The cost of acquiring information by natural selection

This is a short talk that I gave at the Banff International Research Station workshop on Modeling and Theory in Population Biology. The idea is to try to understand how the burden of natural selection relates to the amount of information that selection puts into the genome.

It's based on the first part of this research paper:

The cost of information acquisition by natural selection
Ryan Seamus McGee, Olivia Kosterlitz, Artem Kaznatcheev, Benjamin Kerr, Carl T. Bergstrom
bioRxiv 2022.07.02.498577; doi: https://doi.org/10.1101/2022.07.02.498577

1. The cost of acquiring information by natural selection Carl T. Bergstrom Department of Biology University of Washington with R. McGee, O. Kosterlitz , A.Kaznatcheev , and B. Kerr Photo: Carl Bergstrom

2. Ben Kerr Olivia Kosterlitz Artem Kaznatcheev Ryan McGee

3. The information behind phenotype Photos: Carl Bergstrom

4. Where does this information come from? Photo: Carl Bergstrom

5. natural selection Photo: Carl Bergstrom

6. Photo: Carl Bergstrom In particular, organisms need to match their phenotypes to their environments, their niches, their life-histories, etc.

7. “The environment is light, so grow light fur.” — Mom Given that a light fur allele was inherited, it is likely that light fur has been favored in the past, and thus it is likely beneficial to develop light fur.

8. . Every bit of adaptive information in your genome was paid for in the blood of your ancestors’ children. Photo: Carl Bergstrom

9. But can we quantify it? I think so. Adaptive genetic information refers to the inherited material that reduces an organism's uncertainty about the current environment so that its expected fitness is greater than it would be due to chance alone. Photo: Carl Bergstrom

10. Imagine the state of the environment as a random variable E and the genome G as another random variable.   Natural selection creates mutual Information between E and G . Photo: Carl Bergstrom

11. We can measure how much information has been added looking at how much genotype frequencies have changed due to selection.   Photo: Carl Bergstrom

12. As the frequency of the best genotype increases in the population, the population gains information about the environment.

13. Nearly 70 years ago…. Nearly 70 years ago….

14. Nearly 70 years ago….

15. Selective deaths

16. Selective deaths

17. Substitution load growth rate of optimal type     growth rate of type i

18. “It is appropriate to speak of a cost of selection, since the cost comes from the fact that natural selection is less efficient than divine intervention.” - Joe Felsenstein Substitution load

19. Information gain

20. Information gain Substitution load

21. Information gain Substitution load

22. Substitution load Information gain

23. Substitution load Information gain

24. Beyond a thought-experiment

32.     population growth rate population growth rate optimal type growth rate optimal type growth rate optimal growth rate population growth rate

33.     population growth rate population growth rate optimal type growth rate optimal type growth rate optimal growth rate population growth rate

34. WTF?

35. Aha!

36. time growth rate of optimal type     growth rate of type i Substitution Load growth rate of optimal type in condition j     growth rate of type i in condition j probability of condition j Mismatch Load

37. Regret Loss and regret Photo: Carl Bergstrom

38. In computational learning theory, loss is the payoff cost of mismatch between strategy and environment, and regret is the cost of having to learn the best strategy: the difference between the cumulative loss as the learner updates its strategy over time, and the loss it could have achieved had it played an optimal fixed strategy from the beginning.

39. By thinking about regret, we can broadly extend our results about substitution load. Photo: Carl Bergstrom

40. Load of the evolving population Load of the best type Information gain of evolving population

41. environment genotype “idiosyncratically” stochastic environments

42. environment genotype Cycling environments

43. environment genotype Frequency-dependent fitnesses Rock- Paper- Scissors

44. Load of the evolving population Load of the best type Information gain of evolving population

45. Theorem : Information gain converges to regret, in fixed or stochastic environments, with or without frequency-dependence, etc.

46. Theorem : Information gain is bounded above by empirical regret, a measure of regret taken relative to the ex-post optimal strategy.

47. Teaser : Among learning algorithms, natural selection is never ”far” from optimal in the sense of minimizing regret.