How competition affects evolutionary rescue:

theoretical insight

Matthew OsmondClaire de Mazancourt

MM Osmond

Evolutionary rescue

MM Osmond

Evolutionary rescue

0

Mean fitness

Mean trait value

MM Osmond

Evolutionary rescue

0

Mean fitness

Mean trait value

MM Osmond

Evolutionary rescue

Time

Abundance

00

MM Osmond

Evolutionary rescue

Time

Abundance

00

MM Osmond

Evolutionary rescue

So, which populations are likely to be “rescued” by evolution?

MM Osmond

Evolutionary rescue

Likelihood of rescue increases with:

I genetic variation / mutation rate (faster adaptation)

I initial population size (slower extinction)

Gomulkiewicz & Holt (1995), Orr & Unckless (2008), Chevin & Lande (2010)

MM Osmond

Extending evolutionary rescue

MM Osmond

Extending evolutionary rescue: competition

Competition reduces the abundance of a species ...

Maynard Smith (1989)

MM Osmond

Extending evolutionary rescue: competition

Time (t )

Abundance (

N)

K

dNdt

= rN(

1− NK

)

MM Osmond

Extending evolutionary rescue: competition

Time (t )

Abundance (

N)

K − C

KdNdt

= rN(

1− NK

)dNdt

= rN(

1− N+CK

)

MM Osmond

Extending evolutionary rescue: competition

Competition reduces the abundance of a species ...

... which must make extinction more likely.

Maynard Smith (1989)

MM Osmond

Extending evolutionary rescue: competition

But, competition also influences selective pressures ...

MM Osmond

Competition and selection

Trait value (z)

Fitn

ess (

iso

late

d)

Fitness (in isolation): ——–

MM Osmond

Competition and selection

Trait value (z)

Fitn

ess (

iso

late

d)

Co

mp

etitio

n (

C)

Decreases selectionstrength

Fitness (in isolation): ——–Competition (C): - - - - - - -

MM Osmond

Competition and selection

Trait value (z)

Fitn

ess (

iso

late

d)

Trait value (z)

Co

mp

etitio

n (

C)

Decreases selection Increases selectionstrength strength

Fitness (in isolation): ——–Competition (C): - - - - - - -

MM Osmond

Extending evolutionary rescue: competition

But, competition also influences selective pressures ...

... and selection affects the rate of adaptation.

MM Osmond

Extending evolutionary rescue: competition

But, competition also influences selective pressures ...

... and selection affects the rate of adaptation.

So, competition can sometimes help evolutionary rescue?

MM Osmond

Adaptive dynamics

I Large asexual population

I All individuals have same phenotype

I Beneficial mutations rare and small

MM Osmond

Adaptive dynamics

The rate of evolution:

dz

dt= µ · n(z) · g(z)

z : phenotypeµ: per capita mutational inputn(z): abundanceg(z): selection gradient

MM Osmond

Adaptive dynamics

The rate of evolution:

dz

dt= µ · n(z ,C) · g(z ,C)

z : phenotypeµ: per capita mutational inputn(z ,C): abundanceg(z ,C): selection gradientC: competition

MM Osmond

Competition and adaptation

Trait value (z)

Fitn

ess (

iso

late

d)

Co

mp

etitio

n (

C)

A

B

Decline in abundance: A>BIncreased selection: A

Conclusions

1. Competition lowers abundance, slowing adaptation

2. Competition also impacts selection, potentially speeding adaptation

3. If selection imposed by competition is strong enough toovercome negative effect on abundance, competition can helpevolutionary rescue

MM Osmond

Circumstantial evidence

Extinction rate (Er) of birds on islands increases with sqaure of speciesnumber, suggesting competition increases extinction Moulton & Pimm 1983

Trait value (z)

Fitness (

isola

ted)

Com

petition (

C)

MM Osmond

Evidence

Adaptation of algae to increasedCO2 slowed by competition Collins 2011

Trait value (z)

Fitness (

isola

ted)

Com

petition (

C)

high

2137

high

2699

high

473

high

A

* * * **

* *

MM Osmond

Evidence for ‘helpful’ competition?

Trait value (z)

Fitness (

isola

ted)

Com

petition (

C)

MM Osmond

Adaptive responseTra

it v

alu

e (

ẑ)

z0*

zn*

z0*

zn*

zN c

Time (t )A

bundance (

n̂)

0

K

0

K

00 5000050000

N c

t robst r

MM Osmond

Time at risk influenced by:

Magnitude of change (z0*− z

n

*)

Tim

e a

t ri

sk (

tr)

00

∆z** ∆z*

Critical fraction of max abundance (N c K )

0 10

Tim

e a

t ri

sk (

tr)

Environmental tolerance (σk)σk*

0σk**0

Tim

e a

t ri

sk (

tr)

Ori

gin

al environm

ent

New

environm

ent

z0* zn*zN c Trait value (ẑ)

K

Kn

N c

0

MM Osmond