Vertical & Oblique Transmission under Fluctuating Selection

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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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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

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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

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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

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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

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

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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

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Model Phenotypes Two phenotypes that affect ﬁtness: phenotype A B freq. ﬁtness 9/45

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Model Transmission Offspring inherit phenotype from: » parent with probability » random non-parental adult with probability where is the vertical transmission rate. 10/45

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Model Recurrence equation The frequency of phenotype in the next generation: Mean ﬁtness: 11/45

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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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Periodic environment 15/45

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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

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

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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

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A1B1 If vertical transmission rate increases then stable frequency decreases 21/45

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A1B1 So, with vertical transmission, the frequency of decreases just before it is favored again. That is not good. 22/45

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A1B1 Indeed, the stable mean ﬁtness decreases with the vertical transmission rate: 23/45

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Evolution of the transmission mode Can the transmission mode itself evolve? Photo by Matthew Henry on Unsplash 24/45

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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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Modiﬁer model Pheno- genotype frequency ﬁtness rate 26/45

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Modiﬁer model Recurrence equation 27/45

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Modiﬁer model Recurrence equation 28/45

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Stability analysis Photo by Austin Neill on Unsplash 29/45

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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

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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

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Periodic environment: A1B1 » and switch between and every generation. » Initial resident modiﬁer: . » Invaders reduce rate by . 32/45

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Reduction principle Photo by Brendan Church on Unsplash 33/45

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Reduction principle for vertical transmission In the selection regime, evolution tends to reduce vertical transmission and increase oblique transmission. 34/45

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The plot thickens... Photo by Cindy Tang on Unsplash 35/45

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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

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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

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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

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Polymorphism Photo by Tatiana Lapina on Unsplash 39/45

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

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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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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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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

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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

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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