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
   

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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)
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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
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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
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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?
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6. Vertical vs. non-
   vertical
   transmission
   Differences in
   » persistence
   » reversibility
   » speed
   » timing
   » direction
   » regulation
   Photo by William Bout on Unsplash 6/45
   

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7. Oblique transmission
   Offspring inherit traits from
   non-parental adults.
   *Oblique = Diagonal
   Photo by Samuel Zeller on Unsplash 7/45
   

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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:
   phenotype A B
   freq.
   fitness
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10. 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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11. Model
    Recurrence equation
    The frequency of phenotype in the next generation:
    Mean fitness:
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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
    

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15. Periodic environment
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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
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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
    

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18. Periodic environment
    Result 3. For general and , a protected
    polymorphism exists if
    otherwise fixation of one phenotype is stable.
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19. 19/45
    

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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
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21. A1B1
    If vertical transmission rate
    increases
    then stable frequency
    decreases
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22. A1B1
    So, with vertical
    transmission, the frequency
    of decreases just before
    it is favored again.
    That is not good.
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23. A1B1
    Indeed, the stable mean
    fitness decreases with the
    vertical transmission rate:
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24. Evolution of the transmission mode
    Can the transmission mode itself evolve?
    Photo by Matthew Henry on Unsplash 24/45
    

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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
    

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26. Modifier model
    Pheno-
    genotype
    frequency
    fitness
    rate
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27. Modifier model
    Recurrence equation
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28. Modifier model
    Recurrence equation
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29. Stability analysis
    Photo by Austin Neill on Unsplash 29/45
    

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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?
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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.
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32. Periodic environment: A1B1
    » and switch between
    and every generation.
    » Initial resident modifier:
    .
    » Invaders reduce rate by
    .
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33. Reduction principle
    Photo by Brendan Church on Unsplash 33/45
    

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34. Reduction principle for vertical transmission
    In the selection regime, evolution tends to
    reduce vertical transmission and increase oblique
    transmission.
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35. The plot thickens...
    Photo by Cindy Tang on Unsplash 35/45
    

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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
    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.
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39. Polymorphism
    Photo by Tatiana Lapina on Unsplash 39/45
    

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40. Polymorphism
    » Constant environment:
    polymorphism lasts longer
    with oblique transmission.
    Photo by Tatiana Lapina on Unsplash 39/45
    

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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
    

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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
    

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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
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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.
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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.
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46. Acknowledgments
    Funding: Stanford Center for Evolution and Human
    Genomics
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47. Thank you!
    Yoav Ram / Feldman Lab
    yoavram@stanford.edu
    @yoavram
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