HELGOI-~NDER MEERESUNTERSUCHUNGEN
Helgol~nder Meeresunters. 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 fish 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 methods are described for detecting mortality due to parasitic infections in natural
fish populations. They are: (a) t h r o u g h autopsies; (b) by d e t e r m i n i n g the frequency of infections
k n o w n to be eventually lethal; (c) by observing a decrease in the p r e v a l e n c e of a long-lived parasite
(or p e r m a n e n t scar from a parasite) with host age; (d) by o b s e r v i n g a decrease in the v a r i a n c e / m e a n
ratio for the parasites with host age; (e) by c o m p a r i n g the observed frequency 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 events with the calculated probability of their occurrence; a n d finally {f) by
comparing the observed frequency distribution of the parasite, with a projected frequency b a s e d on
data from lightly infected fish. In this technique, n e g a t i v e binomials are fitted to the data a n d
truncated 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 methods are given,
together with examples. The methods do not necessarily provide definitive answers, but they are
indicative of w h e t h e r or not significant parasite-related mortality m a y b e occurring, a n d in some
cases provide an estimate of its p r o b a b l e m a g n i t u d e in terms of the total host mortality rate.
INTRODUCTION
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 . In 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 to b e a m a j o r c o n t r i b u t o r to
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 to 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).
In 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
the damage in individual fish; we can measure physiological changes in fish as 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 field.
S e v e r a l a p p r o a c h e s h a v e b e e n u s e d i n r e c e n t y e a r s to d e t e r m i n e w h e t h e r a p a r a s i t i c
i n f e c t i o n is l i k e l y to b e a f f e c t i n g t h e h o s t m o r t a l i t y r a t e i n a n a t u r a l p o p u l a t i o n . O t h e r
t e c h n i q u e s n e e d to b e d e v e l o p e d a n d a l l n e e d t o b e m o r e w i d e l y a p p l i e d t o g i v e u s s o m e
a n s w e r s to w h a t is a f u n d a m e n t a l q u e s t i o n i n e c o l o g i c a l p a r a s i t o l o g y . S i x m e t h o d s a r e
d e s c r i b e d b e l o w t o g e t h e r w i t h a n e x a m p l e of e a c h . T h i s is n o t a n e x h a u s t i v e list. O t h e r
techniques have been used in specific situations. For example, Burrough & Kennedy
(1979) f o u n d t h a t s t u n t i n g i n r o a c h a s a r e s u l t of h i g h p o p u l a t i o n d e n s i t y w a s a l l e v i a t e d
f o l l o w i n g a n e p i d e m i c of Ligula intestinalis. M a n y i n f e c t e d f i s h a p p a r e n t l y d i e d a n d t h i s
© Biologische Anstalt Helgoland, H a m b u r g
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 that w a s affecting the 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 the 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 but o n e w h i c h shows p a r t i c u l a r p r o m i s e is the c o m p a r i s o n of r e c o v e r y
rates 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 am a w a r e this
has not y e t b e e n used.
N o m e t h o d by itself c a n p r o v i d e a d e f i n i t i v e answer. In most cases an o b s e r v e d
p o s i t i v e result c a n arise from conditions other 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 be r u l e d out before w e can be 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. This 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 should not n e c e s s a r i l y
be 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 but 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 into account, the m e t h o d s d e s c r i b e d
below, p a r t i c u l a r l y the statistical methods, can b e e x t r e m e l y useful for, at the very 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 systems w e should look at m o r e closely.
T h e m e t h o d s w h e n correctly 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 carrying a
p a r t i c u l a r p a r a s i t e load are l i k e l y to h a v e a h i g h e r mortality 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 the 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 that 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 section " D i s c u s s i o n " .
METHODS USED FOR ESTIMATING MORTALITY
Method
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 the m a i n m e a n s of d e t e r m i n i n g the cause 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 findings
m a y b e m i s l e a d i n g . C o n s i d e r the case of a p e r s o n w h o b r e a k s a l e g and 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 he dies. D e t e r m i n i n g the factor that sets in
m o t i o n a c h a i n of e v e n t s that result in d e a t h is difficult e v e n w h e n a u t o p s i e s are possible.
H o w e v e r , one r a r e l y finds d e a d or m o r i b u n d fish. This is p r e s u m a b l y b e c a u s e predators
a n d s c a v e n g e r s t a k e sick 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 further 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 the p r o p o r t i o n of the p o p u l a t i o n affected, at least in wild
populations.
D e a d fish are u s u a l l y s e e n d u r i n g e p i z o o t i c s w h e n l a r g e n u m b e r s are d y i n g at one
time. A n n u a l mass m o r t a l i t i e s of t h e m u l l e t Liza carinata h a v e b e e n r e p e a t e d l y o b s e r v e d
in p o s t s p a w n i n g a g g r e g a t i o n s in a l a g o o n off t h e Gulf of S u e z (Paperna & Diamant,
1984). L a r g e n u m b e r s of t h e m o n o g e n e a n Benedenia monticelli w e r e found on d y i n g
a n d d e a d fish. T h e s e v e r e d e r m a l e r o s i o n p r o d u c e d by h e a v y infestations of this parasite
w a s t h o u g h t to b e a m a j o r contributor to t h e c a u s e of d e a t h in t h e s e fish. Burreson (1981}
f o u n d that 39 of 48 j u v e n i l e s u m m e r f l o u n d e r s t r a w l e d in late J a n u a r y from the l o w e r
York River, U.S.A., w e r e dead. All fish from w h i c h b l o o d could still b e c o l l e c t e d w e r e
i n f e c t e d w i t h Trypanoplasma bullocki a n d most of t h e fish h a d s e v e r e ascites. T h e
Methods for e s t i m a t i n g mortality
55
deaths coincided with a h e a v y mortality i n e x p e r i m e n t a l fish that h a d earlier b e e n
inoculated with T. bullocki. T h e r e were n o deaths i n the control (uninfected) group. He
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
during J a n u a r y 1981 died as a result of T. bullocki infections.
If parasite-affected fish are n o r m a l l y t a k e n by predators before they die, autopsies
on predators c a n give us the proportion of parasitized versus 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 example, f o u n d that cormorants i n the N e t h e r l a n d s took
roach parasitized b y Ligula intestinalis more f r e q u e n t l y t h a n they took n o n - p a r a s i t i z e d
roach. The p r e d a t i o n rate on the infected fish was a b o u t five times higher. To d e t e r m i n e
the significance of this differential mortality some m e a s u r e of the overall mortality 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 dead fish are rarely found, fish carrying infections that u n d e r laboratory
conditions are i n v a r i a b l y t e r m i n a l are occasionally e n c o u n t e r e d . From the f r e q u e n c y of
infection a n estimate of the n u m b e r s of fish d y i n g from the disease 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 the laboratory results are directly applicable to the field. Also, as i n d i v i d u a l fish will vary i n their resistance to the disease, it m a y
be difficult to decide w h i c h infections i n the field are g o i n g to l e a d to death, a n d over
what time scale. A further c o m p l i c a t i o n is that d e a t h of larval or j u v e n i l e fish m a y occur
in such a short time that few parasitized j u v e n i l e s are ever caught.
Burreson (1984), i n a n e x t e n s i o n of his work m e n t i o n e d above, successfully 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 Atlantic coast of
North America. He e s t i m a t e d that 10 to 20 % of the f l o u n d e r off the coast of V i r g i n i a died
each winter.
The fungus Ichthyophonus hoferi r e a d i l y causes 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 the laboratory a n d is likely to h a v e the s a m e effect i n the field.
Periodic epizootics off the 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 in h e r r i n g a n d m a y have h a d a role in 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
(Sindermann, 1970). McVicar (1981) looked at infections i n plaice i n Scottish waters. He
considered that the disease was i n v a r i a b l y terminal, a n d e s t i m a t e d that 55 % of the
a n n u a l mortality i n plaice i n one area north of Scotland was a t t r i b u t a b l e to the parasite.
He w e n t o n to d e t e r m i n e the proportion of infected 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. Using this, together with i n f o r m a t i o n o n the 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 survivorship curve for infected fish, it is possible to calculate the a v e r a g e
survival time for a n infected fish, a s s u m i n g rates of infection 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
host age
M a n y parasites, particularly larval h e l m i n t h s , are t h o u g h t to r e m a i n alive in the fish
for e x t e n d e d periods, often for the life of the fish. Other parasites, t h o u g h they die, l e a v e
a scar or a mass of a m o r p h o u s necrotic tissue i n d i c a t i n g their former presence. As a host
cohort ages, the f r e q u e n c y of such parasites or scars will i n i t i a l l y increase, a n d t h e n after
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 the 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
possibility is that i n f e c t e d hosts are 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 . (Other p o s s i b i l i t i e s i n c l u d e poor s a m p l i n g t e c h n i q u e , and an e r r o n e o u s
a s s u m p t i o n that the 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 best if o n e cohort 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 span 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 the a v a i l a b i l i t y of i n f e c t i v e stages m a y
vary 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 with any d e g r e e of
certainty 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 are g e n e r a l l y poorly understood.
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 the p e a k
sample.
H e n r i c s o n (1977) f o u n d that the p t e r o c e r c o i d s of both Diphyllobothrium dendriticum
a n d D. ditremum in t w o y e a r classes of c h a r Salvelinus alpinus i n c r e a s e d d u r i n g the 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 that 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 by 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
did 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 but as both parasites h a d o v e r d i s p e r s e d
distributions the a b s e n c e of just o n e or two 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 could
h a v e a c c o u n t e d for his results.)
P r o b a b l y the 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 the lesions c a u s e d by the n e m a t o d e Crassicauda
sp. in the skulls of d o l p h i n s Delphinus delphis of different ages. P r e s e n c e or a b s e n c e
rather t h a n the n u m b e r of p a r a s i t e s w a s u s e d in their calculations, m a k i n g the latter
i n d e p e n d e n t of the form of the 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
the 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 the parasitic infection.
E s t i m a t e s b a s e d on this m e t h o d are l i k e l y to b e u n d e r e s t i m a t e s for if 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 are d i s a p p e a r i n g from the p o p u l a t i o n t h e n the o b s e r v e d p e a k in the
l e v e l of p a r a s i t a e m i a is l i k e l y to b e too low. Perrin & Powers h a d to a s s u m e that t h e r e
w a s no mortality prior to t h e p e a k , a n d no n e w lesions o c c u r r e d after the peak.
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
M e t h o d 4: O b s e r v i n g
a decrease
in the variance/mean
with host age
57
ratio for t h e p a r a s i t e s
Gordon & 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 associated with 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, the 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 Apatemon gracilis. The m e a n n u m b e r of
c~
QJ
Voriance decreases
meon
u~
Q_
E
2
. . . . .
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 the 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, until
at a certain point the 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 , thus
c a u s 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. T h e y c o n c l u d e d that the 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 paper, 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 aspects 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 results c o n f i r m e d its validity,
but in a d d i t i o n t h e y s h o w e d that c h a n c e effects b e c o m e critically i m p o r t a n t w h e n host
s a m p l e sizes are small, a n d t h e y p o i n t e d out that a d e c l i n e in t h e d e g r e e of p a r a s i t e
dispersion in t h e o l d e r a g e classes m a y b e g e n e r a t e d by 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 by a r e d u c t i o n in the d e g r e e of
h e t e r o g e n e i t y in t h e infection rate of o l d e r fish, or by 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 in t h e Culaea/Apatemon system. G o r d o n & Rau
(1982) did not try to e s t i m a t e w h a t proportion of the 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 be easiest to do u s i n g a s i m u l a t i o n model. Like the 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 that that entails.
M e t h o d 5: C o m p a r i s o n of 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 t w o
i n d e p e n d e n t e v e n t s w i t h t h e 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 o c c u r r e n c e
In a few cases parasitic i n f e c t i o n m a y occur i n d e p e n d e n t l y in two or m o r e different
organs. C o n s i d e r a s i m p l e i n s t a n c e of this w h e r e only two organs are i n v o l v e d but the
p r o b a b i l i t y of the organs b e i n g i n f e c t e d is not n e c e s s a r i l y the same. By t h e m u l t i p l i c a t i v e
58
R . J . G . Lester
l a w for g e n e r a t i n g the 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 probability of both 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 the c o n d i t i o n of the other. S u p p o s e w e are a b l e to assess these
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 infected; 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 the e x p e c t a t i o n of f i n d i n g a fish with both sides
infected, 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 mortality is g r e a t e s t in the
most 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 with both sides infected will be
o b s e r v e d t h a n p r e d i c t e d from t h e a b o v e calculation.
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 use the totals, as they are to
s o m e e x t e n t d e p e n d e n t on t h e n u m b e r of d o u b l e infections 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 one axis and lefti 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 Atherestes stomias off British C o l u m b i a are occasionally
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. This d e v e l o p s in the e y e of the
fish. Of a s a m p l e of 64 fish, Kabata (1969) f o u n d that 50 h a d the right e y e infected, and 18
t h e left eye. Of these, 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 die w i t h s i n g l e infections, the p r o b a b i l i t y of g e t t i n g an infection 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, the p r o b a b i l i t y of
h a v i n g both eyes i n f e c t e d w a s 0.76 x 0.21 = 0.16, i.e. 10 fish. This is less than 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 infections, so t h e data s u g g e s t that t h e r e is no mortality
a s s o c i a t e d w i t h the infection.
This 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. To carry out a formal
test to d e t e r m i n e w h e t h e r the o b s e r v e d data are consistent with the h y p o t h e s e s that fish
survival is i n d e p e n d e n t of infection, a n d left a n d r i g h t e y e infections occur i n d e p e n d e n t l y of one another, X2 v a l u e s c a n b e c a l c u l a t e d from the 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 the o b s e r v e d and
e x p e c t e d v a l u e s are not 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 infections 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 on P. cincinnatus s u g g e s t that 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 both 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 and p r o b a b l y die from starvation (Kabata, 1970). T h e failure of the statistical analysis to d e t e c t any 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 reflects the s m a l l size of the s a m p l e (Fisher's Exact Test 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 right e y e infections a r e i n d e p e n d e n t
events. It w o u l d b e v a l u a b l e to collect m o r e data on this i n t e r e s t i n g parasite.
Method
6: C o m p a r i s o n of t h e o b s e r v e d f r e q u e n c y of t h e p a r a s i t e w i t h
projected frequency based on data from the lightly-infected fish
a
In most cases i n f e c t i o n is not a r a n d o m p r o c e s s a n d w e h a v e to resort to other m e a n s
to p r e d i c t the f r e q u e n c y of m u l t i p l e infections. This r e q u i r e s m a k i n g an assumption
a b o u t the form of t h e p a r a s i t e ' s d i s t r i b u t i o n a m o n g t h e hosts at t h e t i m e of infection.
Parasite distributions are almost i n v a r i a b l y o v e r d i s p e r s e d a n d u s u a l l y follow a n e g a t i v e
b i n o m i a l t y p e of distribution. This is t h e case c o n s i d e r e d here, t h o u g h in s o m e circumstances a different distribution m a y be m o r e a p p r o p r i a t e , such as a Poisson or N e y m a n A,
in w h i c h case this w o u l d b e u s e d in p l a c e of t h e n e g a t i v e b i n o m i a l .
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 Crofton (1971), r e q u i r e s that 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 parasites present. Thus, t h e o b s e r v e d f r e q u e n c y distribution of the
parasite (Fig. 3; histogram) will l a c k fish p a r t i c u l a r l y in t h e tail of the distribution. In
reality w e do not k n o w the v a l u e s for t h e o r i g i n a l distribution ( r e p r e s e n t e d by dots in the
u)
E
Z
•
0 1 2 3
6
•
•
•
7 8 9 10 11 12 13 14
Number of parasites
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 the a s s u m p t i o n that like the 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
some 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 total n u m b e r in t h e sample) b y fitting t h e
distribution to the o b s e r v e d data by o n e statistical m e a n s or another. T h e e x t e n t to w h i c h
the distribution fits the data can b e a s s e s s e d by a X2 statistic.
If w e n o w omit the 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
distribution to the f r e q u e n c i e s of fish w i t h 0 to 9 parasites, 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 that 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 from 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.
The 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 can be c a l c u l a t e d for direct c o m p a r i s o n with
o b s e r v e d frequencies.
The m e t h o d u s e d by the author is an 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 X2 to d e t e r m i n e
the best fit (Lester, 1977). Local m i n i m a in t h e X2 v a l u e s c a n occur, so it is best to start
with the full distribution a n d w o r k back, 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 the result of s e v e r a l factors other than 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 the i n f e c t e d fish, the loss of
parasites 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 an i n a p p r o p r i a t e t h e o r e t i c a l distribution. For the t e c h n i q u e to work, small n u m b e r s of p a r a s i t e s should h a v e little effect on
mortality. In addition, t h e s a m p l e s h o u l d e i t h e r be d r a w n from fish of t h e s a m e age, 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 occurred.
A d j e i (pers. comm.) c o u n t e d t h e n u m b e r s of Caltitetrarhynchu$ gracili$ blastocysts in
452 m a l e and 445 f e m a l e Saurida turnbH. In both sexes, as t h e fitted c u r v e w a s
60
R . J . G . Lester
p r o g r e s s i v e l y truncated, t h e e s t i m a t e d total n u m b e r in the s a m p l e increased. In the
males, a distribution 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 parasites (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 than was
o b s e r v e d . From 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 that this w a s a result of parasite-
200
ru3
~_100
E
Z
O
0
0
0
0
6
7+
~
0
1
2
3
4
5
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 affecting t h e h e a v i l y - i n f e c t e d fish. In the females, the fitted curve
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 , the s h a p e s of the curves w e r e very different. T h o u g h the ratio of uninf e c t e d fish to fish with o n e p a r a s i t e was s i m i l a r in both sexes, r e l a t i v e l y f e w e r fish with 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 females. This s u g g e s t e d that t h o u g h
the 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 parasites at m u c h t h e s a m e rate, m u l t i p l e
infections in the m a l e s w e r e m u c h rarer. Thus the third 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 not a r e l i a b l e i n d i c a t o r of the o r i g i n a l distribution.
F u r t h e r e v i d e n c e that the m a l e s w e r e m o r e affected by the parasite t h a n the f e m a l e s
c o m e s from t h e results of t h e p r o g r e s s i v e t r u n c a t i o n s (Fig. 6). As the m a l e s w e r e
truncated, the b i g g e s t i n c r e a s e in the e s t i m a t e d total n u m b e r occurred b e t w e e n 3 and 4
p a r a s i t e s p e r fish. In the f e m a l e s it w a s b e t w e e n 4 a n d 5 p a r a s i t e s p e r fish. E v i d e n t l y four
p a r a s i t e s p e r fish w e r e m o r e h a r m f u l to m a l e s t h a n to females.
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
0
,
1
0
2
3
4
5
O
t
6
O
1
7+
Number of parasites
Fig. 5. Frequency distributions of C. gracilis blastocysts in 445 females S. tumbil. The circles
represent the n e g a t i v e b i n o m i a l distribution that best fits the first four values
+20CO~
~o
O---O
~c
~5~ ÷10ck~o
.c_
3
4
5
6
Truncation point
(number of parasites per fish)
2
Fig. 6. The differences b e t w e e n the observed total n u m b e r of fish a n d the estimated total n u m b e r
from distributions fitted to progressively more of the histograms in Figures 5 a n d 6. Solid lines, male
fish; dotted lines, female fish
A s e v e n t h e first f e w p o i n t s of t h e m a l e d i s t r i b u t i o n w e r e s u s p e c t , h o w c o u l d t h e
s h a p e of t h e o r i g i n a l d i s t r i b u t i o n b e d e t e r m i n e d ? F o r t u n a t e l y , t h e y h a d t h e d a t a f r o m t h e
females. The latter were caught at the same time, had evidently become infected at
62
R . J . G . Lester
a b o u t t h e s a m e size (100 to 140 mm}, w h e n f e e d i n g on the 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 parasites p e r fish, thus
p r o v i d e d an e s t i m a t e of the 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 the 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 the 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
200
¢g3
"5
oJ
,.{3
100"
E
Z
0
0
1
2
3
4
5
Number of perosites
6
7*
Fig. 7. Frequency distribution of the parasite in male fish (from Fig. 4} with an estimate of the
probable original distribution (shaded area}
from 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 the
females. It predicts that a b o u t 12 % of t h e m a l e s are m i s s i n g from t h e sample. 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 that f e m a l e s w i t h l o w n u m b e r s of parasites are
not affected.
A m o r e s o p h i s t i c a t e d statistical analysis of this data is in preparation.
DISCUSSION
I h a v e a t t e m p t e d to show in this p a p e r that t h e r e are w a y s w e can d e t e c t the
c o m p o n e n t of n a t u r a l mortality that is a s s o c i a t e d w i t h p a r a s i t i c d i s e a s e in a w i l d fish
p o p u l a t i o n . A n i m a l s die from a c o m b i n a t i o n of factors, t h e i r position in time a n d p l a c e
b e i n g p e r h a p s as i m p o r t a n t as t h e i r p h y s i o l o g i c a l condition. P e r h a p s the q u e s t i o n w 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
63
should ask is, if a p a r a s i t e i n c r e a s e d the l i k e l i h o o d of death, is this of any 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 animals, the
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 survive.
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 important.
In practical terms, w e n e e d to t a c k l e t h e question, if t h e p a r a s i t e w a s absent, w o u l d
there be more fish? In m a n y cases the h i g h e r m o r t a l i t y rate 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 predators (see for e x a m p l e D o b b e n , 1952). Predators 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 catch 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 the p a r a s i t e w e r e absent, the
predator 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 that m o r e p r e y w o u l d
survive.
H o w e v e r , the factors that control p o p u l a t i o n size are v a r i e d a n d f r e q u e n t l y not w e l l
understood. H i g h l y territorial s p e c i e s m a y b e restricted by t h e a v a i l a b i l i t y of territory,
others by the a v a i l a b i l i t y of shelter. In t h e s e cases, if the h a b i t a t is n e a r its c a r r y i n g
capacity 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 (though 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 the size 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 mortality that occurs after that s t a g e will p r e s u m a b l y affect
the p o p u l a t i o n size. From a fisheries point of view., the 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 et al. (1983) h a v e p o i n t e d out,
after the fry s t a g e a n d b e f o r e t h e fish are r e c r u i t e d to the fishery. This is a s t a g e w h i c h
should 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 the m e t h o d s above, that an i n f e c t i o n is
c a u s i n g serious mortality 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 the 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
one m o r e or less free of t h e parasite. 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 proportion of y o u n g e r i n d i v i d u a l s t h a n in the 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 infections like other diseases, are 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
increase w h e n the 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 reality? Until w e h a v e m o r e results 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.
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Oxford, 245-281.
Anderson, R. M., 1982. Host-parasite population biology. In: Parasites - their world and ours. Ed. by
D. F. Mettrick & S. S. Desser. Elsevier, Amsterdam, 303-312.
Anderson, R. M. & Gordon, D. M., 1982. Processes influencing the distribution of parasite numbers
within host populations with special emphasis on parasite-induced host mortalities. - Parasitology 85, 373-398.
Anderson, R. M. & May, R. M., 1979. Population biology of infectious diseases. Part II. - Nature,
Lond., 280, 455-461.
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