Sperm competition occurs when females mate with more than one male in each sexual cycle and sperm from rival males compete to fertilize the ova 1 . A large body of evidence has accumulated over the last few years showing that sperm competition is a potent evolutionary force that has shaped many reproductive traits 2 3 4 . An almost universal response to sperm competition across taxa is an increase in sperm numbers, which enhances males' fertilization success in competitive contexts 5 6 7 8 .

Early theoretical models proposed that the increase in sperm numbers under sperm competition was achieved at the expense of a reduction in their size, leading to the evolution of tiny sperm 9 10 . The presumed trade-off between sperm numbers and size is one of the most widely accepted assumptions in studies of gamete evolution, particularly in relation to the evolution of anisogamy 9 11 . Most empirical studies have therefore assumed that a positive relationship between sperm numbers and size is evidence against the predicted trade-off, and following this reasoning it has been concluded that there is no support for the sperm size/number trade-off except in cases of sperm gigantism 12 13 (reviewed in 14 ). However, sperm competition game models are not based on the "direct trade-off", which assumes a fixed budget for ejaculate expenditure and predicts a trade-off between sperm size and numbers 15 . Instead, such models are based on the "indirect trade-off" which assumes a fixed budget for male reproductive activity and proposes that investment in ejaculates is traded-off against energy spent on mate acquisition. Irrespective of this distinction, it is assumed that ejaculate expenditure is the product of the number of sperm and their size 14 . Models developed by Parker 16 considered different advantages that could derive from an increase in sperm size, and concluded that, if the main selective benefit is that sperm become more competitive, sperm competition should not select for an increase in sperm size. Recent models 15 suggest that, even under the indirect trade-off, sperm size and number do effectively trade-off directly, even though both can increase with levels of sperm competition as the total investment on the ejaculate increases. Other types of theoretical models used physical and biomechanical principles and concluded that, in the micro-environment in which sperm perform, a relationship between sperm size and competitive ability (swimming velocity) is unlikely 17 . These theoretical models had a profound influence in this field.

Contrary to these theoretical predictions, an alternative hypothesis proposed that, if an increase in size conferred a competitive advantage to sperm, sperm competition should select simultaneously for an increase in sperm numbers and size, and no trade-off between these two traits should be expected 18 . Preliminary analyses with the evidence available at the time suggested that sperm competition did favour an increase in sperm size which resulted in faster swimming speeds 18 .

This hypothesis generated an intense controversy which stimulated a great deal of work on the topic. Empirical work produced an increasing amount of evidence showing that levels of sperm competition were associated with increases in sperm size when interspecific studies were carried out on taxa as diverse as birds, frogs, fish, butterflies, moths, nematodes (reviewed in 19 ) and snakes 20 . In some species in which females posses sperm storage organs, this relationship did not become apparent until the size of the female storage organ was taken into account 5 21 (reviewed in 22 ).

Different hypotheses were proposed to explain the functional significance of increases in the length of different sperm components: an increase in the flagellum would increase the thrust needed to propel the sperm forward 18 , an increase in midpiece volume would increase the amount of energy to fuel sperm motility 20 23 24 , and an elongation of the sperm head would reduce the drag experienced by the sperm cell resulting in an increase in sperm swimming velocity 25 . It has also been suggested that the ratios between different sperm components could influence sperm swimming velocity 25 and, in particular, that the ratio sperm head length/flagellum length should play an important role 17 .

Recent studies in mammals 19 , birds 26 , and fish 27 have also provided evidence that sperm size is associated with sperm swimming speed, after phylogenetic effects are taken into account, lending further support to the original hypothesis 18 . Furthermore, intraspecific studies have shown that sperm swimming speed is the main determinant of fertilization success both in competitive 28 29 and non-competitive 30 31 32 contexts.

However, the evidence linking sperm competition levels and sperm size in mammals remains contentious due to inconsistencies between studies. An analysis using a large sample of species reported a relationship between levels of sperm competition and sperm size, but the relation did not remain significant after phylogenetic effects were taken into account 33 . Because this study included many more species that others, it has been generally assumed that the information provided was more reliable and, as a consequence, it is widely accepted that no relationship exists between sperm competition and sperm length among mammals (see, for example, review in 34 ). In addition, further studies on mammals reported either no relationship between sperm competition and sperm size 35 , or an effect exclusively on midpiece volume 23 24 .

The aim of this study was to carry out the most extensive study to date of the relationship between levels of sperm competition and sperm design in mammals using all the information currently available, which includes a much larger data set and better resolved phylogenies than those used in previous studies. In addition, we examine the relationship between sperm size and sperm swimming velocity, controlling for phylogenetic effects, in a larger data set than previously reported.

In the study sample of 226 mammals (see additional file 1), total sperm length ranged from 28 μm to 258 μm (CV = 43.8 ± 2.6). The head length accounted for a mean 9.4% of the total sperm length, and it ranged from 3.0 to 15.2 μm (CV = 29.5% ± 0.2). Midpiece length represented a mean 19.9% of the total sperm length (range 3.0-103.1 μm) and it showed higher interspecies variability (CV = 71.2% ± 0.9) than any other sperm component. The principal piece accounted for 70.5% of the total sperm length (range: 15.6-142.6 μm; CV = 41.7% ± 1.9). Body mass and testes mass were extremely variable (CV = 450.53% ± 29928.7 and 494.17% ± 27.6, respectively) when compared to sperm dimensions. On the other hand, relative testes mass, which ranged from 0.07 to 5.23, presented a variability (CV = 84.1% ± 0.1) closer to that seen for sperm dimensions. A summary of information on body mass, relative testes mass and sperm dimensions is shown in additional file 2.

We found a significant positive association between testes mass corrected for body mass (thereafter, relative testes mass) and total sperm length after controlling for phylogenetic effects (Table 1, Figure 1A). However, total sperm length was not associated with body mass.

The same pattern emerged when the different sperm components (head, midpiece, principal plus terminal piece, and flagellum length) were analyzed separately, since all of them became longer as relative testes mass increased, but were unrelated to body mass after controlling for phylogenetic effects (Table 1, Figure 1B-E). The strength of the relationship with relative testes mass was similar for all sperm components except for midpiece length which was just below significance level. In addition, as relative testes mass increased sperm heads became more elongated (measured as the ratio head length/head width) (Table 1, Figure 1F).

Total sperm length showed a strong positive association with sperm swimming velocity (Table 1, Figure 2A). Sperm swimming velocity was also significantly associated with relative testes mass, but not with body mass (Table 1, Figure 2B). It is worth noting that relative testes mass showed a stronger association with sperm swimming velocity than with the size of any sperm component after controlling for phylogenetic effects, and that the relationship between sperm size and sperm swimming velocity is highly significant.

The ratio between head length and total flagellum length was significantly associated with straight line velocity (Table 1, Figure 3) so that as the proportion of the flagellum length in relation to head length decreased, sperm velocity also decreased.

In the present study we found evidence suggesting that, in mammals, sperm competition is associated with an increase in total sperm length, which results from an increase in size of all sperm components: head, midpiece, principal plus terminal piece and, hence, flagellum. All relationships between relative testes size (a proxy of sperm competition levels) and sperm dimensions remained significant after controlling for phylogenetic effects, except for the midpiece, which was just below significance level.

The use of relative testes mass as an index of levels of sperm competition is widely accepted, since inter-specific phylogenetic analyses and intra-specific comparisons have shown that both are closely associated (reviewed in 8 36 ). In addition, artificial selection experiments have shown that the relationship is causal, since experimental increases in sperm competition levels lead to increases in relative testes size 37 . Recent interspecific analyses, controlling for other variables also believed to influence testes size, show that relative testes mass is clearly related to levels of sperm competition in mammals 38 . The reason why an increase in relative testes size, and therefore sperm production, seems a universal response to levels of sperm competition is that in most taxa sperm numbers influence fertilization success and enhance male fertilization success in competitive contexts 5 6 7 8 36 .

Our results contrast with those reported by Gage and Freckleton 33 who also found clear relationships between sperm length, and the size of the different sperm components, and relative testes size, although these relationships were lost after controlling for phylogenetic effects. The reasons for this discrepancy may have to do with the fact that our study has a much larger sample size (226 species in our study versus 83 species in that by Gage and Freckleton 33 ) and that these authors used an incorrect grouping of some species (e.g., giraffe was included in Cervidae, Theropithecus gelada was placed in the same group with Erythrocebus patas and Cercopithecus aethiops rather than with Papio, and Homo sapiens was separated from a group formed by Gorilla, Pan and Pongo). According to Purvis and Garland 39 these topological errors may affect the performance of phylogenetic control methods, to "an unknown and potentially serious degree".

However, we believe that the main reason for the disparity is that Gage and Freckleton 33 used a very poorly resolved phylogeny that included 12 "soft" polytomies" (i.e., polytomies not due to true simultaneous speciation events but to lack of information about branching pattern) encompassing 57 out of the 83 (69%) species in their study. The reason for this high number of polytomies is that they used a phylogeny which was only resolved up to the family level 40 . In contrast, the phylogeny we used in this study includes only one soft polytomy that affects 3 out of 226 species (1.3%) because we have integrated phylogenetic information for specific groups to avoid the problems associated with low resolution.

There has been much discussion about the effect of polytomies on phylogenetic control methods, and while some authors conclude that a low quality phylogenetic reconstruction is preferable to no phylogenetic control at all 41 42 , most studies agree that soft polytomies cause analytical problems for these kind of methods 39 43 44 . Moreover, although these studies recommend possible solutions in the form of analytical methods that reduce degrees of freedom 39 43 , estimative approaches using complementary variables 45 , random sampling of constrained phylogenies 46 , and incorporation of phylogenetic uncertainty into the model via Bayesian methods 47 , these approaches have lower statistical power when compared with an analysis that uses a better resolved phylogeny. It is unclear whether Gage and Freckleton 33 used any of these methods to account for the lack of resolution of their phylogeny. The contrast between results (and conclusions) obtained with phylogenies varying in the degree of resolution highlights the need to obtain detailed phylogenetic information to avoid losing meaningful biological relationships when controlling for phylogenetic effects.

To directly examine the possible impact of a poorly resolved phylogeny, we re-analyzed the data in Gage and Freckleton 33 using the detailed phylogenetic reconstruction we used for this study. When doing so, we realized that data for a very few species in Gage and Freckleton's dataset were in fact inadequate. We decided not to include these data to avoid further errors in the analyses. Out of a total of 83 species in the study by Gage and Freckleton 33 we chose to exclude 5 species for the following reasons. Gage and Freckleton 33 included only one species of marsupial (Antechinus stuartii) despite the fact that data for many species of marsupials were available at the time of their study 2 48 . The reasons why Gage and Freckleton selected only one species of marsupial is not given in their work and we felt that inclusion of only one species of this clade seriously biased the analysis; the inclusion of a single species from a distantly related clade could affect the outcome of phylogentic analyses. Furthermore, marsupials have a different reproductive biology so the predictions in relation to sperm size are likely to differ. Future studies should address evolution of marsupial sperm taking these factors into consideration. The analysis originally carried out by Gage and Freckleton 33 also included a single cetacean species (Megaptera novaeangliae). We decided not to include it in the analyses for the same reasons (i.e., there was information for more cetacean species 48 49 and it was not clear why this particular species was chosen), plus the fact that in cetaceans the scaling of organ/body size is under rather unique constraints (in particular, the testes) due to the selection on streamlined bodies in marine environments. Finally, we also did not include three ungulate species: two species (Cervus elaphus, Equus grevyi) were not considered because data on sperm size came from "approximations" calculated from drawings that had no scale (data originally from 48 ) whereas one species (Tayassu tajacu) was not included because data come from measurements of testis sections (data originally from 48 ) and this ignores the post-testicular changes in morphology experimented by spermatozoa.

Thus, when we carried out the re-analysis using the data in the original study by Gage and Freckleton (with the exclusion of questionable data from only 5 out of 83 species) and a well-resolved phylogeny, we found strong positive associations between relative testes size and all sperm components. To verify that the outcome of this re-analysis was not due to the exclusion of the 5 species, we also re-analyzed this dataset using the original phylogeny used by Gage and Freckleton 33 . The results showed no significant association between relative testes size and sperm dimensions (with the exception of head length, which showed a significant association). Thus, when controlling for phylogenetic effects, the same dataset revealed significant relationships with a well-resolved phylogeny which were lost when a poorly-resolved phylogeny was used. We conclude that the lack of association between relative testes size and sperm dimensions in the study by Gage and Freckleton 33 was due mainly to the use of a poorly-resolved phylogeny. Therefore, and contrary to the conclusion by Gage and Freckleton 33 , our analyses allow us to conclude that the relationship between sperm dimensions and sperm competition in mammals remains robust after adequately controlling for phylogenetic effects.

There are also some discrepancies between our results and those in other studies on mammals. They can be explained, at least partly, by the different representation of species from different orders in the data sets used. A study on bats found no relationships between levels of sperm competition and sperm dimensions 35 . Because female bats store sperm during hibernation, the need for sperm to survive inside the female reproductive tract for up to several months could imply that in bats sperm competition favours sperm traits which enhance their longevity, rather than their swimming speed. Studies by Dixson and colleagues failed to find relationships between levels of sperm competition and sperm length, or length of various sperm components, first in primates 23 and, subsequently, in mammals 24 . However, since their data derived from samples collected from caudae epididymides during post-mortem dissections of their zoo animals, it consisted primarily of artiodactyls and primates, and included a low number of carnivores and only two species of rodents. Thus, the lack of a relationship between levels of sperm competition and the dimensions of different sperm components found in these studies could be due to an over representation of artiodactyls, carnivores and primates which have lower diversity in sperm dimensions 50 . Intriguingly, Dixson and colleagues found a relationship between sperm competition levels and sperm midpiece volume 23 24 . The reason why midpiece volume but not midpiece length showed a significant relation is not clear, since data show that there is very little variation in midpiece length in artiodactyls, carnivores and primates (see additional file 1). It may be that the width of the midpiece accounts for most of the variation in midpiece volume because of the way it was calculated in that study.

Sperm competition seems to act on all sperm components in an integrative manner, because they are all functionally important and may all contribute in complementary ways to enhance sperm swimming velocity: an increase in midpiece size probably increases energy output 23 , and longer principal pieces will generate greater thrust to propel the sperm along the female reproductive tract 18 and generate additional energy 19 . In addition, our study also found that sperm competition levels are also associated to the degree of elongation of the sperm head, a trait which has received little attention despite the major role it could play in sperm hydrodynamics. Recent intraspecific studies have shown that the degree of elongation of the sperm head has the strongest impact upon sperm swimming velocity 25 , because it reduces the degree of drag and thus the energy needed for sperm movement 51 . Thus, relatively subtle differences in the shape of the sperm head seem to have a great impact upon swimming performance.

We have also been able to show that as sperm become longer, sperm swimming velocity increases. These findings expand on previous work 19 and agree with those recently reported for birds 26 , fish 27 and sea urchin 52 . Furthermore, we have been able to reveal a direct relationship between levels of sperm competition and sperm swimming speed, a link that other studies have failed to find 26 . Interestingly, relative testes size is more strongly associated with sperm swimming velocity than it is with the size of any sperm component, and the relationship between sperm size and sperm swimming velocity is by far the strongest of all the relationships found. This means that relatively small changes in the size of all sperm components and the shape of the head have a major impact on sperm swimming velocity.

Finally, we show that sperm velocity is inversely related to the ratio between head length and flagellum length. Humphries et al. 17 suggested that, since sperm cells are extremely small, thus operating in a low Reynolds number environment, sperm velocity should be determined by the balance between the propulsive force (which would increase with flagellum length) and drag (which would be related to head length). Our findings represent the first comparative evidence supporting this hypothesis, for which a recent intraspecific study also found support 53 .

While the picture emerging from interspecific studies seems to support the hypothesis that sperm competition favours increases in sperm size, which enhance sperm swimming velocity resulting in improved fertilization success, the intraspecific studies seem contradictory. Thus, a number of studies show a relationship between sperm dimensions and velocity 25 53 54 , whereas a recent review revealed that some intraspecific studies did not find a relationship 17 . This may be due to the fact that the methodology used has enough resolution to detect relationships between species because they differ to a large extent in sperm size, but is insufficient to detect them at the intraspecific level given the small magnitude of differences and the large degree of variation within species and within males. A recent intraspecific study 52 has shown that when sperm data on size and swimming velocity come from the same spermatozoa, the relationship is clear. However, when data on size come from a different sperm subsample than data on sperm swimming velocity (as is the case in most studies) such relationships are not found.

Other intraspecific studies have concluded that small sperm are more competitive (e.g. 55 56 . Studies on insect models suffer from the limitation that so far it has not been possible to evaluate sperm swimming velocity in these species. Thus, the potential relationships between sperm size and sperm swimming velocity cannot be evaluated in these taxa until the technical difficulties are solved. It should also be noted that most intraspecific studies do not actually measure "fertilization success" but rather some measure of paternity success. Thus, they cannot exclude other factors that could be playing a role at any stage after fertilization and during embryo development.

Despite these caveats, it is plausible that the benefits of increasing/decreasing sperm size vary between taxa. Since many intraspecific studies have been carried out on insects, one possibility is that because in this particular group sperm remain in storage organs for long periods of time, variables other than sperm size may be more important at determining fertilization success. Thus, sperm longevity may be the major determinant of fertilization success. If so, small sperm may be at an advantage if they are able to survive for longer, as shown in external fertilizers 31 , but the information currently available does not allow to test this hypothesis properly.

The relevance of our findings for other taxa is supported by evidence from a recent review showing that the relationship between sperm competition and sperm size is widespread across taxa 19 . Since female mammals have no sperm storage organs, sperm survive for short periods of time in the female reproductive tract and have to overcome relatively long distances to reach the ova. Under these conditions fertilization success is determined mainly by sperm swimming velocity 32 , and there are no confounding effects of co-evolution between sperm size and female storage organs. Thus, it is in this system that the race to fertilize the ova is likely to be the most important underlying mechanism explaining fertilization success in competitive contexts. The outcome is that sperm competition selects for both increased sperm numbers and size, so total ejaculate expenditure increases. The increase in ejaculate expenditure is energetically costly 57 58 , but whether it requires a trade-off with mating acquisition, or other life-history traits [e.g. 59 60 61 ], remains to be explored.

Our findings provide further support to the original hypothesis that the main adaptive value of changes in sperm design under sperm competition is that they increase sperm swimming velocity 18 . Since a number of studies have shown that sperm swimming velocity is a main determinant of fertilization success 19 28 29 32 62 , this explains why it is targeted by sexual selection so efficiently.

This study presents phylogenetically-robust evidence that sperm competition in mammals favours an increase in the size of all sperm components and an elongation of the head, which result in faster swimming speeds.

The study sample includes all eutherian mammals for which information was obtained. In those cases in which different values for the same species were available from different studies, averages were used. We have not included in the analysis a few species for which the only data available were "approximations from Retzius' illustrations" because they lacked a reference scale (see Methods and footnote to Table 1 in 48 ). Additionally, we have not included Chiroptera due to their unusual reproductive traits which include sperm storage for long periods of time in the female tract.

All authors designed and performed research, carried out data compilation and analyses, and participated in preparation of the manuscript. All authors read and approved the final manuscript.

M. Tourmente enjoyed a Boehringer Ingelheim Travel Grant and a postdoctoral fellowship of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina. M. Tourmente is currently a postdoctoral researcher funded by the Programa Nacional de Movilidad de Recursos Humanos de Investigación of the Spanish Ministry of Education.