Welcome to the third installment of Animal Territoriality Week. See part 1 here, and part 2 here.

In 1994, a disease called sarcoptic mange swept through Bristol's fox population, severely crippling the population and killing most of the individuals. Professor Stephen Harris of the University of Bristol, who had been studying the movements and territories of those foxes, noticed that as the animals in one territory died, neighboring foxes were able to colonize the vacant areas in 3-4 days. He suspected that this was because the scent marks of the foxes remained active for 3-4 days, but didn't have any way to verify it.

Studies of animal territoriality are particularly hard to conduct, because territorial behavior exists across multiple levels of analysis, from the individual animal, to groups, to entire populations. In addition, experimenters must be able to explain how individual interactions between animals, which are defined over small spatial scales and only last for a brief time can build stable, long-lasting territorial patterns. In other words, in attempting to explain territorial behavior, researchers rely on macroscopic-level descriptions of entire systems, which ignore the microscopic-level individual interactions that are at the core of territorial behavior itself.

Fast forward seventeen years from Harris's initial observation. A new paper was published today in PLoS Computational Biology that addresses this very question.

Luca Giuggioli and colleagues from the University of Bristol noticed that the animal territoriality problem - the reliance on macroscopic descriptions without measuring microscopic interactions - resembles a problem that exists in chemistry. An ideal gas is comprised of a set of "randomly-moving, non-interacting point particles." But how could a set of randomly-moving particles also be non-interacting? Eventually one particle must smack into another. This sort of gas is only theoretical, but it provides researchers with a useful way to describe the behavior of gases in mathematical terms, because it describes the gas on a macroscopic level, at the expense of detailing the individual-level microscopic interactions. This is exactly the way that animal behaviorists usually model territorial behavior. Instead, Giuggioli wanted to identify a mechanism that could account for the macroscopic observations that had been made, but that would build on careful descriptions of microscopic-level interactions.

Giuggiolo and colleagues developed a mathematical model for animal territory maintenance using olfactory (scent-related) markings, based on two simple rules. First, animals can move randomly in any direction. In order to simplify the calculations, they limited the random movements to two perpendicular axes. Think: north, south, east, and west. Second, upon encountering the scent of another individual, the animal would retreat randomly away from that location. These rules strike a balance between the ideal and real gas models: like an ideal gas, individuals generally move randomly and do not interact with each other. Like a real gas, however, movement isn't always random, since an animal retreats upon encountering the scent of another, which forms the basis of an interaction.

For example, in the diagram above, each animal walks around and continuously deposits scent markers at each location. Animal two (in red) can move randomly in any of the four possible directions from its current spot. Animal one (in blue), on the other hand, has encountered a scent mark from animal two. In response, it would randomly retreat away from it, back into its own territory, in either of the two possible indicated directions.

Critically, since olfactory markings have a limited lifespan, an individual must periodically revisit each marked spot in order to refresh the scent marking. Imagine that animal one (blue) is at coordinate (4, 2) and the scent from animal two (red) has already dissipated. Instead of retreating, animal one would scent-mark that location. When animal two finally returns to that spot, he would find the scent of animal one, and retreat. In this way, the boundaries between the two territories would change, just a bit.

This all seems reasonable, but its still a mathematical model. How well might this idealized model fit real world animal interactions at microscopic and macroscopic levels?

Giuggiolo used a dataset representing the movements of red foxes (Vulpes vulpes) in Bristol, England, in a 50 square meter area. The movement patterns of the foxes was recorded via radiotelemetry during the springs of 1978 and 1991, and the summer of 1990. The foxes were radio-tracked for between 5 and 11 days, and their locations were recorded every five minutes. The real-world data from the foxes fit Giuggiolo's model quite well. In fact, the model predicted that the scent marks from these foxes would last approximately 0.6 - 5.4 days.

The key finding is that the size of an animal's territory is determined by the amount of time it takes for him (or her) to move between the boundaries of its territory, but that this is restricted by the amount of time during which the scent mark remains active. For example, if the scent marks need to be refreshed more often, then the animal will need to be able to cross his or her territory faster, meaning that the territory will have to be, on average, smaller.

By combining a mathematical model with real-world data, Harris's original observation - that when an animal in one territory died, neighboring animals were able to incorporate the new territory within three to four days - could be verified. It also validated Harris's original hypothesis: that this pattern emerges because the scent marks from the original fox last only three to four days. Taken together, this means that territory size in general is determined by an important trade-off between speed and smelliness.

Luca Giuggioli, Jonathan R. Potts, & Stephen Harris3 (2011). Animal Interactions and the Emergence of Territoriality PLoS Computational Biology, 7 (3) : 10.1371/ journal.pcbi.1002008. (Direct link to open access paper)

American red fox image via Wikimedia Commons

For more on foxes:

Might Pleistocene Fido Have Been A Fox?

Man's New Best Friend? A Forgotten Russian Experiment in Fox Domestication

For more on territory behavior:

Is Peeing on the Wall Just For The Dogs?

It Pays To Have a Bigger Brain

For more on using scent to navigate:

Nosejobs for Ants