Abstract
In 2006, Valiant introduced a variation to his celebrated PAC model to Biology, by which he wished to explain how such complex life mechanisms evolved in that short time by two simple mechanisms - random variation and natural selection. Soon after, several works extended and specialized his work to more specific processes. To the best of our knowledge, there is no such extension to the prokaryotic world, in which gene sharing is the prevailing mode of evolution.
Here we extend the evolvability framework to accommodate horizontal gene transfer (HGT), the transfer of genetic material between unrelated organisms. While in a separate work we focused on the theoretical aspects of this extension and its learnability power, here the focus is on more practical and biological facets of this new model. Specifically, we focus on the evolutionary process of developing a trait and model it as the conjunction function. We demonstrate the speedup in learning time for a variant of conjunction to which learning algorithms are known. We also confront the new model with the recombination model on real data of E. coli strains under the task of developing pathogenicity and obtain results adhering to current existing knowledge.
Apart from the sheer extension to the understudied prokaryotic world, our work offers comparisons of three different models of evolution under the same conditions, which we believe is unique and of a separate interest.
The code of the simulations is freely available at: https://github.com/byohay/LearningModels.git.
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Notes
- 1.
We need to calculate the expected performance of two random monotone conjunction functions. This is done by using a combinatorial computation. For n variables, the expected performance rate is almost \(1-2^{-\frac{3n}{4}}\). Thus if \(\epsilon \) is smaller than \(2^{-\frac{3n}{4}}\), the chance of a high performance at generation 0 is relatively low. For \(n=40\), we need to choose a number smaller than \(2^{-30}\), therefore we chose \(\epsilon \) to be \({2^{-31}}\).
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Snir, S., Yohay, B. (2018). Extending the Evolvability Model to the Prokaryotic World: Simulations and Results on Real Data. In: Zhang, F., Cai, Z., Skums, P., Zhang, S. (eds) Bioinformatics Research and Applications. ISBRA 2018. Lecture Notes in Computer Science(), vol 10847. Springer, Cham. https://doi.org/10.1007/978-3-319-94968-0_29
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