Population genetics of rapid adaptation and the predictability of evolution


Richard Neher
Biozentrum, University of Basel


slides at neherlab.org/201704_UBasel_Zoology.html

Evolution of HIV


  • Chimp → human transmission ~1900 gave rise to HIV-1 group M
  • Diversified into subtypes that are ~20% different
  • evolves at a rate of about 0.1% per year
image: Sharp and Hahn, CSH Persp. Med.


Population sequencing to track all mutations above 1%

  • diverge at 0.1-1% per year
  • almost full genomes coverage in 10 patients
  • full data set at hiv.tuebingen.mpg.de
Zanini et al, eLife, 2015; antibody data from Richman et al, 2003

Diversity and hitchhiking

  • envelope changes fastest, enzymes lowest
  • identical rate of synonymous evolution
  • diversity saturates where evolution is fast
  • synonymous mutations stay at low frequency
Zanini et al, eLife, 2015

Frequent version of previously beneficial mutations

  • HIV escapes immune systems
  • most mutations are costly
  • humans selects for different mutations
  • compensation or reversion?
Zanini et al, eLife, 2015

Inference of fitness costs

  • mutation away from preferred state with rate $\mu$
  • selection against non-preferred state with strength $s$
  • variant frequency dynamics: $\frac{d x}{dt} = \mu -s x $
  • equilibrium frequency: $\bar{x} = \mu/s $
  • fitness cost: $s = \mu/\bar{x}$

Fitness landscape of HIV-1

Zanini et al, Virus Evolution, 2017

Selection on RNA structures and regulatory sites

Zanini et al, Virus Evolution, 2017

The distribution of fitness costs

Zanini et al, Virus Evolution, 2017

Fitness - diversity correlation

Zanini et al, Virus Evolution, 2017

Population genetics models

evolutionary processes ↔ trees ↔ genetic diversity

Neutral models and beyond

Neutral models
  • all individuals are identical → same offspring distribution
  • Kingman coalesence and diffusion theory are dual descriptions
  • everything is easy to calculate
  • perturbations like background selection can be included

What if selection is everywhere?

Clonal interference and traveling waves

  • extensive work on speed of adaptation, but this speed is not observable
  • genetic diversity is what we observe
  • depends on the properties of trees

What if selection is everywhere?
RN, Annual Reviews, 2013

Kingman coalescent

strong selection

Bolthausen-Sznitman Coalescent

RN, Hallatschek, PNAS, 2013; see also Brunet and Derrida, PRE, 2007

U-shaped polarized site frequency spectra



RN, Hallatschek, PNAS, 2013
Zanini et al, eLife, 2015

Bursts in a tree ↔ high fitness genotypes

Can we read fitness of a tree?




  • Influenza virus evolves to avoid human immunity
  • Vaccines need frequent updates

nextflu.org

nextstrain.org

Predicting evolution

Given the branching pattern,
  • can we predict fitness?
  • pick the closest relative of the future?
RN, Russell, Shraiman, eLife, 2014

Fitness inference from trees

$$P(\mathbf{x}|T) = \frac{1}{Z(T)} p_0(x_0) \prod_{i=0}^{n_{int}} g(x_{i_1}, t_{i_1}| x_i, t_i)g(x_{i_2}, t_{i_2}| x_i, t_i)$$
RN, Russell, Shraiman, eLife, 2014

Validate on simulation data

  • simulate evolution
  • sample sequences
  • reconstruct trees
  • infer fitness
  • predict ancestor of future
  • compare to truth
RN, Russell, Shraiman, eLife, 2014

Validation on simulated data

RN, Russell, Shraiman, eLife, 2014

Validation on simulated data

RN, Russell, Shraiman, eLife, 2014
nextflu.org

Prediction of the dominating H3N2 influenza strain

RN, Russell, Shraiman, eLife, 2014

HIV acknowledgments

  • Fabio Zanini
  • Jan Albert
  • Johanna Brodin
  • Christa Lanz
  • Göran Bratt
  • Lina Thebo
  • Vadim Puller

Influenza and Theory acknowledgments

  • Boris Shraiman
  • Colin Russell
  • Trevor Bedford
  • Oskar Hallatschek