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Science Corner: Developing a Complex

While the equilibrium number of genes is different in each case, all three roads lead to higher complexity. (Image by Andy Walsh; click to enlarge)

For the past few weeks, we’ve been conducting experiments in the Quandary Den, a simple game simulation where the players evolve strategies. We’ve been looking at how complex solutions can evolve from simpler ones. So far, no single technical definition captures everything we mean informally by complexity, but for our purposes here I am describing a solution as more complex if it involves more distinct parts that are each individually essential. Last week we confirmed that there are neutral roads to such complexity, meaning the changes involved in going from a simpler solution to a more complex one do not change fitness and are not selected for. Nevertheless, even though we are not selecting for higher complexity either directly or indirectly, complexity always increases in these experiments. Then I identified a way in which I might have inadvertently made greater complexity more likely, and proposed a modification to our experimental setup that would mitigate that potential bias. Did the road still lead to more complex solutions? What did you find? Let’s look at my results.
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Science Corner: Traveling on the Level

Increasing numbers of genes with positive LOTB indicates more genes are essential. (Image by Andy Walsh; click to enlarge)

When we last visited the Quandary Den, we saw how our players could take an adaptive path to complexity. By complexity, I mean that the solution to the challenge of the room involved multiple players making distinct and essential contributions. We saw that they were essential by looking at the last-on-the-bus (LOTB) score which looks at the difference between the team’s result with that player and without. If a player has a LOTB score of zero, then their contributions are not essential; they might score one or more points but when they are not there someone else is capable of scoring them. And I say the path to that complexity was adaptive because the experiment started with random actions and applied positive selection whenever mutations added players or actions that contributed to a solution. Then I asked whether other pathways to complexity were possible and provided a simulation for answering that question.
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Science Corner: Don’t Miss the Bus

It’s not just that there are multiple players; most of the players are making nonredundant contributions. (Image by Andy Walsh; click to enlarge)

Two weeks ago, we revisited the Quandary Den to see what happens when multiple players are able to work together. We did this by modeling gene duplication, a known biological process. Last week we saw some results showing that solutions involving multiple players could evolve, and when multiple players got involved solutions tended to come faster. At the same time, more wasn’t always better; we saw that when players were added too quickly, they were more likely to get in the way and inhibit solutions. This little model gives us a picture for how organisms might evolve complexity, that is solutions involving distinct, coordinated parts. In this case, we have an adaptive pathway to complexity, since adding players provides opportunities to potentially increase fitness. But is that the only road to complexity?
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Science Corner: Better with Friends?

How do you think the lower limit on gene number impacts the equilibrium of the 1e-2 result? (Image by Andy Walsh; click to enlarge)

Last week, we talked about gene duplication and looked at some simulation results. For starters, I was just simulating a random walk in the number of genes. The probability of adding a gene (taking a step ‘up’) remained the same, but I varied the probability of losing a gene (taking a step ‘down’). And I prevented the number from ever getting to zero or lower. You can see the results to the right (click for a bigger version). When the probability of losing a gene is 10x higher than gaining (purple/darkest line), the number of genes (averaged over 128 trials) basically stays at 1. No big surprise there; any time a gene is gained, we’d expect to lose it again very quickly before another one is added. Conversely, when the probability of losing a gene is 10x lower than gaining (yellow/lightest line), the average number of genes just keeps on growing; again, not a big surprise. But when the probability of gaining and losing a gene is the same (green/intermediate line), the average number of genes creeps up, possibly leveling off somewhere just above 10. You’d probably expect some kind of equilibrium, but would you have predicted that’s where it would be?
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Science Corner: Better with Friends

A simulation of gene duplication and loss when the genes have no fitness effect. (Image by Andy Walsh; click to enlarge)

Over the weekend, our household reached the point where all of us are fully vaccinated for COVID-19. We celebrated this milestone with an escape room outing. That got me thinking about my little escape room model, the Quandary Den. You can read more details here`, but the short version is that the Quandary Den simulates a game where a player has to “solve” the challenge of the room. My family’s in-person escape room involved lots of combination locks, and here on the blog we simulated some password challenges of a similar sort. In our initial visits to the Quandary Den, we also simulated a challenge where a player had to “solve” the room by tagging the opposing players without getting tagged. That might not seem like much of a puzzle for a real escape room, but when the information about where the opposing players are has to be learned through exploration with feedback, the difficulty goes up a bit. In a real escape room, we can reduce the difficulty (and increase the fun) by adding friends. Does that work in the Quandary Den?
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