Today is my last morning in Tulsa at SEAC 2017. I spent all day yesterday in the "Paleoindian and Early Archaic Southeast" symposium: 18 papers that included state-by-state updates of what we know and the data we have and treatments of topics such as megafauna in the Southeast, plant use by early foragers in the region, wet site archaeology in Florida, lithic technologies, etc. It was a marathon. 

My presentation with David Anderson was last in the lineup. I was tasked with an effort at a "big picture" demography paper. It was a lot to talk about in a short time (20 minutes) -- a difficult balancing act to discuss the dense data from such a large area and be able to explain how I tried to integrate it all into a geographical/chronological model that can be evaluated on a region-by-region basis. Anyway . . . the detail will be there in the publications that result from the endeavor.

I uploaded a pdf of my presentation here. Some of the details will change as we work through the process of refining the analysis and dividing the content into multiple papers. But you should be able to get a decent idea of what we were going for. 

I'm happy to announce the publication of a new paper of mine in The Journal of Artificial Societies and Social Simulation (JASSS). JASSS is an open access journal focusing on the use of computer simulations as a tool for understanding social systems. I love publishing papers that anyone can get to at any time, without requiring logins, subscriptions, or fees. I wish every paper could be open access, and I wish I had the funds at my disposal to throw money at journals like JASSS to support such efforts. If I ever do have the money, that's the direction I'm going to throw it.

My paper, titled "A Model-Based Analysis of the Minimum Size of Demographically-Viable Hunter-Gatherer Populations" will appear in Volume 20, Issue 4 (due to be released on October 31). You can read the paper online here. It should be available in pdf form soon.

If you really want to get into the nitty gritty, the raw model code and an explanation are available here.
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The focus of the paper using an agent-based model to revisit the question of how large human groups have to be to be demographically viable (i.e., able to survive over the course of many generations). This is a key question for understanding the size and structure of ethnographically- and archaeologically-known hunter-gatherer social systems as well as fleshing out scenarios of hunter-gatherer groups colonizing empty landscapes. Here is the abstract:

"A non-spatial agent-based model is used to explore how marriage behaviors and fertility affect the minimum population size required for hunter-gatherer systems to be demographically viable. The model incorporates representations of person- and household-level constraints and behaviors affecting marriage, reproduction, and mortality. Results suggest that, under a variety of circumstances, a stable population size of about 150 persons is demographically viable in the sense that it is largely immune from extinction through normal stochastic perturbations in mortality, fertility, and sex ratio. Less restrictive marriage rules enhance the viability of small populations by making it possible to capitalize on a greater proportion of the finite female reproductive span and compensate for random fluctuations in the balance of males and females."

My main finding is that, under the varying conditions I investigate with my model, I find no support for the often-repeated idea that a society of about 500 persons is required to ensure demographic viability.  Students of American anthropological archaeology -- especially, I suspect, those of us that went to the University of Michigan or were taught by U of M alums -- will immediately recognize the "magic number 500" as a concept that emerged from the research of Joseph Birdsell and (later) H. Martin Wobst. As I discuss in the paper, I think neither Birdsell nor Wobst intended the number 500 to take on the meaning that it did -- it became a kind of shorthand gloss for setting a general lower boundary on the size of hunter-gatherer social systems.

My modeling results suggest that the number of people required for demographic viability can be safely pushed down south of 200.  In over 67,000 model runs (under varying conditions of mortality, fertility, and marriage rules) where the mean population exceeded 150 people, the population went extinct only nine times.  I'd take those odds.

All the modeling was done under conditions with no logistical constraints to identifying and obtaining marriage partners:  no spatial component to interaction, no impediments to the flow of information. Logically, putting the model systems in space and dispersing the populations across a social/physical landscape would have the ultimate effect of raising the population size required for demographic viability. Would it double or triple it, though? I highly doubt it.  But the great thing about modeling is that we don't have to be satisfied to simply suppose things -- we can model the problem.  Understanding that less than 200 people are required for demographic viability assuming no interaction issues, we can then unpack the issue to ask why hunter-gatherer societies are often much larger. What role does the structure of mobility play? What about the need to maintain a geographically-extensive social fabric to buffer large-scale environmental variability? Here are a couple of paragraphs from my conclusion:
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Following the spring break hiatus, the Broad River Field School will be back in session tomorrow. We'll be shifting gears a bit to carefully work our way into what appears to be a buried Late Archaic/Early Woodland component. I'm also anticipating continued work on the deeper deposits at the site. Hopefully it will be an eventful day. It's supposed to be sunny and in the mid 60's. I'll just leave it at that.

Here are a few quick updates on other things for those playing along at home: a new modeling paper about the minimum size of demographically viable hunter-gatherer populations, new Fake Hercules Swords en route, and an identification of last Friday's whatzit. 

Finally, following up on yesterday's post about Against Me!, I would like to encourage you to listen to the song "Rebecca" if you like the rock'n'roll music. It's on repeat in Andyland. 

I've found that the notes I make on my website are much easier for me to find later than the things I scrawl on pieces of scrap paper. The shoe fits, so I'm going to wear it whether or not it's interesting or useful to anyone else.

I've spend much of my time since Monday working to get the agent-based model I'm currently messing around with (version 3 of ForagerNet3_Demography) to work in version 2.4 of Repast Simphony. Something went awry with my previous installation (2.0) and it made sense to start trying to fix things with the most current version. After many frustrating loops of install/uninstall/reinstall, I finally got a good installation of 2.4 and got my source files moved in and working.

One thing that I wasn't able to make functional in the last version was the batch mode.  Batch mode lets you run jobs in batches, speeding up computation by farming out the computational workload to different processors or machines, etc. (doing runs in parallel rather than serial). It wasn't too troublesome that I couldn't get the embedded batch mode working before, as the model I'm working with isn't terribly demanding. There are bigger things coming down the road, however, so I was happy to see the batch mode appeared to be active and ready to go with the new installation.

I spent most of yesterday trying to figure out how to use the batch mode while preserving the data output format that I've created on my own and that works for me. The way I've written the model, it produces a summary data file at the end of each run. The file (just a simple .txt file that I can open in a spreadsheet) preserves information on all the parameter settings used in the run as well as data on the outcomes. In the Repast/Eclipse batch mode, however, that .txt file wasn't getting produced. I was frustrated to learn that I apparently had to redo all the data capturing in the model so that the software could use something called a "file sink" to collect information. I was then relieved to learn that there was a workaround to using the "embedded system:" you can specify an "Optional Output File Pattern:"

The "Pattern" is the name of the file produced by the model. I changed the file name to "TestBatchMode.txt" in my code for the purposes of experimenting with where and under what circumstances the file would be created. The "Local Path" is what you want the file to be called that the batch mode creates (it will appear in the output directory specified above). Check the "Aggregate" box so that it saves the output from each run and then gloms it all together in a single file. I left "Has Header" unchecked because my data doesn't have a header.

Repast seems to be picky about the settings in the "batch_params.xml" and "parameters.xml" files, wanting them to match. I get null pointer exceptions when I clear everything but the random seed out of the files, so I just left a parameter in to keep the software happy (it does nothing, as it's a constant and doesn't affect any of the settings in the model). 

I'm still testing out the batch mode and the model to make sure everything is working properly. My plan then is to modify version 3 to create version 4, which will include some different mortality settings (which, in turn, will necessitate rewriting some of the code that calculates age-specific mortality outcomes). After all that's done, I'm planning on doing some new modeling work to formally follow up on some preliminary observations I presented at the SAA meetings a few years ago.

I devoted yesterday afternoon and most of today to (finally) producing the updated documentation for Version 3 of the ForagerNet3_Demography model, one of the agent-based models that I've been working with. You can read all about it on this page, and you can even download the raw code if you like. Files and citation information for the model are also available on OpenABM.org.

I used a version of this model (implemented in Repast J rather than Repast Simphony) in a recent paper published in Uncertainty and Sensitivity Analysis in Archaeological Computational Modeling (edited by Marieka Brouwer Burg, Hans Peeters, and William Lovis).

Over the summer I used to model to generate data for a paper on the minimum viable population (MVP) size of human groups. That's in the editing stages now -- hopefully I'll be able to get it done and submitted somewhere before the Christmas break.

​Onward.

As far as I know, humans are unique among animals in having an extended period between weaning and being able to subsist on their own.  We call this “childhood.”  The long period of post-weaning dependence provides our large brains with a lot of time to mature.  It also requires a lot of parental investment (in terms of time, energy, calories, etc.) and means that we would have to wait a long time between offspring if each one had to independent before the mother could have another.   We don’t do that, tending to have a shorter interval between subsequent births (the inter-birth interval, or IBI) than other great apes.  The long period of childhood dependence and the short IBI mean that, as a species, humans tend to have multiple, dependent offspring of different ages at the same time.  Speaking as a parent of multiple, dependent offspring of different ages, I can tell you that this is often no walk in the park.  This peculiar human strategy has a lot of costs.

Understanding when, how, and why this distinctly human reproductive strategy developed is a great evolutionary question.  Reducing the IBI increases the potential fertility of human populations, but also creates new demands on the energies of parents and families.  Human families today often offset those extra energy demands by getting help (evolutionary anthropologists call it “cooperative breeding”).  A new paper in the Journal of Human Evolution titled “When Mothers Need Others” by Karen Kramer and Erik Otárola-Castillo tries to further our understanding of where cooperative breeding comes from, using an “exploratory model” to try to understand the selective pressures associated with the evolution of human-like patterns of reproduction and child-rearing.  The goal of the paper “is to develop a model to predict those life history transitions where selective pressure would have been strongest for cooperative childrearing” (pg. 5). 

Kramer and Otárola-Castillo call their model the “Force of Dependence Model.”  Their model is a simple one, calculating “the net cost of offspring as a function of dispersal age, birth intervals and juvenile dependence” as a 3-dimensional surface (Supplementary Online Material  from Kramer and Otárola-Castillo 2015).  The authors use several different combinations of settings to represent a range of conditions from “ancestral” (juvenile independence at age 10, IBI of 6 years, and a dispersal age of 14) to “most derived” (juvenile independence at age 20, IBI of 3 years, and a dispersal age of 20).  Their graphs show that “net costs” within a domestic group (a mother and her offspring) are lower when offspring are spaced further apart and become independent at a younger age.  When offspring hang around past the age of juvenile independence, there is a net benefit to the domestic group as their productive capacities can be used to offset the drain of their younger siblings. The authors find that the strain points – where selective pressures for assistance would be greatest – occur in domestic groups with the most derived set of characteristics: late juvenile independence and a low IBI (lots of children who remain dependent for a long time).   

As I understand it, the “net cost” in this model more-or-less mirrors the dependency ratio (the ratio of consumers to producers) of a domestic group or family, something anthropologists have been interested in understanding for a long time.  The higher the ratio of consumers to producers, the higher the dependency ratio, and the higher the “cost” to each producer supporting the family.  The dependency ratio changes through the lifespan of a family in a patterned way: every domestic group that has children goes through a “pinch” period when the dependency ratio is highest, and the pinch period logically corresponds to the time when there are a lot of dependent offspring.  As I wrote in my 2013 paper in the Journal of Anthropological Archaeology (“Subsistence Economics, Family Size, and the Emergence of Social Complexity in Hunter-Gatherer Systems in Eastern North America,” available here):

“the duration and amplitude of the ‘pinch’ is affected by the rapidity of the addition of offspring and how quickly those offspring turn from consumers into producers.  The rapidity of addition of offspring will depend on factors such as fertility, infant and childhood mortality, and the number of wives. The productive potential of children will be affected by the presence and distribution of resources that can be procured by children and the foraging strategies that are employed to exploit those resources” (White 2013:128).

The main part of that paper used an agent-based model (ABM) to try to understand how the distribution of family size changes when the age at which children become producers (the “age of juvenile independence” in Kramer and Otárola-Castillo’s model) decreases and there is an incentive for polygynous marriage.  In addition to the ABM, I used a simple spreadsheet model to show how the dependency ratio changed through the course of the developmental cycle of an individual family in cases where the age at production was low (8 years old) and where it was high (14 years old).  In this simple model, I used an IBI of 3, a dispersal age of 16 for females and 20 for males, and a female reproductive period spanning ages 20-35 years (giving a total fertility of 6 offspring).

The figure below compares Kramer and Otárola-Castillo’s graphs from their cases with early and late juvenile independence (holding IBI at 3 and dispersal age at 14) with my data on changes in dependency ratio through the developmental cycle in cases with a single reproducing female and an age at production of 8 (top) and 14 (bottom).   My model data are the same as in my 2013 paper (Figure 5), but I have re-graphed them to make comparison with Kramer and Otárola-Castillo’s figure easier.  I have redrawn the graphs from Kramer and Otárola’s Figure 1 (third graphs from the left, top and bottom rows).   The dotted lines on the graphs of my results indicate a dependency ratio of 1.75, which is what I have generally used in my modeling efforts as a “typical” dependency ratio among hunter-gatherers (following Binford 2001:230).

My results showed the same pattern as Kramer and Otárola-Castillo’s:  the peak of the “pinch” comes earlier and is less severe when children become producers at an earlier age.  Even though our models have some differences (and some of the values of the parameters were different), the correspondence in results is notable. Compare, for example, when the amplitude of the “pinch” (peak dependency ratio in my results, greatest net cost in Kramer and Otárola-Castillo’s results; marked by stars) is greatest and the differences in amplitude between the early and late ages of juvenile contributions to subsistence.

The correspondence between my results and Kramer and Otárola-Castillo’s is unsurprising.  The idea that the dependency ratio of a domestic group changes through the course of its developmental cycle in a somewhat predictable way is not new (and the idea that the “pinch” comes when you have lots of little kids running around at the same time won’t come as a revelation to anyone who has multiple children).   This is a phenomenon that has been studied for decades (e.g., Chayanov 1966; Donham 1999; Fortes 1958; Goody 1958) and recognized as a key aspect of how hunter-gatherers organize themselves (Binford 2001:229).

So where does this kind of work put us in terms of understanding the evolution of human reproduction, society, and family life?  I think it primarily puts us in a spot where we’re asking some good questions.  Going back to the issue of the origins of monogamous pair-bonding (which I touched on briefly in this post about birth assistance and this post about australopithecine sexual dimorphism), having a two person (male-female) unit forming the core of a domestic group would have a mitigating effect on the strain caused by a decrease in IBI (i.e., you’d be adding another producer into the equation).  If the appearance of male-female pair-bonding was associated with a sexual division of labor (which is I think what most of us would hypothesize), males and females would presumably be focused on procuring somewhat different sets of subsistence resources.  Offspring could be largely “independent” with regards to some of those resources but not to others – think about the difference between collecting berries and running down large game.  A sexual division of labor and an environment where relatively young children could make some contribution to their own subsistence (even if that contribution does not include the full range of resources that are exploited) would go a long way toward easing the “pinch” that comes from having more children spaced closer together.

When does this happen in human evolution?  Of course that’s a tough thing to get at directly.  I think if you took a poll, the winner would probably be “around the time our genus emerges” or “with Homo erectus.”  An increase in total fertility (coincident with a lowering of the IBI) would help explain the population growth that must have been part of the dispersal of our species out of Africa prior to 1.8 million years ago.  It would also fit nicely with the evidence for an increased exploitation of animal resources around that same time.  Maybe Glynn Isaac was right all along to propose the emergence of human-like central place foraging with home bases and a sexual division of labor at the beginning of the Lower Paleolithic?

But what if monogamous pair-bonding and a sexual division of labor appeared much earlier – with australopithecines or even some pre-australopithecine like Ardipithecus?  If those things came along with bipedal locomotion, would a decreased IBI and increased fertility have followed automatically?  Maybe not.  Perhaps those earlier hominids just didn’t have the wherewithal to exploit their environments like later hominids did – perhaps the diversity of the resource base they could exploit wasn’t great enough to really leverage a sexual division of labor until animal products became readily attainable.  That may have required a suite of anatomical adaptations for daytime exhaustion hunting (loss of body hair, skin pigmentation, greater body size, stiffer foot) and cognitive/behavioral adaptations for making and using stone tools to process carcasses.  The date of the “earliest” proposed use of stone tools continues to be pushed  back (now it’s at 3.3. million years ago), but as far as I know the density of stone tools and butchered animal bones that appears at about 1.8 million years ago is unlike anything that precedes it.

More modeling work will be required to really understand how changes in the dependency ratio might have articulated with changes in reproductive, social, and technological behaviors deep in human prehistory.  In order to understand what changes in reproduction might have meant in terms of social interactions, however, we’ll need a different grade of model than that used by Kramer and Otárola-Castillo.  Of course I’m going to say that complex systems modeling is the way to go on this:  it will let us get past the limitations of deterministic inputs and help us understand how constraints, costs, and interactions would have played out within a society.   In order for “others” to help with raising and provisioning multiple dependents, those others had to have existed within these small-scale hominid societies and (again, speaking as someone involved in raising multiple small kids) there wouldn't have been some inexhaustible Plio-Pleistocene babysitting pool of “others” out there just waiting to step in and provide extra calories for a few years.  A different kind of modeling effort with broader scope will let us get at the group- and society-level contexts in which family-level changes in child-bearing and child-rearing would have played out. Stay tuned.

References

Binford, Lewis R.  2001. Constructing Frames of Reference: An Analytical Method for Archaeological Theory Building Using Hunter-Gatherer and Environmental Data Sets.  University of California Press, Berkeley.

Chayanov, A. V.  1966.  A. V. Chayanov on the Theory of Peasant Economy.  University of Wisconsin Press, Madison.

Donham, Donald L. 1999.  History, power, ideology: Central issues in Marxism and anthropology.  University of California Press, Berkeley.

Fortes, Meyer.  1958.  Introduction.  In The Developmental Cycle in Domestic Groups, edited by Jack Goody, pp. 1-14.  Cambridge Papers in Social Anthropology.  Cambridge University Press, London.

Goody, Jack.  1958.  The Fission of Domestic Groups among the LoDagaba.  In The Developmental Cycle in Domestic Groups, edited by Jack Goody, pp. 53-91.  Cambridge Papers in Social Anthropology.  Cambridge University Press, London.