We found that mate encounter rates and thus mating opportunities increased with both group size and density. Despite this, the average individual mating rate remained largely constant and close to the earlier detected fitness optimum of the female function in C. sandrana . Importantly, the observed increase in mate encounters across densities by ~100% did not transform in a statistically detectable increase in mating rate, where the maximum change rendered undetectable due to noise in the data does not exceed a 15% increase across densities (upper 95% CI bound of regression slope). This at best weak effect can largely be attributed to reduced mating activity at the lowest mate encounter rates, indicating that under such conditions optimal mating rates are difficult to maintain, whereas mating rates remain stable at higher densities where mate encounters are sufficiently frequent.
Although the existing variation in mating rate implies strong between-individual differences in mating activity, the documented absence of significant group size and density effects clearly contradicts the general notion of a tight positive relationship between mate availability and average mating rate as previously reported from other simultaneously hermaphroditic [20, 19] and separate sex [9, 10] species. Instead, our findings indicate that the average daily mating rate in C. sandrana is largely independent of mate availability and close to the female fitness optimum, as long as the latter can be realized. These findings challenge the general notion of male driven mating rates in simultaneous hermaphrodites and suggest three alternative scenarios. First, conflict over mating rate may be minute or even absent if both sexual functions share similar mating rate optima, i.e. when the here detected average mating rate is close to the female and male mating optimum. In this case, no sex function would ultimately control matings, but realized mating rates result from mutual interest. Such low male mating rate optima are plausible if remating in the male sexual function generates accelerating costs, e.g. via sperm digestion by the sperm recipient . However, previous work in C. sandrana contradicts this scenario of accelerating male costs because animals are easily capable of donating sperm up to eight times within 9 h . Second, realized mating rates may be intermediate between divergent male and female optima while providing roughly similar fitness returns for both sexual functions (representing inherent sexual antagonism;). Under this scenario, mating rate represents the balanced result of opposing sex-specific interests. Our previous finding that realized field mating rates are close to the female fitness optimum  do not lend support to this scenario. Third, assuming that the male mating rate optimum exceeds that of the female function (see  for conforming data in freshwater planarians), then mating rate should be largely controlled by the female function as it is close to the female fitness optimum of C. sandrana . This last scenario is currently most concordant with the available data but detailed information on mating rate effects on male fitness are clearly needed to substantiate this conclusion.
Interestingly, our findings conform to recent theoretical predictions for separate sex species by Härdling & Kaitala . Their model predicts that females evolve constant mating rates that are largely independent of mate availability if the following three central assumptions are met. First, female fitness solely depends on the number of different male partners, not on the individual quality of certain males. Thereby the model explicitly excludes female choosiness for high quality males as an adaptive trait. Second, mating probability is under full female control, excluding systems in which females accept matings due to sexual harassment. Third, female fitness is maximized at an intermediate mating rate at which the fecundity benefits and the mortality costs of multiple mating balance. All these three key model assumptions appear to be met in our study system C. sandrana. First, polyandry-mediated benefits primarily depend on the number of different mating partners, not on the identity or quality of mates . The production of multiply sired egg masses seems to represent a diversifying genetic bet-hedging strategy that increases the probability of offspring survival under fluctuating environmental conditions . Female fitness is thus a direct function of mating frequency irrespective of male quality. Second, male acting individuals do not show any harassment or otherwise manipulative behavior of female mating activity [24, 28]. This is further supported by the observation that realized mating rates both under laboratory and field conditions  are close to the female fitness optimum. Third, female fitness is maximized at an intermediate mating rate, where fecundity costs of multiple matings appear to be offset through increased offspring viability .
We further found that fitness measures for the female function were independent of variation in group size and solely a function of density, with fecundity being maximized at an intermediate density. Because mating rate remained constant across all these treatments, density-dependent differences in fecundity are unlikely to represent mere differences in allosperm availability. Instead, reduced fecundity at low densities might represent costs due to increased mate searching. Interestingly, previous work in C. sandrana showed that repeated matings with the same male result in decreased fecundity relative to repeated matings with different males . Because the probability of mating with the same partner is higher at lower densities, the same currently unidentified mechanism might contribute to reduced offspring production at low densities. In this context it remains puzzling, however, why group size, i.e. the actual number of available mating partners, had no comparable effect on fecundity in the present study, because the likelihood of copulating repeatedly with the same partner equals 1 in our pair treatment. Perhaps, differences in social group size do not reflect differences in mating group size, with the latter being primarily affected by the actual distance between animals (i.e. density).
Decreasing fecundity at the highest densities may be the result of a shift in sex allocation towards the male function. Although our data provide no direct measure of sex allocation, various studies confirmed rapid strategic reallocation of resources towards a hermaphrodite's male function with increasing social group size (reviewed in ). For example, in Macrostomum lignano, testis size tends to increase with social group size while ovary size significantly decreases . Although constancy in average daily mating rate may suggest little variation in mean sex allocation in C. sandrana, resource allocation may have been adjusted in response to mate availability rather than to mating rate. Unlike in M. lignano, however, sex allocation cannot be measured in vivo in C. sandrana, rendering definite conclusions on sex allocation adjustment difficult. Possible components of resource re-allocation that should be explicitly addressed in follow-up studies include the amount of sperm or seminal fluid transferred, the composition of these seminal fluids (e.g. with respect to manipulative substances, ), or energetic investment in other male components such as precopulatory interactions, all of which may contribute to compromised female fecundity at high densities. Finally, declining fecundity at high densities may have been caused by waste products or certain metabolites, which have been suggested to act as egg laying inhibitory substances in pulmonate gastropods . Although water was regularly exchanged and experimental containers were frequently cleaned to reduce such effects, it is possible that inhibitory substances accumulated at higher densities or were actively produced by animals in response to higher mate encounter rates.
The here documented differential effects of group size and density on reproductive behaviour imply that studies on mate availability effects need to carefully disentangle both factors by applying an appropriate experimental design. However, our findings also indicate that a non-random distribution of animals over the available space may make a clear differentiation between the relative contributions of group size and density on mating opportunities difficult, even though the applied experimental design allows, in theory, to do so. For example, while mate encounter rate would be expected to increase at higher densities as the distance between individuals is reduced , mate encounter rates in our study also increased with group size independent of density. Given that mating aggregations are prevalent in many animal systems, future experimental work that directly manipulates spatial distribution is needed in order to shed light on the detailed relationship between aggregation behavior and reproductive behavior.