J. Parasitol., 94(5), 2008, pp. 1022–1030 ᭧ American Society of Parasitologists 2008 QUANTITATIVE ESTIMATION OF THE COST OF PARASITIC CASTRATION IN A HELISOMA ANCEPS POPULATION USING A MATRIX POPULATION MODEL N. J. Negovetich* and G. W. Esch Department of Biology, Wake Forest University, Winston-Salem, North Carolina 27109. e-mail: [email protected] ABSTRACT: Larval trematodes frequently castrate their snail intermediate hosts. When castrated, the snails do not contribute offspring to the population, yet they persist and compete with the uninfected individuals for the available food resources. Parasitic castration should reduce the population growth rate ␭, but the magnitude of this decrease is unknown. The present study attempted to quantify the cost of parasitic castration at the level of the population by mathematically modeling the population of the planorbid snail Helisoma anceps in Charlie’s Pond, North Carolina. Analysis of the model identified the life-history trait that most affects ␭, and the degree to which parasitic castration can lower ␭. A period matrix product model was constructed with estimates of fecundity, survival, growth rates, and infection probabilities calculated in a previous study. Elasticity analysis was performed by increasing the values of the life-history traits by 10% and recording the percentage change in ␭. Parasitic castration resulted in a 40% decrease in ␭ of H. anceps. Analysis of the model suggests that decreasing the size at maturity was more effective at reducing the cost of castration than increasing survival or growth rates of the snails. The current matrix model was the first to mathematically describe a snail population, and the predictions of the model are in agreement with published research. Life-history theory predicts that an organism will exhibit a mental factors and the presence of certain predators have been strategy that maximizes its reproductive value (Roff, 1992). implicated in causing these changes (Brown et al., 1985; Byrne Predation, for example, is a strong selective force, and the prey et al., 1989; Lam and Calow, 1989; Crowl and Covich, 1990); population must adapt to maintain existence in the habitat. In however, reciprocal transfer studies with C. californica have populations where large individuals are more likely to be cap- also demonstrated a genetic component on which castration can tured by a predator, the prey generally mature at a smaller size, act (Lafferty, 1993a). reproducing before being consumed (Reznick et al., 1990; In snail populations, prevalence of parasites increases with Hutchings, 1993). Similarly, if most predation occurs on small shell length, suggesting that large snails are more likely to be- juveniles, then accelerated growth of the prey population would come castrated than the smaller individuals. Fecundity increases reduce the threat of predation (Crowl and Covich, 1990; Rez- with size of the snail, so castration of the largest individuals nick et al., 1990; Hutchings, 1993). results in an immediate loss of more eggs than if small indi- Parasitic castration is similar to predation in that infected viduals are castrated. Unfortunately, few studies have quanti- individuals are reproductively dead. They persist in the habitat, tatively estimated the cost of castration on the growth rate of but do not contribute to the overall reproductive success of the snail populations. A few investigators have observed that snail population. Snails are the requisite first intermediate hosts for populations are smaller in size when castration occurs (Lafferty, most digenetic trematodes, including species of medical impor- 1993b; Fredensborg et al., 2005). In addition, field studies that tance, i.e., Schistosoma spp. Infection by trematodes frequently artificially increased the number of trematode eggs in a habitat results in partial or complete castration of the snail host (Sor- have demonstrated that parasitic infections could significantly ensen and Minchella, 2001). In Charlie’s Pond (North Caroli- decrease the number of snails in an aquatic system (Nagano, na), the snail Helisoma anceps is completely castrated by the 1966; Lie, 1973; Pointier and Jourdane, 2000; Suhardono et al., dominant trematode species Halipegus occidualis (Crews and 2006). However, the decrease in population growth rate caused Esch, 1986). In 1984, prevalence of H. occidualis reached 60%, by a fixed probability of castration remains unknown. indicating that 60% of the snails were lost from the population One approach to estimate the population cost of infection is of reproductively active snails. The high prevalence of castra- with mathematical models. Perhaps the most famous host–par- tion is likely a significant selection pressure, when considering asite model is 1 that examined factors that could regulate both that a 20% reduction of a fish population was sufficient to alter the host and parasite populations (Anderson and May, 1978; the observed growth rate of various fish species (Roff, 1992). May and Anderson, 1978). The model was based on the Lotka– Interest in the population cost of parasitic infection has been Volterra predator–prey equations that used a set of differential focused on comparing snail densities from populations with dif- equations to describe the parasite and host population dynamics. ferent intensities of infection. In marine systems, Cerithidea Differential equations, converted to matrix form, can also be californica and Zeacumantus subcarinatus population densities employed to model age- and size-structured populations (Cas- are negatively correlated with prevalence of a castrating trem- well, 2001). These matrix models have been used in several atode (Lafferty, 1993b; Fredensborg et al., 2005). Furthermore, conservation studies, primarily to determine which life-cycle both species mature at a smaller size when the risk of parasitic castration is high (Lafferty, 1993a; Fredensborg and Poulin, stages should be protected to maintain and promote population 2006). Snails often exhibit phenotypic plasticity in their life- growth (Crouse et al., 1987; Crowder et al., 1994; Marschall history traits, primarily growth rates and fecundity. Environ- and Crowder, 1996). The analyses involved altering life-history traits, and then estimating the corresponding change to the pop- ulation growth rate. Similar analyses can be performed with Received 1 May 2007; revised 12 September 2007; accepted 11 snail–trematode systems. Specifically, population growth rate March 2008. can be calculated in the presence and absence of infection, and * Current address: Department of Infectious Diseases, St. Jude Chil- dren’s Research Hospital, 332 North Lauderdale Street, MS No. 330, changes to the growth rate can be observed for various values Memphis, Tennessee 38105. of key life-history traits. The traits that may offset the cost of 1022 NEGOVETICH AND ESCH—MATRIX MODEL OF H. ANCEPS 1023 TABLE I. Monthly mean fecundity (eggs/month) of snails in each size class. Individuals Ͻ6 mm were not reproductively active, so those data were excluded from the table. Monthly transition March– April– May– June– July– August– September– October– November– Size class April May June July August September October November March 6–7 0 0 0 0 0 12.86 12.86 5.57 0 7–8 66.86 49.29 0 18.43 9 35.14 15.86 5.57 0 8–9 104.57 70.71 24.86 41.14 44.14 60 23.14 3 0 9–10 129.43 111.86 40.71 51.86 41.57 46.29 9.43 0 0 10–11 181.29 114.43 81.43 61.29 50.14 46.29 0.86 5.14 0 11ϩ 203.14 122.14 123.86 82.71 46.29 29.14 7.71 0 0 infection are growth rate, fecundity, and survival (Sorensen and do not grow into a larger size class. For the Ͻ5-mm size class, SPG Minchella, 2001). was calculated with 3.5 mm. SPG was transformed to millimeters/month for each size class (Table II). The goal of the present study is to determine quantitatively Survival, infection, and self-cure probabilities were estimated from the effect of a castrating trematode infection on the population the capture histories with the use of Program MARK (White and Burn- of H. anceps in Charlie’s Pond. Estimates of life-history traits ham, 1999). Analysis of the capture histories was performed with mul- were previously calculated (Negovetich and Esch, 2008), and tistate models. This allowed estimation of infection and self-cure prob- abilities of snails Ͼ6 mm. Infection status does not affect survival (Ne- they will be used to construct a period matrix product popula- govetich and Esch, 2008), so a second analysis ignoring infection status tion model. With the use of the model, the response of popu- was performed with the use of the Cormack–Jolly–Seber (CJS) model. lation growth rate to various levels of parasitic infection will Estimates of survival from the CJS model were obtained for almost all be investigated. Additionally, the effect of changes in life-his- size classes and months. tory strategy on population growth rate will be determined. Model construction METHODS A period matrix product model was constructed with 8 size classes (Fig. 1) and 9 transition matrices. This model was chosen because it Data collection accounts for the seasonal variation in life-history traits (Caswell, 2001). Life-history traits were calculated from field experiments in Charlie’s All but 1 of the transition matrices describe the change in population Pond, North Carolina; a description of the fecundity experiment and structure from 1 month to the next, and each is unique. The overwinter mark–recapture methods can be found in Negovetich and Esch (2008). matrix describes the change from November to March. The top row of Estimates were made for 2 locations within the pond, but because of each transition matrix represents the number of new individuals that the lack of difference between the sites (Negovetich and Esch, 2008), enter the population (Fij). The remaining elements of the matrices in- the snails from each site were pooled and estimates derived for the clude survival and growth probabilities, in addition to the probability entire pond.