Epidemiological studies

We analysed egg count and miracidial genotypic data derived from two epidemiological studies: one conducted in Zanzibar as part of the ‘Zanzibar Elimination of Schistosomiasis Transmission’ (ZEST) alliance and the ‘Schistosomiasis Consortium for Operational Research and Evaluation’ (SCORE) [31, 39] and the other conducted in mainland Tanzania, as part of Schistosomiasis Control Initiative (SCI) activities [7, 31]. The SCORE/ZEST study was a cluster-randomised trial involving three study arms (with differing control pressures / intervention strategies) implemented in 90 randomly selected shehias (small administrative regions) on both islands of the Zanzibar archipelago, Pemba and Unguja [37]. Parasitological and genotypic data on S. haematobium were collected from 224 children and adults in 2012, before onset of the clinical trial, and 214 children and adults in 2016, after 10 rounds of biannual MDA. The SCI study was undertaken in the Lake Victoria region of Tanzania, collecting parasitological and genotypic data on S. mansoni from 151 schoolchildren attending two primary schools between 2005 and 2010, before and during MDA (delivered annually in one school with a missed treatment in 2008, and delivered in 2005, 2007 and 2010 in the other school) [31]. In both studies, samples were collected two months before treatment with praziquantel.

Parasitological methods

In the Zanzibarian (SCORE/ZEST) study, urine samples were collected from each individual and urine filtration was used for egg identification and quantification of the intensity of S. haematobium infection. Infection intensity was expressed as eggs per 10 ml of urine. In the Tanzanian (SCI) study, duplicate Kato-Katz thick smears were prepared from individual stool samples from each child, eggs were counted, and infection intensity of S. mansoni was expressed as eggs per gram (epg) of stool. S. mansoni eggs were then purified from separately prepared stool samples from each infected child and hatched into individual miracidia [40]. Egg hatching and isolation of S. mansoni and S. haematobium was performed by concentrating eggs from all infected urine samples by filtration using a Pitchford Funnel, rinsing and transferring into a clean Petri dish containing mineral water and exposing eggs to light to facilitate hatching of miracidia [41].

Molecular methods

In both studies, the number of unique female S. haematobium and S. mansoni genotypes within each individual, n, was estimated by analysing multiplexed microsatellite genotypic data of individual miracidia (hatched from eggs) using sibship reconstruction methods [36]. Sibship reconstruction is a category of parentage analysis which can be used to estimate the number of parents when genetic data are available on offspring only [33–36]. Essentially, data on neutral genetic markers are used to divide offspring into groups of full siblings (monogamous mating) or groups of full siblings and half siblings (polygamous mating) to reconstruct and identify unique (male and/or female) parental genotypes. Hence the technique can be used to estimate worm burdens ([30], and see for examples [31, 32, 42]) after statistical adjustment for the number of offspring (here, miracidia) sampled [38].

The number of miracidia sampled per individual, m, ranged from 1 to 28 in the Zanzibarian (S. haematobium) study, and from 1 to 20 in the Tanzanian (S. mansoni) study. Complete details on the molecular analysis and sibship reconstruction can be found in studies by Gower et al. 2017 [31] and by the ZEST alliance and SCORE [31, 39].

Statistical modelling

We fitted log-linear statistical models of the general form (1) where Y is a vector of observed eggs per unit volume of faeces or urine (i.e. epg or eggs per 10ml urine), N is a vector of inferred female worm burdens per host and the coefficients β₀ and β₁ denote, respectively, the per worm fecundity (i.e. the egg output for N = 1) and the direction and severity of density dependence (Fig 1). The error term e is assumed to be normally distributed, such that the of distribution of Y + 1 is log normal with median . The matrix X comprises additional covariates, with corresponding coefficients denoted γ. For the Zanzibarian study (S. haematobium), X comprised indicator variables for island (Pemba or Unguja), age group (child or adult), sex (male or female) and year (2012 or 2016). For the Tanzanian study (S. mansoni), X comprised indicator variables for school (Bukindo or Kisorya), sex (male or female) and year (2005, 2006 or 2010).

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Fig 1. Functional relationship between schistosome egg count and female worm burden inferred from sibship reconstruction.

The log-linear regression model implies a relationship between the median egg count per host, μ_Y, and the female worm burden N of the form , where β₀ denotes the per worm egg production (fecundity) in the absence of density dependence (i.e. when N = 1) and β₁ governs the direction (and severity) of density dependence. The solid purple line indicates a proportional (density-independent) relationship for β₁ = 1, the dashed yellow line a facilitating (positive) density-dependent relationship for β₁ > 1 and the dotted blue line a constraining (negative) density-dependent relationship when β₁ < 1.

https://doi.org/10.1371/journal.pntd.0009396.g001

Regression calibration

We used a regression calibration technique [43] to integrate uncertainty (measurement error) in N on the estimated coefficient of density dependence, β₁. We achieved this by simulating 1,000 datasets N₁, N₂, …, N₁₀₀₀ from the posterior distribution defined in Neves et al. [38], (2) and refitting the regression model (Eq 1) to each replica dataset. The posterior f(N|n, m) captures uncertainty in N derived from the number of unique female genotypes, n, being identified from a finite sample of miracidia, m. The most precise estimates of N are achieved when n ≪ m [38].

Sensitivity analysis

We assumed that the prior distribution f(N) was uniform with support N ∈ [n, N_max]. That is, we assumed that the minimum number of female worms in a host was given by the n unique genotypes identified by sibship reconstruction (i.e. there was no false identification of unique genotypes) and the maximum by parameter N_max, which is required to ensure the posterior has a finite upper bound when m/n → 1 [38]. The only information on the maximum number of schistosomes a human can (plausibly) harbour comes from two autopsy studies that counted a maximum of 350 adult female S. mansoni and 250 female S. haematobium directly from 103 and 197 people respectively (excluding individuals with Symmer’s fibrosis) [28, 29]. However, to explore the impact of this assumption on the coefficients of density dependence we repeated the statistical modelling and regression calibration approaches for values of N_max ranging from 100 to 2,000.

Comparison with previous findings

Density-dependent fecundity in schistosome infections has long been a controversial and debated topic. The phenomenon was initially reported in 1985 following analysis [16] of S. mansoni human autopsy data [29], but later refuted after new analyses of the same and additional autopsy data [14, 15, 17, 28]. In 2001, taking a different approach, Polman et al. [44] found that the relationship between circulating S. mansoni antigens and egg counts was not proportional, potentially indicative of density-dependent fecundity. However, the interpretation of this relationship relies on the assumption that measured antigen levels relate to worm burdens in a linear or proportional manner, which remains unclear.

A recent study by Gower et al. [31], using the same Tanzanian S. mansoni data as here, found a higher mean egg output per adult worm pair (inferred by sibship reconstruction) following 5 years of MDA treatment, which could be consistent with a relaxation of density-dependent constraints. In our study, we took a more conservative approach by accounting explicitly for the uncertainty in the estimated female worm burden [38], which is driven principally by the number of miracidia genotyped per host and the nominal maximum possible number of worms a host can harbour, N_max (i.e. the upper bound of our prior assumption on N). Hence, while for values of N_max ≳ 500, we found evidence for density-dependent fecundity (Fig A in S1 Text)—consistent with the observations of Gower et al. [31]—we cannot reach a definitive conclusion because for N_max ≲ 500 the upper uncertainty interval of the density-dependent coefficient frequently intersected 1.

A previous analysis of density-dependent fecundity in S. haematobium [28] (analysing 197 infected cases at autopsy) did not find significant evidence of density dependence. The apparently contradictory nature of our findings compared to the autopsy study may be explained partly by the different methodological approaches, and partly by differences in the representativeness of sampling. In the autopsy study, technical challenges of perfusion could lead to incomplete recovery of all worms in human cadavers. It is also possible that post-mortem extraction of urine leads to differential recovery of schistosome eggs than would be found when naturally expelled. The nature and immune status of individuals from the autopsy study is also very different from our study, since it was performed using deceased patients who had been terminally ill and had heavy worm burdens, whereas our study was conducted primarily using data from children attending primary schools. Our method of exploring density dependence is more indirect (but practicable), and necessarily invokes modelling assumptions (to which the results can be sensitive) which are fundamentally challenging to validate and which we fully acknowledge as a limitation. On the other hand, a major advantage of our approach is that it permits much more representative sampling of a host population compared to sampling at autopsy. This will be particularly important if factors related to the general health of the host (such as immunocompetence [45]) play a role in mediating density dependence.

Limitations, uncertainty and validation

The sensitivity of our results to N_max for the S. mansoni data—which we do not see for S. haematobium—stems from the difference in the ratio of the number of miracidia sampled to the number of unique female genotypes identified, m/n for each species. A higher proportion of the S. mansoni data had m/n → 1 which magnifies the influence of N_max (see Fig 4). Parameter N_max is required to define a (here uniform) prior distribution for the number of female worms per host which in turn ensures a bounded posterior distribution. Other non-uniform priors, such as the negative binomial distribution [38], are possible, but entail more prior assumptions of unknown parameters (a mean and overdispersion parameter). Irrespective of the choice of prior, it is intuitive that when m/n → 1 (i.e. each offspring/miracidia in a sample is identified as coming from a unique female genotype) the data hold no information on the likely number of female worms and therefore assumptions on the prior dominate the inference. Hence, our cautious interpretation of the S. mansoni data highlights the importance of robust sensitivity analysis when applying our method. It also reiterates the imperative of sampling effort to obtain as many accessible offspring parasite stages (in this case, miracidia) for genotyping as possible [38].

An additional limitation related to the nature of data is that we could not account for the possibility that some individuals may have been sampled repeatedly, leading to potential correlation among these repeated measures. For the Zanzibarian (SCORE/ZEST) study, data were recorded as independent cross-sections at each sampling time. That is, at each sample collection time, data from each individual were assigned a new identifier, but this was not matched (for individuals who may have been sampled repeatedly) between different years. Nevertheless, the percentage of individuals contributing repeated measures is likely to be low, because both the participants and the subset of participants contributing samples for population genetic analysis were randomly selected at each year. For the Tanzanian (SCI) study, the percentage of individuals sampled in 2005 and followed up in 2006 was 2.5% in one school, and 19% in the other school [40]. In 2010, this percentage is likely to be even lower, since only the children who were 7 or 8 years old in 2005 or 2006 could have been resampled in 2010.

A key methodological aspect of our approach is the use of a regression calibration technique to account for inherent bias and uncertainty in the number of inferred female schistosomes. The number of unique worm genotypes identified using sibship reconstruction is always an underestimate of the true number of reproductively active females because of the finite miracidial sample size. Similar to the influence of N_max, the degree of bias and uncertainty is dependent on the ratio m/n [38]. Hence, as demonstrated here, it is critical that a calibration approach is used to adjust for these effects for each choice of prior parameters (here, just N_max but priors with more parameters are possible [38]). Systematic bias (underestimation) alters the shape of the relationship between egg counts and worm burdens, potentially leading to erroneous inference if ignored.

In addition to the statistical limitations of the approach used here, there exist a variety of population biological and genetic assumptions not considered here explicitly that may affect the accuracy of sibship reconstruction. These include assumptions of monogamous versus polygamous mating and of Mendelian inheritance and Hardy Weinberg equilibrium of parental genotypes (see [38] for a more detailed discussion). Moreover, the number and type of microsatellite markers used in the analysis and the possible existence of clonal worms within hosts (due to the asexual reproduction of the parasite in snails; but note that cercariae mix in water before infecting hosts which likely mitigates this effect) are also limitations of the sibship reconstruction method. Notwithstanding, the statistical relationship between the estimated number of fecund female worms and the number of unique parental genotypes identified from a finite sample of (miracidial) offspring will be unaffected by the specific assumptions used for sibship reconstruction.

Ultimately, validation of the approach would require that the number of female worms per host inferred by sibship reconstruction be compared with directly observed counts. This could be achieved in humans where adult helminths can be enumerated directly (e.g. soil-transmitted helminths by chemoexpulsion) or in animals where parasites can be counted either by chemoexpulsion or dissection (e.g. in an abattoir setting or experimental system). For example, dissection has been used to count adult S. mansoni parasites in 37 olive baboons, where no density-dependent relationship between egg counts and (directly observed) worm burdens was found [46]. In principle, in any situation where offspring can be genotyped and adult worms counted directly, the posterior distribution of inferred female worm burden could be compared with the directly observed counts.

The public health importance of density dependence

Notwithstanding the need for validation—and while we cannot profess to have resolved the question of density-dependent fecundity in human schistosomiasis—our method represents a promising new approach to evaluate density dependencies, processes which are essential for the regulation of parasite populations and profoundly influence their transmission dynamics and resilience to intervention [18–21]. Intuitively, as drug-based or other interventions reduce the size of the parasite populations, density dependencies are relaxed, transmission becomes more efficient, and it becomes harder to maintain progress towards elimination endpoints. Understanding density dependencies is thus important for predicting (modelling) the likely impact and effectiveness of intervention strategies. For example, when models are calibrated to pre-intervention (endemic) epidemiological data, the assumed severity of density dependence leads to different estimates of the basic reproduction number, R₀ [18], and different predictions on the intensity and duration of intervention efforts required to achieve control or elimination.

Knowing whether egg production is regulated in a density-dependent manner is also key to interpreting routine parasitological (egg count) monitoring and evaluation data, because for schistosomiasis—and indeed many other helminthiases—egg counts are used as a proxy for infection intensity. The WHO goals for controlling schistosomiasis morbidity and achieving elimination as a public health problem are defined as reaching less than 1% prevalence of heavy-intensity infections in school-aged children (SAC; 5–14 years old). Countries that achieve morbidity control can progress towards interruption of transmission [10]. Thus, the thresholds used to define light and heavy intensity S. haematobium infections (50 eggs/10ml urine), and light, medium and heavy S. mansoni infections (100 and 400 epg respectively) [11] provide empirical benchmarks for decision-making on how long MDA should be maintained. Yet depending on the (non-linear) relationship between egg counts and infection intensity (worm burden), the thresholds will have different meanings for the likelihood of sustained control or resurgent infection [37, 47]. As interventions progress and interruption of transmission becomes possible in some foci [11], targets with a stronger alignment to parasite breakpoints—which integrate facilitating (parasite mating) and constraining density dependencies [20, 21, 48]—may be necessary.

Density-dependent fecundity in human helminthiases has perhaps been best studied in Ascaris lumbricoides [21, 49], where adult worms are easily accessible by chemoexpulsion techniques. Interestingly, although density dependence is found consistently, both the reproductive output of female worms and the severity of density dependence has been found to be highly geographically variable [49]. This poses a substantial challenge to predicting the impact of interventions in different locations and also to interpreting egg count data in terms of control and elimination prospects. Data are currently too scarce to determine whether the reproductive output of schistosomes varies geographically (although here we did find differences in the fecundity of S. haematobium between Pemba Island and Unguja and of S. mansoni between schools in Tanzania, see Tables A and B in S1 Text). However, the method outlined in this paper—combining parasitological and genotypic data—could be used to explore this and potentially provide new insights for informing egg count thresholds that are tailored to specific settings or locations.

Improving our understanding of density-dependent population processes also has broader and longer-term importance for safeguarding the effectiveness of MDA programmes, not just for schistosomiasis but other helminthiases with heavy reliance on chemotherapeutic control. Density dependencies could enhance the spread of emerging drug resistance, due to enhanced reproduction rates in resistant or reduced-susceptibility parasites [50]. In the event of emerging resistance, understanding density-dependent processes would thus be key in understanding the likely rate of spread, informing timeframes for implementing alternative or complementary interventions, such as snail control [51] or eventually a vaccine [52, 53]. Density dependencies may also complicate the interpretation of data from vaccine trials [53] and from efficacy monitoring activities [54] if interpretation is predicated on a proportional relationship between adult schistosomes and egg output (e.g. the release of fecundity constraints on surviving parasites after treatment could be falsely interpreted as reduced drug efficacy [54]).

The importance of density-dependent processes on the population biology and transmission dynamics of schistosomiasis and other helminthiases is clear and much work (including this paper) focuses on phenomenological identification, often for the purpose of integrating into mathematical models. Less clear are the biological mechanisms that drive these processes. The most straightforward explanations are putative crowding effects and competition for resources. But in schistosomiasis, more complex mechanisms may also be involved. For example, epidemiological and modelling studies have shown evidence for anti-fecundity immunity such that egg production is reduced by the host’s immune response, albeit susceptibility to new infections is sustained [55, 56]. In baboons, it has been shown that adult worm pairs that had stopped egg production in a chronic infection started excreting eggs when they were transplanted into a naïve baboon [57]. Anti-fecundity immunity has also been shown in cattle infected with S. bovis [58, 59]. It has also been suggested that worm fecundity declines with worm age (reproductive senescence) and that adult worms stimulate immune responses against cercarial infection (concomitant immunity) [60].