Modeling the unobservable developmental stability using a Bayesian

Modeling the unobservable developmental stability using a Bayesian latent variable model Stefan van Dongen Dept. Biology, University of Antwerp

OUTLINE • Introduce biological problem – developmental stability • Develop statistical model • Show some simulation results • Interesting results in humans – keep paying attention this is important

What is developmental stability? • We develop from 1 cell to what we are now • During development mistakes occur due to random noise (DN) – Fluctuations in concentrations – Somatic mutations – Death of cells • There are mechanisms that correct for these mistakes: DEVELOPMENTAL STABILITY

What is developmental stability? • Our genotype and environment in which we live determine our size and shape – unknown in most cases • BUT there is some degree of stochasticity • PROBLEM: how to estimate this stochastic contribution which has two components (noise and stability) • SOLUTION: Look at symmetric traits

How to estimate developmental stability? • Left and right side develop often under exactly the same environmental conditions (but e. g. handedness) and obviously share the same genotype • In the absence of noise they should develop to the same size or shape • Noise will cause asymmetry • Stability will counteract this effect

How to estimate developmental stability? Measure asymmetry • Asymmetry estimates the joint action of noise and stability

The picture is not so clear Gynandromorphs NO STRESS Directional asymmetry or EFFECT antisymmetry: adaptive and genetically determined

The picture is not so clear Under severe stress only Binary Phenodeviants & deformations Early action of stress Continuous scale Subtle forms of asymmetry

Why study developmental stability? Charles Darwin EVOLUTION CONSERVATION BIOLOGY FITNESS (reproductive success, survival, …. ) Difficult to measure in field May be related to stability High stability => sufficient energy to achieve high fitness

Why study developmental stability? Charles Darwin INDIVIDUAL LEVEL EVOLUTION CONSERVATION BIOLOGY FITNESS (reproductive success, survival, …. ) Difficult to measure in field May be related to stability High stability => sufficient energy to achieve high fitness

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Asymmetries are usually small: take bias due to measurement error into account FLUCTUATING ASYMMETRY muind[i, j]=interc[i]+side[i, j] unb_FA[i] where: interc[i]~N(0, 2) and: unb_FA[i]~N(0, 2 FA[i]) expected[i, j]=intercept+slope side[i, j] DIRECTIONAL ASYMMETRY measure[i, j]~N(0, 2 ME) ERROR

The association between asymmetry and stability unb_FA[i]~N(0, DI[i]) Assume DN to be constant DI[i]=DN (1 -DS[i]) DS[i]~beta( 1, 2)

The association between asymmetry and stability N=500, 2500 and 5000 DN constant, DS beta-distr. ‘good’ estimate of DS overestimate of DN ‘worse’ estimate of DS ‘good’ estimate of DN ‘failure’ to estimate bimodal pattern of DS

The association between asymmetry and stability

The association between asymmetry and fitness[i]=interfit+slopefit DS[i]

Further developments • Multiple-trait analyses • robustness against deviations of model assumptions (normality vs. log-normality) • Include variation in DN (stochastic or constant)

Interesting results in humans • • • Symmetric persons have higher IQ Criminals have higher asymmetry Symmetric males and females are more attractive Symmetric males have more sexual partners in their life Symmetric males are ‘better lovers’ Female breast asymmetry decreases around period of ovulation • Females are more selective for symmetric males around this ovulation period • …. .

One case study