BACKGROUND
although several theories regarding the evolution of sperm size exist , there is a general assumption in the literature on sperm competition that selection will favour males with longer sperm, due to their enhanced swimming velocity and therefore competitiveness.
this assumption rests broadly on three observations.
first, a number of comparative studies have reported that sperm are on average longer in polyandrous species compared to monandrous species .
these evolutionary associations are generally taken as evidence that selection for enhanced sperm competitive ability favours increased sperm length in polyandrous species, where females mate with more than one male during a single reproductive episode and sperm from different males must compete to fertilize available ova  <cit> .
second, a handful of studies have reported that relative sperm size can be associated with competitive fertilization success .
and third, four studies have reported that sperm swimming velocity, and therefore possibly sperm competitiveness, covaries with some measure of sperm length, hinting at a functional relationship between these phenotypic traits  <cit> .
while the first two of these observations are correlational, the last suggests a mechanistic relationship linking sperm structure to function.
however, empirical evidence of such a link is conflicting .
explaining why longer sperm might be more competitive than shorter ones, and how selection acts on this difference, is fundamental to our understanding of sperm evolution.
thus, our aim here is to re-evaluate the proposed link between sperm length and swimming speed using theory from physics and biomechanics.
we explore the hydrodynamic environment in which sperm operate, which we argue invalidates common assumptions that link sperm shape and length to swimming velocity.
we then argue that because of the underlying hydrodynamic interactions governing sperm motion, there is no reason to expect a simple association between sperm length and sperm velocity.
instead, we propose alternative measures that take account of these interactions in an attempt to guide future studies that link sperm competition with sperm evolution.
we argue that the focus on sperm speed and length has come at the expense of neglecting alternative mechanisms that can help explain a wider variety of the data available.
key: +, positive correlation between length and speed; -, negative correlation between length and speed; and  <dig>  correlation analysis performed, but no relationship between length and speed found.
methods and
RESULTS
insight from physics
we argue that the complex physical constraints governing sperm locomotion may obscure simple relationships between sperm length and swimming velocity, thus accounting for the inconsistent patterns of covariance between these traits reported in the literature.
to illustrate this, we first explore the hydrodynamic environment in which sperm operate, which we argue invalidates common assumptions that link sperm shape and length to swimming velocity.
shape and drag
the diversity of sperm size and shape is considerable , but in general the body plan of a flagellate spermatozoon follows the pattern of a head containing the nuclear material, a midpiece containing mitochondria, and a tail based on the eukaryotic flagellum.
superficially, the shape of the tail and the motion of swimming are eel-like, and it is often assumed that locomotion too works in a similar way.
however, small size and low swimming speeds mean that, in hydrodynamic terms, sperm operate in a very different regime from the one that we are used to.
this regime can be defined by the use of the reynolds number, which is equal to the relative ratio between inertia and viscosity.
the reynolds number is given by re = ul/μ, where u is speed, l is a characteristic length of the object of interest , and μ is the kinematic viscosity of the fluid relative to which the object is moving.
in the context of biology, size and speed tend to be positively correlated  <cit> , so that in their natural environments small organisms operate in a low reynolds number regime  <cit> .
streamlining, the modification of shape to reduce drag, is commonly seen in human vehicles, as well as in birds, fish, insects and aquatic mammals.
streamlining acts to reduce the costs of transport by reducing the amount of resistance that the body experiences while moving through a fluid, by delaying separation of the flow from the surface of the object.
the idea that the more streamlined the sperm head appears to be, the faster it will be able to swim is attractive, but misguided .
this is because sperm operate in a low reynolds number world  <cit>  where our intuition is often wrong.
in fact, the very concept of streamlining at low reynolds numbers is invalid, as streamline separation only occurs when inertia becomes the dominant force at work.
the peculiarities of life at low reynolds number mean that the conventional idea of streamlining is at best futile .
the knowledge that a streamlined shape reduces drag in the reynolds number regime of our own experience , however, is a compelling idea and has propagated several misconceptions in the literature when applied to low reynolds number conditions.
indeed, the processes of fluid movement are often so counter-intuitive that problems with interpretation exist throughout biology .
although streamlining has rarely been implicated directly in determining sperm swimming velocity , the belief that streamlining is a 'good thing' appears to be widespread  <cit> .
for example, moore & taggart  <cit>  suggest that sperm pairing in the opossum monodelphis domestica, allows the two sperm heads to form a more hydrodynamic unit than a single head.
however, any reduction in drag is unlikely to offset the additional drag of a larger head unit.
the combined beating and synchronisation of the two flagella  <cit>  is, we think, a more probable explanation for the increased velocity recorded, given the energetic advantages of similar coordination in cilia  <cit> .
in another study, malo et al.
<cit>  concluded that the shape of the sperm head of red deer, cervus elaphus hispanicus, is a key determinant of their swimming speed.
while the reasoning of these papers is essentially sound from the perspective of the human scale, the complexity of the underlying fluid dynamics means that intuition regarding movement in fluids has been misguidedly applied to the low reynolds number regime experienced by sperm.
the mismeasure of length
with the differences between locomotion of sperm and of larger organisms in mind, we now ask whether sperm length should influence sperm swimming velocity.
there seems to be a persistent trend to cite katz & drobnis  <cit>  and gomendio & roldan  <cit>  as support for the idea that sperm or flagellum length is proportional to, and so determines, swimming speed.
an examination of the literature provides  <dig> cases  where one or both of these papers are cited as evidence for a link between sperm or flagellum length and swimming speed.
however, the points made by katz & drobnis  <cit>  have frequently been misinterpreted.
katz & drobnis  <cit>  discuss the forces generated by sperm movement, focusing in particular on forces generated by sperm in contact with the egg.
a key statement in their conclusion is that "in general, the longer the sperm flagellum, the greater the forces generated by its motions" .
katz & drobnis are perfectly correct in this assertion, but unfortunately it appears to have been consistently misread: the statement only deals with the forces generated by the flagellum.
in the case discussed by katz & drobnis  <cit>  the force generated by the flagellum is applied to an effectively stationary egg, a very different situation to the case of a free-swimming sperm.
when any object moves through a medium at a constant speed the thrust  required is balanced by the drag  experienced as it moves through the medium.
we can simplify the case of a swimming sperm by assuming that only the flagellum produces thrust and only the head produces drag.
if we assume, as do katz & drobnis  <cit> , that the force  produced by the flagellum is proportional to it's length , in addition we can say that the drag due to the head is proportional to some measure of it's size , and the velocity at which it travels .
given that surface area will be proportional to the square of some linear head measure , we now have a simple relationship for the balanced forces:
lt∝dh2u
from which we can see that
u∝ltdh <dig>
the speed attained by the sperm will therefore be proportional to the balance between drag from the head and thrust from the flagellum.
we can simplify this further by noting that if lt >> dh, the ratio given above  tends to lt/dh as lt increases.
as a result we suggest that the ratio between flagellum and head length may provide a reasonable predictor for sperm swimming speed.
an alternative, but more complex measure would be the ratio between flagellum length and the surface area of the head.
assuming that the head approximates a prolate spheroid, its surface area ah can be estimated from
ah=2πlh2+2πlhwhesin⁡−1e
where lh is the length of the head , wh is its width , and e is the ellipticity of the spheroid, given by
e=1−lh2wh <dig>
the arguments above suggest that, while force generation does indeed increase with flagellum length, the implications of this for swimming speed are strongly dependent on the size  of the head and the drag that it generates.
in fact, in table  <dig> and additional file  <dig> we show that, because of these underlying hydrodynamic interactions, there is no reason to expect an association between sperm length and sperm velocity.
comparative studies indicate that head length tends to covary with flagellum length with either isometry or a positive allometry  <cit>  .
this diversity of patterns in head to flagellum scaling in different groups can explain the diversity of total length to velocity relationships found in the literature .
a corollary of the above arguments is that several relationships between flagellum and head lengths result in a total length-to-velocity relationship that is an asymptotic function of total length .
this has an important implication, in that if total length is selected upon by the female reproductive tract  increasing sperm length  is not detrimental to the sperm's swimming speed.
this suggests that past a critical total length we can expect selection for speed to be weakened such that further elongation of the flagellum with respect to a given head size does not change the speed of the sperm.
in these instances, selection on flagellum or total length, for example via cryptic female choice , can act to influence sperm length without detrimental effects on swimming speed.
discussion
we suggest that, irrespective of which measure  is used, attempts to correlate any single measure of length to speed are likely to be futile.
in fact, we argue that the rather confusing patterns reported in the literature are due to the use of single measures of sperm length, and that accounting for the balance between drag from the head and thrust from the flagellum will allow us to extend our understanding of the link between sperm form and function.
in this context, we start our discussion by reviewing the literature on sperm length in order to address three key questions relating to the assumption that longer sperm swim faster and are more competitive:
does sperm competition favour increased sperm length?
a number of studies suggest that the selective pressure of sperm competition extends beyond simply favouring males producing larger ejaculates .
for example, it is commonly argued that longer sperm will be favoured by selection for increased swimming performance, and therefore enhanced competitiveness  <cit> .
other theories include links between sperm length and longevity  <cit> , between midpiece size and energy availability  <cit> , and between size and ability to displace smaller sperm from the female tract  <cit> .
these ideas have gained weight in the light of several comparative studies that show that average sperm lengths are greater in species where polyandry  is more prevalent  <cit> .
however, this pattern is not universal and the magnitude of sperm competition can be negatively associated with sperm length  <cit> , while in other groups there is no significant association between indices of sperm competition  and sperm length .
across species of passerine birds, positive-, negative- and no- relationship have all been found between levels of sperm competition and sperm midpiece length  <cit> , while in primates the volume of the midpiece is greater in species with relatively large testes and polyandrous mating systems  <cit> .
snook  <cit>  summarizes most of these studies in her table  <dig>  in short, the comparative data clearly fail to show a consistent relationship between the risk  or intensity  of sperm competition and sperm length.
does sperm length enhance competitive success?
few studies have tested specifically whether variation in relative sperm length among rival males influences competitive fertilization success, and thus whether intrasexual selection has the potential to act on this trait.
two studies have reported a fertilization advantage for relatively larger sperm in species with aflagellate amoeboid sperm  <cit> .
however, we are here concerned with the structure and function of flagellate sperm.
in the snail viviparus ater the length of oligopyrene sperm was the best predictor of relative paternity, explaining 38% of the deviance in second male paternity in competitive fertilization trials  <cit> .
however, oligopyrene sperm do not contain the full complement of chromosomes and do not fertilize eggs.
while the function of oligopyrene sperm remains unknown, it is clear that these data cannot be taken as evidence for a functional relationship between the length and performance of fertilizing sperm.
while gage et al.
<cit>  failed to find a relationship between total sperm length and competitive fertilization success in atlantic salmon salmo salar, vladiæ et al.
<cit>  reported that in this species the length of the flagellum's end piece did predict fertilization ability.
by contrast, gage & morrow  <cit>  reported that crickets with relatively shorter sperm have a fertilization advantage, while others report no evidence for a role of sperm length in influencing competitive fertilization success in crickets  <cit> , or bluegill sunfish  <cit> .
does sperm length predict swimming speed?
empirical evidence that sperm swimming speed is a positive function of a measure of sperm length is limited .
a positive relationship between total sperm length and maximum sperm swimming velocity was reported in a comparative study across five species of mammal  <cit> , with recent reanalysis and control for phylogeny at the family level providing further support  <cit> .
in an intraspecific study of red deer, malo et al.
<cit>  found that sperm with shorter midpieces but longer heads and longer relative components of the flagella swam more quickly than sperm with long midpieces, shorter heads and relatively shorter flagella components.
while cardullo & baltz  <cit>  postulate a link between energy supply, speed and the determination of flagellum length by mitochondrial volume.
pitcher et al  <cit>  reported a positive relationship between head length and speed in the guppy, poecilia reticulata, but not between other length measures.
elsewhere, others have failed to establish a relationship between sperm swimming speeds and any component of sperm length .
for example, minoretti and baur  <cit>  found no relationship between total sperm length and sperm swimming velocity in the hermaphroditic land snail arianta arbustorum.
likewise, birkhead et al.
's  <cit>  study of zebra finches taeniopygia guttata revealed no evidence that the length of the sperm flagellum, midpiece or tail were correlated with sperm swimming speed, while gage et al.
<cit>  similarly found no relationship between total sperm or flagella length and sperm motility in atlantic salmon salmo salar.
the assertion that longer sperm exhibit faster swimming velocities is therefore largely unsupported by the available evidence.
female-derived effects on sperm evolution
finally, while the simplicity of relating morphology to velocity in sperm is attractive, a further source of selection on sperm phenotype comes from cryptic female choice  <cit> .
for example, in internally fertilizing species, sperm must operate inside the females' reproductive tract.
due to conditions that engineers call 'wall effects', the lining of the female reproductive tract can have important effects on sperm performance, because the movement of fluid generated by a swimming sperm becomes constrained when it approaches a solid boundary .
this 'wall effect' can take several forms, the two most commonly studied of which have been changes in swimming speed, and attraction of the sperm to the wall surface.
all sperm encounter solid surfaces in the form of the egg, but in internally fertilizing species, the female reproductive tract means that a solid  surface is present for the entire functional lifetime of the sperm.
in addition to influencing movement of sperm in internal fertilizers, and providing a potential mechanism allowing females to manipulate sperm in vivo, the unfortunate combination of speed changes due to the presence of boundaries, and attraction to those boundaries, poses a potential problem for current sperm velocity measurement techniques in vitro, and the biological significance of those patterns.
velocity measurements from samples on slides may not be truly comparable between studies if the impact of wall effects is not quantified, and the swimming velocities achieved by sperm on slides may not represent those achieved in their natural environments.
the potential importance of female-derived effects can be seen in the increasing body of comparative work on mammals  <cit> , birds  <cit> , and insects  <cit>  showing that sperm length is positively associated with the length of the sperm storage organs of females.
interestingly, closer examination of the relationship between sperm competition and sperm length in birds reveals that it is selection from the female reproductive tract that directly explains variation in sperm length  <cit> .
thus, sperm length appears to respond positively to evolutionary increases in female reproductive tract dimensions  <cit> .
female sperm choice, mediated by active transport of sperm by the female coupled with variation in female reproductive tract morphology, therefore seems a highly plausible hypothesis to help explain sperm-female coevolution.
we also note that there is no a priori reason to expect cryptic female choice to favour long or short sperm.
indeed, female choice often imposes divergent patterns of selection across taxonomic groups so that positive or negative associations between sperm length and the degree of polyandry are equally accommodated by the cryptic female choice hypothesis.
garcía-gonzález and simmons  <cit>  have recently shown that in dung beetles  males with relatively short sperm enjoy higher reproductive success than their longer-sperm rivals during competitive fertilization trials.
however, in their study they also showed that the success of males with different sperm lengths was contingent on the size of the female's sperm storage organs: the advantage of shorter sperm was greater when competing for fertilization in females with larger spermathecae  <cit> .
crucially, a recent quantitative genetic analysis of male and female reproductive traits confirmed that sperm length is genetically correlated  with spermathecal size  <cit> , providing explicit support for the evolution of sperm phenotypes via cryptic female choice.
the results from dung beetles parallel previous findings in drosophila melanogaster, where sperm length likewise interacts with female reproductive tract morphology to determine the reproductive success of competing ejaculates  <cit> .
in the case of drosophila, however, males with longer sperm have the fertilization advantage, illustrating the divergent nature of cryptic female choice acting on sperm morphology.
again, these studies also provided evidence that increased sperm length was genetically correlated with female reproductive tract morphology: selection for increased seminal receptacle length in female d. melanogaster generated a correlated response in sperm length, a result expected if these traits are in linkage disequilibrium  <cit> .
CONCLUSIONS
it seems clear that some assumptions regarding the physics of sperm locomotion have hampered our progress in understanding the processes mediating sperm competition.
this synthesis of literature from diverse fields highlights the problems of thinking about biological evolution in isolation from physical constraints.
while relating sperm length to speed has clear implications for sperm competition, there is a lack of consistent evidence linking the two.
however, by taking account of fluid dynamic interactions it is possible to reconcile these conflicting patterns, which should allow future work in this area to progress rapidly.
scaling of the flagellum:head ratio may be more important than simplistic ideas of large and small sperm with differing morphologies.
however, due to the influence of wall effects, sperm competition is unlikely to act on sperm length and motility in isolation from female effects.
this suggests to us that definitive links between and measure of sperm length are unlikely to be found consistently in internally fertilising species, further complicating any attempts to correlate length to swimming speed.
nonetheless, incorporating realistic fluid dynamics into our theories should enable progress in this area.
we recommend that future studies examine the flagellum:head ratio as a potential link between sperm form and function, but recognise that its use is particularly appropriate for external fertilisers, as this group will be least affected by wall effects, and has almost instantaneous fertilisation so that sperm longevity can be ignored.
while external fertilisers may offer the best opportunity to test our ideas, internal fertilisers will also be affected in the same way, albeit with the additional effects of walls and other mechanisms of female cryptic choice.
we also advocate the reporting of slide-well depths and sperm diameters in all studies and encourage the development of velocity measurement methods less influenced by wall effects than current techniques.
we suggest that physical constraints on sperm swimming ability, coupled with the potential for sperm-female coevolution, demand a critical reappraisal of the belief that sperm competition selects for longer, more powerful sperm.
taking account of physics in this way may lead to the development of a framework that allows for non-mutually exclusive alternative explanations for why sperm phenotype seems to exhibit such great variation.
authors' contributions
sh carried out the mathematical analysis.
all authors jointly conceived of the study, helped to draft, and approved, the final manuscript.
supplementary material
additional file 1
supplementary materials.
click here for file
acknowledgements
sh is funded by a nerc advanced fellowship, and jpe and lws are funded by the australian research council.

 although several theories regarding the evolution of sperm size exist, there is a general assumption in the literature on sperm competition that selection will favour males with longer sperm, due to their enhanced swimming velocity and therefore competitiveness. this assumption rests broadly on three observations. first, a number of comparative studies have reported that sperm are on average longer in polyandrous species compared to monandrous species. these evolutionary associations are generally taken as evidence that selection for enhanced sperm competitive ability favours increased sperm length in polyandrous species, where females mate with more than one male during a single reproductive episode and sperm from different males must compete to fertilize available ova. second, a handful of studies have reported that relative sperm size can be associated with competitive fertilization success. and third, four studies have reported that sperm swimming velocity, and therefore possibly sperm competitiveness, covaries with some measure of sperm length, hinting at a functional relationship between these phenotypic traits. while the first two of these observations are correlational, the last suggests a mechanistic relationship linking sperm structure to function. however, empirical evidence of such a link is conflicting. explaining why longer sperm might be more competitive than shorter ones, and how selection acts on this difference, is fundamental to our understanding of sperm evolution. thus, our aim here is to re-evaluate the proposed link between sperm length and swimming speed using theory from physics and biomechanics. we explore the hydrodynamic environment in which sperm operate, which we argue invalidates common assumptions that link sperm shape and length to swimming velocity. we then argue that because of the underlying hydrodynamic interactions governing sperm motion, there is no reason to expect a simple association between sperm length and sperm velocity. instead, we propose alternative measures that take account of these interactions in an attempt to guide future studies that link sperm competition with sperm evolution. we argue that the focus on sperm speed and length has come at the expense of neglecting alternative mechanisms that can help explain a wider variety of the data available. key: +, positive correlation between length and speed; -, negative correlation between length and speed; and correlation analysis performed, but no relationship between length and speed found. methods and  insight from physics we argue that the complex physical constraints governing sperm locomotion may obscure simple relationships between sperm length and swimming velocity, thus accounting for the inconsistent patterns of covariance between these traits reported in the literature. to illustrate this, we first explore the hydrodynamic environment in which sperm operate, which we argue invalidates common assumptions that link sperm shape and length to swimming velocity. shape and drag the diversity of sperm size and shape is considerable, but in general the body plan of a flagellate spermatozoon follows the pattern of a head containing the nuclear material, a midpiece containing mitochondria, and a tail based on the eukaryotic flagellum. superficially, the shape of the tail and the motion of swimming are eel-like, and it is often assumed that locomotion too works in a similar way. however, small size and low swimming speeds mean that, in hydrodynamic terms, sperm operate in a very different regime from the one that we are used to. this regime can be defined by the use of the reynolds number, which is equal to the relative ratio between inertia and viscosity. the reynolds number is given by re = ul/μ, where u is speed, l is a characteristic length of the object of interest, and μ is the kinematic viscosity of the fluid relative to which the object is moving. in the context of biology, size and speed tend to be positively correlated, so that in their natural environments small organisms operate in a low reynolds number regime. streamlining, the modification of shape to reduce drag, is commonly seen in human vehicles, as well as in birds, fish, insects and aquatic mammals. streamlining acts to reduce the costs of transport by reducing the amount of resistance that the body experiences while moving through a fluid, by delaying separation of the flow from the surface of the object. the idea that the more streamlined the sperm head appears to be, the faster it will be able to swim is attractive, but misguided. this is because sperm operate in a low reynolds number world where our intuition is often wrong. in fact, the very concept of streamlining at low reynolds numbers is invalid, as streamline separation only occurs when inertia becomes the dominant force at work. the peculiarities of life at low reynolds number mean that the conventional idea of streamlining is at best futile. the knowledge that a streamlined shape reduces drag in the reynolds number regime of our own experience, however, is a compelling idea and has propagated several misconceptions in the literature when applied to low reynolds number conditions. indeed, the processes of fluid movement are often so counter-intuitive that problems with interpretation exist throughout biology. although streamlining has rarely been implicated directly in determining sperm swimming velocity, the belief that streamlining is a'good thing' appears to be widespread. for example, moore & taggart suggest that sperm pairing in the opossum monodelphis domestica, allows the two sperm heads to form a more hydrodynamic unit than a single head. however, any reduction in drag is unlikely to offset the additional drag of a larger head unit. the combined beating and synchronisation of the two flagella is, we think, a more probable explanation for the increased velocity recorded, given the energetic advantages of similar coordination in cilia. in another study, malo et al. concluded that the shape of the sperm head of red deer, cervus elaphus hispanicus, is a key determinant of their swimming speed. while the reasoning of these papers is essentially sound from the perspective of the human scale, the complexity of the underlying fluid dynamics means that intuition regarding movement in fluids has been misguidedly applied to the low reynolds number regime experienced by sperm. the mismeasure of length with the differences between locomotion of sperm and of larger organisms in mind, we now ask whether sperm length should influence sperm swimming velocity. there seems to be a persistent trend to cite katz & drobnis and gomendio & roldan as support for the idea that sperm or flagellum length is proportional to, and so determines, swimming speed. an examination of the literature provides cases where one or both of these papers are cited as evidence for a link between sperm or flagellum length and swimming speed. however, the points made by katz & drobnis have frequently been misinterpreted. katz & drobnis discuss the forces generated by sperm movement, focusing in particular on forces generated by sperm in contact with the egg. a key statement in their conclusion is that "in general, the longer the sperm flagellum, the greater the forces generated by its motions". katz & drobnis are perfectly correct in this assertion, but unfortunately it appears to have been consistently misread: the statement only deals with the forces generated by the flagellum. in the case discussed by katz & drobnis the force generated by the flagellum is applied to an effectively stationary egg, a very different situation to the case of a free-swimming sperm. when any object moves through a medium at a constant speed the thrust required is balanced by the drag experienced as it moves through the medium. we can simplify the case of a swimming sperm by assuming that only the flagellum produces thrust and only the head produces drag. if we assume, as do katz & drobnis, that the force produced by the flagellum is proportional to it's length, in addition we can say that the drag due to the head is proportional to some measure of it's size, and the velocity at which it travels. given that surface area will be proportional to the square of some linear head measure, we now have a simple relationship for the balanced forces: lt∝dh2u from which we can see that u∝ltdh the speed attained by the sperm will therefore be proportional to the balance between drag from the head and thrust from the flagellum. we can simplify this further by noting that if lt >> dh, the ratio given above tends to lt/dh as lt increases. as a result we suggest that the ratio between flagellum and head length may provide a reasonable predictor for sperm swimming speed. an alternative, but more complex measure would be the ratio between flagellum length and the surface area of the head. assuming that the head approximates a prolate spheroid, its surface area ah can be estimated from ah=2πlh2+2πlhwhesin⁡−1e where lh is the length of the head, wh is its width, and e is the ellipticity of the spheroid, given by e=1−lh2wh the arguments above suggest that, while force generation does indeed increase with flagellum length, the implications of this for swimming speed are strongly dependent on the size of the head and the drag that it generates. in fact, in table and additional file we show that, because of these underlying hydrodynamic interactions, there is no reason to expect an association between sperm length and sperm velocity. comparative studies indicate that head length tends to covary with flagellum length with either isometry or a positive allometry. this diversity of patterns in head to flagellum scaling in different groups can explain the diversity of total length to velocity relationships found in the literature. a corollary of the above arguments is that several relationships between flagellum and head lengths result in a total length-to-velocity relationship that is an asymptotic function of total length. this has an important implication, in that if total length is selected upon by the female reproductive tract increasing sperm length is not detrimental to the sperm's swimming speed. this suggests that past a critical total length we can expect selection for speed to be weakened such that further elongation of the flagellum with respect to a given head size does not change the speed of the sperm. in these instances, selection on flagellum or total length, for example via cryptic female choice, can act to influence sperm length without detrimental effects on swimming speed. discussion we suggest that, irrespective of which measure is used, attempts to correlate any single measure of length to speed are likely to be futile. in fact, we argue that the rather confusing patterns reported in the literature are due to the use of single measures of sperm length, and that accounting for the balance between drag from the head and thrust from the flagellum will allow us to extend our understanding of the link between sperm form and function. in this context, we start our discussion by reviewing the literature on sperm length in order to address three key questions relating to the assumption that longer sperm swim faster and are more competitive: does sperm competition favour increased sperm length? a number of studies suggest that the selective pressure of sperm competition extends beyond simply favouring males producing larger ejaculates. for example, it is commonly argued that longer sperm will be favoured by selection for increased swimming performance, and therefore enhanced competitiveness. other theories include links between sperm length and longevity, between midpiece size and energy availability, and between size and ability to displace smaller sperm from the female tract. these ideas have gained weight in the light of several comparative studies that show that average sperm lengths are greater in species where polyandry is more prevalent. however, this pattern is not universal and the magnitude of sperm competition can be negatively associated with sperm length, while in other groups there is no significant association between indices of sperm competition and sperm length. across species of passerine birds, positive-, negative- and no- relationship have all been found between levels of sperm competition and sperm midpiece length, while in primates the volume of the midpiece is greater in species with relatively large testes and polyandrous mating systems. snook summarizes most of these studies in her table in short, the comparative data clearly fail to show a consistent relationship between the risk or intensity of sperm competition and sperm length. does sperm length enhance competitive success? few studies have tested specifically whether variation in relative sperm length among rival males influences competitive fertilization success, and thus whether intrasexual selection has the potential to act on this trait. two studies have reported a fertilization advantage for relatively larger sperm in species with aflagellate amoeboid sperm. however, we are here concerned with the structure and function of flagellate sperm. in the snail viviparus ater the length of oligopyrene sperm was the best predictor of relative paternity, explaining 38% of the deviance in second male paternity in competitive fertilization trials. however, oligopyrene sperm do not contain the full complement of chromosomes and do not fertilize eggs. while the function of oligopyrene sperm remains unknown, it is clear that these data cannot be taken as evidence for a functional relationship between the length and performance of fertilizing sperm. while gage et al. failed to find a relationship between total sperm length and competitive fertilization success in atlantic salmon salmo salar, vladiæ et al. reported that in this species the length of the flagellum's end piece did predict fertilization ability. by contrast, gage & morrow reported that crickets with relatively shorter sperm have a fertilization advantage, while others report no evidence for a role of sperm length in influencing competitive fertilization success in crickets, or bluegill sunfish. does sperm length predict swimming speed? empirical evidence that sperm swimming speed is a positive function of a measure of sperm length is limited. a positive relationship between total sperm length and maximum sperm swimming velocity was reported in a comparative study across five species of mammal, with recent reanalysis and control for phylogeny at the family level providing further support. in an intraspecific study of red deer, malo et al. found that sperm with shorter midpieces but longer heads and longer relative components of the flagella swam more quickly than sperm with long midpieces, shorter heads and relatively shorter flagella components. while cardullo & baltz postulate a link between energy supply, speed and the determination of flagellum length by mitochondrial volume. pitcher et al reported a positive relationship between head length and speed in the guppy, poecilia reticulata, but not between other length measures. elsewhere, others have failed to establish a relationship between sperm swimming speeds and any component of sperm length. for example, minoretti and baur found no relationship between total sperm length and sperm swimming velocity in the hermaphroditic land snail arianta arbustorum. likewise, birkhead et al.'s study of zebra finches taeniopygia guttata revealed no evidence that the length of the sperm flagellum, midpiece or tail were correlated with sperm swimming speed, while gage et al. similarly found no relationship between total sperm or flagella length and sperm motility in atlantic salmon salmo salar. the assertion that longer sperm exhibit faster swimming velocities is therefore largely unsupported by the available evidence. female-derived effects on sperm evolution finally, while the simplicity of relating morphology to velocity in sperm is attractive, a further source of selection on sperm phenotype comes from cryptic female choice. for example, in internally fertilizing species, sperm must operate inside the females' reproductive tract. due to conditions that engineers call'wall effects', the lining of the female reproductive tract can have important effects on sperm performance, because the movement of fluid generated by a swimming sperm becomes constrained when it approaches a solid boundary. this'wall effect' can take several forms, the two most commonly studied of which have been changes in swimming speed, and attraction of the sperm to the wall surface. all sperm encounter solid surfaces in the form of the egg, but in internally fertilizing species, the female reproductive tract means that a solid surface is present for the entire functional lifetime of the sperm. in addition to influencing movement of sperm in internal fertilizers, and providing a potential mechanism allowing females to manipulate sperm in vivo, the unfortunate combination of speed changes due to the presence of boundaries, and attraction to those boundaries, poses a potential problem for current sperm velocity measurement techniques in vitro, and the biological significance of those patterns. velocity measurements from samples on slides may not be truly comparable between studies if the impact of wall effects is not quantified, and the swimming velocities achieved by sperm on slides may not represent those achieved in their natural environments. the potential importance of female-derived effects can be seen in the increasing body of comparative work on mammals, birds, and insects showing that sperm length is positively associated with the length of the sperm storage organs of females. interestingly, closer examination of the relationship between sperm competition and sperm length in birds reveals that it is selection from the female reproductive tract that directly explains variation in sperm length. thus, sperm length appears to respond positively to evolutionary increases in female reproductive tract dimensions. female sperm choice, mediated by active transport of sperm by the female coupled with variation in female reproductive tract morphology, therefore seems a highly plausible hypothesis to help explain sperm-female coevolution. we also note that there is no a priori reason to expect cryptic female choice to favour long or short sperm. indeed, female choice often imposes divergent patterns of selection across taxonomic groups so that positive or negative associations between sperm length and the degree of polyandry are equally accommodated by the cryptic female choice hypothesis. garcía-gonzález and simmons have recently shown that in dung beetles males with relatively short sperm enjoy higher reproductive success than their longer-sperm rivals during competitive fertilization trials. however, in their study they also showed that the success of males with different sperm lengths was contingent on the size of the female's sperm storage organs: the advantage of shorter sperm was greater when competing for fertilization in females with larger spermathecae. crucially, a recent quantitative genetic analysis of male and female reproductive traits confirmed that sperm length is genetically correlated with spermathecal size, providing explicit support for the evolution of sperm phenotypes via cryptic female choice. the results from dung beetles parallel previous findings in drosophila melanogaster, where sperm length likewise interacts with female reproductive tract morphology to determine the reproductive success of competing ejaculates. in the case of drosophila, however, males with longer sperm have the fertilization advantage, illustrating the divergent nature of cryptic female choice acting on sperm morphology. again, these studies also provided evidence that increased sperm length was genetically correlated with female reproductive tract morphology: selection for increased seminal receptacle length in female d. melanogaster generated a correlated response in sperm length, a result expected if these traits are in linkage disequilibrium.  it seems clear that some assumptions regarding the physics of sperm locomotion have hampered our progress in understanding the processes mediating sperm competition. this synthesis of literature from diverse fields highlights the problems of thinking about biological evolution in isolation from physical constraints. while relating sperm length to speed has clear implications for sperm competition, there is a lack of consistent evidence linking the two. however, by taking account of fluid dynamic interactions it is possible to reconcile these conflicting patterns, which should allow future work in this area to progress rapidly. scaling of the flagellum:head ratio may be more important than simplistic ideas of large and small sperm with differing morphologies. however, due to the influence of wall effects, sperm competition is unlikely to act on sperm length and motility in isolation from female effects. this suggests to us that definitive links between and measure of sperm length are unlikely to be found consistently in internally fertilising species, further complicating any attempts to correlate length to swimming speed. nonetheless, incorporating realistic fluid dynamics into our theories should enable progress in this area. we recommend that future studies examine the flagellum:head ratio as a potential link between sperm form and function, but recognise that its use is particularly appropriate for external fertilisers, as this group will be least affected by wall effects, and has almost instantaneous fertilisation so that sperm longevity can be ignored. while external fertilisers may offer the best opportunity to test our ideas, internal fertilisers will also be affected in the same way, albeit with the additional effects of walls and other mechanisms of female cryptic choice. we also advocate the reporting of slide-well depths and sperm diameters in all studies and encourage the development of velocity measurement methods less influenced by wall effects than current techniques. we suggest that physical constraints on sperm swimming ability, coupled with the potential for sperm-female coevolution, demand a critical reappraisal of the belief that sperm competition selects for longer, more powerful sperm. taking account of physics in this way may lead to the development of a framework that allows for non-mutually exclusive alternative explanations for why sperm phenotype seems to exhibit such great variation. authors' contributions sh carried out the mathematical analysis. all authors jointly conceived of the study, helped to draft, and approved, the final manuscript. supplementary material additional file 1 supplementary materials. click here for file acknowledgements sh is funded by a nerc advanced fellowship, and jpe and lws are funded by the australian research council.
using information from physics, biomechanics and evolutionary biology, we explore the implications of physical constraints on sperm performance, and review empirical evidence for links between sperm length and sperm competition. a common theme in the literature on sperm competition is that selection for increased sperm performance in polyandrous species will favour the evolution of longer, and therefore faster swimming, sperm. this argument is based on the common assumption that sperm swimming velocity is directly related to sperm length, due to the increased thrust produced by longer flagella. we critically evaluate the evidence for links between sperm morphology and swimming speed, and draw on cross-disciplinary studies to show that the assumption that velocity is directly related to sperm length will rarely be satisfied in the microscopic world in which sperm operate. we show that increased sperm length is unlikely to be driven by selection for increased swimming speed, and that the relative lengths of a sperm's constituent parts, rather than their absolute lengths, are likely to be the target of selection.
 using information from physics, biomechanics and evolutionary biology, we explore the implications of physical constraints on sperm performance, and review empirical evidence for links between sperm length and sperm competition. a common theme in the literature on sperm competition is that selection for increased sperm performance in polyandrous species will favour the evolution of longer, and therefore faster swimming, sperm. this argument is based on the common assumption that sperm swimming velocity is directly related to sperm length, due to the increased thrust produced by longer flagella.  we critically evaluate the evidence for links between sperm morphology and swimming speed, and draw on cross-disciplinary studies to show that the assumption that velocity is directly related to sperm length will rarely be satisfied in the microscopic world in which sperm operate.  we show that increased sperm length is unlikely to be driven by selection for increased swimming speed, and that the relative lengths of a sperm's constituent parts, rather than their absolute lengths, are likely to be the target of selection. all else being equal, we suggest that a simple measure of the ratio of head to tail length should be used to assess the possible link between morphology and speed. however, this is most likely to be the case for external fertilizers in which females have relatively limited opportunity to influence a sperm's motility. 