Monday, October 23, 2017

Drafting: a mechanism for the origins of life?

I've been wanting for a while to prepare something rigorous to develop this idea. Since I've simply not found the opportunity to do so, and I don't at the moment foresee when a good block of time in the near future will open for this to happen, and since one never knows what tomorrow will bring, I wanted to present the idea in a crude fashion. 

As yet, while scientists appear to be homing in on the necessary conditions for the origins of life, the actual physical mechanism that generates life from inanimate matter still appears to be elusive. Some recent discussions:

Until actual life is generated from a bunch of inanimate molecules, it is safe to say that none of the proposed processes are proven to represent an actual origin of life. 

So, since it is still an open question, in a very crude form, I suggest a possible contributing mechanism.  Although my paper "The peloton superorganism and protocooperative behavior" (1), and our other papers (2-3) set out the mechanism I refer to here, these papers do not suggest how the principles might apply to origin-of-life mechanisms. This is a first sketch of such an application.

I have also written blog posts with similar videos to the one below, but this one is made with the specific purpose of demonstrating a simple possible mechanism for life to emerge from a collection of otherwise inanimate molecules. The video is poor quality, and the simulation platform doesn't allow an applet to be generated, but the simulation itself is what is important..

In the simulation, the circles or balls represent a collection of molecules. It is assumed that the appropriate molecules have aggregated in our primordial soup, so I need not name them.

The appropriate energetic source for the process proposed is more likely to be a thermal vent of some kind, since the collection of molecules is driven by a constant energetic source to aggregate, divide, and re-aggregate. 

The aggregation and division process here is facilitated in part by an energy saving mechanism that allows larger aggregates to move through the heated liquid medium faster than smaller aggregates. Although not by any means conclusive, this short simulation is constructed with the same basic principles as in papers (1-3), and the process of larger groups moving faster than smaller ones is somewhat indicated in the video.

Whether such an energy saving mechanism is present among moving molecule aggregates, is not something I have researched at this point, and hence why this is a crude beginning.  However, it is known that drafting occurs among comparatively small particles in a liquid medium (4), so I suggest it is not far-fetched that a drafting-like mechanism may be present among molecule aggregates, and certainly worth investigating further.  

In the video, the molecules are first in aggregate motion under a comparatively low energetic input. However, we can reconfigure the group of molecules by driving them with higher energetic output, which may sort them into groups of different molecular size. In the simulation, the molecules are the same physical size, but they have their own intrinsic "output capacity" which is equivalent to size. 

This hypothesized sorting process would occur because larger molecules would permit greater drafting opportunities: below a critical threshold, smaller particles can stick with larger ones at the same energetic input by virtue of drafting which equalizes differences in energetic capacity (internally or externally driven), but above that threshold, they are driven to separate, and may tend to group by size. This is a process we have modelled in (1-3), and (4) provides some indication of how this might work for small particles in water. More work would certainly need to be done to demonstrate the process under true molecular conditions.

Nonetheless in this simplified model, in our thermal vent, the sorting processes would be fairly continuous in view of temperature fluctuations in the vent and due to re-positioning of molecule aggregates across cooler and hotter vent regions. Thus there would be ongoing group reintegration and division. 

The simulation also demonstrates the presence of a continual convective motion on the peripheries of the molecule aggregates. This is fairly easy to see with the naked eye, although below I show a plot from (1) that indicates this process. Further data and analysis are obviously required to demonstrate this. This convective motion represents a mechanism for the formation of protocell membranes. This convective process is largely generated by the coupling mechanism of drafting; molecules rotate on peripheries as internal molecules are less free to advance positions.  Thus protocells are generated which re-integrate and divide. Under this continual process, eventually they sort into the appropriate configuration to generate RNA and/or DNA structures.  If a sufficient number emerge at the same time, this continuing process of reintegration and and division sets in motion the evolutionary process.

This is what this short video demonstrates:

It is worth noting that a convective dynamic traces a sinusoidal trajectory on a two-dimensional plot. This translates in 3-dimensions to a helical motion as the aggregate moves forward in space. A double convective motion (i.e. rotations forward on both peripheries and falling backward down the middle) produces a double-helical pattern as the aggregate moves forward in space.  Below is Figure 8 from (1).  It shows a division and re-integration dynamic among 50 agents (simulated cyclists in this case). The black circles show group divisions, and the red circles show re-integrations.  We can see approximately sinusoidal trajectories among the cyclists as they rotate from the back of the group to the front, and back again. Much the same dynamic is occurring in the video above.

How this process might solidify or become fixed into a helical structure is unknown, but we can hypothesize that the noted temperature changes in the liquid medium may be involved.  

1.Trenchard, H., 2015. The peloton superorganism and protocooperative behavior. Applied Mathematics and Computation270(C), pp.179-192.

  1. 2. A deceleration model for bicycle peloton dynamics and group sorting, Hugh Trenchard, Erick Ratamero, Ashlin Richardson, and Matjaž Perc, Appl. Math. Comput. 251, 24-34 (2015)
  1. 3. Collective behavior and the identification of phases in bicycle pelotons, Hugh Trenchard, Ashlin Richardson, Erick Ratamero, and Matjaž Perc, Physica A 405, 92-103 (2014)
4. Wang, L., Guo, Z.L. and Mi, J.C., 2014. Drafting, kissing and tumbling process of two particles with different sizes. Computers & Fluids96, pp.20-34.

Saturday, September 2, 2017

The emergence of cooperation, resource abundance, and critical transitions

Cooperation tends to emerge in conditions of resource abundance, and diminishes in conditions of resource scarcity. This was one of the significant findings of my paper, The peloton superorganism and protocooperative behavior (2015)*. 

My paper considers individual cyclists within pelotons, or groups of cyclists. Every cyclist generates his or her own individual maximal capacity to do work. Each cyclist, therefore, contributes differentially to the highest cost positions according to their maximal work capacities. This is most evident when peloton speeds are relatively high, since stronger cyclists can contribute more to high cost positions than weaker cyclists, who by necessity must exploit drafting (energy saving) positions to reduce their work load.  My paper examines how these relative work capacities affect collective cooperative behavior.

The wider applicability of my results to other collective organisms was stated hypothetically. Now I see a recent paper by Dr. Brian Connelly and collaborators, Resource abundance and the critical transition to cooperation (2017) that appears to be consistent with my hypothesis.  

The proposition that cooperation emerges in conditions of resource abundance is not obvious or necessarily intuitive. One could easily think that cooperation is more likely to emerge when resources are scarce because organisms must work together for their mutual benefit.  In times of abundance, one might think that organisms can lounge around and gorge themselves in the fields of plenty without interaction or cooperation.  However, my paper suggests otherwise, as does the Connelly et al. (2017) study.

At the risk of oversimplifying their results, Connelly et al. (2017), using computer simulations and empirical experiments involving bacteria, present evidence for increasing cooperation among bacteria in conditions of external resource abundance, and decreasing cooperation in conditions of diminishing resources. Decreasing cooperation can be thought of as increased tendency to free-ride, or as "cheating". 

In my paper, I examine energetic resources that are internal to individual cyclists (i.e. resources are present as stored energy and expended by the metabolic functions within cyclists' bodies), whereas Connelly et al. (2017) look at external (environmental) resources which, by implication, are consumed by bacteria. However, internal and external resources are equivalent in this context because they are both part of a wider process in which resources are located, consumed and then converted to useful work. 

In my paper, I model and quantify the transition between cooperative behavior and free-riding. Below, in Fig 2 (from my paper (2015)), I show where a transition occurs from high density peloton behavior occurs, to "stretched" behavior -- see the orange "stretch" curve that rises markedly around 12 m/s. 

Below this critical threshold, the highest cost front position (position of highest aerodynamic drag) can be shared fairly equitably among all cyclists, regardless of strength. Below, figures 5 and 6 (from my paper (2015)), show cyclists travelling at two different relatively low speeds (assumed flat road) and show that the time spent by cyclists in the highest cost front position is fairly randomly distributed. Indeed there are some cyclists who spend little or no time at the front, but this is not because they are weak; rather this may be due to positional reasons, such as being blocked by riders ahead and who might never, or rarely, approach the front.

By contrast, at a speed that becomes difficult to sustain for a large proportion of the cyclists, I show how only the stronger cyclists tend to share the highest cost front position, while at the same time there is tendency for the weaker ones to free-ride. In fact, at sufficiently high speeds, weakest riders spend no time at the front, and thereby do not contribute at all to peloton pace-making (cooperate). See Fig 4 below (from my paper (2015)).  The results indicate that the highest cost positions are dominated by stronger cyclists who have sufficient resources to sustain the speed, whereas weak ones must free-ride to sustain the speed, and thereby "survive" as part of the collective unit.

My results are not unlike those of Connelly et al. (2017).  In their Figure 2(a) below, we can see how the proportion of cooperators increases as a function of resource level. The more abundant the resource, the greater the cooperative behavior. (To keep this commentary as simple as possible, I won't delve into their Figures 2(b-d)).

In their Figure 3(a) (2017), Connelly et al. show the dominance of cheaters in resource poor environments, and the reverse situation in resource-rich environments in Figure 3(b).  Similarly they show this effect in their Figure 4. 

My results are, of course, generated in the context of cyclists in motion, and in the presence of an energy saving mechanism (drafting).  However, cyclists' forward motion is simply the means by which they expend energetic resources, and is equivalent to any process of energetic expenditure. 

Drafting permits weaker cyclists to sustain speeds of stronger ones, and allows us to readily model the threshold between dominant cooperation and dominant free-riding. But even in the absence of an obvious energy saving mechanism, the "protocooperative" threshold should, I suggest, generally emerge relative to intrinsic maximal capacities, such that, in general, organisms cooperate when their intrinsic capacity to do work exceeds a critical threshold. 

If, for whatever reason, external or internal resources become strained, relative cooperation simply scales according to the range of work capacities among the collective.  Consider a highly simplified example: at a given level of resource scarcity that may be manageable by half the population who are sufficiently strong, or who carry enough energy, to move about and go foraging (or, say, to secrete biofilms), we would expect cooperation to occur among the strongest half of the population, and free-riding to occur among the weaker half.  At higher levels of scarcity, the pinch increases: fewer members of the population cooperate, while greater numbers free-ride. 

In principle, this seems to be consistent with the findings of Connelly et al. (2017). Yes, unlike my study, Connelly et al (2017), do not appear to discuss a range of differential outputs among individual bacteria, and how these differences may produce relative cooperation.  But they do discuss certain mechanisms that regulate collective processes, such as quorum sensing, the production of biofilms, or the secretion of biosurfactants. The authors describe these processes as public goods that can be attributed to cooperative behavior. I suggest that each of these activities requires some work capacity, and presumably not all bacteria have equal metabolic work capacities. Thus, I suggest that the model I have developed, based on differential outputs and a threshold between abundant internal resources and diminishing internal resources, may potentially be incorporated into the Connelly et al. (2017) model. 


*As an aside, I regret including 'superorganism' in the title of this paper. This concept is a minor and relatively unimportant component of the paper, and probably distracts attention from the more important part, namely what I refer to as protocooperative behavior (which is different from protocooperation).


1.  Trenchard, H., 2015. The peloton superorganism and protocooperative behavior. Applied Mathematics and Computation270, pp.179-192.

2.Connelly, B.D., Bruger, E.L., McKinley, P.K. and Waters, C.M., 2017. Resource abundance and the critical transition to cooperation. Journal of evolutionary biology30(4), pp.750-761.

Monday, July 31, 2017

Trilobite pelotons: a response to the criticisms

First off, I wish to thank the podcast commentators (“PCs”) for taking the time to consider and to review our paper. There are obviously countless papers they could have chosen to discuss, and it is certainly a privilege for our paper to have received some exposure. The podcast is here, starting at 45:45:

The following addresses the major concerns raised by the PCs in their podcast. I refer to their comments in their entirety, so I do not identify which specific commentator has made any given comment.

1.      Why do we not talk about birds?

This is a fair question. The authors discussed this during the drafting process. In an earlier draft, we did mention other animal species that exploit energy saving mechanisms of some kind, and other species that travel in single files.  However, other than cyclists, rather than mentioning various other species, like birds, fish, dolphins, and others which exploit drag reduction and exhibit single-files or staggered single files and related formations, we decided to identify primarily arthropods that have been shown to exhibit single-file behavior in terms of “collective locomotion” (p. 2 of our paper), regardless of whether that behavior has been shown to originate from drag reduction.  Primarily, we refer to spiny lobsters, which have in fact been shown to reduce drag by single file formations.  At pages 2 to 3 of our paper, we do mention other species that involve hydrodynamic drafting; but, aside from cyclists, we do not mention other species that exploit aerodynamic energy saving mechanisms because of the obvious criticism that water and air are different, not to mention that birds and trilobites are vastly different animals.

That of course leads to the question (which is a fair one): if you are excluding other animal species that exploit aerodynamic energy saving mechanisms, then why are you comparing trilobites to human cyclists, who are racing and who use strategies and team tactics in an aerodynamic medium? 

We specifically addressed this question by stating, at page 2:

“Although driven in part by human-based competitive strategy, pelotons exhibit self-organized collective behaviours that emerge largely as a function of the metabolic outputs of the individuals within the group, and the power output reductions afforded by drafting (Trenchard et al. 2014). As cyclists approach their maximal sustainable capacities, formations stretch into single-file lines (queues); below a certain output threshold, single-file lines tend to collapse into compact unidirectional formations, as shown in Figure 1A, B (Trenchard et al. 2014, 2015; Trenchard 2015).” (emphasis added)

Here the referenced peloton papers specifically model collective behaviors that emerge from differential metabolic outputs between leaders and followers, coupled by drafting. As far as I am aware, no other research has done this, and this includes research on bird vee-formations and fish schooling formations.  In the cited references, my collaborators and I have conducted computer simulations of the threshold power outputs that generate certain collective behaviors, including single file lines and “compact” formations, examples of which are shown in Figure 1.

There are of course many papers that discuss the fluid dynamics involved in drag reductions.  There are also other models of flocking behavior, a general term that also includes fish schooling and similar collective animal behavior. However, there are no other studies I am aware of that involve the noted metabolic differentials, mediated by drafting, that allow predictions of formation phase changes as a function of changing collective metabolic outputs. Our peloton model focusses on self-organized collective behavior, as we have explicitly stated – this means that we have stripped away human-based racing strategy from the fundamental modelled behaviors, leaving basic physical and physiological principles that drive the emergence of collective behavior. These basic behaviors can then be analyzed for other animal species where those principles appear to be involved.

Thus, we did not want simply to compare the single file formation between species, which we could well have done by presenting images of birds flying in vee-formations or in single file.  Rather, the aim was to rely on published models of collective behaviors that emerge at critical metabolic thresholds. Now perhaps we could have elaborated on the meaning of “self-organized collective behavior” to more explicitly address the concerns raised by the PCs, and to have curtailed potential misunderstanding. This is a fair criticism.  However, it should be plain to attentive readers that we are applying a model of general collective behavior which may more broadly be referred to as “peloton behavior”, and that such a model is not otherwise used in the literature.

On a related note, one of PCs refers to Figure 1 and the comparison between pelotons and trilobites as a “construction”. Again, a careful consideration of the mathematical model, as applied by reference to peloton papers, would lead an attentive reader to see plainly that the comparison is not at all a mere construction or some superficial analogy.  Unfortunately, the PCs appear to give short shrift to the model presented, but instead appear largely to prefer to take umbrage with minor aspects of the paper.

Similarly, the PCs do not discuss the potential wider significance of the model, but instead, as I have noted, seem to drown-out the wider potential significance by focussing on what are largely minor considerations and their implication that the peloton analogy is merely superficial.  They do not ask the question: what is the variation range hypothesis – what is that all about? This hypothesis is fundamental to the paper and, in giving it minimal attention, the PCs appear to have missed one of the critical and potentially important elements of the paper.
2.      The relationship between energy saving and size variation

That said, in fairness to the PCs, they briefly acknowledge the application of the mathematical model to trilobite formations, albeit in a rather dismissive fashion. They do touch on what we argue about the energy saving quantity and our attempt to relate that quantity to the size variation among trilobites. First, however, the PCs erroneously suggest we refer to papers from the “60’s or 70’s” to support the idea that larger animals tend to be stronger. Here we say, at p. 3:

“We consider the behavioural consequences of these differentials, and their effects on the relative sizes of individual trilobites. In this context, certain scaling rules are applicable: except for birds and very large animals, speeds tend to scale with body mass (Garland 1983); speed is also proportionate to body length, a rule that applies across the range of running and swimming organisms from bacteria to arthropods to whales (Meyer-Vernet 2015) and as indicated by Jamieson et al. (2012); this is discussed in detail below. Moreover, juveniles tend to be slower, weaker and less agile than adults of the same species (Carrier 1996). It is thus reasonable to assume that larger trilobites were capable of higher speeds than smaller trilobites. Also, because drafting generates reductions in metabolic and power requirements, it is reasonable to conclude that smaller trilobites could sustain speeds by drafting that were otherwise unsustainable when travelling in isolation. In this paper we model these effects.”

Where in this context is the reference to papers from the 60s and 70s?  It is true that in the context of basic hydrodynamics, we do refer to the seminal work of Hoerner from 1965, a well-cited leading reference, but the PCs are obviously wrong that we refer to papers from the 60s and 70s regarding the scaling of animal size to their speeds. That’s a minor concern, but there is an unfounded implication that we may be relying on old material that may no longer be relevant.

Next, and more substantively, the PCs suggest we do not connect the energy saving quantity to any data. While it is fair to say that we did not conduct an exhaustive literature review of reported size ranges among trilobite clusters (which we acknowledged), we do refer our model back to the Blazejowksi queues, and other papers.  At page 10, we say:

“Speyer & Brett (1985) reported size-segregated clusters of Middle Devonian Phacops rana, Greenops boothi, and Dechenella rowi from the Windom Smoke Creek Bed (Windom Shale, Hamilton Group) and from the Murder Creek Bed (Wanakah Shale) both from western New York State. The authors reported cephalon length ranges of 0.6–1.4 cm (57% range, where cephalon length correlates with body length; Trammer & Kaim 1997) and cephalon length ranges of 0.4–1.0 cm (60% range), respectively. Further, the authors reported spatially separated clusters of different mean size, indicating that specific instar classes associated among themselves to the exclusion of other classes.  

In a similar finding, Karim & Westrop (2002) reported a non-linear cluster of Late Ordovician Homotelus bromidensis from the Bromide Formation, Dunn Quarry (Oklahoma) with cephalic lengths between 1.0 and 2.25 cm (56% range), and a second non-linear cluster with cephalic lengths between 1.0 and 2.75 cm (64% range).  These cases indicate that group members travelled together due to their approximate size equality, and suggest that groups of different mean speeds would arrive at stopover points at different times. This proposition does not challenge a gregarious behavioural explanation for instar segregation, but rather complements such an explanation while providing insight into the more primitive origins of gregarious segregation. Kin & Błazejowski (2013) reported that among 78 examples of Late Devonian (Famennian) Trimerocephalus queues from the Kowala Quarry (Poland), specimens ranged in size from 0.5 to 2.0 cm body length (75% range). Although this range exceeds the range of c. 62% predicted by the variation range hypothesis, the overall 0.5–2.0 cm body length (75% range) appears to represent the size range among all specimens in the study but does not distinguish between size segregated groups and narrower size-ranges among the queues themselves. Following the Kin & Błazejowski (2013) study, Błazejowski et al. (2016) reported that for the same 78 queues, the size ranges for individual queues were between 0.7 and 1.9 cm (63% range), thus supporting the assertion that the 75% range reported by Kin & Błazejowski (2013) was for the entire sample population and not queue-specific. It is also noteworthy that in their study of queues from the Kowala Quarry, Radwanski et al. (2009) reported that ‘The majority of queues are formed from the largest individuals.  The smaller-sized individuals are arranged as a rule in short files consisting of only two individuals’ (p. 467). From this it appears that the queues had indeed sorted themselves in much the way predicted by the variation range hypothesis. Kin & Radwanski (2008) also reported specimens from the Kowala Quarry in files, of mature growth stage, between 1.8 and 2.4 cm (25% range) …

In another study, Gutierrez-Marco et al. (2009) reported monospecific clusters of large Middle Ordovician trilobites Ogyginus forteyi and Asaphellus in Arouca Geopark (Portugal), 7–17 in number, of ‘similar sized specimens’ (p. 444), but the authors did not report precise ranges.” (emphasis added).

Now, in looking at our conclusions, we might have done well to say rather more directly “there is some evidence in the literature to support the variation range hypothesis” which a reader might well be expecting to see in the conclusion.  However, one need only look back at the Abstract and page 10 as quoted above, and the expected size range we have proposed (~62%) (or narrower, which is consistent with the hypothesis), to see that we have presented some evidence for the hypothesis. I do acknowledge that we have not provided an exhaustive literature review, but we have presented some evidence for the proposition and a falsifiable hypothesis. Further, in our conclusions, we clearly have recognized the need for further data.

3.      The criticism regarding our reference to ant single files.

The PCs argue, rather cynically, that we should be aware that ants use pheromones to establish single file lines, and that we have erroneously claimed that ants form single files as a means of drag reduction. However, the PCs are simply wrong to suggest we claim that ant single files are a means of drag reduction. First, drag reduction is just one mechanism of collective energy saving, and nowhere do we assert that drag reduction is the only such means, nor do we suggest that single files among species involve exclusively drag reduction. In the case of ants, we made no representation whatsoever that they exploit drag reduction as a means of energy saving nor do we assert that drag reduction is the source of ants in single file.  All we said was that “single-file travelling formations have been observed among other arthropods, including ants…” Further on, we say, “Among these, ant single file formations have been modelled and studied in terms of energy optimization (Chaudhuri & Nagar, 2015), but we found no reports quantifying the energy savings obtained by such formations.” 

Let’s look briefly at the Chaudhuri & Nagar (2015) paper, which the PCs ought to have done if they were going to allege that we had wrongly referred to the mechanism underlying ant single file formations. Indeed, the very first line of the abstract states:

“We present a model of ant traffic considering individual ants as self-propelled particles undergoing single file motion on a one-dimensional trail."

At p. 4 of the Chaudhuri & Nagar paper, in discussing their methods, the authors describe an aspect of ant single file line optimization that occurs by adjustments in velocity reduction when touching or colliding with each other:

“The reduction of velocity fluctuation with density led to our choice for the diffusion constant getting exponentially suppressed with increase in local density. This ensures that the ant fluid reduces the local effective temperature when density increases, to keep a control over the local pressure. This means that while ants do not completely avoid collisions among themselves, they do make sure that the number of collisions per unit time are kept largely unchanged.”

The point is that arguably there is some form of energy optimization that occurs with single files, NOT that single files necessarily involve drag reduction.  We absolutely did not make such a representation, and the commentators are simply wrong to assert that we somehow implied that ant single file formations involve drag reduction.

Further, I specifically researched ant single-file formation that did not necessarily involve pheromones. The PCs should ask themselves why we chose the E.O. Wilson (1959) and the Hansen and Klotz (2005) references when there are myriad others that talk about ant pheromone signalling and that show ant single files in easily accessible images and photos. In fact, the references were carefully selected to address the very criticism that the PCs have raised.

The E.O. Wilson reference (1959) speaks of ant tandem-running which involves tactile coordination. Wilson, states, at p. 34:

“The behavior of compressus resembles that of paria except that as many as ten or twenty workers follow in a single file behind the leader… Nevertheless, it will have to be remembered that in Cardiocondyla, at least, tandem running is a highly evolved behavioral pattern in its own right. It can be fairly said to include more complex individual behavior than trail-laying and trail-following.”

As an aside, also see “Teaching in tandem-running ants”, by Franks and Richardson (2006. Nature, Vol. 439 January). It is interesting that Franks and Richardson say, “an individual is a teacher if it modifies its behavior at some cost to itself, in order to set an example so that the other individual can learn more quickly.” This is yet another energy saving mechanism among ants, and more generally, that does not involve drag reduction, because pupils save time and energy by not having to learn by trial and error. Pheromones are not specifically or necessarily involved in this energy saving principle.

The Klotz and Hansen (2005), p. 135, reference simply cites another example of ant tandem-running, which the Wilson reference has already said involves single files:

“The methods used to recruit carpenter ants to food sources range from primitive tandem running, to group recruitment, to more advanced behaviors (Holldobler and Wilson 1990). In tandem running, a scout leads while a follower maintains antennal contact with her.”

I suppose we could have identified ant single files in our paper as specifically of the “tandem-running” variety, and discussed why the behavior is not necessarily dominated by pheromone signals, but it was unnecessary to do so in the generalized context.

4.      The criticism regarding the position of enrolled juveniles on a different bedding plane.

The PCs take issue with our having mentioned the position of juveniles on a different bedding plane, as discussed by Blazejowsksi et al. (2016). They go so far as to quote from our paper, but before they read out loud the quote that would have answered their own question, they stopped short. Had they continued they would have read out the following:

“However, because they appear on a different bedding plane, the small enrolled juveniles may have arrived at their positions at a different time, or may have already been at their positions in ‘nursery grounds’ before the queues arrived as Błazejowski et al. (2016) tentatively explained, and probably did not migrate with the queues containing their much larger counterparts.”

We had originally drafted this point slightly differently and, in its original form, was raised by one of the reviewers as requiring revision.  The above is how we addressed the concern. As far as I can tell from the PCs concern, the quoted paragraph quite squarely addresses the issue they have raised.

5.      The Draganits (1998) reference.

One of the PCs suggests the figure we referenced from the Draganits (1998) paper does not show what we claim.  Figure 6 from the Draganits paper is described: “Sharply defined beaten track c. 30 cm wide and more than 1.5 m visible on the bedding surface consisting of more than a dozen individual trackways of probable eurypterids. Single trackways and their walking directions are hard to determine.”

If that was, by itself, the reference we were seeking to use as support for single file behavior among eurypterids, then I would absolutely agree with the PCs criticism. In fact, had I seen this paper by itself, I would not have thought to refer to it.  However, that is why we have included the reference to the Braddy (2001) paper, which is where we find support for our reference and the implication of possible single file behavior.  At p. 127 of Braddy:

“It is interpreted that they were produced at approximately the same time due to the concentrations of trackways on the same bedding planes. A further interesting observation is a ‘beaten track’ with more than a dozen parallel eurypterid trackways (Draganits et al., 1998, Fig. 6), possibly indicating that the eurypterids were following one another.”  (emphasis added).

Now, I can see that Braddy’s reference to parallel trackways could be interpreted to mean following side-by-side rather than in single files, but it seems to me when someone argues for “following” behavior, they are usually speaking of one-behind the other, and the relative narrowness (30 cm) of the ‘beaten’ trackways seems to imply one-behind-the-other following, more so than side-by-side. And, common knowledge suggests that we do not see comparatively long lines of directly horizontally linear side-by-side following to occur much in nature (which does not mean to say it is never seen, but the intuitive interpretation is for one-behind the other following behavior).  In our paper, in the highly general introductory first paragraph, we simply say, “Fossilized ‘beaten’ trackways of probable eurypterids indicate similar queuing behavior (Draganits et al., 1998, fig 6; Braddy, 2001)”. If the PCs want to criticize the implication of possible single files, then they should address the Braddy discussion.  Regardless, our paper is not about eurypterids, and for our purposes it frankly makes no difference whether eurypterids travelled in single files or not – it was simply an example, for the sake of context and interest, of where in the fossil record similar kinds of behavior may be indicated, whether or not the actual events of millions of years ago were as they have been interpreted or suggested in the literature. 

The PCs, however, take umbrage with the reference and charge us with misrepresentation, which is a serious accusation of academic misconduct.  Such an accusation is misguided and out of proportion to the context given that the reference is such a minor component of the paper with no significance to our findings -- not to mention that the PCs allegation is easily refuted in any event on closer look at the Braddy reference.  I suggest, and respectfully request that the PCs retract their allegation of misrepresentation.

6.      The presentation of Figure 1

The PCs have asked why Figure 1 is not much larger and suggest the trilobite images are cropped or low resolution JPEGs.  First, the images from the Radwanksi et al. (2009) paper are not cropped, and whether the images are the highest resolution quality or not is such an insignificant issue that I won’t bother addressing it further. Secondly, perhaps Figure 1 could have been larger, as the PCs suggest; but again, that is such a minor consideration that I won’t bother with it further.  It should also be noted that neither of the peloton images are from the Tour de France, as the PCs suggest, but that is minor.

7.      Summary

I have addressed the question raised as to why we did not refer to birds in our paper. I have further explained why pelotons are indeed an appropriate starting point to model certain collective behaviors of trilobites. 

The PCs have made three more major criticisms they say undermine the entire paper. One of these is an allegation of academic misconduct. First, I have addressed the PCs misguided criticism regarding our reference to ants.  The second major criticism is in suggesting that we had misrepresented the Draganits (1998) paper. The PCs’ have made this allegation without recognizing that the Braddy (2001) paper was the true source of our reference on that point.  I respectfully request the PCs to retract publicly their allegation in this regard.

A third criticism suggests that we have not connected our hypothesis to data, which I have addressed in the foregoing.

Generally, in saying there were “two strikes against” our paper, which were not well-founded criticisms in any event, the PCs seem to have, rather unfortunately, thrown out the baby with the bathwater and have failed to consider its wider context and potential importance, which lies in its proposed physiological and physical (i.e. non-gregarious/behavioral) mechanism to explain how and why trilobites sorted themselves into groups of certain size ranges. By extension, this applies to other species where there is an energy saving mechanism involved, including birds, which we have discussed to some extent in Trenchard and Perc (2016) “Energy saving mechanisms, collective behavior and the variation range hypothesis in biological systems: a review”.

Again, my thanks to the commentators for taking the time to consider and to review our paper, which is much appreciated.

Tuesday, July 4, 2017

Peloton theory and contractual relations

A contract between parties is a cooperative venture.  The contracting parties seek to exchange something of value from the bargain; otherwise they would not enter it.  There are many theories of contractual relations (e.g. as noted in 1), which I do not propose to discuss in detail.  What I do want to explore, however, are some of the resource-related conditions under which parties are likely to enter contracts.  Similarly, I wish to explore certain conditions under which parties are unlikely to enter contracts, even if the parties are willing and able to enter such contracts and would choose to do so if the appropriate conditions for doing so existed.

More specifically, I wish to explore the hypothesis that contracts tend to be formed under conditions of relative personal or business prosperity, and that as parties' prosperity diminishes, the likelihood that they will enter a contract also diminishes. Another way to state this is that as parties' resources become increasingly strained, so diminishes the likelihood that parties will form contracts.

There is nothing particularly novel about this; indeed it may seem obvious that parties must have some minimum level of affluence in order to contemplate entering contracts of any kind. However, from what limited research I have done, there does not appear to be much literature that identifies the threshold level of resource scarcity at which parties will choose not to enter the kind of cooperative bargain that a contract entails. The actual presence of such a threshold does seem to be implied by the work of Ronald Coase, for example, some of whose work (2, 3) I will look at here in more detail, and no doubt many others.  Yet the question of how and where that threshold occurs, if it exists, seems to be rather an open one, and this is the subject of this present exploration.  I aim to elucidate this problem by what I suggest are simple analogous dynamics: the dynamics of bicycle pelotons.

Enter peloton theory

Pelotons are groups of cyclists coupled by the energy saving benefits of drafting. Commonly known among competitive cyclists, drafting occurs when a cyclist follows sufficiently near another in a region of reduced air pressure; this permits the following cyclist to ride with reduced power output at the pace set by the leading cyclist.  

A peloton may seem to be an odd source of inspiration for understanding aspects of contract theory. However, it is not as far-fetched as it may seem.  For instance, the strategies of cyclists in mass-start bicycle races (and who therefore form pelotons) are highly amenable to game-theory analysis, which involves implied bargains, cooperation and defection (Mignot, 2016).  Any sort of bargain is contractual in nature due to the parties’ exchange of some consideration of value.

Such strategies and game theory analysis would thus be an obvious source of any analogies between contract theory and pelotons. However, I propose to drill down farther to look beneath the deliberate and conscious strategies that cyclists might employ, toward basic physical principles that underlie unconscious self-organizing peloton behaviors.  These “unconscious” behaviors are global, or collective, in the sense that they emerge holistically among the entire peloton, independently of the behavior of individual cyclists.  In this respect, collective peloton behavior cannot be directly predicted by analyzing the behavior of an individual cyclist in isolation.

The basic physical principles that drive collective peloton behavior are differentials in cyclists’ maximal sustainable outputs, or their fitness or metabolic capacities, as mediated by the energy saving benefits of drafting.  In (5, 6) we describe phases of peloton behavior that emerge across domains of cyclists' metabolic outputs. Between these domains, or phases, are certain collective output thresholds that separate these phases, identifiable by their different descriptions of quantifiable global behaviors.  

In (5, 6) we describe two primary phases by their topologies and energetic principles: a stretched formation in which the cyclists ride at near maximal-sustainable outputs (MSO); a compact formation, in which cyclists collectively ride below their MSOs.  We also describe the compact formation as a convective phase, for reasons I don’t discuss here. We can quantify the threshold between these phases as corresponding to the quantity of energy saving generated by drafting (5, 6).  

In (7) I proposed an alternative description for these phases, and introduced the notion of "protocooperative behavior" (which, it should be noted, is different from "protocooperation").  This describes the range of self-organizing peloton dynamics that includes the above-noted primary phases, but described differently as 1), a cooperative phase; and 2) a predominantly free-riding phase. The cooperative phase is the same as the compact or convective phase, and occurs at sufficiently low collective power or metabolic outputs so as to permit cyclists to share time in the highest cost non-drafting positions; while the free-riding phase is the stretched phase that emerges at a comparatively high collective metabolic output -- in this phase cyclists are forced to maximize time in drafting positions when it is physiologically impossible for cyclists to share time in the highest-cost front position. Of course, if the collective speed drops, cyclists can then generally resume sharing time in the front (non-drafting) positions, in which case the cooperative phase is re-established.  As stated, these dynamics emerge naturally from the coupled metabolic outputs of the cyclists as facilitated by the power reductions obtained by draftinga,b

In (7) I proposed certain principles of protocooperative behavior, including that:
·    Protocooperative behavior emerges in pelotons as a function of differentials in cyclists’ energetic requirements, whose outputs are coupled by the energy saving mechanism of drafting.

·      At comparatively low speeds when cyclists’ capacity to pass others is abundant, there is a tendency for cyclists to share time spent in the highest cost non-drafting positions. This tendency diminishes as collective speeds increase and free-riding (i.e. extended exploitation of the lowest-cost positions) increases. 

·      There is a quantifiable threshold between the cooperative phase and the predominantly free-riding phase. This “protocooperative threshold” exists as a function of the quantity of energy saved by drafting, and the difference between the output of the leading rider and maximum capacities of the following riders. Coupled cyclists thus approach this threshold when following riders approach their maximal sustainable outputs at the speed set by the front rider, even when drafting, since the follower’s ability to pass the front rider by accelerating is reduced to a near-impossibility. And, as indicated, below this threshold, cooperative passing behavior and the sharing of costly front positions occurs more abundantly; and above this threshold, free-riding is generally a physiological necessity.

Perhaps one of the potentially more controversial, and counter-intuitive, implications of this theoretical framework is that cooperation does not emerge in times of high stress, as might be the intuitive conclusion. Rather, I am suggesting that cooperation tends to emerge when resources are plentiful. In other words, cooperation is a luxury and when individuals are strained to their maximum capacities and their available resources are severely limited, individuals are less likely to cooperate and tend to act predominantly in their self-interest. This is counter to the intuitive conclusion that stressful conditions necessitate or precede cooperation to alleviate the collective stress (at present I don’t have a good citation for this).

At this point I confess that I cannot cite exhaustive evidence to support the assertion that cooperation is a luxury; for this reason I embark only on an exploration for such evidence, some of which appears to be found among elements of contract theory. All of this a developing work in progress.

Connecting peloton theory and contract theory

So how does peloton protocooperative behavior shed any light on the hypothesis that parties to a contract will execute their agreements in conditions of relative prosperity, and that there is an identifiable threshold between cooperative contracts and free-riding contractual relations?

     First let us turn to the work of Ronald Coase, and his seminal work, The Nature of the Firm (1937).  Coase earned a Nobel prize in 1991 for work that originated in his 1937 paper (8). 

Coase describes the function of firms and how they emerge in a free market to reduce “transaction costs”, or costly inefficiencies in contractual relations. Coase describes it this way (p. 390):
The main reason why it is profitable to establish a firm would seem to be that there is a cost of using the price mechanism.  The most obvious cost of “organising” production through the price mechanism is that of discovering what the relevant prices are.  This cost may be reduced but it will not be eliminated by the emergence of specialists who will sell this information.  The costs of negotiating and concluding a separate contract for each exchange transaction which takes place on a market must also be taken into account. Again, in certain markets, e.g. produce exchanges, a technique is devised for minimising these contract costs; but they are not eliminated.  It is true that contracts are not eliminated when there is a firm but they are greatly reduced. A factor of production (or the owner thereof) does not have to make a series of contracts with the factors with whom he is co-operating within his firm, as would be necessary, of course, if this co-operation were as a direct result of the working of the price mechanism. For this series of contracts is substituted one.
   In view of Coase’s description of the emergence of the firm as a means of reducing inefficient transaction costs, I suggest, albeit perhaps over-simplistically, that the emergence of a firm is analogous to the cooperative phase of peloton dynamics at comparatively low collective output.  In this view, a firm emerges when there is some comparative abundance of resources and energy available to the managers and employees who comprise the firm. The firm thus precedes and/or prevents the incremental increase in transaction costs required for a series of individual contracts, which costs potentially increase until contracting parties reach the limits of their financial or operational resources.   

Thus, on one hand, it seems fair to say that that the firm emerges not as a response to high transaction costs, but prior to the point at which parties incur such costs. On the other hand, it is also perhaps fair to say that the emergence of the firm is indeed a rational and expected response to the high transaction costs of a series of costly individual contracts. If it is the latter, then the firm represents the collapse, if you will, of the high-output free-riding phase that occurs in times of high-transaction cost contracts. Under both these perspectives, the peloton analogy is sustainable, but perhaps it is not entirely consistent with a strict view that cooperation emerges only in times of luxury. Perhaps we are left with a kind of chicken-or-egg scenario that is impossible to resolve.

Oscillating contractual conditions

At this juncture, it is premature, based on this limited exploration, to conclude with any degree of certainty that efficient contractual conditions, such as the emergence of firms, arise in times of relative luxury. However, we appear to be left with a viable analogue of oscillating contractual conditions: high transaction cost relationships are like the stretched phase of peloton behavior in which resources are strained to their maximum availability; the emergence of firms is like the lower-cost cooperative (or compact, or convective) phase of peloton dynamics. In a given economy, we may imagine that these conditions will oscillate over time, very much as the sorts of oscillating phase dynamics we observe in pelotons.

At this point, I suggest that the peloton analogy goes farther than merely illustrating a point about oscillating contractual relationships in a broad economic context.  Rather, I suggest that the analogy describes a real theoretical framework for investigating the presence of quantifiable energetic-related thresholds of contractual relations.  Obviously, a lot more work needs to be done to develop this, however.

     With this limited and simplistic foray into some new explorations, I will leave off.  In a further installment, I’ll look at Coase’s discourse on “The Problem of Social Cost”, and how contracts for compensation and litigation damages tend to equalize differentials in parties’ economic positions. I argue that equalization of these differentials is rather like the effect of the energy saving mechanism of drafting in pelotons, by which cyclists equalize their output differentials. I’ll also consider standard form contracts, otherwise known as adhesion contracts, how they tend to reduce transaction costs and promote free-riding (Waddams et al., 2000) and identify analogous peloton behaviors.


a As noted, here I am not concerned with dynamics that result from cyclists' deliberate strategies. Some might argue that it is impossible to separate cyclists' conscious strategies from the collective dynamics of the peloton. However, the fact that we can simulate basic collective behavior of pelotons and their phase dynamics, as we have done in (6) based on a few basic parameters and without introducing volitional strategies, strongly suggests that certain basic peloton dynamics self-organize independently of these volitional strategies.  

b Some might point to a third phase that emerges at very low metabolic outputs, when free riding is also abundant because riders do not tend to share costly front positions. To the extent such a phase exists, it is distinguishable from high-output free-riding that occurs by physiological necessity. In this high-output phase, cyclists are physically unable to share the front position and must free ride to sustain the pace set by the front rider. In the low-output phase, cyclists have a choice to share the front position and, should they do so, a general increase in speed is observed as cyclists attempt to shift positions within the peloton to achieve front positions or other non-drafting positions, such as while moving up along perimeters -- hence generating the compact, or cooperative phase.


1.  Waddams, S.W., Trebilcock, M.J., Waldron, M.A. 2000. Cases and Materials on Contracts. Ch 1. Perspectives on Contract Law.  Edmond Montgomery Publications Limited, Toronto, Canada.

2.  Coase, R.H., 1960. The problem of social cost. The Journal of Law and Economics, (3), 1-44.

3.   Coase, R.H., 1937. The nature of the firm. Economica, New series, 4(16), 386-485.

4. Mignot, J.F., 2016. Strategic Behavior in Road Cycling Competitions. In The Economics of Professional Road Cycling (pp. 207-231). Springer International Publishing.

5.  Trenchard, H., Richardson, A., Ratamero, E. and Perc, M., 2014. Collective behavior and the identification of phases in bicycle pelotons. Physica A: Statistical Mechanics and its Applications405, pp.92-103.

6.   Trenchard, H., Ratamero, E., Richardson, A. and Perc, M., 2015. A deceleration model for bicycle peloton dynamics and group sorting. Applied Mathematics and Computation251, 24-34.

7.  Trenchard, H. The peloton superorganism and protocooperative behavior. Applied Mathematics and Computation 270 (2015): 179-192.