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La sélec)on naturelle en évolu)on moléculaire

histoire, statut et perspec.ves

Guillaume Achaz

Atelier de Bioinforma4que, UMR 7205, Museum Na4onal d’Histoire Naturelle, Paris SMILE, UMR 7241, Collège de France, Paris

(2)

Molecular Evolu4on

Micro-evolu4on (popula4ons)

Polymorphisms (transient states) Popula4on gene4cs

Phylogeography

Macro-evolu4on (species)

Divergence (fixed differences) Specia4on process

Phylogeny Molecular component of evolu4on

(mostly gene4cs)

assess the evolu4on of and from molecules to

(3)

Molecular Evolution (sensu lato)

Historical Glimpse

Origin of Popula4on Gene4cs (20’s-30’s) The Modern Synthesis (40’s-60’s)

Neutral Theory (70’s-80’s) Contemporary View

Tools

Mathema4cal models

determinis4c (i.e. selec4on) stochas4c (i.e. gene4c dri^) Data

Intra-specific homologous loci

polymorphism ( >1 allele )

(4)

Popula4on Gene4cs

Selec)on

s : selec4on coefficient ρ : rate of selec4on events Muta)on

µ : muta4on rate Gene)c dri;

N : census popula4on size N

e

: effec4ve popula4on size Misc

Popula4on structure Demography

Time

(5)

A quick

historical perspective

(6)

Sir Ronald A. Fisher

(1890-1962)

(7)

Sewall Wright

(1889-1988)

(8)

1932

John B.S. Haldane

(1892-1964)

(9)

Adapta4on

Macromolecules are constantly adap4ng to their environment

Polymorphisms result from a selec.on-muta.on equilibrium

E(tpol)= 2. ln(N)/s

E(tmut)= 1/Nµ

Various pajern of selec4on are described (posi4ve, purifying, balancing, sexual, …)

(10)

The modern synthesis (40’s-60’s)

From wikipedia « Modern Synthesis » Promoted by

J. Huxley

Evolu.on: The modern synthesis, 1942

E. Mayr

G.L. Stebbins T. Dobzhansky E.B. Ford

B. Rensch

I. Schmalhausen G.G. Simpson (among others)

(11)

A paradigm shi^

The “reference” model

1859 - ~1970: Evolu4on is driven by adapta4on

1970 – today: Molecular evolu4on is driven by gene4c dri^

Kimura (1968) Evolu.onary Rate at the Molecular level Jukes and Kings (1969) Non Darwinian Evolu.on

An influen)al figure M Kimura

1950-1970 : major mathema4cal outbreaks 1970-1994 : causes of molecular evolu4on The Neutral Theory of Molecular Evolu4on (1983)

(12)

1983

Motoo Kimura

(1924-1994)

(13)

The Neutral Theory

All muta4ons are neutral

Polymorphisms result from a muta.on-driD equilibrium

freq

Time

E(tfix)=2Ν E(tpol)= 2 (1+ ln(N) )

E(tmut)= 1/Nµ

More polymorphisms are expected under neutrality, for a given muta4on rate

(14)

Deeper into the so-called

Standard Neutral Model

(15)

- dri;

ΔH ≈ - H/N

The muta4on-dri^ paradigm (H0)

At equilibrium, ΔH=0 => H* = 2Nµ

+ muta)on

ΔH = + 2µ

Molecular diversity

H

(16)

Standard Neutral Models

(17)

The Wright-Fisher model

1 genera4on = all individuals die and are replaced by a random sample

Wright-Fisher model

The fixation trajectories (forward perspective)

The coalescent trees (backward perspective)

time time

0 1 freq

0 1 freq

time time

(18)

The fixa4on process

E[tfix] = 2N E[tfix] = N

From a random 4me From the MRCA

Forward .me

Wright-Fisher model

The fixation trajectories (forward perspective)

The coalescent trees (backward perspective)

time time

0 1 freq

0 1 freq

time time

(19)

The coalescent process

E[tMRCA] = N E[tMRCA] = 2N

From the fixa4on 4me From a random 4me

Backward .me

Wright-Fisher model

The fixation trajectories (forward perspective)

The coalescent trees (backward perspective)

time time

0 1 freq

0 1 freq

time time

(20)

H0

=

standard neutral model

=

Kingman coalescent

The current paradigm

(21)

Kingman coalescent trees

f (T

i

) = λ

i

e

−λiT

λi = i(i 1) 2

Ti = 4me while there are exactly i lineages.

E[TMRCA] = 2 × (1− 1 n)

E[T2]=1

E[T3] =1 3

E[T4]=1 6

Time is counted in N genera)ons ; N -> ∞

Sample size n

(22)

Kingman trees

n[5]_m0 n[8]_m0 n[3]_m0 n[9]_m2 n[1]_m3 n[4]_m1 n[2]_m0 n[0]_m0 n[6]_m3 n[7]_m1 0.1

n[8]_m0 n[7]_m0 n[1]_m2 n[5]_m0 n[4]_m2 n[2]_m0 n[9]_m0 n[6]_m0 n[3]_m0 n[0]_m7 0.2

n[3]_m1 n[5]_m0 n[2]_m0 n[0]_m0 n[8]_m0 n[1]_m2 n[7]_m0 n[9]_m0 n[6]_m4 n[4]_m11 0.2 n[3]_m10 n[9]_m1 n[4]_m0 n[0]_m0 n[8]_m1 n[6]_m0 n[2]_m2 n[1]_m0 n[5]_m0 n[7]_m2 0.2

(23)

With recombina4on…

No single tree can be inferred but…

(24)

Genome-wide = expected diversity

Sample size n Today

(sampling)

Muta4ons

S : total # of muta4ons:

E[S] = 2 Nµ x (

Σ

1/i) (Waterson, 1975)

Other measures of diversity:

E[π] = 2 Nµ (Tajima, 1983) E[

ξ

1] = 2 Nµ (Fu and Li, 1993) E[

ξ

i] = 2 Nµ / i (Fu, 1995)

(25)

Mostly neutral with excep4ons

local genomic diversity

chromosome position

Baseline

Neutral loci Selected locus Neutral but

linked to selected locus

Genome-wide hunts for selec4ve sweep (Lactase, Immune system, etc.)

(26)

The case of

The Ne (des)illusion

(27)

Let’s Pause and Ponder

Can we evaluate the Neutral model?

Within species nucleo4de diversity Effec.ve popula4on size Muta4on frequencies

Distribu4on of muta4on frequencies

At the locus scale Large variance

Hard to reject H0

At the genome scale

Recombina4on = average many loci current approach

(28)

From model to real popula4ons

(29)

Assessing species diversity

(Lewon4n & Hubby, 1966)

Lynch and Connery, 2003 Lefler et al., 2012

Why diversity does not scale linearly with N?

(Lewon4n’s varia4on paradox, 1974)

(30)

Examples of Ne vs N

Species N (census size) Ne

H. sapiens 7 . 109 104

G. gorilla 105 103

D. melanogaster ? 106

C. elegans ? 105

A. thaliana ? 105

P. kergelensis ? 10

F. Psychrophilum 109/ml of cult. 106

E. coli 109/ml of cult. 108

HIV (within pa.ent) 1010 103

Why is Ne unrelated to current census size? Demography?

(31)

The case of the

Yoruba demography

(32)

Expected Site Frequency Spectrum (H0)

Under H0, full SFS is propor4onal to 1/i

n[3]_m10 n[9]_m1 n[4]_m0 n[0]_m0 n[8]_m1 n[6]_m0 n[2]_m2 n[1]_m0 n[5]_m0 n[7]_m20.2

(33)

0 0,05 0,1 0,15 0,2 0,25

0 20 40 60 80 100 120

0 0,05 0,1 0,15 0,2 0,25

0 20 40 60 80 100 120

Visual test for H0

(34)

SFS with demography

SFS with demography (e.g. exp growth or any scenario)

Constant Size

(35)

0 0,05 0,1 0,15 0,2 0,25

0 20 40 60 80 100 120

Demography with SFS

Adding demography greatly improves the fit

(36)

Human demography and migra4ons

One of the favorite “game” of human popula4on gene4cists…

Schlebusch et al., 2017 Na4onal Geographic, 2006

(37)

Do demography explains diversity?

Nice fit to data

Demographical inferences work approximately well provided the « correct Ne » is used.

Several scenarios are indistinguishable (Lapierre et al., 2017) Structure is completely neglected (Mazet et al. 2016)

What is N

e,

when accounting for demography?

Ne(0), the "current effective population size" would be…

33,000 ???

(38)

The case of the

Global species diversities

(ongoing work with F Freund, S Matuszewski, J Jensen, A Lambert)

(39)

0 0,05 0,1 0,15 0,2 0,25

0 50 100 150 200 250

0 0,2 0,4 0,6 0,8 1 1,2

0 50 100 150 200 250

Then came the U spectrum

Unfolded SFS normalized … and transformed

Departure from H0: an excess of low & high frequency alleles

(40)

Yoru ba

No simple demography can account for the U-shape!

… in all species

(41)

Mul4ple Merger => U-shaped spectra

(Gillespie 2000a, 2000b, …) Selec4on + Recombina4on

(reviewed in Neher 2013)

Very large popula4on size (gene4c dra^)

Never-ending adapta4on

Recurrent par)al sweep

Neutral variance in offspring numbers

Hedgecock and Pudovkin (2011). This group of organ- isms and genotyping data has been instrumental in the development of the statistical application of MMC mod- els. The aim is here to infer from SNP data the rate of sweepstake events, that is, how often they occur and which percentage of the population is affected. Likeli- hood methods have thus been developed for the Λ-coa- lescent (Birkner et al. 2011), beta-coalescent (Birkner &

Blath 2008; Steinr€ucken et al. 2013) or w-coalescent (Eldon & Wakeley 2006; Cenik & Wakeley 2010; Eldon 2011) to infer the parameters of interest based on the site frequency spectrum.

A population with strong density-dependent size reg- ulation between juveniles and adults is included in Schweinsberg (2003) or in Eldon and Wakeley w-coales- cent models. These are based on the classic sweepstake (A)

(B)

(C)

Fig. 3 Schematic representation of key life cycles and life history traits giving rise to multiple merger coalescent models. (A) Model of sweepstake reproduction common to many in marine organisms withN being the adult population size, which is also the carrying capacity of the population. Variance in offspring production is very large, and the production of eggs and juveniles largely exceeds the carrying capacity. Density-dependent regulation thus maintains the population at size N. (B) Demographic events drive random neutral evolution in crop pathogens over 3 years with seasonality (winter = W, summer = S). As the host plants grow during the year, the pathogen population grows. Harvest decreases dramatically the availability of hosts, as pathogen can only survive then on volunteer crops or wild relatives, generating regular periodic bottlenecks in pathogen density (y-axis). (C) Events in the parasite pop- ulation: neutral stochastic events during interhost transmission and selective events during intrahost dynamics. Host individuals are denoted by the green solid rectangles, while parasite particles are the small filled circles. Adaptation in the parasite population is continuous in maintaining the fittest individuals within each infected host (green dotted arrow), while recurrent bottlenecks occur during interhost transmission (black dotted arrows).

©2014 John Wiley & Sons Ltd

A P P L I C A T I O N O F M U L T I P L E M E R G E R C O A L E S C E N T 2645

(from Tellier and Lemaire, 2014)

few individuals have many offsprings

(42)

The gene4c dra^

(Recurrent selec4ve sweeps in very large popula4ons)

(Maynard Smith and Haigh 1974, …, Gillespie 2000a, 2000b, …)

At the neutral locus

Selec4on would be the cause of (low) gene4c diversity

(43)

From data to models, and vice-versa

Observa4ons

Sequences do change

Homologous loci show diversity The (unknown) Cause of Molecular Evolu4on

Neutral theory (standard neutral models, H

0

)

Adapta4on theory (mul4ple mergers coalescent) Demography

Popula4on structure

Ul4mately, assess the Biological Relevance of models

Kingman (H

0

) -- small stable popula4ons-- Mul4ple mergers, -- large popula4ons—

The rela)ve role of selec)on and dri; needs careful rethink

(44)

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