Vertical & Oblique Transmission under Fluctuating Selection

Oblique transmission occurs when a trait is passed to offspring from non-parental members of the parental generation. This can occur, for example, via social learning, mobile genetic elements, epigenetics, and the microbiome. We (i.e. Drs Ram, Uri Liberman, and Marcus Feldman) developed a model in which both vertical (i.e. from parent to offspring) and oblique transmission occur in a population evolving under fluctuating selection. Our analytical and numerical results highlight scenarios in which oblique or vertical transmission are likely to evolve; surprisingly, in some cases, oblique transmission does not evolve, even though it increases population mean fitness. We also examine the effect of the transmission mode on maintenance of diversity in the population.

Transcript

1. Vertical & Oblique Transmission under Fluctuating Selection : Yoav Ram October 31, 2017 : Work with Marc Feldman & Uri Liberman Photo by Kelly Sikkema on Unsplash
2. Who I am » Yoav Ram (www.yoavram.com) » Postdoc at Feldman lab, Stanford University » PhD in mathematical biology at Hadany lab, Tel- Aviv University » Evolution of the mutation and recombination rate » Estimating fitness in microbes » Also: Python training for engineers & data scientists (python.yoavram.com) 2/45
3. The Modern Synthesis Genetic inheritance as the transmission mode of traits between generations. > Genetic changes that improve the fitness of individuals will tend to increase in frequency over time. -- Evolution, Bergstrom and Dugatkin 2012, ch. 1.1 Considered to be vertical: parent to offspring 3/45
4. Non-genetic inheritance » Cultural evolution: Imitation, learning... » Epigenetics » Microbiome: symbionts, parasites, pathogens » Prions: infectious proteins such as [Het-s],[PSI+], [URE3], spongiform Often non-vertical 4/45
5. Non-vertical genetic inheritance » Horizontal gene transfer: transformation, transduction, conjugation (plasmids & transposable elements), integrons » Host-parasite gene transfer » Cross-species gene transfer » Chimerism? 5/45
6. Vertical vs. non- vertical transmission Differences in » persistence » reversibility » speed » timing » direction » regulation Photo by William Bout on Unsplash 6/45
7. Oblique transmission Offspring inherit traits from non-parental adults. *Oblique = Diagonal Photo by Samuel Zeller on Unsplash 7/45
8. Focus: mixed vertical & oblique transmission Offspring inherit traits either from parent or from non-parental adults. Examples: » Social learning in humans, birds, dolphins... » Microbiome » Genetic inheritance + horizontal gene transfer 8/45
9. Model Phenotypes Two phenotypes that affect fitness: phenotype A B freq. fitness 9/45
10. Model Transmission Offspring inherit phenotype from: » parent with probability » random non-parental adult with probability where is the vertical transmission rate. 10/45
11. Model Recurrence equation The frequency of phenotype in the next generation: Mean fitness: 11/45
12. 12/45
13. Constant environment Result 1. If is favored by natural selection over and *, fixation of phenotype is globally stable. * With perfect oblique transmission ( ) or neutral evolution ( ) the recursion is and there is no change in frequency. Photo by Amy Humphries on Unsplash 13/45
14. 14/45
15. Periodic environment 15/45
16. Periodic environment Consider environments that favor for generations and for generations: - - - » Fitness of the favored phenotype (whatever it is at a given time) is » Fitness of the unfavored phenotype is 16/45
17. Periodic environment Result 2. If then fixation of either phenotype is unstable and a protected polymorphism exists. Photo by Scott Webb on Unsplash 17/45
18. Periodic environment Result 3. For general and , a protected polymorphism exists if otherwise fixation of one phenotype is stable. 18/45
19. 19/45
20. Periodic environment A1B1 We saw that when there is a protected polymorphism. We can find it for . Result 4. For A1B1 there is a unique stable polymorphismx x is the frequency of at the end of even generations 20/45
21. A1B1 If vertical transmission rate increases then stable frequency decreases 21/45
22. A1B1 So, with vertical transmission, the frequency of decreases just before it is favored again. That is not good. 22/45
23. A1B1 Indeed, the stable mean fitness decreases with the vertical transmission rate: 23/45
24. Evolution of the transmission mode Can the transmission mode itself evolve? Photo by Matthew Henry on Unsplash 24/45
25. Modifier model We model competition between two modifier alleles: » with vertical transmission rate , » with vertical transmission rate . Photo by Cloudvisual on Unsplash 25/45
26. Modifier model Pheno- genotype frequency fitness rate 26/45
27. Modifier model Recurrence equation 27/45
28. Modifier model Recurrence equation 28/45
29. Stability analysis Photo by Austin Neill on Unsplash 29/45
30. Modifier model » Initial population: » only with modifier allele » at equilibrium between phenotypes and ( ) » Now, allele is introduced at a low frequency Can increase in frequency and invade the population, or is stable to invasion? 30/45
31. Periodic environment: A1B1 Result 7. A modifier allele with vertical transmission rate is: » stable to invasion of allele with rate if , » unstable if . The evolutionary stable rate in therefore and oblique transmission is likely to evolve. 31/45
32. Periodic environment: A1B1 » and switch between and every generation. » Initial resident modifier: . » Invaders reduce rate by . 32/45
33. Reduction principle Photo by Brendan Church on Unsplash 33/45
34. Reduction principle for vertical transmission In the selection regime, evolution tends to reduce vertical transmission and increase oblique transmission. 34/45
35. The plot thickens... Photo by Cindy Tang on Unsplash 35/45
36. Periodic environment: AkBk More generally, there is no reduction of the vertical transmission rate. With environmental periods the stable vertical transmission rate is high (>0.4). 36/45
37. Periodic environment: AkBk Moreover, the stable transmission rate does not maximize the geometric mean fitnessg. g Geometric average of the population mean fitness over generations. 37/45
38. Periodic environment: AkBk Moreover, the stable transmission rate does not maximize the geometric mean fitnessg. Reminder: these modifiers are not neutral as they reduce effect of selection. g Geometric average of the population mean fitness over generations. 38/45
39. Polymorphism Photo by Tatiana Lapina on Unsplash 39/45
40. Polymorphism » Constant environment: polymorphism lasts longer with oblique transmission. Photo by Tatiana Lapina on Unsplash 39/45
41. Polymorphism » Constant environment: polymorphism lasts longer with oblique transmission. » Periodic environment: polymorphism is maintained in shorter periods with oblique transmission Photo by Tatiana Lapina on Unsplash 39/45
42. Evolution of oblique transmission » Rapidly changing environments favor oblique transmission. » Slow and constant environments favor vertical transmission. Photo by Ray Hennessy on Unsplash 40/45
43. Phenotype switching Several studiesξ assumed - periodically changing environment - vertical transmission of phenotype - phenotype switch by transmission fidelity - fidelity determined by a genetic modifier ξ Leigh 1970, Ishii et al. 1989, Jablonka 1996, Kussel & Leibler 2005, King & Masel 2007, Liberman et al. 2011 41/45
44. Phenotype switching » Switching rate evolves toward where is the period lengthμ. » Environmental statistics encoded by the modifier. μ Doesn't work if is large or if selection not symmetric. 42/45
45. Phenotype switching With oblique transmission: » Phenotype switch caused by oblique transmission rather then transmission errors. » Environmental statistics encoded by the stable population phenotype distribution if environmental changes are frequent and selection is weak. 43/45
46. Acknowledgments Funding: Stanford Center for Evolution and Human Genomics 44/45
47. Thank you! Yoav Ram / Feldman Lab yoavram@stanford.edu @yoavram 45/45