Raphaël Leblois

Champak Beeravolu

François Rousset

Simulation studies

Keywords: Algorithms Mut & Demo Models Software Demo Simulation studies Future Software Demo Simulation studies Future Conclusions Intro Models Software Demo Simulation studies Future Conclusions Models Software Demo Simulation studies Future Algorithms Mut & Demo Models Software Demo Simulation studies Future Availlable mutation models : KAM/PIM, SMM, GSM, ISM Inference Availlable mutation models : KAM/PIM, SMM, GSM, ISM Models Software Demo Simulation studies Future Conclusions Models Software Demo Simulation studies Future Conclusions

Allelic data (microsatellites), short DNA sequence data, SNPs AIM Assess validity and robustness of the method : Bias, RMSE, coverage properties of confidence intervals robustness to realistic but "uninteresting" mis-specifications → provide an "easy to use" software based on a validated method Leblois, Beeravolu & Rousset () Migraine SSMPG, June 2013

Overview

p(H k ) = {H k-1 } p(H k |H k-1 )p(H k-1 )
Expending the recursion over all ancestral histories compatible with the sample, leads to :

p(H k ) = {H k-1 } p(H k |H k-1 )p(H k-1 )
Expending the recursion over all ancestral histories compatible with the sample, leads to :

p(n) = p(H 0 ) = E p [p
p(H k ) = {H k-1 } p(H k |H k-1 )p(H k-1 )
Importance Sampling (IS) technic is used: Let Q(H k-1 ) be a proposal distribution such that

p(H k ) = {H k-1 } p(H k |H k-1 ) p(H k-1 ) Q(H k-1 ) Q(H k-1 ) = E Q p(H k |H k-1 ) p(H k-1 ) Q(H k-1 )
but need an efficient proposal distribution...

IS Coalescent-based algorithms used in Migraine

The ideal proposal:

Q(H k-1 ) = p(H k-1 |H k )
The ideal proposal is the backward transition probability p(H k-1 |H k ), then

p(H k |H k-1 ) p(H k-1 ) Q(H k-1 ) = p(H k ∩ H k-1 ) p(H k-1 |H k ) = p(H k )
and a single tree reconstruction allows exact likelihood computations (null variance).

p(H k-1 |H k ) is unknown, instead we use approximations p(H k-1 |H k ):

E Q p(H k-1 ) p(H k |H k-1 ) p(H k-1 |H k ) = p(H k )
but then many trees are necessary to get a good estimation of the likelihood.

IS Coalescent-based algorithms used in Migraine

The likelihood of the present configuration can then be written as a product of importance weights:

p(n) = p(H 0 ) = E p p(H 0 |H -1 ) p(H -1 |H 0 ) • • • p(H -m+1 |H -m ) p(H -m |H -m+1 ) p(H -m ) Wr = E p p(H → ) p(H ← )
Then we use Monte Carlo simulations on the absorbing backward Markov chain process describe above, using the IS transition probabilities, to infer the likelihood for a given parameter point Θ Stephens & Donnelly 2000 : much more efficient IS proposal for a single isolated population (1-100 trees).

L(Θ) = p Θ (n) ≈ 1 R R 1 r =1 W r Leblois,
deIorio & Griffiths 2004a, b : generalization of SD2000 proposal for structured population models (30-100 trees).

IS Coalescent-based algorithms used in Migraine

Additional approximate but fast algorithm : the PAC-likelihood Migraine also uses an heuristic approximation known as PAC-likelihood defined by Li andStephens 2003, Cornuet andBeaumont 2007 Based on π an approximation of π(j, α|n) the probability that, given an observed sample configuration n, the next sampled gene is of type j and from population α (same approx. than SD2000 & DIG2004)

No tree reconstruction, only based on the different type of gene observed in the sample

IS Coalescent-based algorithms used in Migraine

Additional approximate but fast algorithm : the PAC-likelihood Migraine also uses an heuristic approximation known as PAC-likelihood defined by Li andStephens 2003, Cornuet andBeaumont 2007 Based on π an approximation of π(j, α|n) (same approx. than SD2000 & DIG2004)

No tree reconstruction, Basic idea : each sampled genes is added one by one with associated probability π(j, α|n) to reconstruct the whole sample No tree reconstruction, Demographic models implemented in Migraine: Npop Two populations connected by migration (Eq.)

p(n) = p(n -1)π(j, α|n -1) ≈ p(n -1)π(j, α|n -1)
LPAC (θ) = 1 R R 1 r =1 M n i=2 n π(gene i |n i = {gene k } k<i ) R random
Four parameters:

N T , q 1 = N 1 /N 2 , m 1→2 and m 1→2
Availlable mutation models : KAM/PIM, SMM, GSM, ISM Inference of 4-5 scaled parameters:

[pGSm], θ = 2N T µ, q 1 , M 1 = 2N 1 m 1→2 , M 2 = 2N 2 m 2→1
More Populations?

Isolation by distance: Parameters

Deme size N, dispersal probability m, mutation probability µ distribution of dispersal distance: geometric decrease with distance, with scale parameter g .

special interest in the neighborhood size ∝ Dσ 2 where D is population density and σ 2 is second moment of dispersal distance (marginal 1D distribution in 2D model).

Likelihoods computed under the classical limit N → ∞, µ → 0 for given Nµ; and likewise m → 0 for given Nm ("diffusion limit")

Special interest in IBD models 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q q q qq q q q q q q q q q q q qq q q q q q q q q q q qq q q q 2 N µ = 0.08 KS: 0.212 c(0, 1) rel.Bias, rel.RMSE 0.011, 0.18 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qq q q qq q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qqqq q q q q q q q q q q q q q 2 N m = 20 KS: 0.995 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q q q q q q q q q qq q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q qqq q qq q q q q q q q q q q q q q q q qq q q qq q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q g = 0.25 KS: 0.776 c(0, 1) q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q qq q q q q q Nb = 44.444 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q q q qq q q q q q q q q q q q qq q q q q q q q q q q qq q q q 2 N µ = 0.08 KS: 0.212 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qq q q qq q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qqqq q q q q q q q q q q q q q 2 N m = 20 KS: 0.995 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q q q q q q q q q qq q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q qqq q qq q q q q q q q q q q q q q q q qq q q qq q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q g = 0.25 KS: 0.776 c(0, 1)

Bias, RMSE -0.023, 0.14 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q qq q q q q q Nb = 44.444 KS: 0.888 c(0, 1) rel.Bias, rel.RMSE -0.0038, 0.25 c(0, 1)

ECDF of p-values

First result: very good LRT distributions → validation of the method

Results under ideal conditions: validating the whole inference process and finding limits... 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q q q qq q q q q q q q q q q q qq q q q q q q q q q q qq q q q 2 N µ = 0.08 KS: 0. 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qq q q qq q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qqqq q q q q q q q q q q q q q 2 N m = 20 KS: 0.995 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q q q q q q q q q qq q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q qqq q qq q q q q q q q q q q q q q q q qq q q qq q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q g = 0.25 KS: 0.776 c(0, 1)

Bias, RMSE -0.023, 0.14 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q qq q q q q q Nb = 44. 1.0 q q q q q q q q q q q q q q q qq q q qq q q q q q q q q qq q q q qq q q q q q q q q q q q qq q q q q q q q q q q q q qq q q q qq q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q qq q q q q q q q q q qq q q q q qqq q q q qq q q q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q 2 N µ = 0.08 KS: 0.52 c(0, 1) rel.Bias, rel.RMSE 0.0091, 0.17 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q qq q q q q q q q q q qq q q q q q q q q q q q q qq q qqq q qq qq q q q q qq q q q q q q q q q q q q q qqq q 2 N m = 20 KS: <1e-12 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q qq qq q q q qq q q qqq q q qq q q q qq q q q q q q q q q q q q q q qq q q q q qq qqq q q q q qq qqq q qq g = 0.25 q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q q q qq q qq q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qqq q q q q q qq q q q q q q qq q q q Nb = 44.444 KS: 0.288 c(0, 1) rel.Bias, rel.RMSE -0.07, 0.2 c(0, 1)

ECDF of p-values

Something wrong ?

Results under ideal conditions: validating the whole inference process and finding limits... 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qqq q q q q q q q q q qq q q q q q q q q q q q qq q q q q q q q q q q qq q q q 2 N µ = 0.08 KS: 0. 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qq q q qq q qq q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q qq q q qq q q q q q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q qqqq q q q q q q q q q q q q q 2 N m = 20 KS: 0.995 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q qq q q q q q q q q q qq q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q qqq q qq q q q q q q q q q q q q q q q qq q q qq q q qq q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q g = 0.25 KS: 0.776 c(0, 1)

Bias, RMSE -0.023, 0.14 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q qq q q q q q Nb = 44. 1.0 q q q q q q q q q q q q q q q qq q q qq q q q q q q q q qq q q q qq q q q q q q q q q q q qq q q q q q q q q q q q q qq q q q qq q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q qq q q q q q q q q q qq q q q q qqq q q q qq q q q q q q q q qq q q q q q q q qq q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q 2 N µ = 0.08 KS: 0.52 c(0, 1) rel.Bias, rel.RMSE 0.0091, 0.17 1.0 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q qq q q q q q q q q q qq q q q q q q q q q q q q qq q qqq q qq qq q q q q qq q q q q q q q q q q q q q qqq q 2 N m = 20 KS: <1e-12 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q qq q q qq q q q q q q q q q qq qq q q q qq q q qqq q q qq q q q qq q q q q q q q q q q q q q q qq q q q q qq qqq q q q q qq qqq q qq g = 0.25 q q q q q q q q q q q q qqq q q q q q q q q q q q q q q q q q qq q qq q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q qqq q q q q q qq q q q q q q qq q q q Nb = 44.444 KS: 0.288 c(0, 1) rel.Bias, rel.RMSE -0.07, 0.2 c(0, 1)

ECDF of p-values

Diffusion approximation→ bias in Nm estimation increases with m

Results under ideal conditions: validating the whole inference process and finding limits.. Results under ideal conditions: another limit du to Nm, g covariance 3d main result: no information to infer Nm and g separately Performance in messy/realistic conditions q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q 200 500 1000 2000 5000 10000 50000

Regression PAC-likelihood Nb q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q ratio of RMSE: 0.62

Leblois, Beeravolu & Rousset () Migraine SSMPG, June 2013
ML inferences under isolation by distance: summary

Likelihood inferences perform in an ideal way in (restrictive) ideal conditions

Likelihood estimation still prohibitively long in large networks of populations. PAC-likelihood more feasible.

Additional imperfections (Likelihood and PAC-likelihood) due to the diffusion approximation when m is large. Nµ and Nm inferences most affected.

In practice, the parameter easiest to estimate is the neighborhood size Nb = 4πDσ 2 . q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q qq q q q qq q qq q q q qq qq q q q q qq q q q qq q q q q qq q q q q q q q qq q q q qq qq q q q qq q q q q q q q q q q q q qq q qq q q q q qq q q q q q q q q 2Nmu = 0.4 q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q qqq q qq q q q q q q q q q q q q q q qq q q q q q qqq qq q q q qq q qqq q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q qq q D = 1.25 q q q q q q q q qq qqq q q q q q qqq qq q qq q q qq q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q qq q q q q q qq q q qq q q q q q q q q q qq q q q q q qq q qq q qq qq q q q q q q q q q q q q q qq q q qq q 2Nancmu = 400 q qq qq q q q qq q q q q q q qq q q q q qq q q qqq qq q q q q q q q q q q q q q q qqq q qq qq q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q Nratio = 0.001 q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q qq q q q qq q qq q q q qq qq q q q q qq q q q qq q q q q qq q q q q q q q qq q q q qq qq q q q qq q q q q q q q q q q q q qq q qq q q q q qq q q q q q q q q 2Nmu = 0.4 q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q qqq q qq q q q q q q q q q q q q q q qq q q q q q qqq qq q q q qq q qqq q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q qq q D = 1.25 q q q q q q q q qq qqq q q q q q qqq qq q qq q q qq q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q qq q q q q q qq q q qq q q q q q q q q q qq q q q q q qq q qq q qq qq q q q q q q q q q q q q q qq q q qq q 2Nancmu = 400 q qq qq q q q qq q q q q q q qq q q q q qq q q qqq qq q q q q q q q q q q q q q q qqq q qq qq q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q Nratio = 0.001 1e-08 1e-02 1e+04 q q q q q q q q q q T= 10 generations TwoNmu 0 2 4 6 8 10 1e-10 1e-02 1e+06 q q q q q q q q q q T= 10 generations T 0 2 4 6 8 10 1e-08 1e-02 1e+04 q q q q q q q q q q T= 10 generations TwoNancmu 0 2 4 6 8 10 1e-08 1e-04 1e+00 q q q q q q q q q q T= 50 generations TwoNmu 0 2 4 6 8 10 0.05 0.20 0.50 q q q q q q q q q q T= 50 generations T 0 2 4 6 8 10 20 30 40 60 q q q q q q q q q q T= 50 generations TwoNancmu 0 2 4 6 8 10 1e-08 1e-04 1e+00 q q q q q q q q q q T= 100 generations TwoNmu 0 2 4 6 8 10 0.1 0.2 0.5 1.0 2.0 q q q q q q q q q q T= 100 generations T 0 2 4 6 8 10 20 40 60 q q q q q q q q q q T= 100 generations TwoNancmu 0 2 4 6 8 10 1e-06 1e-02 q q q q q q q q q q T= 500 generations TwoNmu 0 2 4 6 8 10 0.5 1.0 2.0 5.0 q q q q q q q q q q T= 500 generations T 0 2 4 6 8 10 5 10 50 200 q q q q q q q q q q T= 500 generations

Overview

TwoNancmu

Expected performances for very recent to very ancient change T varies from 10 to 3000 generations (D = T /2N from 0.025 to 7.5) 1e-08 1e-02 1e+04 q q q q q q q q q q T= 10 generations TwoNmu 0 2 4 6 8 10 1e-10 1e-02 1e+06 q q q q q q q q q q T= 10 generations T 0 2 4 6 8 10 1e-08 1e-02 1e+04 q q q q q q q q q q T= 10 generations TwoNancmu 0 2 4 6 8 10 1e-08 1e-04 1e+00 q q q q q q q q q q T= 50 generations TwoNmu 0 2 4 6 8 10 0.05 0.20 0.50 q q q q q q q q q q T= 50 generations T 0 2 4 6 8 10 20 30 40 60 q q q q q q q q q q T= 50 generations TwoNancmu 0 2 4 6 8 10 1e-08 1e-04 1e+00 q q q q q q q q q q T= 100 generations TwoNmu 0 2 4 6 8 10 0.1 0.2 0.5 1.0 2.0 q q q q q q q q q q T= 100 generations T 0 2 4 6 8 10 20 40 60 q q q q q q q q q q T= 100 generations TwoNancmu 0 2 4 6 8 10 1e-06 1e-02 q q q q q q q q q q T= 500 generations TwoNmu 0 2 4 6 8 10 0.5 1.0 2.0 5.0 q q q q q q q q q q T= 500 generations T 0 2 4 6 8 10 5 10 50 200 q q q q q q q q q q T= 500 generations TwoNancmu

  based algorithms used in Migraine n = {n αi }: sample configuration H = {H k ; k = 0, -1, . . . , -m}: ancestral history of the sample

  ,...,H -m ) p(H 0 |H 1 ) . . . p(H -m+1 |H -m )p(H -m ) = E p [p(H 0 |H 1 )...p(H -m+1 |p(H -m )] basedalgorithms used in Migraine n = {n αi }: sample configuration H = {H k ; k = 0, -1, . . . , -m}: ancestral history of the sample

  (H 0 |H 1 )...p(H -m+1 |p(H -m )] However: Forward transition prob. p(H k |H k-1 ) can not be directly used in a backward process Backward transition prob. p(H k-1 |H k ) are generaly unknown (except for parent independent mutations (PIM) in a single panmictic population) based algorithms used in Migraine n = {n αi }: sample configuration H = {H k ; k = 0, -1, . . . , -m}: ancestral history of the sample

  based algorithms used in Migraine Griffiths & Tavaré 1994, Nath & Griffiths 1996, Bahlo & Griffiths 2000 : "uniform" IS proposal, not very efficient (millions of trees).

  good agreement between genetic and demographic estimates → quite realistic model for fine scale population genetics Migrainevalidation procedure Check ideal performance under ideal conditions Check robustness under non-ideal conditions (various mis-specifications) Migrainevalidation procedure Check ideal performance under ideal conditions Ideal performance := valid confidence intervals ⇔ uniform distribution of p-values of (profile) LR tests of true simulation parameters

N: 40000 →

 40000 40; m: 0.00025 → 0.25; µ: 10 -6 → 10 -3

N: 40000 →

 40000 40; m: 0.00025 → 0.25; µ: 10 -6 → 10 -3

Leblois

  Demographic estimate D e σ 2 e =555 ind (D e =0.003 ind.m -2 , σ e =125 m) Watts et al. Mol. Ecol. 2007 Leblois, Beeravolu & Rousset () Migraine SSMPG, June 2013 A realistic setting Demographic estimate D e σ 2 e =555 ind (D e =0.003 ind.m -2 , σ e =125 m) Genetic regression estimate D e σ 2 e =753 ind (CI 319 -3162). Watts et al. Mol. Ecol. 2007 D e σ 2 e =555 ind (D e =0.003 ind.m -2 , σ e =125 m) Genetic regression estimate D e σ 2 e =753 ind (CI 319 -3162). Genetic PAC-likelihood estimate D e σ 2 e =1110 ind (CI 600 -3125)

  Simulations settings: 40 × 40 array, N = 50, m=0.5, g = 0.5, µ = 10 -4 200 individuals, 10 loci Performance in messy/realistic conditions Simulations settings: 40 × 40 array, N = 50, m=0.5, g = 0.5, µ = 10 -4 200 individuals, 10 loci Analysis settings: 20 × 20 grid of bins, (few CPU days per sample) Performance in messy/realistic conditions Simulations settings: 40 × 40 array, N = 50, m=0.5, g = 0.5, µ = 10 -4 200 individuals, 10 loci Analysis settings: 20 × 20 grid of bins, (few CPU days per sample)

  -specification of mutation processes Microsatellite markers show complex mutation processes Mutations do not fit SMM, indels of more than one repeat often occur OnePopVarSize : mis-specification of mutation processes Microsatellite markers show complex mutation processes Mutations do not fit SMM, indels of more than one repeat often occur Better mutation model = Generalized Stepwise Model (GSM) indels of X (geometric) repeats commonly found value in "natura" : pGSM ≈ 0.22 OnePopVarSize : mis-specification of mutation processes Solution : bottleneck model includes GSM (work with P. Pudlo) One more parameter (pGSM) ⇒ 4 param. to infer Longer runs are needed because of larger param. space

  Performance in messy/realistic conditions

	Intro Intro	Algorithms Algorithms	Mut & Demo Models Mut & Demo Models	Software Software	Demo Demo	Simulation studies Simulation studies	Future Future	Conclusions Conclusions
	Unknown mutation model Unknown dispersal distribution Cannot consider continuous populations (i.e. N=1) Leblois, Beeravolu & Rousset () Migraine Unknown mutation model Simulations of samples under SMM, analysis under KAM Unknown dispersal distribution Simulation of samples under "Sichel" model (Chesson & Lee, 2005) Analysis under the geometric dispersal model Cannot consider continuous populations (i.e. N=1) 434 000 434 500 435 000 435 500 436 000 436 500 437 000 98 800 99 000 99 200 99 400 99 600 99 800 100 000 100 200 A binning step is incorporated Leblois, Beeravolu & Rousset () Migraine SSMPG, June 2013 47 / 64 Performance in messy/realistic conditions Unknown mutation model Simulations of samples under SMM, analysis under KAM Unknown dispersal distribution Simulation of samples under "Sichel" model (Chesson & Lee, 2005) Analysis under the geometric dispersal model Cannot consider continuous populations (i.e. N=1) 434 000 434 500 435 000 435 500 436 000 436 500 437 000 98 800 99 000 99 200 99 400 99 600 99 800 100 000 100 200 A binning step is incorporated → Many things can go wrong, but neighborhood estimation is relatively SSMPG, June 2013 Performance in messy/realistic conditions robust

Leblois, Beeravolu & Rousset () Migraine SSMPG, June 2013

Previous method: Rousset's regression (1997)F ST -based method implemented in Genepop Leblois, Beeravolu & Rousset () Migraine SSMPG, June 2013

Performance in messy/realistic conditions Complex effects of binning on Nm and g estimation Bad: depend on the number of samples per bin → difficult to infer dispersal rates and shape Expected > 50% negative bias of Nµ estimates under the SMM (no bias under correctly specified mutation model)

Neighborhood estimation is more robust Gains in efficiency relative to the spatial regression method: ratios of RMSE from 0.27 to 0.62

OnePopVarSize : Bias, MSE, LRT on simulated data Same analyses as for IBD : (+ bottleneck detection rate) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q qq q q q qq q qq q q q qq qq q q q q qq q q q qq q q q q qq q q q q q q q qq q q q qq qq q q q qq q q q q q q q q q q q q qq q qq q q q q qq q q q q q q q q 2Nmu = 0.4 q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q qqq q qq q q q q q q q q q q q q q q qq q q q q q qqq qq q q q qq q qqq q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q qq q D = 1.25 q q q q q q q q qq qqq q q q q q qqq qq q qq q q qq q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q qq q q q q q qq q q qq q q q q q q q q q qq q q q q q qq q qq q qq qq q q q q q q q q q q q q q qq q q qq q 2Nancmu = 400 q qq qq q q q qq q q q q q q qq q q q q qq q q qqq qq q q q q q q q q q q q q q q qqq q qq qq q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q Nratio = 0.001 q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q qq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q qq q q q q 2Nmu = 0.4 qq q q qq qq q q q q q qq q q qq q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q q q q qq q q q q q qq q q q q qqq q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q D = 0.25 q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q qq q qq q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q 2Nancmu = 40 q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q q q qq q q q q q q q q q q q q q q q q q qq q q q q qq q qq q q q q qq q q q q qq q q q q q q q q qq q q qq q q q q q qq q q q q q q q q q q q q q q q q q q q qq q q q qq q q q qq q q q qqq Nratio = 0.01 q q q q q q q q q q q q q q q q q q q q q q q q qq q qq q q q q q qq q q q qq q qq q q q qq qq q q q q qq q q q qq q q q q qq q q q q q q q qq q q q qq qq q q q qq q q q q q q q q q q q q qq q qq q q q q qq q q q q q q q q 2Nmu = 0.4 q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q q q q qqq q qq q q q q q q q q q q q q q q qq q q q q q qqq qq q q q qq q qqq q q q q q q q qq q q q q q q q q q q qq q q q q q q q q q q q q q q qq q q q q qq q D = 1.25 q q q q q q q q qq qqq q q q q q qqq qq q qq q q qq q q q q q q q q q q q q q qq q q qq q q q q q q q q q q q q qq q q q q q qq q q qq q q q q q q q q q qq q q q q q qq q qq q qq qq q q q q q q q q q q q q q qq q q qq q 2Nancmu = 400 q qq qq q q q qq q q q q q q qq q q q q qq q q qqq qq q q q q q q q q q q q q q q qqq q qq qq q q q q q q q q q q q q q q qq q q q q q q q qq q q q q q q q q q qq q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q Nratio = 0.001 OnePopVarSize : conclusions and perspectives


domain: sdv info

text:
Edith Pajot
email: edith.pajot@jouy.inra.fr

E Pajot-Augy

BIOINSPIRED NOSE DEVICES

HAL is

Our work on bioinspired nose devices was carried out in the framework of 2 successive European projects : SPOT-NOSED (Single PrOTein NanObioSEnsor griD array) 2003-2006 and BOND (Bioelectronic Olfactory Neuron Device, http://bondproject.org/) 2009-2012, aimed at using ORs carried by nanoscale liposomes as sensing elements of an electrochemical array, for specifically detecting target odorants from complex odorant mixtures. These projects have potential applications in medical diagnosis, but also in agroalimentary or cosmetics quality control, security, and environment.

In the natural mammalian olfactory system, more than a thousand ORs exhibit various levels of specificity and sensitivity to odorants. For bioinspired nose devices dedicated to detecting a target VOC, the relevant ORs to monitor this target odorant first have to be identified by single-cell RT-PCR on neurons exhibiting a calcic response to this odorant. In addition, we developed a dedicated procedure that (i) automates homology modeling of mammalian ORs based on the available 3D structures of G protein-coupled receptors and (ii) performs the docking of odorants on these models and scores the complexes. Since ORs exhibit low sequence similarities with other GPCRs, a fold recognition technique is used to obtain a robust initial alignment. An analysis of the resulting in silico complexes for a previously characterized human OR suggests interesting results as to the docking position of antagonists or agonists relative to the putative binding pocket (http://genome.jouy.inra.fr/GPCRautomodel) [1]. Visualizing the complexes allows the identification of key functional residues involved in the process of ligand recognition, which can help refinining the choice of the ORs best suited to bind a given odorant.

The selected ORs are then tagged and heterologously expressed in S. cerevisiae. ORs functionality can be tested in yeast membrane fraction by Bioluminescence Resonance Energy Transfer [START_REF] Sanz | Olfactory Receptors : Methods and Protocols[END_REF]. Sonication of the membrane fraction yields natural nanoscale vesicles carrying the ORs on their lipid bilayer. The deposition of these nanovesicles onto substrates is monitored by Atomic Force Microscopy : nanovesicles flatten without rupturing on glass substrates, with reproducibly high substrate coverages. Surface chemistry modification of gold substrates indicates a higher affinity of natural nanovesicles for acid modified surfaces. Nanosomes grafting is performed most efficiently onto surfaces functionalized by activated carboxylic thiol SAMs [START_REF] Calò | [END_REF].

The active part of the bioelectronic sensor consists of a silicon nanoelectrode with an electrochemical cell and a dedicated electronic chip. To provide the sensor with high sensitivity, gold nanoparticles can be generated on the gold surface by electrochemical chronoamperometry to favor nucleation. Gold nanoparticles induce a surface area increase, thus immobilization of a larger amount of nanosomes, measured by Atomic Force Microscopy and by a decrease in charge transfer resistance in Electrochemical Impedance Spectroscopy. The tagged receptors can be specifically immobilized on surfaces carrying antibodies against the tag, as monitored by electrochemical measurements.

Nanoelectrodes are fabricated using e-beam lithography, with sizes in adequation with the nanosomes. Adequate nanoelectronics for low-noise and wide-bandwidth measurements is designed to be directly connected to the nanoelectrodes. Significant changes in Electrochemical Impedancemetric Spectroscopy measurements are monitored along the process of electrodes functionalization, nanosomes grafting, and finally upon ORs conformational change induced by odorant binding.

Using this whole concept, prototypes exhibiting very low detection thresholds comparable to the animal nose were conceived [4].