Category Archives: Species

Gombe Chimpanzees, Yellowstone Wolves, Agent-Based Models, and the Benefits of Larger Territory Size

12 August 2022

I’m very happy to announce the publication of a new paper from our lab, led by newly minted Ph.D., Dr. Kristy Crouse.

Work on this paper began back in August, 2012, when Kristy emailed me, asking for advice about graduate studies. Kristy had recently earned her bachelor’s degree from the University of Minnesota, where she had taken pretty much all of the classes I had taught over the past two years. When we met, she said, “I have a background in Anthropology and Computer Science. Is there anything I can do with that?” I had some ideas. We began meeting together to discuss them, together with Clarence Lehman, an ecologist who also has a professional background in computer science.

At the time, I had started to compile data on lethal aggression in chimpanzees. Male chimpanzees defend group territories. There are some obvious benefits to having a larger territory. Perhaps the most obvious benefit is that, all else being equal, a larger territory should have more fruiting trees, shrubs, and vines, providing more food for chimpanzees to eat. Analysis of long-term data from Gombe had found that when the territory size was larger, chimpanzees traveled in larger parties, and females reproduced more quickly (Williams et al., 2004). Controlling for age and reproductive state, individuals weighed more when the territory was larger (Pusey et al., 2005).

Another benefit of large territory size occurred to me. Chimpanzees are most likely to meet their neighbors along the periphery of their range. Geometrically, as the territory increases in size, the perimeter increases linearly, while the area of the territory increases by the square of the radius. As a result, with increasing territory size, the periphery should constitute an increasingly smaller proportion of the total range. If intergroup killings occur mainly in the periphery, and the periphery constitutes a smaller proportion of larger territories, then larger territories should provide an additional benefit: more safe area within the territory. As a result, overall risk of death from intergroup aggression should be smaller in larger territories.

An illustration of the conceptual model with small (a) and large (b) square territories.

Another consequence of this occurred to me. If mortality from intergroup aggression is lower in larger territories, then females should have higher fertility. Chimpanzees tend to kill male rivals more often than females, but they do sometimes kill females from other communities. More importantly, attackers often kill the infants of females from neighboring communities. In a larger territory, females should suffer fewer such losses, and so be able to produce more offspring. About half of these will be males, who stay in their birth community and add to the ranks of territorial males. With increased production of male defenders, chimpanzees in larger territories should be increasingly able to win intergroup battles, and thus further increase their territory size. A virtuous cycle would therefore ensue: larger territories reduce intergroup mortality, leading to higher female fertility, leading to faster production of male defenders, leading to greater odds of winning intergroup fights, resulting in larger territories. The rich would just keep getting richer, until some other factor, such as infighting within the group, led to a change, such as a group fission.

The geometry seemed simple enough. But would it hold up in reality? Real territories are not perfect circles. Intergroup killings could take place anywhere, not just along the periphery. We could test the model empirically with data, but good long-term data on such systems are scarce, and sample sizes are bound to be small. This seemed an excellent system to test using agent-based computer models.

Kristy set to work on the project, and soon developed a working model. She created artificial chimpanzees that lived in color-coded territories. They roamed their virtual landscape, and beat up on any neighbors they encountered.

Snapshot of a LethalGeometry simulation.

And sure enough, analysis of the resulting data indicated that per capita intergroup mortality was higher in smaller territories.

Results from the agent-based model

In February, 2013, I presented on this model to the Behavior Group in the Department of Ecology, Evolution and Behavior in Minnesota. In addition to describing results from Kristy’s modeling, I also analyzed data from multiple chimpanzee study sites, collated for another paper (Wilson et al., 2014). Both the empirical data and the modeling data were consistent: individuals in larger territories experienced a lower risk of intergroup mortality.

This seemed to have implications for human societies as well. In a world of hostile neighbors, killing is most likely to occur along the edges of territories, where invaders first encounter defenders. Over historical time, the maximum size of territories has increased, from the home ranges of hunter-gatherers, to the city-states of early agricultural societies in places like Mesopotamia, to the empires that gradually grew and swallowed up those city-states. Are people living within empires safer than people living in smaller states, or in hunter-gatherer societies? Does the virtuous cycle of reduced mortality and increased fertility support the growth of empires?

Kristy applied to graduate school, and I began serving as her co-advisor, along with Clarence. In 2014, while I was on sabbatical at the University of Montpellier in the south of France, Clarence visited with me. We talked about this project we had been working on with Kristy. It seemed like with just a bit more work, we could wrap the paper up and submit it for publication.

Once Kristy started grad school, though, coursework and teaching and grant proposal writing and other pressing matters demanded her time. Moreover, Kristy wasn’t satisfied with her model. She saw ways she could do things more elegantly, so she continued to tinker with it. Work continued on the paper, and graduate student Nisarg Desai joined to help with statistical analysis. Finally, in the fall of 2019, Kristy submitted the manuscript to a high-profile journal. The editor rejected it almost immediately, without sending it out for review. This was discouraging. Kristy set the paper aside for a while to focus on her dissertation research.

We eventually developed the paper in two new ways.

First, we recruited additional collaborators to provide more empirical data. Kira Cassidy had published some very nice work on intergroup aggression in wolves, which parallel chimpanzees in many ways: they defend group territories, and have high rates of intergroup killing (Cassidy et al., 2015). I knew Kira from having served on her master’s thesis committee. I contacted her and asked if she would be interested in collaborating on this comparison with chimpanzees and virtual agents. She agreed, and brought in Erin Stahler, another biologist working on the Yellowstone wolf project.

Second, Kristy was becoming increasingly interested in a fundamental problem of agent-based models. How do you know that the model is doing what it is supposed to do? Every model is a simplified view of something more complex; an abstraction from reality, an approximate match to the real system. As British statistician George Box famously said, “All models are wrong, but some models are useful.” How do you know whether a model you have created is useful?

Other researchers in agent-based modeling and suggested methods for developing models to ensure the they match the target system sufficiently well to provide useful information about that system. How exactly to follow those suggestions, however, was not always clear from the existing literature. So Kristy took our paper as an opportunity to explore these issues in more detail. We had a simple geometrical model, an agent-based model, and two sets of empirical results from different species. These different sets of information provide ways to check one another, to give us more confidence that what we are modeling applies to real-world systems.

We submitted this revamped version of the paper to Ecological Modelling, where it has now been published.

We hope this paper will be useful to others, both for those interested in further exploring the impacts of territory size on mortality and those seeking to develop agent-based models of other systems. 


Box, G. E. (1976). Science and statistics. Journal of the American Statistical Association71(356), 791-799.

Cassidy, K. A., MacNulty, D. R., Stahler, D. R., Smith, D. W., & Mech, L. D. (2015). Group composition effects on aggressive interpack interactions of gray wolves in Yellowstone National Park. Behavioral Ecology26(5), 1352-1360.

Crouse, K. N., Desai, N. P., Cassidy, K. A., Stahler, E. E., Lehman, C. L., & Wilson, M. L. (2022). Larger territories reduce mortality risk for chimpanzees, wolves, and agents: Multiple lines of evidence in a model validation framework. Ecological Modelling471, 110063.

Pusey, A. E., Oehlert, G. W., Williams, J. M., & Goodall, J. (2005). Influence of ecological and social factors on body mass of wild chimpanzees. International Journal of Primatology26(1), 3-31.

Williams, J. M., Oehlert, G. W., Carlis, J. V., & Pusey, A. E. (2004). Why do male chimpanzees defend a group range?. Animal behaviour68(3), 523-532.

Wilson, M. L., Boesch, C., Fruth, B., Furuichi, T., Gilby, I. C., Hashimoto, C., … & Wrangham, R. W. (2014). Lethal aggression in Pan is better explained by adaptive strategies than human impacts. Nature513(7518), 414-417.