Our study revealed a strong positive association between the shape and the curvature of the apical hook of murine sperm and the risk of sperm competition inferred from relative testis mass. Our results are the first evidence that the shape and curvature of the apical hook of rodent sperm heads is influenced by the risk of sperm competition, and that sperm cooperation is likely to be a general pattern in rodents that may have evolved in response to sperm competition.
Sperm competition may be divided into (i) the competition between sperm of rival males (inter-male sperm competition due to diploid selection 
), and (ii) the competition among the sperm from a single male's ejaculate (intra-male sperm competition due to haploid selection 
). In the European woodmouse, it has been shown that only those sperm at the tip of a ‘train’ are capable of fertilisation whereas all others undergo the acrosome reaction to separate from each other, rendering them infertile 
. If sperm cooperation is costly to some sperm and beneficial to others sperm within one ejaculate might compete for the benefiting position. Therefore, if sperm cooperation increases the fertilisation success of a male in sperm competition, diploid selection is expected to drive the evolution of sperm cooperation, whereas haploid selection opposes sperm cooperation if cooperation is costly. The genetic relationship between the sperm of one male is 0.5 which is the same relationship as between full siblings. Therefore, Hamilton's rule for the evolution of cooperation applies 
and sperm cooperation may still evolve despite haploid genetic influences if the selective pressure (e.g., due to high risk of sperm competition) is intense enough 
. Sperm cooperation occurs in other taxonomic groups 
and in American marsupials, paired sperm perform better in viscous media than individual sperm 
, and in the fishfly, Parachauliodes japonicus
, swimming velocity increases with increasing number of sperm composing a sperm bundle 
The observation of sperm groups in the Norway rat and the house mouse is consistent with our hypothesis that the apical hook plays a role in sperm cooperation in rodents, although in these species the main function of the hook appears to be to maintain the stability of sperm groups rather than the actual attachment of sperm to each other. As in the European woodmouse 
, in the Norway rat and the house mouse sperm attached to each other at the lower ventral region of the apical hook. In the latter two species, as soon as a group was formed the hook appeared to prevent the random detachment of sperm. Sperm separated themselves from the group only by moving rigidly forward. In the European woodmouse, electron-dense adhesive material has been found in the inner curvature of the hook 
which may facilitate attachment between individual sperm. A similar mechanism might exist in the sperm of the Norway rat and the house mouse. The hypothesis of the stabilising effect of the hook on group formation is supported by the fact that the shape and curvature hook appear to influence the duration for which sperm remain attached to each other: in the Norway rat and in the house mouse, sperm stayed as a group in vitro
for a maximum of 10 minutes compared to a maximum of 90 minutes in the European woodmouse. In addition, the apical hook in the European woodmouse is flexible and actively moves to lock up with either the hook or flagellum of another sperm which might influence the stability of sperm train formation. No such movement was observed in the Norway rat or house mouse.
The functional significance of sperm groups in rodents is not yet fully understood. An advantage in straight-line velocity does not hold in the house mouse where individual sperm were faster than sperm groups. It is possible that although the sperm groups in the house mouse are slower than individual sperm, they have greater thrusting force. In the European wood mouse, sperm ‘trains’ exhibited increased thrusting force in viscous media 
, which may be advantageous for example to penetrate the cervical mucus in the female reproductive tract. Alternatively, sperm groups may have evolved in response to the gelatinous copulatory plugs left by males during copulation 
: sperm groups might advance further up the female reproductive tract and therefore avoid being trapped when the plug is formed. A necessary next step therefore is to test the performance of sperm groups of different rodent species including the Norway rat and the house mouse in viscous media and in situ
Other explanations for the evolution of the apical hook of rodent sperm have been proposed but none substantiated. First, the apical hook might facilitate the attachment of sperm to the wall of the female reproductive tract prior to fertilisation 
, although subsequent data have suggested that this hypothesis is unlikely as mouse and rat sperm swim along the epithelium of the female tract by contact with the lateral surface of the sperm head and not the apical hook 
. Second, the apical hook may physically bind the sperm to the outer zona pellucida surface of the oocyte and/or protect the region of the sperm head that binds to and fuses with the oolemma 
. A comparative study of three species of conilurine rodents failed to find a relationship between the complexity of the sperm head and the zona thickness 
. However, further studies are needed to investigate the interaction between sperm and ovum in rodents.
Sperm cooperation may be the main selective force favouring the evolution of an apical hook which is such a common feature of rodent sperm. The fact that sperm cooperation may be a widespread phenomenon adds new aspects to the mechanisms of postcopulatory sexual selection and sperm competition in particular. Establishing the relative importance of diploid versus haploid selection in the evolution of sperm shape and function should be a major task for future studies.