Parasite distribution among hosts is a fundamental aspect of host–parasite interactions. Aggregated parasite distributions within and across host species are commonly reported and potentially influenced by many factors, whether host or parasite specific, or related to host–parasite encounter and compatibility. Yet, the respective role of each in observed parasite distributions are often unclear. Here, we documented the distribution of the acanthocephalan parasite Pomphorhynchus laevis sensu lato (s.l.) in two replicate fish host populations. Aggregated distributions were observed in both populations, within and across fish host species. We found a positive abundance–prevalence relationship across fish species, suggesting that resource availability (fish host biomass density) was the main driver of P. laevis s.l. distribution. This was supported by further positive associations between mean parasite load and fish biomass density. We found little evidence for intensity-dependent regulation within host (i.e. intra-host competition among co-infecting parasites). Furthermore, P. laevis s.l. infection had no detectable effect on fish condition indices, except on the body condition of female barbel (Barbus barbus). Therefore, P. laevis s.l. tended to accumulate with size/age within fish species, and with fish biomass density among fish species, with apparently negligible limitations due to intra-host intensity-dependent regulation of parasite, or to parasite-induced morbidity in fish. The relative availability of final hosts for trophic transmission thus appears to be the main driver of P. laevis s.l. distribution among fish.

Malaria and leishmaniasis are among the two most important health problems of many developing countries especially in the Middle East and North Africa. It is common for vector-borne infectious diseases to have similar hotspots which may be attributed to the overlapping ecological distribution of the vector. Hotspot analyses were conducted to simultaneously detect the location of local hotspots and test their statistical significance. Spatial scan statistics were used to detect and test hotspots of malaria and cutaneous leishmaniasis (CL) in Afghanistan in 2009. A multivariate negative binomial model was used to simultaneously assess the effects of environmental variables on malaria and CL. In addition to the dependency between malaria and CL disease counts, spatial and temporal information were also incorporated in the model. Results indicated that malaria and CL incidence peaked at the same periods. Two hotspots were detected for malaria and three for CL. The findings in the current study show an association between the incidence of malaria and CL in the studied areas of Afghanistan. The incidence of CL disease in a given month is linked with the incidence of malaria in the previous month. Co-existence of malaria and CL within the same geographical area was supported by this study, highlighting the presence and effects of environmental variables such as temperature and precipitation. People living in areas with malaria are at increased risk for leishmaniasis infection. Local healthcare authorities should consider the co-infection problem by recommending systematic malaria screening for all CL patients.

The Poisson model can be applied to the count of events occurring within a specific time period. The main feature of the Poisson model is the assumption that the mean and variance of the count data are equal. However, this equal mean-variance relationship rarely occurs in observational data. In most cases, the observed variance is larger than the assumed variance, which is called overdispersion. Further, when the observed data involve excessive zero counts, the problem of overdispersion results in underestimating the variance of the estimated parameter, and thus produces a misleading conclusion. We illustrated the use of four models for overdispersed count data that may be attributed to excessive zeros. These are Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial models. The example data in this article deal with the number of incidents involving human papillomavirus infection. The four models resulted in differing statistical inferences. The Poisson model, which is widely used in epidemiology research, underestimated the standard errors and overstated the significance of some covariates.

We developed a method for studying the synchrony of behaviour based on calculations of overdispersion of a binomial process. The lying behaviour of cows was investigated under two different housing units inside the same barn. The first unit housed 30 cows undergoing conventional milking and the second unit housed 27 cows undergoing automatic milking. The lying behaviour of the cows was observed over 3 weeks in 12 periods of 6 h each. Every 5 min, we counted the number of cows lying down in the cubicles. As external cues, like feeding and conventional milking, can promote synchrony in dairy cows, we expected that cows conventionally milked would show more behavioural synchrony than automatically milked cows. Cows lied down synchronously in both units (overdispersion 1.67, P < 0.01). Lying synchrony tended to be slightly bigger in automatically than in conventionally milked cows (overdispersion 1.76 v. 1.58, P = 0.09), although the proportion of cows lying down was on average greater in conventionally than in automatically milked cows (60.7% v. 45.6%). This suggests that synchronized lying behaviour in cows is a constant phenomenon that depends on social facilitation rather than on external cues. The overdispersion index appears to be a useful tool for studying the synchrony of animal behaviour when observations are made at the group level.

Progress has been made in mapping and predicting the risk of schistosomiasis using Bayesian geostatistical inference. Applications primarily focused on risk profiling of prevalence rather than infection intensity, although the latter is particularly important for morbidity control. In this review, the underlying assumptions used in a study mapping Schistosoma mansoni infection intensity in East Africa are examined. We argue that the assumption of stationarity needs to be relaxed, and that the negative binomial assumption might result in misleading inference because of a high number of excess zeros (individuals without an infection). We developed a Bayesian geostatistical zero-inflated (ZI) regression model that assumes a non-stationary spatial process. Our model is validated with a high-quality georeferenced database from western Côte d'Ivoire, consisting of demographic, environmental, parasitological and socio-economic data. Nearly 40% of the 3818 participating schoolchildren were infected with S. mansoni, and the mean egg count among infected children was 162 eggs per gram of stool (EPG), ranging between 24 and 6768 EPG. Compared to a negative binomial and ZI Poisson and negative binomial models, the Bayesian non-stationary ZI negative binomial model showed a better fit to the data. We conclude that geostatistical ZI models produce more accurate maps of helminth infection intensity than the spatial negative binomial ones.

We consider variation of observed claim frequencies in non-life insurance, modeled by Poisson regression with overdispersion. In order to quantify how much variation between insurance policies that is captured by the rating factors, one may use the coefficient of determination, R2, the estimated proportion of total variation explained by the model. We introduce a novel coefficient of individual determination (CID), which excludes noise variance and is defined as the estimated fraction of total individual variation explained by the model. We argue that CID is a more relevant measure of explained variation than R2 for data with Poisson variation. We also generalize previously used estimates and tests of overdispersion and introduce new coefficients of individual explained and unexplained variance.

Application to a Swedish three year motor TPL data set reveals that only 0.5% of the total variation and 11% of the total individual variation is explained by a model with seven rating factors, including interaction between sex and age. Even though the amount of overdispersion is small (4.4% of the noise variance) it is still highly significant. The coefficient of variation of explained and unexplained individual variation is 29% and 81% respectively.

Naturally infected Biomphalaria glabrata snails were collected at two sites near Belo Horizonte, Brazil, and Schistosoma mansoni cercariae isolated from single snails were used to infect individual mice. Genetic comparison of single worm DNA was accomplished by hybridization of Southern blots to a polymorphic repetitive DNA element. Genetic profiles of parasite individuals revealed a diverse array of parasite genotypes in naturally infected intermediate hosts. The observed distribution of schistosome genotypes among intermediate hosts indicates that over half of the infected snails harbour multiple miracidia. Snails were more likely to carry multiple infections than expected by chance. This degree of overdispersion combined with high levels of genetic variability facilitates multi-genotype transmission and helps maintain parasite genetic diversity.

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

Despite evidence for the existence of interspecific interactions between helminth species, there has been no theoretical exploration of their effect on the distribution of the parasite species in a host population. We use a deterministic model for the accumulation and loss of adult worms of 2 interacting helminth species to motivate an individual-based stochastic model. The mean worm burden and variance[ratio ]mean ratio (VMR) of each species, and the correlation between the two species are used to describe the distribution within different host age classes. We find that interspecific interactions can produce convex age-intensity profiles and will impact the level of aggregation (as measured by the VMR). In the absence of correlated exposure, the correlation in older age classes may be close to zero when either intra- or interspecific synergistic effects are strong. We therefore suggest examining the correlation between species in young hosts as a possible means of identifying interspecific interaction. The presence of correlation between the rates of exposure makes the interpretation of correlations between species more difficult. Finally we show that in the absence of interaction, strong positive correlations are generated by averaging across most age classes.

The influence of density-dependent processes on the transmission of parasitic helminths is determined by both the severity of the regulatory constraints and the degree of parasite overdispersion among the host population. We investigate how overdispersed parasite distributions among humans influence transmission levels in both directly- and indirectly-transmitted nematodes (Ascaris lumbricoides and Onchocerca volvulus). While past work has assumed, for simplicity, that density dependence acts on the average worm load, here we model density-dependence as acting on individual parasite burdens before averaging across hosts. A composite parameter, which we call the effective transmission contribution, is devised to measure the number of transmission stages contributed by a given worm burden after incorporating overdispersion in adult worm mating probabilities and other density-dependent mechanisms. Results indicate that the more overdispersed the parasite population, the greater the effect of density dependence upon its transmission dynamics. Strong regulation and parasite overdispersion make the relationship between mean worm burden and its effective contribution to transmission highly non-linear. Consequently, lowering the intensity of infection in a host population using chemotherapy may produce only a small decline in transmission (relative to its initial endemic level). Our analysis indicates that when parasite burden is low, intermediate levels of parasite clustering maximize transmission. Implications are discussed in relation to existing control programmes and the spread of anthelmintic resistance.

The dynamics of host-macroparasite infections pose considerable challenges for stochastic modelling because of the need to take into account a large number of relevant factors and many nonlinear interactions between them. This paper focuses attention on the infection transmission process and the effects of specific modelling assumptions about the mechanisms involved. Some dramatically simplified linear models are considered; they are based on multidimensional linear birth and death processes, and are designed to illuminate qualitative effects of interest. Both single and compound infections are allowed. It is shown that such simple models can generate and increase dispersion of parasite counts, even among homogeneous hosts.

This paper reports on the influence of maternal exposure to Ascaris suum on worm burden distributions in experimentally infected piglets. In the first study, sows were inoculated before and during gestation (6 months, long-term exposure) with 10000 A. suum eggs twice weekly. In a second study, sows were inoculated during gestation only (3 months, short-term exposure) with increasing doses of eggs (10000–40000 eggs twice weekly). Helminth-naive sows served as controls in both studies. The third study used the same design as the short-term exposure study, but piglets from exposed and control sows were cross-suckled within 4 h of birth before colostrum uptake. All piglets were inoculated 2 or 3 times with 50 A. suum eggs on days 4 and 7 (and 14) after birth, and left with the sows. At 10 weeks of age all piglets were necropsied, and liver lesions and worm burdens were recorded. Surprisingly, in piglets born to long-term exposed sows, the prevalence of A. suum infection and the mean worm burden were significantly higher than those in piglets from control sows. In contrast, neither worm burdens nor prevalence were significantly different between piglets from short-term exposed sows compared with their controls. In the cross-suckling experiment, 67% of piglets suckling control sows harboured worms at slaughter, compared with 15%of piglets suckling exposed sows. Maximum likelihood analysis of worm burden distribution and the degree of parasite aggregation showed 3 distinctly different types of overdispersed distributions: worm counts in piglets from control sows, in piglets from short-term exposed sows and in piglets from long-term exposed sows. When the worm burden data were analysed including the cross-suckled piglets by biological mother, it appeared that the control and short-term distributions converged and that only the long-term exposure was significantly different. Overall, the degree of parasite aggregation in piglets infected with A. suum decreased with exposure of the sows. A non-linear relationship was observed between prevalence of infection and mean worm burden, which was different for piglets from exposed and control sows, and similar to relationships of this type that previously have been found in human A. lumbricoides infections. It was concluded that in porcine A. suum infections maternal exposure alters the distribution of worms in their offspring, in which the duration of exposure appeared to be an important influence. The results of the cross-suckling further suggest that maternal factors, e.g. antibodies, are transferred via colostrum.

The distribution of helminth parasites within their host population is usually overdispersed and can be described by the negative binomial distribution. The causes of this overdispersion are poorly understood, but heterogeneity in the distribution of infective stages within the environment has been implicated as a possible factor. Here we describe the distribution of infective stages of the rat intestinal nematode parasite Strongyloides ratti among the faecal pellets of its host. The distribution of infective stages between faecal pellets is overdispersed and well described by the negative binomial distribution. This overdispersion increases during the course of infection and occurs over a range of infection intensities. Overdispersion of nematode infective stages among faecal pellets may result in increased spatial heterogeneity of the infective stages in the environment and thus may contribute to the generation of overdispersion of adult parasitic stages. In addition, these findings raise important issues regarding the accurate quantification of helminth egg counts from faecal samples.

This paper describes the distribution of Ascaris suum in experimentally and naturally infected pigs, and offers a comparison with A. lumbricoides infections in humans. In the first study, worms were recovered post-mortem from a group of 38 pigs that had been trickle inoculated with 10000 infective A. suum eggs twice weekly for 12 weeks. In the second study, worms were collected from a group of 49 pigs that had been kept on a pasture contaminated with infective A. suum eggs for 10 weeks, after which they received treatment with an anthelmintic; they then were turned out on the same pasture for a second 10-week period before slaughter. The worm burdens of the naturally infected pigs were recorded both at treatment and post-mortem. Mean worm counts were similar at all occasions but the prevalence of infection was higher in the trickle infected and naturally reinfected pigs. Furthermore, the prevalence in naturally infected pigs increased significantly over the study period. Worm burden distributions in all groups were heavily overdispersed, but the distribution patterns differed significantly between groups: lower exposure (initial natural infection) gave a low prevalence and an almost uniform distribution of worm burdens among infected hosts. Continued or higher exposure (trickle and natural reinfection) resulted in increased prevalence and a reduction in the proportion of hosts with increasing worm load. A positive correlation was found between initial and reinfection worm burdens in the naturally infected pig population, suggesting that individual pigs are predisposed to a high or low intensity of infection. The prevalence and intensity as well as the distribution observed for A. suum infection in pigs were comparable to those reported for A. lumbricoides in endemic areas, and there is evidence for predisposition to A. suum in pigs, with an estimated correlation coefficient similar to that found in humans. It is concluded that A. suum infections in pigs are a suitable model to study the population dynamics of A. lumbricoides in human populations.

To study the infection dynamics of metacercariae of the digenean Cryptocotyle lingua, wild living Atlantic cod, Gadus morhua, were caged for 18 months close to the shore. Here they were exposed to naturally occurring transmission stages of the parasite. First, both the abundance and the variance to mean ratio of metacercariae increased, but during the second half of the study the abundance levelled out, and the variance to mean ratio showed a significant decrease. Host mortality was negligible throughout the study. Based on the relationship between pigment spots and metacercariae observed by skin digestion, there was no indication of density-dependent parasite mortality. We conclude that the infrapopulations of metacercariae on the caged cod probably were regulated by density-dependent host responses acting against the cercariae.