BACKGROUND
diversity in intromittent genitalia  is a widespread evolutionary phenomenon that is hypothesised to result from postcopulatory sexual selection  <cit> .
consistent with this general pattern, the mammalian baculum  is characterised by extreme anatomical variation across diverse mammalian species   <cit> .
however, current evidence of sexual selection on the baculum is limited, based on comparative and indirect studies of baculum size  <cit> .
here, we test if baculum size in wild house mice   predicts male reproductive success under competitive conditions.
the house mouse is a model species for studies of reproductive behaviour  <cit> , and regularly mates promiscuously in the wild  <cit> .
to quantify key components of male reproductive success under competitive conditions we used four discrete experimental populations of house mice in very large outdoor enclosures, providing natural and controlled conditions within which all animals could be sampled .
our analyses include expected effects of dominance and body size on male mating and fertilisation success  <cit>  and test for the effects of additional traits predicted to influence the outcome of postcopulatory sexual selection   <cit> .
RESULTS
variation in male reproductive success
a total of  <dig> surviving offspring were sired by  <dig> focal males in the outdoor enclosures.
the number of offspring sired per male ranged from  <dig> to  <dig> .
overall, 67% of litters were multiply sired.
focal males that achieved at least one copulation from which offspring were identified  sired an average of  <dig>  ±  <dig>   offspring per litter .
variation in male reproductive success and high levels of multiple paternity reveal evidence of intense competition between males in our experimental populations.
in the following sections, we analyse male traits contributing to variation in reproductive success.
mean measurements of morphological traits  and results of pearson correlation tests between traits  are provided as supplementary information.
baculum size
baculum size significantly predicted the reproductive success of male house mice after controlling for effects of body mass and other reproductive traits .
specifically, baculum shaft width significantly predicted the number of offspring sired by focal males in our study populations .
baculum shaft width and base width were also significant predictors of the mean number of offspring sired per litter , consistent with an influence on differential reproductive success under postcopulatory sexual selection.
by contrast, baculum length had no significant influence on measures of male reproductive success independent of body mass and other reproductive traits.
generalized linear mixed model to investigate morphological traits influencing the reproductive success of male house mice, showing the best model for the total number of offspring sired.
data for morphological traits were log transformed prior to analysis.
body mass was retained in the model as a covariate.
population and sibling group were included as random effects .
Δaic = the change in the aic if the single term is dropped.
number of observations =  <dig>  sibling groups =  <dig>  populations =  <dig>
linear mixed model to investigate morphological traits influencing the reproductive success of male house mice, showing the best model for the average number of offspring sired per litter.
data for morphological traits were log transformed prior to analysis.
body mass was retained in the model as a covariate.
population and sibling group were included as random effects .
Δaic = the change in the aic if the single term is dropped.
number of observations =  <dig>  sibling groups =  <dig>  populations =  <dig>
other traits linked to male reproductive success
body mass, testis mass and the mass of the seminal vesicles  were also significant predictors of the total number of offspring sired by male house mice under competitive conditions .
by contrast the mass of the preputial glands, which are used in scent marking and reliably linked to male dominance  <cit> , did not predict male reproductive success.
discussion
our findings reveal that baculum morphology  predicts the reproductive success of male house mice independently of other key traits linked to competitive ability .
perhaps the most likely explanation for this finding is that a wider baculum facilitates increased stimulation of the female reproductive tract.
in house mice there is ample opportunity for such stimulation to occur during a prolonged copulatory sequence consisting of multiple intromissions with thrusting  <cit> .
copulatory stimulation is known to trigger complex neuroendrocrine responses in female mammals, including house mice, and may assist in sperm transport as well as maintenance of pregnancy  <cit> .
a wider baculum might also assist in dislodging copulatory plugs left by rival males during pre-ejaculatory intromissions, or in achieving intromission  <cit> .
however, the precise mechanisms by which the baculum might promote differential fertilisation success remain to be determined.
our findings support previous suggestions that baculum size is subject to sexual selection.
for example, it has been hypothesised that positive allometry and heightened coefficients of phenotypic variation may be indicative of sexual selection on genitalic and other traits  <cit>  .
accordingly, several studies of rodents and carnivores report evidence of positive allometry and high variability in measures of baculum length or width  <cit> .
in addition, comparative analyses indicate that baculum size may be subject to sexual selection in rodents and carnivores, with increased baculum length favoured under high levels of sperm competition  <cit> .
in the present study however, we find baculum width to be a more important predictor of reproductive success for male house mice under conditions of intense postcopulatory sexual selection, which is consistent with relatively high intraspecific variation  <cit>  and positive allometry  <cit>  in this aspect of penile morphology.
significant effects of body mass and testes mass on male reproductive success are to be expected under pre- and postcopulatory sexual selection.
large males may gain a reproductive advantage through contest competition or female choice  <cit> .
similarly, large testes are expected to confer an advantage in sperm competition, by facilitating increased numbers of sperm per ejaculate and more frequent ejaculation  <cit> .
here we also report a significant influence of seminal vesicles on male reproductive success.
our findings provide the first such evidence under competitive conditions, consistent with the hypothesis that a larger copulatory plug  may be more effective in delaying female remating and/or promoting sperm transport  <cit> .
measuring reproductive success under natural conditions is challenging  <cit>  and particularly so in relation to genital morphology.
importantly, potential confounding effects normally present in natural populations were either controlled within our experimental enclosures  or taken into account in our analyses .
the capture of all surviving offspring produced over sequential reproductive events , further strengthens our conclusions.
nonetheless, future experimental studies would be beneficial to explore our findings further under controlled laboratory conditions, ideally involving a creative approach to manipulate baculum size independently of other reproductive traits .
CONCLUSIONS
in conclusion, our finding that penile morphology predicts key components of male reproductive success under natural and controlled conditions provides a significant advance in the study of genital evolution, complementing increasing numbers of comparative and laboratory-based studies in diverse taxa  <cit> .
more specifically our results support the hypothesis that baculum diversity is driven by sexual selection, with broad implications for understanding patterns of morphological diversification and speciation  <cit> .
in particular, a focus on divergence in baculum morphology between closely related species or diverging populations is likely to advance understanding of genital evolution and speciation processes, as is increasingly being recognised in arthropod taxa  <cit> .
further work is now required to determine the mechanisms by which the baculum interacts with female reproductive traits to affect the outcome of postcopulatory sexual selection, driving the extraordinarily divergent evolution of penile morphology.

 diversity in intromittent genitalia is a widespread evolutionary phenomenon that is hypothesised to result from postcopulatory sexual selection. consistent with this general pattern, the mammalian baculum is characterised by extreme anatomical variation across diverse mammalian species. however, current evidence of sexual selection on the baculum is limited, based on comparative and indirect studies of baculum size. here, we test if baculum size in wild house mice predicts male reproductive success under competitive conditions. the house mouse is a model species for studies of reproductive behaviour, and regularly mates promiscuously in the wild. to quantify key components of male reproductive success under competitive conditions we used four discrete experimental populations of house mice in very large outdoor enclosures, providing natural and controlled conditions within which all animals could be sampled. our analyses include expected effects of dominance and body size on male mating and fertilisation success and test for the effects of additional traits predicted to influence the outcome of postcopulatory sexual selection.  variation in male reproductive success a total of surviving offspring were sired by focal males in the outdoor enclosures. the number of offspring sired per male ranged from to. overall, 67% of litters were multiply sired. focal males that achieved at least one copulation from which offspring were identified sired an average of ± offspring per litter. variation in male reproductive success and high levels of multiple paternity reveal evidence of intense competition between males in our experimental populations. in the following sections, we analyse male traits contributing to variation in reproductive success. mean measurements of morphological traits and results of pearson correlation tests between traits are provided as supplementary information. baculum size baculum size significantly predicted the reproductive success of male house mice after controlling for effects of body mass and other reproductive traits. specifically, baculum shaft width significantly predicted the number of offspring sired by focal males in our study populations. baculum shaft width and base width were also significant predictors of the mean number of offspring sired per litter, consistent with an influence on differential reproductive success under postcopulatory sexual selection. by contrast, baculum length had no significant influence on measures of male reproductive success independent of body mass and other reproductive traits. generalized linear mixed model to investigate morphological traits influencing the reproductive success of male house mice, showing the best model for the total number of offspring sired. data for morphological traits were log transformed prior to analysis. body mass was retained in the model as a covariate. population and sibling group were included as random effects. Δaic = the change in the aic if the single term is dropped. number of observations = sibling groups = populations = linear mixed model to investigate morphological traits influencing the reproductive success of male house mice, showing the best model for the average number of offspring sired per litter. data for morphological traits were log transformed prior to analysis. body mass was retained in the model as a covariate. population and sibling group were included as random effects. Δaic = the change in the aic if the single term is dropped. number of observations = sibling groups = populations = other traits linked to male reproductive success body mass, testis mass and the mass of the seminal vesicles were also significant predictors of the total number of offspring sired by male house mice under competitive conditions. by contrast the mass of the preputial glands, which are used in scent marking and reliably linked to male dominance, did not predict male reproductive success. discussion our findings reveal that baculum morphology predicts the reproductive success of male house mice independently of other key traits linked to competitive ability. perhaps the most likely explanation for this finding is that a wider baculum facilitates increased stimulation of the female reproductive tract. in house mice there is ample opportunity for such stimulation to occur during a prolonged copulatory sequence consisting of multiple intromissions with thrusting. copulatory stimulation is known to trigger complex neuroendrocrine responses in female mammals, including house mice, and may assist in sperm transport as well as maintenance of pregnancy. a wider baculum might also assist in dislodging copulatory plugs left by rival males during pre-ejaculatory intromissions, or in achieving intromission. however, the precise mechanisms by which the baculum might promote differential fertilisation success remain to be determined. our findings support previous suggestions that baculum size is subject to sexual selection. for example, it has been hypothesised that positive allometry and heightened coefficients of phenotypic variation may be indicative of sexual selection on genitalic and other traits. accordingly, several studies of rodents and carnivores report evidence of positive allometry and high variability in measures of baculum length or width. in addition, comparative analyses indicate that baculum size may be subject to sexual selection in rodents and carnivores, with increased baculum length favoured under high levels of sperm competition. in the present study however, we find baculum width to be a more important predictor of reproductive success for male house mice under conditions of intense postcopulatory sexual selection, which is consistent with relatively high intraspecific variation and positive allometry in this aspect of penile morphology. significant effects of body mass and testes mass on male reproductive success are to be expected under pre- and postcopulatory sexual selection. large males may gain a reproductive advantage through contest competition or female choice. similarly, large testes are expected to confer an advantage in sperm competition, by facilitating increased numbers of sperm per ejaculate and more frequent ejaculation. here we also report a significant influence of seminal vesicles on male reproductive success. our findings provide the first such evidence under competitive conditions, consistent with the hypothesis that a larger copulatory plug may be more effective in delaying female remating and/or promoting sperm transport. measuring reproductive success under natural conditions is challenging and particularly so in relation to genital morphology. importantly, potential confounding effects normally present in natural populations were either controlled within our experimental enclosures or taken into account in our analyses. the capture of all surviving offspring produced over sequential reproductive events, further strengthens our conclusions. nonetheless, future experimental studies would be beneficial to explore our findings further under controlled laboratory conditions, ideally involving a creative approach to manipulate baculum size independently of other reproductive traits.  in conclusion, our finding that penile morphology predicts key components of male reproductive success under natural and controlled conditions provides a significant advance in the study of genital evolution, complementing increasing numbers of comparative and laboratory-based studies in diverse taxa. more specifically our results support the hypothesis that baculum diversity is driven by sexual selection, with broad implications for understanding patterns of morphological diversification and speciation. in particular, a focus on divergence in baculum morphology between closely related species or diverging populations is likely to advance understanding of genital evolution and speciation processes, as is increasingly being recognised in arthropod taxa. further work is now required to determine the mechanisms by which the baculum interacts with female reproductive traits to affect the outcome of postcopulatory sexual selection, driving the extraordinarily divergent evolution of penile morphology. 
although functionally enigmatic, diversity in baculum form is hypothesised to result from sexual selection. by providing the first evidence linking baculum morphology to male reproductive success, our results support the hypothesis that evolutionary diversity in baculum form is driven by sexual selection. baculumcryptic female choicegenital evolutionos penispenile morphologypostcopulatory sexual selectionsperm competition after controlling for body size and other reproductive traits, the width of the house mouse baculum predicts both the mean number of offspring sired per litter and total number of offspring sired. here we show that baculum size explains significant variation in the reproductive success of male house mice under competitive conditions. diversity in penile morphology is characterised by extraordinary variation in the size and shape of the baculum found in many mammals.
 diversity in penile morphology is characterised by extraordinary variation in the size and shape of the baculum found in many mammals. although functionally enigmatic, diversity in baculum form is hypothesised to result from sexual selection. according to this hypothesis, the baculum should influence the outcome of reproductive competition among males within promiscuous mating systems. however, a test of this key prediction is currently lacking.  here we show that baculum size explains significant variation in the reproductive success of male house mice under competitive conditions. after controlling for body size and other reproductive traits, the width of the house mouse baculum predicts both the mean number of offspring sired per litter and total number of offspring sired.  by providing the first evidence linking baculum morphology to male reproductive success, our results support the hypothesis that evolutionary diversity in baculum form is driven by sexual selection. baculumcryptic female choicegenital evolutionos penispenile morphologypostcopulatory sexual selectionsperm competition 