 Richard Bucharest, who's a man of many hats, like we like here at the Infractive Mind Center. He's currently a director of the Max Planck Institute in Leipzig for Human Behavior, Culture and Evolution. Yes, in some order. In some order, yes. And the professor at UC Davis in Anthropology. And as the students at ConSci know very well, he has been both working very intensely on figuring out social learning and culture in humans, but also since he's been working on anthropological data, which are amongst the most messy data ever, and trying to figure out how do we deal with the uncertainty that comes from this sort of data. And in that version, he has actually written a fantastic handbook called the Statistical Rethinking, which helped people thinking about their problems in a statistical fashion from a Bayesian perspective, which is highly recommended. But he hasn't forgotten his anthropological and actually even classic backgrounds. So what you see in the handbook is that statistics is also seen as a situated practice of getting to know the work. And that's what makes Richard's work the most interesting, trying to combine these two sides, the methods and the important content question and letting them leak into each other. And I'm really excited to see what you're going to say today. So thank you for coming. Thank you. All right. Thank you all for coming. See this talk, I understand it's exam period, and of course it would be. So it's my pleasure to be here. This is a really interesting group of people to talk to about this topic in particular. So I'm at the Moscow Institute for Ethnology and Life-Safe, which is a holistic death-loose grand apology institute focused on understanding where people come from. Small problem. And my department focuses on the role of culture and behavior in human evolution. So let me step back and take a broad view of what that means for death-loose grand apology. So this is an elegant embryo, 16 weeks old. I think it's a fascinating thing about animal and plant life that giant, robust adults subject their offspring to being reduced to single cells. Right? It seems like a terrible idea, right? So if you're an elephant, a 30-year-old elephant, you're big, there aren't very many natural majors other than people in your world, why would you then choose to continue your lineage by reducing it to a single cell and making it grow? We don't have an answer to that in illusory biology, but we do know that development that results from this, the fact that every generation has to grow up again, generates a whole range of interesting constraints and possibilities that define the cognitive and behavioral lifestyles of organisms. So for elephants, they grow very large, we take 30 years for a male to reach adult size, that's a long juvenile period. It's been a long time for things to happen. Other organisms like this small dinosaur, the starling, share certain life history constraints that arise from the way they get about. So flight as a lifestyle imposes constraints on how fast you have to grow up and how heavy you can get. And so starlings, like most birds, they have to grow up in a year. That's all you've got. Often it's less than a year. And they need massive energy investments from their parents and possibly their older siblings as well in order to do that. You must pledge in less than a year or you're dead. Why? Because you have to be able to fly to make a living. You just have to. And that's a constraint that means that their childbirths are truncated, nevertheless birds can live for 20 years. Starlings can easily live for 20 years if they do successfully pledge. Very different from, say, your lives where you spend substantial proportions being a juvenile. So the possibilities for starlings are quite different from our possibilities, but equally interesting. And snakes, I think snakes are also interesting in lots of ways. People often overlook our cold-blooded relatives. So this is not a hat, right? This is a snake. The best thing to think about snakes and other animals that can regulate their metabolism and slow it down is that when they get a windfall of food, like, say, an elephant, they can make full use of it. They can digest the whole thing. They don't have to share it. They have neither need nor opportunity to share at the windfall. Again, very different from all of us. If you were to come across a dead elephant, you probably could not ingest it all on a ticket nap, right? But that's not a mistake, though. As a consequence, and this is what I'm going to flesh out and talk, humans deal with surplus is different. And when we generate a surplus, that opens up other possibilities, social possibilities that are different from those that the snake has. And we are allowed to have, as primates, long, juvenile periods. And we can do things for those juvenile periods that the starling can't do because it just can't take the time to grow up. And that's the part of the puzzle of human evolution is why we have organisms like this, where we spend long periods of our lives, up to a third of our life, being small and vulnerable and underskilled, but practicing often in quite awkward and entertaining ways adult protective skills. That, once for adults, produce tremendous surpluses of energy, far more energy than we need to sustain ourselves. And we share that surplus with younger generations, with our colleagues, and create, well, we create society, social societies, with social insurance, that fund the next generation and keep the cycle going. How we get from a life history like the other apes, where many of these features are absent, some are present and many are absent, we don't know. And that's part of the puzzle to understand. And what I'm going to talk about today is, if you will, a meta-analytic project, which aims to measure, quantify some of the parts of the maintenance of this life history so that we can better fit models about the evolutionary origins of it. So think about part of what we do with this long-term human period, of course, is we learn locally specific productive skills and bodies of knowledge that help us thrive in particular places. Humans are successful not because we do the same thing in a really good way everybody spoke, but because we do different things in different places. And part of what we do as children, and even as adults, is we continue learning the local culture to be cruelly of different places. And so with the same basic naked tropical late physiology, some find an adaptation, of course, but with the same basic naked tropical late physiology, we can be successful Amazonian foragers like Issa Che in Parkway. This is East Africa, East African pastoralists, making a living in an arid and highly seasonal environment where agriculture is mainly not possible, but making use of livestock to do it, high altitude Tibetan and Nepalese groups, which are fascinating in part because they actually have marriage systems, polyanger situations where women marry multiple men, which are economically very adaptive. They make their work. Where high latitude cold weather pastoralism as well, like in Northern Scandinavia and Siberia. We do all this for tropical apes, but we manage to do all these things by harnessing this little history and the cognitive development that's built into it to build and sustain cultural adaptations to different places. And that's my obsession as an anthropologist, is understanding the fit between our cognition and the pace of our aging in life history and the behavioral evolution it sets in motion. Again, it's the crudely, the cultural evolution that happens because of the life history that we have. So I think about what's the killer app of the human species, right? The killer app of the starling is that it can fly, and it's also quite clever. The killer app of the human species is that we have law form adaptation. Our form of adaptation is that we have enough time within our individual lives to acquire complex productive skills that we'll use as adults. That's through prolonged development and intense investment from productive adults in our lives. When we acquire those complex skills that creates energy surpluses, we can use to invest in the next generation and we can improve on these complex skills during our lifetimes because we live a quite long time. And then we have flexible process reality which enhances all of these things as well. We create social institutions that can be quite different in different places that help us do more than any individual could do alone. And I think it eases the hallmarks of human adaptation and they're all exaggerated forms of general age adaptations as well. And how did we get to be like this? How did we get a life history that sets in motion cultural evolution to allow us to act? So anthropologists, I'm sure I don't have to tell you about this room, have a strange fascination with foraging. There's something about foraging, it's almost a fetish. And I'm very sensitive to the fetishistic aspect of this. I don't think foragers are fossils, so let me say that right off the beginning. Foraging is worth studying for many reasons, but for two key reasons that I want to say right now. The first is that it's present every place. Foraging is not something relic of a distant past in the Pleistocene. Every human society there is subsistence foraging. It's at low frequencies in some places, I'm guessing here, there probably aren't a lot of people who spend too much time foraging, but chances are many of you have gathered wild mushrooms. So that's foraging, it counts. In fact, the knowledge, the experience of civic knowledge you need to know about which mushrooms gather. And the same is true in many places, there's lots of subsistence that is done this way, depending on what part of the world it is, and maybe called hunting, and maybe called pushy, but it's all the same activity. Foraging never drops out of our portfolio of adaptations, even if there are many individuals who don't do it. It's a persistent human adaptation. It's the original economy and it never goes away. That's a reason to study it as well. The other reason is it's a lot simpler. Studying agriculture, because often the production is in individuals or small groups, and so it's a good place to start to understand skill development and how adult skills and sub-adult skills lead to production. So if we want to understand the connections between cognitive development, what individuals are learning through their cognitive development, and then how that translates into energy, then this is a nice focal area to start theorizing about. And that's one of the reasons. Those are the good reasons, I think, to be interested in foraging. They're also better. Oh, so I also wanted to say, in these photos, foraging is intensely socially learned. This is a cultural practice. Humans are now born knowing how to forage. There are specific technologies involved. So here, the haza, the women can't stand. This is a young woman with her mother learning to dig tubers, and these are Achea Targway. There's a young man with his father learning to track animals. Bows and arrows that they've made themselves. These things are essentially monkey-hard foods, if you want to think about them that way. So this is all of these are social skills that we learned. Forging is also interesting because it's embedded in technology. Forging, as you know, ethnographically is only possible through complicated inter-generationally transmitted technologies like bows and arrows, but also guns and snares and dogs, which are technology. Right. Dog is a great organic technology for haza. And so this is in the haza. Haza society is interesting for many reasons. One of those reasons is every adult knows how to make lethal nerve poisons. So they make it from larvae, and here it is that they embed it in a resin matrix, a sat matrix, and then they heat it, and then they rub it on these air vents that they make themselves. They trade for industrial nails for their agricultural neighbors, and then they count them into these really nice broadcast arrows laced with lethal nerve poisons. It's a polite society. So the skills to do this, right, individuals don't discover every generation which caterpillar has poisoned in it, which it sequesters from particular plants. And you have to be taught this information. And so haza forging by organic plants is made possible, and the amount of energy individuals can capture is only made possible by this body of cultural knowledge that evolved through the long life histories of individuals in any past generations and is now transmitted forward. We're interested in modeling those dynamics and how we should create an organism that places its bets on such a seemingly fragile system. Finally, forging is intensely cooperative. While it is usually small cooperative groups which face the analysis easier, forging is not some human against nature sort of thing. It's humans against nature. It's cooperative. And it's not just in the sense that the actual harnessing of the energy here is cooperative like these two haza foragers. Haza typically forage in groups of two, by the way. They have partners. But also in the sense that the returns are shared quite far because it's a social insurance scheme. It's the original socialism forage. It's so stochastic in the returns that you have to share to make it work, right? Everybody has a bad day or a bad week. So all of the key features of what I think of as the human killer act are present in foraging. It's a nice area to analyze and help us think about how we've got to be people. So let me very quickly, before I get into the meat of what I and my colleagues are doing, set some constraints for you. So the borders on what we think we know about human life history and its pace and what needs to be explained. I'm going through this fairly quickly. I apologize. But it's kind of a cartoon and that's okay. My history theory is complicated and we have to do a whole light-tinted course on it and we're not going to do that. But just a few slides to give you an idea. The peculiar thing about humans, compared to the other age season, is that our growth is delayed while our brains grow. We have very, we're born. So what about chimps first? Look at the top. So at birth a chimpanzee has almost half the brain. It's ever going to have. Maybe a little more than a third of the brain is ever going to have. And its volume and its brain grow at about the same rate until around age four it's weeding. And it's self-sufficient. A four-year-old chimpanzee or just almost all its own food. There's almost no food sharing in chimpanzee groups. And that's how the other age are, as far as you can tell. They're very cognitive organisms. They're very flexible. They use tools like eggs late in the wild. But their brains grow at the same rate as their bodies. And they're born with most of their brain already. It's sort of interesting. Humans are quite different in the sense that we're born with a very small fraction of our eventual brain size. I can't do the math on that right away, but is that like a sixth? Something like that? A fifth? And it grows incredibly rapidly, early in life. Actually all the way until about age seven. It grows very, very rapidly. And then slows down. And by age 10, we have most of the brain rate where we're going to get. But of course, there's still lots of brain development going on. I don't have to tell this audience. There's lots of brain development going on after the age of 10. Growth of the body is greatly delayed here in this period because brains are expensive. How expensive? Well, let me show you. So this is from a paper in 2014 from Chris Kozala, this colleague. So they use CT scan data to measure energy consumption in brains kids of different ages. So you can actually get nice measurements to put on this. And you see that it's both for males and females to make difference being the body curve. Male growth is delayed. But the brain curves are the same. Brains grow very rapidly right after birth and then it slows down. The body curve is really fast. It gets you out of that vortex of mortality, of child mortality that happens at recruitment in humans. Right? The human child mortality is very high, often higher than other ages, actually. And once they get out of that vortex, the body switches over to basically the body size freezes. Those of you with kids know this, right? Eventually they stop getting heavier and their heads get bigger. And this goes on until about 10 years old. And then the brain goes slows down and then they start getting big and hard to push around. Right? And this is the future. This is a derived human characteristic. The other aged don't have this. And there are still lots of unanswered questions about why it should be this way. But the obvious speculations would be that they're setting up the brain to learn stuff. The humans are born into a cultural world. There's a lot they need to learn. They have to develop the brain in the mirror capacity and the linguistic skills to get it. And they do that first. And they delay their size increase which makes them motorable. So there are definitely costs to that. And then so the story of finding anthropology textbooks goes something like this. Here's the human needs compared to AIDS. So what we're looking at is this is energy consumption across the lifespan taken from two different 4G groups in South America. And this is energy production across the lifespan again taken from two different 4G groups in South America. And so early on we're parasitic. Right? Because we have lots of groups to be funded and we're majorly painting a burden on our parents. Right? And eventually we start panning our own way but it takes a long time. So it isn't until about 20 years old in these groups at least that individuals start bringing in more energy than they cost to the local group. And then there's this massive surplus being shared out to other individuals. Not just their own children but other people's children as well. And we remain productive for a very long time well into the 60s. And then a decline in productivity below that. This is the, these are chimpanzee curves. I'm just going to show you the one guess about what chimpanzees are like. We don't actually know by the way what chimpanzee age specific energy production is. We don't know. These are hypothetical curves produced by assuming the body weight of a chimpanzee and how much energy we need to maintain that body weight to be changed. But there's not hard data here. There's not a lot of hard data. This is what I'm going to talk about today. On these two curves, this is from two groups and these are intensely smoothed curves. Now I don't criticize this paper. This is one of my favorite papers. This 2000 paper from Catholic, Hill, Lancaster, and Bertardo. It's a fantastic paper. But the statistics that go into drawing these curves will make you cringe a little bit. It's a massive smoothing. And so what I and my colleagues have to do on two fronts is to get much better cross-cultural data on these curves. For human tangency and the other areas. What I'm going to talk about today is the human part of this. But we're also working on the chimpanzee side. And there's reason to worry about variability across human groups and across chimpanzee groups. Let me just give you an example. A very recent paper out this year by Brian Wood colleagues analyzing the indogo-chimpanzee population. This is the indogo in red compared to other chimpanzee groups. This is a life table. So this is fraction of individuals surviving in a cohort at a different age. The indogo-chimps are rocking. It's one of the only chimpanzee groups that's growing naturally in the wild. Doing really, really well. And here's what I love. You compare them to human foraging populations they have, they've overlapped. And in fact, they have way lower infant mortality than ethnographically known contemporary horticultural and fortuitous of humans. The variability in chimpanzees is bigger than we ever thought it was. There's a good chance that the variability in humans by history and production curves is greater than we think it is. So we need the data to do it. So this part of the reason to worry about variability and not be satisfied with just examples, the still scary type of examples. The goal is to get better measurements so we can beat them into evolutionary models. I'm not going to talk through this graphic detail. It's just to say that people are now working on optimality based evolutionary models of life history and brain growth. Here's a recent paper 2017 by Maricio Gonzales de Aero who's at St. Andrews right now. A brilliant mathematician who has this optimal control model of human life history where you get the evolution of growth of the brain and the body and the skill that results of antiretroduction is kind of important. At different ages and this is an optimal control solution I'm not going to do the details but Maricio needs to really test this model are estimates of a specific skill and we don't have good estimates of that. So these measurements I'll show you today are meant to be plugged into models of this kind. They will obviously then tell us that the models are wrong and we will, the wheel of time will go on. Okay, that's the setup. So let me try to summarize that setup like all the Borderlands knowledge and like with all Borderlands we've been discovered that there's not really a border there service and illusion. That's okay. So humans, we grow very slow, especially for an animal our size. We delay growth for a long time but during that time your brains are growing very fast. There are open questions about what we're doing with those brains. What we're learning. I think there's good reason to think we're learning adult skills that will let us generate sort of pluses that pay for the next generation. Lower our survival as adults so that we can enjoy all the skills we've learned. We can live long enough to make to pay for the investment in our childhood. In order to test such models and understand how such a life history could ever arise, we need to understand how big the surplus is in different places. Is there a place like the Oche that graph I showed you before or not? The speed, the pace of skill gain compared to the pace of development of the brain is very interesting for testing detailed models. And the variability itself is interesting because some ecologies are hard. Some are easy. In some ecologies these things will be bothered with social insurance schemes and so on. Individual variation is equally interesting because if some individuals are twice as productive at the same age as others, that drastically changes the incentives for share. So understanding the social economy depends upon getting measurements of these things as well. Okay, so this is the project I want to talk to you about today. This is still ongoing. We have a draft manuscript but now we're in the phase of worrying again about everything we've done. But soon this will all be out including all the data and code. Here are all the co-authors to think about. This is a big project mainly headed by myself and my colleague Dr. Jared McAuster who's at the University of Cincinnati. Jared works in Denver Rockwell but he's a neighborhood foragers. And what I want to say about this project is that most of the effort is data collection. Almost all of our colleagues here spend time in the field following individuals and weighing the things they're going back like this delicious piece of meat right here. And that's the bulk of the effort and really is what makes all this possible. Field work is hard, it's difficult, it's essential. It's not the glamorous part of doing this work but without this we can't learn what's going on. Then there's data processing. This is all Jeremy. Jeremy is one of the few forager researchers who everybody likes and so everybody will give him their data and he writes to all these people and they're like oh yeah remember we had a great time at a workshop and he's like by the way can I have your data? And so people send him data and as you can imagine many different fantastic formats and sometimes all the floppy bits. He once received an Excel spreadsheet that had inside of it a screenshot of an Excel spreadsheet. So Jeremy is very capable of being a scientist in addition to being a georanticologist and he has spent lots of many many frustrating hours turning these data into something we can analyze. So really Jeremy's done way more work than I have on this. I want to be clear about that. And then this is what I've done this last little green sliver that I'm going to talk to you about today. And really the server has done most of the work. What have we done? Well we have tried to collect as many data sets as we know as many samples where there are forging returns for individuals where we can associate a package what we call a harvest a package of meat. So this is not plant-based foraging unfortunately because there just isn't a big literature on that. But meat-based foraging where we can associate the kilograms of meat that were brought in with a labor input that is how long it took to produce it and with an individual with a known age. Now I'll talk about about known means later because we all know asking someone to age in the field is not always an easy thing. And it turns out there is a lot of stuff like this. It isn't always anthropology. Some of its ecology researchers interested in bushy because they want to know the impact of humans on the local ecology and so they have fantastic quantitative data sets from communities about how much individuals are harvesting from wildlife. And so Jeremy has so far been able to get 39 data sets. We're anticipating a few more rolling in actually so that you want to think about this project as constantly rolling in the future and if we can get new studies going inspired by this project we'll roll them into the same model and just keep up with it as we go. You'll notice the distribution is very concentrated in the tropics. We've got a few high latitude sites. I would love to have more so if anybody wants to go to work in high latitude let me know. I might be able to throw some funding here. These latitudes up high people don't like them very much but that's not your idea of vacations but it's those are the people that live up there are intensely interested. Okay. So these data sets the best ones are incredible because you get repeat samples on the same foragers across different ages and these are the data that give you the best information about changes in productive stable across the lifespan. So to give you an example this is from Kim Hill and Keith Kidtide their work on summarizing the Ache data set this is a great paper describing 20 years of data more than 20 years of data now on the Ache Highway you're the same individuals in 1978 when the study began they were young and in pictures taken in 2009 and there are foraging records over and it's not continuous it's not that they did that every year but there are hundreds of foraging records from these two individuals spanning the development of their adult productivity really incredible. Most of the samples aren't this good most of the samples were shorter time periods more cross-sectional fewer eventors on the same individuals so some statistical care is needed to handle this and that's that's what my job comes in I can have some value on this so what's the goal we're interested crudely does the pattern that's in the textbooks hold how much variation is there a cross-culture by the pattern I mean peak productivity is arise after physical maturity individuals reach their peak after long after 18 and the other question is and I should also say individuals remain productive quite late isn't that they're only productive in their 30s they're main productive into their 60s there's a question about how much variability there is and also I think of this being a quads uninterested in always pushing the statistical boundaries of what we think we can do and I would like to I envision a future where we have many long-term studies going on with large amounts of data coming in and we want to have models of human life history to make use of all these data with all of their imperfections because fieldwork is always going to be a mess and so a part of this project the attraction of this project to me is working on that statistical frontier and trying to develop a model which is diligent about the imperfections of the data doesn't hide any of those imperfections it tries to make the best use of the information and I'm going to tell you about what that means in a second so what's the sample we have 39 sites so far 1821 unique individuals with unique ID numbers associated with different returns 21,160 trips this is a trip that's associated with the labor input per person and that's associated with slightly more harvest because some of these trips are pairs of individuals who go out and kind of split they come back together but they kind of they bring back they bag a different game and then they come back together but it's the same trip in a sense it's semi-cooperative in a sense and I say uncountable hands I'm not sure what the count is but you could imagine cleaning the data here is very difficult and lots of stuff goes on okay what do we get to these data this is a case where we get the model that was in our grant proposal I think this is a pre-registered model and I want to say this is that the temptation here is to try different models until you get something that fits well and we didn't do that now so there will be things about these models which I can endlessly criticize but at least I can say we did look as in the grant proposal and it's not bad so there are things about it but it's not bad the idea was we wanted to have some function which wasn't well basically wasn't the polynomial early on in the journey of course we did this project he said well we can fit like a human polynomial I'm like no I refuse on religious grounds to the polynomial and absolutely refuse and so we we lived in the life history literature trying to find something that we thought could fit data and what we did we wanted something that would be able to take on a range of shapes where there's an initial rapid increase and then there's a peak somewhere and we wanted it to have as few parameters as possible and what we ended up with is something that's called the Monroe-Anthony growth model originally used in fish life history I think so now this is called as the people as fish model but this is just the simplest life history model that you can get and all it asserts is that there are a bunch of processes which create a be celebrated increase in this case in skill and then there are processes of SNESIS which create decline in age and it turns out if you multiply those things together you get a peak per purpose and so with three parameters an increase parameter which we're going to call k think of that as knowledge or something like that a SNESIS parameter which I call m for mortality and then an allometry parameter b which scales the importance of the knowledge component you can get a bunch of different curves here and so three parameters this is very constrained compared to a cubic polynomial but it has some theory behind it and the parameters have some meaning which I think is kind of interpretation not to say this is the right model or the perfect model but it was the one that was in our great proposal so I can honestly say tied our hands to get it this is a good experience for me it feels good because you don't feel like you have to defend it this is what I did there are things about it which didn't work out we can learn from those things this is just how it can take on a lot of different shapes so the resulting skill functions across age don't even necessarily have to have peaks you can get lots of things from variable increase rates combined with variable deployments so we're going to fit these parameters for every individual in the sample to predict the returns though skill doesn't manifest as a peckery you don't have peckery in the days and we have kilograms of meat it's you said you need a production option and in this case again the model that was in our great proposal we just go to economics textbooks and pull out the most basic textbook production model called the Cobb-Douglas model Cobb-Douglas is basically just the law of linear production model it assumes that everything is synergistic so that production is proportional to the skill of an individual raised to some exponent called an elasticity this is a coefficient because if you log this whole thing this is the law of linear model right you've got the coefficient a times log skill that's why it's called the law of linear model and think of the elasticity is how much skill matters for production and then the labor so the more units of labor the more skill matters the more skill matters the more labor matters that's why it's a synergy model and then technology matters what's technology some of these trips have done some of them have dolls those are the two main points of technology they're also the systems which is another a third foreign technology assistant needs your son who's not actually a forward team but is carrying things for you and that matters because it means you can bring more back when your son is schlepping the deer around right that means they can bring back twice as much so those technology terms go in here and there's elasticity for that so they say if you want to think what's the strong assumption here strong assumption is that everything is centered this way that's a strong assumption that's probably not quite right but that's a strong assumption and so the problem is again it can create a lot of different things think about this data keep in mind is you can have different elasticities for skill and labor and tech or different components of production notably about 60% of all of the forward team records in this data are total failures they're zeros because most of the trips fail this is the thing about forward it's true the way they get something it could be quite large so this is a highly zero inflated data set so the model that we have to have just a production function for whether you get anything at all and then we have to have a production function for harvest size and these things multiply to provide expected returns and so expected returns can vary by skill and skill can relate differentially to success and harvest and then there can be variations due to the cooperative group size and other things as well which go into technology with me just a little bit you just need a cartoon understanding of this okay so what's the model now this is a simple model it is this isn't some complicated Bayesian neural network deep learning thing right this is a pretty simple model Bayesian graphics told me the whole model every individual has two parameters which describe their life history there's a third parameter which is specific to a group that be parameter and then there are the elasticities on the skills for each group there are those are convenient to people and so in each site the model isn't too complicated it's a pretty simple hierarchy model the only thing that makes it look fancy is there's no polygons the skill function is that we're thinking of experiments so that's the only part of the look fancy it's actually simpler than a traditional problem on the model so this is just something you could do now before pretty much maybe not but it almost you could almost do it now anymore and but we've got a bunch of sites and we want to pool within sites and across sites and so this is what makes the model challenging to fit is that there's a hierarchical structure the model gets replicated across individuals within sites and then across sites and this generates a lot of replicated parameter numbers that we have to deal with so there's pooling within each site which is to say there's a fictional average forage or within each site and we estimate the variances around that and that lets us do pooling because why don't we do this those of you who read some of my books you know the sermon if you have sampling and balance pressure and visuals you can deal with that in a rational way and pooling is a good honest way to do it to avoid over the day so we know way more about some borders than others because they appear in the inside one that's the basic problem so we do pooling within sites and we let each site have its own sort of ideal type of orager and its own variances so because in some sites the differences in productivity across borders could be massive and other sites could be small right technology for example we suspected going in and this has a way of flattening still differences in any of the variables so the model needs to be able to fit that and then we pool the cross-sites and a second level of pooling so this is what I call the true hierarchical model is not that this is cross-classified it's that there are unique variants components of hyper-parameters within each site and then those hyper-parameters are pooled in a higher level across sites and so we get parameters I'll look for you to do later which we think of as kind of the oer society this is the the average human society in this sample at least so statistical fiction but it's a focus of inference to say what the average still function is across all of these sites with me in a cartoon way at least yeah so all this emerges just from what I call duty trying to be honest to the data structure and you pooling imposes on this this model of time there are other issues of duty and diligence as well as this and these are really common to all kinds of studies I think especially the anthropology data is we often have missing data so for example for some of the trips we don't know the labor input because somebody is recording it happens right it's not like a lab experiment where you don't expect any missing values and anthropology is not like that you have lots of missing values you also have measurement error I should also say technology sometimes we don't know if there was a dog or president right because it wasn't recorded there could have been a dog there the dogs may have been good but they have a really huge effect on their parents so we have measurement error in ancient age people will tell you your age in these contexts and you don't know whether you should believe it or not right calendar age is a strange construct and in fact it's not even clear the calendar age is the thing we care about I'm not going to talk about that too much today so we don't always believe the age that we have to deal with error issues with age so now normally all of us have have problems like this in many observational data sets sociologists have these problems as well as anthropologists and we know we're supposed to care about these things and worry about them but it's so hard to deal with these problems that we use it as like yeah we're not these cases yeah let's take the midpoint page or something like that and I've done that plenty I've made all my sense before all of these days so in this project then as I said we're trying to push the frontier and so we decided we would do to do the elements on these and we would try and we would work as hard on these inconvenient things that make us sleep on our keyboards as much as we work on fun parts and so additional complexity in the modeling comes about with trying to solve these problems and statisticians have developed solutions to these problems in the 20th century problems of 20th century solutions to these problems and now we have the computational power of the desktop to actually execute them and the solutions are imputation and for things like missing data of labor we can define statistical assumptions on the distribution of labor we can estimate the state-set distribution from the observed cases and then we can compute statistically what the labor would be for the cases where it was observed with full uncertainty and this is better than dropping cases so let's just say all the assumptions that let you drop cases because of the value so let's say what's the value of this which is a nice conservative kind of statement and then marginalization which is related which is a case where we don't actually compute the value but we average over our lack of knowledge but it's statistically speaking it's very similar but it's computationally very efficient so we employ both of these techniques here to deal with these problems where we have bins on age and we estimate error and then we have unknown labor inputs and unknown presence of dogs it could have been a dog okay the end result is that we end up with a very large model with 27,470 parameters so you can imagine this discussion right this is a model it's a huge model and it's a huge model because most of the statistical techniques that all of us learn in our introductory stats classes are premised on the notion that we're going to use optimization with different models in the data and optimization does not work in my decisions it doesn't work because it's hard because it will take you for it it doesn't work because the mode is irrelevant in high dimensions I don't have time I'm talking about this over coffee with some of you later this is one of the coolest and most fascinating things about statistics I think this is a thing called concentration of measure and in high dimensions the probability max can be unreasonably far from the most likely combination of random numbers and so it's that's again just a fact it's well known in statistics it's called concentration of measure what do you do then? well you can't optimize you have to do something else and this is why our budget has gotten so popular and by the way 27,000 isn't where this starts this starts at about a hundred is when you really need to worry about it long before 27,000 so and again this is about pushing the frontier and so everybody talks about big data right that we're in the big data world now where everybody wants big data I don't have big data to do it we either trade much data and but the thing about big data is it uses trade-offs and so often as our so when we have very little data nobody thinks they can fit a complicated model to it right and we fit low dimensional models when we have small samples because that's all we have to do efficiently we know better than we think we can do before as sample size increases our emissions increase we start to fit the models we like and then as data gets big we just have to simplify the models because we want to publish the paper eventually right eventually we're going to have a review and the paper needs to be out we can't say it's still running maybe it doesn't like that so what part of what we're trying to do in my department is bend this curve and try to make fewer sacrifices and marry big data as they cause and that's part of this push as well there are serious computational challenges here but they're being solved and so how are they being solved most notably by algorithms like Hamiltonian Monte Carlo the Stan library makes this practical given some additional learning curve to do so skipping over the details we've agonized a lot over getting this work we make data from simulations and then we get them all working on that first before we ever put the real data in so simulation and validation part took a long time about a month and a half before we actually got any model to run under simply to take it correctly but then when we put in the real data it worked well it was very satisfying and we took two days off on credit so it was very nice so let me tell you now and I'll go quickly what happens now I can tell you after all of that statistical effort the general patterns we see in these data what the sources of variation are that we see and then mainly that for me this is actually thinking about what needs to be done to do better there are some strong things that you can make in these data and but maybe strong things just simply cannot be made in these data but that tells us what we would need going forward in terms of better data sets so let me walk you through for a single society the Ace de Hara way it's number 15 what we get at it so this is looking at individual orager skill functions just posterior means there's a certain key around each of these lines but this is for each line as a person what you're looking at up here this is the number of people there are 147 individuals in the sample and 14,000 trips and the orange range is the range of ages for which we actually have observations so no one in the outside is foraging before age I don't know what that is 15 this is about 12 something like that and there's no one who is foraging after like you know 77 or so the dashed line, vertical dashed line is the peak of the average forager with the average forager peaks when they reach their crest and that's at 38 right so any of you coming up on 38 congratulations you have something to look forward to you were past it, I'm sorry now this varies as you're going to see but it's quite late compared to the age of physical age then this translates into production functions production is nearly always more variable than the skill functions because the elasticities can magnify the differences in production and in a sense there can be still thresholds in the production function for actually getting something and so small differences in skill can translate into big differences in production especially late live so looking at the IJ this is the probability of getting anything across the lifespan you see it's much more variable than the inline skill estimates very little variation provided you've gotten something in how big it's going to be and that's because of the ecology this is South America everything's small but this is Africa I feel a little different this is basically if you get Israel you're at the moon a little different Catherine Ardillo not so good really multiply these two things together you get expected returns a cage and here I superimpose the average empirical returns and each unique age over it to show you that this fits the data remarkably well for a three-gram model I felt like it was okay now it's not perfect there are things that I can immensely criticize about this so just give you an idea of how it works these two points by the way are single individuals okay here's the whole sample I don't expect we're not going to go through this I'm thinking about the things you want to do today just as I added land so what I want you to see is that the peak is after physical maturity everywhere but at the same time it's often quite flat there's not a lot that's very special about the peak individuals reach 80 excess of 80 percent of their maximum production quite early right by age 20 and they maintain it for quite a long time in some places well until they're late years so the best forwarders in the Alchea in particular can stay nearly a maximum until they stop it's really incredible you'll notice some of these societies like this one they're clustered tightly together that's an artifact of how hard it is to visualize Bayesian estimates the model doesn't think they're all the same the model doesn't now have different day arms so these are posterior genes and it lonesome together so let me show you just very quickly if we instead sample from the posterior distribution in each of these sites some random fictional hunters you can see that then they get more scattered the model expects a lot of variation across individuals and each group according to the posterior fit there are individuals who are twice as productive in any given age as other individuals and that matters a lot from the intramodal perspective because it sets up sharing economies sets of cases where some individuals are putting in a lot more than other individuals and I may start to think about moving that's a kind of response to that right and how you can society solve those problems the unequal investments is very important finally last last crazy slide like this this is the production version just to show you that variation often goes up so the Achei have a much narrower range of variation of skill than they do in returns because there are threshold effects you have to be sufficiently skilled to bring something back is what's going on there okay let me show you the oer society as I call it it's sort of at the top level of pooling there's this fictional society we can sample forage response let me show you what that is so this is a statistical fiction but inside the model this exists as a way to do the pooling it's the center of statistical gravity it's the average societal there's a lot of uncertainty about this average so what I've done here in the black line a little bit camouflaged the black line is the posterior mean average society skill functions and then these are samples from around that mean to show you the uncertainty about it and what we can say is across society the average peak is at 31 which is a long time after peak physical maturity so men and women have peak strength in their 20s typically in their early 20s and so this is a good time after that of course they start to produce the weight of course so it's interesting why an animal would have a life history where it makes investments and skill after it starts to produce it's hard to make a life history model but that makes sense actually you should well that is your model saying you should delay reproducing until you make all your skill investments and then you should spin right so this is why I think it's a kind of students delay counterfeit until they finish their 80s and that makes sense from a life history perspective doesn't make as much as from other perspectives it makes sense from a life history perspective if we look at what happens in an 18 year old taking 18 as physical maturity which does some violence to the facts actually you know that varies across societies quite a lot an 18 year old has 86% of maximum skill and has about the same skill as a 55 year old which is nice to say when you need an 18 year old to know there is still this 55 year old make him feel good about this so this is the point to say that the increase is pretty rapid and they're not unsteal but then there are increases and decline is a lot slower than the increase or more ties in that investment I read this as the general pattern that we have for the other studies is of health this is there's good inference that the other groups fit the general pattern but the cycle factor is mass and ecological variation across these days so this is just uh I won't read through this this is just the word slide the same one I just said before let me jump straight to the bottom of this list why do you care about this again? I've said this before we care about this because the pace of interview supply and demand feeds into the wide history model it tells us how many dependents can be supported to be changed how much sharing is needed across individuals about their uncertainty and production how much interview supply needs just to pay for your own leadership given activity levels all those things going into figuring out how you have a pace that you can do and then feeds into kind of development and so on how do we pay for our grants how do we pay for our grants through adult production so knowing how much adult production is being done tells us how it's based on parts of the data I think this is an interesting paradoxical thing for humans of course because all of these curves we've estimated are conditional on the existence of technologies and social institutions with the price of cultural evolution which only exists because the brands exist so there's the feedbacks that are really cancelizing and I can't speak to those with these data but I just want to remind you that they're there Finally, individuals vary quite a lot the model outputs uncertainties at the individual level here's storage of 1,329 is to show most of the data that this individual is from young years because they're still young this is still a young man the model predicts what they might do in old age but it's quite uncertain given the estimates from the model does this make sense here's an individual of whom we have as a whole lifespan the model is quite confidence about what the skill function is for that individual across life this is a lot of failures by the probability of failures which is why it's important so there are parameters in the model for variation across the visuals so we can look at it at that level so within sites I know this is among sites so across sites might explain variation to the life history parameters most of the variation across sites this is like saying there's variation in the average forager in different samples what explains that variation more of it is due to rates of increase and rates of decline so just saying if you were trying to say what makes different groups different it's some of the takeoff faster values I interpret this at least very loosely as fitting with the idea that there's a common socializing environment in the different groups that everybody plugs into and affects rates of increase and but those are different socialities in different places that affect it but we don't have communities this is just what we got at the individual variation level if this is related to flips so now we can within each group there are parameters for differences between individuals and in this case within each group individuals are different from one another more because of rates of decline so that the client has been known as then because of rates of gain the rates of gain do matter it's not that they're inconsequential it's just that it's more than some individuals will senesce actually and so life history there's still functions are different and they end up being less productive over their lifespan so we don't know why it should be this way but this helps this is a kind of borderland that helps us constrain our view rights okay thank you for listening to all this I swear off things to talk in a moment so this is just a summarized variation thing again to get up and jump to the italics to say that we care about individual differences because they structure the chair and the client it's not that they're just a federal thing they're not error they're things that people have to strategize to plan or care about individual differences because they affect the conscious societies that are possible and functional so estimating the size of those differences would be important and the site differences seem to be mainly about early life rates of increase and not about late life that constrains our view rights and again think about what it is about how socialization works on when there are effects and I think this is fair and acceptable I thought when we were going into this that those late life is when things can vary although early life is so important in the cognitive health literature so all the differences between individuals who have to do good things and have to earn money but it's not what we get with insights here we get the opposite effect that everybody gets the same basic algorithm is what we call the same but then late life some individuals get injured and we climb the better data is might not hold up I don't know but that's what we find okay last slide we confirmed the general pattern we're into textbooks gay textbooks they're right occasionally the peak is after maturity and we're productive long after reproduction substantial individual differences the labor does pay but this is conditional cultural evolution this is a story about maintenance of being humans it's not how you think to be humans from the age of life history because to start you don't have a cultural institution that bows an arrow at you to start so it's a very different problem right just keep that in mind I've got no solutions to the ordinance problem just to say this is about maintenance so again the value all these estimates feed into specific evolutionary models about how humans pay for humans and how the knowledge fits into productivity and builds across generations what's really needed of course are new long-term studies and the commitment from our scientific institutions in supporting such long-term studies which may not have the glam value to be in nature anyway thank you for your time I hope this is interesting to you