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Preliminary Results

Our preliminary results indicated very clearly that our model was indeed behaving as expected. Figures 1 and 2 depict the fusing of colonies which allorecognize each other. Figure one shows a stolon colony (red, $ ff\alpha \alpha $) fusing with a fused mat colony (yellow, $ ff r\alpha $). Because the fused mat colony began in a corner, its reproductive potential was somewhat hampered. Between timestep 100 and 150, the colonies touch and successfully recognize each other. This recognition is evidenced by the lack of dead or dying cells in the vicinity of the intersection. This experiment was run for 5000 timesteps, the last of which is depicted in the final image in Figure 1. Here we can clearly see the slow diffusion of the two colonies into each other, as shown by irregular border and the splotchiness in that area.

Passive rejection is illustrated in Figure 2, in which two unfriendly ( $ ff\alpha \alpha $ and $ rr\beta \beta $) fused mat colonies are placed in the same vicinity. At time step 140, we can see the small region of passive rejection in which neither reproduction as evidenced by the lack of diffusion seen in the previous figure or fighting as evidenced by the lack of a band of dead cells separating the two colonies. Figure 3 illustrates hostile rejection, in which a stolon colony (red, $ ff\alpha \alpha $) rejects a fused mat colony (yellow, $ rr\beta \beta $). Because all fights between stolon and fused mat cells result in a dead fused mat cell, the stolon colony quickly overwhelms the fused mat colony.

An interaction between two hostile and aggressive colonies, such as stolon or unfused mat colonies, results in a more dynamic picture. Figure 4 illustrates such an interaction, in which a stolon colony (red, $ ff\alpha \alpha $) engages an unfused mat colony (blue, $ rr\beta \beta $). The black thread which initially emerges in time step 140 and continues throughout the experiment is evidence of the ongoing struggle for dominance between the two colonies. Here, the balance between the unfused mat colony's higher reproductive rate and the stolon colony's slight advantage in a fight is seen, as this particular dead-zone remains fairly stable between the colonies.

Deeper Results

Having established that our model correctly mimics the behaviors described in the assignment, we set out on the more complex experiments. One dynamic which we found to be dominate in most heterogeneous simulations in which the genotypes were not predefined, was that of one colony which is neutral to both aggressors colonizing the dead-zone between them. This phenomenon was only seen to occur between two aggressive hostile colonies (fights between stolon and unfused colonies), as the dead-zone is fairly stable in such fights. In fights with fused mat colonies, the winning colony moves the dead-zone away from the potential colonizer too quickly for it to be colonized. However, as we can see in Figure 5, once the colonizer has moved into the niche created by the fight, the fighting ceases as the warring colonies have been buffered by the third party, to which both the aggressors are neutral. This situation is exactly the kind which we were cautious about and motivated us to forego basing cell-fights on the size of their colony.

In some circumstances, one colony will dominate the others; this is particularly true, if the dominating colony is able to exclude several more vulnerable colonies, perhaps fused mat colonies or small stolon/unfused mat colonies. In Figure 6, we see an unfused mat colony (blue, $ rr\beta \beta $) colony competitively exclude the other two colonies (red and yellow, $ ff\alpha \alpha $ and $ ff\alpha \alpha $). The dominating colony is not inherently at an advantage over the other two colonies, but rather is able to first destroy the defenseless fused mat colony, and then slowly whittling away the remaining stolon colony. The fused mat colony, in effect, prevented the stolon colony from growing to a size large enough to hold off the unfused mat colony.

There's no way to feasibly construct a system with a dynamical balance such as that of the game rock-paper-scissors. This failure is due to inherent limitations of the model, namely that fighting is reflexive. In order to have a rock-paper-scissors situation, all three morphologies must have both a weakness and a strength; however, fused mat cells have no strengths, and the weakness of unfused mat cells versus stolon cells is not substantial enough to create the desired dynamic. As suggested in the assignment, we tried a simulation having two colonies that fuse compete against one rejecting colony. Figure 7 depicts the resulting dynamics. The fusing colonies both attack the remaining colony, slowly reducing the defending colony's numbers.

In activating genotypic mutation, we were unsure what to expect. However, the changes in dynamics were significant. Previously, the buffering phenomenon was the most common result between warring colonies in a genotypically diverse environment. Generally, in a prolonged engagement between aggressive colonies, a third party, neutral to both, would colonize the war zone producing a buffered-peace between the aggressive colonies. With genotypic mutation activated, such homogeneous buffer zones were less stable. In particular, a warring colony would generate its own buffer as a result of a genotypic mutation which produces a viable neutral third genotype within the dead-zone. We would frequently see such spontaneous buffers emerge in several locations along the dead-zone, creating a heterogeneous buffer. Further, fused mat buffers were generally unstable, as any mutation which produced an agent hostile to the buffer would destroy it. Figure 8 illustrates an experiment with genotypic mutation activated that resulted in such dynamics. The border between the stolon and unfused colonies first shows the expected dead-zone, but it is quickly neutralized by the emergence of small buffers of neutral cells. Figure 9 illustrates another interesting run using the same parameters as those used in Figure 8. We can see that initially, the aggressive unfused mat and stolon colonies create a buffer to stem their battle, while the fused and stolon colonies fuse peacefully. However, a genotypic mutation results in the hostile stolon subcolony shown in time step 410 eating into the fused colony. Meanwhile, the reproductive advantage of the unfused mat colony allows it to round the tip of the stolon colony and begin attacking the fused colony as well. Genotypic mutation, however, saves the unfused mat colony from complete destruction as patch of fused cells which are neutral to the aggressive stolon subcolony persist (time step 1000).

Activating morphological mutation without also activating genotypic mutation did not lead to an significantly different dynamics. One might think that such additional flexibility might allow the fused mat colonies to defend themselves slightly better (by opening up the possibility of creating stolon or unfused mat cells), but we did not observe this increased flexibility to prevent the fused mat colonies from being engulfed by more aggressive colonies. Further, once the system reached a relatively stable genotypic steady state, the presense of morphological mutation resulted in a morphological soup in which a colony became a diverse mixture of the various genetically identical morphologies.

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Next: Discussion and Conclusion Up: Hydractinia Previous: Experiments