Evolution of Non-Vertical Inheritance in Changing Environments

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

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

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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 8/46

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Model: Phenotypes Two phenotypes that aﬀect ﬁtness 9/46

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

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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. 11/46

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

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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. 14/46

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Periodic environment 16/46

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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 17/46

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

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

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

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

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

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

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Modiﬁer model Pheno- genotype frequency ﬁtness rate 27/46

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Modiﬁer model Recurrence equation 28/46

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Modiﬁer model Recurrence equation 29/46

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Stability analysis 30/46

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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? 31/46

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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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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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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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The plot thickens... 35/46

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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). 36/46

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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. 37/46

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

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Conclusions 39/46

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Polymorphism 40/46

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

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

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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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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