Following the Infection Dynamics of the Tropical Trematode Oligogonotylus Mayae in Its Cambridge.Org/Jhl Intermediate and Definitive Hosts for 13 Years

Journal of Helminthology Following the infection dynamics of the tropical trematode Oligogonotylus mayae in its cambridge.org/jhl intermediate and definitive hosts for 13 years

Research Paper A.L. May-Tec, N.A. Herrera-Castillo, V.M. Vidal-Martínez and M.L. Aguirre-Macedo Cite this article: May-Tec AL, Herrera-Castillo NA, Vidal-Martínez VM, Aguirre-Macedo ML Laboratorio de Patología Acuática, Departamento de Recursos del Mar, Centro de Investigación y de Estudios (2020). Following the infection dynamics of the Avanzados del Instituto Politécnico Nacional, Unidad Mérida, Carretera Antigua a Progreso Km 6, Mérida, Yucatán, tropical trematode Oligogonotylus mayae in its intermediate and definitive hosts for 13 years. CP 97310, Mexico Journal of Helminthology 94, e208, 1–12. https://doi.org/10.1017/S0022149X20000875 Abstract

Received: 8 June 2020 We present a time series of 13 years (2003–2016) of continuous monthly data on the preva- Revised: 21 September 2020 lence and mean abundance of the trematode Oligogonotylus mayae for all the hosts involved in Accepted: 22 September 2020 its life cycle. We aimed to determine whether annual (or longer than annual) environmental Key words: fluctuations affect these infection parameters of O. mayae in its intermediate snail host Temporal variation; trematodes; seasonality; Pyrgophorus coronatus, and its second and definitive fish host Mayaheros urophthalmus long-term studies; dynamic of infection from the Celestun tropical coastal lagoon, Yucatan, Mexico. Fourier time series analysis was used to identify infection peaks over time, and cross-correlation among environmental Author for correspondence: forcings and infection parameters. Our results suggest that the transmission of O. mayae in M.L. Aguirre-Macedo, E-mail: [email protected] all its hosts was influenced by the annual patterns of temperature, salinity and rainfall. However, there was a biannual accumulation of metacercarial stages of O. mayae in M. urophthalmus, apparently associated with the temporal range of the El Niño-Southern Oscillation (five years) and the recovery of the trematode population after a devasting hurricane. Taking O. mayae as an example of what could be happening to other trematodes, it is becoming clear that environmental forcings acting at long-term temporal scales affect the population dynamics of these parasites.

Introduction Trematodes are major components of aquatic ecosystems and thought to be important for ecosystem function (Kuris et al., 2008; Morley, 2012). The complex life cycles of trematodes, which include at least one intermediate and one definitive host, have a high ecological significance, because, in many instances, they can impact the population size of critical species in food webs, which, in turn, influences ecosystem dynamics (Gordon & Rau, 1982; Lafferty et al., 2006; Bullard & Overstreet, 2008). However, we are still far from understanding properly how environmental forcings affect trematode transmission dynamics, especially in tropical latitudes. The wealth of publications dealing with trematode transmission dynamic aspects refer to their life cycles, and most studies are confined to the analysis of seasonal dynamics of infection in either intermediate or definitive hosts. Most of this literature comes from temper- ate and subtropical latitudes emphasizing the role of temperature as one of the main environmental forcings driving the infection levels of both larval and adult stages of trematodes (e.g. Chubb, 1979 (and references therein); Hughes & Answer, 1982; Galaktionov, 1992;Kubeet al., 2002; Jiménez-Garcia & Vidal-Martínez, 2005; Galaktionov et al., 2006; Fermer et al., 2010). The few extant long-term studies on trematode infections have suggested that the infection-level fluctuation has an association with several factors, such as the life span of the hosts (Fernandez & Esch, 1991a, b;Snyder&Esch,1993;Loy& Haas, 2001;Klockarset al., 2007;Faltynkováet al., 2008), temporal heterogeneity of host abundance (Fernandez & Esch, 1991a, b;Snyder&Esch,1993;Mouritsenet al., 1997; Granovitch et al., 2000;Levakinet al., 2013), eutrophication (Hofmann et al., 2016), variations in rainfall (Pech et al., 2011;Vidal-Martínezet al., 2014;Namsanoret al., 2015)and water temperature patterns (Vidal-Martínez et al., 2014;Zemmeret al., 2017), as well as the effects of hydrometeorological phenomena such as hurricanes (Aguirre-Macedo et al., 2011). Recently, Nikolaev et al.(2020) published a long-term study (11 years) emphasizing © The Author(s), 2020. Published by the effect of water temperature on the temporal dynamics of larval trematode stages from Cambridge University Press the subarctic region. In the case of tropical trematodes, many authors have speculated that they have a weak seasonal pattern of transmission with almost no inter-annual variation (Chubb, 1979; Fernandez & Esch, 1991a; Väyrynen et al., 2000; Kube et al., 2002; Yurlova et al., 2006; Gérard et al., 2008; Namsanor et al., 2015; Byers et al., 2016; Zemmer et al., 2017; Galaktionov et al., 2018).

Downloaded from https://www.cambridge.org/core. University of Athens, on 05 Oct 2021 at 08:23:02, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0022149X20000875 2 A.L. May‐Tec et al.

However, this speculation has been made without proper long- Materials and methods term data sets. Relatively long-term (five years at most) data Study site and sampling procedures sets from tropical latitudes have demonstrated that the infection levels of trematodes and nematodes show strong seasonal patterns Celestun is a tropical coastal lagoon located in the north-west of every year, with infection peaks every two years (Pech et al., 2011; the Yucatán Peninsula (20°52′46.68′′N, 90°21′15.4′′W) (supple- May-Tec et al., 2013; Vidal-Martínez et al., 2014). Therefore, the mentary fig. S1). It receives fresh water from an interconnection question is whether these peaks occur every two years independ- of the freshwater spring hydrodynamic flow and groundwater ently of longer-term climate oscillations, such as the El discharges, which vary with rainfall (Herrera-Silveira, 1994; Niño-Southern Oscillation (ENSO), or if they appear after these Herrera-Silveira & Morales-Ojeda, 2009). oscillations occur. An additional, but no less important, environ- Long-term data of the prevalence of O. mayae were obtained mental forcing is the tropical hurricane. Aguirre-Macedo et al. monthly from samples collected of the snail P. coronatus (from (2011) showed that in 2003, following Hurricane Isidore over May 2007 to December 2016) from the Baldiosera freshwater the coastal lagoon of Celestun, Yucatan, Mexico, the populations spring (20°52′N, 90°21′W). Prevalence and mean abundance of the snail Cerithidea pliculosa and its parasite community were (sensu Bush et al., 1997)ofO. mayae were obtained severely affected, and it took six years to recover the original para- monthly from the cichlid fish M. urophthalmus (from January site species composition. Indeed, there are many relevant eco- 2003 to December 2016) inhabiting the brackish water zone of logical questions that have not been properly addressed, mainly the Celestun lagoon. because the length of the available data sets used to date is not In total, 22,772 P. coronatus snails (0.5–8.0 mm length) were enough (five years) to capture the temporal variability of longer- collected from the submerged vegetation (10–80 cm depth) on term climate oscillations such as El Niño or La Niña, which can the freshwater spring known as ‘Baldiosera’ within the Celestun last between two and seven years (NOAA, 2005). lagoon. Supplementary table S1 shows the sample size of snails During the last 13 years, one of us (M.L.A.-M.) has been collected and examined. Snail sampling size was based on the collecting monthly data on the prevalence of the trematode method proposed by des Clers (1994). In this method, it is Oligogonotylus mayae in snail (first intermediate ‘1IH’) and the assumed that the prevalence of the parasite follows a Poisson fre- prevalence and mean abundance in fish second (‘2IH’) and defini- quency distribution in the host population, the accepted level of tive (‘DH’) hosts, as part of a long-term ecological monitoring risk is α = 0.05 and that the diagnostic sampling method has a program. Thus, the time series of O. mayae is suitable to tackle 75% sensitivity due to human error (handling and identification) questions such as whether the population dynamics of the trema- (May-Tec et al., 2013). Based on these assumptions, the formula tode are affected by seasonal events each year, or every two n = 4/prev was used, where n was the snail sample size, 4 origi- years, or by longer-term climate oscillations such as the ENSO. nated from –Ln (α x sensitivity of the diagnostic method) and Oligogonotylus mayae is an abundant parasite in Celestun, prev was the prevalence of the O. mayae in the snail. where its parthenitae (mother rediae, daughter rediae, sporocysts Preliminary samplings have shown that the prevalence values of and cercariae) are found in the hydrobiid snail Pyrgophorus O. mayae in P. coronatus were in the range of 2–5%. Based on coronatus (Ditrich et al., 1997), and the metacercarial and adult this result, we determined that a monthly sample size as near as stages are in the native cichlid fish Mayaheros urophthalmus possible to 200 snails would be safe to detect the lowest prevalence (Scholz et al., 1994, 1995a, b; Salgado-Maldonado & Kennedy, value detected (2%). For this reason, in the supplementary table S1, 1997). Two aspects of the life cycle of O. mayae are peculiar the sample size was around 200 snails for most months. However, within the Cryptogonimidae. First, M. urophthalmus acquires there were months in which, due to tropical storms or small hur- cercariae of O. mayae from two sources, mainly by eating ricanes, we were not able to obtain the planned sample size, and, P. coronatus infected with cercariae of this trematode. These cer- therefore, the prevalence values for those months should be con- cariae develop into metacercariae and encyst mainly in the anter- sidered with care (supplementary table S1). For the entire 116 ior intestine (Scholz et al., 1994). Additionally, M. urophthalmus months sampled, the mode of the number of snails sampled acquires cercariae released by P. coronatus into the water per month was 210, with a mean value of 198.24 ± 31.02 snails column, which become encysted in skin, lateral line and fins per month, and the lowest and highest sampling size values (Salgado-Maldonado & Kennedy, 1997). Second, young M. were 29 and 234 for one month each (supplementary table S1). urophthalmus and eight additional fish species develop meta- The species M. urophthalmus was caught by hook and line cercariae of O. mayae from the two previous sources in near the freshwater spring ‘Baldiosera’. This sampling method Celestun lagoon (Sosa-Medina et al., 2015); subsequently, provided us a partial control of the fish size, making these samples these young fish are eaten by older M. urophthalmus,which comparable over time. The mean values of the standard fish develop the adult stages of the trematode. Our hypothesis length were between 12.68 and 21.57 cm (17.28 ± 1.76) without wasthatitismorelikelythatthetransmissionpatternsofO. significant differences in size per month (Kruskal–Wallis test, mayae, in both the first and second (and definitive) host in H(123–166) = 130.89, P = 0.29). The fish sampling size per month Celestun, respond more to annual patterns of temperature, sal- was also based on the method proposed by des Clers (1994). inity and rainfall than to climate oscillations such as El Niño or Based on previous samplings, the minimum prevalence values La Niña, or to extreme weather events such as hurricanes or of O. mayae in M. urophthalmus in metacercarial and adult stages tropical storms. Consequently, in this study, we examined the were 60 and 30%, respectively. Based on the des Clers (1994) monthly temporal variability of the infection parameters of method, the adequate sample size to detect the lowest prevalence the trematode O. mayae on its first intermediate host P. coro- value was 13 fish per month. Since we sampled 15 fish per month, natus and its second (and definitive) host M. urophthalmus, we safely represented the prevalence of both the metacercarial and with the aim to determine whether annual (or longer than adult stages. However, there were months where we were unable annual) environmental forcings affect these transmission to obtain the planned sample size due to tropical storms or patterns. small hurricanes. For the entire 166 months sampled, the mode

of the number of fish sampled per month was 15, with a mean month in this study. The significance of all statistical analyses value of 14.65 ± 1.32 fish per month; the lowest sampling size was established at α < 0.05. Statistical analyses were performed value was 4 for only one month during the entire sampling period in Statistica version 6 (Statsoft©, Tulsa, Oklahoma, USA ). The (supplementary table S1). results obtained were reported with ranges (minimum and max- In situ, water temperature (°C) and salinity (PSU) were imum values) and their mean ± standard deviation. measured using a multiparameter meter Hanna© model HI9829 (Hanna instruments, Mexico, Mexico city). Rainfall (mm) data were obtained from the National Water Commission Results (Comisión Nacional del Agua) situated 5 km from Celestun. Oligogonotylus mayae infecting P. coronatus (2007–2016) The fish captured were transported alive in lagoon water and oxy- genated with a battery pump to the laboratory using a 200-L tank. Parthenitae stages The snails were transported alive in 1-L plastic bottles with water Between 2007 and 2016, the prevalence in P. coronatus infected and vegetation from the lagoon. All hosts were examined for para- with parthenitae stages fluctuated between 1 and 5%, with the sites, usually within 24–72 h after capture. maximum prevalence value observed during August 2011 In the laboratory, the snails were removed from the shell and (fig. 1). Spectral analysis of O. mayae showed peaks of high vari- then examined under a stereomicroscope using the compression ability every six, ten and 24 months (fig. 2a). In situ, the water method. The parthenitae of O. mayae were observed in temporary temperature fluctuated between 18.20 and 30.6°C (26.36 ± 1.92), mounts for identification, and some specimens were fixed in while observed salinity values were between 3 and 28.50 PSU hot 4% formaldehyde solution for subsequent specific identifica- (13.82 ± 7.10); the maximum month rainfall value was 278 mm tion following standard recommended procedures (e.g. Yamaguti, (60.32 ± 62.70) (supplementary fig. S2a). 1971; Scholz et al., 1994; Ditrich et al., 1997; Scholz & Water temperature presented peaks of variability every six, 18 Aguirre-Macedo, 2000). The fish were weighed, measured (total and 56 months. Salinity values showed a marked high variability body length) and dissected following the procedures recom- every 12 and 24 months. Rainfall presented only one peak of high mended by Vidal-Martínez et al.(2001). With the exception of variability every 12 months (supplementary fig. S2b). There was a blood, all organs of each fish were examined for parasites. significant association at lag 0 between the prevalence of O. mayae Enumeration of O. mayae metacercariae and adults was per- parthenitae and water temperature (fig. 2b). We found a delay of formed by opening half of the fish stomach and intestine and pla- six months (lag 6) between rainfall and the prevalence of cing them between two glass slides (12 × 10 × 0.3 cm) marked O. mayae. Salinity and the prevalence of O. mayae showed a sig- with 1 × 1-cm squares under the dissecting microscope. Other nificant association with a lag of three months (fig. 2b). organs, such as skin, fins and gills, were also examined under the dissecting microscope using dissection needles. Oligogonotylus mayae infecting M. urophthalmus (2003–2016) Metacercariae stages Data analysis The prevalence of O. mayae metacercariae in M. urophthalmus Spectral analysis by Fourier series was used to observe the vari- fluctuated between 13 and 100% (fig. 3a). The mean intensity ability and periodic cycles of O. mayae in their hosts and the value fluctuated between 4 and 63,984 (6380 ± 9880), reaching a environmental variables per month. In this study, the temporal maximum value during January 2016 (fig. 3b). A highly import- data sets were equally spaced in time and based on a monthly ant pattern in the metacercarial stages of O. mayae in M. sampling frequency. The data were transformed into harmonic urophthalmus was the increase of the mean intensity values frequencies of different amplitudes measured as spectral density through the 13 years of the sampling program. The O. mayae that collectively smooth the original time series, which represent prevalence did not correlate with M. urophthalmus total length temporal trends in a periodogram (Scharlemann et al., 2008). (r = −0.118, P = 0.13), nor with the mean intensity (r = 0.114, The extraction of cyclical patterns was expressed as a combination P = 0.14). of a set of waves, allowing us to detect recurrent cyclic patterns in Spectral analysis showed peaks of maximum variability for the variables (Chatfield, 1980; Scharlemann et al., 2008). The fre- O. mayae prevalence every six, nine and 15 months (fig. 4a). quency peaks were interpreted as the temporal scale of maximum The O. mayae mean intensity showed a peak of maximum vari- variability in the temporal distribution of prevalence (parthenitae, ability every 12, 24 and 40 months (fig. 4a). metacercariae and adult stages), mean intensity (metacercariae Cross-correlation analysis showed significant associations in and adults) of O. mayae, rainfall, water temperature and salinity lags 4 and 12 between O. mayae prevalence and water tempera- of Celestun. All these variables were then used to calculate cross- ture, salinity and rainfall (fig. 4b). Significant associations correlation coefficients to quantify temporal interactions between between the mean intensity of O. mayae and the water tempera- the dependent variables (the infection parameters) and the inde- ture were found in lags 1 and 8 (fig. 4c). Salinity and rainfall had a pendent environmental variables (Legendre & Legendre, 1998; significant association with the mean intensity of O. mayae in lags Olden & Neff, 2001). Cross-correlation provides a measure of 6 and 7, respectively (fig. 4c). the positive or negative association of the values of the dependent and independent variables at different time lags and determines Adult stages the extent to which data sets exhibit correlated periodic variations. The prevalence values of O. mayae adults in M. urophthalmus Time lags refer to delayed responses in the dynamics of depend- fluctuated between 13 and 100% (fig. 5a). The mean intensity ent variables following fluctuations in independent variables value of O. mayae was 2–164 (26.13 ± 28.37), with the maximum (Olden & Neff, 2001). The time lag with the highest correlation value during September 2011 (fig. 5b). The O. mayae prevalence coefficient is taken as the smallest time lag between the two did not correlate with M. urophthalmus total length (r = −0.118, time series (Wei, 1990). Each lag used is equivalent to one P = 0.12) or with the mean intensity (r = 0.23, P = 0.003).

Fig. 1. Temporal variation of prevalence of Oligogonotylus mayae parthenitae in Pyrgophorus coronatus from the Baldiosera freshwater spring of Celestun, Yucatan (2007– 2016).

Fig. 2. (a) Spectral analysis of Oligogonotylus mayae prevalence and (b) cross-correlation between O. mayae prevalence and environmental variables.

Spectral analysis of O. mayae prevalence showed peaks of high months (fig. 6a). Cross-correlation of O. mayae prevalence variability every ten, 22 and 40 months (fig. 6a). With respect to showed a significant association (lags −1, 1 and 12) with salinity, O. mayae mean intensity, peaks occurred every 12, 24 and 40 rainfall and water temperature, respectively (fig. 6b). The O. mayae

Fig. 3. Temporal variation of Oligogonotylus mayae metacercariae (mtc) infecting Mayaheros urophthalmus from Celestun, Yucatan (2003–2016). (a) Variability of prevalence of O. mayae in metacercariae stages in M. urophthalmus; (b) mean intensity of O. mayae in metacercariae stages in M. urophthalmus. The red lines represent the lower limit (95%) and upper limit (95%).

mean intensity showed significant associations with the water metacercariae was observed in the fish. Finally, cross-correlation temperature, salinity and rainfall at lag 1 (fig. 6c). analysis showed a significant association between the maximum prevalence of metacercariae and the maximum prevalence value of adult stages in the fish (lag 0). Cross-correlation analysis of the lifecycle stages of O. mayae Cross-correlation analysis among the prevalence of O. mayae Discussion (parthenitae, metacercarial and adult stages) in its intermediate, P. coronatus, and second (and definitive) hosts, M. urophthalmus, Our results suggest that the original hypothesis in this paper was showed significant associations with a delay of three to six months partially correct since transmission patterns of O. mayae in both (fig. 7). These associations suggest that three months after the first and second (and definitive) host at Celestun coastal the occurrence of maximum variability in the prevalence of lagoon were responding at the annual temporal scale where yearly O. mayae adults, there is an increase in the parthenitae prevalence patterns of temperature, salinity and rainfall occur. However, in the snail. Then, three months after the maximum variability of there was an increasing accumulation pattern of O. mayae meta- parthenitae, an increase in the prevalence of O. mayae cercariae over time. This increase has at least two competing

Fig. 4. (a) Spectral analysis of prevalence and mean intensity of Oligogonotylus mayae metacercariae (mtc) in Mayaheros urophthalmus; (b) cross-correlation between prevalence of O. mayae mtc and environmental variables; (c) cross-correlation between mean intensity of O. mayae mtc and environmental variables.

explanations. The first one is that climate oscillations occurring at release free-swimming cercariae, which become established in larger temporal scales, such as the ENSO, influence water tem- the body skin, fins and gills of M. urophthalmus (Scholz et al., perature, which could affect the O. mayae population dynamics 1994). These authors suggested that M. urophthalmus is infected in the long term. The second explanation is that the O. mayae by cercariae of O. mayae by ingesting infected snails, which is the population is still recovering from Hurricane Isidore, which main pathway through which metacercariae develop and encyst in occurred in 2002 (Aguirre-Macedo et al., 2011). Apart from the intestine (Scholz et al., 1994). Adult M. urophthalmus predate these explanations, the peaks in prevalence and mean intensity upon the young stages of nine fish species (including those of M. of O. mayae life stages at 24 and 40 months were apparently repli- urophthalmus) in the Celestun lagoon infected with metacercariae cates of the original annual pattern. These strong patterns in the of O. mayae (see table 2 in Sosa-Medina et al., 2015 for a complete infection parameters of O. mayae were most likely produced by list of all these 2IH) and develop the adult stages of this trema- the seasonal, annual and interannual fluctuation patterns of the tode. Several of these fish species acting as 2IH, such as abiotic factors (rainfall, salinity and water temperature) in Floridichtys carpio, Eucinostomus argenteus, Lutjanus griseus, Celestun. In the following paragraphs, we present a detailed Sphoeroides testudineus and M. urophthalmus are abundant in account of the influence of abiotic factors on the different life Celestun (Vega-Cendejas, 2004). Since the density of intermediate stages of O. mayae at different time scales. hosts is an important factor in the transmission of trematodes (Voutilainen et al., 2009), the greater abundance of hosts increases the probability of encounters with transmission stages in the Yearly patterns and their replicates environment (Wilson et al., 2002) and facilitates the completion The O. mayae prevalence presented a marked seasonality appar- of the O. mayae life cycle. ently associated with high temperatures (fig. 2a). During the The infection levels of O. mayae in P. coronatus apparently dry season in Yucatan (March to May), high temperatures, low respond to seasonal variability in water temperature during the rainfall and organic matter decomposition in Celestun lagoon dry season (fig. 2b), which, in turn, can influence the number (Tapia Gonzalez et al., 2008) apparently influence the reproduc- of cercariae released from infected snails. These cercariae tion of trematodes in the definitive host, increasing the availability released by P. coronatus into the water column become encysted of O. mayae eggs to infect the snails. An important number of in skin, the lateral line and fins (Salgado-Maldonado & Kennedy, these infected snails are eaten by M. urophthalmus since they 1997). Similar patterns have been observed for other trematode are an important food item for the cichlid fish species in different latitudes such as Acanthoparyphium sp., (Martínez-Palacios & Ross, 1988, our own observation). Those Himasthla rhigedana and Parorchis acanthus,withanincrease P. coronatus not eaten by the fish but infected can eventually in the number of cercariae released from their intermediate

Fig. 5. Temporal variation of Oligogonotylus mayae adults infecting Mayaheros urophthalmus from Celestun, Yucatan (2003–2016). (a) Variability of prevalence of O. mayae adults in M. urophthalmus; (b) mean intensity of O. mayae adults in M. urophthalmus. The red lines represent the lower limit (95%) and upper limit (95%).

host when temperature increases (Takahashi et al., 1961; that, month after month, individual fish of approximately the Fingerut et al., 2003;Koprivnikar&Poulin,2009;Koprivnikar same size were examined for parasites, making samples compar- et al., 2014;McCreeshet al., 2014,Mehlhorn,2016;Schade able over time. et al., 2016). The peaks in the number of metacercariae in fish occurred There is one caveat in fish size before starting with the pat- from May to July and from November to January (fig. 3a), terns of metacercariae and adult stages. It has been postulated just at the beginning of the rainy and north seasons. During that there is a positive correlation between fish length and larval these seasons, the increases in organic matter, water flow and helminth intensity (Pulkkinen & Valtonen, 1999; Poulin & turbidity in the coastal lagoon (Orduña-Rojas et al., 2002) Valtonen, 2001). However, in our study, fish size did not signifi- could act as environmental triggers, probably enhancing both cantly correlate with O. mayae prevalence or with mean inten- the increase in the number of the first intermediate host sity, most likely because the hook size used to capture the fish (P. coronatus) and the number of cercariae released looking excluded small individuals. Therefore, there is bias in the sam- for the second intermediate fish hosts. Pech et al.(2011)also pling procedure. However, the advantage of this procedure is suggested that freshwater discharges from the water springs

Fig. 6. (a) Spectral analysis of prevalence and mean intensity of Oligogonotylus mayae adults in Mayaheros urophthalmus; (b) cross-correlation between prevalence of O. mayae adults and environmental variables; (c) cross-correlation between mean intensity of O. mayae adults and environmental variables.

along the Celestun coastal lagoon during the rainfall season O. mayae is persistent throughout the entire year, but with would also enhance the transmission of cercariae. peaks previously described throughout the year. The seasonal increase in the number of adult stages of O. mayae in M. urophthalmus corresponds to the period July–November Long-term temporal patterns (fig. 5) – the time of the reproductive peak of M. urophthalmus and when parental care takes place (Martínez-Palacios & Ross, The long-term data set of all lifecycle stages of O. mayae 1988). We speculate that during this time the sexually mature (parthenitae, metacercariae and adult stages) in their hosts adult stages of O. mayae shed eggs into the intestine of M. (P. coronatus and M. urophthalmus) showed interannual pat- urophthalmus, which eventually release them into the nest area, terns every two years, with an increase in the mean intensity where they are ingested by P. coronatus. The infection patterns of values especially evident in the last five years (figs 1, 3 and 5). O. mayae metacercariae and adult stages in the fish showed a This biannual accumulation pattern has previously been delay time with respect to maximum values of water temperature observed for O. mayae and other larval trematodes such as and rainfall (figs 4b, c and 6b, c). A possible explanation for the Ascocotyle (Phagicola) nana in M. urophthalmus from the first peak is that high temperatures trigger the intensity of mollusc Celestun lagoon (Pech et al., 2011; May-Tec et al., 2013; consumption by the fish (Martínez-Palacios & Ross, 1988); regard- Vidal-Martínez et al., 2014). The biannual accumulation pattern ing the second peak, rainfall influences the dispersion of infected found in this study might be related to the life span of the hosts. snails and cercariae, which subsequently encyst in the fish (Pech ThelifespanofP. coronatus,beingaHydrobiidae,isestimated et al., 2011; Vidal-Martínez et al., 2014). to be about 13–24 months with annual recruitment (Drake & Our results show that prevalence peaks of adults and metacer- Arias, 1995; Mladenka & Minshall, 2001). Young P. coronatus carial stages in fish occurred approximately three to six months begin their life uninfected. However, as these snails become after the increase in the prevalence peaks of parthenitae in the older there is an increase in the probability that they could ingest mollusc (fig. 7). However, in experimental studies, it has been O. mayae eggs and develop miracidia. Since these snails live up observed that the development of cercariae into infective metacer- to 24 months, the older members of the population would be the cariae of O. mayae was relatively quick (14–20 days) (Scholz et al., ones with the highest prevalence, which, in turn, would explain 1994), similar to that of other Cryptogonimidae (Greer & the biannual peak of prevalence shown in fig. 2a. Further sup- Corkum, 1979). Therefore, it is evident that the transmission of port for this interpretation comes from Sousa (1990)and

Fig. 7. Cross-correlation among the prevalence (prev) of snails infected with Oligogonotylus mayae parthenitae, prevalence of metacercariae (Mtc) and prevalence of adult stages of O. mayae in M. urophthalmus through time.

Faltynková et al. (2008), who have recognized that as snails aged and rainfall (Stenseth et al., 2003; NOAA, 2005). In the same way, there is an increase in the prevalence of trematode infections. A the increased water temperature and decreased salinity as a con- similar pattern of increase of prevalence and mean abundance sequence of the ENSO have been associated with the increase in can be expected in M. urophthalmus with increasing age. This the number of cases of Perkinsus marinus in Crassostrea virginica is because older fish have more time and major probabilities from the Gulf of Mexico (Soniat et al., 2009). Therefore, the of ingesting infected snails and small fishes infected with meta- ENSO periodicity may explain the general increase observed cercariae of O. mayae. over time in the number of O. mayae in fish (figs 3 and 5), but Based on the fact that the captured M. urophthalmus were this is difficult to test without a much longer time series. always in the same size range due to the bias in the fishing pro- A second but equally possible explanation for the increase in cedure (see Material and Methods section), we would expect to the number of metacercariae throughout the 13 years of the sam- have more or less the same mean intensity range over time. pling program is that of the recovery of the O. mayae population However, this was not the case – there was an increase in in Celestun following the 2002 Hurricane Isidore. The point is the mean intensity values of metacercariae in fish over time that the values of prevalence and mean intensity of O. mayae (fig. 3b). Apparently, this increase in O. mayae mean intensity metacercariae before Isidore were in the range of those we was associated with the variability in water temperature and rain- report herein for 2016 (31,480.98 ± 17,379.17). Salgado- fall observed through the entire sampling period, but with marked Maldonado (1993) reported a mean abundance value of 42,808 ± increases from 2011 up to 2016 (fig. 3b). This last period of time 82,116 metacercariae of O. mayae infecting M. urophthalmus at also coincided with high values of parthenitae prevalence and the Celestun. Therefore, it is possible that the population of mean intensity of metacercariae and adults in the fish (figs 1, 3b O. mayae has been recovering from Hurricane Isidore during and 5b). In 2015 particularly, rainfall values were below average in the last 13 years, and is only now reaching the number of meta- Celestun (656.10 ± 35.41 mm) (SMN, 2015). In this sense, the cercariae prior to the hurricane. combined effect of high temperature and lower rainfall promoted In conclusion, our results suggest that the transmission pat- an increase in the availability of infected first intermediate hosts, terns of O. mayae in both the first and second (and definitive) which, in turn, enhanced the accumulation of metacercariae of host at Celestun are influenced by environmental forcings (tem- O. mayae in M. urophthalmus. In addition, during 2015, there perature, salinity and rainfall) acting at the annual temporal were record values for the annual average temperature associated scale. With respect to long-term temporal patterns, at this with ENSO (Varotsos et al., 2016). This climate oscillation occurs point it is not possible to distinguish whether the increasing accu- every two to seven years, influencing the variability of temperature mulation pattern of the metacercarial stages of O. mayae over time

was affected by the ENSO, by the recovery process following Drake P and Arias AM (1995) Distribution and production of Chirononomus Hurricane Isidore or by both forcings. However, taking salinarius (Diptera: Chironomidae) in a shallow coastal lagoon in the Bay of – O. mayae as an example of what could be happening to other tre- Cádiz. Hydrobiologia 299, 195 206. matodes, it is becoming clear that environmental forcings acting Faltynková A, Valtonen ET and Karvonen A (2008) Spatial and temporal at long-term temporal scales affect the population dynamics of structure of the trematode component community in Valvata macrostoma (Gastropoda, Prosobranchia). Parasitology 135, 1691–1699. these parasites, at least in the Gulf of Mexico. Fermer J, Culloty SC, Kelly TC and O’Riordan RM (2010) Temporal variation of Meiogymnophallus minutus infections in the first and second inter- Supplementary material. To view supplementary material for this article, mediate host. Journal of Helminthology 84, 362–368. please visit https://doi.org/10.1017/S0022149X20000875 Fernandez J and Esch GW (1991a) The component community structure of Acknowledgements. Our sincere thanks to all of the staff at the Laboratorio larval trematodes in the pulmonate snail Helisoma anceps. Journal of – de Patología Acuática CINVESTAV-IPN Unidad Mérida, including Clara Parasitology 77, 540 550. Vivas-Rodríguez, Gregory Arjona-Torres, Nadia Herrera-Castillo, Francisco Fernandez J and Esch GW (1991b) Guild structure of the larval trematodes in Puc-Itza, Efrain Sarabia-Eb and Arturo Centeno-Chalé who helped with the snail Helisoma anceps: patterns and processes at the individual host – field and laboratory work at different times over the past 13 years. We level. Journal of Parasitology 77, 528 539. would also like to thank anonymous reviewers fort heir helpful comments Fingerut JT, Zimmer CA and Zimmer RK (2003) Patterns and processes of that contribute to improve the manuscript. larval emergence in an estuarine parasite system. Marine Biological Laboratory 205, 110–120. Financial support. This study was supported by the Consejo Nacional de Galaktionov KV (1992) Seasonal dynamics of age composition in component Ciencia y Tecnología (CONACyT), Mexico, project D 44590-Q populations of daughter sporocyst of microphallids of the ‘‘pygmaeus’’ ‘Invertebrados como hospederos intermediarios de helmintos de Lutjanus gri- group (Trematoda, Microphallidae) in the intertidal molluscs Littorina sax- seus y otros peces de importancia comercial en dos lagunas costeras de atilis in the Barents Sea. Parazitologiya 26, 462–469. Yucatán’ (M.L.A.-M., grant number 44590); SEP-PROMEP, who supported Galaktionov KV, Irwin SWB, Prokofiev VV, Saville DH, Nikolaev KE and our project ‘Propuesta sobre Calentamiento Global y Cambio Climático de Levakin IA (2006) Trematode transmission in coastal communities— la Red Académica de Instituciones SEP-PROMEP del Sureste: área temperature dependence and climate change perspectives. pp. 85–90 in Sensibilidad Marina’, and a FOMIX Yucatán award in support of the project 11th International Congress of Parasitology (ICOPA XI), Glasgow ‘Sensibilidad y vulnerabilidad de los ecosistemas costeros del sureste de (Scotland, United Kingdom), August 6–11, 2006. Medimond International México ante el Cambio Climático Global’ YUC-2008-C06-108929; Proceedings. CONACyT (J.Q.G.-M., grant numbers 15689-2014 and 251622-2015); and Galaktionov KV, Nikolaev KE, Aristov DA, Levakin IA and Kozminsky EV by the National Council of Science and Technology of Mexico–Mexican (2018) Parasites on the edge: patterns of trematode transmission in the Ministry of Energy–Hydrocarbon Trust (project number 201441). This is a Arctic intertidal at the Pechora Sea (South-Eastern Barents Sea). Polar contribution of the Gulf of Mexico Research Consortium and the Coastal Biology 49, 1719–1737. Resilience Laboratory research CONACyT project 299063 ‘Laboratorio Gérard C, Carpentier A and Paillisson JM (2008) Long-term dynamics and Nacional de Resiliencia Costera’. community structure of freshwater gastropods exposed to parasitism and other environmental stressors. Freshwater Biological Association 53, 470–484. Conflicts of interest. None. Gordon DM and Rau ME (1982) Possible evidence for mortality induced by the parasite Apatemon gracilis in a population of brook sticklebacks (Culaea Ethical standards. All procedures were reviewed and approved by the inconstans). Parasitology 84,41–47. Institutional Animal Care and Use Committee (IACUC) of the Center for Granovitch AI, Sergievsky SO and Sokolova IM (2000) Spatial and temporal Research and Advanced Studies (CINVESTAV) of the National Politechnical variation of trematode infestation in coexisting populations of intertidal Institute (Protocol number: 0138-15). gastropods Littorina saxatilis and L. obtusata in the White Sea. Diseases of Aquatic Organisms 41,53–64. Greer JG and Corkum KC (1979) Life cycle studies of three digenetic trematodes, including descriptions of two new species (Digenea: Cryptogonimidae). Proceedings of the Helminthological Society of References Washington 46, 188–200. Aguirre-Macedo ML, Vidal-Martínez VM and Lafferty KD (2011) Herrera-Silveira JA (1994) Spatial heterogeneity and seasonal patterns in a Trematode communities in snails can indicate impact and recovery from tropical coastal lagoon. Journal of Coastal Research 10, 738–746. hurricanes in a tropical coastal lagoon. International Journal for Herrera-Silveira JA and Morales-Ojeda SM (2009) Evaluation of the health Parasitology 41, 1403–1408. status of a coastal ecosystem in southeast Mexico: assessment of water qual- Bullard SA and Overstreet RM (2008) Digeneans as enemies of fishes. pp. ity, phytoplankton and submerged aquatic vegetation. Marine Pollution 817–976 in Eiras JC, Segnar H, Wahli T and Kapoor BG (Eds) Fish diseases. Bulletin 59,72–86. Enfield, Science Publishers. Hofmann H, Blasco-Costa I, Knudsen R, Matthaei CD, Valois A and Lange Bush AO, Lafferty KD, Lotz JM and Shostak AW (1997) Parasitology meets K (2016) Parasite prevalence in an intermediate snail host is subject to mul- ecology on its own terms: Margolis et al. revisited. Journal of Parasitology tiple anthropogenic stressors in a New Zealand river system. Ecological 83, 575–583. Indicators 60, 845–852. Byers JE, Holmes ZC and Blakeslee AMH (2016) Consistency of trematode Hughes RN and Answer P (1982) Growth, spawning and trematode infection infection prevalence in host populations across large spatial and temporal of Littorina littorea (L.) from an exposed shore in North Wales. Journal of scales. Ecology 7, 1643–1649. Molluscan Studies 48, 321–330. Chatfield C (1980) The analysis of time-series: an introduction. London, Jiménez-García MI and Vidal-Martínez VM (2005) Temporal variation in Chapman & Hall. the infection dynamics and maturation cycle of Oligogonotylus manteri Chubb JC (1979) Seasonal occurrence of helminths in freshwater fishes. Part (Digenea) in the cichlid fish, “Cichlasoma” urophthalmus, from Yucatán, II. Trematoda. Advances in Parasitology 17, 142–313. México. Journal of Parasitology 91, 1008–1014. des Clers S (1994) Sampling to detect infections and estimate prevalence in Klockars J, Huffman J and Fried B (2007) Survey of seasonal trematode aquaculture. Stirling, Scotland, Pisces Press. infections in Helisoma trivolvis (Gastropoda) from lentic ecosystems in Ditrich O, Scholz T, Aguirre-Macedo L and Vargas-Vazquez J (1997) Larval New Jersey, U.S.A. Comparative Parasitology 74,75–80. stages of trematodes from freshwater mollusks of the Yucatán Peninsula, Koprivnikar J and Poulin R (2009) Interspecific and intraspecific variation in Mexico. Folia Parasitologica 44, 109–127. cercariae release. Journal of Parasitology 95,14–19.

Koprivnikar J, Ellis D, Shim KC and Forbes MR (2014) Effects of tempera- Poulin R and Valtonen ET (2001) Interspecific association among larval hel- ture and salinity on emergence of Gynaecotyla adunca cercariae from the minths in fish. International Journal for Parasitology 31, 1589–1596. intertidal gastropod Ilyanassa obsoleta. Journal of Parasitology 100, 242– Pulkkinen K and Valtonen ET (1999) Accumulation of plerocercoids 245. of Triaenophorus crassus in the second intermediate host Coregonus Kube S, Kube J and Bick A (2002) Component community of larval trema- lavaretus and their effect on growth of the host. Journal of Fish Biology todes in the mudsnail Hydrobia ventrosa: temporal variation in prevalence 55, 115–126. in relation to host life history. Journal of Parasitology 88, 730–737. Salgado-Maldonado G (1993) Ecología de helmintos parásitos de Cichlasoma Kuris AM, Hechinger RF, Shaw JC, et al. (2008) Ecosystem energetic impli- uropthalmus (Gunther) (Pisces: Cichlidae) en la Península de Yucatán, cations of parasite and free-living biomass in three estuaries. Nature 454, Mexico. Doctoral thesis, CINVESTAV IPN Mérida, Mexico. 515–518. Salgado-Maldonado G and Kennedy CR (1997) Richness and similarity of Lafferty KD, Dobson AP and Kuris AM (2006) Parasites dominate food web helminth communities in the tropical cichlid fish Cichlasoma urophthalmus links. Proceedings of the National Academy of Sciences of the United States of from the Yucatán Peninsula, México. Parasitology 114, 581–590. America 103, 11211–11216. Schade FM, Raupach MJ and Wegner KM (2016) Seasonal variation in para- Legendre P and Legendre L (1998) Numerical ecology. 2nd edn. Amsterdam, site infection patterns of marine ﬁsh species from the Northern Wadden Sea the Netherlands, Elsevier Science BV. in relation to interannual temperature fluctuations. Journal of Sea Research Levakin IA, Nikolaev KE and Galaktionov KV (2013) Long-term variation in 113,73–84. trematode (Trematoda, Digenea) component communities associated with Scharlemann JPW, Benz D, Hay SI, Purse BV, Tatem AJ, Wint GRW and intertidal gastropods is linked to abundance of final hosts. Hydrobiologia Rogers DJ (2008) Global data for ecology and epidemiology: a novel algo- 706, 103–118. rithm for temporal Fourier processing MODIS data. PLoS ONE 3, e1408. Loy C and Haas W (2001) Prevalence of cercariae from Lymnaea stagnalis Scholz T and Aguirre-Macedo MA (2000) Metacercariae of trematodes para- snails in a pond system in Southern Germany. Journal of Parasitology sitizing freshwater fish in Mexico: a reappraisal and methods of study. pp. Research 87, 878–882. 101–115 in Salgado-Maldonado G, García Aldrete AN, Vidal-Martinez VM Martínez-Palacios CA and Ross LG (1988) The feeding ecology of the Central (Eds) Metazoan parasites in the neotropics: a systematic and ecological per- American cichlid Cichlasoma urophthalmus (Gunther). Journal of Fish spective. Mexico, Instituto de Biologia, UNAM. Mexico City. Biology 33, 665–670. Scholz T, Lavadores JI, Vargas J, Mendoza EF, Rodríguez R and Vivas C May-Tec AL, Pech D, Aguirre-Macedo ML and Vidal-Martínez VM (2013) (1994) Life cycle of Oligogonotylus manteri (Digenea: Cryptogonomidae), Temporal variation of Mexiconema cichlasomae (Nematoda: a parasite of cichlid fishes in Southern México. Journal of the Daniconematidae) in the Mayan cichlid fish Cichlasoma urophthalmus Helminthological Society of Washington 61, 190–199. and its intermediate host Argulus yucatanus from a tropical coastal lagoon. Scholz T, Vargas-Vázquez J, Moravec F, Vivas-Rodríguez C and Parasitology 140, 385–395. Mendoza-Franco E (1995a) Cenotes (sinkholes) of the Yucatán Peninsula, McCreesh N, Arinaitwe M, Arineitwe W, Tukahebwa E M and Booth M México, as habitat of adult trematodes of fish. Folia Parasitologica 42,37–47. (2014) Effect of water temperature and population density on the popula- Scholz T, Vargas-Vázquez J, Moravec F, Vivas-Rodríguez C and tion dynamics of Schistosoma mansoni intermediate host snails. Parasites Mendoza-Franco E (1995b) Metacercariae of trematodes of fishes from & Vectors 7, 503. cenotes (sinkholes) of the Yucatán Peninsula, México. Folia Parasitologica Mehlhorn H (2016) Digenea. pp. 689–708 in Mehlhorn H (Ed.) Encyclopedia 42, 173–192. of parasitology. Berlin, Heidelberg, Springer. Servicio Meteorológico Nacional (2005) Resumen de la temporada de Mladenka GC and Minshall GW (2001) Variation in the life history and ciclones Tropicales 2005. Available at http://smn.conagua.gob.mx/tools/ abundance of three populations of Bruneau hot springsnails (Pyrgulopsis DATA/Ciclones%20Tropicales/Resumenes/2005.pdf (accessed 10 October bruneauensis). Western North American Naturalist 61, 204–212. 2020). Morley NJ (2012) Cercariae (Platyhelminthes: Trematoda) as neglected com- Snyder SD and Esch GW (1993) Trematode community structure in the pul- ponents of zooplankton communities in freshwater habitats. Hydrobiologia monate snail Physa gyrina. Journal of Parasitology 79, 205–215. 691,7–19. Soniat TM, Hofmann EE, Klinck JM and Powell EN (2009) Differential Mouritsen KN, Jensen T and Jensen KT (1997) Parasites on an intertidal modulation of eastern oyster (Crassostrea virginica) disease parasites by Corophium-bed: factors determining the phenology of microphallid the El-Niño-Southern Oscillation and the North Atlantic Oscillation. trematodes in the intermediate host populations of the mud-snail International Journal of Earth Sciences 98,99–114. Hydrobia ulvae and the amphipod Corophium volutator. Hydrobiologia Sosa-Medina T, Vidal-Martínez VM and Aguirre-Macedo ML (2015) 355,61–70. Metazoan parasites of fishes from the Celestun coastal lagoon, Yucatan, Namsanor J, Sithithaworn P, Kopolrat K, Kiatsopit N, Pitaksakulrat O, Mexico. Zootaxa 4007, 529–544. Tesana S, Andrews RH and Petney TN (2015) Seasonal transmission of Sousa WP (1990) Spatial scale and the processes structuring a guild of larval Opisthorchis viverrini sensu lato and a Lecithodendriid trematode species trematode parasites. pp. 41–67 in Esch GW, Bush AO and Aho JM (Eds) in Bithynia siamensis goniomphalos snails in northeast Thailand. Parasite communities: patterns and processes. London, Chapman & Hall. American Journal of Tropical Medicine and Hygiene 93,87–93. Stenseth NC, Ottersen G, Hurrell JW, Mysterud A, Lima M, Chan KS, Nikolaev KE, Levakin IA and Galaktionov KV (2020) Seasonal dynamics of Yoccoz NG and Dlandsvik B (2003) Studying climate effects on ecology trematode infection in the first and the second intermediate hosts: a long- through the use of climate indices: the North Atlantic Oscillation, El term study at the subarctic marine intertidal. Journal of Sea Research 164, Niño Southern Oscillation and beyond. Proceedings of the Royal Society 101931. Biological Sciences 270, 2087–2096. NOAA (2005) National Oceanic Data Center: coastal water temperature guide. Takahashi T, Mori K and Shigeta Y (1961) Phototactic, thermotactic and Available at http://www.cpc.noaa.gov/index.php (accessed 4 February 2018). geotactic responses of miracidia of Schistosoma japonicum. Japanese Olden JD and Neff BD (2001) Cross-correlation bias in lag analysis of aquatic Journal of Parasitology 10, 686–691. time series. Marine Biology 138, 1063–1070. Tapia González FU, Herrera-Silveira JA and Aguirre-Macedo ML (2008) Water Orduña-Rojas J, Robledo D and Dawes CJ (2002) Studies on the tropical quality variability and eutrophic trends in karstic tropical coastal lagoons of the agarophyte Gracilaria cornea J. Agardh (Rhodophyta, Gracilariales) from Yucatán Peninsula. Estuarine Coastal and Shelf Science 76, 418–430. Yucatan, Mexico. I. Seasonal physiological and biochemical responses. Varotsos CA, Tzanis CG and Sarlis NV (2016) On the progress of the Botanica Marina 45, 453–458. 2015-2016 El Niño event. Atmospheric Chemistry and Physics 16, 2007– Pech D, Aguirre-Macedo ML, Lewis JW and Vidal-Martínez VM (2011) 2011. Rainfall induces time-lagged changes in the proportion of tropical aquatic Väyrynen T, Siddall R, Tellervo Valtonen E and Taskinen J (2000) Patterns hosts infected with metazoan parasites. International Journal for of trematode parasitism in lymnaeid snails from northern and central Parasitology 40, 937–944. Finland. Annales Zoologici Fennici 37, 189–199.

Vega-Cendejas ME (2004) Ictiofauna de la reserva de la Biosfera Celestún, Wilson K, Bjornstad ON, Dobson AP, Merler S, Poglayen G, Randolph SE, Yucatán: una contribución al conocimiento de su biodiversidad. Anales Read AF and Skorping A (2002) Heterogeneities in macroparasite infec- del Instituto de Biología, Universidad Nacional Autónoma de México. tions: patterns and processes. pp. 6–44 in Hudson PJ, Rizzoli A, Grenfell Serie Zoología 75, 193–206. BT, Heesterbeek H and Dobson AP (Eds) The ecology of wildlife diseases. Vidal-Martínez VM, Aguirre-Macedo ML, Scholz T, González-Solís D and Oxford, UK, Oxford University Press. Mendoza-Franco E (2001) Atlas of the helminth parasites of cichlid fish of Yamaguti S (1971) Synopsis of digenetic trematodes of vertebrates. Parts I, II. Mexico. Academia, Prague. 165 pp. Tokyo, Keigaku Publishing Co. 1074 pp. Vidal-Martínez VM, Pal P, Aguirre-Macedo ML, May-Tec AL and Lewis JW Yurlova NI, Vodyanitskaya SN, Serbina EA, Biserkov VY, Georgiev BB and (2014) Temporal variation in the dispersion patterns of metazoan parasites Chipev NH (2006) Temporal variation in prevalence and abundance of of a coastal fish species from the Gulf of Mexico. Journal of Helminthology, metacercariae in the pulmonate snail Lymnaea stagnalis in Chany Lake, 88, 112–122. West Siberia, Russia: long-term patterns and environmental covariates. Voutilainen A, Van Ooik T, Puurtinen M, Kortet R and Taskinen J (2009) Journal of Parasitology 92, 249–259. Relationship between prevalence of trematode parasite Diplostomum sp. and Zemmer SA, Wyderko J, Da Silva Neto J, Cedillos I, Clay L, Benfield population density of its snail host Lymnaea stagnalis in lakes and ponds in EF and Belden LK (2017) Seasonal and annual variation in trema- Finland. Aquatic Ecology 43, 351–357. tode infection of stream snail Elimia proxima in the southern Wei WWS (1990) Time series analysis: univariate and multivariate methods. Appalachian Mountains of Virginia. Journal of Parasitology 103, New York, Adisson–Wesley. 213–220.