Table 3 Heads or tails?

The simplified argument that velocity is not likely to be determined purely by length alone (equation (2)), is supported by the results from both slender body theory [70–74], and the simpler, but less accurate, resistive force theory [both reviewed by [14]]. Both treatments indicate that drag due to the head, and the hydrodynamic interaction between the head and the flagellum of a sperm, will both play a role in determining forward speed.

As few studies consider multiple length measures as well as speed [e.g. [9]], and none provide adequate data for further analysis, we used a reanalysis of Higdon's [71] results (see Additional file 1) to estimate relative forward swimming speeds for sperm of a range of different species whose head and flagellum lengths were given in the literature. Where raw data were unavailable, data points were extracted from published figures using GraphClick^® (Arizona software, http://www.arizona-software.ch). Our flagellum length measures represent the flagellum plus midpiece, except for fishes where the midpiece is an integral part of the head. All analyses were carried out using R v. 2.5.1 [75] with the SMATR package [76]. No phylogenetic correction was used, as the necessary data were not available, and because we were interested in the patterns resulting from different scaling relationships, not the form of individual relationships per se. Reduced Major Axis (RMA) regression was used to describe the relationship between sperm head length and flagellum length (Additional file1). We decided between linear and power functions (log head vs. log flagellum length) on the basis of the amount of variation explained by the two models, selecting the one with the higher R². We arbitrarily designated an adjusted R² of 15% as the cut-off for the percentage variance explained by the regression model before we considered there to be no relationship between the two variables. We characterised data where no relationship was found by the ratio of variances between them, and represent these cases by vertical and horizontal lines in the figures.

Figure 1 illustrates that the allometry of head and flagellum lengths appears to be taxon-specific and not consistent across species. We next plotted total sperm length (head plus flagellum) against our estimates of swimming speed (Figure 1, rhs). The result is a mix of patterns that cannot be predicted from knowledge of total length alone. Qualitatively similar patterns are seen when other single length measures, such as flagellum length, are used to estimate speed instead of total length. The diversity of patterns also remains if the linear relationship between head and flagellum is relaxed to include curvilinear relationships (data not shown).

These results show that the sperm length-velocity relationships commonly reported to take a number of forms (including no apparent link) can likely be explained by the scaling between structural components of sperm cells. It is impossible to consistently predict sperm swimming speed from knowledge of length parameter alone, so it is not surprising that previous studies attempting to link the two have been unsuccessful. However, use of the ratio of head to flagellum length can provide insight into swimming velocity.

We focus on sperm length to illustrate that the simple measures used in the majority of sperm competition studies are inadequate to allow proper understanding of the link between sperm morphology and swimming speed. However, flagellar beat dynamics are a primary determinant of swimming speed [14, 71, 73, 77] with swimming velocity highly dependent on the beat amplitude of the flagella. Thus future studies should attempt to characterise sperm kinematics if we are to fully understand the link between morphology and velocity of sperm.