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.

Transcript

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
   

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2. Genetic changes that improve the
   fitness of individuals will tend to
   increase in frequency over time.
   — Evolution, Bergstrom and Dugatkin 2012
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3. The Modern Synthesis
   Genetic inheritance as the
   mode of transmission of traits
   between generations.
   Inherently vertical: parent to
   offspring.
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4. Non-genetic inheritance
   — Cultural evolution:
   imitation, learning...
   — Epigenetics with trans-
   generational effects
   — Associated microbes:
   microbiome, pathogens
   — Prions: infectious proteins
   O!en non-vertical
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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)
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6. Vertical vs. non-vertical transmission
   Differences in
   — persistence
   — reversibility
   — speed
   — timing
   — direction
   — regulation
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7. Oblique transmission
   Offspring inherit traits
   from non-parental adults.
   * Oblique = Diagonal
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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
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9. Model: Phenotypes
   Two phenotypes that affect fitness
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10. Model: Phenotypes
    Two phenotypes that affect fitness:
    phenotype A B
    frequency
    fitness
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11. Model: Transmission
    Offspring inherit phenotype
    from:
    — parent with probability
    — random non-parental adult
    with probability
    where is the vertical
    transmission rate.
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12. Model: Recurrence equation
    The frequency of phenotype
    in the next generation:
    and is the population mean
    fitness:
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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.
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16. Periodic environment
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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
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18. Periodic environment
    Result 2.
    If then fixation of either
    phenotype is unstable and a
    protected polymorphism exists.
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19. Periodic environment
    Result 3.
    For general and , a protected
    polymorphism exists if
    otherwise fixation of one
    phenotype is stable.
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20. Periodic environment
    We saw that when there is a protected
    polymorphism.
    We can find it for .
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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
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22. Periodic environment: A1B1
    If vertical transmission rate
    increases
    then stable frequency
    decreases
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23. Periodic environment: A1B1
    So, with vertical transmission,
    the frequency of decreases
    just before it is favored again.
    That is not good.
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24. Periodic environment: A1B1
    Indeed, the stable mean fitness
    decreases with the vertical
    transmission rate:
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25. Evolution of the transmission mode
    Can the transmission mode itself evolve?
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26. Modifier model
    We model competition
    between two modifier alleles:
    — with vertical transmission
    rate ,
    — with vertical transmission
    rate .
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27. Modifier model
    Pheno-
    genotype
    frequency
    fitness
    rate
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28. Modifier model
    Recurrence equation
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29. Modifier model
    Recurrence equation
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30. Stability analysis
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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?
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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:
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33. Periodic environment: A1B1
    — Fitness of and switch
    between and every
    generation.
    — Initial resident modifier with
    vertical transmission rate
    .
    — Invaders reduce
    transmission rate by .
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34. Reduction principle for vertical transmission
    When the environment changes every generation,
    evolution tends to reduce vertical transmission and
    increase oblique transmission.
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35. The plot thickens...
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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).
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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.
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38. Periodic environment: AkBk
    Also, for a wide range of
    environment periods.
    Some oblique transmission is
    still advantageous.
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39. Conclusions
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40. Polymorphism
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41. Polymorphism
    — Constant environment:
    polymorphism lasts longer
    with oblique transmission.
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42. Polymorphism
    — Constant environment:
    polymorphism lasts longer
    with oblique transmission.
    — Periodic environment:
    polymorphism is maintained
    in more environments with
    oblique transmission
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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
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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
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45. Phenotype switching
    — Switching rate evolves
    toward where is the
    period lengthμ.
    μ Doesn't work if is large or if selection not
    symmetric.
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46. Phenotype switching
    With oblique transmission:
    — Phenotype switch caused by
    oblique transmission rather
    then transmission errors.
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47. Acknowledgments
    Funding:
    - Stanford Center for Computational, Evolutionary
    and Human Genomics
    - The Morrison Institute for Population and Resources
    Studies, Stanford University
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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
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