A few o f the v e r t e b r a e adjacent to the precaudal region may have s m a l l , s h o r t p l e u r a l r i b s . 66 In carangiform motion, i n which the amplitude . of the p r o p u l s i v e wave i n c r e a s e s caudad s t a r t i n g somewhere a f t e r h a l f way along the body, the r i b b e d precaudal r e g i o n apparently does not c o n t r i b u t e s i g n i f i c a n t l y to p r o p u l s i o n . T h e r e f o r e , the caudal v e r t e b r a e are here termed locomotor v e r t e b r a e i n the sense of Spouge and L a r k i n (1979), as those v e r t e b r a e a c t i v e l y i n v o l v e d i n p r o p u l s i o n and the remainder of v e r t e b r a l column, precaudal and Weberian apparatus vertebrae are r e f e r r e d to as s t r u c t u r a l v e r t e b r a e . V e r t e b r a l number and s i z e V e r t e b r a l s i z e has been expressed as a p r o p o r t i o n of the standard l e n g t h of the f i s h to allow comparison of v e r t e b r a l s i z e between d i f f e r e n t s i z e s and s p e c i e s of Nannostomus. Table 4 g i v e s a summary of t h e . v e r t e b r a e number i n the t h r e e r e g i o n s of the v e r t e b r a l column, and mean v e r t e b r a s i z e i n the c a u d a l r e g i o n . Vertebrae count f o r other Nannostomus s p e c i e s as reported i n Weitzman (1966) are i n c l u d e d f o r comparison because h i s samples covered more s p e c i e s and wider range.. F u n c t i o n a l r e g r e s s i o n s of mean caudalmost and locomotor vertebrae s i z e s versus standard l e n g t h f o r the f o u r s p e c i e s s t u d i e d here are given i n f i g u r e s 10, 11, 12, and 13. A l l r e g r e s s i o n s are s i g n i f i c a n t at P(0.05) l e v e l . Covariance a n a l y s i s was performed on the r e g r e s s i o n s t o t e s t f o r e g u a l i t y of s l o p e s (b) and i n t e r c e p t s (a) between the s p e c i e s . The t e s t f o r the hypothesis of common slope f o r the four s p e c i e s with the n u l l h y p o t h e s i s as: H : b1 = b2 = b3 = b4 was not s i g n i f i c a n t at P(0.05) l e v e l , and gave common s l o p e s of 0.016 67 f o r caudalmost v e r t e b r a e and 0.019 f o r locomotor- v e r t e b r a e , so th a t the n u l l hypothesis of common slope was accepted. However, a t e s t f o r the common equation; i . e . , t e s t i n g f o r the i n t e r c e p t s i n c e t h e r e i s a common s l o p e , was r e j e c t e d at P(0.05) l e v e l . When Nannostomus egues and Nannostomus u n i f a s c i a t u s which swim o b l i g u e l y are t e s t e d together f o r a common r e g r e s s i o n eguation, t h e r e i s no s i g n i f i c a n t d i f f e r e n c e i n the i n t e r c e p t f o r both caudalmost and locomotor vertebrae g i v i n g the f o l l o w i n g common eguations: Y = 0.017 + 0.014X f o r caudalmost vertebrae Y = 0.053 + 0.017X f o r locomotor vertebrae A separate t e s t f o r the i n t e r c e p t i n Nannostomus t r i f a s c i a t u s and Nannostomus b e e f o r d i shows a s i g n i f i c a n t d i f f e r e n c e at P(0.05) f o r both caudal and locomotor v e r t e b r a e . s Covariance a n a l y s i s i n v a r i o u s combinations f o r these s p e c i e s shows t h a t the caudalmost v e r t e b r a e r e g r e s s i o n of Nannostomus t r i f a s c i a t u s has a common eguation Y = 0.002 + 0.014X with those f o r Nannostomus egues and Nannostomus u n i f a s c i a t u s , but that the locomotor v e r t e b r a r e g r e s s i o n s d i f f e r . I n a d d i t i o n , Nannostomus b e e f o r d i i s very d i f f e r e n t from the r e s t . 68 Table 4. Vertebrae number and s i z e i n Nannostomus s p e c i e s . F i g u r e s i n pare n t h e s i s f o r vertebrae number are from Weitzman (1966). VERTEBRAE NUMBER f SPECIES Nannostomus egues Nannostomus u n i f a s c i a t u s Nannostomus t r i f a s c i a t u s Nannostomus b e e k f o r d i CAUDAL 14- 15 (15) 13 (12-13) 16-17 (16-17) 15- 17 (15-16) PRECAUDAL 19 (18-19) 21 (21) 19 (19) 18-19 (18-20) MEAN VERTEBRAE SIZE/S.L. CAUDALMOST 0.0143 ± .0004 0.0146 ± .0003 0.0147 ± .0006 0.0167 ± .0007 LOCOMOTOR 0.0189 ± .0003 0.0190 ± .0003 0.0194 ± .0003 0.0207 ± .0005 69 Table 4 continued i T — ; T • ~\ I I VERTEBRAE NUMBER | MEAN VERTEBRAE SIZE/S.L. | i SPECIES | CAUDAL | PRECAUDAL| CAUDALMOST j LOCOMOTOR | INannostomus | | I j I I b i f a c i a t u s | (17) | (19) | I I I Nannostomus i l l I I | diqrammus | (15-16) | (18-19) | | | I Nannostomus I . I I 1 I I esjgei I (15) | (18) | | I I Nannostomus | I I I . I I h a r r i s o n i | (17-18) | (21) | | I I Nannostomus I I I I I | marqina tus | (13-14) | (17-19) | I I 70 F i g u r e IQ. Caudalmost and locomotor v e r t e b r a s i z e - S t a n d a r d l e n g t h r e g r e s s i o n f o r Nannostomus u n i f a s c i a t u s C A U D A L M O S T V E R T E B R A S I Z E V S S T A N D A R D L E N G T H Y = - 0 . 29B9E -01 * 0.1578E-01OC N = I S SO- H I . SS- H 3 . B 4 - 5 5 - S S - 2 7 . 2 B - B 9 - 3 0 -S T A N O A R D L E N G T H I N M M L O C O M O T O R V E R T E B R A S I Z E V S S T A N D A R D L E N G T H Y = O-lCea * 0.1-493E-01-X z n kl Ul N 15 B O . B l . 2 S « H3> E 4 H 7 - S B - 5 3 . 3 0 . S T A N D A R D L E N G T H I N M M 71 F i g u r e U m Caudalmost and locomotor v e r t e b r a s i z e - S t a n d a r d l e n g t h r e g r e s s i o n f o r Nannostomus egues C A U D A L M O S T V E R T E B R A S I Z E V S S T A N D A R D L E N G T H y = C - I S S S E - O l • 0.13G9E-01»X N 0 - 6 0 , . I S H 1 1 J ±_ 5 0 A . B 2 . H 3 . 2 4 - f f i . B S . B 7 . a B . 2 3 - 3 0 - 3 1 - 3 B - 3 3 . 3 4 - 3 5 STANDARD LENGTH IN MM L O C O M O T O R V E R T E B R A SI Z E V S S T A N D A R D L E N G T H Y = 0-EB4GE-O1 * 0-1789E-01»X N 15 e 0 - E l . B 2 . S 3 - 2 4 . 2 5 . c e . 5 7 . c 9 . ? 3 . 3 0 . 3 1 . 3 2 . 3 3 . 3 4 . 3 5 . STANDARD LENGTH IN MM 72 F i g u r e 12. Caudalmost and locomotor v e r t e b r a s i z e - S t a n d a r d a r d l e n g t h r e g r e s s i o n f o r Nannostomus b e e f o r d i C A U D A L M O S T V E R T E B R A S I Z E V S S T A N D A R D L E N G T H Y = - 0 - 5 G 0 7 E - 0 1 • 0 - 1 B B 3 E - O 1 - X N = 1 8 0-70 _ Z-H in SO- SI- SS- S3- 2 4 . SS- SS- S7- SB- S3- 30- 3 1 - 3 2 - 3 3 -STANDARD LENGTH IN K M L O C O M O T O R V E R T E B R A S I Z E V S S T A N D A R D L E N G T H Y = - O . S S 4 7 E - 0 1 • 0 - 2 E 0-75 _ - 0 1 » X N = I S 2 0 - 2 1 . 2 2 . 2 3 - 2 4 - 2 5 . 2 S « 2 7 - 2 8 - 2 3 - 3 0 - 3X- 35- 33-STAMHAfJD LENGTH IN K M 73 F i g u r e 13. Caudalmost and locomotor v e r t e b r a s i z e - S t a n d a r d l e n g t h r e g r e s s i o n f o r Nannostomus t r i f a s c i a t u s C A U D A L M O S T V E R T E B R A S I Z E V S S T A N D A R D L E N G T H Y = - 0 - 3 E 7 3 E - 0 1 * O - 1 5 B 3 E - 0 1 - X N = 1 2 O-GO _ 1 5 - 0 1 7 - 0 1 3 - 0 2 1 - 0 2 3 - 0 2 5 - 0 2 7 - 0 5 9 - 0 3 1 - 0 3 3 - 0 3 5 - 0 S T A N 3 A R O L E N G T H I N M M L O C O M O T O R V E R T E B R A S I Z E V S S T A N D A R D L E N G T H Y = - 0 ' 7 0 4 E E - 0 1 + 0 ' E 1 7 B E - 0 1 » X N - 1 5 0 - 7 0 3 0 - G G . . z o-es.. H O'SB .. Ul 0 - S 4 . . i 0 - 5 0 . . 0 . 4 S . . 5 0 - 4 2 . . 0 - 3 8 . . 0 - 3 4 . . 0 - 3 0 1 5 - 0 1 7 . 0 1 9 - 0 2 1 - 0 B 3 . 0 5 5 . 0 E 7 . 0 5 9 - 0 3 1 - 0 3 3 - 0 3 5 - 0 S T A N D A R D L E N G T H I N M M 74 CAUDAL FIN I n t r o d u c t i o n In the p r o g r e s s i o n of f i s h p r o p u l s i o n from a n g u i l l i f o r m t o carangiform modes, th e r e have been e l a b o r a t i o n and more involvement of the caudal f i n as a major source .of p r o p u l s i v e f o r c e . There are p r i m a r i l y two l i n e s of e l a b o r a t i o n o f the caudal f i n and the adjacent a x i a l system f o r p r o p u l s i v e e f f i c i e n c y . One l i n e : i n c l u d e s group of f a s t swimmers and p e l a g i c c r u i s e r s . The s t r a t e g y here i s to minimise drag due to v o r t e x shedding at the t r a i l i n g edge while producing s u f f i c i e n t p r o p u l s i v e f o r c e . The caudal f i n i n t h i s l i n e ranges from the h i g h l y swept-back forms (e.g., i n some c a r a n g i d s , such as S e r i o l a ) t o the lunate caudal f i n s common i n tuna and t u n a - l i k e f i s h e s with a l a r g e aspect r a t i o ( N u r s a l l , 1958). L i g h t h i l l (1970) and Chopra (1974) give d e t a i l s of the hydrodynamical i > advantages of t h i s f i n and the s t r u c t u r a l m o d i f i c a t i o n s a s s o c i a t e d with i t , such as narrowing of the cau d a l peduncle and f u r t h e r enlargement and f l a t t e n i n g o f the trunk r e g i o n . The other l i n e of development i s the one which produced caudal f i n s of r e l a t i v e l y l a r g e area, round or moderately lobed and with a low t o in t e r m e d i a t e aspect r a t i o . The f i n i s u s u a l l y f l e x i b l e i n terms of independent a c t i v i t i e s of the lobes and ray movements. T h i s f i n i s s u i t e d f o r high a c c e l e r a t i o n and ma n e u v e r a b i l i t y . In a sudden s t a r t from r e s t where the angle o f attack of the caudal f i n i s u s u a l l y very l a r g e and moves l a t e r a l l y at high speed, a h i g h l y swept-back t a i l would s t a l l and conseguently i s u n s u i t a b l e f o r high a c c e l e r a t i o n . 75 However, the majority of the f i s h have c a u d a l f i n s which are compromises between the extremes of these l i n e s . Thus i t becomes d i f f i c u l t i n these i n t e r m e d i a t e forms to r e l a t e s t r u c t u r e and f u n c t i o n to p a r t i c u l a r modes of l i f e and swimming s t r a t e g i e s , although some e f f o r t s have been made (Nag, 1967; Eybachuk, 1976). Because of the p e c u l i a r h a b i t o f o b l i g u e swimming i n the f i s h s t u d i e d here, i t i s of i n t e r e s t t o compare t h e i r c a u d a l f i n s with those of t h e i r c l o s e l y - r e l a t e d h o r i z o n a t a l l y swimming r e l a t i v e s . T h i s a n a l y s i s i s aimed at i d e n t i f y i n g m o rphological and anatomical adaptations and r e l a t i n g t h e i r f u n c t i o n a l s i g n i f i c a n c e t o the. l i f e s t y l e and swimming h a b i t s of these f i s h . Terminology Most of the c a u d a l f i n t e r m i n o l o g i e s were . developed i n e i t h e r d e s c r i p t i v e s y s t e m a t i c works or anatomical works concerned with e s t a b l i s h i n g p h y l e t i c r e l a t i o n s h i p s of f i s h e s ( H o l l i s t e r , 1936; G o s l i n e , 1961a, b; N y b e l i n , 1963; P a t t e r s o n , 1968)..As a r e s u l t f u n c t i o n a l u n i t s of the c a u d a l f i n elements are not very c l e a r from these t e r m i n o l o g i e s . Whitehouse (1910) d e f i n e d most elements as f u n c t i o n a l u n i t s . His t e r m i n o l o g i e s are misleading i f one c o n s i d e r s i n t e r r e l a t i o n s h i p s i n terms of the s t r u c t u r e , o r i g i n and homologies of the elements, h i s d e f i n i t i o n s are s t i l l u s e f u l i f one c o n s i d e r s only the f u n c t i o n a l a s p e c t s of the v a r i o u s elements of the caudal f i n . In t h i s study the b a s i c terminology of Nybelin (1963) w i l l be used because i t o f f e r s a good b a s i s f o r comparison among 76 d i f f e r e n t s p e c i e s , e s p e c i a l l y with regard t o the v e r t e b r a l elements s u p p o r t i n g the caudal f i n . Some m o d i f i c a t i o n s i n terminology of u r o n e u r a l s and hypurals from Nybelin's (1963) w i l l a l s o be used (Pa t t e r s o n , 1968; Monod, 1968). Thus the vertebrae w i l l be i d e n t i f i e d with r e f e r e n c e t o the one b e a r i n g the l a s t hemal arch; i . e . , the f i r s t p r e - u r a l v e r t e b r a (P01). Vertebrae p o s t e r i o r t o PU1 w i l l be counted caudad i n i n c r e a s i n g order as u r a l v e r t e b r a e . 0 1 , U2, e t c . a n t e r i o r to P01, v e r t e b r a e w i l l be counted c r a n i a d as PU2, PU3, PU4, and so on. Uroneurals are d e f i n e d as p a i r e d bones d i r e c t e d upwards and backwards, l o c a t e d on the l a t e r a l and d o r s a l f a c e s of the u r o s t y l e ( P a t t e r s o n , 1968; Harder, 1976). C a r e f u l d i s s e c t i o n of the p r e s e n t s p e c i e s r e v e a l e d t h a t the t e r m i n a l upturned p a r t o f the compound v e r t e b r a which has commonly been termed the u r o s t y l e i n c h a r a c o i d s (Weitzmann, 1962; Roberts, 1969, 1974) i s a c t u a l l y a p a i r of uroneurals as i n d i c a t e d i n the c a u d a l s t r u c t u r e of c h a r a c o i d s by Rosen and Greenwood (1970). Therefore counts of uroneurals i n t h i s study show one more than the number reported i n previous s t u d i e s of t h i s group which c a l l e d the f i r s t u r o n e r a l the u r o s t y l e . . The hemal spine of PU1 w i l l be termed parhypural a f t e r Monod (1968), because i t i s a d i s t i n c t i v e s t r u c t u r e which i combines the f u n c t i o n s of hemal s p i n e s and h y p u r a l elements and i n most s p e c i e s c a r r i e s the d i s t i n c t i v e spine, the parhypuraphysis, f o r the. attachment of the hypochordal l o n g i t u d i n a l muscles (Nursal, 1963b). Caudal f i n muscle terminology w i l l f o l l o w t h a t of N u r s a l (1963a). 77 A b b r e v i a t i o n s used i n f i g u r e s EP E p i u r a l HS Hemal spine HYP Hypural element NS Neural s p i n e PHYP Par h y p u r a l element PO P r e u r a l v e r t e b r a SPNP S p e c i a l i z e d n e u r a l process 0 U r a l v e r t e b r a UN Uroneur.al Caudal f i n o f Nannostomus The only o s t e o l o g i c a l study of the t r i b e Nannostomini (Weitzman, 1964) d i d not deal with the cau d a l f i n . N e v e r t h e l e s s , s i n c e the caudal f i n of Nannostomus egues and Nannostomus u n i f a s c i a t u s i s always used to e x p l a i n t h e i r s l a n t i n g o r i e n t a t i o n , i t was deemed necessary t o d e s c r i b e i n d e t a i l the osteology of the nannostomine caudal f i n . The p a t t e r n of the nannostomine caudal s k e l e t o n i s very s i m i l a r i n a l l the s p e c i e s examined i n t h i s study: Nannostomus b e e f o r d i , Nannostomus egue, Nannostomus t r i f a s c i a t u s and Nannostomus u n i f a s c i a t u s . The f i r s t p r e - u r a l v e r t e b r a i s f u s e d to the u r a l v e r t e b r a forming a compound v e r t e b r a . The p o s t e r i o r end of t h i s compound vertebra curves at an angle p o i n t i n g upwards and backwards. Behind the compound v e r t e b r a there are two p a i r s of u r o n e u r a l s , the f i r s t (UN1) a r t i c u l a t i n g d i r e c t l y with the compound v e r t e b r a . D i s s e c t i o n show t h a t the f i r s t p a i r of the u r o n e u r a l s (UN1) end as f l a n k s on the s i d e s of the 78 p o s t e r i o r end of the compound v e r t e b r a . The second p a i r o f uroneurals (UN2) i s smal l and i s h e l d l o o s e l y p o s t e r i o r to the f i r s t p a i r s t a r t i n g at the base o f the t h i r d h y p u r a l . In some specimens, e s p e c i a l l y i n Nannostomus ec[ues and Nannostomus u n i f a s c i a t u s , the second p a i r i s completely f r e e of t h e . f i r s t p a i r . The u r o n e u r a l s and the parhypural form a wide V opening backwards and i n between them there are always s i x h y p u r a l p l a t e s . The second h y p u r a l p l a t e i s always c o n t i n o u s with the compound centrum and the remaining f i v e . h y p u r a l s are autogenous. Hypurals 4-6 are anchored between the two halves of the second uroneural. In a l l the nannostomine s p e c i e s examined there are always 2 e p i u r a l s (Figure 14) The f u n c t i o n a l caudal f i n i n c o r p o r a t e s PU2 and P03 which support some of the p r o c u r r e n t c a u d a l f i n rays. P04 forms the a n t e r i o r boundary of the u r a l f a n . The hemal s p i n e s of P03, PD2 and the par h y p u r a l are elongated and f l a t t e n e d f o r the f u n c t i o n of s u p p o r t i n g the f i n r a y s . The pa r h y p u r a l supports the l a s t 2 p r i n c i p a l f i n r a y s and the hemal spines of PU3 and PU2 support the p r o c u r r e n t r a y s . The n e u r a l spine of PU3 i s f l a t t e n e d and elongated to support the l a s t few p r o c u r r e n t r a y s of the d o r s a l l o b e . The n e u r a l spine of PD2 i n most specimens of nannostomine s p e c i e s examined i s modified i n t o a shor t and much broadened p l a t e l o o k i n g very much l i k e the s p e c i a l i s e d n e u r a l process o f the compound centrum. Above these, two s p e c i a l i s e d n e u r a l processes are the two e p i u r a l s which support the remaining procurrent r a y s . However, i n some few cases t h e . n e u r a l s p i n e , of PU2 i s as f l a t t e n e d and elongated as t h a t of PD3 and extends out 79 to support the p r o c u r r e n t rays. The muscles which o r i g i n a t e from the s p e c i a l i s e d n e u r a l process and the base of PU3 and PU2 n e u r a l arches are the deep d o r s a l f l e x o r muscles which take part i n the:movements of the i n d i v i d u a l rays of the d o r s a l l o b e of the caudal f i n . As d e s c r i b e d i n the swimming modes, the ray s of the d o r s a l lobe are i n constant motion, c r e a t i n g a s e r i e s of c o n t i n o u s waves from the top f r e e end to the mid r e g i o n of the f i n , whereas the lower lobe remains r e l a t i v e l y i n a c t i v e . T h e r e f o r e the m o d i f i c a t i o n o f the n e u r a l spine of PU2 i n t o a l a r g e f l a t s u r f a c e i s i n t e r p r e t e d as an a d a p t a t i o n to p r o v i d e . a l a r g e s u r f a c e : area f o r the attachment of the deep d o r s a l f l e x o r muscles. Examination of the parhypural show no development of the parhypuraphysis f o r the attachment of the hypochordal l o n g i t u d i n a l muscles. These muscles are attached from the mid p a r t of the compound ,centrum c o n t i n u i n g to the lower p a r t of the parhypural and f i r s t h y p u r a l p l a t e . There i s a s m a l l knob on t h i s muscle's p o i n t of attachment on the compound centrum. In a l l the s p e c i e s there are 10 p r i n c i p a l c a u d a l f i n r a y s o r i g i n a t i n g from the d o r s a l hypurals (HYP3 - HYP6) and 9 o r i g i n a t i n g from the lower lobe, the parhypural and the f i r s t 2 h y p u r a l s . T h i s ray formular of 10+9 i s c h a r a c t e r i s t i c of a l l c h a r a c o i d s (Weitzman, 1962, 1964; Roberts, 1969, 1973). However, i n the two s p e c i e s Nannostomus- egues and Nannostomus u n i f a s c i a t u s , two of the p r i n c i p a l rays o r i g i n a t i n g from the upper lobe HYP3, end e x t e r n a l l y i n the lower lobe of the caudal f i n . In a d d i t i o n , the p r i n c i p a l r a y s of the lower lobe are l a r g e r towards the margin because of t h e i r branching, 80 while at the same time those rays towards the outer edge adjacent t o the p r o c u r r e n t rays grow much longer than those of the d o r s a l l o b e . The s t r u c t u r a l r e s u l t i s an e x t e r n a l l y asymmetrical c a u d a l f i n with the lower lobe l a r g e r than the d o r s a l lobe (Figure 15). The t r a i l i n g p o i n t s of the l o b e s are smooth and round thus i n c r e a s i n g t o t a l area of the f i n . U n l i k e these two s p e c i e s , the others have e x t e r n a l l y symmetrical caudal f i n s with sharp t r a i l i n g p o i n t s on the l o b e s , thus reducing the s u r f a c e area and drag, much as i n f a s t swimmers. Caudal f i n of T h a y e r i a o b l i g u a T h a y e r i a o b l i g u a i s another c h a r a c o i d f i s h which swims with a head-up o r i e n t a t i o n l i k e the p e n c i l f i s h Nannostomus egues and Nannostomus u n i f a s c i a t u s , and t h e r e f o r e i t s c a u d a l morphology and anatomy i s a l s o worth comparing. The b a s i c p a t t e r n of the caudal s k e l e t o n i s the t y p i c a l c h a r a c o i d type d e s c r i b e d f o r Nannostornus. There - are 2 e p u r a l s and 2 p a i r s of u r o n e u r a l s . The second p a i r of u r o n e u r a l s i s not f r e e , as i n Nannostomus, but i s t i g h t l y held t o the f i r s t p a i r and extends down n e a r l y to the o r i g i n of the t h i r d hypural where i t i s wedged (Figure 16). The n e u r a l arch of PU2 v e r t a b r a i s enlarged l i k e t h a t o f Nannostomus to provide a l a r g e surface f o r deep d o r s a l f l e x o r muscles.. However the n e u r a l spine i s not modified but extends outwards to support the. d o r s a l l o b e p r o c u r r e n t r a y s . The f u n c t i o n a l caudal f i n extends up to PU4. PU5 forms the a n t e r i o r boundary of the u r a l f a n . The involvement of PU4 i n s u p p o r t i n g the p r o c u r r e n t r a y s appears to be r e l a t e d t o the 81 i n c r e a s e d number of these rays, 9 - 1 0 on the d o r s a l edge and 8-9 v e n t r a l l y . There i s no true parhpuraphysis, but there i s a l a t e r a l e l e v a t i o n forming a s h e l f from the middle of the compound centrum and c o n t i n u i n g i n t o the base of the p a r h y p u r a l . The hypochordal l o n g i t u d i n a l muscles a t t a c h on t h i s e l e v aton and on the base of the f i r s t h y p u r a l . The p r i n c i p a l caudal ray formula i s 10+9 j u s t as i n a l l other Characoids. However, the rays of the lower l o b e , e s p e c i a l l y those near the outer margin are l o n g e r and have l a r g e r spaces between them than t h e i r c o u n t e r p a r t s on the upper l o b e . In a d d i t i o n , the rays of the:lower lobe l e a v e the base at a l a r g e r angle (lobe angle) than the upper lobe r a y s . The r e s u l t i s an asymmetrical caudal f i n with the lower lobe l a r g e r than the upper.. T h i s asymmetry, which i s a l s o found i n T h a y e r i a b o e h l k e i i s exaggerated from a d i s t a n c e because the black band on the lower lobe c o n t r a s t s with the h y a l i n e upper lobe. Caudal f i n s of C h i l o d u s punctatus and Leporinus maculatus The c a u d a l s k e l e t o n s of C h i l o d u s punctatus- and Leporinus maculatus are very s i m i l a r . Both are the t y p i c a l c h a r a c o i d type. There are 3 e p u r a l s and two p a i r s of u r o n e u r a l s , the second p a i r being t i g h t l y attached to the f i r s t and wedged a t the base. In Leporinus maculatus there i s v a r i a b i l i t y i n the.nature of the second p r e u r a l v e r t e b r a and i t s hemal s p i n e . In some specimens the s t r u c t u r e i s s h o r t and does not reach out to support the p r o c u r r e n t rays and i n others i t reaches out normally as t h a t o f C h i l o d u s punctatus (Figure 1 7 ) . The main f u n c t i o n a l d i f f e r e n c e between the two s p e c i e s i s 82 t h a t PU4 i n Leporinus maculatus supports the c a u d a l f i n and PU5 forms the a n t e r i o r margin of the u r a l f a n , whereas i n C h i l o d u s punctatus the caudal f i n i s supported o n l y by PU2 and PU3, while PU4 forms the a n t e r i o r margin of the u r a l f a n . Moreover, i n Ch i l o d u s punctatus only the hemal spine o f PU3 supports the procu r r e n t r a y s of the lower lobe and i t s n e u r a l spine i s not i n v o l v e d i n s u p p o r t i n g the d o r s a l p r o c u r r e n t r a y s . . These d i f f e r e n c e s are t o be expected as Leporinus maculatus i s much more a c t i v e than C h i l o d u s punctatus and always uses the caudal f i n i n subcarangiform mode. Chilodus punctatus i s a l e s s a c t i v e swimmer s t a y i n g s l a n t e d most of the time and u s i n g subcarangiform mode of locomotion only when escaping. Caudal f i n of A_bramist.es microeephalus T h i s c a u d a l f i n i s the t y p i c a l c h a r a c o i d type, very s i m i l a r to that of Ch i l o d u s punctatus. P03 i s t h e . l a s t v e r t e b r a i n caudal f i n support and PU4 forms the a n t e r i o r margin of the u r a l f a n . As i n C h i l o d u s punctatus, only the hemal spine of P03 supports the proc u r r e n t r a y s , while i t s n e u r a l spine i s s h o r t and s i m i l a r to those a n t e r i o r t o i t (Figure 18). 85 F i g u r e 16 Caudal s k e l e t o n o f ThaY.eria o b l i g u a 87 F i g u r e 18. Caudal s k e l e t o n of A b r a m i s t e s a i c r o c e p h a l u s NS _ EP1 HYP4 88 GENERAL DISCUSSION From the r e l a t i v e p o s i t i o n s of the c e n t r e . of mass and centre of buoyancy i n Nannostomus egues, Nannostomus u n i f a s c i a t u s , and C h i l o d u s punctatus,- i t i s e v i d e n t t h a t p i t c h i n g moments which could o r i g i n a t e from the s e p a r a t i o n o f these two c e n t r e s along the l o n g a x i s of the. body are not r e s p o n s i b l e f o r the o b l i g u e o r i e n t a t i o n s observed. In f a c t , the p o s i t i o n s of these c e n t r e s are the reverse of what would be expected from simple h y d r o s t a t i c s . These r e s u l t s are i n c o n t r a s t to Hoedeman's (1974) s p e c u l a t i o n t h a t the sharp narrowing of the swimbladder i n Nannostomus egues and Nannostomus•unifasciatus would give l e s s upward pressure and t h e r e f o r e be r e s p o n s i b l e f o r t h e i r s l a n t e d posture. The nature and form of the swimbladder i n themselves cannot be used to e v a l u a t e . p i t c h i n g moments. For example, c h a r a c o i d f i s h e s show gre a t v a r i a t i o n i n the r e l a t i v e p r o p o r t i o n s of the a n t e r i o r and p o s t e r i o r lobes of the swimbladder (Rowntree, 1903; Nelson 196 1) so i t i s not p o s s i b l e to simply c o r r e l a t e these d i f f e r e n c e s with the angles of o r i e n t a t i o n , without a l s o t a k i n g i n t o account the d i s t r i b u t i o n o f body mass. And even when laws of h y d r o s t a t i c s are a p p l i e d , as i n t h i s study, the p i t c h i n g moments caused by the s e p a r a t i o n of the c e n t r e of mass and c e n t r e o f buoyancy do not n e c e s s a r i l y account f o r the o r i e n t a t i o n of l i v e f i s h , as we have seen with Nannostomus egues x Nannostomus u n i f a s c i a t u s , and C h i l o d u s punctatus. The r e s u l t s f o r these t h r e e s p e c i e s suggest that they use the a c t i o n of t h e i r f i n s t o maintain the s l a n t i n g o r i e n t a t i o n and do so at the expense of r e v e r s e d mass d i s t r i b u t i o n . 89 Nannostomus egues and Nannostomus u n i f a s c i a t u s use both p e c t o r a l and caudal f i n to c r e a t e the p i t c h i n g moment. The. main l i f t i n g component comes from the p e c t o r a l f i n s , as t h e i r removal completely e l i m i n a t e d upward-slanting o r i e n t a t i o n . The i n f l u e n c e of the caudal f i n seems t o be only supplementary, because i t s removal does not change the angle of o r i e n t a t i o n ; i n s t e a d , the p e c t o r a l f i n s i n c r e a s e t h e i r b e a t i ng r a t e t o compensate f o r the l o s s . The movements of the caudal f i n a l s o suggest t h a t i t s main c o n t r i b u t i o n t o the. r a i s i n g of the head comes from i t s upper l o b e , c o n t r a r y to the g e n e r a l view t h a t the lower lobe i s the prime c o n t r i b u t o r (Hoedeman, 1950, 1974; Weitzman, 1978). T h i s p o i n t w i l l be d i s c u s s e d f u r t h e r below under the working of the caudal f i n . In c o n t r a s t t o Nannostomus s p e c i e s , i n C h i l o d u s punctatus a good p r o p o r t i o n of the l i f t r e s p o n s i b l e f o r s l a n t i n g comes from the c a u d a l r a t h e r than the. p e c t o r a l f i n s . . The f i s h can compensate . f o r the l o s s of i t s p e c t o r a l s and maintain i t s negative p i t c h by i n c r e a s i n g i t s c a u d a l - f i n a c t i v i t y . The caudal f i n o f C h i l o d u s punctatus i s very f l e x i b l e so that i t s movements, j u s t as i n most t e l e o s t (Aleev, 1963), can c r e a t e v e r t i c a l , forward, and t r a n s v e r s e f o r c e s . i 1 The change i n the.angle of i n c l i n a t i o n with s i z e i n both Nannostomus egues and Chilodus punctatus can be accounted f o r i n hydromechanical terms by the i n c r e a s e i n weight of the f i s h . As the f i s h becomes l a r g e r , the weight i n c r e a s e s and t h e r e f o r e more f o r c e i s r e g u i r e d to i n c l i n e the body. T h i s i s a reasonable e x p l a n a t i o n f o r the angular change i n l a r g e r i n d i v i d u a l s of both these s p e c i e s , because they are s l i g h t l y dense than water and 90 t h e i r c e n t r e of mass i s the 'wrong way round' to the ce n t r e o f buoyancy. I t would have been i n t e r e s t i n g , t h e r e f o r e , i f t h e i r angles of o r i e n t a t i o n c o u l d have been expressed i n terms o f t h e i r weight i n s t e a d of t h e i r l e n g t h . R e s u l t s f o r Thayeria b o e h l k e i are i n accordance with other r e s u l t s f o r f i s h which have a p o s i t i v e p i t c h . Alexander (1966) found t h a t i n the c a t f i s h , C ryptopterus b i e i r r h i s , which hovers with a p o s i t i v e p i t c h , the c e n t r e of mass i s behind the c e n t r e of buoyancy. In T h a y e r i a b o e h l k e i the centre of mass i s a l s o behind the c e n t r e of buoyancy. Thus as the f i s h hovers t h e r e i s always a tendency f o r i t s hind part to drop and i t s f o r e p a r t t o r i s e . The f i s h c o r r e c t s t h i s tendency by using the p e c t o r a l and caudal f i n s t r o k e s to r a i s e i t s hind p a r t and lower i t s head. Since the centre of mass i s behind the c e n t r e of buoyancy, i t i s reasonable t o expect the . s l a n t i n g angle e i t h e r to remain constant o r i n c r e a s e with i n c r e a s i n g s i z e , as observed. Removal of the caudal f i n had an e f f e c t on the g e n e r a l behaviour of the T h a y e r i a b o e h l k e i . The co n t i n o u s swimming which developed with the removal of the caudal f i n was necessary f o r c o r r e c t i n g the s i n k i n g tendency of the t a i l r e g i o n . According to Braemer (1957), Braemer and Braemer (1958), and P f e i f f e r (1968), T h a y e r i a b o e h l k e i and Th a y e r i a o b l i g u a when hove r i n g i n t h e i r normal s l a n t i n g o r i e n t a t i o n have t h e i r u t r i c u l a r s t a t o l i t h s , the l a p i l l i , i n a h o r i z o n t a l plane. T h e r e f o r e , d e v i a t i o n s from the s l a n t i n g o r i e n t a t i o n would cause t i l t i n g of the u t r i c u l a r s t a t o l i t h and s l i d i n g o f the l a p i l l i over the sensory h a i r s and thus would l e a d t o c o r r e c t i n g movements to b r i n g the l a p i l l i back t o the h o r i z o n t a l (Von H o i s t , 1950), which may account f o r 91 the continous swimming response. T h i s study has r e v e a l e d i n t e r e s t i n g r e l a t i o n s h i p s among the c e n t r e s of mass and buoyancy, and the f u n c t i o n of the enlarged lobe of the c a u d a l f i n i n Nannostomus egues and Nannostomus u n i f a s c i a t u s not p r e v i o u s l y d e s c r i b e d . T h e r e f o r e i n the f o l l o w i n g s e c t i o n the working of the caudal f i n w i l l be a nalysed to e l u c i d a t e i t s r e l a t i o n s h i p with the two c e n t r e s . The t h r e e methods used to determine the r e l a t i v e p o s i t i o n s of the c e n t r e s of mass and buoyancy showed t h a t the c e n t r e o f mass i s i n f r o n t of the c e n t r e of buoyancy and t h a t t h e i r s e p a r a t i o n i s l a r g e enough to develop a n e gative p i t c h i n g moment. T h i s have been shown by those f i s h i n which the p e c t o r a l f i n s were removed and by the way i n which the specimens a n a e s t h e t i z e d i n MS 222 achieved s t a t i c e g u i l i b r i u m . The d i r e c t i o n of the p i t c h i n g moment i s opposite to t h a t which would be expected from the normal o r i e n t a t i o n angle of the f i s h . Since i n d i v i d u a l s use t h e i r p e c t o r a l f i n s to maintain t h i s s l a n t i n g p o s i t i o n , one would expect that they would need l e s s energy to hold t h a t posture i f the p e c t o r a l a c t i v i t y was supplemented by a s t a t i c p o s i t i v e p i t c h i n g moment, as i n T h a y e r i a b o e h l k e i and T h a y e r i a o b l i g u a . In f a c t i t was t h i s p l a u s i b l e e x p l a n a t i o n t h a t l e d Hoedeman (1974) t o suggest t h a t d i f f e r e n c e s i n the s t r u c t u r e of the p o s t e r i o r lobe of the swimbladder were r e s p o n s i b l e f o r the s l a n t i n g p o s i t i o n i n these two s p e c i e s . But there i s ' no evidence of t h i s e f f e c t i n the r e s u l t s of the present study. The experiments above have a l s o shown th a t , i n Nannostomus egues and Nannostomus u n i f a s c i a t u s , n e i t h e r the whole caudal f i n 92 nor i t s two l o b e s a c t i n g independently are v i t a l l y important f o r m a i n t a i n i n g p o s i t i v e p i t c h . Removing the c a u d a l f i n d i d not change the;angle of o r i e n t a t i o n . I n s t e a d , the freguency of the p e c t o r a l - f i n beat i n c r e a s e d to compensate f o r the l o s s of the caudal f i n . The prime importance of p e c t o r a l f i n s i n producing the p i t c h was demonstrated by the f a c t t h a t amputating the p e c t o r a l f i n s while l e a v i n g the caudal f i n i n t a c t , completely e l i m i n a t e d the p o s i t i v e p i t c h . . I n f a c t , most of the specimens so t r e a t e d developed a negative p i t c h . I t has been suggested or i m p l i e d (Hoedeman, 1950, 1974; Weitzman, 1978) that the e n l a r g e d lower lobe of the caudal f i n may be r e s p o n s i b l e f o r the head-up p o s i t i o n of Nannostomus egues and Nannostomus u n i f a s c i a t u s . T h i s s u g g e s t i o n d e r i v e s from Kermack's (1943) a n a l y s i s of the working of the caudal f i n i n a r e c o n s t r u c t e d model of the e x t i n c t p t e r a p s i d , Pterap_sis r o s t r a t a . According t o Kermack, these f i s h were denser than water because they had a heavy bony armour and l a c k e d a swimbladder. Therefore they c o u l d only r i s e to the middle l e v e l s by using t h e i r e x t e r n a l l y asymmetrical caudal f i n , the l a r g e r lower lobe of which must have had a hypobatic e f f e c t . Thus, during p r o p u l s i o n , the e n l a r g e d lower lobe would produce a dynamic l i f t d epressing the hind p a r t and i n c l i n i n g the body with a p o s i t i v e p i t c h . Lundberg and Baskin (1969) have made s i m i l a r s u g g e s t i o n to account f o r the m i d - l e v e l f e e d i n g of some bottom-dwelling c a t f i s h e s t h a t a l s o have a l a r g e r lower lobe on t h e i r caudal f i n s . The i d e a of l i f t simply causing moments around the c e n t r e of mass o f the f i s h may be m i s l e a d i n g as i n d i c a t e d f o r 93 h e t e r o c e r c a l t a i l s of sharks (Simons, 1970; Thomson, 1976; Thomson and Simaner 1977). I n order f o r the t a i l t o produce a p o s i t i v e p i t c h i n g moment, the r e s u l t a n t of i t s t h r u s t f o r c e must act downward and pass behind the c e n t r e of mass. The common denominator of Kermack's (1943) a n a l y s i s and Lundberg's and Baskin's (1969) s u g g e s t i o n , r e g a r d l e s s of whether t h e i r analyses are c o r r e c t o r , i n c o r r e c t , i s t h a t the l i f t i n g f o r c e r e s p o n s i b l e f o r the. p i t c h i n g moment i s a dynamic one. Therefore, i t can only be produced when the caudal f i n i s i n motion. However, t h i s reguirement i s not f u l f i l l e d by Nannostomus egues and Nannostomus u n i f a s c i a t u s . These f i s h maintain t h e i r p o s i t i v e p i t c h while hovering i n a s t a t i o n a r y p o s i t i o n without moving t h e i r caudal f i n s l a t e r a l l y or without producing any s e r i e s of v e r t i c a l waves on the enlarged lower lobe of t h e i r caudal f i n s . . In f a c t , these f i s h l o s e t h e i r p o s i t i v e p i t c h when swimming f a s t with l a r g e l a t e r a l movements of t h e i r caudal f i n s . I f the caudal f i n ' s c o n t r i b u t i o n i s not necessary f o r the head-up o r i e n t a t i o n adopted by these s p e c i e s when hovering or swimming s l o w l y , then what i s the f u n c t i o n of the enlarged lower lobe of the c a u d a l f i n , found only i n these two nannostomine s p e c i e s ? R e s u l t s from the experiments on c a u d a l - f i n amputations and o b s e r v a t i o n s of f a s t s t a r t s have provided e m p i r i c a l evidence that the asymmetrical caudal f i n of Nannostpmus egues and Nannostomus u n i f a s c i a t u s r a i s e s the hind p a r t of the f i s h d u r i n g such a c t i v i t y . The i d e a s f i r s t i ntroduced by A f f l e c k (1950) on the working of asymmetrical caudal f i n s , and the biomechanical model 94 developed by Thomson (1976), and Thomson and Simaner (1977) f o r h e t e r o c e r c a l t a i l s i n sharks, may be a p p l i e d here. Some m o d i f i c a t i o n s based on o b s e r v a t i o n s of the present s p e c i e s are r e q u i r e d , however, before the e x p l a n a t i o n of how such f i n s may have an e p i b a t i c e f f e c t durinq r a p i d s t a r t s can be.made, to f i t the observed movements of Nannostomus egues and Nannostomus u n i f a s c i a t u s . The b a s i s of the model i s the d i s t i n c t i o n of the two component f o r c e s , forward ( F ) , and t r a n s v e r s e (T), generated by the l o b e s of the caudal f i n d u r i n g the l a t e r a l s t r o k e s . In the hydrodynamic a n a l y s i s of swimming i n f i s h e s with homocercal t a i l s , the r e s u l t a n t t h r u s t from the caudal f i n i s assumed to act through or very c l o s e to the c e n t r e of mass ( L i g h t h i l l , 1969, 197 0). Because of the c o n t r o l and f l e x i b i l i t y of t h e i r c audal f i n r a y s , most t e l e o s t s can a l t e r the d i r e c t i o n of the r e s u l t a n t t h r u s t with r e s p e c t to t h e i r centre of mass and with the a i d of the p e c t o r a l s , can c r e a t e t u r n i n g moments i n the v e r t i c a l p lane. Transverse component The outer margins of the caudal f i n lead the c e n t r a l r e g i o n during l a t e r a l s t r o k e s of the caudal f i n , and e s p e c i a l l y when moving with l a r g e amplitude:and high l a t e r a l v e l o c i t y . At the same time the f r o n t edge near the caudal peduncle l e a d s the p o s t e r i o r margin with the wave of c o n t r a c t i o n s t i l l v i s i b l e passing backwards on the two l o b e s . T h i s c o n f i g u r a t i o n seems t o be p a s s i v e because of the s t i f f n e s s of the. r a y s decreases p o s t e r i o r l y , as the t i s s u e around the ra y s d i m i n i s h e s ( V i d e l e r , 1975)..This c o n f i g u r a t i o n of the caudal f i n d u r i n g t r a n s v e r s e movement i s common i n t e l e o s t s (Bainbridge, 1958, 1963; V i d e l e r , 95 1975, 1977). During these l a t e r a l movements the lobes of the f i n thus are r o t a t e d around the l o n g i t u d i n a l a x i s and can be v i s u a l i s e d as forming moving i n c l i n e d planes i n the d i r e c t i o n o f the t r a n s v e r s e movement. Both the upper and the lower lobes w i l l be e x p e r i e n c i n g a p e r p e n d i c u l a r f o r c e (P) on t h e i r s u r f a c e s opposite t o the d i r e c t i o n of t r a n s v e r s e movement. T h i s f o r c e can be r e s o l v e d i n t o h o r i z o n t a l (H) and v e r t i c a l (L) components (Figure 19) . The v e r t i c a l component (L) i s the l i f t f o r c e a c t i n g upwards on the d o r s a l lobe (Ld) and downwards on the lower lobe (Lv). As can be seen from the f i g u r e the magnitude of L depends d i r e c t l y on the degree of r o t a t i o n t h a t i s the angle of i n c l i n a t i o n of the outer margin. In a symmetrical t a i l these two l i f t s are egual and t h e r e f o r e c a n c e l each other. The h o r i z o n t a l components also average t o zero through a complete c y c l e of the s t r o k e as they change d i r e c t i o n and t h e r e f o r e the f i s h swims i n a h o r i z o n t a l plane. In the asymmetrical caudal f i n s of Nannostomus egues and Nannostomus u n i f a s c i a t u s , where the lower lobe i s l a r g e r than the upper, i f the two l o b e s are r o t a t e d at about the same angle during l a t e r a l s t r o k e s then Lv w i l l be l a r g e r than Ld. T h i s discrepency w i l l have a hypobatic e f f e c t , d e p r e s s i n g the t a i l and r a i s i n g the head. As a r e s u l t i f the f i s h i s f r i g h t e n e d and can a c t i v a t e i t s p e c t o r a l f i n s a t a s u i t a b l e angle of a t t a c k , the forward t h r u s t thus generated w i l l d r i v e the f i s h upwards at an angle and shoot out of the water. Such behaviour i n f a c t i s very common i n both Nannostomus- egues and Nannostomus 96 u n i f a s c i a t u s . They o f t e n l e a p out of aquarium tanks. There i s no i n f o r m a t i o n about t h i s behaviour i n t h e i r n a t u r a l environment, or whether they can s k i t t e r . . By c o n t r o l l i n q the rays of the lower lobe and makinq i t more r i g i d d urinq a c c e l e r a t i o n , these f i s h can reduce the angle of r o t a t i o n of the lower lobe, thus reducing Lv and removing the hypobatic e f f e c t of the t r a n s v e r s e movement. At the.same time i f the upper lobe leads the lower l o b e , making the whole caudal f i n act as an i n c l i n e d plane with a s m a l l angle of r o t a t i o n , t h i s e f f e c t combined with the lobe angle of the lower lobe (forward component) w i l l give a r e s u l t a n t t h r u s t t h a t i s upwards and behind t h e . c e n t r e of mass. This t h r u s t would r a i s e the p o s t e r i o r part and depress the head. Such c o n s i d e r a t i o n s l e a d me to suggest t h a t the e n l a r g e d lower lobe of the caudal f i n i n Nannostomus egues and Nannostomus u n i f a s c i a t u s r a i s e s the hind p a r t during a r a p i d s t a r t , c a u s i n g the f i s h to swim h o r i z o n t a l l y . T h i s e f f e c t would have two main advantages. F i r s t , i f the f i s h f o l d s the lower lobe a f t e r the i n i t i a l a c c e l e r a t i o n , then any f u r t h e r p r o p u l s i v e f o r c e from the caudal f i n would pass through or very near the centre of mass, which would make swimming hydrodynamically more e f f i c i e n t than any o f f - c e n t r e p r o p u l s i v e f o r c e ( L i g h t h i l l , 1975; Weihs, 1973), which would mostly be l o s t i n p i t c h i n g moments. The second advantage l i e s i n the response Nannostomus egues and Nannostomus u n i f a s c i a t u s would have t o p r e d a t o r s . The body form i n most p r e d a t o r s i s such they minimise t a r g e t d e v i a t i o n s i . e . , yawing when s t a r t i n g or swimming very f a s t , (Webb, 1978). This c o n t r o l makes them very a c c u r a t e at s t r i k i n g a prey. 97 F i g u r e 19. D i a g r a m a t i c p r e s e n t a t i o n of the r e a r view of the c a u d a l f i n i n t r a n s v e r s e motion 98 Nannostomus egues, Nannostomus u n i f a s c i a t u s , T k H S S i S b o e h l k e i , and T h a y e r i a o b l i q u a s l a n t e d near the s u r f a c e are exposed to p r e d a t o r s from below. I f , however, they change t h e i r o r i e n t a t i o n d r a m a t i c a l l y d u r i n g t h e i r i n i t i a l a c c e l e r a t i o n to escape t h e i r a t t a c k e r , then a predator whose s t r a t e g y i s t o minimize yaw at t h i s phase o f a t t a c k i s l i k e l y t o miss. T h i s s h i f t i n o r i e n a t t i o n can be considered an a c c e l e r a t i o n maneuver s t r a t e g y (Webb, 1976) f o r these s l a n t i n g s p e c i e s . I t i s tempting to suggest t h a t the eyespot ( o c e l l u s ) i n Nannostomus u n i f a s c i a t u s may f u n c t i o n f u r t h e r to m i s d i r e c t t h e : p r e d a t o r s to the c a u d a l r e g i o n , as suggested f o r other Characoid f i s h e s (MacPhail, 1977). U n f o r t u n a t e l y very l i t t l e i s known about the ecology of these, f i s h e s ( M a r l i e r , 1968; Roberts, 1972). The aguarium l i t e r a t u r e i s f u l l of s p e c u l a t i o n s of the use of c o l o u r bands and s l a n t i n g p o s i t i o n f o r camouflage (Gery, 1969). Most o f these hypotheses are t e s t a b l e i n terms of proximate advantages i of the. i n d i v i d u a l s , i f t h e i r n a t u r a l predators are known (MacPhail, 1977). But i t i s d i f f i c u l t to assess the f u n c t i o n i n terms of i t s s e l e c t i v e value f o r i n d i v i d u a l s ( i n the sense o f Hinde 1975). The d i s t r i b u t i o n o f mass and the hovering o r i e n t a t i o n o f Nannostomus egues, Nannostomus u n i f a s c i a t u s -, and C h i l o d u s punctatus provide f u r t h e r evidence f o r the argument, t h a t s h i f t i n g the p r o p u l s i v e f o r c e to the h o r i z o n t a l plane through the centre of mass i s the b a s i s f o r a guick escape response. In Nannostomus egues and Nannostomus u n i f a s c i a t u s , the c e n t r e o f mass i s i n f r o n t of the centre of buoyancy. T h e r e f o r e , i f the p e c t o r a l s are f o l d e d as they are when the f i s h a c c e l e r a t e or 99 swim f a s t , then the weight of the f i s h and the. l i f t from the caudal f i n a c t together to change the l i n e of t h r u s t . T h i s change a l s o occurs i n C h i l o d u s punctatus, as i t becomes almost h o r i z o n t a l i t changes the movements of the caudal f i n l o b e s and uses ca r a n g i f o r m locomotion. I t appears t h a t t h e s e : f i s h e x p l o i t the u n s t a b l e b i a s e s due t o t h e i r mass d i s t r i b u t i o n f o r t h e i r own advantage i n maneuvering. I s there another f u n c t i o n of s l a n t i n g o r i e n t a t i o n i n these s p e c i e s ? For example f e e d i n g have been suggested f o r many s l a n t i n g s p e c i e s such as c y p r i n o d o n t o i d s (Greenway, 1965; M a r s h a l l , 1971; Roberts 1972). However, most of s l a n t i n g s u r f a c e f e e d e r s do not permanently s l a n t at such l a r g e angles as Nannostomus egues and Nannostomus u n i f a s c i a t u s . As noted e a r l i e r , s u r f a c e f e e d i n g f i s h e s have followed two l i n e s o f a d a p t a t i o n , i n v o l v i n g e i t h e r upturning of the mouth p a r t s , or s l a n t i n g of the whole body towards the s u r f a c e . S l a n t i n g o r i e a n t a t i o n i s hydrodynamically advantageous because the whole f i s h need not come too c l o s e . t o the s u r f a c e . I f the whole f i s h swims h o r i z o n t a l l y ver.y c l o s e t o the s u r f a c e , the d o r s a l f i n may break the i n t e r f a c e and i n c r e a s e drag c o n s i d e r a b l y . Thus most of these near s u r f a c e swimmers tend to have backward placed d o r s a l f i n . E x p l o i t a t i o n of the oxygen-rich s u r f a c e l a y e r has a l s o been suggested f o r upward s l a n t i n g f i s h . , Lewis (1970) t e s t e d e x p e r i m e n t a l l y the s u r v i v a l r a t e s of some s u r f a c e s l a n t i n g c y p r i n o d o n t i d s compared with normally swimming f i s h i n oxygen depleted waters. He found t h a t those f i s h which were o b l i g u e swimmers had higher s u r v i v a l than those with normal posture, as 100 oxygen l e v e l s were lowered, and t h e r e f o r e i n t e r p r e t e d s l a n t i n g s u r f a c e swimming as a morphological a d a p t a t i o n t o e x p l o i t oxygen r i c h s u r f a c e waters. However, h i s r e s u l t s need care i n i n t e r p r e t a t i o n because of the design of the experiments. Most of the l e b i s i a n i d f i s h e s are known to s u r v i v e w e l l i n slow f l o w i n g and sometimes stagnant waters of s m a l l streams i n t r o p i c a l South America. Some of them are known t o be f a c u l t a t i v e a i r b r e a t h e r s , using the swimbladder or other accessory organs (Carter and Beadle, 1961; Weitzman, 1964; Graham e t . a l , 1977, 1978) and show anatomical a d a p t a t i n s i n t h e i r swimbladders f o r t h i s f u n c t i o n . N e i t h e r Nannostomus egues nor Nannostomus u n i f a s c i a t u s have any anatomical a d a p t a t i o n s , such as unusual v a s c u l a r i s a t i o n of the swimbladder or a l i m e n t a r y c a n a l . Therefore i f they do u t i l i z e . t h e oxygen r i c h s u r f a c e l a y e r i t i s l i k e l y t o be through a morphological a d a p t a t i o n , i n the sense o f Lewis (1970). S t u d i e s by G e i s l e r (1969) do not show any d i f f e r e n c e ; i n the oxygen demands of Nannostomus b e e f o r d i and Nannostomus u n i f a s c i a t u s ( h i s Nannostomus anomalus and P o e e i l o b r y c o n u n i f a s c i a t u s ) . He p o i n t s out t h a t m o r t a l i t y of f i s h d u r i n g p e r i o d s of c o l d wind i s due t o the u p r i s i n g of bottom water with l i t t l e or no oxygen t o the s u r f a c e , and not to the f a l l i n temperature. Under such c o n d i t i o n s , t h e r e f o r e , a b i l i t y t o u t i l i z e atmospheric oxygen or s u r f a c e oxygen s a t u r a t e d waters may be very important f o r s u r v i v a l . In t h i s c o n t e x t i t i s worth mentioning an i n t e r e s t i n g u n n a tural event observed i n the course of my experiments. The l a b o r a t o r y i n which these f i s h were kept was once exposed to excessive smoke and heat from f i r e i n a nearby room. Of a l l the 101 f i s h which were i n the tanks at the time, 10 C h i l o d u s punctatus, 6 Abramistes microcephalus, 6 Leporinus maculatus, 18 Nannostomus egues, 4 Nannostomus- u n i f a s c i a t u s , 8 Nannostomus t r i f a s c i a t u s , and 4 Nannostomus b e e f o r d i only 2 Nannostomus b e e f o r d i , 13 Nannostomus egues and a l l 4 Nannostomus u n i f a s c i a t u s s u r v i v e d . Thus Nannostomus egues and Nannostomus u n i f a s c i a t u s had a very high r a t e of s u r v i v a l under these c o n d i t i o n s . A l l s u r v i v o r s were found with t h e i r mouths r i g h t on the s u r f a c e . Since t h i s was j u s t one i n c i d e n t , not much can be deduced, but i t does show how r e s i s t a n t these s p e c i e s are! The o r i e n t a t i o n of C h i l o d u s punctatus has a l s o been a s s o c i a t e d with feeding and p r o t e c t i o n . Bottom f e e d i n g i s probably more a s s o c i a t e d with an i n f e r i o r mouth than with downward o b l i g u e swimming. Leporinus maculatus has an i n f e r i o r mouth and o b s e r v a t i o n o f i t s f e e d i n g i n the l a b o r a t o r y shows i t o c c a s s i o n a l l y n i b b l e s a t the bottom, although i t feeds i n the middle l e v e l s as w e l l . C h i l o d u s punctatus p r e f e r s t o n i b b l e at p l a n t stems and l e a v e s not f a r from the. bottom but a l s o f r e g u e n t l y p i c k s food p a r t i c l e s from the bottom. Young C h i l o d u s punctatus o r i e n t almost v e r t i c a l l y when feeding and a l s o feed more f r e g u e n t l y from the bottom. Stud i e s of t h e i r gut c o n t e n t s (Knoppel, 1970) showed only f i n e sand and mud, which i n d i c a t e s bottom f e e d i n g i n nature, whereas s t u d i e s by M a r l i e r (1968) showed t h a t Leporinus maculatus feeds on p l a n t s . However, these s t u d i e s t e l l us very l i t t l e about s e l e c t i v e . f e e d i n g by these f i s h , because the r e l a t i v e amounts of the food items a v a i l a b l e i n the environment are not given. For example I have observed i n the l a b o r a t o r y t h a t Leporinus maculatus w i l l p r e f e r a r t i f i c i a l 102 food 't e t r a m i n ' to aquarium p l a n t s and feed on p l a n t s only i n the absence o f t e t r a m i n . In c o n t r a s t Abramistes mierocephalus w i l l always eat aquarium p l a n t s even i f f e d 'tetramin'. The nature and v a r i a t i o n o f the mouths of the c h i l o d o n t i d s and the c l o s e l y r e l a t e d f a m i l y Anostomidae are very i n t e r e s t i n q but very l i t t l e can be i n f e r r e d i n the absence of i n f o r m a t i o n on t h e i r ecoloqy and feedinq h a b i t s . At present t h e r e i s very l i t t l e i n f o r m a t i o n from f i e l d s t u d i e s ( M a r l i e r 1968; Gery, 1969; Knoppel, 1970; Lowe-McConnell, 1975). Whereas the. mouth i s t e r m i n a l or n e a r l y so i n C h i l o d u s punctatus, i t i s d i s t i n c t l y i n f e r i o r i n Caenotropus, the other qenus i n the same f a m i l y (Gery, 1964). In Anostomidae, many s p e c i e s of Anpstomus which a l s o spend much time.standinq o b l i q u e l y on t h e i r heads, have s u p e r i o r mouths (Myers, 1950). S u p e r f i c i a l l y they look as thouqh they are s u r f a c e feeders, and i n f a c t they may be f e e d i n q on s u r f a c e s o f v e r t i c a l l y qrowinq p l a n t s . Gery (1969) r e p o r t s t h a t most of these f i s h l i v e under rocks and feed on the ' c e i l i n q s ' of these r o c k s , so the upturned mouths may be an a d a p t a t i o n a s s o c i a t e d with t h i s h a b i t . However complete b i o l o q i c a l s i q n i f i c a n c y of t h i s o b l i q u e swimminq i s s t i l l f a r from beinq c l e a r . I n t e r p r e t a t i o n f o r the r e s u l t s of v e r t e b r a l number and s i z e i n Nannostomus spp. i s d i f f i c u l t because only s m a l l samples of f o u r s p e c i e s have been i n v e s t i q a t e d , and these d i d not i n c l u d e Nannostomus h a r r i s o n i , which has t h e h i q h e s t number of v e r t e b r a e of a l l the nannostomines (table 5). A few q e n e r a l i z a t i o n s can be e x t r a c t e d from the r e s u l t s . The number of caudal and p r e c a u d a l v e r t e b r a e of a l l 103 Nannostomus s p e c i e s other than Nannostomus h a r r i s o n i o v e r l a p very much although t h e r e may be, some r a c i a l v a r i a t i o n s (Weitzman, 1978). T h e r e f o r e , i f there i s any v e r t e b r a l d i f f e r e n c e a s s o c i a t e d with d i f f e r e n t swimming s t r a t e g i e s , i t probably should be sought i n the s i z e , r a t h e r than the number o f vertebrae. Omura (1971) i n v e s t i g a t e d the r e l a t i o n s h i p between v e r t e b r a l s i z e and the movements of baleen whales. He found t h a t the f a s t swimmers and long d i s t a n c e migrants have l a r g e r and b e t t e r developed c a u d a l v e r t e b r a e . The hydrodynamics of whale swimming i s t h a t of a l u n a t e caudal f i n (Wu, 1971a) which u t i l i z e s low amplitude, high freguency movements, .This type of swimmers have l a r g e vertebrae ( N u r s a l l , 1958) and l e s s f l e x i b l e caudal v e r t e b r a l column t h a t r e s t r i c t l a t e r a l motion. The advantage a r i s e s from a p o s t e r i o r p a r t that p r o v i d e s a s t i f f a x i s which f u n c t i o n s as a s p r i n g . T h i s r e s t r i c t i o n i s c a r r i e d to extremes i n s a i l f i s h e s , where the l a s t few c a u d a l vertebrae are locked by the zygapophyses t o form a s t i f f a x i s (Rockwell e t . a l . , 1938; F i e r s t i n e and Walters, 1968; Lund, 1967), thus i n c r e a s i n g the e f f i c i e n c y of high freguency o s c i l l a t i o n s . In s p e c i e s which use l a r g e c a u d a l - f i n amplitudes at low freguency, however, f l e x i b i l i t y of the p o s t e r i o r p a r t of the caudal v e r t e b r a l column i s more important, e s p e c i a l l y d u r i n g a c c e l e r a t i o n . Therefore s m a l l v e r t e b r a l s i z e i n f r o n t of the u r a l fan should be looked f o r i n those f i s h which i n c o r p o r a t e the L-shaped phase duri n g a c c e l e r a t i o n . In f a c t , the caudad decrease i n v e r t e b r a l s i z e c h a r a c t e r i s t i c of most f i s h (Ford, 1937), together with the accompanying decrease i n muscle t i s s u e , 104 serve to i n c r e a s e the amplitude c a u d a l l y . Nannostomus egues and Nannostomus u n i f a s c i a t u s compared with Nannostomus t r i f a s c i a t u s , have n e a r l y equal caudalmost v e r t e b r a but s m a l l e r locomotor v e r t e b r a e . Nannostomus b e e f o r d i have l a r g e r caudalmost and locomotor vertebrae than the r e s t , as would be expected from t h e i r d i f f e r e n t swimming h a b i t s . Nannostomus egues and Nannostomus u n i f a s c i a t u s use caudal p r o p u l s i o n only d u r i n g a c c e l e r a t i o n and f a s t swimming and t h e r e f o r e would r e g u i r e r e l a t i v e l y l a r g e caudalmost v e r t e b r a . t o a t t a i n high maximum l a t e r a l v e l o c i t y of the caudal f i n , and s m a l l e r locomotor vertebrae ahead o f the u r a l t o f a c i l i t a t e bending.. Nannostomus b e e f o r d i and Nannostomus t r i f a s c i a t u s use low-amplitude caudal p r o p u l s i o n f o r most of t h e i r swimming a c t i v i t i e s . Because the sample, s i z e s used i n t h i s study were very s m a l l , i t was not p o s s i b l e t o analyse f u l l y the a s s o c i a t i o n o f v a r y i n g v e r t e b r a l number with v e r t e b r a l s i z e . There i s some i n d i c a t i o n t h a t the r e l a t i v e s i z e of vertebrae expressed as a p r o p o r t i o n of standard l e n g t h remains constant i n each s p e c i e s . F i s h with few vertebrae tend to be s m a l l . T h i s r e l a t i o n s h i p i s a p p l i c a b l e i n s t u d i e s of pleomerism and environmental e f f e c t s on v e r t e b r a l numbers. T h i s constancy of r e l a t i v e v e r t e b r a l s i z e may imply t h a t i n the hydrodynamics o f carangiform swimming f o r f i s h of a p a r t i c u l a r shape, i t i s the vertebrae s i z e which may be more important than numbers. 105 CONCLUSIONS 1. R e l a t i v e p o s i t i o n s of the c e n t r e of mass . and c e n t r e o f buoyancy i n Nannostomus egues, Nannostomus u n i f a s c i a t u s and C h i l o d u s punctatus are the r e v e r s e of those expected from t h e i r hovering p i t c h . The c e n t r e of mass i s behind of the ce n t r e of buoyancy i n C h i l o d u s punctatus and i n f r o n t of i t i n Nannostomus egues and Nannostomus u n i f a s c i a t u s . In Th a y e r i a b o e h l k e i and Thayeria o b l i g u a the c e n t r e of mass i s behind the centre of buoyancy as expected producing a p a s s i v e p o s i t i v e p i t c h i n g moment. 2. Nannostomus egues, Nannostomus u n i f a s c i a t u s and C h i l o d u s punctatus use t h e i r p e c t o r a l and caudal f i n s to maintain t h e i r p i t c h . In Nannostomus egues and Nannostomus u n i f a s c i a t u s the p e c t o r a l f i n s p r o v i d e : the g r e a t e r p r o p o r t i o n of the p i t c h i n g moment. In C h i l o d u s punctatus both the caudal and the p e c t o r a l f i n s are important.. 3. The enlarged lower lobe of the cau d a l f i n i n Nannostomus egues, - Nannostomus u n i f a s c i a t u s , T h a y e r i a b o e h l k e i and Tha y e r i a o b l i g u a does not provide a hypobatic e f f e c t d u r i n g hovering as p r e v i o u s l y thought. The.normal f u n c t i o n of t h i s lobe i s to r a i s e the caudal r e g i o n when the f i s h i s swimming f a s t o r a c c e l e r a t i n g . I t i s a l s o used i n T h a y e r i a b o e h l k e i and Thayer i a o b l i g u a to c o r r e c t f o r the p a s s i v e p o s i t i v e p i t c h a r i s i n g from the s e p a r a t i o n of the c e n t r e s of mass and buoyancy. I t may a l s o be used i n jumping by Nannostomus egues and Nannostomus u n i f a s c i a t u s . 106 R a i s i n g the .caudal r e g i o n i n Nannostomus egues, Nannostomus u n i f a s c i a t u s , T h a y e r i a b o e h l k e i and Thayer i a o b l i q u a d u r i n g f a s t swimminq imparts a more h o r i z o n t a l t h r u s t throuqh the c e n t r e , of mass which, a c c o r d i n q to hydrodynamics t h e o r i e s , should i n c r e a s e e f f i c i e n c y . H o r i z o n t a l swimminq chanqes the o r i e n t a t i o n of the f i s h from the s l a n t i n q hoverinq p o s i t i o n which may be advantaqeous f o r these prey s p e c i e s . Nannostomus egues, Nannostomus u n i f a s c i a t u s , T h a y e r i a b o e h l k e i and T h a y e r i a o b l i g u a are s u r f a c e f e e d e r s so t h i s change i n t h e i r o r i e n t a t i o n during f a s t s t a r t from r e s t should decrease t h e i r chances of being s t r u c k by p r e d a t o r s from below. In Nannostomus egues, Nannostomus u n i f a s c i a t u s and C h i l o d u s punctatus t h e . r e l a t i v e . p o s i t i o n s of the c e n t r e of mass and buoyancy help to b r i n g the body h o r i z o n t a l when the l i f t i n g f o r c e s of the f i n s are removed. R e l a t i v e v e r t e b r a l s i z e i n Nannostomus egues and Nannostomus u n i f a s c i a t u s compared with. Nannostomus t r i f a s c i a t u s and Nannostomus b e e f o r d i bear some r e l a t i o n s h i p to t h e i r swimming h a b i t s and are as would be expected from t h e o r i e s of the hydrodynamics of f i s h p r o p u l s i o n . The numbers of caudal v e r t e b r a e s u p p o r t i n g the u r a l fan i n C h i l o d u s punctatus, Leporinus maculatus and Abramistes mierocephalus are r e l a t e d to t h e i r swimming h a b i t s . 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