One of the most famous examples of the cooperative management of natural resources known to anthropology is the Subaks System in Bali. Subaks are collectives of Balines farmers who get together and manage irrigation with which they grow paddy rice and they've been doing this for 1000 years. So in this study we're going to talk about a model to compare the effectiveness of different Subaks along a river in Bali. We have inscriptions dating from the 9th century that would speak of irrigation tunnel builders, so this is a very ancient system. Once a year or maybe more often Balines farmers who share the same irrigation system will get together, have a meeting and decide what they're going to plant and when they will plant it. And that decision will determine how much water needs to flow into each field. These decisions are usually taken in water temples, and farmers like to bring offerings like these to give thanks to the gods and goddesses who make their island so prosperous. Meetings may include representatives from multiple Subak, but the basic level of cooperation is within each Subak. So, in this study, we used a very simple technique, a game called the ultimatum game, to figure out if there are differences in the willingness to cooperate of farmers in different Subaks. The ultimatum game isn't even a game really, it's just a very simple thing in which an experimenter, in this case me, gives some gift equivalent to a day's wage. So let's say maybe $100 to someone who then has the opportunity to keep it all or to give some fraction of that gift to someone else. The identity of the donor and the recipient are kept secret. So we gave the equivalent of a day's wage to the farmers in each of eight Su box and said here you go. You may share as much or as little as you like with the other farmers in your Subak. In addition, we asked the farmers how successful is your Subak? How cooperative is your Subak? So here are the results, on this axis, the y axis is the size of the gift. How much was the farmer willing to give to someone else in his Subak anonymously on the x axis the condition of their Subak so this is very bad, that's very good. We see two patterns, that downstream Subak which are experiencing some difficulties show a pattern in which the worse the condition of the Subak, the lower the gift, the less willing they are to be generous. On the other hand, the upstream Subak showed just the opposite pattern. Here, the very largest gifts were given by the upstream Subak, that was in the worst condition. That Subak is having problems with its irrigation system. So under those circumstances, this Subak rather than giving up, they're doubling down and be even more generous to their neighbors. So we see really two quite different contrasting patterns just using that simple little ultimatum game. It's a suggestion that patterns of cooperation vary not just between individuals but between whole Subak, It's a property of the Subak itself as a social institution. So here are the results of a survey that we did as we had the farmers play. The ultimatum game took each farmer about half an hour, we looked at questions like, what's the structure of the community? What about their farming practices? What about religious practices, and how do they manage conflict? We also see two very clear patterns here, with respect to sanctions here the lower Subak here the upper Subak. Sanctions are much more effective in the upper Subaks than in the lower Subaks, the line in the middle is the median or the mean value. And then this span is the range of variation, so we can see in general. The upper Subaks are much more willing to follow the sanctions imposed on them by their Subak. Here's the effectiveness of the Subak and managing collective labour. Once again, we see this difference the upstream Subaks are much more effective in managing labour, here's temple rituals. Both of them are pretty good at temple rituals, but the upstream Subaks again, are more effective at managing temple rituals. On the other hand, interestingly, land ownership is just about the same, there's no real difference. So the differences between the Subaks appear not to have to do with large discrepancies in the amount of land that farmers have, In fact, they're almost the same. So here we analyze the results of that survey, here are the variables class cast, condition of the Subak attendance and meetings and so forth. Here we plot them in In a principal component analysis, that red circle indicates whether the results are significant. The angle of these arrows indicates how closely correlated the responses are. So number 1, number 7 and number 2 are very closely correlated. The arrows are right next to each other, and they're also very large. One, seven and two are caste, class and sanctions, that means that those three variables work the same way. However, what we're really interested in is the comparison between the upstream Subaks and the downstream Subaks. So here's what we see, just glancing at these pictures you can see that the arrows point in very different directions with the upstream and the downstream Subaks. We have two different patterns of dynamical behavior captured here by the principal components analysis. The next step in the analysis was to ask well then, if we have an effect successful and less successful Subaks, what would it take for an unsuccessful upstream Subak downstream Subak to become more like the upstream Subaks. In other words, which variables might dominate a transition between those points, which ones count, what would make the difference and here we see adapted from physics and analysis of the energy landscape. So we're looking at principal component space and looking at the relationship between variables and we're seeing which ones would dominate transition path between the center of this dynamical pattern and the center of that one. Notice that the upstream Subak behavioral system, they're all very similar, and they're quite different from the downstream Subaks. So, in this we capture not only the dynamics, but also the possible transition paths between two patterns of behavior, one more cooperative, one less cooperative. Here's another way to look at the same picture, we're looking at the two patterns, upstream and downstream. We're finding that one is very deep meaning that the patterns of behavior are very similar, the other is much more spread out. After we finished the model that explore the reasons for transitions between regimes among the Subaks on the Sungi river. A friend of mine here at into you, physicists, Lock Chwe Yue, and his graduate student Hendrik Sugiarto, became interested in the question whether they could apply some concepts from Game Theory. To understand better the transitions between cooperation and defection in the model, I'm about to describe their model. It is by far the most complicated piece of mathematics in this lecture, so you can have, you have a choice. Now you can either plow ahead with me and see if you can understand the model they developed, or you can skip ahead to the next section, where we go to a video in which I explained more colourful, the dynamics of cooperation in the Subaks. It's your choice, If you've chosen to stick with me, let's have a look at the model that Lock Yue and Hendrik developed. The model that Lock Yue and Hendrik developed is based on an earlier model published by Tavoni-Schluter and Simon Levine, It's a model of common pool resource use. Now in this model, the resource level Rt is renewed logistically and is extracted at a rate proportional to the communal effort. E a time t, in order to set up the game theoretical treatment of individual strategies. The communal effort is written explicitly as a sum over efforts by cooperators and defectors, and the fraction of cooperators f sub c. The contest between cooperators and defectors is written in terms of their different payoffs. It's computed in terms of a production function F, which depends on the communal effort E, as well as the resource level R. Those of you who are not familiar with the concept of a production function can look up the Cobb Douglas production function that's commonly used by economists. There's an interesting surprises in this model, so let's start here, here's the fraction of co-operators, and here's the resource inflow. So when resources are low, most people cooperate and then as the amount of resources increases, some defectors appear. We see the cooperative regime begin to change, you see the production that the number of cooperators is gradually going down to 80% to about 60%. And then here, right around 60% there's a regime shift, meaning the system now becomes dominated by the defectors and production collapses. Now interestingly, if we back off a little on the resources, then cooperators begin to appear again, and gradually they increase the fraction of cooperators increases as we reduce the resources. So the need to cooperate becomes obvious to everybody. And we go back until we hit a second regime shift, and then it will return to the cooperative regime and effective use of the resources. So here we see, history says that means the system gets locked in here. Low productivity, but as the resources dwindle because nobody's cooperating, then gradually it comes back up, until it returns to the cooperative vision. Next step was to add a conductivity convention to the model. So here, K Is connectivity it means what is the average connection of one farmer to other farmers how many farmers are grouped together. In other words, it's the kind of index of a social bond, so here we have very strong connectivity, a very tightly connected network K equals 45. And then compared to K equals five, a very sparsely connected network, so the behavior with K equals 45 is just as the previous model predicted. It shows history says this looks like the first model. But as we decrease the conductivity of the system, going down to K equals five sparsely connected system, then we see a different behavior. Here's that curve, It's a smooth drop as the resource inflow increases, then the proportion of co-operators steadily declines until it gets too close to zero. So, connectivity has a major effect on the behavior of this dynamical system. Another way to see how the possibility of a regime shift can depend upon the conductivity of the network is to plot the steady state resource level against resource inflow. So here we have k equals five, that is a very sparsely connected network. And the curve goes like this utilization increases as the resource inflow increases, then it drops and then it smoothly recovers there is no historises there is no regime shift, but if we increase the conductivity to K equals 15 that's the blue picture. Then we get a historises loop, meaning it will drop and then recover as an overshoot. And thus a regime shift a shift between two different regimes, as we continue to increase K to 25. Those are the blue triangles, you can see that the regime shift loop histories this loop is larger. And finally when k is 45 you get the very most dramatic example of a historises loop. Together with a few other collaborators Lock Yue and Hendrik investigated how this regime shift picture would change when there's a community structure in the social network of farmers. In the simplest case of two communities of farmers where a farmer within one of the communities will be connected to many other farmers in the same community, but to fewer farmers in the other community. They found that instead of a single regime shift, it's now possible to have two regime shifts between three regimes. The first regime is cooperative, and both communities are dominated by co operators. In contrast, the third regime is defective in that both communities are dominated by defectors. But the second newly emerged regime consists of a cooperative community and a defective community. Lock Yue and Hendrik called it the third regime disharmonious What Lock Chew and Henrick discovered is that by incorporating results of relations between farmers into communities, a new regime appears. So here we have three different kinds of regimes, one of them is cooperative that's down here, the second is defective. And the defective regime It's also evident from the model, but they also discovered this transitional regime which he calls disharmonious. And that has to do with relations within the village rather than the inflow of resources. So with that insight, it became possible to get a much richer, more nuanced picture of the possibility of regime shifts between the Subaks. And that insight was very helpful to me as I explored the survey data from a much richer and larger survey of Subaks that we had just completed. And the next section of the lecture will go to a video, I'll take you to Bali.