Evolution is exponentially more powerful with frequency-dependent selection

Abstract

Valiant [1] proposed to treat Darwinian evolution as a special kind of computational learning from statistical queries. The statistical queries represent a genotype's fitness over a distribution of challenges. And this distribution of challenges along with the best response to them specify a given abiotic environment or static fitness landscape. Valiant's model distinguished families of environments that are "adaptable-to" from those that are not. But this model of evolution omits the vital ecological interactions between different evolving agents -it neglects the rich biotic environment that is central to the struggle for existence.In this article, I extend algorithmic Darwinism to include the ecological dynamics of frequencydependent selection as a population-dependent bias to the distribution of challenges that specify an environment. This extended algorithmic Darwinism replaces simple invasion of wild-type by a mutant-type of higher scalar fitness with an evolutionary game between wild-type and mutanttype based on their frequency-dependent fitness function. To analyze this model, I develop a game landscape view of evolution, as a generalization of the classic fitness landscape approach that is popular in biology.I show that this model of eco-evo dynamics on game landscapes can provide an exponential speed-up over the purely evolutionary dynamics of the strict algorithmic Darwinism proposed by Valiant. In particular, I prove that the noisy-Parity environment -which is known to be not adaptable-to under strict algorithmic Darwinism (and conjectured to be not PAC-learnable)is adaptable-to by eco-evo dynamics. Thus, the ecology of frequency-dependent selection does not just increase the tempo of evolution, but fundamentally transforms its mode.The eco-evo dynamic for adapting to the noisy-Parity environment proceeds by two stages: (1) a quick stage of point-mutations that moves the population to one of exponentially many local fitness peaks; followed by (2) a slower stage where each 'step' follows a double-mutation by a point-mutation. This second stage allows the population to hop between local fitness peaks to reach the unique global fitness peak in polynomial time. The evolutionary game dynamics of finite populations are essential for finding a short adaptive path to the global fitness peak during the second stage of the adaptation process. This highlights the rich interface between computational learning theory, evolutionary games, and long-term evolution.

The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer

“…Here, the per capita growth rate of cancer cells of type i is given by their expected payoff (fitness) (A q) i minus the mean fitness of the entire population q T A q. This fitness is frequency-dependent [49,112] and captures non-cell-autonomous effects that are central to the ecology of cancer [65,113,125].…”

“…If such an ESS in tumors exists, reaching it using available therapies could provide a means for achieving long-term stabilization of tumors and a significant increase in progression-free and overall survival [56,113,194]. However, it is important to be aware of the timescales involved and that the equilibria might not be reached [49,111,112], for example due to ecological constraints on population size [87].…”

Measuring competitive exclusion in non-small cell lung cancer

“…11,[14][15][16][17] As a consequence, we must understand both the absolute fitness advantages of particular subpopulations in the selecting environment (monoculture), as well as how competing clones modulate that advantage as a function of population frequency (co-culture). 18 This frequencydependent growth can transform the power of evolution 19 and acts to shape treatment-naïve tumor ecosystems and influences inevitable development of resistance in post-treatment environments. [20][21][22][23] As traditional treatment protocols continue to fail, more evolutionary-based treatments that rely on judicious treatment schedules and cooperative dynamics between populations have gained in popularity.…”

The contribution of evolutionary game theory to understanding and treating cancer

“…Here, the per capita growth rate of cancer cells of type i is given by their expected payoff (fitness) (A q) i minus the mean fitness of the entire population q T A q. This fitness is frequency-dependent [46,108] and captures non-cell-autonomous effects that are central to the ecology of cancer [121,109,62].…”