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.
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.