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.

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