Hugh, Even if it has nothing to do with sperm it is a nifty model.
There is an idea lurking here that i dont know whether it plays a covert role in your thinking or not, but what about the fate of a "genefur" peletonizing. My email program is misbehaving and my computer is about to crash so I wont say more, now. 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: <nickthomp...@earthlink.net>; The Friday Morning Applied Complexity Coffee Group <friam@redfish.com> > Date: 3/27/2010 10:54:41 AM > Subject: Re: [FRIAM] Sperm pelotons; article in Nature > > Thanks for taking a peek at my post. Great questions, and they help me to > see how/where my descriptions can be clarified. > > On the paradox part - that is one of the really interesting features of a > peloton: the energy savings effect of drafting narrows the range of fitness > between the strongest and weakest riders. In contrast, think of a pack of > runners of varying fitness levels. There is negligible drafting effect - > there is some, esp if running into a headwind, but overall it's small enough > that it can be ignored for this illustration. Say there are 50 runners, all > separated incrementally by 1% difference in fitness; say they run a couple > of miles. If they all start off slowly at say the max speed of the slowest > runner, they can all run in a big group, separated only by enough distance > between them to keep them from kicking and elbowing each other. As they > pick up speed, the group thins into a line and are separated incrementally > by distances that correspond to their differences in fitness. In the space > of two miles, they all finish individually in a single long line according > to their fitness, and it can be predicted accurately where runners will > finish if you know their starting levels of fitness. > > This is not the case with a peloton. For example at 25mph, riders can save > at least 25% by drafting (approx savings 1%/mph) - all the riders who are > within 25% fitness of the fastest rider can ride together even at the max > speed of the strongest rider. So their fitness levels are effectively > narrowed, and they can all finish together as a group (ie. globally coupled > by finishing within drafting range of each other), and so the paradox. Part > of the paradox is also that, while fitness levels are effectively narrowed > by drafting, it means, conversely, that a broader range of fitness levels > can ride together in a group, which maybe isn't something that is clear from > my initial post (though it is certainly implied). Also, there are other > important things going on in a peloton which precede the sorting of riders > into groups, some of which I see I do need to clarify to make my model > clearer. > > Of these, particularly important are 1) the occurrence of peloton rotations, > and 2) points of instability when riders are forced into positions where > they do not have optimal drafting advantage. Below a certain output > threshold, when all drafting riders in a group are sufficiently below max > output, riders have sufficient energy to shift relative positions within the > peloton, and in this particular phase, a self-organized rotational pattern > forms whereby riders advance up the peripheries and riders are forced > backward down the middle of the peloton. However, instabilities in pace > occur along the way, caused by such things as course obstacles, hills (when > lower speeds reduce drafting advantage, but when output may be at least as > high), cross-winds, narrowing of the course, or short anaerobic bursts among > riders at the front - all of which cause splits (i.e. PDR>1 at these > points). In a competitive situation, instabilities occur frequently > causing temporary splits at various places in the peloton, but these are > often closed when the cause of the instability has ceased. Sorting thus > occurs according to some combination of peloton rotations in which stronger > riders are able to get to the front and the continual splits in the peloton > at points of instability and reintegrations. I would need to develop the > model some more to show this as an equation (though I touch on a basic > version of it in my Appendix). > > For sperm, I don't know what the initial state of the aggregates are when > they begin their travels, but I am assuming (perhaps quite incorrectly), > that there is some initial phase in which they are mixed (such as cyclists > on a starting line), and then they begin to sort as they increase speed. > During the process, they aggregate like cyclists because a broader range of > fitness levels can aggregate together (causing an effective narrowing of > fitness). As in a peloton, there are instabilities that allow for > continuous re-adjustments to the relative positions of all the sperm, and > over time they begin to sort into groups where each have fitness levels > closer to the average. This is my hypothesis, at least. > > On the second last question, there would be an advantage to sperm among the > first pulse aggregation if all the pulsed aggregations do not mix first, but > the principles apply to each aggregation. However, I don't know whether > there is some other process of mixing first among all the pulses of sperm > aggregations before they begin traveling (I imagine I could find the answer > in the literature), in which case there could easily be a sperm in, say, > the second pulse, which could end up impregnating the egg. > > I don't know about the kamikaze sperm - I'll leave that one for now! But I > do remember that scene from the movie as clear as day! > > In any event, my aim is really to ask the question - are there energetic and > coupling principles that allow sperm to end up in groups which otherwise > appear to have occurred because genetically related sperm can somehow > identify each other? I am really only suggesting the existence of some > dynamics of the sperm aggregations that could be studied for, which don't > yet appear to have been addressed. > > Hugh > > ----- Original Message ----- > From: "Nicholas Thompson" <nickthomp...@earthlink.net> > To: <friam@redfish.com> > Sent: Friday, March 26, 2010 8:04 PM > Subject: Re: [FRIAM] Sperm pelotons; article in Nature > > > > 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 > > >
============================================================ 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
