Game landscapes: from fitness scalars to fitness functions

My biology writing focuses heavily on fitness landscapes and evolutionary games. On the surface, these might seem fundamentally different from each other, with their only common feature being that they are both about evolution. But there are many ways that we can interconnect these two approaches.

The most popular connection is to view these models as two different extremes in terms of time-scale.

When we are looking at evolution on short time-scales, we are primarily interested which of a limited number of extant variants will take over the population or how they’ll co-exist. We can take the effort to model the interactions of the different types with each other, and we summarize these interactions as games.

But when we zoom out to longer and longer timescales, the importance of these short term dynamics diminish. And we start to worry about how new types arise and take over the population. At this timescale, the details of the type interactions are not as important and we can just focus on the first-order: fitness. What starts to matter is how fitness of nearby mutants compares to each other, so that we can reason about long-term evolutionary trajectories. We summarize this as fitness landscapes.

From this perspective, the fitness landscapes are the more foundational concept. Games are the details that only matter in the short term.

But this isn’t the only perspective we can take. In my recent contribution with Peter Jeavons to Russell Rockne’s 2019 Mathematical Oncology Roadmap, I wanted to sketch a different perspective. In this post I want to sketch this alternative perspective and discuss how ‘game landscapes’ generalize the traditional view of fitness landscapes. In this way, the post can be viewed as my third entry on progressively more general views of fitness landscapes. The previous two were on generalizing the NK-model, and replacing scalar fitness by a probability distribution.

In this post, I will take this exploration of fitness landscapes a little further and finally connect to games. Nothing profound will be said, but maybe it will give another look at a well-known object.

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