This is fun to think about. Hopefully, REC will help me: Is there a paradox here. let it be the case that sperm sort themselves by fitness; let it further be the case that sperm in peletons have an advantage over sperm that dont. Isnt it now the case that sperm are no longer sorting themselves by fitness?
Ok, forget that: so let be the case that "fitness" is not defined by fertization probability, but more in the sense of "physical fitness". Some of the sperm go to the gym, and some don't. Or some are more muscular than others. So let it be the case that sperm sort themselves by swimming speed. The more muscular sperm swim side by side and the less muscular sperm swim side by side. But wait a minute, other things being equal wouldnt everybody bet the peleton effect? Ok, forget THAT, too. All these models assume that everbody starts from the same starting point, right? Are they jostling at the starting gate in the prostate as they are mixed with the seminal fluid. Is there an advantage to being in the first pulsation? So f orth. Wouldnt these factors overwhelm the peleton effect? And, what about the kamakaze sperm, that stick pumps in the spokes of unrelated sperm as in that unforgettable scene in Breaking Away. Ok. Sorry. Forget the whole thing. I do so like metaphors. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University (nthomp...@clarku.edu) http://home.earthlink.net/~nickthompson/naturaldesigns/ http://www.cusf.org [City University of Santa Fe] > [Original Message] > From: Hugh Trenchard <htrench...@shaw.ca> > To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com> > Date: 3/26/2010 8:38:22 PM > Subject: [FRIAM] Sperm pelotons; article in Nature > > On February 12, Roger Critchlow posted a reference to "sperm pelotons", > which inspired me to read the Nature article and to think a bit about how > principles of peloton interactions could be applied to sperm aggregations. > I've outlined some thoughts below. > > > > __________________________________________ > > DRAFT > > > > Applications of a peloton model to sperm aggregration dynamics > > An analysis of article: Fisher, H., Hoekstra, H. (2010) Competition drives > cooperation among closely related sperm of deer mice. Nature. Vol. 463, 11 > Feb 801-803 > > Hugh Trenchard > > > Abstract > > The Nature article by Fisher and Hoekstra suggests that a mechanism exists > among the sperm of certain species of mice to identify genetic relatives. > The identification mechanism itself is not apparent and, based upon > observations of analogous processes in bicycle pelotons, an alternative > hypothesis is suggested. There are similarities between bicycle pelotons > and sperm aggregations: they are both competitive dynamical systems, and > there are energy savings mechanisms by which agents couple and facilitate > self-organized aggregate formations. A model for the division of a peloton > at critical output levels is shown and suggested as analogous to certain, > but not all, sperm aggregations, and a model for the relative energy > consumption of coupled and non-coupled aggregates is shown, which suggests > how sub-aggregates may form that are composed of agents within a narrowed > fitness range, and also why the strongest individual agents may not always > reach the target objective first. This suggests that no mechanism is > required for the identification of genetic relatives, but that sorting > occurs according to a self-organized metabolic process whereby sperm with > close fitness levels will aggregate. Sorting among sperm is hypothesized to > occur at a critical output threshold, and is more likely to occur among > promiscuous species than monogamous species because sperm velocity of > monogamous species may not be high enough to reach the critical sorting > threshold. Genetically related sperm are more likely to have closer average > fitness levels, and so will naturally sort into groups composed of > predominantly related sperm. Thus proposed is an alternative framework by > which to analyze the data. > _______________________ > > > > > > Introduction > Fisher and Hoekstra (2010) provide evidence that supports the > hypothesis that sperm identify related sperm, aggregate and cooperate with > them and, through increased velocity when travelling in aggregations, > provide an advantage to genetically related sperm in advancing one of their > kind to impregnate the egg. The authors report a species of mouse whose > sperm exhibits "the ability to recognize sperm based on genetic relatedness > and preferentially cooperate with the most closely related sperm." The > question was raised: "how do sperm identify their brothers?" (FRIAM, 2010). > The question reveals a problem in Fisher's and Hoekstra's analysis, and a > clear mechanism for this identification process does not appear to be > suggested in their article. > > Observations of peloton dynamics allow an alternative explanation to the > cooperative aggregates that Fisher and Hoekstra (2010) have observed. Here > presented, instead, is the hypothesis that any aggregation among genetically > related sperm is coincidental to what is better explained by aggregates that > form due to coupling among groups of sperm as a result of an energy savings > effect that occurs when sperm travel closely together, an effect that is > similar to drafting in a bicycle peloton. This is a self-organized process > and, as such, no mechanism is required for sperm to identify genetically > related sperm to adjust their positions to be near each other. This process > includes a sorting of individual sperm into groups with proportionately high > numbers of sperm whose swimming fitness is closest to their own. > Genetically related sperm are more likely to have similar swimming fitness > levels than are unrelated sperm. Hence grouping is based upon swimming > fitness and not genetic relatedness, which also partially explains why > aggregates are not entirely homogenous according to relatedness: genetically > unrelated sperm with fitness levels near others, who may be related, will > group with them. > > For simplicity, here this self-organized energetic process is referred to as > drafting, although for sperm the energy savings mechanism is a hydrodynamic > one (Lauga and Powers, 2009; Woolley et al, 2009). Similarly, the > interactive dynamic between sperm that allows for this energy savings to > occur is referred to as coupling. Coupling of this nature has been > described as a synchronization of flagellar motion and optimal positioning > of sperm-heads for friction reduction and increased sperm velocities when > travelling in coupled formations as opposed to individually (Woolley, et al, > 2009). Woolley et al (2009) describe the mechanism for coupling in bull > sperm as follows: > > The subject of the present study, the flagellar synchronisations, resulted > from chance contacts between individual spermatozoa. These events will be > called 'conjunctions'. In a few instances, the two spermatozoa separated > again after a period of conjunction and they resumed the swimming speeds and > beat frequencies that they had shown before the conjunction. > > > > Woolley et al. (2009) go on to show distinct increases in mutual speeds > when coupled (i.e. in conjunction states). Their article does not, however, > appear to discuss overall average savings in energy as sperm accelerate and > decelerate while alternating between conjunctive and separated states > between different sets of coupled sperm, nor do they appear to discuss the > durations of conjunctions/separations, which would provide clues as to > relative differences in inherent fitness and whether sperm aggregations form > with sperm whose range of fitness is relatively narrow. Here it is > hypothesized that this is, however, what does in fact occur: this narrowed > fitness range among sperm sub-aggregates due to sorting is more likely to be > the mechanism underlying the genetically related sperm aggregations in the > Fisher and Hoekstra (2010) findings. > > The Woolley et al (2009) article suggests that, similarly to cyclists who > save energy by coupling in a peloton, it is unnecessary for sperm to be of > equal physical fitness to travel at the same (mutually increased) speed: to > travel at equal velocity while being of unequal fitness is facilitated by a > coupled energy savings mechanism. Similarly, Riedel et al (2005), and Lauga > and Powers (2009), for example, appear to support the notion that there is > in fact some form of energy savings occurring among sperm aggregates. > > > > > > The peloton sorting model > > In bicycle pelotons, drafting allows riders within a range of output > capacities to sustain the same speed: weaker riders drafting can maintain > the same speed as stronger riders ahead according to the equation > > PDR = (Wa-Wb/Wa) / D*100 > > ¡ Wa is maximum sustainable power (watts) of cyclist A at any given moment > > ¡ Wb is maximum sustainable power of cyclist B at any given moment > > ¡ D/100 is the percent energy savings at the speed travelled > > > > This is referred to as the Peloton Divergence Ratio (PDR) (Trenchard, 2009; > 2005). Cyclists save energy by drafting at approximately 1% per mile an hour > (Hagberg and McCole, 1990). So, if for example, cyclists are traveling at > 25 mph, they save approximately 25% energy by drafting riders ahead. > Extending the illustration, if stronger cyclist A has a maximum sustainable > output at 400w at 25mph, and cyclist B has a maximum sustainable output of > 300w, cyclist B could not sustain the same speed as cyclist A if they were > travelling individually and without drafting. Thus where cyclist B has only > 75% the output capacity of cyclist A, PDR = (400-300/400) /D*100; PDR=1. As > long as PDR is <1, cyclists can maintain the same speed. If PDR>1, cyclists > will not be able to maintain the same speed and will diverge, or decouple. > So, at a speed of 25mph, all cyclists within a range of 25% output capacity > can travel at the same speed. > > Here it is suggested that PDR applies to certain types of sperm > aggregations, though not necessarily to all types, as there are several > different types of sperm morphology (Immler, et al. 2007), and their > respective energy savings mechanisms therefore cannot be assumed to be the > same. In fact, PDR does not appear to apply to the Woolley et al (2009) > bull sperm observations, although it may to the Riedel (2005) observations, > the Moore et al. (2002) and Immler (2007) observations of "train" > aggregations, which in pelotons occur during a distinctive phase of energy > output when all riders are riding at or near maximum sustainable speeds, or > when riders are at or near PDR=1. The phase is unstable and small > increases in speed or disturbances in rider positioning can put riders at > PDR>1 and precedes peloton separations and the formation of sub-pelotons. > > When cyclists in a peloton approach PDR=1, a sorting process occurs whereby > sub-pelotons form that are composed of cyclists within a smaller range of > inherent fitness levels; i.e. each cyclist in the group has an inherent > fitness level (max sustainable output) that is closer to the average of the > sub-group than it is to the larger aggregate. When peloton divisions occur > at points of instability (PDR >1) and cyclists in a competitive situation > exert maximal efforts to remain among the composition of the group ahead, > but are unable to do so, it is self-evident that the average fitness of the > group behind is less than that ahead, and that each of the groups contain > cyclists of closer average fitness than when among the undivided aggregate. > > The range of fitness within each sub-group is also effectively narrowed > further by the drafting process, as evidenced by the fact that sub-pelotons > in a mass-start bicycle race finish a race with nearly identical finishing > times (eg. see data in Trenchard, H., Mayer-Kress, G., 2005). This would not > be self-evident or a reasonable conclusion if the groups were not all > proceeding at maximum sustainable outputs, but had divided for > non-competitive reasons. > > This conclusion, however, does not preclude the possibility that some > cyclists with fitness levels which could sustain them in faster groups do > end up in slower groups (i.e. fitness levels that are substantially above > the average of the group), and so there may be a small proportion of > cyclists with fitness levels that overlap the ranges of different groups, as > would there be among sperm sub-aggregates. > > The sorting process and formation of aggregates with close average fitness > is well illustrated by imagining a peloton composed of 75 cyclists with a > broad range of abilities: 25 cyclists are professional level and can sustain > speeds of 50k an hour on the flat without drafting, 25 cyclists are medium > amateur level and can sustain speeds of 30km on the flat without drafting; > 25cyclists are kids who can sustain speeds of 15km per hour on the flat > without drafting. If they all start together, the peloton is 75 strong up > to approximately 20km/h (because the kids can draft, they can go faster than > they could without drafting); at 21 km/h, the peloton sorts into two groups: > 25 kids, and 50 medium and pro cyclists. The group of 50 accelerates, and > when they travel at approximately 36km/h the peloton divides again. It > divides at 36km/h and not 30km/h because the medium-level riders can draft > up to speeds approximately 20 percent faster than they could achieve on > their own without drafting. When speeds of 36km/h are sustained, eventually > all the medium-level cyclists will be separated from the professional > cyclists, and most, if not all, will end up together in a group. At this > point the original peloton has divided into three groups containing riders > with fitness levels near to the average of the group. In an actual > competition and peloton that is composed of all professional riders, the > sorting process is more subtle because average fitness of all the cyclists > is very close from the outset, but the effect is fundamentally the same. > > > > Applying the peloton model to sperm aggregations and the Fisher and Hoekstra > findings > > Here it is hypothesized that a similar sorting dynamic occurs in sperm > aggregations and may provide a clue as to the composition of the > sub-aggregates and the proportional representation of conspecific and > heterospecific sperm in any given aggregate, as identified by Fisher and > Hoekstra (2010). Thus if the sperm of two males, say heterospecific in the > first example the authors provide, is mixed into an initial single > aggregate, the aggregate will begin to divide according to PDR as the sperm > accelerate. Sorting occurs as weaker sperm end up being "dropped" into > trailing sub-aggregates, as in the peloton illustration above. Thus, if a > set of sperm from an individual conspecific male are, as a group, fitter > than those of the heterospecific competitor, there will be a self-organized > tendency for sperm of close physical fitness to group together. Some > individual sperm from other groups, however, will be capable of sustaining > the speed of fitter sperm if they group with fitter sperm, as long as they > are at PDR<1 The proposition is thus that genetically related sperm are > naturally closer in physical fitness and therefore will tend to aggregate > together through self-organized coupling dynamics, as presented here. > > The composition of sperm aggregates is thus determined by individual sperm > fitness levels and the energy savings due to drafting at the velocity > travelled. Divergences in the aggregates occur at critical individual > output/speed levels. This is particularly so in the case of the promiscuous > species, P. maniculatus, and here it is assumed that sperm in a competitive > situation naturally swim at or near maximum sustainable speeds. This is a > reasonable assumption in a competitive situation, in which all sperm are > seeking to reach the egg first. > > However, as indicated in the Fisher and Hoekstra article, in the case of P. > polionatus, the monogamous species, sperm may not travel at or near maximum > sustainable speeds, which suggests that the same degree of sorting does not > occur as among their faster swimming P. maniculatus counterparts. This > provides an explanation why P. polionatus sperm tend to mix > indiscriminately, as the authors describe (see Table 1); i.e. the sperm have > adapted to swimming at less than maximum speeds as an intrinsic > characteristic of monogamous species, and the sorting of sperm into groups > with nearly equal fitness does not occur because the critical output > threshold is not reached for this to happen. > > Table 1 summarizes findings presented in the Fisher and Hoekstra article and > provides an alternative peloton model explanation. Fisher and Hoekstra show > results for three experiments involving different combinations of mouse > species sperm mixes. Table 1 summarizes both the results of the Fisher and > Hoekstra study, and the alternative peloton model explanation: > > > Test > Result > Peloton model explanation > > 1 > Sperm from one heterospecific (P. polionotus) male and one conspecific > (P. maniculatus) male are mixed in vivo assay > "found that overall groups were composed of significantly more > conspecific sperm than expected at random" > Sperm from each of the conspecific males exhibit closer physiological > fitness than as between heterospecifics; i.e. conspecific males have average > fitness close to each other, as do rival heterospecifics to each other . > Some sperm for each sets, however, exhibit close physiological fitness > levels, and these represent the proportion of the aggregates that are not > from conspecific males. There are also percentages of each of > heterospecifics and conspecifics whose fitnesses are such that they are > capable of travelling with groups, but which are "trapped" in the slower > travelling groups. > > 2 > Sperm from two unrelated male P. maniculatus, a promiscuous species, > are mixed > "sperm group significantly more often with sperm of the same male than > expected at random" > The explanation above applies to the related conspecific maniculatus > males > > 3 > Sperm from two unrelated conspecific males of P. polionatus, a > monogamous species, are mixed > "aggregations form indiscriminately in assays" > The speed at which these sperm aggregations travel is relevant. It may > be that the sperm of monogamous species travel slower (due to decreased > competition) than the critical speed at which self-organized sorting occurs. > > 4 > Sperm from related P. maniculatus was mixed > "found a greater proportion of sperm from the same male grouped > together than was expected at random." > The explanation in cases 1 and 2 above applies to the related > conspecific maniculatus males > > > Table 1 > > In cases 1,2 and 4, the sorting process described in the foregoing provides > a reasonable alternative explanation to the formation of sperm aggregrations > with close average fitness, and the proposition that it is likely that sperm > of one male have closer average fitness than another male, whether it is > related or not. Some proportion of the two sets of sperm will mix, but at > the critical threshold when sorting occurs, sperm with nearest average > fitness will aggregate. > > In case 3, the lower vitality of monogamous sperm, as the authors' finding > indicate, and the smaller testes of P. polionatus suggests that sperm > swimming speeds are slower and/or do not proceed at near maximal output > levels. The slower sperm speeds of monogamous species is supported by other > finding (Nascimento, 2008; Fitzpatrick et al. 2009), although it is not > clear whether sperm are simply slower with a lesser maximum output capacity, > or whether they are in fact capable of swimming faster, but simply do not. > If the peloton model holds, then the inference is that the sperm of > monogamous species are capable of swimming faster but do not do so and, as a > result, are less likely to reach the critical output threshold by which they > will sort into sub-aggregates that contain sperm of near equal fitness > levels. These relative speeds and output levels should be investigated and > confirmed. > > > > Conclusion > > The analysis here presents an alternative hypothesis for the findings > presented in the Fisher and Hoekstra article. Based upon analogous behavior > observed in bicycle-pelotons, it provides an analytical and experimental > framework by which existing data could be re-analyzed or further experiments > conducted to test for the observations and principles outlined. > > References > > > > FRIAM email listserv Feb 12, 2010, R. Critchlow. Vertical axis windmills and > sperm pelotons. > > > > Hagberg, J. and McCole, S. 1990. The effect of drafting and aerodynamic > equipment on energy expenditure during cycling. Cycling Science 2:20. > > Immler, S., Harry D.M. Moore, H., William G. Breed, W., Birkhead, R. (2007). > By Hook or by Crook? Morphometry, Competition and Cooperation in Rodent > Sperm, PLoS ONE. 2(1): e170. > > Published online 2007 January 24. > > > > Lauga, E., Powers, T. The hydrodynamics of swimming microorganisms. Rep. > Prog. Phys. 72 (2009) 096601 > > > Moore, H., Dvorakova, K., Jenkins, N. Breed., W. (2002). Exceptional sperm > cooperation in the wood mouse. Nature 418, 174-177 > > > Nascimento JM, et al.(2008) The use of optical tweezers to study sperm > competition and motility in primates. J R Soc Inter 5:297-302. Published > online 2007 July 24. doi: 10.1098/rsif.2007.1118. > > Fitzpatrick, J., Montgomerie, R., Desjardins, J., Kelly, S., Kolm, N., > Balshine, S. Female promiscuity promotes the evolution of faster sperm in > cichlid fishes PNAS January 27, 2009 vol. 106 no. 4 1128-1132 > > > Riedel, et al. 2005. A Self-Organized Vortex Array of Hydrodynamically > Entrained Sperm Cells > > Science 8 July 2005: 300-303 > > Trenchard, H., Mayer-Kress, G. (2005) Self-organized oscillator coupling > and synchronization in bicycle pelotons during mass-start bicycle racing. > Intl Conference on Control and Synchronization of Dynamical Systems. Oct 4-7 > Leon, Gto. Mexico. > > > > Trenchard, H. (2009). Self-organized coupling dynamics and phase > transitions in bicycle pelotons. AAAI Fall Symposium, Arlington VA. > Technical Report Series FS-09-03. > > > > Woolley, D., Crockett, R., Grook. W., Revell, S. (2009). A study of > synchronisation between the flagella of bull spermatozoa, with related > Observations. The Journal of Experimental Biology 212, 2215-2223 > > > > Yang, Y., Elgeti, J, Gompper, G. (2008) Cooperation of sperm in two > dimensions: synchronization, attraction, aggregation through dynamic > interactions. Phys Rev. E. 061903 > > > > > > Appendix A > > Further development of the peloton/sperm aggregation model > > Note that PDR is a useful model if an energy savings mechanism exists > whereby one of two coupled sperm benefits from the energy savings mechanism, > while the other does not. This may be the mechanism in the mouse species > described in the Moore (2002) and Immler (2007) articles, as indicated by > the "train" formation, which is similar to "single paceline" peloton > formations when cyclists are aligned near or at PDR=1 to each other > (Trenchard, 2009; 2005). > > There do appear, however, to be other energy savings mechanisms in sperm > aggregates, such as for example the conjunction and synchronized dynamic of > bull sperm (Woolley et al, 2009). In a sperm conjunction (Woolley et al, > 2009), the PDR equation does not strictly apply and must be adjusted because > the stronger sperm also appears to benefit from the coupled formation, which > does not occur to any significant degree between coupled cyclists; i.e. in a > peloton the front riding cyclist does not receive any reduction in output > from the rider behind, while the rider behind benefits substantially by > drafting; for bull sperm, it appears that both coupled sperm benefit by > increased velocity. > > This leads to a further hypothesis that the stronger sperm increases speed > with some reduction in metabolic cost, while the weaker sperm increases > speed with little or no change in metabolic cost, although they both travel > faster than they would individually. Thus it is the stronger sperm that > benefits by energy savings, while the weaker sperm benefits by increased > speed, but with no savings in energy. There is an implication that the > stronger sperm will always be able to advance to the front of the sperm > aggregation faster than weaker sperm. However, this is not necessarily so, > as it depends on the relative durations of coupling and separations. That > is to say, a weaker sperm could advance farther and faster than a stronger > sperm if it spends sufficiently more time coupled than a stronger sperm > which may spend relatively more time isolated. Thus the faster sperm are > not necessarily those that are stronger, but those whose proportion of total > coupling time exceeds the percent differences in their relative fitness > levels. > > The following model is descriptive for coupled organisms that may alternate > durations of time spent coupled with time spent non-coupled, and which > mutually benefit from coupling because it accounts for the proportions of > total time spent both saving energy in coupled positions and not saving > energy in non-coupled positions. It is a simplified model because there are > other factors that affect total output than time spent in energy-saving > positions (coupled) and positions where there is no energy savings. > However, it provides insight into the energetic dynamics of coupled agents > of varying degrees of fitness and why they do not necessarily achieve > positions based on inherent fitness. > > > > TO = Wa-(Wa*%E) * T) / Wb-(Wb*%E) * T) > > > > · Where TO is ratio of total output of two agents in coupled > positions (not necessarily with each other) with identical objective (e.g. > to win a race or impregnate an egg); here, sperm or cyclist; in the case of > sperm, millijoules; for cyclists, calories > > · T is total time spent in coupled positions and travelling at > mutually faster velocities than achievable in isolation > > · %E is percent energy savings in coupled formation > > · Wa is the maximum sustainable power output; picoNewtons for sperm, > watts for cyclists of stronger agent A (cyclist or sperm) at a given moment > , assuming that in a competitive situation, agents are travelling as fast as > their metabolisms will allow. > > · Wb is the maximum sustainable power output at a given moment of > weaker agent B, again assuming that in a competitive situation, agents > travel as fast as metabolisms will allow. > > > > For example (quantities and units for illustration only): if stronger sperm > A has max sustainable output of 50pN, and B has max sustainable output of > 45pN, and A saves an average of 10% output when coupled and spends a total > of 10 minutes coupled, total output for A is 50-5*10, or 450mj, while the > weaker sperm saves no energy when coupled, but spends 11 minutes in coupled > positions, we have 45-0*11, 495; and 450/495 = 0.91. Thus where this ratio > is <1, the weaker sperm potentially can be ahead of the stronger sperm over > the duration of the coupling interactions. Thus this ratio indicates why it > is not necessarily the case that stronger sperm will impregnate the egg. > > > > > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
