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The regulation of mortality and fecundity in Schistosoma mattheei following a single experimental infection in sheep
hrernorio~l Jourmdfir Parasirology Vol. 21, No. 8, pp. 877482, Printed in Grear Briloin
1991 0
OOZO-7519/91 $3.00 + 0.00 PergQmon Press plc .Socieryfor Pamhhgy
1991 Aurrra/im
THE REGULATION OF MORTALITY AND FECUNDITY IN MATTHEEI FOLLOWING A SINGLE EXPERIMENTAL INFECTION IN SHEEP
SCHISTOSOMA
MICHAEL
J. COYNE and GARY SMITH
Section of Animal Health Economics, University of Pennsylvania, School of Veterinary Medicine, New Bolton Center, 382 West Street Rd, Kennett Square, PA 19348, U.S.A. (Received 29 November
1990; accepted 12August 1991)
AbstiaCG-cOYNE M. .I. and SMITH G. 1991. The regulation of mortality and fecundity in Schistosoma mattheei following a single experimental infection in sheep. Znternatiorud Journalfor Parasitology 21: 877882. The regulation of mortality and fecundity of Schistosoma mattheei in sheep was examined using a series
of mathematical models applied to data culled from the literature. Parasite mortality (p) was found to be an increasing linear function of the magnitude of the initial infection over the ranges of doses examined (20091,000 cercariae) where p = 9.78 x lo-’ + 3.476 x lo- ’ * infection dose. Parasite fecundity (a) was found to be inversely related to the duration of the infection. The best fit model for parasite fecundity was one in which fecundity decreased exponentially with time since initial infection, il= I& 4’mO.There was no evidence for density-dependent regulation of fecundity. INDEX KEY WORDS: Schistosoma mattheei; sheep; mortality; fecundity; mathematical models.
MATERIALS AND METHODS
INTRODUCTION THE
density-dependent regulation of fecundity of nematode and trematode parasites of man and domestic animals provides a potent mechanism for the maintenance of parasite population numbers between the bounds that experienced workers regard as typical. It has been unequivocally demonstrated
to occur in a variety of helminth species (Smith, Grenfell & Anderson, 1987; Smith, 1987) but there are conflicting claims for some others (Coyne, Smith & Johnstone, 1991). For example, Medley & Anderson (1985) and Jones, Breeze & Kusel (1989) report that the fecundity of Schistosoma mansoni is regulated by density-dependent processes despite the contrary evidence in Cheever & Duvall (1974) and Wertheimer, Vermund, Lumey & Singer (1987). The fecundity of S. bovis is inversely related to the duration of infection in cattle, sheep and mice, but there is no demonstrable density-dependent regulation (Massoud, 1973; Saad, Hussein, Dargie, Taylor & Nelson, 1980; Saad & Hussein, 1984). In Schistosoma mattheei, density-dependent regulation was reported for infections in calves on a high plane of nutrition, but not in calves on a poorer diet (Lawrence, 1973). However, in subsequent work, this finding could not be replicated (Lawrence, 1977), although fecundity was found to be inversely related to the duration of infection. In the present paper we examine the regulation of the mortality and fecundity of S. mattheei in sheep following a single infection using data found in the literature.
of mortality. The mortality of S. mattheei in sheep following a single infection was determined using data found in McCully & Kruger (1969), Lawrence (1974), Van Wyk, Heitmann & Van Rensburg (1975), Van Wyk, Van Rensburg & Heitmann (1976), Taylor, James, Nelson, Bickle, Dunne, Dobinson, Dargie, Berry & Hussein (1977), Dargie, Berry, Holmes, Reid: Breeze; Taylor, James & Nelson (19771 and Van Rensbura & Van Wvk (1981). Previous‘wori with a number of parasite genera in&cat& that parasite survivorship following a single infection can be approximated as a simple exponential decay (e.g. Anderson & Michel, 1977; Barger & Le Jambre, 1988). Using this model, the instantaneous mortality (p) for S. mattheei was estimated as Measurement
where P(t) was the total number of parasites at the time of slaughter, t was time in days, and P(0) was the number of parasites in the initial infecting dose (Smith, 1982). Regulation offecundity. Parasite fecundity (eggs per female per day) was obtained from data found in Van Wyk et al. (1976) and Lawrence (1980). The data were evaluated to examine the effects of parasite density and duration of infection on fecundity. The general strategy was as follows. First, changes in parasite number were fitted to a model comprising three coupled first order linear differential equations (see below). Using the expected value for mature parasite burdens obtained in this way we examined various 877
878
M.J. COYNE~~~G.SMITH
models for parasite egg output with respect to their goodnessof-fit to the actual calculated fecundity. The fitting procedure used the non-linear least squares methods available in CONSAAM (Bermann & Weiss, 1978). Other statistical
analyses were carried out using the maximum likelihood methods provided by GLIM (Payne, 1985).
a. 0.50
0.40 0.30
RESULTS Mortality rates Analysis of the regression of mortality upon infective dose revealed a significant deviation of the slope of the regression line from zero (P < 0.001, df = 123) (Fig. la), in other words, parasite mortality (p) following a single infection increased over the range of infective doses examined (20&91,000). The average mortality was 0.012 worm-’ day-’ (* 0.0018 95% CZ). The analysis was constrained by the data available from the literature and there was a substantial bias in the distribution of observations. Nevertheless, excluding the observations corresponding to infective doses higher than 10,000 cercariae made no significant difference to the result of the regression analysis (P = 0.011, df = 115) (Fig. lb). Regression of fecundity on parasite number We based our initial analysis on data provided by Van Wyk et al. (1976). Regression analysis of their data revealed no significant relationship between parasite fecundity and the number of mature female parasites, or the total number of mature parasites (male and female) at the time of slaughter, respectively (Fig. 2a,b) (P > 0.25). The average fecundity at time of slaughter (68.4 days) was 282 eggs per female parasite per day ( f 44,95% Cl). In$uence of parasite density and the duration of infection Changes in total adult worm burdens in sheep infected once only with 3000 S. mattheeicercariae were obtained from data found in Lawrence (1980). The changes were modeled using the following series of coupled differential equations:
-=
dl,,, dt
dF,l, dt
-=
dt
-id(,)-
u,z,,+qt- r)
= 40 I@ 0 - 5) - Pz,l,
(1 - 4) a, I,,) O(t- T) - h MO
(4)
where I(,, was the number of immature worms, F(,, was the number of mature female worms, MC,, was the number of mature male worms and t was the minimum pre-patent period (42 days, Van Wyk et al.,
0.20
+
0.10 0 0
20
40
60
100
30 (Thoumndd
NUMBER
OF
CERCARIAE
b. 0.50
-
0.400.300.20-
+
+ + +
+
+
+ +
$+I 0
2
4
A
+ +
~
+*
+++4 6
8
10
I1houoandol NUMBER
OF
CERCARIAE
FIG. 1. Changes in the instantaneous mortality rate (worms per day) of S. mattheei in sheep infected once with various doses of cercariae. a. Changes in the instantaneous mortality rate over the total range of infective doses reported in the literature (200-91,000 cercariae). b. Changes in the instantaneous mortality rate between 200 and 10,000 cercariae. Solid line represknts predicted values @ = 9.78 x 10-j (+ 1.93 x lo-*) + 3.476 x lO_‘(f 1.711 x lo-‘)*dose.r* = 0.117). Data from McCully &. Kruger (1969), ‘Lawrence (1974), Van Wyk et al. (1975, 1976), Taylor et al. (1977), Dargie et al. (1977) and Van Rensburg & Van Wyk (198 1).
1976). All other parameters are defined in Table 1. The model was fitted to the data shown in Fig. 3 using the non-linear least squares method provided in CONSAAM (Bermann & Weiss, 1978). Numerical estimates for the population parameters are given in Table 2. Having obtained a model for changes in parasite abundance it was possible to investigate further whether there were any constraints on parasite fecundity. Since reproduction in S. mattheei requires paired matings, the probability of female worms being mated was determined using the equation for mating probability (male and female worms distributed together, monogamous mating system) described in May (1977). Using a mean parasite burden of 1505 S. mattheei, and varying k from 0.1 to 4.0, a range of mating probabilities from 99.39 to 98.01% was obtained. Since the number of mature male worms was
Fecundity TABLE I-
in S. mattheei
879
POPULA~ON VARIABLESAND PARAMETERS
Number of hosts Distribution parameter Time (in days) following initial infection Minimum pre-patent period (42 days) (i = 1,2) The instantaneous mortality rate of each stage, l/p is the mean life span (i = 1) The transition rate between development stages, l/u, is the mean time spent in the stage Step function (if t < f, 8 = 0, if t 2 r, 0 = 1) Proportion of immature worms which develop into females Per capita fecundity rate (eggs per female per day) Fecundity constant
TABLE 2 -
PARAMETERESTIMATESFOR POPULATION MODEL
Parameter PI A -1 9
Estimate
95% CI
0.00831 0.00113 0.09790 0.3802
f f f f
2500 .
2000 -
0.0169 0.0037 0.2296 0.4282
1500-
.
l-
.
‘“j 0
i”^‘l---‘c 100
200
300
DAYS
POST
INFECTION
700. .
.
500 400 -
:.
200 -
.
200 -
.
.
.:* .--
.
..
g.
.
.
. 100 0 100
.
. 200
300
400
NUMBER OF
600
600
PARASITES
.
.
400 a00 200
.
. . a,
. .
100
.
"
so0
710
NUMBER OF
FIG. 3. Best fit model of mature S. mattheei worm burden following a single infection with 3000 cercariae. Solid line represents predicted values, (A) number of mature female worms, (0) total number of mature worms. Data from Lawrence (1980).
greater than the number of mature female worms in the data presented in Lawrence (1980), we made the
.
.
(5) .
..
. .
.
.
0
210
500
assumption that all mature females were mated and produced eggs. Changes in egg output were represented by the following differential equation
$* a '2 .
400
.
b.
600
.
1000
a.
600 -
.
.
1000
12so
1800
PARASITES
FIG. 2. Regression of fecundity (eggs per female S. mattheei per day) at slaughter on (a) total mature female S. mattheei wormburden[fecundity = exp(5.619(f 0.0879)-6.018 x IO-’ (f 2.17 x 10m4) * worm burden), r* = O.OO] and (b) total mature S. mattheei worm burden [fecundity = exp(5.652 ( f 0.0947) - 9.589 x 10m6 ( f 9.50 x lo-‘) * worm burden), r* = O.OO]. Solid line represents predicted values. Data from Van Wyk et al. (1976).
where EC,)was the total number of eggs laid since the start of the infection and 1 was the fecundity per female worm per day. Four hypotheses regarding the nature of A were tested using the cumulative egg data provided in Lawrence (1980). The first hypothesis assumed that the number of eggs per worm per day remained constant irrespective of worm burden or the duration of infection (A constant, function 1, Table 3). In the second hypothesis, the number of eggs per worm per day varied with the duration of infection. The time dependency was assumed to follow a simple exponential decay (function 2, Table 3). The third and fourth hypotheses assumed that parasite fecundity was a declining exponential function of the intensity of infection. The functional forms shown in Table 3 reflect the necessity to take into account the manner in which the parasites are distributed amongst the host
880
M. J. COYNEand G. SMITH TABLE 3
Function
MODELSOF FECUNDITY(A)
k
6
Al
Sums of squares
(4 1. &
359.7 7.69) 527.0 (* 33.64) 360.7 (+ 3234) 498.5 (* 57.39)
1.337 x IO6
(*
2, & e-s(l-r) 3. A,,e-y1 + (P,,,/Hk)*(I -e-‘))-(‘+” 4. & em6(‘+r)(l +(P,,,/Hk)*(l -e~Sc’~d)))c*+‘)
4.36 (+ 8.04 4.67 (* 8.49 1.66 (* 2.0
IO-’ IO-3 1O-6 10-3 1o-6 10-6)
6.477 x 10S 3.92 (* 68.25) 2.09 (* 15.75)
1.341 x IO6 6.955 x 10’
a.
population in calculating the average egg output per day over all hosts. We assumed that S. mattheei, like many other helminth parasites, was highly overdispersed and used the negative binomial probability distribution as a phenomenological model. The method of deriving functions like those in Table 3 is given in May (1977) and Smith (1987). The fourth hypothesis differed from the third in that it also incorporated a time-dependent element. Based upon the sums of squares of deviations between the observed and predicted values, the best description of the cumulative egg output from sheep infected once with 3000 cercariae described in Lawrence (1980) was provided by the second hypothesis which assumed that fecundity was a declining exponential function of the duration of infection (Table 3, Fig. 4a, b). DISCUSSION The mortality of S. mattheei in sheep was found to increase linearly over the range of infective doses examined. The overall mean expected life span (l/p) of primary infections of S. mattheei in sheep was 87 days. In sheep infected with 200 cercariae, the mean expected life span of the parasite was approximately 101.5 days; in sheep infected with 91,000 cercariae, the mean expected life span was 24.1 days. The dose-dependent mortality following single infections of S. mattheei is not unique, and has been reported in a number of nematode and trematode parasites of ruminants (Horak, 1967; Anderson & Michel, 1977; Smith, 1987, 1990; Smith & Galligan, 1988; Coyne et al. 1991). Lawrence (1980) estimated the fecundity of S. mattheei to be 420 eggs per female worm per day between weeks 8 and 24 post-infection. Re-estimating this 8-24 week post-infection average using the best fit model of the fecundity of S. mattheei derived above gave a very similar value (392 f 44 eggs per female per day). Both these values are larger than that obtained by Van Wyk et al. (1976). Lawrence (1980) suggested this difference was due to the sensitivity of the egg counting technique used. The fecundity of S. mattheei was found to be a decreasing function of the duration of the infection. There was no evidence for density-dependent reg-
x x x x x x
60 -
40 -
20 -
0
0
100 DAYS
200
POST
INFECTION
POST
INFECTION
b. 60
40 -
20
0
0
100 DAYS
200
200
FIG.
4. The fecundity of S. maftheei following a single infection with 3000 cercariae. a. Fecundity remains constant over duration and intensity of infection. b. Fecundity decreases with the duration of infection. Solid line represents predicted
values, (0)
observed values. Data from Lawrence (1980).
ulation of fecundity in S. mattheei either in the initial analysis of the data presented in Van Wyk et al. (1976), or in the subsequent analysis involving the comparison of various plausible functional forms for parasite fecundity. Time-dependent changes in the fecundity of S. mattheei have been reported by other workers. For example, Van Wyk et al. (1976) found that the total fecal egg output was more significantly correlated with the number of female S. mattheei in sheep early in the
Fecundity in S. mattheei infection than later. In cattle, Lawrence (1977) concluded that the decrease in the fecal egg count following a single infection with S. mattheei was due only in part to a decrease in the worm burden. He suggested the principal mechanism was a reduction in the egg output by the parasite. This suggestion was buttressed by the observation that there was also a decline in the number of eggs in tissue and so the measured decrease in fecal egg output per worm could not be explained merely in terms of increased retention of eggs in the tissues. Lawrence (1980) later reported a similar decrease in fecal egg output in sheep infected with S. mattheei, but did not, in this case, find any evidence that there was a decrease in the level of tissue egg retention. The fecundity of other Schistosoma species has also been found to decrease with the duration of infection. Massoud (1973), for example, found a decrease in the egg production per female worm and a decrease in tissue accumulation of eggs in cattle following infection with S. bovis. Saad et al. (1980) also found a decrease in the fecal output of S. bovis eggs in cattle and suggested that this was caused by a reduced fecundity of individual worms in addition to a decline in worm numbers. However, it should be noted that they also found that there was an increase in the number of eggs accumulating in the tissues of the cattle. Time-dependent decreases in fecundity have also been reported in S. bovis in mice (Saad & Hussein, 1984), and in S. mansoni and S. japonicum in monkeys (Cheever & Powers, 1969; Cheever & Duvall, 1974; Cheever, Erickson, Sadun & von Lechtenberg, 1974). Density-dependent regulation of fecundity for Schistosoma species has been reported. Medley & Anderson (1985) suggest that density-dependent regulation of the fecundity of S. mansoni occurs in chronically infected human beings. However, Wertheimer et al. (1987) utilizing similar data determined that the estimated fecundity of S. mansoni was not significantly different from a constant value over the observed range of female worms recovered from an individual human being. Jones et al. (1989) found evidence for density-dependent control of fecundity in S. mansoni following single infections in mice, with a significant decrease in the number of epg (feces and/or tissue) per female worm as the intensity of infection increased. Our observations show a decrease in the number of worms over the duration of infection. However, there is no concomitant increase in parasite fecundity as would be expected if density-dependent regulation was operating. The development of a parasite-specific immune response by the host, worm competition for resources, inimical changes in the parasites environment and worm senescence are all plausible explanations for the decrease in fecundity with duration of infection observed above.
881
work was funded by a Training Grant in Epidemiology and Health Economics provided by the Commonwealth of Pennsylvania Department of Agriculture. AcknowledgementsThis
REFERENCES ANDERSONR. M. & MICHELJ. F. 1977. Density dependent of Ostertagia oitertagi. survival in populations International Journal for Parasitoloav 7: 321-329. BARGER I. A. & LE ~A,EIR, L. F--1988. Regulation of Haemonchus contortus populations in sheep: mortality of established worms. International Journal for Parasitology 18: 269-273. BERMANNM. & WEISS M. F. 1978. SAAM Manual, Version
SAAM27, DHEW Publication No. (NIH) 78-180. National Institutes of Health, Bethesda, MD 20014. CHEEVERA. W. & POWERSK. G. 1969. Schlstosoma mansoni infection in rhesus monkeys: changes in egg production and egg distribution in prolonged infections in intact and splenectomized monkeys. Annals of Tropical Medicine and Parasitology 63: 83-93. CHEEVERA. W. & DUVALL R. H. 1974. Single and repeated infections of grivet monkeys with Schistosoma mansoni: parasitological and pathological observations over a 31month period. American Journal of Tropical Medicine and Hygiene 23: 884894. CHEEVER A. W., ERICKSON D. G., SADUN E. H. & LECHTENBERGF. VON 1974. Schistosoma japonicum infection in monkeys and baboons: parasitological and pathological findings. American Journal of _ Tropical _ Medicine and Hygiene 23: 5164. COYNEM. J.. SMITHG. & JOHNSTONE C. 1991. A studv of the mortality and fecundity of Haemonchus contortus ih sheep following experimental infections. International Journalfor Parasitology 21: 847-853. DARGIEJ. D.:BERRY C. I., HOLMESP. H., REIDJ. F. S., BREEZE R.. TAYLORM. G., JAMESE. R. & NELSON G. S. 1977. Immunization of sheep against a virulent strain of Schistosoma mattheei using a strain of S. mattheei attenuated by hamster passage. Journal of Helminthology 51: 347-357. HORAK I. G. 1967. Host parasite relationships of Paramphistomum microbothrium in experimentally infected ruminants, with particular reference to sheep. Onderstepoort Journal of Veterinary Research 34: 451-540. JONESJ. T., BREEZEP. & KUSEL J. R. 1989. Schistosome
fecundity: influence of host genotype and intensity of infection. International Journal for Parasitology 19: 769777. LAWRENCEJ. A. 1973. Schistosoma mattheei in cattle: variations in parasite egg production. Research in Veterinary Science 14: 402-404. LAWRENCEJ. A. 1974. Schistosoma mattheei in sheep: the host-parasite relationship. Research in Veterinary Science
17: 263-264. LAWRENCEJ. A. 1977. Schistosoma mattheei in the ox: observations on the parasite. Veterinary Parasitology 3: 291-303. LAWRENCEJ. A. 1980. The pathogenesis of Schistosoma mattheei in the sheep. Research in Veterinary Science 29: l-7. MASSOUDJ. 1973. Parasitological and pathological observations on Schistosoma bovis Sonsino, 1876, in calves, sheep and goats in Iran. Journal of Helminthology 47: 155164. MAY R. M. 1977. Togetherness among schistosomes: its effects on the dynamics of the infection. Mathematical Biosciences 35: 301-343.
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M. J. COYNE and G. SMITH
MCCULLY R. M. & KRUGER S. P. 1969. Observations on bilharziasis of domestic ruminants in South Africa. Onderstepoort Journal of Veterinary Research 36: 129-162. MEDLEY G. & ANDERSON R.M. 1985. Density-dependent fecundity in Schistosoma mansoni infections in man. Transactions of the Royal Society of Tropical Medicine and Hygiene 19: 532-534. PAYNEC. D. 1985. The GLIM System Release 3.77 Manual, Royal Statistical Society 1985. Numerical Algorithms Group Ltd., Oxford, U.K. RENSBURGL. J. VAN & WYK J. A. VAN 198 1. Studies on schistosomiasis. 10. Development of Schistosoma mattheei in sheep infected with equal numbers of male and female cercariae. Onderstepoort Journal of Veterinary Research 48: 77-86. SAAD A. M., HUSSEIN M. F., DARGIEJ. D., TAYLOR M. G. & NELXIN G. S. 1980. Schistosoma bovis in calves: the development and clinical pathology of primary infections. Research in Veterinary Science %lOSzl 11. SAAD A. M. & HUSSEIN M. F. 1984. Observations on the infectivity and fecundity ofa Sudanese isolate of Schistosoma bovis in albino mice. Journal of Helminthology 58: 267-270. SMITHG. 1982. An analysis of variations in the age structure of Fasciola hepatica populations in sheep. Parasitology 84: 4961. SMITH G. 1987. The regulation of trematode populations by density-dependent processes. International Journal for Parasitology 17: 541-548. SMITH G., GRENFELL B. T. & ANDERSON R. M. 1987. The regulation of Ostertagia ostertagi populations in calves: density-dependent control of fecundity. Parasitology 95: 373-388.
SMITH G. & GALLIGAN D. T. 1988. Mathematical models of the population biology of Ostertagia ostertagi and Teledorsagia circumcincta and the economic evaluation of disease control strategies. Veterinary Parasitology 27: 7383. SMITH G. 1990. The use of computer models in the design of strategic parasite control programs. In: Epidemiology of Bovine Nematode Parasites in the Americas (Edited by GUERRERO J. and LEANING W. H. D.), pp. 107-114. Veterinary Learning Systems Co., Inc., Princeton. TAYLORM. G., JAMESE. R., NELSONG. S., BICKLEQ., DUNNE D. W., DOBINSON A. R., DARGIE J. D., BERRY C. I. & HU~YEINM. F. 1977. Modification of the pathogenicity of Schistosoma mattheei for sheep by passage of the parasite in hamsters. Journal of Helminthology 51: 337-345. WERTHEIMERS. P., VERMUNDS. H., LUMEYL. H. & SINGERB. 1987. Lack of demonstrable density-dependent fecundity of schistosomiasis mansoni: analysis of Egyptian quantitative human autopsies. American Journal of Tropical Medicine and Hygiene 31: 79-84. WYK J. A. VAN, HEITMANNL. P. & RENSBURGL. J. VAN 1975. Studies on schistosomiasis. 7. A comparison of various methods for the infestation of sheep with Schistosoma mattheei. Onderstepoort Journal of Veterinary Research 42: 71-74. WYK J. A. VAN, RENSBURGL. J. VAN & HEITMANNL. P. 1976. Studies on schistosomiasis. 8. The influence of age on the susceptibility of sheep to infestation with Schistosoma mattheei. Onderstepoort Journal of Veterinary Research 43: 43-54.
1991 0
OOZO-7519/91 $3.00 + 0.00 PergQmon Press plc .Socieryfor Pamhhgy
1991 Aurrra/im
THE REGULATION OF MORTALITY AND FECUNDITY IN MATTHEEI FOLLOWING A SINGLE EXPERIMENTAL INFECTION IN SHEEP
SCHISTOSOMA
MICHAEL
J. COYNE and GARY SMITH
Section of Animal Health Economics, University of Pennsylvania, School of Veterinary Medicine, New Bolton Center, 382 West Street Rd, Kennett Square, PA 19348, U.S.A. (Received 29 November
1990; accepted 12August 1991)
AbstiaCG-cOYNE M. .I. and SMITH G. 1991. The regulation of mortality and fecundity in Schistosoma mattheei following a single experimental infection in sheep. Znternatiorud Journalfor Parasitology 21: 877882. The regulation of mortality and fecundity of Schistosoma mattheei in sheep was examined using a series
of mathematical models applied to data culled from the literature. Parasite mortality (p) was found to be an increasing linear function of the magnitude of the initial infection over the ranges of doses examined (20091,000 cercariae) where p = 9.78 x lo-’ + 3.476 x lo- ’ * infection dose. Parasite fecundity (a) was found to be inversely related to the duration of the infection. The best fit model for parasite fecundity was one in which fecundity decreased exponentially with time since initial infection, il= I& 4’mO.There was no evidence for density-dependent regulation of fecundity. INDEX KEY WORDS: Schistosoma mattheei; sheep; mortality; fecundity; mathematical models.
MATERIALS AND METHODS
INTRODUCTION THE
density-dependent regulation of fecundity of nematode and trematode parasites of man and domestic animals provides a potent mechanism for the maintenance of parasite population numbers between the bounds that experienced workers regard as typical. It has been unequivocally demonstrated
to occur in a variety of helminth species (Smith, Grenfell & Anderson, 1987; Smith, 1987) but there are conflicting claims for some others (Coyne, Smith & Johnstone, 1991). For example, Medley & Anderson (1985) and Jones, Breeze & Kusel (1989) report that the fecundity of Schistosoma mansoni is regulated by density-dependent processes despite the contrary evidence in Cheever & Duvall (1974) and Wertheimer, Vermund, Lumey & Singer (1987). The fecundity of S. bovis is inversely related to the duration of infection in cattle, sheep and mice, but there is no demonstrable density-dependent regulation (Massoud, 1973; Saad, Hussein, Dargie, Taylor & Nelson, 1980; Saad & Hussein, 1984). In Schistosoma mattheei, density-dependent regulation was reported for infections in calves on a high plane of nutrition, but not in calves on a poorer diet (Lawrence, 1973). However, in subsequent work, this finding could not be replicated (Lawrence, 1977), although fecundity was found to be inversely related to the duration of infection. In the present paper we examine the regulation of the mortality and fecundity of S. mattheei in sheep following a single infection using data found in the literature.
of mortality. The mortality of S. mattheei in sheep following a single infection was determined using data found in McCully & Kruger (1969), Lawrence (1974), Van Wyk, Heitmann & Van Rensburg (1975), Van Wyk, Van Rensburg & Heitmann (1976), Taylor, James, Nelson, Bickle, Dunne, Dobinson, Dargie, Berry & Hussein (1977), Dargie, Berry, Holmes, Reid: Breeze; Taylor, James & Nelson (19771 and Van Rensbura & Van Wvk (1981). Previous‘wori with a number of parasite genera in&cat& that parasite survivorship following a single infection can be approximated as a simple exponential decay (e.g. Anderson & Michel, 1977; Barger & Le Jambre, 1988). Using this model, the instantaneous mortality (p) for S. mattheei was estimated as Measurement
where P(t) was the total number of parasites at the time of slaughter, t was time in days, and P(0) was the number of parasites in the initial infecting dose (Smith, 1982). Regulation offecundity. Parasite fecundity (eggs per female per day) was obtained from data found in Van Wyk et al. (1976) and Lawrence (1980). The data were evaluated to examine the effects of parasite density and duration of infection on fecundity. The general strategy was as follows. First, changes in parasite number were fitted to a model comprising three coupled first order linear differential equations (see below). Using the expected value for mature parasite burdens obtained in this way we examined various 877
878
M.J. COYNE~~~G.SMITH
models for parasite egg output with respect to their goodnessof-fit to the actual calculated fecundity. The fitting procedure used the non-linear least squares methods available in CONSAAM (Bermann & Weiss, 1978). Other statistical
analyses were carried out using the maximum likelihood methods provided by GLIM (Payne, 1985).
a. 0.50
0.40 0.30
RESULTS Mortality rates Analysis of the regression of mortality upon infective dose revealed a significant deviation of the slope of the regression line from zero (P < 0.001, df = 123) (Fig. la), in other words, parasite mortality (p) following a single infection increased over the range of infective doses examined (20&91,000). The average mortality was 0.012 worm-’ day-’ (* 0.0018 95% CZ). The analysis was constrained by the data available from the literature and there was a substantial bias in the distribution of observations. Nevertheless, excluding the observations corresponding to infective doses higher than 10,000 cercariae made no significant difference to the result of the regression analysis (P = 0.011, df = 115) (Fig. lb). Regression of fecundity on parasite number We based our initial analysis on data provided by Van Wyk et al. (1976). Regression analysis of their data revealed no significant relationship between parasite fecundity and the number of mature female parasites, or the total number of mature parasites (male and female) at the time of slaughter, respectively (Fig. 2a,b) (P > 0.25). The average fecundity at time of slaughter (68.4 days) was 282 eggs per female parasite per day ( f 44,95% Cl). In$uence of parasite density and the duration of infection Changes in total adult worm burdens in sheep infected once only with 3000 S. mattheeicercariae were obtained from data found in Lawrence (1980). The changes were modeled using the following series of coupled differential equations:
-=
dl,,, dt
dF,l, dt
-=
dt
-id(,)-
u,z,,+qt- r)
= 40 I@ 0 - 5) - Pz,l,
(1 - 4) a, I,,) O(t- T) - h MO
(4)
where I(,, was the number of immature worms, F(,, was the number of mature female worms, MC,, was the number of mature male worms and t was the minimum pre-patent period (42 days, Van Wyk et al.,
0.20
+
0.10 0 0
20
40
60
100
30 (Thoumndd
NUMBER
OF
CERCARIAE
b. 0.50
-
0.400.300.20-
+
+ + +
+
+
+ +
$+I 0
2
4
A
+ +
~
+*
+++4 6
8
10
I1houoandol NUMBER
OF
CERCARIAE
FIG. 1. Changes in the instantaneous mortality rate (worms per day) of S. mattheei in sheep infected once with various doses of cercariae. a. Changes in the instantaneous mortality rate over the total range of infective doses reported in the literature (200-91,000 cercariae). b. Changes in the instantaneous mortality rate between 200 and 10,000 cercariae. Solid line represknts predicted values @ = 9.78 x 10-j (+ 1.93 x lo-*) + 3.476 x lO_‘(f 1.711 x lo-‘)*dose.r* = 0.117). Data from McCully &. Kruger (1969), ‘Lawrence (1974), Van Wyk et al. (1975, 1976), Taylor et al. (1977), Dargie et al. (1977) and Van Rensburg & Van Wyk (198 1).
1976). All other parameters are defined in Table 1. The model was fitted to the data shown in Fig. 3 using the non-linear least squares method provided in CONSAAM (Bermann & Weiss, 1978). Numerical estimates for the population parameters are given in Table 2. Having obtained a model for changes in parasite abundance it was possible to investigate further whether there were any constraints on parasite fecundity. Since reproduction in S. mattheei requires paired matings, the probability of female worms being mated was determined using the equation for mating probability (male and female worms distributed together, monogamous mating system) described in May (1977). Using a mean parasite burden of 1505 S. mattheei, and varying k from 0.1 to 4.0, a range of mating probabilities from 99.39 to 98.01% was obtained. Since the number of mature male worms was
Fecundity TABLE I-
in S. mattheei
879
POPULA~ON VARIABLESAND PARAMETERS
Number of hosts Distribution parameter Time (in days) following initial infection Minimum pre-patent period (42 days) (i = 1,2) The instantaneous mortality rate of each stage, l/p is the mean life span (i = 1) The transition rate between development stages, l/u, is the mean time spent in the stage Step function (if t < f, 8 = 0, if t 2 r, 0 = 1) Proportion of immature worms which develop into females Per capita fecundity rate (eggs per female per day) Fecundity constant
TABLE 2 -
PARAMETERESTIMATESFOR POPULATION MODEL
Parameter PI A -1 9
Estimate
95% CI
0.00831 0.00113 0.09790 0.3802
f f f f
2500 .
2000 -
0.0169 0.0037 0.2296 0.4282
1500-
.
l-
.
‘“j 0
i”^‘l---‘c 100
200
300
DAYS
POST
INFECTION
700. .
.
500 400 -
:.
200 -
.
200 -
.
.
.:* .--
.
..
g.
.
.
. 100 0 100
.
. 200
300
400
NUMBER OF
600
600
PARASITES
.
.
400 a00 200
.
. . a,
. .
100
.
"
so0
710
NUMBER OF
FIG. 3. Best fit model of mature S. mattheei worm burden following a single infection with 3000 cercariae. Solid line represents predicted values, (A) number of mature female worms, (0) total number of mature worms. Data from Lawrence (1980).
greater than the number of mature female worms in the data presented in Lawrence (1980), we made the
.
.
(5) .
..
. .
.
.
0
210
500
assumption that all mature females were mated and produced eggs. Changes in egg output were represented by the following differential equation
$* a '2 .
400
.
b.
600
.
1000
a.
600 -
.
.
1000
12so
1800
PARASITES
FIG. 2. Regression of fecundity (eggs per female S. mattheei per day) at slaughter on (a) total mature female S. mattheei wormburden[fecundity = exp(5.619(f 0.0879)-6.018 x IO-’ (f 2.17 x 10m4) * worm burden), r* = O.OO] and (b) total mature S. mattheei worm burden [fecundity = exp(5.652 ( f 0.0947) - 9.589 x 10m6 ( f 9.50 x lo-‘) * worm burden), r* = O.OO]. Solid line represents predicted values. Data from Van Wyk et al. (1976).
where EC,)was the total number of eggs laid since the start of the infection and 1 was the fecundity per female worm per day. Four hypotheses regarding the nature of A were tested using the cumulative egg data provided in Lawrence (1980). The first hypothesis assumed that the number of eggs per worm per day remained constant irrespective of worm burden or the duration of infection (A constant, function 1, Table 3). In the second hypothesis, the number of eggs per worm per day varied with the duration of infection. The time dependency was assumed to follow a simple exponential decay (function 2, Table 3). The third and fourth hypotheses assumed that parasite fecundity was a declining exponential function of the intensity of infection. The functional forms shown in Table 3 reflect the necessity to take into account the manner in which the parasites are distributed amongst the host
880
M. J. COYNEand G. SMITH TABLE 3
Function
MODELSOF FECUNDITY(A)
k
6
Al
Sums of squares
(4 1. &
359.7 7.69) 527.0 (* 33.64) 360.7 (+ 3234) 498.5 (* 57.39)
1.337 x IO6
(*
2, & e-s(l-r) 3. A,,e-y1 + (P,,,/Hk)*(I -e-‘))-(‘+” 4. & em6(‘+r)(l +(P,,,/Hk)*(l -e~Sc’~d)))c*+‘)
4.36 (+ 8.04 4.67 (* 8.49 1.66 (* 2.0
IO-’ IO-3 1O-6 10-3 1o-6 10-6)
6.477 x 10S 3.92 (* 68.25) 2.09 (* 15.75)
1.341 x IO6 6.955 x 10’
a.
population in calculating the average egg output per day over all hosts. We assumed that S. mattheei, like many other helminth parasites, was highly overdispersed and used the negative binomial probability distribution as a phenomenological model. The method of deriving functions like those in Table 3 is given in May (1977) and Smith (1987). The fourth hypothesis differed from the third in that it also incorporated a time-dependent element. Based upon the sums of squares of deviations between the observed and predicted values, the best description of the cumulative egg output from sheep infected once with 3000 cercariae described in Lawrence (1980) was provided by the second hypothesis which assumed that fecundity was a declining exponential function of the duration of infection (Table 3, Fig. 4a, b). DISCUSSION The mortality of S. mattheei in sheep was found to increase linearly over the range of infective doses examined. The overall mean expected life span (l/p) of primary infections of S. mattheei in sheep was 87 days. In sheep infected with 200 cercariae, the mean expected life span of the parasite was approximately 101.5 days; in sheep infected with 91,000 cercariae, the mean expected life span was 24.1 days. The dose-dependent mortality following single infections of S. mattheei is not unique, and has been reported in a number of nematode and trematode parasites of ruminants (Horak, 1967; Anderson & Michel, 1977; Smith, 1987, 1990; Smith & Galligan, 1988; Coyne et al. 1991). Lawrence (1980) estimated the fecundity of S. mattheei to be 420 eggs per female worm per day between weeks 8 and 24 post-infection. Re-estimating this 8-24 week post-infection average using the best fit model of the fecundity of S. mattheei derived above gave a very similar value (392 f 44 eggs per female per day). Both these values are larger than that obtained by Van Wyk et al. (1976). Lawrence (1980) suggested this difference was due to the sensitivity of the egg counting technique used. The fecundity of S. mattheei was found to be a decreasing function of the duration of the infection. There was no evidence for density-dependent reg-
x x x x x x
60 -
40 -
20 -
0
0
100 DAYS
200
POST
INFECTION
POST
INFECTION
b. 60
40 -
20
0
0
100 DAYS
200
200
FIG.
4. The fecundity of S. maftheei following a single infection with 3000 cercariae. a. Fecundity remains constant over duration and intensity of infection. b. Fecundity decreases with the duration of infection. Solid line represents predicted
values, (0)
observed values. Data from Lawrence (1980).
ulation of fecundity in S. mattheei either in the initial analysis of the data presented in Van Wyk et al. (1976), or in the subsequent analysis involving the comparison of various plausible functional forms for parasite fecundity. Time-dependent changes in the fecundity of S. mattheei have been reported by other workers. For example, Van Wyk et al. (1976) found that the total fecal egg output was more significantly correlated with the number of female S. mattheei in sheep early in the
Fecundity in S. mattheei infection than later. In cattle, Lawrence (1977) concluded that the decrease in the fecal egg count following a single infection with S. mattheei was due only in part to a decrease in the worm burden. He suggested the principal mechanism was a reduction in the egg output by the parasite. This suggestion was buttressed by the observation that there was also a decline in the number of eggs in tissue and so the measured decrease in fecal egg output per worm could not be explained merely in terms of increased retention of eggs in the tissues. Lawrence (1980) later reported a similar decrease in fecal egg output in sheep infected with S. mattheei, but did not, in this case, find any evidence that there was a decrease in the level of tissue egg retention. The fecundity of other Schistosoma species has also been found to decrease with the duration of infection. Massoud (1973), for example, found a decrease in the egg production per female worm and a decrease in tissue accumulation of eggs in cattle following infection with S. bovis. Saad et al. (1980) also found a decrease in the fecal output of S. bovis eggs in cattle and suggested that this was caused by a reduced fecundity of individual worms in addition to a decline in worm numbers. However, it should be noted that they also found that there was an increase in the number of eggs accumulating in the tissues of the cattle. Time-dependent decreases in fecundity have also been reported in S. bovis in mice (Saad & Hussein, 1984), and in S. mansoni and S. japonicum in monkeys (Cheever & Powers, 1969; Cheever & Duvall, 1974; Cheever, Erickson, Sadun & von Lechtenberg, 1974). Density-dependent regulation of fecundity for Schistosoma species has been reported. Medley & Anderson (1985) suggest that density-dependent regulation of the fecundity of S. mansoni occurs in chronically infected human beings. However, Wertheimer et al. (1987) utilizing similar data determined that the estimated fecundity of S. mansoni was not significantly different from a constant value over the observed range of female worms recovered from an individual human being. Jones et al. (1989) found evidence for density-dependent control of fecundity in S. mansoni following single infections in mice, with a significant decrease in the number of epg (feces and/or tissue) per female worm as the intensity of infection increased. Our observations show a decrease in the number of worms over the duration of infection. However, there is no concomitant increase in parasite fecundity as would be expected if density-dependent regulation was operating. The development of a parasite-specific immune response by the host, worm competition for resources, inimical changes in the parasites environment and worm senescence are all plausible explanations for the decrease in fecundity with duration of infection observed above.
881
work was funded by a Training Grant in Epidemiology and Health Economics provided by the Commonwealth of Pennsylvania Department of Agriculture. AcknowledgementsThis
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