Algorithmic biology of evolution and ecology

Any process can be seen as an algorithm; its power and its limits can then be analysed with the techniques of theoretical computer science. To analyse algorithms, we divide the world in two: the problem space that shapes what might happen and the dynamics of what does happen. If we fix an idealised framework for one of the two, then we can obtain powerful general results by abstracting over the other. This “algorithmic lens” can be used to view both artificial and natural processes, including the natural processes of biological evolution.
In Part I, I idealize the space of evolution as a fitness landscape so that I can abstract over the possible evolutionary dynamics. I show that fitness landscapes can be represented by gene-interaction networks that encode the structure of epistasis.
For some landscapes, the epistatic structure produces a computational constraint that prevents evolution from finding even a local fitness optimum—thus contradicting the traditional assumption that local fitness peaks can always be reached quickly by natural selection. I introduce a distinction between easy landscapes, where local fitness peaks can be found in a moderate number of steps, and hard landscapes where finding any such local optimum requires an infeasible amount of time. Hard examples exist where strong-selection weak-mutation dynamics cannot find a local peak in polynomial time, even when it is known to be unique. More generally, I show that hard fitness landscapes exist where no evolutionary dynamics—even ones that do not follow adaptive paths—can find a local fitness optimum in polynomial time. Moreover, on hard landscapes, the fitness advantage of nearby mutants cannot drop off exponentially fast but must follow a power-law, similar to the one found by long-term evolution experiments, associated with unbounded growth in fitness. Thus, the constraint of computational complexity enables open-ended evolution on finite landscapes. I present candidates for hard landscapes at scales from single genes, to microbes, to complex organisms with costly learning (Baldwin effect) or maintained cooperation (Hankshaw effect). Finally, by looking closer at the fine structure of epistasis, I also extend the class of provably easy landscapes to include all those with tree-structured gene-interaction networks.
In Part II, I idealize the dynamics of evolution as replicator dynamics so that I can abstract over the space of ecologies (interactions between organisms). This requires replacing the fitness-as-scalar concept used in fitness landscapes by a fitness-as-function concept derived from evolutionary game theory. Since they have not been adequately defined or interpreted in the context of microscopic biology, I provide two interpretations of the central objects of game theory: one that leads to what I call “reductive games” and the other to “effective games”. These interpretations are based on the difference between views of fitness as a property of tokens versus fitness as a summary statistic of types. Reductive games are typical of theoretical work like agent-based models. Effective games correspond more closely to experimental work and allow for empirical abstraction over poorly characterized interaction mechanisms like spatial structure.
This empirical abstraction allows me to analyse the in vitro evolution of resistance to cancer therapy. I develop a game assay to directly measure effective evolutionary games in co-cultures of non-small cell lung cancer cells that are sensitive vs resistant to the targeted drug Alectinib. I show that the games are not only quantitatively different between different environments, but that the presence of the drug or the absence of cancer-associated fibroblasts qualitatively switches the type of game being played by the in vitro population. This observation provides empirical confirmation of a central theoretical postulate of evolutionary game theory in oncology: we can treat not only the player, but also the game.
Thus through the whole thesis, I demonstrate how the algorithmic lens and abstraction can help us derive new ways of seeing and understanding both evolution and ecology.

Keywords: valued constraint satisfaction problems
algorithmic biology
evolutionary game theory
cancer
local search
evolution
fitness landscapes
Advisor: Jeavons, P