Wednesday, May 11, 2016

Our new paper: Trenchard H., Perc, M. "Equivalences in biological and economical systems: Peloton dynamics and the rebound effect."

Our paper has just been published in PLOS ONE. This paper foreshadows what I anticipate will ultimately be a more important paper about energy savings mechanisms in biological systems, also co-authored with Matjaz Perc, currently under consideration for publication. When that paper comes out, I'll have more to say about some implications of what we discuss there in relation to what we discuss in this PLOS ONE paper. 

On a related side note, I am also hoping to hear definitive word soon on another paper prepared in collaboration with Andrew Renfree and Derek Peters from the University of Worcester, in which we apply our peloton model to groups of runners and test the effects of drafting on certain collective running dynamics. I have also now resumed work on a collaborative analysis of fish schooling dynamics that applies the peloton model.

So, in a sense this new PLOS ONE paper is a companion piece to the larger review paper in which we review literature on energy savings mechanisms in natural systems, and wherein we identify certain principles of the collective dynamics of pelotons that are common to other natural systems.

It is difficult to anticipate how our PLOS ONE paper may be viewed, if it gets much attention at all. I don't deny that we are somewhat perilously pushing the envelope of the peloton analogy into the realm of economics. Broadly speaking, some might argue that our attempts at identifying commonalities between certain economic parameters and biological ones are naive and audacious. There are risks to this interdisciplinary endeavor, but scientific breakthroughs are impossible without such risks and occasional failures. Regardless, clearly PLOS ONE and the reviewers have judged the analysis of sufficient merit to publish it for further appraisal in the wider cauldron of academic consideration.

A brief summary:
Our model of the rebound effect is premised on four main factors: 1. the price of the energy service, externally imposed upon the consumer; 2. the consumer’s maximum capacity (or budget) to pay for the energy service; 3. the reduction in cost to the consumer due to some energy service efficiency, as a percentage; 4. the rebound quantity, as a percentage. In our paper we identify the first three as the primary ones, but the fourth one is obviously of critical importance and discussed in detail in our paper.

These factors all have equivalences in peloton dynamics, respectively: 1. The speed set by a pacesetter in a non-drafting position (akin to the imposed cost of the service to the consumer); 2. The maximum sustainable output of a following cyclist in a drafting position (akin to the consumer’s available budget); 3. The energy savings quantity due to drafting, as a percentage (akin to the efficiency in the energy service that reduces the service cost to the consumer by some percentage); 4. Potentially some surplus energy facilitated by the energy savings mechanism of drafting that permits the cyclist to achieve higher speeds by drafting than she could without the drafting benefit (akin to the fraction of the consumer’s budget that has been freed for the consumer to purchase more of the energy service as a result of the reduction in cost of the energy service, than previously used).

By adapting a basic equation that describes the relationship of these factors in peloton dynamics, we have derived an analogous equation that describes the relationship between these four economic factors. Thus a ratio that models these factors allows us to identify two main thresholds that we have also identified in peloton dynamics.  The first one is clear: a decoupling threshold between the price of an energy service and a consumers ability to pay for it; the second is less clear but is based on upon the application of an analogous threshold in pelotons: the "protocooperative" threshold between one phase of collective behavior in which cyclists can share costly front positions, and a second phase of collective behavior in which cyclists can sustain the speed of a pacesetter only by exploiting the energy savings mechanism (drafting) but cannot pass the pacesetter in order to share the costly front position.

Our paper has just been published
Our paper has just been publishedI anticipate some criticisms of our approach and more particularly to our interpretation of the model. However, I feel it is prudent at this point first to hear what the criticisms may be before I try to anticipate and enumerate them here. My sense at this early stage is that the rebound ratio equation itself is defensible and, if there are problems in the paper, it isn't in the model itself, but in how best to interpret it. Our present interpretation of it and the effects of it may need to be modified in light of feedback and further analysis. 

If in the passage of time some or other aspects of our analysis turn out to be flawed, and if nothing else is achieved by our new paper in PLOS ONE, I hope that this singular point will stand the test of time: certain principles of peloton dynamics have application across a wide variety of systems, including not only a wide range of natural biological systems, but also among human-centric economic ones.