Evolution of Non-Vertical Inheritance in Changing Environments

5ff2e2cd70421285fff0e6361354993b?s=47 Yoav Ram
March 20, 2018

Evolution of Non-Vertical Inheritance in Changing Environments

The modern evolutionary synthesis assumes that traits are transmitted via genetic inheritance, an inherently vertical transmission mechanism. But non-genetic and non-vertical transmission mechanisms are common, including social learning, microbiome transmission, and horizontal gene transfer.
I describe results from our PNAS paper "Evolution of vertical and oblique transmission under fluctuating selection". We found that oblique transmission (i.e. from non-parental adults) increases phenotypic diversity by protecting maladapted phenotypes from selection. We further found that the population optimal strategy is for most individuals to use oblique transmission, but only low rates of oblique transmission can evolve, unless environmental changes are very rapid.

5ff2e2cd70421285fff0e6361354993b?s=128

Yoav Ram

March 20, 2018
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  1. Evolution of Non-Vertical Transmission in Changing Environments Yoav Ram Stanford

    University Work with Marc Feldman & Uri Liberman January 10, 2018 Photos from www.unsplash.com
  2. Genetic changes that improve the fitness of individuals will tend

    to increase in frequency over time. — Evolution, Bergstrom and Dugatkin 2012 2/46
  3. The Modern Synthesis Genetic inheritance as the mode of transmission

    of traits between generations. Inherently vertical: parent to offspring. 3/46
  4. Non-genetic inheritance — Cultural evolution: imitation, learning... — Epigenetics with

    trans- generational effects — Associated microbes: microbiome, pathogens — Prions: infectious proteins O!en non-vertical 4/46
  5. Non-vertical genetic inheritance -Horizontal gene transfer: transformation, transduction, conjugation (plasmids

    & transposable elements), integrons - Host-parasite gene transfer - Cross-species gene transfer - Chimerism? (Sheets et al, JARG 2017) 5/46
  6. Vertical vs. non-vertical transmission Differences in — persistence — reversibility

    — speed — timing — direction — regulation 6/46
  7. Oblique transmission Offspring inherit traits from non-parental adults. * Oblique

    = Diagonal 7/46
  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 8/46
  9. Model: Phenotypes Two phenotypes that affect fitness 9/46

  10. Model: Phenotypes Two phenotypes that affect fitness: phenotype A B

    frequency fitness 10/46
  11. Model: Transmission Offspring inherit phenotype from: — parent with probability

    — random non-parental adult with probability where is the vertical transmission rate. 11/46
  12. Model: Recurrence equation The frequency of phenotype in the next

    generation: and is the population mean fitness: 12/46
  13. 13/46

  14. 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. 14/46
  15. 15/46

  16. Periodic environment 16/46

  17. 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 17/46
  18. Periodic environment Result 2. If then fixation of either phenotype

    is unstable and a protected polymorphism exists. 18/46
  19. Periodic environment Result 3. For general and , a protected

    polymorphism exists if otherwise fixation of one phenotype is stable. 19/46
  20. Periodic environment We saw that when there is a protected

    polymorphism. We can find it for . 20/46
  21. Periodic environment: A1B1 Result 4. For A1B1 there is a

    unique stable polymorphismx x is the frequency of at the end of even generations 21/46
  22. Periodic environment: A1B1 If vertical transmission rate increases then stable

    frequency decreases 22/46
  23. Periodic environment: A1B1 So, with vertical transmission, the frequency of

    decreases just before it is favored again. That is not good. 23/46
  24. Periodic environment: A1B1 Indeed, the stable mean fitness decreases with

    the vertical transmission rate: 24/46
  25. Evolution of the transmission mode Can the transmission mode itself

    evolve? 25/46
  26. Modifier model We model competition between two modifier alleles: —

    with vertical transmission rate , — with vertical transmission rate . 26/46
  27. Modifier model Pheno- genotype frequency fitness rate 27/46

  28. Modifier model Recurrence equation 28/46

  29. Modifier model Recurrence equation 29/46

  30. Stability analysis 30/46

  31. 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? 31/46
  32. Periodic environment: A1B1 Result 7. An invading modifier allele —

    can invade if it decreases vertical transmission , — cannot invade if increases vertical transmission . The evolutionary stable transmission is complete oblique transmission: 32/46
  33. Periodic environment: A1B1 — Fitness of and switch between and

    every generation. — Initial resident modifier with vertical transmission rate . — Invaders reduce transmission rate by . 33/46
  34. Reduction principle for vertical transmission When the environment changes every

    generation, evolution tends to reduce vertical transmission and increase oblique transmission. 34/46
  35. The plot thickens... 35/46

  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). 36/46
  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. 37/46
  38. Periodic environment: AkBk Also, for a wide range of environment

    periods. Some oblique transmission is still advantageous. 38/46
  39. Conclusions 39/46

  40. Polymorphism 40/46

  41. Polymorphism — Constant environment: polymorphism lasts longer with oblique transmission.

    40/46
  42. Polymorphism — Constant environment: polymorphism lasts longer with oblique transmission.

    — Periodic environment: polymorphism is maintained in more environments with oblique transmission 40/46
  43. Evolution of oblique transmission — Rapidly changing environments favor oblique

    transmission. — Slow and constant environments favor vertical transmission — Despite population-level advantage to oblique transmission — Some oblique transmission is maintained even in slow environments 41/46
  44. 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 42/46
  45. Phenotype switching — Switching rate evolves toward where is the

    period lengthμ. μ Doesn't work if is large or if selection not symmetric. 43/46
  46. Phenotype switching With oblique transmission: — Phenotype switch caused by

    oblique transmission rather then transmission errors. 44/46
  47. Acknowledgments Funding: - Stanford Center for Computational, Evolutionary and Human

    Genomics - The Morrison Institute for Population and Resources Studies, Stanford University 45/46
  48. Thank you! Ram Y, Liberman U, Feldman MW. Evolution of

    vertical and oblique transmission under fluctuating selection. PNAS (In press). Preprint: bioRxiv doi:10.1101/229179 Contact: yoavram@stanford.edu www.yoavram.com 46/46