[A case study of singular spectrum analysis application in parasitology: dynamics of prevalence of Cryptocotyle concavum and Bunocotyle progenetica trematode parthenitae in Hydrobia ventrosa snails at the White Sea]

In this study parasitological data were analyzed by different methods of revealing the structure of time series, namely auto-correlation analysis (ACA), Fourier spectrum analysis (SA) and singular spectrum analysis (SSA), and the results of these analysis were compared (SSA makes it possible to present non-stationary time series as a sum of independent components and to determine the contribution of each component into the dispersion of the initial series--Golyandina et al., 2001). This case study was based on the result of 10-year-long monitoring of changes in the prevalence of Cryptocotyle concavum and Bunocotyle progenetica trematode parthenitae in intertidal snails Hydrobia ventrosa at the White Sea (in total, 45 observations). ACA did not reveal any statistically significant oscillations in the analyzed series. The application of SSA and SA allowed us to reveal at least two quasi-periodical components. In addition, SSA made it possible to reveal a significant dome-shaped trend in the prevalence of B. progenetica parthenitae, which were described by SA as an oscillation with a period equal to the duration of the study, as well as to give proof that there was no trend in the changes of C. concavum parthenitae prevalence. The components (modes) extracted by the SSA described the changes in the prevalence better that the harmonics extracted by the SA. In particular, SSA modes (contrary to SA harmonics) reflected that the amplitude of oscillations of the B. progenetica prevalence increased as the prevalence grew. The sums of SSA modes correlated more with initial prevalence series that the sums of SA harmonics. A possible interpretation of the trends and modes extracted by the SSA in the light of the transmission features of the investigated trematode species in the study area was proposed.

Infection patterns in white sea blue mussels Mytilus edulis of different age and size with metacercariae of Himasthla elongata (Echinostomatidae) and Cercaria parvicaudata (Renicolidae)

Infection of mussels Mytilus edulis L. by 2 trematode species was studied in a natural intertidal population in the Chupa inlet of the White Sea. The prevalence of metacercariae of Himasthla elongata (Mehlis, 1831) and Cercaria parvicaudata (Stunkard & Shaw, 1931) in mussels reached 100% in 3 to 4 yr old molluscs and remained at this level in older individuals. Infection intensity increased evenly with the age of the molluscan host, showing a tendency to decrease only in the oldest (9 yr old) mussels. These patterns of age dynamics of prevalence and infection intensity were associated with accumulation of trematode larvae in the course of the molluscs' lives. Ability of metacercariae to exist in mussels for long periods (at least 2.5 yr) was verified in the course of an experiment, during which infected molluscs were kept in a subtidal net cage. Decrease of infection intensity in the oldest individuals may reflect selective mortality of the most severely infected molluscs. Among mussels of the same age, higher infection intensity values occurred in larger individuals. This may be due to an enhanced pumping rate in large molluscs, which increases the probability of cercariae, free-living trematode larvae, infecting them via water currents.

[The use of the probability model for an estimation of a infection rate of White Sea mussels (MYtilus edulis) by Metacercariae Himasthla elongata (Trematoda: Echinostomidae) ]

A comparison of simple probability analytic model of infection rate depending on host's age with natural infection rate of mussels (Bivalvia: Mythilidae) with metacercariae Himasthla elongata (Trematoda: Echinostomidae) was carried out. Data on the natural rate of infection were accumulated during 3 years; 1152 individuals M. edulis were collected in two horizons within fucoid zone of the Kruglaya inlet and the Chupa inlet of the Kandalaksha bay (White Sea). A size of shell and number of H. elongata metacercariae were defined for each mussel using compressive dissection technique. The infection of mussels per year within our model is considers as independent evens: Pn = 1 - (1 - p)n, where n is the age of mussels, Pn is the theoretical part of infected n-year mussels, p is the probability of infection within one year. The probability of infection within year is assumed equal for every age of host. The estimate of probability of infection per year on the basis of sample of n-year's mussels was calculated as Pn = 1 - n square root of 1 - I(n), where n is the age of mussels, I(n) is the part of infected n-year mussels. The retransformed weighted average value of aresine-transformed p'n was used as p in our model (p = 0.3476). Statistically significant differences between empirical and theoretical (calculated from our models on the basis this value) infection rates were not found (P > > 0.05 chi 2-test). Moreover, statistical significant differences were absent (P > 0.05 Fisher exact test) in pairwise comparisons between empirical and theoretical infection rates for each age of mussels. The model does not take into consideration an effect of such factors as host's resistance, host's migration and increase of mortality in infected hosts. The absence of significant differences between the empirical and theoretical infection rates allows to suggest, that mentioned factors under the conditions of the Kruglaya inlet do not influence essentially onto infection of mussels with metacercariae H. elongata. This conclusions is in certain inconsistency with essential differences in such characteristic as an individual resistance of mussels to the infection with metacercariae H. elongata, detected in experiments in vitro (Gorbushin, Levakin, unpublished data). Analysis of intensity of the invasion of metacercariae H. elongata into mussels allows to suggest the existence of differential death rate of the hosts, which is exhibited in individuals over 7 years old. Studied example of mussels infected with metacercariae H. elongata under conditions of the Kruglaya inlet shows that the simple probabilistic model of the natural infection rate is usable for this kind of investigation. Our study also allows to conclude that in this case the infection rate of hosts is mainly determined by stochastic reasons. However, in some cases the probability of infection rate may not depend on the age and size of the host. The study of infection rate can not be used for analyses of individual differences of hosts in a resistance to parasites and an infection ability of the parasite.