Discussion of Session 4
Kirman: Dr. Couzin, you said in passing that it is very bad to be isolated because you know you are likely to get picked out by a predator. But there is a lot of literature on war regarding the question of whether it is better for ships to sail in convoys or scattered around. It is not so obvious to me mathematically that an isolated individual floating out there is going to attract more attention from some predator than a group. And my second question is: You said that, in some animals, intention is obvious. But bees, for example, vigorously indicate whether they think they have found an advantage for their hive. So, is there more to it?
Couzin: In relation to the first question, there is a lot of work in progress, but it has really been quite difficult to address this issue. So, we have done two things. One is that we looked at controlling one side of this equation: we had real predators, real fish predators, hunting and exerting a selection pressure on a virtual prey population. Nothing in the rules I set made the members of this virtual prey population evolve to isolate themselves individually. They evolved to group together and to move together.
This relates to existing theories. For example, if a predator is at a certain distance from which it can detect your group, if you move close to another individual, you are a little more easy to see, but you have also divided your risk by two. We have shown in the real world that predators really struggle above a certain group size. The per capita probabil-ity to become their meal is very low. But if we slice up these groups to make them into smaller entities, the risk shoots up. For single individuals, the risk is around 98 %. This goes back to old studies in Russia. If you put a single fish in a tank, it will be caught within nine to ten seconds, but if you put in twenty fish, an hour later the predator still has not caught anything.
Now, in relation to what you said about the bees, this is a very different scenario. Bees have evolved to work together for the benefit of their colony and have developed specific signalling mechanisms to communicate with each other. You can think of a bee colony almost as a distributed brain. The organisms that I study are selfish. We have investigated for a long time whether they can indicate their confidence, for example. We have a paper showing that they can actually do this. Their directedness is correlated with how strongly they influence others, even though the others are not aware of it. But they are not identify-ing it like the bees are. Remember, in conflict situations, when there is a small propor-tion of uninformed individuals, the strength of preferences plays no longer a role. That is not because their confidence has changed. It is because the dynamics of the system have changed. So, there are lots of non-trivial non-linearities when you start dealing with these collective systems. Hence, modelling has been very important. Turning to things like physical spin systems which have been studied for a very long time has provided us with insights that other types of models have never provided before.
Discussion of Session 4
Nova Acta Leopoldina NF Nr. 419, 116 –117 (2017) 117
Kirman: Professor Stichweh, one would have thought that what structured societies, cer-tainly early on, was to a large extent geography: being concentrated around rivers or being blocked into certain areas. But you never mentioned somewhat basic geographical considerations.
Stichweh: The physical features of the earth are external to society. As environmental con-ditions, they are nonetheless relevant for the evolution of society. On the other hand, it is remarkable that human social systems have established themselves under all ecological conditions.
Kirman: But today, resources are still geographically located – minerals, oil, and so on.
Stichweh: Yes, of course. But, you know, it is also true that there is a new type of economy arising that surfaces in our information economy. Resources are still important, but not as important as they were for many earlier societies. You cannot explain the economic structures of Switzerland or Israel by pointing to external resources.
Lengauer: Dr. Couzin, it seems to me that you based much of what you said on simula-tion. But some of these things look to me like they may invite closed-form solutions. For instance, are there closed-form analyses of the bifurcation states?
Couzin: I mostly base my knowledge on experiments. But you are right. The models that I showed you here were simulations due to time constraints. If, for example, you look at this story with the uninformed individuals and the role they play in terms of these bifurcations, in the paper, there is also an analytic model. So, we have used moment expansion and mo-ment closure to find an analytic solution. We think this is a general principle because these analytic models give us a solution to the bifurcations.
Nüsslein-Volhard: You said that for motion, the lateral line does not play a role. So, what do they see in the other fish? Did you conduct experiments where your fish have differ-ent sizes or differdiffer-ent colours, species, or speeds of swimming? I mean, they must be very similar if they respond properly according to this model.
Couzin: It is a very interesting question, this issue of what the fish are paying attention to.
There are two aspects. They are paying attention to things like the angle subtended on the retina of other individuals. The angle is subtended, not the orientation. They have no idea of the orientation. Christoph Koch showed earlier that there is a very simple neural model that allows you to do this very quick ranking of objects of different size.
Now, that is not suggesting that this is universal. This fits for escape behaviour. One thing we have done is map the three-dimensional structure of the retina of zebrafish. They have a high-resolution region around 62 degrees coming up. We are beginning to map which areas of the retina are sensitive to temporal changes and which areas are sensitive to other features. So, we trying to get at it from the physiological angle.
We have developed a close-looped virtual reality environment whereby we reconstruct the world at 120 Hertz from the perspective of the eyes of a focal individual, much like the Oculus Rift virtual reality headset. So, now we can have virtual photorealistic fish with motion-captured data or simulated data. It is unbelievable – we can simulate physical ob-jects in the water and you cannot distinguish between them. You can have the virtual fish, virtual food particles, and virtual predators. I think that is going to be one of the technolo-gies that is really going to allow us to represent the exact same stimuli on exactly the same part of the retina repeatedly for different individuals in order to really get the mapping from vision to motor response.
Session 5
Chair: Bärbel Friedrich ML (Berlin)
Nova Acta Leopoldina NF Nr. 419, 121–128 (2017)
121