Sugarscape

Sugarscape is a model artificially intelligent agent-based social simulation following some or all rules presented by Joshua M. Epstein & Robert Axtell in their book Growing Artificial Societies.

The simulation was translated into the Netlogo language by Iain Weaver as a summer internship project and is available from the Netlogo library on the Netlogo web site.

Replicating Sugarscape in NetLogo

GAS Fig./Anim. [1]

Rules

Characteristics

Replication

Animation II-1

({G}, {M})

Terracing

Exact

Animation II-2

({G1}, {M})

Hiving around peaks

Exact

Animation II-6

({G1}, {M})

Migration waves

Good1

Animation II-8

({G1, D1}, {M, P1,1})

Migration away from polluted regions

Good2

Figure III-1

({G1}, {M, S})

Stable population time-series

Poor3a

Animation III-1

({G1}, {M, S})

Stable age distribution

Exact

Animation III-2, 3

({G1}, {M, S})

Population grows to fill tiers 4, 3 & 2

Poor 3b

Figure III-2

({G1}, {M, S})

Diverging vision & metabolism

Good

Figure III-3, 4

({G1}, {M, S})

Population oscillations

Low

Animation III-6

({G1}, {M, K})

Tendency for hives to form one culture

Exact

Animation IV-1

({G1}, {M})

Elaborate trajectories between 2 resources

Good4

Figure IV-3

({G1}, {M, T})

Stable time-series of trade price

Exact

Figure IV-4

({G1}, {M, T})

Erratic time-series of trade volume

Exact

Figure IV-7

({G1}, {M, T})

Erratic time-series of trade price with low-vision agents

Exact

Animation IV-3

({G1, D1}, {M, T, P1,1})

Increase is prices with pollution followed by slow, erratic recovery to equilibrium

Exact

Figure IV-18

({G1}, {M, S})

Evolution of mean foresight

Exact

Animation IV-4

({G1}, {M, T})

Emergent trade networks

Good

Animation IV-5

({G1}, {M, S, L10,10})

Emergent hierarchy and credit networks

Exact5

Animation V-1

({G1}, {M, E})

Eradication of disease with small catalogue

Exact

Animation V-2

({G1}, {M, E})

Persistence of disease with large catalogue

Good6

1. Replication of Migration Waves

This animation is said to use the same settings as animation II-2 except with 2 modifications:

  • Agent vision is distributed between from 1 to 10 as opposed to 1 to 6
  • Agents are clustered in the lower left corner rather than scattered randomly

The other settings then are

  • 400 agents are distributed in the Sugarscape
  • Sugar grows back at a rate of 1/tick
  • Metabolism is distributed from 1 to 4

However, at a glance there are clearly less than 400 agents present in the animation as they form a 20x20 block with roughly 25% gaps. Running this animation in the NetLogo model does not produce the clear waves as Animation II-6 shows. With sugar returning at a rate of 1, migrating agents in the wave quickly double back. Additionally, the high vision and rule M frequently causes agents to jump off the bottom edge of the Sugarscape, around the torus, to more quickly arrive at the opposite sugar hill. I found the waves can be replicated by halving grow back rate of sugar and using a block of 300 agents. This result mirrors a pervious attempt at replicating the Sugarscape [1].

2. Replication of Pollution effects

Applying pollution once then agents had begun hiving about the peaks found the expected effect. The agents migrate away from the peak in waves, ahead of the polluted regions they leave behind. In this model, the majority of agents retreat to the lower sugar levels around the edges. However, animation II-8 shows agents occupying sites with no sugar at all shortly after pollution is turned on. Since agents seek the best sugar to pollution ratio, under these rules there is no possibility of this happening, and there must be some unseen effect at work.

With diffusion turned on, this model fits reasonably closely with animation II-8. Specifically, terracing is seen as agents will occupy the highest sugar levels, while staying as far from the heavily polluted peaks as possible.

3a, b. Replication of Population Dynamics

Under these rules, the NetLogo model finds that as the initial 400 agents reach 60 ticks, the population dives dramatically. This is an artifiact of the program, as all agents are generated with an age of 0, and a minimum life expectancy of 60. An entirely different character occurs in figure III-1 where the population only begins to fall at roughly 100 ticks. After this, the NetLogo population stabilises at ~300 agents, much lower than the 500 indicated in figure III-1. These results can be partially replicated by lowering the initial sugar endowments of agents from the range 50 to 100, to the range 40 to 80, but still fails to replicate the steep population increase in the first 100 ticks.

Further discrepancy can be found in animation III-2 and 3. These animations are presumed to follow the same rules as figure III-1, however, the population seen in the 6th panel of each animation shows over 900 agents present, far above the maximum of ~600 shown in figure III-1. Similarly, panel 2 shows a very sparse distribution of less than 200 agents, far lower than the minimum seen in figure III-1. These animations can be replicated by dramatically lowering the initial sugar endowments to the range of 10 to 40, as demonstrated in a later animation.

4. Replication of hiving about 2 resources

This animation was pleasingly replicated in NetLogo. The only major difference between is the equilibrium distribution of agents. In the NetLogo model, it is assumed that the spice hills are roughly a rotation of the sugar hills. This would mean there is significant overlap of the sugar and spice patches. In this model, agents form a more central distribution whereas animation IV-1 shows agents closer to the edges. This is likely simply due to the geometry of the new Sugarscape which, without a map of the spice distribution, would be difficult to replicate exactly.

5. Replication of Lending rules

Although this application of lending was successful, the final animations of the book include lending with both sugar and spice. It is unclear how this would have been implemented, and is not alluded to. Trade occurs for agents to get their MRS value to 1, indicating an equal need for both sugar and spice while also slightly increasing their welfare. However, loans are made for the purposes of reproduction. Since metabolism and initial values of sugar and spice are entirely independent, loaning spice in the same way as sugar would result in agents taking loans to become fertile (following their initial sugar and spice values), only to trade the resources away to attain an MRS closer to 1 (following their sugar and spice metabolisms).

6. Replication of Disease rules

Again, this model has been successful as reproducing the animations seen in GAS, though there are still some discrepancies. Population density is clearly a large contributing factor to persistence, and it was found it could only be consistently seen with an initial population of 600, as opposed to the usual 400. The way disease and transmission is implemented in GAS is also unclear.

Can a disease be passed to an agent who is immune to it?

For this model, we have said yes. The immune agent will suffer the effects of this disease, and be able to transmit the disease for a single tick before his immune response rule has been implemented (unless the immune response that tick corrupts the memory of that disease).

What order are the 3 stages of rule E carried out?

The 3 stages for the active agent are transmission from the active agent, immune response and removal of diseases the agent is immune to. In this model, they occur in this order allowing agents immune to a disease to catch it and pass it on before being able to remove it. This order has been found to be the most effective at modelling persistence of disease, as other combinations often result in even large disease catalogues being eradicated within 100 ticks.

Can diseases passed on cause duplicates?

GAS states that a disease is selected at random to be transmitted. If the receiving agent already has this disease, does he avoid the need to contract another? In this model, agents will always pass on a new disease where possible.

References

[1] JM Epstein and R Aktell, Growing Artificial Societies (MIT Press, 1996)

[2] A. Bigbee et al, Springer Series on Agent Based Social Systems, 3, pp. 183-190 (2007)

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