How competition affects evolutionary rescue: theoretical insight - - PowerPoint PPT Presentation

How competition affects evolutionary rescue: theoretical insight

Matthew Osmond Claire de Mazancourt

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Evolutionary rescue

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Evolutionary rescue

Mean fitness Mean trait value

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Evolutionary rescue

Mean fitness Mean trait value

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Evolutionary rescue

Time Abundance

0 0

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Evolutionary rescue

Time Abundance

0 0

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Evolutionary rescue

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

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Evolutionary rescue

Likelihood of rescue increases with:

◮ genetic variation / mutation rate (faster adaptation) ◮ initial population size (slower extinction)

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

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Extending evolutionary rescue

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Extending evolutionary rescue: competition

Competition reduces the abundance of a species ...

Maynard Smith (1989)

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Extending evolutionary rescue: competition

Time (t) Abundance (N)

K

dN dt = rN

• 1 − N

K

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Extending evolutionary rescue: competition

Time (t) Abundance (N)

K − C K

dN dt = rN

• 1 − N

K

• dN

dt = rN

• 1 − N+C

K

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Extending evolutionary rescue: competition

Competition reduces the abundance of a species ... ... which must make extinction more likely.

Maynard Smith (1989)

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Extending evolutionary rescue: competition

But, competition also influences selective pressures ...

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Competition and selection

Trait value (z) Fitness (isolated)

Fitness (in isolation): ——–

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Competition and selection

Trait value (z) Fitness (isolated) Competition (C)

Decreases selection strength Fitness (in isolation): ——– Competition (C): - - - - - - -

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Competition and selection

Trait value (z) Fitness (isolated) Trait value (z) Competition (C)

Decreases selection Increases selection strength strength Fitness (in isolation): ——– Competition (C): - - - - - - -

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Extending evolutionary rescue: competition

But, competition also influences selective pressures ... ... and selection affects the rate of adaptation.

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Extending evolutionary rescue: competition

But, competition also influences selective pressures ... ... and selection affects the rate of adaptation. So, competition can sometimes help evolutionary rescue?

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Adaptive dynamics

◮ Large asexual population ◮ All individuals have same phenotype ◮ Beneficial mutations rare and small

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Adaptive dynamics

The rate of evolution: dz dt = µ · n(z) · g(z) z: phenotype µ: per capita mutational input n(z): abundance g(z): selection gradient

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Adaptive dynamics

The rate of evolution: dz dt = µ · n(z, C) · g(z, C) z: phenotype µ: per capita mutational input n(z, C): abundance g(z, C): selection gradient C: competition

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Competition and adaptation

Trait value (z) Fitness (isolated) Competition (C)

A B

Decline in abundance: A>B Increased selection: A<B ⇒ Rate of adaptation: A<B

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Conclusions

• 1. Competition lowers abundance, slowing adaptation
• 2. Competition also impacts selection, potentially speeding adaptation
• 3. If selection imposed by competition is strong enough to
• vercome negative effect on abundance, competition can help

evolutionary rescue

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Circumstantial evidence

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

Trait value (z) Fitness (isolated) Competition (C)

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Evidence

Adaptation of algae to increased CO2 slowed by competition Collins 2011

Trait value (z) Fitness (isolated) Competition (C)

high 2137 high 2699 high 473 high A * * *

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Evidence for ‘helpful’ competition?

Trait value (z) Fitness (isolated) Competition (C)

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Adaptive response

Trait value (z ^)

z0* zn* z0* zn* zN c

Time (t) Abundance (n ^)

K K 50000 50000 N c trobs tr

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Time at risk influenced by:

Magnitude of change (z0

* − zn *)

Time at risk (tr)

∆z** ∆z*

Critical fraction of max abundance (N c K)

1

Time at risk (tr) Environmental tolerance (σk)

σk* σk**

Time at risk (tr)

Original environment New environment z0* zn* zN c Trait value (z ^) K K n N c

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