Homebodies and Hellraisers in
Time and Space:

a simple agent-based model of the effect of social learning on population dynamics

Systems Science 399U: Models in Science, with Teresa D. Schmidt.
Portland State University, 4 December 2010
(Accompanying NetLogo model: [HnH.nlogo]

Abstract

Homebodies and hellraisers is a very simple formalized thought experiment about the influence of learned traits on population dynamics, first proposed by Boyd and Richerson in their book Culture and the Evolutionary Process (1988), and more recently nominated by Derek Gatherer (2005) as a “paradigmatic example in memetics,” a school of thought which seeks explanations for individual and group behaviors in terms of discrete traits acquired and expressed through imitation. In essence, the model proposes a world inhabited by two kinds of people: homebodies who have fewer social interactions but are more likely to reproduce, and hellraisers who have more mobility in their interactions, but a lower reproduction rate. In one form of interaction, both types may reproduce sexually with either kind, and the offspring are assumed to inherit the parents’ traits. The memetic twist comes from the additional possibility of hellraisers to “convert” homebodies into fellow hellraisers. This paper details my implementation of a spatial agent-based simulation to explore a new version of the Boyd–Richerson model, as well as some of my motivation for building such a thing in such a way, and the results of my experiments with it.

Research Design

My model, like most NetLogo simulations, consists of a number of agents, called “turtles,” each of which may belong to a distinct “breed” – in this case, homebody or hellraiser. I use two colors to visually distinguish the breeds. Each turtle has its own position and heading: individual characteristics which play a key role in the spatial aspects of the model. The two breeds have collective characteristics as well; in this case, speed and reproductive rate. The turtles move in fixed ten-step circles with diameters determined by their speeds. The overall population is limited to 1000 agents, so the proportion between the two reproductive rates, rather than their absolute quantities, is the significant factor. The homebodies are subject to an additional parameter: their susceptibility to conversion into hellraisers. Each of these numbers is expressed as a normally distributed probability of some event (reproduction or conversion) occurring to an individual turtle at each time step of the model. Each turtle also has a probability of death at each step, giving each the same expected average lifespan of 100 steps. Reproduction and conversion are subject to spatial constraints, too: neither interaction may occur between turtles unless they are on the same “patch” of the 41 by 41 patch toroidal grid that is their world. Evolution is extremely simple: reproduction is just copying one parent. While not generative of any individual difference, it is however still sexual in the sense that it takes two. The agents also have a sense of modesty (or, less poetically, resource scarcity) in the form of a ‘crowding tolerance’ parameter which, like the life expectancy mentioned above, applies equally to both breeds. The new child immediately moves two steps in a random direction, to alleviate crowding somewhat. I can give little justification for these particular simplifying assumptions; in truth they are an artifact of my hasty development process. Nonetheless, it will not be difficult to extend the model to incorporate sexual dimorphism or other distinctions.

Procedure

Aside from implementing these basic functions and relationships during the model construction phase, I was also tuning the constants and parametric ranges to some extent, in search of an ‘interesting’ region of the parametric space which allowed for the coexistence of the breeds. For many initial conditions, the hellraisers would immediately die off; for others, they would overwhelm and extinguish the homebodies. At this point, if the hellraiser birthrate was below replacement level, the entire population would dwindle to nothing. Verification of the model was easy in that the behavior of the turtles was immediately apparent upon running the model. To help visualize the history of the system, I added a chart of the populations. I think it's interesting that merely having found some satisfactory values of the parameters through twiddling knobs on a live model was not always enough to reproduce the same behaviors, which may have developed through some specific sequence of twiddlings. In that sense, developing this model was very much an interactive and creative, rather than descriptive, process.

Indeed, I must emphasize that I was not attempting to describe or predict any particular population or social circumstance, for which my model as it stands would be a rather poor tool indeed. My experiments were, to the contrary, intended to explore the consequences of an abstract description of a very general phenomenon. Rather than attempting to validate some specific prediction, I worked backward: assuming the condition of coexistence fulfilled, what values of the parameters would obtain? I suspect that this mode of reasoning, familiar to mathematicians, may have some use in the construction of these kinds of models. Having found particular conditions producing particular behaviors, I wonder whether these conditions might somewhere, somehow, correspond to some real data. Could this simple system be grown into a real predictive or descriptive tool?

Results

Much as Gatherer promised, I was able to produce various forms of “fragile equilibrium,” as well as some that didn't seem especially fragile. When I had achieved stability, I was able to run the model faster and observe the patterns that formed in the space. The most surprising finding I had was the formation of a single distinct blob-like metastable spatial region on the toroid, where homebodies bred to the extent permitted by the crowding tolerance. Hellraisers filled the rest of the space, gradually radiating out from the population source cluster. If I reached in and separated the two types into their own regions, they eventually merged again. So, the bounded chaotic inter-dependency relationships which the charts show are not the whole story, at least if the object is to describe a real population of physical entities on the surface of a real planet. On the other hand, clearly, neither is my model. It does make me wonder: what other spatial structures or dynamics might be lurking in more comprehensive models? Can multiple blobs coexist? What about under conditions of limited local resources or spatial barriers? Plus, there might be more than two kinds of people (or traits, or both) in the world, and all sorts of interactions between traits both inherited and learned might be important. For that matter, there might even (hypothetically) be more kinds of interactions between people than just breeding and partying. Or, there might be people who don't just go round in the same circle all the time. You sure wouldn't know from my model!

Conclusion

This project has been illuminating to me. I have learned nothing of any substance about real societies, but I have seen the potential of agent based spatial simulations to give new perspective to established abstract or statistical models. In a slightly larger context, I've gained some appreciation for the model-making process in the social sciences, and had a taste of the kinds of tradeoffs and subtleties it may entail.

References

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