Systems Overshoot And Collapse

TITLE: Systems: Overshoot and Collapse CHANNEL: Donella Meadows DATE: 2017-08-11 ---TRANSCRIPT--- okay okay you remember when I mentioned the four characteristics that I thought were most important of for system dynamics as a method the last one I mentioned was the relationship between feedback loops structure and the behavior of a complex system well I’d like to spend today’s lecture talking about that characteristic of the method in quite a bit more detail by giving you three different models all of which have the same basic structure and the same behavior but in fact are representative of extremely different systems but on the surface you might not expect would behave the same or would have similar dynamic properties I’d also like to get across an other aspect of system dynamics that I think is unique to this method and that is the way we intend to use the models that we make my impression from talking to people who make other kinds of models and you can verify this later in the course is that a number of models are made for the purpose of essentially putting in a question and getting out an answer it’s what I would call blackbox modeling you give a question to black box it tells you the answer and you’re not completely clear what logical process inside that black box gave you the output that you see system dynamicists have a strong revulsion against that kind of modeling that’s why they give it the name black box modeling what we try to do and we’re not always successful in doing it is to build a model that makes our mental understanding of the system so much better that eventually we don’t in fact need the computer model anymore that is what we’re really trying to do is increase our intuition our understanding our mental models of the system that we’re interested in and having done that it’s ideally at least we don’t need the computer anymore at all the computer is a tool to help us increase understanding now give you an example of what I mean by that let’s take a system that you are all entirely too familiar with by this time which is the Kaibab gear growing the deer growing on the Kaibab plateau now you’ve just completed assigned an assignment on this system so you should have a very good understanding of why that system behaves the way it does why the deer grow exponentially why they stopped growing why they fall in a collapse mode and then why they come to a new equilibrium with the food that sustains them did you ever really think or try to say in a few sentences why the Kaibab model or that model that you were working with for your assignment behaved the way it did what was really happening at each moment at each behavior interval what was interacting what was dominating the system why did it overshoot and collapse well let me give you the explanation that I would give from my experience and working with the model just to give you an idea of what what kind of understanding we hope to get when we’ve worked with a model for a long time and you should be able to follow this quite easily because you’re now all experts on the Kaibab deer system as you remember this is the causal diagram for the deer model three that you’ve been working with and the behavior of the system is shown here this is the system before you added policies to it the system going in a natural direction with only a policy of removing the Predators from the plateau and as you remember the deer population was in equilibrium for a long time meaning the number of deer didn’t change the number of predators didn’t change the amount of biomass growing on the plateau didn’t change the predator population started moving down the deer population started growing exponentially and eventually there was this collapse of the deer population collapse of the food supply and a new recursion form out here now remember that I said that exponential growth whenever I see it tells me that there must be a positive feedback loop dominating the system at that time and if you look back at the causal structure of this model the positive feedback loop that is dominating in this section of the model is very clearly there’s only one possibility it’s this birth population positive feedback that starts going around the runway now why wasn’t that systems that loop dominating the system here where everything was in equilibrium equilibrium in system dynamics means that the levels are not changing in value there are two levels in the system the deer populations and the food if if these two things are constant it must mean that the inflow rate is equal to the outflow rate that is that the net increase of the deer was just balanced by the predation rate and that the regeneration rate of the food on the plateau was just balanced by the rate at which the deer ate the food this is in this first equilibrium part of the behavior mode the reason that equilibrium established itself so nicely was that the predation rate which was at that time balancing the net increase rate of the deer was part of a negative feedback loop and this loop is operating to adjust itself so that whatever happens over here to the deer population the predation rate will counteract that tendency for example if there were a particularly bad year let’s say in the deer population fell a little bit what happened would be the deer density would fall the deer the Predators would find it more difficult to find deer and kill them and therefore they would eat fewer the predation rate would be lower in the deer population could regenerate itself again the same thing the other way around if there were sudden helicopter drop of new deer on to the plateau so that the deer population rose a little then the density would rise the the will who would find it easier to find a deer the deer kill per predator would go up there would be more predation and the deer population would be adjusted back down again and therefore is this negative loop was controlling the system no matter what happened to it even if there were small variations over here so that the deer population stayed in equilibrium well below the food the carrying capacity of the plateau in fact this whole part of the system is not active at all during this first equilibrium part of the standard run as a deer model the food is so much in excess that the net increase the food per Deus was well over anything the deer need the net increase rate is at its maximum and all of these arrows down here are unimportant to the operation of the system now what happens when we start bringing the predator population down in this part of the behavior mode well effectively what happens by the time the predator population comes down to zero this whole feedback loop is illuminated from the system is simply not there anymore gone and therefore the balance between the positive feedback and the negative feedback is destroyed and what must happen in that case is the positive feedback loop becomes more and more dominant it takes over controlling the dynamic behavior of the system there’s nothing to keep the deer population down their net increase rate is their birth rate is higher than the natural death rate and therefore this positive feedback loop starts generating and exponentially growing deer population you notice that that takes some time as you might expect a few deer can’t create a whole lot of deer right away takes them a while the little deer have to grow up and have more deer and so on in fact takes about 20 years before that exponential growth becomes very apparent in the system and then finally growth faster and faster and faster in fact a net increase rate is about twenty percent all the way through but twenty percent of a larger number gets to be an even larger number and so the deer population grows very very rapidly at the end there’s only one thing that can at this point in the system that can interrupt that positive feedback loop and that’s the negative feedback loop that goes through food per deer and the net increase rates that is if the deer population gets high enough per deer becomes lower and lower and lower the net increase rate is finally affected the deer the food is no longer in excess and so the net increase rate starts coming down and eventually this net increase here has to become zero in the deer population is again held in equilibrium now that explanation I just gave you would lead to a sigmoid growth of the deer population and final leveling off as the food prettier gets down toward a thousand calories per year per day now why didn’t that happen why didn’t this loop just slowly take over and balance off this positive loop is causing the deer population to grow well the answer is that there’s another level in this system the food level and at the point where the food drops so low that it stops a net increase of deer the food level is then not in equilibrium at that point there are so many deer that the consumption rate is very much higher than the regeneration rate you can tell that on the on the output graph by the fact that at that point the deer are the food supply is falling very rapidly there’s there are thousands and thousands of deer they’re eating the grass much faster than it can grow back and therefore this level is not in equilibrium although this one passes at least momentarily through an equilibrium point this one is still falling and it drags the rest of the system down with it in other words this part of the system begins to dominate whereas before it wasn’t important at all had no effect on the behavior of the system up through about 1920 1930 suddenly at about 1930 this player the system takes over and runs everything for a little while there’s another positive loop down here if you remember which tends to run in a bad direction that is if the food gets depleted it takes longer and longer for it to regenerate the the meristematic tissue the part of the grass that generates new grass is eaten as well and therefore it takes longer and longer for the food to regenerate there’s less food it gets beaten down even further it takes still longer and so on this positive loop to turning in a negative negative direction food longer regeneration time lower regeneration rate still less food and while that’s running the food supply is plummeting down very rapidly now eventually what conflict causes that loop to come to a halt well what happens is it drags the deer population down with it the food becomes so low that food per deer gets below that thousand kilo calorie per gear per day equilibrium point at that rate as you remember at that point as you remember the net increase rate becomes negative the death rate over balance is the birth rate the deer population at that point begins to fall and that’s right here on the output graph and the deer population finally Falls fast enough and far enough that the food consumption rate comes down to the point where it can be again balanced by the food regeneration rate both of them very very much lower than they had been before and finally these two levels are essentially chasing each other unbalancing each other for a while finally they come into a new balance with a little bit of oscillation at the end of the run we’re in equilibrium again in this case the deer populations positive growth loop is balanced by the food loop that is these deer are existing on subsistence deer nutrition standards they’re half starved therefore their net increase rate is just zero their births balance their deaths there happened to be just enough deer left on the plateau to eat grass at exactly the rate that it grows which now is very much slower than it grew before and the system comes in to a new equilibrium both levels are constant again the rates determining the levels are balanced and another equilibrium is possible in fact given different numbers and different conditions all sorts of equilibrium on the Kaibab plateau are possible depending on how many predators how strong this loop is what the net increase rate is what the food regeneration rate is now this total behavior of the system growth followed by collapse followed by a new equilibrium we call an overshoot and collapse mode behavior mode there are a lot of other possible behavior modes of systems of course I’ll tell you about a few more in a moment but I’d like to focus on that behavior mode as a generic thing now let’s get away from the Kaibab plateau and ask what in general have we learned about systems which have positive loops in them and which have carrying capacities that ultimately limit the growth of a positive loop this is an extremely common sort of system one finds it all over ecological problems and ecological models and also in in a number of economic systems and therefore it’s worth looking at in general and not just with regard to the cobweb plateau anytime there is a growing physical system in a finite environment there will be a positive loop that generates the growth and the environment essentially imposes negative loops on that growth and generates some sort of an equilibrium they’re exactly four ways that this accommodation of the growth with the limited environment can happen and these are shown in the next figure I’m going to call the physical limit to the growth whatever it is the carrying capacity which is the ecological name the carrying capacity simply means the number of growing things deer in this case that can be supported by the environment over the long term that is the sustainable number and the carrying capacity is determined by whatever the most limiting factor necessary for growth is now in a growing system there there is a demand on the carrying capacity which is usually some function of the number of individuals in the case of an industrial society it’s not only the number of people it’s also the number of machines and things that people use and there is a carrying capacity which need not be constant in fact in the dirt case it’s not constant most cases it’s not one possibility is what I call the infinite world possibility and that is that the carrying capacity can grow can be changed in an upward direction by something happening perhaps by this by this population figuring out ways of making it grow if that could go on forever then you could have the carrying capacity going up you can have the population demanding more and more of it but it doesn’t matter because the carrying capacity is growing faster that’s that’s fine as long as you know that the term that you are interested the time horizon over which you’re interested in the system is sufficiently short so that this carrying capacity won’t stop growing and this kind of system is observed and I’ll show you some examples in a little while another possible way of interim interaction between a growing population and a carrying capacity is called the sigmoid pattern and in this case there is exponential growth for some time but as the growing population begins to put more and more demands or come closer and closer to the carrying capacity there’s some immediate signal which slows the growth gradually until finally the population levels off at some point under or just at the carrying capacity and this is a smooth gradual adjustment to whatever the limited carrying capacity is this can happen only under one of two conditions either there’s some immediate signal that the population gets telling it how fast to grow as a function of how far it is from its ultimate limit and the population can respond immediately to that signal this is observed for example in bacteria growing in a petri dish with limited nutrient and the bacterium know immediately and how much nutrient there is around it and is it there’s less nutrient growth more and more slowly so such examples do exist the other possible the other way that this behavior mode can be generated is if there is a very high carrying capacity and some natural saturation mechanism that will bring the growth to a halt before it even comes anywhere near the carrying capacity let’s say there’s some social control or something of that sort and in another example there is the territorial behavior of birds bird simply wild bird simply won’t nest unless they can find a large enough territory that they can defend from all other individuals of their species the territory happens in fact probably to be somewhat larger than what they really need to feed their growing brood but if they can’t get that much territory they don’t breed and this probably causes bird populations to level off without really coming anywhere near their ultimate carrying capacity now another way that a growing population can interact with its carrying capacity is that it does get a signal telling it when it’s stretching a limited resource but it gets the signal late it gets a delayed signal or perhaps it gets a signal on time but it responds to the signal after some delay picture Congress responding to a symbol about or a signal about energy supplies or something of that sort and then you get the idea if there is a delayed response the population is likely to overshoot for a short time the actual long-term carrying capacity of the system and then fall back and if there’s still a delayed signal it may oscillate for quite a while may even and oscillate indefinitely around the carrying capacity this diagram is a little deceptive the carrying capacity probably is also oscillating in an opposite manner that is when the population is over the carrying capacity the carrying capacity might be coming down a little as the population comes under the carrying capacity might regenerate itself and so on so you get the two things oscillating around each other this can go on as I said for quite a while or even indefinitely the oscillations might be damped in order to finally produce an equilibrium situation but there is an irreversible damage or erosion of some sort to the carrying capacity then you get an overshoot and collapse behavior mode and in this case as the population because it has a delayed response to where it is with regard to the carrying capacity as the population shoots over the carrying capacity it begins an irreversible erosion process so that the carrying capacity itself goes down finally dragging the population down with it to some new low equilibrium and this now should look very familiar that’s just the behavior mode that we saw in the dealer model before we put any policies on it to try to change that behavior so just to review the overshoot and collapse mode is most likely to be observed first where there is a positive loop that creates growth that’s not balanced by some nearby negative loop a positive growth loop to generate the exponential growth in the first place second if whatever negative loops will interrupt that growth respond in a delayed way and third if the carrying capacity is in some way irreversibly eroded under those conditions you’re likely to find an overshoot and collapse behavior mode and if you’re wondering where the delays are in the deer model system they’re essentially they’re not explicit in the model that is you didn’t see any of those delay signals or delay signs on the flow diagram in fact we didn’t put an explicit delay in this model but each of these levels is in an effect a delay because it can’t respond immediately the food supply can’t respond instantaneously to what the deer population does it’s an accumulation raishin rate and it’s consumption rate it takes a while for the food to regenerate it takes a while for the deer to eat up what’s there so there’s an implicit delay in a level in fact every level is an implicit delay in a system the same thing with the deer they can’t suddenly adjust their numbers to to make them congruent with whatever the carrying capacity is it takes them a while to be born takes them a while to die it takes a while for this negative loop to generate more deer in fact the implicit delay in this system is that 20% maximum growth rate that that is a limit to the rate at which the deer population can respond on the positive side and so they’re in fact quite a few delays in the way these two levels respond to each other and that’s what is the essence of the problem when the collapse mode begins of course originally there was no problem because the there was no positive growth dominating the system in the first place the predation managed to balance the positive growth tendencies just about exactly okay that’s the deer system now I’d like to talk about two other systems which are very different in fact both of these now involve human beings and so they become instantly more complicated than deer and these two systems however had at least the potential for an overshoot and collapse mode the first one I’d like to talk about is a very simple human system it’s a tribe called the Tim Baga who live in a very steep valley in New Guinea if you can imagine a landscape shaped like a V with a river in the bottom and a mountain on the top the timber on the slope a very steep slope they get about 300 inches of rain a year in other words it’s a rain forest and an exceedingly difficult one to manage agriculturally as you might imagine the Tim Baga were described by a very great anthropologist named Roy Rappaport in a book called pigs for the ancestor he went and studied these people their traditions and rituals and their ways of farming and so on and he became interested in the question how the Sambhav managed to make a living in this very difficult terrain so he sent us particularly large amount of time studying their agricultural practices he discovered that they practice a very common sort of agriculture for the tropics it’s called slash-and-burn agriculture every year they go out and into their territory which is jungle if they don’t do anything else to it they pick the amount of land they need for their gardens they chop down the trees and bring them the ash falls onto the soil and makes it quite full of nutrients they plant their gardens the gardens grow for about two years and then the nutrients are exhausted and the people move on to another piece of jungle and burn that down and let the old piece grow up again into into trees which eventually get big enough that they can come back around burn them again create more ash more nutrient and grow another garden the amount of land at the Tim Baga cultivate in any one year is about twenty percent of the total amount of territory they have so at any one time most of what the hell is jungle and only a small patch or two is growing up in gardens and they should back to the old garden which is now jungle again okay I gave the the pigs for the ancestors book to graduate student one summer and said make a model out of it in fact Rappaport put forth a hypothesis about how the Simba managed to keep their population and their carrying capacity in balance and what we wanted to do with the model was test whether his theory was at least mathematically possible whether we could generate the sort of behavior that the Rapa four observed over the long term in the Simba Society well the first diagram that we produced of this society looked like this now we have a human population instead of a deer population there’s also a net increase the more people the more people can be born and so on there’s another resemblance to the deer system in it we assumed this is a primitive population now no health services that the only really important factor on the net increase rate of the human population was the amount of food available and therefore we put in a loop saying more food gives you a higher net increased rate at least up to a limit this is a nonlinear relationship and more people mean less food per person all else equal now in the tambaba society all else is not equal because sandbar grab a poor reports are very clever about county up their numbers deciding how many acres of garden are going to be needed to support that many and then going out and clearing that many acres and so to model their decision about food production we made this set of assumptions as the human population increases the tribe decides that more food is needed therefore they clear more land each year therefore they produce more food and that essentially really keeps food per capita equal because there were more people and therefore the net increase rate remains constant now there’s one other aspect of the system that Rappaport emphasized very strongly that we had to put in and that is if an acre of jungle land is cleared before it has had a chance to grow up fully then it won’t yield quite as good a harvest of sweet potatoes and other things that the Tim burger grow as it might have if they had let it grow up longer and therefore the more acres are cleared especially when it gets over this 20% level the faster they’re going to have to come cycling back and the left field they’re going to get the next time they come through which will be 19 or 18 or so years later and therefore we have a positive feedback loop saying more acres cleared after a long delay during which they cycle over the rest of their territory gives a lower yield per acre and that will decrease the total food production and furthermore if there’s a lower yield per acre the sandbag are also very clever about looking at the forest and deciding what the yield will be and correcting for the fact that they may have come around too soon by clearing more land trying to keep that total food production up so let’s say for if by some accident there were a lot of people all of a sudden they would have to meet they would need more food they would have to clear more acres let’s say they cleared one 17th of their territory instead of one twentieth well they do that very nicely for 17 years they come back and they find that the trees haven’t grown up as much as they should have so they cleared one sixteenth or one fifteenth larger area and therefore they get more food in the short term but now they have to come back after 15 years and they have to clear even more territory because the soil hasn’t had a chance to regenerate so let’s say it’s 1 12 and so on you can see this is a positive feedback loop gradually bringing the yield down now Rappaport was quite sure that this kind of behavior was possible although he himself didn’t observe it the human population the acres cleared and so on were quite stable in the timber population as he found it if we make this our total model toxic sandbag a population the details of this are does this model the equations and so on if you’re interested are book called toward global equilibrium and you can get it from my library if you’re interested or from the Feldberg library if we just model this system the behavior comes out like this this is now a long period of time zero years to 200 years the heavy line here is the human population and this sort of dashed line is the yield per acre and this line is the intensity of essentially the number of acres cleared per year and what happens is pretty much what we predicted by looking at the feedback structure of the system this positive loop is unlimited in fact there’s another positive loop here more people more acres cleared more food or food per capita high net increase rate more people there are two positive loops in this system and at least in a short term when there’s no food problem there’s nothing to limit those positive loops and so exponential growth takes place as a population eventually after this very long delay while they’re cycling one or two or three times around their territory eventually the yield per acre starts falling rapidly and at that point you have an overshoot and collapse mode the human population eventually gets carried down along with the fertility of the soil and at this point you might as well assume that all of the soil is at San Bhagat territory has washed down into the river and there’s there’s nothing left at all now the interesting thing is as I said that’s not what happened to the ten Baga they’ve been there for thousands of years and that has never happened so something is wrong with our model and Rappaport put forth a theory as to why that has never happened and his theory involves knowing a little bit more about the system in particular as a culture cultural part of the system which we as scientists had first wanted to put in our model one thing that Rappaport spends a long time discussing is the tim bog a big festival I done told you that the sandbag acute cakes they do there’s like members of the family they also plant gardens for the pigs and therefore in fact the food needed here is is calculated not only by the number of people but also by the number of pigs SEM baka keep the Tim baka don’t eat these pigs they just keep them around because they like pigs and every now and then they have a huge festival and they invite all the neighboring tribes in they kill off 80% of the pigs they eat them all there right and quit one festival they dance they drink banana beer and and then for a long time nothing happens in the room few remaining pigs generate more pigs and so on the festivals are explained in extremely mystical terms this is all done for the ancestors and for various gods that we’ve been forests and so on but in fact Rapaport hypothesize that these pigs serve yes indeed a ceremonial purpose but also an important ecological stability purpose and when we caught on to that theory we added a whole new structure to the model that I’ve just described we put in the pig population now and as I said the amount of food needed is calculated for both humans and pigs and therefore even more acres have to be cleared and the harvest is divided between people and pigs so there’s not only food per person but there’s food per Pig and that determines the pigs net increase rate pigs we found out after a great deal of research multiplied faster than humans and therefore this population tends to grow a little faster than this population we looked at Rapaport description of these pig festivals and what generated them and what we found out generated them was complaints from the women of the tribe who are the people who have to take care of the pigs what happens apparently is about every eight or nine or ten years the pig population gets so big that the pigs just get in the way you fall over them on the village streets they break into the gardens and eat the food before they’re supposed to their great burden and the women start grousing and when the women start grousing the men start meeting in the middle of the village and saying hey it’s time for pig festival my wife is planning and when enough men agree upon miss then a pig festival is held and so as the pig population increases the pressure for a festival increases it also happens that the human population increases that’s true because the gardens become if the gardens have to be allocated more to humans than it’s harder to keep pigs and so both of these populations together seem to generate let’s call it social pressure to have a festival in the festival the pig population is decimated about 80% of it disappears so this is reduced and immediately after the festival the Tim baaga having filled themselves with pigs immediately declare war on their neighbors this seems to be an intrinsic part of the festival there’s a short skirmish with arrows and things that goes on for a few days and in the process usually about twelve to twenty percent of the young male population of the Tim Baga and the neighboring tribes are killed and therefore the human population is brought down I hope you can see an enormous negative feedback loop emerging here as these populations increase the pressure for the festival builds up eventually a festival is held the pig population is decreased through feasting and the human population is decreased through war and then the positive growth loops are released to generate more population for a while until pressure builds up for the next festival at least that’s the way Rapoport describes it when we put all of that into a into a system dynamics model we get an output of this sort this is a 40 year slice of time in fact the model goes does this the first hundred years this was the year 100 to 140 and it keeps on doing it forever the human population now is here it builds up slowly for about 10 years and then there’s a pig festival and a war it drops down suddenly slowly builds up drops down and so on and about a 10 or 11 year cycle which is what appears to be roughly the Tim bog recycle the pig population build up faster and drop down farther but along the same pattern the intensity the acres of land cleared also increases as the populations do decreases after the festival and war and increases again and the fertility of the soil essentially the yield per acre is never reached that is never diminished by any of the agricultural activity going on in other words this is a stable system and can go on forever now going back to the causes of an overshoot collapse mode the growth potential in this system is obvious in the both the human and the pig net growth loops the delay in the signal is not important in this in this case because in fact the population never approaches anywhere near its carrying capacity it has its own internal control mechanism to keep it from having to adjust itself to the carrying capacity it probably just fell far short of what could ultimately be supported on the land and the signal is the pig population I Rappaport likens it to a thermostat essentially the pigs grow a little faster than the people and therefore they provide the signal saying we’re getting close to the carrying capacity or perhaps not even to close that it’s time to readjust voice and so down we go and so on that’s not a system most of us would like but it seems to be extremely effective on the other hand it has unstable potential if it’s interfered with it happens to have worked for this embargo for thousands of years under no change of course as soon as we get a model made we start changing the system in the model to see how it would behave under alternate assumptions one of the changes that we made in this model was to assume that let’s say a healthcare clinic was established by the World Health Organization on this embargo slope and the death rate of this embargo which is rather high least by modern standards because there they have never had any medical art I of medical care the death rate gets lowered the birth rate presumably stays the same which means that the net increased loop is strengthened a bit only this change in the system and nothing else the result of that is shown in this output now this is a period of 110 years take a 110 years to see this work itself out in fact the cycles look shorter together here just because this time plot is compressed they are in fact still roughly 10 year cycles the pig population is here going up and down in cycles the human population shows the cycles much less because in fact the growth rate is much stronger and eventually over a long period of time the human population builds itself up because the amount of depth and the war are not enough anymore to balance the excess of births over death and the population very slowly the population builds up more land is cleared that’s shown here the yield on the land goes slowly down the first thing when when they get into real trouble the son baggage Edison the pig population entirely in order to feed more humans when they do that the worst stopped the human population builds rapidly and finally the whole thing collapses you can get almost the same result if you do what in fact the Australian government did do for these people and that was abolish war Australian government said you can have your festivals they’re very colorful they pleased the tourists but please no war civilized people don’t do that and the result of that policy which was implemented or about 10 years ago is shown in this output now the human population shows no ups and downs at all it just grows this is backed by the way to the old the old death rate they’ve taken the clinic out the pig population continues to go up and down because the pig festivals are still held but again eventually the human population gets up above the carrying capacity and the system collapses okay now that we talk about a third model very much more complicated than either of these but in fact dominated by the same sorts of dynamic principles that I’ve talked about in the deer population and in the Embargo population and this is the world 3 model the model that was the basis for the book limits to growth which some of you I expect have heard of it it’s a model of about 250 equations and I’m not going to reveal all of its wonderful intricacies to you today I have here a very simplified causal diagram of some of the more important relationships in the models by no means all but it shows you what some of the main levels in the model are these are shown with boxes and some of the primary interconnections this part of the model up here should look very familiar to you in fact it’s the same as the Kaibab and the shambhala models with very different numbers in it but essentially this is now the human population of the world the birthrate more people more births more births more people the death loop more people more deaths more deaths less people with delays for aging because in this model now we keep track of how many ten-year-olds there are in every year we move them on to B 11 year olds and so on the fertility and the mortality determine also the births and the deaths per year and these things now are very highly variable and respond to many other things in the economic system which is represented down here just as a few examples the fertility rate is assumed to decrease as a population industrial eise’s and this is empirically observed rather commonly that as a nation undergoes industrial development after quite a long delay perhaps several generations the fertility drops education and family planning are generated from the service part of the economy that is hospitals and schools and so on and that also can bring down the birth rate mortality is affected by health services by food per capita and by pollution all of these things are generated by the economic sector as a model and here is an important other important positive feedback loop I should tell you about industrial capital is the physical plant that generates industrial output that is the factories the trucks the machines the roads the mines and so on this is the physical capital standing in place each year it produces a certain amount of output that’s essentially all of the industrial production annual industrial production of a country some of that output is more machines tools factories and roads and so on and that is investment to increase the industrial capacity itself some other part of the industrial output are materials for hospitals and schools which go into the service sector or materials for producing food like tractors and and that part of the oil production which is used in tractors fertilizers and so on and that goes on to generate food another part of the output is pollution and another assumption in the model is that as the industrial output goes up it is made from resources there is a resource level more output drains the resource level as the resource level goes down it takes more capital to produce a unit of resource that is you have to drill deeper or run your boats farther or something of that sort therefore you need more output in order to generate a unit of resource the efficiency of capital goes down and that tends to bring down the industrial output okay so that’s a small negative loop which depletes non-renewable resources there are also a lot of renewable resources in the model primarily in the agricultural sector the capital and the land produce food food divided by population gives food per capita that influences mortality and so on pollution also influences food production if it gets too bad industrial capital is depreciated some of it every year becomes worn out or obsolete and has to be replaced depending on the lifetime of the capital net replacement rate be fast or slow that shows you most of the loop so there’s one important interesting loop here there are many like this from the model I only showed one this illustrates the principles by which the model assumes that this industrial output is distributed among all the needs of the population for the food sector it assumes that there’s some standard or desired food per capita here’s a goal you know a negative feedback loop must be coming up there this desire in fact isn’t constant it’s dependent on the income of the population as the population gets richer it usually wants more in higher-quality food up to a point but there that’s a nonlinear relationship it levels off as people become very rich in fact they don’t desire more food they desire services or something else instead anyway the amount of food is compared the amount of food desired is compared with the amount actually available and the gap determines how much of the output should be put into agriculture how much of the total output of the economy should go into agriculture and that builds up agricultural capital there are similar loops like this determining service output determining how much capital is allocated to non-renewable resource a maintenance or obtaining of non-renewable resources and how much is allocated to investment that will increase the productive capacity of the system in the future ok now back to trying to understand something about the dynamic behavior of this system from its structure there are two dominant positive feedback loops in this system and I believe also in the world system one is the population loop that is at the moment in nearly every population of the world the birth rate is higher than the death rate which means this positive loop is dominating this negative loop and the population is growing exponentially the other positive loop also very apparent in the world system is that the investment rate in industrial capital is higher than the depreciation rate which means that the industrial capital stock is growing that allows more output and more of that output then can be invested in further growth of industrial capitals so more capital more output more investment more capital and this is generating exponential growth in industrial capital the world around the growth rate in fact the exponential growth rate of this loop on the world average is about seven percent and of this loop on a world average about two percent per year now all right that’s the first condition necessary for an overshoot and collapse load is exponential growth now we have to ask what negative feedback loop might interrupt that growth do they respond with a delay or instantaneously and is there a possibility of an irreversible erosion of the carrying capacity well there are a number of different answers depending on what part of the system you look at there are some rather instantaneous responses some which some of which we don’t like for example if food becomes scarce it almost immediately raises the death rate and reduces the population that’s a loop which is active in a few places like Bangladesh fortunately not active over most of the world it’s a very efficient and quick one but it’s not one we like one of the loops we like is a lower fertility loop which ultimately could bring this could weaken this positive loop so that it comes in balanced with a negative one and there are several nice ways that fertility can fall one is through industrial development or through education and family planning all of both of which are things people feel are worth striving for their own right but also have the effect of reducing fertility unfortunately with a delay and therefore this although this this loop is active it’s not instantaneous by any means it seems to have a twenty to fifty year delay in the food system is assumed to be a renewable resource a constant rather high in fact increasing carrying capacity because as more industrial output generates more agricultural capital the amount of food that can be raised actually increases and in this model it can increase by something like six to ten fold over current levels worldwide so this is a rising carrying capacity part of the section the pollution level however could be a decrease in carrying capacity that is the if industrial output is allowed to generate too much pollution it can undercut the food production it can also directly turn affect the mortality of the population the one undeniably erode will and irreversibly irritable part of the model is the non-renewable resource sector this is oil and metals and all of those things which we take out of the ground and do not or cannot recycle and to the extent that all of this industrial activity is dependent on that sort of resource this is not this is a constantly eroding level it only has an outflow rate it doesn’t have an inflow rate that is the rate at which oil is generated is so slow that we haven’t even bothered to include it in the model and this therefore is a major aspect of the model with regard to the permanence of the carrying capacity of the system and in fact it says as long as we’re reliant on those resources it’s not a very permanent system there’s much more to say about that and not very much time and so I’ll just show you what some of the output looks like again there’s a very long book if you’re interested you can read the details of these equations and the model itself is in the public library on the DT SS system it’s called world star star star if you want to run it you just call old space world star star star and and it automatically in dynamo so you don’t have to say run dynamo and you can print out the listing you can get a run and you can try changes and see what happens if we let the system run without any changes from what we feel the current state of the system is that is the way we think all of these relationships are working at the moment the output looks like this many of you have seen it already and it’s a classic overshoot and collapse mode I’d expect this is the year 1900 this is the year 2100 this is the population growing exponentially industrial output per capita is also growing exponentially because as I pointed out the industrial capital growth rate is faster than the population growth rate the non-renewable resources are assumed to be extremely high-level but they’re falling rather rapidly now is about here the birth rate is also falling rapidly the death rate as well more rapidly even food per capita is rising for a long time what finally happens to bring about the end of growth here is essentially a disequilibrium between two levels again the non-renewable resource level becomes so depleted that it takes so much capital to get more oil and more iron and more aluminium and more copper that less capital is available for everything else in the system for an investment in future growth for services and for agriculture and it begins to be at about this point in time a great struggle between each of these systems each trying to bring its output level up to its desired level when there isn’t enough capital available and if the capital were diverted from resources then there would be no output at all so resources get first priority and everything else begins to decline as food and and the industrial output decline then these curves turned over food production starts to go down industrial output starts to go down pollution is a delayed product it’s not an instantaneous product of the output level so it continues to rise for some time the population continues to rise for some time because there are many delays in the population response eventually it comes down to it does so because the death rate becomes higher than the birthrate now I hope you have an intuitive understanding of the sort of structural assumptions that led to this behavior you notice that the overshooting is much more gradual takes a much longer time than for example the overshoot and collapse in the deer system which was a very sudden peak and decline that’s because the deer we gave essentially no reactive capacity they either had food or they didn’t and they had no way of increasing their carrying capacity of shifting resources around to try to stave off a collapse the this system gives the human actors in it a lot of choices and a lot of things happen here in terms of trying to maintain growth and trying to stave off the collapse mode all sorts of economic reallocations birth rate changes death rate changes and so on go on and that makes this peak a rather long one and the collapse fairly gradual at least compared to deer and the Kaibab plateau now I don’t want you to get the impression that that’s the only thing the model can do as you know we make models in order to change them to see what assumptions are important and what aren’t to try out policies I will just show you three more outputs to give you an idea of the variety of behaviors that the system can indicate and if you’re interested in more look up a book called dynamics of growth in a finite world which is in the Feldberg library and you can see hundreds of these runs under different conditions one thing you can do and in fact some of our critics did it for us first is to remove all of the limits in the model and then easy way to do that is to put a growth loop on resources and assume that they grow at a certain percent per year essentially put a growth loop and a negative growth loop on pollution and assume that the amount of pollution generated per unit of industrial output is decreased by a certain percent per year and you can also assume that the amount of food raised on a certain amount of land can be increased exponentially at a certain amount per year if you make those three changes these are the three main limits in the model by the way the land the pollution absorption capability and the non-renewable resource level if you make each of those limits grow exponentially you get as you might expect an exponentially growing forever system in this graph the food per capita goes like this and off the graph it continues to grow up to the point where everyone has an essentially an American diet and then it levels off but you can’t see that on this graph industrial output grows indefinitely exponentially population eventually does level off it levels off at about 16 billion people and that happens because this population worldwide has become so industrialised that its fertility has fallen to be roughly equal to its mortality here’s the birth rate and here’s the death rate it goes through this loop because of the population aging process since the birth rate goes down this is a this is in fact and increasing life expectancy but there are slightly more old people in the population so the death rate rises a bit pollution never becomes much of a problem I put this in here to show you that the model can do it and I leave it up to your judgement whether the world can do it if we change those technological assumptions those assumptions about the limits just slightly and assume that the three changes in the system the growth of renewable resources the reduction of pollution and the increase in land yield cost something but is that it takes industrial capital to make those things happen and that it’s a rather linear relationship between the amount of industrial capital required and the amount of pollution abated for example put in only that change and no other and also assume however that abating pollution raising more food and restoring resources are essential priorities of the system then you get a behavior of this sort the industrial output per capita in this graph Rises and then Falls it falls because there isn’t simply enough capital to do all of those things all at once the population Rises and eventually levels off at a fairly high birth rate and death rate food show the great spurt and again levels off there’s still a lot of resources left there isn’t very much pollution again a value judgment always comes in when you read the output of a model is this a better world than this world or this world again I leave that up to you and the other question you have to ask yourself is is a more realistic world one last run I have to show because it’s the one I like best equivalent to the sorts of runs you are trying to get in the Kaibab assignment that is a smoothly adjusting system that does not overshoot its limits in this when I fortunately didn’t have to include a harvest in order to stabilize the population I simply included a smaller desired family size I didn’t weight in other words for industrialization to bring fertility down I added 100% effective birth control and a desire for smaller families it’s very easy to do in a model I also put an upper limit on industrial output per capita in other words I assumed that once people got to a certain degree of richness about equivalent to an average European GNP per capita that then they stopped having to invest in industrial growth and diverted the output either to consumption or pollution abatement or or something of the sort in other words very simply in the model I interrupted the two major positive growth loops before I had before they ran into any limit of any sort this is what we call an equilibrium run there are many different equilibrium equilibrium that can be generated this just shows one the population levels off at about 6 billion food per capita rise is quite high and then levels off because people essentially have all they want to eat industrial output per capita is it about a European level there is very little pollution the pollution control technologies are in there they cost something but there’s quite a lot of capital to to devote to them because so much capital isn’t needed for growth and the non-renewable resource level comes down very slowly again because recycling and this sort of thing big capital are diverting capital from the system but are it’s possible to carry them out essentially again because capital is available okay I don’t want to give the impression that system dynamics models can only produce overshoot and collapse I have zeroed in on one possible behavior mode to date and showing you three examples of it just to give you an idea of structural homology how we look for them and how we find them I could have also showed you systems that oscillate I could have showed you we could have concentrated on equilibrium systems or many other kinds of time behaviors each of which is associated with a different feedback loop structure