Mind the gaps: Theoretical and empirical aspects of plant ecology and population genetics S. peruvianum S. chilense 08.03.2013 Aurélien Tellier Populationsgenetik.

Mind the gaps: Theoretical and empirical Mind the gaps: Theoretical and empirical

aspects of plant ecology and population aspects of plant ecology and population

geneticsgenetics

S. peruvianum

S. chilense

08.03.2013

Aurélien TellierPopulationsgenetik

TUM Weihenstephan, Freising

Research interests:Research interests:Ecology and genetics/genomicsEcology and genetics/genomics

How do plants adapt to their environment?How do plants adapt to their environment?

Major aims Determining the genetic processes involved in adaptation How genetic variation is shaped by evolutionary/ecological

processes

Ecology

ecological time scale

Influence of environmentObservable variation in

phenotypes

Genomics

evolutionary time scale

Apparition and fixation of mutations

Random processes (drift, migration)

Research interests: Two systemsResearch interests: Two systems

Plant-parasite coevolution

Seed banks and seed dormancy

2011

Population genetics: 4 evolutionary forcesPopulation genetics: 4 evolutionary forces

random genomic processes(mutation, duplication, recombination, gene

conversion)

naturalnatural

selectiselectionon

random demographic

process (drift)

random spatialprocess

(migration)

molecular diversitymolecular diversity

Investigate the laws governing the genetic structure of populationsR.A. Fisher, S. Wright, J.B.S. Haldane, …, M. Kimura, T. Ohta, …, B. Charlesworth, J. Maynard-Smith

Coalescent theory is a tool to infer past evolution from sequence data

pathogen

plant cell

pathogen

effectors

direct recognition indirect recognitionplant cell

R proteins

modification

‘guardee’(pathogen target)

‘guard’

specific defense response (HR)

signalling

signalling

basal defense response

unspecific immunity specific immunity

Overview of the immune system in plantsOverview of the immune system in plants

The Gene-For-Gene relationshipThe Gene-For-Gene relationship

Plant

Resistant Susceptible

Fungus

Avirulent

Virulent

Natural selection in coevolution (1)Natural selection in coevolution (1)

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4Frequency of resistance

Frequency

of virulence

0.0

0.2

0.4

0.6

0.8

1.0


Frequency

of virulence

Resistance increases plantfitness in present of pathogen

Virulence increases pathogenfitness on resistant plants

Brown and Tellier, Annual Review Phytopathology, 2011

0.0

0.2

0.4

0.6

0.8

1.0


Frequency

of virulence

Natural selection in coevolution (2)Natural selection in coevolution (2)

0.0

0.2

0.4

0.6

0.8

1.0


Frequency

of virulence

0.0

0.2

0.4

0.6

0.8

1.0


Frequency

of virulence

Cost of resistanceto plant fitness

Cost of virulence to pathogen fitness

Brown and Tellier, Annual Review Phytopathology, 2011

Equilibrium points : instabilityEquilibrium points : instability

Frequency of resistance

1

100

Freq. ofvirulence Unstable equilibrium

Stable equilibria

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,00 0,20 0,40 0,60 0,80

RES frequency

av

r frequency


1

100

Freq. ofvirulence

Stable equilibria

Unstable equilibrium

Equilibrium points : instabilityEquilibrium points : instability

Equilibrium points : stabilityEquilibrium points : stability


1

100

Freq. ofvirulence Stable equilibrium

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,00 0,05 0,10 0,15 0,20 0,25 0,30

RES frequency

av

r frequency


1

100

Freq. ofvirulence Stable equilibrium

Equilibrium points : stabilityEquilibrium points : stability

Why the simple model is unstable (1)Why the simple model is unstable (1)

Taking log of ratio, ρ = log(R/r) … maths easier!

The change in R depends on A but not on R itself

=R( r ) ′ R

r.(1−u)(1−s+sA)

1−ss = cost of diseaseu = cost of resistance

log ρ′ − log ρ = Δρ log ρ′ − log ρ = log(1−u) + log(1−s−sA) − log(1−s)

Taking log of ratio, α = log(A/a)log α′ − log α = Δα log ρ′ − log ρ = log(1−cR) − log(1−b)

The change in A depends on R but not on A itself

=A( a ) ′ A

a. 1−cR

1−bc = cost of AVR on RES

plantb = cost of virulence

Hence dΔρ/dR + dΔα/dA = 0 and stability is impossible

Why the simple model is unstable (1)Why the simple model is unstable (1)

Requirements for stable polymorphismRequirements for stable polymorphism

Tellier and Brown, Proc. Roy. Soc. B, 2007

/ /

.// /

/

/

/R r

RA

R r R r

A aA

R r

A aa

Ra

A

A

The eigenvalues 1,2 = i of the Jacobian Matrix should be in a circle centered on (-1,0) in the complex plane

Jacobian Matrix

(-1,0)

-

/ /R r A a

R A

<0 the sum of the diagonal coefficients of

the Jacobian matrix

Requirements for stable polymorphismRequirements for stable polymorphism

Avirulence selects for increased resistance

Resistance selects for increased virulence

= indirect frequency-dependent selection

→ graph of alleles frequencies (R,a) spirals

Selection for RES weaker as RES more common

Or selection for avr weaker as avr more common

= direct frequency-dependent selection

→ graph spirals to a stable equilibrium point

Tellier and Brown, Proc. Roy. Soc. B, 2007

Boom and Bust cycle: stable and unstable Boom and Bust cycle: stable and unstable dynamicsdynamics

Brown and Tellier Ann Rev Phytopat 2011

Factors promoting stable dynamics:

Biological factors (life history traits):

Polycylicity = several pathogen generations/host generation (Tellier

and Brown, Proc Roy Soc B, 2007)

Perenniality or seed banks in host (Tellier and Brown, Am Nat, 2009)

Genetic factors: Epistasis among R-genes and virulence genes (Tellier and

Brown, Genetics, 2007)

Ecological factors: Environmental variability in space (Laine and Tellier

Oikos 2008; Tellier and Brown BMC Evol Biol 2011)

Stable and unstable dynamicsStable and unstable dynamics


Biological factors (life history traits): Polycylicity, perenniality or seed

banks

Genetic factors: Epistasis

Ecological factors: Environmental variability in space (see work by Laine,

Thrall, Burdon,…)

Expect to find often stable dynamics in natural populations!

(and conversely more unstable dynamics in agro-systems)

Why is it important to know the Why is it important to know the stability/unstability?stability/unstability?

hostpathogen

Stahl et al. Nature 1999, Holub Nat Rev Genet 2001, Woolhouse et al. Nat Rev Genet 2002

balancing selection (trench warfare)ndFDS selection model

positive selection (arms race)selective sweeps model


„„Naive“ Predictions on genomic signaturesNaive“ Predictions on genomic signatures

Ebert Curr Opin Microbiol 2008

hostpathogen

ndFDS selection modelselective sweeps

Predictions on genomic signaturesPredictions on genomic signatures

hostpathogen


Short tree => low genetic diversity

Star like genealogy => excess of singleton SNPs

Negative value of Tajima’s D (<0)

Long tree => high genetic diversity

Long internal branches => excess of intermediate frequency SNPs

Positive value of Tajima’s D (>0)

Sample n = 8

One type present(AVR or avr RES or res)

AVR / RES avr / res

Genomic signature of balancing selectionGenomic signature of balancing selection

Neutral mutations segregating next to the selected SNP

no intra-locus recombination(Charlesworth et al. Genet Res 1997 )

AVR or RES

avr or res

Causal SNP

neutral SNPs

Genomic signature of selective sweepsGenomic signature of selective sweeps

RES

Causal SNP

neutral SNPs

Neutral mutations segregating next to the selected SNP

no intra-locus recombination(Maynard-Smith and Haig Genet Res 1974)

Genome scans to find genes under Genome scans to find genes under coevolutioncoevolution

hostpathogen


Based on statistics of genealogies: Tajima’s D, haplotypes…

However, few genes show these typical However, few genes show these typical signatures…signatures…

Bakker et al. Plant Cell 2006; Bakker et al. Genetics 2008

Cao et al. Nat Genet 2011; Guo et al. Plant Physiol 2011

Ex: RPM1 in Arabidopsis thaliana (Stahl et al. Nature 1999, Bergelson et al. Science 2001)

Pto in Solanum Peruvianum (Rose et al. Genetics 2007)

A major draw back of current theory is that it is based on deterministic models and short-term ecological models

Questions:

1) What is the role of genetic drift for stability or allele fixation?

2) In finite populations, can stable dynamics lead to fixation of alleles? Under which conditions?

3) Are dynamics in the arms race model slower than in the trench warfare model?

4) Expectations for genomic signatures under GFG models?

Why so little genomic evidence for Why so little genomic evidence for coevolution?coevolution?

Exemple of a stable model in finite population (N = 3000)

How?

We build a model of host and parasite with finite size with genetic drift (NH = NP) + mutation between AVR ↔ avr and RES ↔ res

Assess population genetics statistics: time to fixation; how often are alleles close to fixation (freq<0.05 or freq>0.95); number of cycles and amplitude, periods of cycles

For 10,000 generations and various parameter combinations

Finite size modelFinite size model

UNSTABLE dynamicsUNSTABLE dynamics

Fixed mutation rate μ = 10-5

Increasing mutational input (Nμ)


Number of coevolutionary cycles

Fast cyclin

g

Slow cyclin

g


Fixed population mutation rate θ = 4Nμ = 0.01


Result 1:

genetic drift has small effect on speed of coevolutionary cycles

Mutational input determines the speed of cycles

Number of coevolutionary cycles Fast

cycling

Slow cyclin

g




Result 2:

Drift affects the time of allele fixationResistance can only be fixed in plant populations of small size

Percentage of time that allele RES is fixed or near fixation Often

fixed

Never fixed

STABLE dynamicsSTABLE dynamics


Result 3:Genetic drift alone is responsible for driving stable cycles to fixation

More pronounced for small population sizes

Percentage of time of susceptible allele res fixed or near fixation

Never fixed =

polymorphism

Often fixed

= sweeps

2) In finite populations, can stable dynamics lead to fixation of alleles? What conditions?

STABLE dynamicsSTABLE dynamics

Result 4:

The location of the equilibrium point determines the fixation probability (=> importance of costs)

BUT amplitude and period of cycles affect weakly fixation and speed of coevolution

2) What conditions for fixation of alleles in stable model?

STABLE vs UNSTABLE dynamicsSTABLE vs UNSTABLE dynamics

Result 5:

For low values of costs, the speed of coevolution is similar between dynamics

(in contradiction to Woolhouse et al., Ebert)

3) Are dynamics in the arms race model slower than in the trench warfare model?

Number of coevolutionary cycles

Fast cycling

Slow cycling

Unstable model

= selective sweeps

Stable model = balancing

selection

Expected genomic signatures of coevolutionExpected genomic signatures of coevolution

4) Expectations for genomic signatures of GFG models?

How? Simulate frequency dynamics + coalescent theory (Kingman TPB

1982, Donnelly, Tavare, Nordborg, Barton, Etheridge,…) to simulate genetic data

Sample = 40 plants and 40 parasites

..A……….T………T……………..G……

..T……….T………G……………..C……

..A……….A………G……………..C……

Present

= sample

Past

= start of selection


Tajima’s D for Unstable and Stable dynamics over range of parameters

Mean of Tajima’s D over 2,000 replicates, N=1,000 and =10-4


Balancing

selection

Selective

sweeps

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30

cost of virulence = cost of resistance (u=b)

Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6



Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30cost of virulence = cost of

resistance (u=b)

Balancing

selection

Selective

sweepsResult 8:

Balancing selection signature is not observable in populations with small N





Balancing

selection

Selective

sweeps

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30


Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6





Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweepsResult 8:

Balancing selection signature is only observable in populations with high N and in parasites







Balancing

selection

Selective

sweeps

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30


Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6



Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweepsResult 8:

Balancing selection signature is not observable in populations with small N





Balancing

selection

Selective

sweeps

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30


Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6





Cost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweepsResult 8:

Balancing selection signature is only observable in populations with high N and in parasites



Expected genomic signatures of coevolutionExpected genomic signatures of coevolutionC

ost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweeps


over 2,000 replicates, N=1,000 and =10-4

Mean Mode


ost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweeps



Mean Mode


ost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweeps



Mean Mode


ost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweeps



Mean Mode


ost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweeps



Mean Mode


ost

of

bein

g

dis

ease

d (

s)0.0

0

.1

0

.2

0

.3

0.4

0.5

0.6

0.00 0.05 0.10 0.15 0.20 0.25 0.30


resistance (u=b)

Balancing

selection

Selective

sweeps



Mean Mode

ConclusionsConclusions


2) In finite populations, can stable dynamics lead to fixation of alleles? Under which conditions?

Genetic drift does not influence the speed of coevolution, but the fixation rate of alleles

Alleles can get fixed in a stable model (contrary to common wisdom)

Resistance alleles only get fixed in small populations!!! Diversifying selection at Rgenes must have occurred in small plant populations3) Are dynamics in the arms race model slower than in the trench warfare model?

No, for most parameter values there is no difference between the speed of coevolution

Relevance for field studies following changes in allele frequencies 4) Expectations for genomic signatures under GFG models?

Unstable dynamics can lead to a big variation in genomic signatures

Bad news: almost no chance to find balancing selection in genome scans in plants (ex. Arabidopsis thaliana), AND costs determine the equilibrium point

Good news: genome scans can be used to find balancing selection in parasites

Thanks to hazards of migrationThanks to hazards of migration

Wolfgang Stephan Stefan Laurent Daniel Živković

Mamadou Mboup Katharina Böndel

James Brown

T. Giraud (University Paris 13)

J. Enjalbert (INRA, France)A.L. Laine (University

Helsinki)

Anja HörgerThomas Städler


What is the influence of cycle period? Many shorts vs few long cycles?

Here an ideal case = frequency of causal allele is on average fixed to 0.5, varying between 0.8 and 0.2

Values of S Values of Tajima’s D

Result 6bis:

above a limit of number of cycles, outcome is similar


How long does selection need to act to be observable?

Here an ideal case = frequency of causal allele is always fixed to 0.5

Values of S Values of Tajima’s D

Result 6: At least 4N generations

(in line with theoretical expectations from Barton and Etheridge, Genetics 2003)


Ideal GFG models:UNSTABLE dynamics STABLE

dynamics

Values of Tajima’s DResult 7:

Stable models have here homogeneous outcomesunstable model outcome depends on N and mutation

rate ()

Values of Tajima’s D


Role of costs for equilibrium valueRole of costs for equilibrium value

Mind the gaps: Theoretical and empirical aspects of plant ecology and population genetics S. peruvianum S. chilense 08.03.2013 Aurélien Tellier Populationsgenetik.

Documents

migration slide

instability slide

cost of resistance log

freising slide

logaa log log

log of ratio

sequence data slide

present of pathogen