Preview of my SAA2018 paper : Environmental instability, habitat choice, and mobility : An agent-based simulation

The Problem

The work my team and I did in James Bay, Northern Quebec, shows that archaeological sites in the region tend to be located in places that are relatively environmentally stable, but are surrounded by areas with relatively high degree of variability in rates of environmental change.

The region is characterized by rapid land uplift throughout the Holocene, resulting in rates of shoreline displacement that are locally variable, depending on topography. Shoreline displacement is a major driver of environmental change in the region.

When compared with random points on the landscape, known archaeological sites are in locations where shoreline displacement is slow, but are surrounded by areas within a few kilometer radius in which there is a high degree of variability in shoreline displacement rates compared to the overall landscape. The neighbourhoods of archaeological sites have a higher standard deviation of shoreline displacement rates than the average landscape (Figure 1).  In other words, sites seem to favour islands of stability surrounded by relative variability in stability. They tend to occur in neighbourhoods that have a mix of environmentally stable and environmentally unstable locations.

Figure 1: Variability in coastal duration, measured as standard deviation within the specified radius for sites and random points in study area.

Based on this finding, I set out to determine whether, when put in a landscape characterized by a given variability in rates of environmental change, minimally modified sugarscape agents favour neighbourhoods with higher than average variability in rate of environmental change.

I used an agent-based simulation (ABM) to test whether agents prefer neighbourhoods with a high degree of variability in rates of environmental change.

Possible mechanism

If agents do prefer neighbourhoods with higher than average variability in rate of environmental change, it may be that they are relying on the stable patches in their neighbourhood while they wait for potential pay-offs from the unstable patches. Agents in more uniformly stable neighbourhoods minimize risk by relying on stable patches, while agents in more uniformly unstable neighbourhoods gamble by relying on a string of high pay-offs. Agents in neighbourhoods characterized by high variability in environmental stability, have a balanced risk management strategy.

Null hypothesis

There is no difference between 1) the degree of variability in rates of environmental change of random-point neighbourhoods and 2) the degree of variability in rates of environmental change of agent-neighbourhoods over the course of a run.

Method

I used Li and Wilensky’s (1999) constant growback sugarscape NetLogo model as a foundation. I modified it so that:

• agents can look and move within a radius rather than up and down and side to side.
• agents have a capacity to carry some sugar around with them.
• patches have a rate of environmental change (change-rate) that is set randomly up to an upper limit for the landscape.
• When a patch undergoes environmental change, it adjusts the amount of sugar it can grow (max-psugar) randomly up or down.
• There are overall minimum and a maximum values for max-psugar.
• there are agents (called random-points) that move randomly through the landscape. They don’t care about sugar.
• agents and random points can calculate the coefficient of variation of the rates of environmental change of the patches in their immediate neigbourhood (of a given radius)
• the simulation outputs the mean coefficient of variation for agents and for random points to log files once per iteration (tick)
• the landscape calculates its own overall coefficient of variation, which remains constant throughout a given run (which I recorded manually this time, because I am giving myself until the end of summer to learn that newfangled R stuff that all the kids are on about).

The agents and the landscape are otherwise typical for Sugarscape. Agents need a certain amount of sugar to survive. Patches grow sugar at a constant rate, up to their maximum sugar value. When their stock of sugar is below a given threshold, the agents move to the patch with the most sugar within a given radius.

I compared the overall coefficient of variation of environmental change-rate of the landscape with the mean coefficient of variation of agent neighbourhoods and random-point neighbourhoods over the course of each run.

I used two values for maximum rate of environmental change per patch: 0.05% and 0.5%. I used two values for starting population, one well below carrying capacity for the environment (100) and one above carrying capacity (500). I did 20 runs for each pair of parameters. Given the values I used to generate the landscape, carrying capacity was around 350.

Results

Overall, under the set of parameters used, agents spend more time in high variability neighbourhoods than the random points. The null-hypothesis is rejected.

Table 1
% of runs in which agents have higher neighbourhood diversity than random-points
	Change Rate (%)
Starting Pop	0.05	0.50
100	0.90	1
500	0.80	0.95

Table 1 shows the proportion of runs in which agents have higher neighbourhood diversity in environmental change-rate than the random points.  Agents have higher diversity under all four combinations of starting population and maximum change rate for patches.

Figure 2 shows the ratio of agent neighbourhood diversity to random point neighbourhood diversity for all runs.

Discussion

I will discuss methodological challenges more fully in the presentation itself and in a follow up post. For now, I will say that it seems that agents do prefer neighbourhoods characterized by a higher degree of variability in rates of environmental change than the average for the landscape. In other words, agents tend to hang out in places where they are surrounded by a mix of stable and unstable patches, rather than in places where the patches are uniformly stable or uniformly unstable.

Remember that these agents don’t know anything about environmental stability or its rate of variation in their environment. They make their decisions purely in terms of available sugar. This suggests that a balanced risk management approach emerges naturally in the agent population. It could be reinforced in agents that have awareness of more elements of their environment, including rates of environmental change, resulting in the pattern that we see for distribution of archaeological sites in Eastern James Bay.

References

Li J and U Wilensky 2009. NetLogo Sugarscape 2 Constant Growback model, http://ccl.northwestern.edu/netlogo/models/Sugarscape2ConstantGrowback, Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Wren CD, A Costopoulos, M Hawley (submitted, under revision). Settlement choice under conditions of rapid shoreline displacement in Wemindji Cree Territory, subarctic Quebec, Quaternary International.

Code

Output: CoEfVar3