A review of methods for estimating mortality due to parasites in wild fish populations

HELGOI-~NDER M E E R E S U N T E R S U C H U N G E N H e l g o l ~ n d e r M e e r e s u n t e r s . 37, 53-64 (1984)

A r e v i e w of m e t h o d s for e s t i m a t i n g m o r t a l i t y d u e to

p a r a s i t e s in w i l d f i s h p o p u l a t i o n s

R. J. G. Lester

Department of Parasitology, University of Queensland; Brisbane, Australia 4067

ABSTRACT: Six m e t h o d s are d e s c r i b e d for d e t e c t i n g mortality due to parasitic infections in n a t u r a l fish populations. They are: (a) t h r o u g h autopsies; (b) b y d e t e r m i n i n g the f r e q u e n c y of infections k n o w n to b e e v e n t u a l l y lethal; (c) by o b s e r v i n g a d e c r e a s e in the p r e v a l e n c e of a l o n g - l i v e d p a r a s i t e (or p e r m a n e n t scar from a parasite) w i t h host age; (d) b y o b s e r v i n g a d e c r e a s e in the v a r i a n c e / m e a n ratio for the parasites w i t h host age; (e) by c o m p a r i n g t h e o b s e r v e d f r e q u e n c y of a c o m b i n a t i o n of two i n d e p e n d e n t e v e n t s w i t h the c a l c u l a t e d p r o b a b i l i t y of t h e i r occurrence; a n d finally {f) by c o m p a r i n g the o b s e r v e d f r e q u e n c y d i s t r i b u t i o n of the parasite, w i t h a p r o j e c t e d f r e q u e n c y b a s e d on data from lightly infected fish. In this t e c h n i q u e , n e g a t i v e b i n o m i a l s are fitted to the data a n d t r u n c a t e d at various points. Some a d v a n t a g e s a n d d i s a d v a n t a g e s of the different m e t h o d s are given, together with examples. The m e t h o d s do not necessarily p r o v i d e definitive answers, b u t t h e y are indicative of w h e t h e r or not significant p a r a s i t e - r e l a t e d mortality m a y b e occurring, a n d in some cases provide a n e s t i m a t e of its p r o b a b l e m a g n i t u d e i n terms of t h e total host mortality rate.

I N T R O D U C T I O N

T h e r o l e of p a r a s i t i c d i s e a s e i n t h e e c o l o g y of n a t u r a l p o p u l a t i o n s of a n i m a l s is n o t w e l l u n d e r s t o o d . I n t h e o r y , p a r a s i t i c d i s e a s e h a s t h e p o t e n t i a l t o b e a m a j o r c o n t r i b u t o r t o h o s t m o r t a l i t y r a t e s a n d e v e n t o r e g u l a t e h o s t p o p u l a t i o n s i z e . Its t h e o r e t i c a l i m p o r t a n c e h a s b e e n r e c o g n i s e d for m a n y y e a r s a n d h a s b e e n r e s t a t e d r e c e n t l y b y A n d e r s o n (1979, 1982) a n d A n d e r s o n & M a y (1979, 1981).

I n p r a c t i c e t h e i m p o r t a n c e of p a r a s i t i c i n f e c t i o n s i n h o s t p o p u l a t i o n b i o l o g y is e q u i v o c a l ( H o l m e s , 1982). W e c a n l o o k a t h i s t o l o g i c a l s e c t i o n s a n d p r e d i c t t h e e x t e n t of t h e d a m a g e i n i n d i v i d u a l f i s h ; w e c a n m e a s u r e p h y s i o l o g i c a l c h a n g e s i n f i s h a s a c o n s e q u e n c e of i n f e c t i o n ; w e c a n e v e n o b s e r v e f i s h d e a t h i n t h e l a b o r a t o r y a s a r e s u l t of a n i n f e c t i o n ; b u t w e c a n n o t b e s u r e of t h e r e l e v a n c e of t h e s e o b s e r v a t i o n s i n t h e f i e l d .

54 R . J . G . Lester

r e l i e v e d t h e p r e s s u r e of o v e r - p o p u l a t i o n t h a t w a s a f f e c t i n g t h e roach, l e a d i n g to an i n c r e a s e d g r o w t h rate t h e f o l l o w i n g y e a r a m o n g t h e survivors. A n o t h e r m e t h o d not d i s c u s s e d b e l o w b u t o n e w h i c h s h o w s p a r t i c u l a r p r o m i s e is t h e c o m p a r i s o n of r e c o v e r y r a t e s of t a g g e d d i s e a s e d a n d h e a l t h y fish (Munro et al., 1983). As far as I a m a w a r e this h a s not y e t b e e n used.

N o m e t h o d b y itself c a n p r o v i d e a d e f i n i t i v e a n s w e r . In most c a s e s an o b s e r v e d p o s i t i v e r e s u l t c a n a r i s e from c o n d i t i o n s o t h e r t h a n i n c r e a s e d host mortality. In e a c h case t h e a l t e r n a t i v e e x p l a n a t i o n s n e e d to b e r u l e d out b e f o r e w e c a n b e r e a s o n a b l y sure w e are m o n i t o r i n g p a r a s i t e - a s s o c i a t e d losses. T h i s u s u a l l y r e q u i r e s further w o r k such as a d d i t i o n a l s a m p l i n g , or l a b o r a t o r y e x p e r i m e n t s . K e n n e d y (1983) has c a u t i o n e d that e v e n if t h e r e is a c o r r e l a t i o n b e t w e e n fish d e a t h a n d p a r a s i t e b u r d e n it s h o u l d not n e c e s s a r i l y b e t a k e n as e v i d e n c e of c a u s e a n d effect. C o r r e l a t e d b u t i n d e p e n d e n t e v e n t s m a y be c a u s i n g t h e c h a n g e . T a k i n g all t h e s e r e s e r v a t i o n s i n t o a c c o u n t , t h e m e t h o d s d e s c r i b e d b e l o w , p a r t i c u l a r l y t h e statistical m e t h o d s , c a n b e e x t r e m e l y u s e f u l for, at the v e r y least, t h e y c a n tell us w h i c h h o s t - p a r a s i t e s y s t e m s w e s h o u l d l o o k at m o r e closely.

T h e m e t h o d s w h e n c o r r e c t l y i n t e r p r e t e d c a n i n d i c a t e w h e t h e r fish c a r r y i n g a p a r t i c u l a r p a r a s i t e l o a d a r e l i k e l y to h a v e a h i g h e r m o r t a l i t y rate t h a n less h e a v i l y i n f e c t e d or u n i n f e c t e d fish. W h e t h e r this is of s i g n i f i c a n c e to t h e fish p o p u l a t i o n as a w h o l e is a s e p a r a t e q u e s t i o n t h a t is not s p e c i f i c a l l y d e a l t w i t h here. It w a s a d d r e s s e d by M u n r o at this s y m p o s i u m in c o n n e c t i o n w i t h lchthyophonus in p l a i c e (see S i n d e r m a n n , 1984), a n d is c o n s i d e r e d in g e n e r a l t e r m s in t h e s e c t i o n " D i s c u s s i o n " .

M E T H O D S U S E D F O R E S T I M A T I N G M O R T A L I T Y M e t h o d 1: T h r o u g h a u t o p s i e s

In h u m a n a n d v e t e r i n a r y m e d i c i n e t h e m a i n m e a n s of d e t e r m i n i n g the c a u s e of d e a t h is t h r o u g h a p o s t - m o r t e m e x a m i n a t i o n . T h o u g h this m a y s e e m ideal, its f i n d i n g s m a y b e m i s l e a d i n g . C o n s i d e r t h e c a s e of a p e r s o n w h o b r e a k s a l e g a n d as a result of his i n a c t i v i t y c a t c h e s p n e u m o n i a from w h i c h h e dies. D e t e r m i n i n g t h e factor t h a t sets in m o t i o n a c h a i n of e v e n t s t h a t r e s u l t i n d e a t h is difficult e v e n w h e n a u t o p s i e s a r e p o s s i b l e . H o w e v e r , o n e r a r e l y finds d e a d or m o r i b u n d fish. T h i s is p r e s u m a b l y b e c a u s e p r e d a t o r s a n d s c a v e n g e r s t a k e s i c k fish b e f o r e t h e y die. Thus, if w e w e r e a b l e to c o m p l e t e a u t o p s i e s on all d e a d fish, t h e i m m e d i a t e c a u s e of d e a t h in most s p e c i e s is l i k e l y to be " b e i n g e a t e n " ! A f u r t h e r d i s a d v a n t a g e of this m e t h o d is that a u t o p s i e s u s u a l l y do not p r o v i d e us w i t h m u c h i d e a of t h e p r o p o r t i o n of t h e p o p u l a t i o n a f f e c t e d , at l e a s t in w i l d p o p u l a t i o n s .

M e t h o d s for e s t i m a t i n g m o r t a l i t y 55

d e a t h s c o i n c i d e d with a h e a v y m o r t a l i t y i n e x p e r i m e n t a l fish that h a d e a r l i e r b e e n i n o c u l a t e d with T.

bullocki.

T h e r e w e r e n o d e a t h s i n the control ( u n i n f e c t e d ) group. H e suggested that all y e a r l i n g s u m m e r f l o u n d e r that r e m a i n e d i n Lower C h e s a p e a k e Bay d u r i n g J a n u a r y 1981 d i e d as a r e s u l t of

T. bullocki

infections.

If parasite-affected fish are n o r m a l l y t a k e n b y p r e d a t o r s before t h e y die, a u t o p s i e s on predators c a n g i v e us the p r o p o r t i o n of p a r a s i t i z e d v e r s u s n o n - p a r a s i t i z e d fish b e i n g consumed. D o b b e n (1952), for e x a m p l e , f o u n d t h a t c o r m o r a n t s i n t h e N e t h e r l a n d s took roach p a r a s i t i z e d b y

Ligula intestinalis

m o r e f r e q u e n t l y t h a n t h e y took n o n - p a r a s i t i z e d roach. T h e p r e d a t i o n rate o n the i n f e c t e d fish w a s a b o u t five t i m e s h i g h e r . To d e t e r m i n e the s i g n i f i c a n c e of this d i f f e r e n t i a l m o r t a l i t y some m e a s u r e of the overall m o r t a l i t y rate d u e to cormorants is n e e d e d .

M e t h o d 2: D e t e r m i n i n g t h e f r e q u e n c y of l e t h a l i n f e c t i o n s

T h o u g h d e a d fish are r a r e l y found, fish c a r r y i n g i n f e c t i o n s t h a t u n d e r l a b o r a t o r y c o n d i t i o n s are i n v a r i a b l y t e r m i n a l are o c c a s i o n a l l y e n c o u n t e r e d . From t h e f r e q u e n c y of i n f e c t i o n a n e s t i m a t e of the n u m b e r s of fish d y i n g from the d i s e a s e c a n b e m a d e . A n obvious difficulty lies i n the a s s u m p t i o n that t h e l a b o r a t o r y r e s u l t s a r e d i r e c t l y a p p l i c - a b l e to the field. Also, as i n d i v i d u a l fish will v a r y i n t h e i r r e s i s t a n c e to the disease, it m a y be difficult to d e c i d e w h i c h i n f e c t i o n s i n the field are g o i n g to l e a d to death, a n d over w h a t time scale. A further c o m p l i c a t i o n is that d e a t h of l a r v a l or j u v e n i l e fish m a y occur i n such a short t i m e that few p a r a s i t i z e d j u v e n i l e s are e v e r c a u g h t .

Burreson (1984), i n a n e x t e n s i o n of his w o r k m e n t i o n e d a b o v e , s u c c e s s f u l l y a p p l i e d this t e c h n i q u e to

Trypanoplasma-infected

f l o u n d e r c a u g h t a l o n g the A t l a n t i c coast of North America. He e s t i m a t e d that 10 to 20 % of t h e f l o u n d e r off the coast of V i r g i n i a d i e d each winter.

T h e f u n g u s

Ichthyophonus hoferi

r e a d i l y c a u s e s d e a t h i n s e v e r a l m a r i n e a n d freshwater species i n t h e l a b o r a t o r y a n d is l i k e l y to h a v e t h e s a m e effect i n the field. Periodic epizootics off t h e North A m e r i c a n east coast w e r e b e l i e v e d to c a u s e w i d e s p r e a d mortality i n h e r r i n g a n d m a y h a v e h a d a role i n d e t e r m i n i n g h e r r i n g a b u n d a n c e ( S i n d e r m a n n , 1970). M c V i c a r (1981) l o o k e d at i n f e c t i o n s i n p l a i c e i n Scottish waters. He c o n s i d e r e d that the d i s e a s e was i n v a r i a b l y t e r m i n a l , a n d e s t i m a t e d that 55 % of the a n n u a l m o r t a l i t y i n p l a i c e i n o n e a r e a n o r t h of S c o t l a n d w a s a t t r i b u t a b l e to t h e parasite. He w e n t o n to d e t e r m i n e the p r o p o r t i o n of i n f e c t e d fish p r o d u c i n g d e t e c t a b l e a n t i b o d y to the parasite. U s i n g this, t o g e t h e r w i t h i n f o r m a t i o n o n t h e rate of a n t i b o d y p r o d u c t i o n a n d the form of the s u r v i v o r s h i p curve for i n f e c t e d fish, it is p o s s i b l e to c a l c u l a t e the a v e r a g e survival time for a n i n f e c t e d fish, a s s u m i n g rates of i n f e c t i o n a n d a n t i b o d y p r o d u c t i o n are constant.

M e t h o d 3: O b s e r v i n g a d e c r e a s e i n t h e p r e v a l e n c e of a l o n g - l i v e d p a r a s i t e w i t h h o s t a g e

56 R . J . G . Lester

C

•

. . .

k

0 ~

Host age

Fig. 1. Hypothetical example of a fish population in which the abundance of a long-lived parasite decreases with host age. The solid line represents the average number of parasites observed {or some other measure of degree of parasitaemia); the shaded area, the change in parasite abundance

due to lost hosts

r e a c h i n g a p e a k m a y d e c r e a s e in t h e fish r e m a i n i n g a l i v e (Fig. 1). If this h a p p e n s , one p o s s i b i l i t y is t h a t i n f e c t e d hosts a r e b e i n g s e l e c t i v e l y r e m o v e d from t h e p o p u l a t i o n s a m p l e d . ( O t h e r p o s s i b i l i t i e s i n c l u d e p o o r s a m p l i n g t e c h n i q u e , a n d an e r r o n e o u s a s s u m p t i o n t h a t t h e p a r a s i t e or scar r e m a i n s v i s i b l e for life.)

It is b e s t if o n e c o h o r t c a n b e f o l l o w e d t h r o u g h o u t its life s p a n or at least for a s u b s t a n t i a l p e r i o d of its life (the " p r o s p e c t i v e " a p p r o a c h of Doll & Hill, 1954), as the b u l k of t h e i n f e c t i o n m a y b e p i c k e d u p at o n e a g e a n d t h e a v a i l a b i l i t y of i n f e c t i v e s t a g e s m a y v a r y from y e a r to year. U n f o r t u n a t e l y this can not often b e d o n e w i t h a n y d e g r e e of c e r t a i n t y as t h e m o v e m e n t s of n a t u r a l fish p o p u l a t i o n s a r e g e n e r a l l y p o o r l y u n d e r s t o o d . Thus, this p o t e n t i a l l y p o w e r f u l t e c h n i q u e , or a n y m e t h o d that d e p e n d s on s e q u e n t i a l s a m p l i n g , m a y b e difficult to a p p l y in m a n y instances. In addition, for the m e t h o d to work, h e a v i l y i n f e c t e d i n d i v i d u a l s h a v e to s u r v i v e l o n g e n o u g h to a p p e a r in t h e p e a k s a m p l e .

H e n r i c s o n (1977) f o u n d t h a t t h e p t e r o c e r c o i d s of b o t h

Diphyllobothrium dendriticum

a n d

D. ditremum

i n t w o y e a r c l a s s e s of c h a r

Salvelinus alpinus

i n c r e a s e d d u r i n g t h e first s e v e n a n d e i g h t years, a n d t h e n d e c r e a s e d in 8 a n d 9 + fish. H e c o n c l u d e d t h a t the l o w e r i n t e n s i t y of p a r a s i t e s in o l d e r c h a r w a s c a u s e d b y t h e d e a t h of h e a v i l y i n f e c t e d fish. (He d i d not d e t e r m i n e w h a t p r o p o r t i o n w e r e lost b u t as both p a r a s i t e s h a d o v e r d i s p e r s e d d i s t r i b u t i o n s t h e a b s e n c e of just o n e or t w o h e a v i l y i n f e c t e d fish from his s a m p l e s c o u l d h a v e a c c o u n t e d for his results.)

P r o b a b l y t h e b e s t a q u a t i c e x a m p l e of this t e c h n i q u e , t h o u g h not from a fish, is that of Perrin & P o w e r s (1980). T h e y c o u n t e d t h e l e s i o n s c a u s e d b y t h e n e m a t o d e

Crassicauda

sp. in t h e skulls of d o l p h i n s

Delphinus delphis

of d i f f e r e n t a g e s . P r e s e n c e or a b s e n c e r a t h e r t h a n t h e n u m b e r of p a r a s i t e s w a s u s e d in t h e i r c a l c u l a t i o n s , m a k i n g the latter i n d e p e n d e n t of t h e f o r m of t h e p a r a s i t e ' s distribution. T h e y e s t i m a t e d that 11 to 14 % of t h e total a n n u a l n a t u r a l m o r t a l i t y w a s r e l a t e d to t h e p a r a s i t i c infection.

M e t h o d s for e s t i m a t i n g m o r t a l i t y 57 M e t h o d 4: O b s e r v i n g a d e c r e a s e i n t h e v a r i a n c e / m e a n r a t i o f o r t h e p a r a s i t e s

w i t h h o s t a g e

G o r d o n & Rau (1982) p r o p o s e d a n i n g e n i o u s m e t h o d for d e t e c t i n g m o r t a l i t y associ- a t e d w i t h h i g h l e v e l s of p a r a s i t a e m i a {Fig. 2). In t h e i r system, t h e fish

Culaea inconstans

w e r e c o n t i n u a l l y a c q u i r i n g m e t a c e r c a r i a e of

A p a t e m o n gracilis. T h e

m e a n n u m b e r of

c~ QJ u~

Q_

E

2

Voriance d e c r e a s e s meon

. . .

Host age

Fig. 2. Hypothetical example of a parasitized fish population in which the degree of dispersion of the parasite decreases with respect to the mean number of parasites, due to the loss of heavily infected individuals (Method of Gordon & Rau), The vertical bars represent the dispersion observed; the horizontal bars, the observed means; the dotted curve connects the "true" means, i.e. if no mortality had occurred; the dotted vertical lines the "true" dispersion if no mortality had occurred parasites per fish, the v a r i a n c e a n d t h e v a r i a n c e / m e a n ratio all i n c r e a s e d w i t h time, u n t i l at a c e r t a i n p o i n t t h e v a r i a n c e s t o p p e d i n c r e a s i n g a n d e v e n b e g a n to d e c r e a s e , t h u s c a u s i n g a d e c r e a s e in t h e v a r i a n c e / m e a n ratio. T h e y c o n c l u d e d t h a t t h e d e c r e a s e w a s d u e to h e a v i l y i n f e c t e d fish b e i n g r e m o v e d from t h e p o p u l a t i o n .

In a s u b s e q u e n t p a p e r , A n d e r s o n & G o r d o n (1982) u s e d s i m u l a t i o n m o d e l s to e x p l o r e the t h e o r e t i c a l a s p e c t s of this t e c h n i q u e . E s s e n t i a l l y t h e i r r e s u l t s c o n f i r m e d its v a l i d i t y , b u t in a d d i t i o n t h e y s h o w e d t h a t c h a n c e effects b e c o m e c r i t i c a l l y i m p o r t a n t w h e n h o s t s a m p l e sizes are small, a n d t h e y p o i n t e d o u t t h a t a d e c l i n e i n t h e d e g r e e of p a r a s i t e d i s p e r s i o n in t h e o l d e r a g e c l a s s e s m a y b e g e n e r a t e d b y factors o t h e r t h a n p a r a s i t e - i n d u c e d mortality. T h e s a m e effect c o u l d b e c a u s e d b y a r e d u c t i o n i n t h e d e g r e e of h e t e r o g e n e i t y in t h e i n f e c t i o n r a t e of o l d e r fish, or b y a c q u i r e d i m m u n i t y . T h e r e w a s no e v i d e n c e that e i t h e r of t h e s e w a s a c t i n g i n t h e

Culaea/Apatemon

system. G o r d o n & R a u (1982) did not try to e s t i m a t e w h a t p r o p o r t i o n of t h e fish p o p u l a t i o n w a s b e i n g r e m o v e d . It m a y b e e a s i e s t to do u s i n g a s i m u l a t i o n m o d e l . L i k e t h e p r e v i o u s m e t h o d , this m e t h o d r e q u i r e s s e q u e n t i a l s a m p l i n g a n d thus is s u b j e c t to t h e h a z a r d s t h a t t h a t entails.

58 R . J . G . L e s t e r

l a w for g e n e r a t i n g t h e p r o b a b i l i t i e s of c o m b i n a t i o n s of i n d e p e n d e n t events, the proba- b i l i t y of b o t h o r g a n s b e i n g i n f e c t e d is t h e p r o d u c t of t h e p r o b a b i l i t i e s of e a c h o n e b e i n g i n f e c t e d i r r e s p e c t i v e of t h e c o n d i t i o n of t h e other. S u p p o s e w e are a b l e to assess t h e s e p r o b a b i l i t i e s ; for e x a m p l e of left a n d r i g h t o r g a n s b e c o m i n g i n f e c t e d ; t h e p r o d u c t of t h e s e s h o u l d g i v e us s o m e i d e a of t h e e x p e c t a t i o n of f i n d i n g a fish w i t h b o t h sides i n f e c t e d , if all fish h a v e t h e s a m e risk of n a t u r a l mortality. If m o r t a l i t y is g r e a t e s t i n t h e m o s t h e a v i l y i n f e c t e d fish a s m a l l e r p r o p o r t i o n of fish w i t h b o t h sides i n f e c t e d w i l l be o b s e r v e d t h a n p r e d i c t e d f r o m t h e a b o v e c a l c u l a t i o n .

To c a l c u l a t e t h e p r o b a b i l i t i e s of i n f e c t i o n w e c a n n o t u s e t h e totals, as t h e y are to s o m e e x t e n t d e p e n d e n t o n t h e n u m b e r of d o u b l e i n f e c t i o n s o b s e r v e d . Instead, t h e y are c a l c u l a t e d u s i n g a 2 x 2 table, r i g h t - i n f e c t e d a n d r i g h t - u n i n f e c t e d on o n e axis a n d left- i n f e c t e d a n d l e f t - u n i n f e c t e d on t h e o t h e r axis.

For e x a m p l e , f l o u n d e r A t h e r e s t e s stomias off British C o l u m b i a are o c c a s i o n a l l y p a r a s i t i z e d b y t h e c o p e p o d Phrixocephalus cincinnatus. T h i s d e v e l o p s in t h e e y e of t h e fish. Of a s a m p l e of 64 fish, K a b a t a (1969) f o u n d that 50 h a d t h e r i g h t e y e infected, a n d 18 t h e left eye. Of t h e s e , 15 w e r e d o u b l e infections. F r o m t h e 2 x 2 t a b l e a b o v e a n d a s s u m i n g no fish d i e w i t h s i n g l e i n f e c t i o n s , t h e p r o b a b i l i t y of g e t t i n g an i n f e c t i o n in the r i g h t e y e w a s 35/46 = 0.76, a n d in t h e left e y e 3/14 = 0.21. Thus, t h e p r o b a b i l i t y of h a v i n g b o t h e y e s i n f e c t e d w a s 0.76 x 0.21 = 0.16, i.e. 10 fish. T h i s is less t h a n the actual n u m b e r o b s e r v e d w i t h d o u b l e i n f e c t i o n s , so t h e d a t a s u g g e s t t h a t t h e r e is no m o r t a l i t y a s s o c i a t e d w i t h t h e infection.

T h i s c a l c u l a t i o n is b a s e d on a r e l a t i v e l y s m a l l n u m b e r of fish. T o carry out a formal test to d e t e r m i n e w h e t h e r t h e o b s e r v e d d a t a are c o n s i s t e n t w i t h the h y p o t h e s e s that fish s u r v i v a l is i n d e p e n d e n t of i n f e c t i o n , a n d left a n d r i g h t e y e i n f e c t i o n s o c c u r i n d e p e n - d e n t l y of o n e a n o t h e r , X 2 v a l u e s c a n b e c a l c u l a t e d from t h e 2 x 2 t a b l e d e s c r i b e d above. In this e x a m p l e , t h e s u m of t h e c h i - s q u a r e d v a l u e s is 0.4 i n d i c a t i n g that t h e o b s e r v e d a n d e x p e c t e d v a l u e s are n o t s i g n i f i c a n t l y different. In fact, w i t h a s a m p l e of only 64 fish, t h e r e w o u l d h a v e to b e a m o r t a l i t y of o v e r 50 % in t h e d o u b l e e y e i n f e c t i o n s before it c o u l d b e d e t e c t e d at t h e 95 % l e v e l of c o n f i d e n c e .

O t h e r o b s e r v a t i o n s o n P. cincinnatus s u g g e s t t h a t t h e p a r a s i t e is q u i t e p a t h o g e n i c ; fish w i t h b o t h e y e s p a r a s i t i z e d e v e n t u a l l y b e c o m e b l i n d a n d p r o b a b l y d i e from starva- t i o n (Kabata, 1970). T h e f a i l u r e of t h e statistical a n a l y s i s to d e t e c t a n y i n c r e a s e in m o r t a l i t y p e r h a p s r e f l e c t s t h e s m a l l size of t h e s a m p l e (Fisher's E x a c t T e s t m a y h e l p here), or an e r r o n e o u s a s s u m p t i o n that t h e left a n d r i g h t e y e i n f e c t i o n s a r e i n d e p e n d e n t e v e n t s . It w o u l d b e v a l u a b l e to c o l l e c t m o r e d a t a on this i n t e r e s t i n g p a r a s i t e .

M e t h o d s for e s t i m a t i n g m o r t a l i t y 59 T h e m e t h o d , first p r o p o s e d b y C r o f t o n (1971), r e q u i r e s t h a t m o r t a l i t y i n c r e a s e s w i t h the n u m b e r of p a r a s i t e s p r e s e n t . Thus, t h e o b s e r v e d f r e q u e n c y d i s t r i b u t i o n of the p a r a s i t e (Fig. 3; h i s t o g r a m ) w i l l l a c k fish p a r t i c u l a r l y in t h e tail of t h e d i s t r i b u t i o n . In reality w e do not k n o w t h e v a l u e s for t h e o r i g i n a l d i s t r i b u t i o n ( r e p r e s e n t e d b y dots in t h e

u)

E Z

• • • •

0 1 2 3 6 7 8 9 10 11 12 13 14 Number of p a r a s i t e s

Fig. 3. Hypothetical example of the frequency distribution of a parasite in a fish population. The circles represent the original distribution at the time of infection, and the histogram the distribution observed after some of the more heavily infected fish had died. Theoretical distributions fitted to the observed data truncated at progressively fewer parasites will approach the original distribution figure). H o w e v e r , w e m a k e t h e a s s u m p t i o n t h a t l i k e t h e m a j o r i t y of p a r a s i t e s it f o l l o w e d s o m e form of n e g a t i v e b i n o m i a l r e a s o n a b l y closely. V a l u e s c a n b e e s t i m a t e d for t h e n e g a t i v e b i n o m i a l p a r a m e t e r s p, k, a n d N (the t o t a l n u m b e r in t h e s a m p l e ) b y fitting t h e d i s t r i b u t i o n to t h e o b s e r v e d d a t a by o n e statistical m e a n s or a n o t h e r . T h e e x t e n t to w h i c h the d i s t r i b u t i o n fits the d a t a c a n b e a s s e s s e d b y a X 2 statistic.

If w e n o w o m i t t h e last o b s e r v e d p o i n t in the figure, a n d fit a n e g a t i v e b i n o m i a l d i s t r i b u t i o n to t h e f r e q u e n c i e s of fish w i t h 0 to 9 p a r a s i t e s , a n d s u b s e q u e n t l y 0 to 8, 0 to 7, etc., an i n c r e a s i n g e s t i m a t e d v a l u e of N w i l l s u g g e s t t h a t t h e r e are f e w e r h e a v i l y i n f e c t e d fish t h a n o n e w o u l d e x p e c t f r o m t h e f r e q u e n c y d i s t r i b u t i o n of t h e l i g h t l y i n f e c t e d fish. T h e i n d i v i d u a l e x p e c t e d f r e q u e n c i e s c a n b e c a l c u l a t e d for direct c o m p a r i s o n w i t h o b s e r v e d f r e q u e n c i e s .

T h e m e t h o d u s e d b y t h e a u t h o r is a n i t e r a t i v e t e c h n i q u e , m i n i m i z i n g X 2 to d e t e r m i n e the b e s t fit (Lester, 1977). Local m i n i m a in t h e X 2 v a l u e s c a n occur, so it is b e s t to start w i t h the full d i s t r i b u t i o n a n d w o r k b a c k , t r u n c a t i n g in s m a l l steps.

A n u n e x p e c t e d l y i n f r e q u e n t o c c u r r e n c e of h e a v i l y i n f e c t e d fish in t h e s a m p l e m a y be t h e result of s e v e r a l factors o t h e r t h a n i n c r e a s e d host mortality, such as s a m p l i n g error, d e v e l o p m e n t of a v o i d a n c e b e h a v i o u r or r e s i s t a n c e in t h e i n f e c t e d fish, t h e loss of p a r a s i t e s from h e a v i l y i n f e c t e d fish, or c h o o s i n g a n i n a p p r o p r i a t e t h e o r e t i c a l distribu- tion. For the t e c h n i q u e to work, s m a l l n u m b e r s of p a r a s i t e s s h o u l d h a v e little effect on mortality. In a d d i t i o n , t h e s a m p l e s h o u l d e i t h e r b e d r a w n from fish of t h e s a m e a g e , or from a g e classes after i n f e c t i o n a n d m o r t a l i t y h a v e o c c u r r e d .

60 R . J . G . L e s t e r

p r o g r e s s i v e l y t r u n c a t e d , t h e e s t i m a t e d total n u m b e r in t h e s a m p l e i n c r e a s e d . In the m a l e s , a d i s t r i b u t i o n fitted to t h e f r e q u e n c i e s of fish w i t h 0 to 3 p a r a s i t e s (Fig. 4) p r e d i c t e d that o n e w o u l d h a v e e x p e c t e d a b o u t 5 % m o r e fish in the s a m p l e t h a n w a s o b s e r v e d . F r o m o t h e r o b s e r v a t i o n s it s e e m e d l i k e l y t h a t this w a s a r e s u l t of p a r a s i t e -

200

r - u3

~_100

E Z

O

0 0 0

0 ~

0 1 2 3 4 5 6 7+

Number of parGsites

Fig. 4. The histogram represents the frequency distribution of blastocysts of Callitetrarhynchus gracilis in 452 male Saurida tumbil (from Adjei, pers. comm.). The circles are from the negative

binomial distribution that best fits the first four points of the histogram

r e l a t e d m o r t a l i t y a f f e c t i n g t h e h e a v i l y - i n f e c t e d fish. In t h e f e m a l e s , the fitted c u r v e p r e d i c t e d 2 to 3 % m o r e fish (Fig. 5).

H o w e v e r , t h e s h a p e s of t h e c u r v e s w e r e v e r y different. T h o u g h t h e ratio of u n i n - f e c t e d fish to fish w i t h o n e p a r a s i t e w a s s i m i l a r in b o t h sexes, r e l a t i v e l y f e w e r fish w i t h 2 or m o r e p a r a s i t e s w e r e o b s e r v e d in m a l e s t h a n in f e m a l e s . T h i s s u g g e s t e d that t h o u g h t h e m a l e s a n d f e m a l e s w e r e p i c k i n g up p a r a s i t e s at m u c h t h e s a m e rate, m u l t i p l e i n f e c t i o n s in the m a l e s w e r e m u c h rarer. T h u s t h e t h i r d a n d fourth points of the m a l e c u r v e w e r e p r o b a b l y n o t a r e l i a b l e i n d i c a t o r of t h e o r i g i n a l distribution.

M e t h o d s for e s t i m a t i n g m o r t a l i t y 61 200

ZZ

"s

,- 100

E Z

O O

0 , t 1

0 1 2 3 4 5 6 7+

Number of parasites

Fig. 5. F r e q u e n c y distributions of C. gracilis blastocysts i n 445 f e m a l e s S. tumbil. T h e circles r e p r e s e n t the n e g a t i v e b i n o m i a l d i s t r i b u t i o n t h a t b e s t fits t h e first four v a l u e s

+20- CO~ ~ o

~ c ~5~ ÷10- c k ~ o

.c_

O - - - O

2 3 4 5 6

Truncation point (number of parasites per fish)

Fig. 6. The differences b e t w e e n the o b s e r v e d total n u m b e r of fish a n d the e s t i m a t e d total n u m b e r from distributions fitted to p r o g r e s s i v e l y more of the h i s t o g r a m s in Figures 5 a n d 6. Solid lines, m a l e

fish; dotted lines, f e m a l e fish

62 R . J . G . L e s t e r

a b o u t t h e s a m e s i z e (100 to 140 mm}, w h e n f e e d i n g o n t h e s a m e food (Adjei, pers. comm.). T h e i r distribution, p a r t i c u l a r l y w h e n t r u n c a t e d at 3 p a r a s i t e s p e r fish, thus p r o v i d e d a n e s t i m a t e of t h e e x p e c t e d p a r a s i t e d i s t r i b u t i o n in m a l e fish in t h e a b s e n c e of p a r a s i t e - r e l a t e d mortality. F i g u r e 7 s h o w s t h e results of t h e s i m p l e s t a p p l i c a t i o n of this data: t h e p r e d i c t e d o r i g i n a l n u m b e r s of m a l e s b a s e d on a n e g a t i v e b i n o m i a l d e r i v e d

¢-

g3

"5

oJ ,.{3

E

Z

200

100"

0

0 1 2 3 4 5 6 7* Number of perosites

Fig. 7. Frequency distribution of the parasite in male fish (from Fig. 4} with an estimate of the probable original distribution (shaded area}

f r o m t h e n u m b e r of m a l e s w i t h zero, a n d t h e p a n d k p a r a m e t e r s e s t i m a t e d from t h e f e m a l e s . It p r e d i c t s t h a t a b o u t 12 % of t h e m a l e s are m i s s i n g f r o m t h e s a m p l e . This is a m i n i m u m e s t i m a t e as w e h a v e a s s u m e d t h a t f e m a l e s w i t h l o w n u m b e r s of p a r a s i t e s are n o t a f f e c t e d .

A m o r e s o p h i s t i c a t e d statistical a n a l y s i s of this d a t a is i n p r e p a r a t i o n .

DISCUSSION

M e t h o d s for e s t i m a t i n g m o r t a l i t y 63 should ask is, if a p a r a s i t e i n c r e a s e d t h e l i k e l i h o o d of death, is this of a n y c o n s e q u e n c e to the host p o p u l a t i o n ? W h e n it occurs in r e l a t i v e l y old p o s t r e p r o d u c t i v e a n i m a l s , t h e answer in g e n e r a l m a y b e no, e x c e p t if it a l l o w s m o r e of a y o u n g e r a g e g r o u p to s u r v i v e . Mortality in p r e - b r e e d i n g i n d i v i d u a l s , h o w e v e r , m a y b e m u c h m o r e i m p o r t a n t .

In p r a c t i c a l terms, w e n e e d to t a c k l e t h e q u e s t i o n , if t h e p a r a s i t e w a s absent, w o u l d there be m o r e fish? In m a n y c a s e s t h e h i g h e r m o r t a l i t y r a t e of p a r a s i t i z e d fish c o m p a r e d to n o n - p a r a s i t i z e d m a y e v e n t u a l l y b e s h o w n to b e b e c a u s e t h e y are s e l e c t i v e l y r e m o v e d by p r e d a t o r s (see for e x a m p l e D o b b e n , 1952). P r e d a t o r s t a k e t h e m p r e s u m a b l y b e c a u s e it r e q u i r e s less e n e r g y to c a t c h t h e m c o m p a r e d to n o n - p a r a s i t i z e d fish. If a p r e d a t o r h a s a fixed total a m o u n t of e n e r g y for c a t c h i n g prey, t h e n if t h e p a r a s i t e w e r e absent, t h e p r e d a t o r w o u l d t a k e less prey, a n d t h e r e f o r e o n e m i g h t e x p e c t t h a t m o r e p r e y w o u l d survive.

H o w e v e r , t h e factors t h a t control p o p u l a t i o n s i z e a r e v a r i e d a n d f r e q u e n t l y n o t w e l l u n d e r s t o o d . H i g h l y t e r r i t o r i a l s p e c i e s m a y b e r e s t r i c t e d b y t h e a v a i l a b i l i t y of territory, others by t h e a v a i l a b i l i t y of shelter. In t h e s e cases, if t h e h a b i t a t is n e a r its c a r r y i n g c a p a c i t y a d e c r e a s e in losses a s s o c i a t e d w i t h p a r a s i t e s m a y not i n c r e a s e total p o p u l a t i o n size ( t h o u g h it m a y affect t h e a g e structure). O n t h e o t h e r h a n d , w h e r e t h e s i z e of a y e a r class is m o r e or less d e t e r m i n e d b y say t h e a v a i l a b i l i t y of food d u r i n g t h e e a r l y l a r v a l stages, t h e n any a d d i t i o n a l m o r t a l i t y t h a t occurs after t h a t s t a g e w i l l p r e s u m a b l y affect the p o p u l a t i o n size. F r o m a f i s h e r i e s p o i n t of view., t h e p e r i o d w h e n d i s e a s e - a s s o c i a t e d mortality is h a v i n g its g r e a t e s t effect m a y be, as M u n r o e t al. (1983) h a v e p o i n t e d out, after t h e fry s t a g e a n d b e f o r e t h e fish a r e r e c r u i t e d to t h e fishery. T h i s is a s t a g e w h i c h s h o u l d r e c e i v e m o r e attention.

W h e r e t h e r e is e v i d e n c e , p e r h a p s from o n e of t h e m e t h o d s a b o v e , t h a t a n i n f e c t i o n is c a u s i n g serious m o r t a l i t y a m o n g a d u l t fish, it m a y b e p o s s i b l e to c o m p a r e t h e a g e structure of two a d j a c e n t p o p u l a t i o n s or s u b - p o p u l a t i o n s , o n e h e a v i l y p a r a s i t i z e d a n d o n e m o r e or less f r e e of t h e p a r a s i t e . In t h e p a r a s i t i z e d p o p u l a t i o n o n e w o u l d e x p e c t to find a g r e a t e r p r o p o r t i o n of y o u n g e r i n d i v i d u a l s t h a n in t h e n o n - p a r a s i t i z e d p o p u l a t i o n . Finally, in theory, p a r a s i t i c i n f e c t i o n s l i k e o t h e r d i s e a s e s , a r e a b l e to r e g u l a t e host p o p u l a t i o n size. For true r e g u l a t i o n to occur, losses a s s o c i a t e d w i t h p a r a s i t e s s h o u l d i n c r e a s e w h e n t h e p o p u l a t i o n is l a r g e a n d d e c r e a s e w h e n t h e p o p u l a t i o n is small. D o e s this h a p p e n in r e a l i t y ? U n t i l w e h a v e m o r e r e s u l t s w e c a n n o t say.

Acknowledgements, I am indebted to Mr. A. Barnes of the University of Queensland for statistical advice, and to Dr. G. Lauckner of the Biologische Anstalt Helgoland for critically reviewing the manuscript.

LITERATURE C I T E D

Anderson, R. M., 1979. The influence of parasitic infection on the dynamics of host population growth. In: Population dynamics. Ed. by R. M. Anderson, B. D. Turner & L. R. Taylor. Blackwell, Oxford, 245-281.

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