• Alleles affect multiple traits

• Falconer (1952): G-by-E is a special case of pleiotropy

Allele increases one trait, but decreases the other

Allele 2 increases both traits

• Effect in context A, no effect in context B
• Also called conditional neutrality

Which of these mechanisms contibute to adaptation?

• Pleiotropy "types" are special cases
• Quantitative questions:
  • How costly is the wrong allele?
  • How difficult would it be to compensate?

Null-hypothesis tests:

• exclude weak but important effects
• throw away quantitative information
• underestimate pleiotropy

Null-hypothesis tests:

• excludes weak, but important effects
• throw away quantitative information
• underestimate pleiotropy

It would be better to:

• Use all the data
• Quantify rather than classify
• Estimate effect sizes and their uncertainty

\[ \tau = \frac{\arcsin (\sin(2 \theta))}{\arcsin(1)} \]

• Non-parametric bootstrap of effects in each context
• Distribution of \(\tau\) and vector lengths

• Average over bootstraps in downstream analyses.

• Does not depend on the direction of the effect!

• 1 = positive pleiotropy
• 0 = non-pleiotropy (conditional neutrality)
• -1 = negative pleiotropy

• 1 = positive pleiotropy
• 0 = non-pleiotropy (conditional neutrality)
• -1 = negative pleiotropy
• (matches direction of genetic correlation)

• 1 = positive pleiotropy
• 0 = non-pleiotropy (conditional neutrality)
• -1 = negative pleiotropy
• (matches direction of genetic correlation)
• And everything in between!

• Data from 4 reciprocal transplant experiments:
  • Arabidopsis thaliana (Ågren et al. 2013)
  • Avena barbata (Latta et al. 2009)
  • Boechera stricta (Anderson et al. 2014)
  • Hordeum spontaneum (Verhoeven et al. 2004)
• F₂-derived linkage-mapping populations
• Genotyped at 100-350 markers
• Log relative fitness of each marker

• Histrogram of \(\tau\) across all markers

• Trade-offs across most of chromosomes 3, 4, 5
• More extensive than were detected through mapping.

• Histograms shifted right

• Dispersal limits spread?
• Genetic load?

• Anderson et al. (2013), "Genetic trade‐offs and conditional neutrality contribute to local adaptation", Mol. Ecol.

• Pleiotropy is a continuum
• Statistical tests underestimate pleiotropy

• Pleiotropy is a continuum

• Statistical tests underestimate pleiotropy

• Using \(\tau\) allows you to quantify pleiotropic mechanisms
• Estimate effect and quantify uncertainty

• Does not depend on the direction of the effect

• Applicable whenever you can quantify 'effects':
  • Phenotypes of individuals/strains/lines
  • Allelic effects
  • Wherever you can measure a 'reaction norm'

• Applicable whenever you can quantify pairs of 'effects':
  • Phenotypes of individuals/strains/sexes
  • Allelic effects
  • Wherever you can measure a 'reaction norm'
• True for pleiotropy and GxE

• Applicable whenever you can estimate a reaction norm:
  • Phenotypes of individuals/strains/lines
  • Allelic effects
  • Wherever you can measure a 'reaction norm'
• True for pleiotropy and GxE
  
• R package sintillate available:
  • https://github.com/ellisztamas/sintillate
  • Should scale to large datasets

• Correlations in large phenotype databases
• Extensible to multivariate pleiotropy, with caution
• Quantify epistasis and dominance

• A. thaliana project:
  • Jon Ågren (Uppsala)
  • Doug Schemske (MSU)
  • Chris Oakley (MSU, Purdue University)
  • Many helpers, especially Mattias Vass, Linus Vikström, Jenny Glans
• And Magnus Nordborg and the GMI

• Fitness components in A. thaliana (Ågren et al. 2013)
  • Reciprocal transplants in Italy and Sweden
  • Recombinant inbred lines + local parents
  • Line mean survival and fecundity
  • 3 years

• RIL = recombinant inbred line, selfed from an F₂ cross

• RIL = recombinant inbred line, selfed from an F₂ cross

• Link parents, RIL phenotypes, and marker effects.

• Correlations due to pleiotropy
  • Same genes affect both traits
  • \(\tau > 0\)
• Or:
  • Different genes affect each trait
  • \(\tau \sim 0\)

• Log relative fitness of the Swedish allele at each marker:
  • Univariate
  • Includes effects of linked loci

• Observed (bars) with bootstrap means (points)

• \(\tau \sim 0 \rightarrow\) non-pleiotropy

• Distribution shifted right \(\rightarrow\) positive pleiotropy

• \(\tau\) between 0 and 1.

• Observed \(\tau\) for parental phenotypes ± 95% confidence intervals

• Grey lines = 95% confidence intervals from 1000 bootstraps ## Rescaling vector norm

• Scale: relative fitness