The role of sexual selection in fuelling genital evolution is becoming increasingly apparent from comparative studies revealing interspecific divergence in male genitalia and evolutionary associations between male and female genital traits. Despite this, we know little about intraspecific variance in male genital morphology, or how male and female reproductive traits covary among divergent populations. Here we address both topics using natural populations of the guppy, Poecilia reticulata, a livebearing fish that exhibits divergent patterns of male sexual behaviour among populations. Initially, we performed a series of mating trials on a single population to examine the relationship between the morphology of the male's copulatory organ (the gonopodium) and the success of forced matings. Using a combination of linear measurements and geometric morphometrics, we found that variation in the length and shape of the gonopodium predicted the success of forced matings in terms of the rate of genital contacts and insemination success, respectively. We then looked for geographical divergence in these traits, since the relative frequency of forced matings tends to be greater in high-predation populations. We found consistent patterns of variation in male genital size and shape in relation to the level of predation, and corresponding patterns of (co)variation in female genital morphology. Together, these data enable us to draw tentative conclusions about the underlying selective pressures causing correlated patterns of divergence in male and female genital traits, which point to a role for sexually antagonistic selection.
Male genitalia typically exhibit striking patterns of diversity and specificity and are among the most rapidly evolving morphological traits in animals with internal fertilization . Indeed, genital structures exhibit far greater levels of complexity than is thought necessary for simply transferring sperm to females, and there is now widespread evidence that sexual selection is responsible for such complexity [1,2]. Much of this evidence comes from studies linking variation in male genital morphology to either mating success [3–6] or paternity success [7–11], although further evidence comes from comparative studies revealing positive associations between the rate of divergent evolution of male genitalia and the intensity of sexual selection acting on these traits (e.g. ).
An increasing body of work has focused on the potential for sexual selection to fuel coevolutionary patterns of selection on male and female reproductive traits. To date, the available studies revealing such patterns have focused on interspecific variation in male genitalia and associated covariance in female reproductive traits [13–20]. Yet, there is also considerable intraspecific variation in male genital morphology in some species [21–24], although in many of these cases the functional basis for such variation remains enigmatic, and the evolutionary relationships with female reproductive traits have yet to be elucidated.
Poeciliids are a family of livebearing fishes with internal fertilization in which the males' anal fin is modified to form a copulatory organ, the gonopodium. The shape and length of the male gonopodium exhibit substantial inter- and intraspecific variability [25–28], and this morphological variation is thought to be associated with the frequency with which males employ gonopodial thrusting, a coercive mating tactic in which males forcibly inseminate females [25,29–31]. Among the poeciliid family, guppies (Poecilia reticulata) also exhibit substantial intraspecific divergence in male genital traits, which in turn is thought to reflect differences in the relative occurrence of forced matings among populations . Guppies inhabit freshwater bodies throughout Venezuela and Trinidad (West Indies). Many Trinidadian streams exhibit strong discontinuities in the level of predation along their course, with lowland rivers typically characterized by high levels of predation in relation to upstream sections of the same river . In all habitats, male guppies employ both courtship and forced matings to achieve copulations, but the extent to which either tactic is employed varies with the level of predation, with courtship being more prevalent in low-predation populations and forced matings more common in high-predation populations . Forced matings, in turn, may be costly for females, both in terms of lost foraging opportunities and potential reductions in fecundity , but also because they may impose direct physical damage to the females' genital region caused by the complex bony structures at the distal tip of the male's gonopodium [25,36].
In this paper, we seek to understand the functional significance and evolutionary basis for variation in male genital morphology in natural guppy populations. We employ three complementary approaches to address these questions. First, we use geometric morphometric techniques to test whether variation in the shape of the gonopodium's distal tip is associated with insemination success during forced copulations. We focus only on the tip of the gonopodium for these analyses as this is the portion of the male's intromittent organ that enters the female's genital tract during copulation [30,37]. Second, we determine whether male genital morphology varies predictably among populations according to the level of predation, since predation intensity covaries with the relative prevalence of forced matings  and therefore potentially with the strength or direction of selection acting on male genital morphology. Third, because forced copulations are likely to be costly for females , we anticipated that counter-selection would result in the divergence of female genital traits among populations. This final analysis therefore also serves as a prospective test for intraspecific covariance in male and female genital morphologies, and lays the foundations for future studies designed to test among competing hypotheses to explain the evolutionary origins for such relationships.
(a) Male genital morphology and mating success
(i) Mating trials
We initially conducted a series of mating trials on n = 36 male–female pairs taken from the Lower Quaré population, a high-predation site in the Oropouche drainage of Trinidad's Northern Mountain Range. Fish were transported to the University of the West Indies where females were isolated individually in 5 l containers (containing river weed and an airstone) until they produced a brood. Offspring were removed immediately and each post-partum female was subsequently maintained individually within the same container for a further 14 days before taking part in the mating trials. This process of isolating females for 14 days prior to the trials was essential because it ensured that all females were at the same reproductive stage (approximately mid-way through their brood cycle) and sexually unreceptive (post-partum females are only sexually receptive to male courtship for 2–3 days after producing a brood and are never sexually receptive during the middle of their brood cycles; see ). The focal males were maintained in mixed-sex groups until 3 days before the mating trials, at which time they were isolated in 5 l containers to ensure that they had replenished sperm stores when entering the mating trials . On the evening before each trial, females were placed individually in a 45 × 30 × 30 cm mating tank (filled to 20 cm) and allowed to settle overnight. The mating tanks contained a small amount of river weed and natural river stones collected from the Lower Quaré site. On the following morning, a male was placed in the tank and left for 2 h to interact with the female. We then observed the male's sexual behaviour for 15 min, recording the number of gonopodial thrust attempts (no prior courtship, male swings his gonopodium forward at least 90° and attempts a forced mating) that resulted in genital contact with the female (‘contact success’). Such contacts were immediately recognizable from the females' ‘startle’ response and were used as a measure of ‘success’ because they potentially signal intromission. After each observation, the two fish were left in the mating arena until 5 h had elapsed since the trial commenced, at which point the male and female were separated so that we could recover sperm from the female's reproductive tract (see below). Immediately after the mating trials, males were anaesthetized (Benzocaine) and digitally photographed. Standard length for each male was estimated to within 0.5 mm by taking the distance (in mm) between the male's snout and the tip of his caudal peduncle. Gonopodium length was taken as the distance (in mm) between the base of the gonopodium and its distal tip. Each anaesthetized male was then killed through ice immersion and preserved in Dietrich's fixative (30% pure ethanol, 10% formalin, 2% glacial acetic acid, 58% DI H2O) for the subsequent geometric morphometric analysis of gonopodial shape (see below).
(ii) Sperm recovery from females
As a measure of insemination success, we recovered and counted sperm extracted from the female's reproductive tract at the completion of each behavioural trial. Sperm recovered from females in this way must have arisen from forced copulations that took place during the mating trials because sperm are not recoverable from the female's reproductive tract more than 7–8 days post-parturition [41,42]. Females in our trials had been isolated from males for 14 days, meaning that they were both sexually unresponsive and without freshly inseminated sperm. The technique for extracting sperm from recently mated females is described in detail elsewhere , but briefly this process involves flushing the female's genital pore five times with saline solution (0.9% NaCl). The number of sperm recovered in these flushes was then estimated using an Improved Neubauer haemocytometer .
(b) Population comparisons
(i) Populations surveyed
We sampled guppy populations from upstream and downstream sites within each of five river systems in Trinidad's Northern Mountain Range. Four of these rivers (Aripo, Tacarigua, Quaré and Turure) exhibited the typical upstream–downstream predation gradient (upstream sites = low predation, downstream sites = high predation) seen in many Trinidadian rivers , while the fifth (Oropouche) was characterized by high levels of predation both in the upstream and downstream sites . By incorporating the Oropouche River in the analyses, we attempted to account for variation in physical and ecological factors (other than predation intensity) that may drive interpopulation diversification of phenotypic traits. Thus, differences in male or female traits between the two Oropouche sites would not be owing to the effects of predation, but some other (unmeasured) variable. All of the rivers sampled here have been extensively surveyed for predator abundances in previous studies [38,45], and we have monitored these populations to confirm their predation status since these original surveys (e.g. ).
(ii) Characterizing variation in male genital traits
We examined variation in the shape of the gonopodium's distal tip from n = 225 males taken from the 10 populations (at least 20 males per population) and the 36 males used in the mating trials (above). For both analyses, we estimated the length (in mm) of each male's gonopodium from photographs of fresh specimens before preserving the males in Dietrich's fixative (see above). All males were preserved within one week of each other and were maintained under identical conditions before being photographed again for the analysis of gonopodium shape. Fixation times and holding conditions were therefore standardized among populations and these conditions did not differ between the mating trials and population comparisons. In all cases, a digital image of the lateral (left) side of each male's gonopodium was captured with a Leica DFC320 fitted to a Leica MZ75 stereomicroscope under transmitted light- and dark-field illumination. Images were captured at ×50 magnification to include the distal tip of the gonopodium (electronic supplementary material, figure S1a).
We examined variation in the shape of the gonopodium's distal tip using geometric morphometric analyses . We digitized eight fixed landmarks on each image (electronic supplementary material, figure S1a) using tpsDig2 software . Partial warps and uniform components were subject to relative warp analysis using the program tpsRelw . Relative warps analyses correspond to a principal components analysis and serve to reduce multivariate shape data to relative warps that describe most of the variation in shape. The relative warp analyses (including the uniform component) returned five relative warp scores (RWS-1–5), explaining 90 per cent of variance in gonopodial shape in the mating trials and 86 per cent in the population comparison trials. In our subsequent analyses of male genital traits (see below), variation in gonopodial shape could be visualized as deformations of a thin-plate spline (tps), where each tps plot displays deformations of the consensus configuration corresponding to a point in the space spanned by a particular pair of relative warps (§3).
(iii) Female genital morphology and offspring size measurements
Approximately 20 females from each of the 10 populations were included in our analysis of female genital tract morphology (total n = 195). Immediately after collection, gravid females were isolated individually in a 4 l container until they produced their first brood. At this stage, we counted the number of offspring produced by each female and measured the maximal width of each offspring's head (using the eye as a landmark) to within 0.05 mm for five offspring per brood. After giving birth, females were isolated individually for a further 3–4 days before being killed with an overdose of anaesthetic. In this way, all females were preserved at approximately the same reproductive stage (3–4 days postpartum) to minimize variation among females in the anatomy of the reproductive tract, which can occur during gestation . Females were then preserved individually in Dietrich's fixative until required for the morphological analyses. As with males, fixation times for females did not vary systematically among populations.
Dissections were subsequently carried out under a stereomicroscope. Each female was placed with her ventral side exposed and a scalpel was used to make an incision from the gills to the anus. The ventral abdomen muscles and skin were then removed to expose the peritoneal cavity. We carefully removed visceral organs and fat within the cavity, leaving the ovary and the oviduct intact. At this stage, an image of each female's oviduct was captured using a digital camera fitted to the stereomicroscope. Images were stored and analysed using Leica IM500 image manager software. Oviduct length was taken from the point closest to the egg sac to the urogenital sinus (i.e. the oviduct opening, in which males insert their gonopodial tips). Oviduct width was estimated mid-way along this tract (electronic supplementary material, figure S2. NB: the oviduct is roughly cylindrical, and its width did not change substantially along the entire length of the tract.). We specifically focused on this portion of the female's reproductive tract as this is the region that is physically contacted by the gonopodium during copulation (mean ± s.d. oviduct length = 2.37 mm ± 0.48; gonopodium = 4.24 ± 0.29). In a subsample of 45 females, we took two independent measurements of each trait (i.e. oviduct length and width) and tested for consistency in these measures by calculating the intraclass coefficient for repeated measures . The two measures were performed by the same operator working blind of the identity of each sample. Intraclass correlation coefficients (R) for both traits were high (oviduct length: ANOVA F42,85 = 38.2, p < 0.001, R = 0.95; oviduct width: F43,87 = 107.8, p < 0.001, R = 0.98).
Finally, we estimated female body size by taking the distance between the oviduct opening and the snout, rather than the more usual measurement of standard length (as in males—see above). We used this measurement because caudal fin tissue had been taken from each female for genetic analyses in a different study . This method of estimating female size was strongly correlated with standard length, as confirmed by correlating both measurements using a subsample of females (Pearson correlation: r = 0.95, n = 33, p < 0.0001).
(c) Statistical analysis
(i) Mating trials
We initially tested whether gonopodium length and shape influenced the likelihood of successful genital contact during the mating trials (i.e. our measure of ‘contact success’). For this analysis, we used a generalized linear model (with binomial error distribution and a logit link function), in which the number of thrusts that resulted in contact between the males' and females' genitalia was entered as the dependent variable (with the total number of mating attempts as the binomial denominator). The predictor variables in this analysis included male body size (standard length), female body size (snout-to-oviduct opening), gonopodium length and the shape variables RWS-1–5. Three replicates could not be included in these regressions because photographs were unavailable for geometric morphometric analyses. Hence, our final analyses were based on n = 33 replicates.
Next, we tested whether variation in gonopodium length and shape was associated with the number of sperm recovered from females (hereafter ‘sperm recovered’). To address this question, we used linear multiple regression using the same predictor variables described above. In the analysis of sperm recovered, a log transformation was used to improve the distribution of the data.
To estimate the effect of the predictors in both analyses (contact success and sperm recovered), we used an information theoretic approach [52,53], which recognizes the uncertainty in model selection inherent in other ‘best model’ approaches by estimating the average effect of each predictor over the total possible combinations of predictors. We first calculated the Akaike information criterion, with second-order correction (AICc) for small samples, for models including the intercept only to those containing all predictors (n models = 2048). For the generalized linear model, we accounted for overdispersion by using the quasi-AICc (QAICc). The regression coefficient (b) of each predictor was obtained for all possible models using the RSEARCH function in GenStat. Models were then ranked according to their AICc or QAICc values (smallest = best), which were used to weight each model on the basis of its likelihood . The likelihood of being the best model in each case was calculated as a function of the difference from its AICc value and the AICc value of the best model (also called ‘Akaike weight’, see formula (3) in ). The Akaike weight is an estimate of the probability that a given model is the best of all n models (total Akaike weights sum to 1). For each predictor, an average parameter (in this case the regression coefficient b) was calculated by summing the parameter values in each model (models in which the predictor was not selected had a value of zero), weighted for the likelihood of each model. This is a type of shrinkage estimator that gives less weight to the predictors with a weak relationship to the response . For the regression coefficients, 95% confidence intervals (CIs) were calculated from the variance in the predictor coefficients . Regression coefficients whose 95% CI did not include zero were considered statistically significant. Statistical analyses were performed using SPSS 16.0 (SPSS Inc., Chicago, IL, USA) and GenStat 12 (VSN International Ltd, Hemel Hempstead, UK). All probabilities are two-tailed.
(ii) Population comparisons of male and female traits
We used linear mixed-effects models with restricted maximum likelihood (REML) estimation to compare male and female genital traits between predation regimes among populations (rivers). The initial multivariate model included RWS-1–5 as response variables, with predation as a fixed factor (two levels, high and low predation), and both river (five levels) and sampling locality (10 levels) entered as random effects. In these analyses, we also included gonopodium length as a covariate. Univariate linear mixed-effects models (including the same fixed and random terms as the multivariate model) were then used to identify the specific traits contributing to the divergence in male genital size and shape among populations.
In the analysis of female traits, estimates of oviduct width and length were entered as response variables, with predation (fixed) and both river and sampling locality (random) entered as factors. In these analyses, we also included female body length (which was correlated with oviduct measures—§3) and mean offspring size (which varied among populations—§3) as covariates. In both analyses (males and females), we ensured homogeneity of slopes by testing the significance of the interaction between the fixed factor (predation) and the covariates. These interaction terms were all non-significant (p > 0.20), satisfying the assumptions of these models.
(a) Male genital morphology and the success of forced matings
We found that males with relatively longer gonopodia achieved significantly higher contact success than those with shorter gonopodia, whereas gonopodium shape (as described by RWS-1–5) was not significantly associated with contact success (table 1). However, we did find significant effects of gonopodium shape (RWS-1 and RWS-3) on the number of sperm recovered after the mating trials (table 1). Both of these relative warp scores (RWS-1 and RWS-3) were associated with variation in the length of the male's gonopodial tip (electronic supplementary material, figure S1b). Overall, males with relatively short gonopodial tips (i.e. positive values of RWS-1 and RWS-3) were more successful at transferring sperm to females than males with relatively long gonopodial tips. To visualize overall differences in gonopodial shape between minimally and maximally successful males (i.e. those that transferred the least and most sperm, respectively), we used the program tpsRegr , which enabled us to characterize total shape variation across the samples analysed and relate this variation to insemination success (electronic supplementary material, methods). Overall, these plots confirmed our conclusions from the analysis of the relative warp scores (table 1) by revealing that relatively short gonopodial tips were associated with higher insemination success (electronic supplementary material, figure S1c). Finally, we detected a weak but significant relationship between female body size and the number of sperm recovered (table 1).
(b) Population comparisons of male and female genital morphology
Our analysis revealed overall significant divergence among populations in male genital traits, which in turn was attributable to differences in the level of predation at each site. Although high-predation males had relatively longer gonopodia than their low-predation counterparts (mean fitted values reported in table 2a), this difference was not significant even when we controlled for differences in body size (table 2b). By contrast, the shape of the distal portion of the gonopodium differed significantly between predation regimes (linear mixed-effects MANOVA: predation, F5,16.7 = 6.36, p = 0.002; gonopodium length (covariate), F5,412.2 = 1.55, p = 0.17; results were similar if the covariate was removed from the model). Subsequent univariate analyses revealed that two of the relative warps (RWS-1 and RWS-3, accounting for 40 and 14% of the overall variance in male genital morphology, respectively) differed significantly between and high- and low-predation populations (table 2b). Briefly, males from high-predation populations had gonopodia with less elongated distal tips (evident from variance in RWS-1; figure 1a) and reduced hook angles (RWS-3; figure 1b) than their low-predation counterparts.
Our analysis of female genital morphology focused on the width and length of the oviduct. These two measurements were correlated with female body length, which in turn was positively associated with the mean size of offspring at parturition (r = 0.31, p < 0.0001, n = 195). In our analysis of female oviduct length and width, we therefore included both female body length and the mean size of offspring as covariates in the model. This analysis revealed that oviduct width (but not length) differed consistently with predation intensity, when controlling for variation in female body length and offspring size (table 3).
In summary, females from high-predation populations had relatively wider oviducts than their low-predation counterparts. This difference is unlikely to be owing to the production of larger offspring in these populations, because females from high-predation streams tend to produce smaller, not larger offspring . Indeed, our measurements of mean offspring size among populations confirmed that females from high-predation sites produced significantly smaller offspring than their low-predation counterparts (table 3).
(c) Covariance between male and female genital morphology
Given the significant divergence among populations in both male and female genital morphology, we looked for evidence of coevolutionary patterns of selection on these traits using multiple regression in which oviduct width was entered as a response variable and RWS-1 and RWS-3 were included as predictors. We specifically focus on these components of male and female genital shapes as they varied among populations in relation to predation intensity, and in the case of male genital traits, both RWS-1 and RWS-3 were associated with insemination success in the behavioural trials. Because oviduct width was positively correlated with both female body length and the mean size of offspring at birth (see above), we also included female body length and mean offspring size as covariates in this analysis. This enabled us to test how oviduct width covaried with male genital shape among populations when controlling for differences in female and offspring body size. We then used the model-averaging procedure described above to identify predictors that were more strongly associated with variation in oviduct width. This analysis revealed a significant negative association between relative oviduct width and RWS-1 (table 4), revealing that increasingly wide oviducts were associated with lower RWS-1 scores (i.e. relatively shorter gonopodium tips; figure 2).
The results from our mating trials revealed that variation in both the size and shape of the male's intromittent organ was associated with the success of forced matings. Males with relatively longer gonopodia were more successful at achieving genital contacts with females than those with relatively short gonopodia, although surprisingly we found no difference in the relative length of the gonopodium among populations (c.f. ), despite the higher prevalence of forced matings in high-predation sites. We also found a significant relationship between male genital shape and insemination success (number of sperm recovered from the female's genital tract). This latter finding accords with early work on this species and other poeciliid fishes, showing that the distal tip of the gonopodium plays an important role in sperm transfer. For example, Rosen & Gordon  observed that in the genera Poecilia and Xiphophorus, only the tips of the gonopodium were inserted into the female's gonopore. They further suggested that contact between the male and female during copulation was maintained by ‘holdfast’ devices that project from rays 3 and 4 of the gonopodium (e.g. hooks). These findings were subsequently corroborated in xiphophorin fishes by Clark et al. , who demonstrated experimentally that these structures were necessary for successful insemination. More recent work has revealed that the experimental removal of the paired hooks from the male guppy's gonopodial tip impairs subsequent sperm transfer . Importantly, the effects of this manipulation on insemination success were only apparent during forced (unsolicited) matings , again underscoring our suspicion that variation in this region of the gonopodium is shaped by divergent male-mating tactics among populations.
We also found that female body size was a significant predictor of insemination success, although the strength of this relationship was relatively weak compared with the effects of gonopodium shape on sperm recovered (table 1). This finding accords with previous work on the mosquitofish Gambusia holbrooki, where the probability of a female being inseminated through forced matings increased with female length . Whether this relationship between female body size and insemination success is owing to males preferentially allocating mating effort (and/or sperm) towards larger (more fecund) females , or the increased ability of males to undermine the choice of relatively large females (owing to increased ‘target’ size, enhanced manoeuvrability, etc. ) remains to be tested.
Our population comparisons revealed that the shape of the distal tip of the gonopodium varied with predation intensity. Males from high-predation populations had gonopodia with less elongated distal tips and reduced hook angles than their low-predation counterparts. These patterns are therefore consistent with our findings from the mating trials, by indicating that the size and shape of the gonopodium vary predictably among populations that differ in the relative intensity of forced matings. The pattern of trait divergence for the genital hooks is also consistent with the general pattern for the poeciliid family, where the degree of gonopodial elaboration varies with mating system. Specifically, species that rely predominantly (or exclusively) on forced matings (i.e. without courtship) tend to have relatively ‘unarmed’ gonopodia, while those that rely more on courtship have far more elaborated gonopodia adorned with various ‘holdfast’ structures such as hooks, claws and serrae . Although male guppies use both mating tactics interchangeably, our data suggest that the extent to which either tactic is used in the population selects for variation in the relative shape of these traits. Interestingly, males from high-predation populations had more ‘streamlined’ hooks, potentially making them more adapted to the higher prevalence of forced matings by these males. However, hook shape was not a significant predictor of mating success in the single population used in our behavioural trials. This is probably because among-population variance for this trait greatly exceeds within-population variance. Indeed, visualizations of the five relative warp scores (using the software tpsRelw) describing male genital morphology in the mating trials revealed that none of these was associated with changes in the angle of the genital hooks (figures not provided). This suggests that there is very limited variability in this trait within a single population. Thus, population crosses or gonopodium experimental manipulation would be required to assess the role that genital hooks play in mediating the success of forced matings (but see ).
Our analysis also revealed corresponding patterns of trait diversification in female genital morphology (relative oviduct width). Although our current investigation, in conjunction with earlier work [30,37,56], enables us to draw tentative conclusions about the role that male genital shape plays in mediating the success of forced matings (above), we can only speculate about the significance of variability in female genital morphology. One possibility that we are currently pursuing is that variation in female genital tract morphology influences the success of forced matings, which in turn would potentially reduce the costs associated with the higher prevalence of forced matings in high-predation populations .
In summary, we have provided evidence for intraspecific (co)variance in male and female genital traits, and combined these comparative analyses with behavioural data that reveal an association between male genital morphology and the outcome of an antagonistic mating encounter. In order to provide evidence that these patterns of correlated trait divergence reflect a history of sexually antagonistic selection, a topic that is still generating considerable controversy , it is necessary to demonstrate: (i) that variation in female genital morphology reflects adaptations that limit the costs associated with male sexual harassment; (ii) that these patterns of morphological covariance are driven by differences in the level of sexual harassment endured by females among populations; and (iii) that patterns of genetic (co)variation underlying the expression of these traits do not impede their evolutionary potential. Our ongoing work addresses all of these questions.
All animal work was conducted according to the University of Western Australia's Animal Ethics Committee (Research Integrity Office, permit number 05/100/513).
We thank Raj Mahabir and Bryan Neff for help with the fish collections, Emily Trainer for taking images of gonopodia, Andrea Cardini and James Rohlf for advice on geometric morphometrics, Goran Arnqvist for helpful suggestions with mixed-model approaches and Michael Jennions, Locke Rowe, Leigh Simmons, Joe Tomkins and two anonymous reviewers for discussion and comments on earlier drafts of the manuscript. We also thank Carlotta Mazzoldi for her advice on the female morphological analyses. Financial support from the Australian Research Council (grant no. DP0663574), the University of Padova (grants nos. CPDA031972 and CARIPARO 2007), the Italian Minister for University and Research (A.P. and C.G.) and the Natural Sciences and Engineering Research Council of Canada (T.E.P.) is also gratefully acknowledged.
- Received November 9, 2010.
- Accepted December 23, 2010.
- This Journal is © 2011 The Royal Society