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Evolution of Non-Vertical Inheritance in Changing Environments

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.

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

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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
    2/46

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  3. The Modern Synthesis
    Genetic inheritance as the
    mode of transmission of traits
    between generations.
    Inherently vertical: parent to
    offspring.
    3/46

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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
    4/46

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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)
    5/46

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  6. Vertical vs. non-vertical transmission
    Differences in
    — persistence
    — reversibility
    — speed
    — timing
    — direction
    — regulation
    6/46

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  7. Oblique transmission
    Offspring inherit traits
    from non-parental adults.
    * Oblique = Diagonal
    7/46

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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
    8/46

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  9. Model: Phenotypes
    Two phenotypes that affect fitness
    9/46

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  10. Model: Phenotypes
    Two phenotypes that affect fitness:
    phenotype A B
    frequency
    fitness
    10/46

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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.
    11/46

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  12. Model: Recurrence equation
    The frequency of phenotype
    in the next generation:
    and is the population mean
    fitness:
    12/46

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  13. 13/46

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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.
    14/46

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  15. 15/46

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  16. Periodic environment
    16/46

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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
    17/46

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  18. Periodic environment
    Result 2.
    If then fixation of either
    phenotype is unstable and a
    protected polymorphism exists.
    18/46

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  19. Periodic environment
    Result 3.
    For general and , a protected
    polymorphism exists if
    otherwise fixation of one
    phenotype is stable.
    19/46

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  20. Periodic environment
    We saw that when there is a protected
    polymorphism.
    We can find it for .
    20/46

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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
    21/46

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  22. Periodic environment: A1B1
    If vertical transmission rate
    increases
    then stable frequency
    decreases
    22/46

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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.
    23/46

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  24. Periodic environment: A1B1
    Indeed, the stable mean fitness
    decreases with the vertical
    transmission rate:
    24/46

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  25. Evolution of the transmission mode
    Can the transmission mode itself evolve?
    25/46

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  26. Modifier model
    We model competition
    between two modifier alleles:
    — with vertical transmission
    rate ,
    — with vertical transmission
    rate .
    26/46

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  27. Modifier model
    Pheno-
    genotype
    frequency
    fitness
    rate
    27/46

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  28. Modifier model
    Recurrence equation
    28/46

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  29. Modifier model
    Recurrence equation
    29/46

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  30. Stability analysis
    30/46

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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?
    31/46

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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:
    32/46

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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 .
    33/46

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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.
    34/46

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  35. The plot thickens...
    35/46

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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).
    36/46

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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.
    37/46

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  38. Periodic environment: AkBk
    Also, for a wide range of
    environment periods.
    Some oblique transmission is
    still advantageous.
    38/46

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  39. Conclusions
    39/46

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  40. Polymorphism
    40/46

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

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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
    40/46

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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
    41/46

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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
    42/46

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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.
    43/46

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  46. Phenotype switching
    With oblique transmission:
    — Phenotype switch caused by
    oblique transmission rather
    then transmission errors.
    44/46

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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
    45/46

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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:
    [email protected]
    www.yoavram.com
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