How competition affects evolutionary rescue: theoretical insight

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1 How competition affects evolutionary rescue: theoretical insight Matthew Osmond Claire de Mazancourt

2 Evolutionary rescue

3 Evolutionary rescue Mean fitness 0 Mean trait value

4 Evolutionary rescue Mean fitness 0 Mean trait value

5 Evolutionary rescue Abundance 0 0 Time

6 Evolutionary rescue Abundance 0 0 Time

7 Evolutionary rescue So, which populations are likely to be rescued by evolution?

8 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)

9 Extending evolutionary rescue

10 Extending evolutionary rescue: competition Competition reduces the abundance of a species... Maynard Smith (1989)

11 Extending evolutionary rescue: competition K dn dt ( ) = rn 1 N K Abundance (N) Time (t)

12 Extending evolutionary rescue: competition K C Abundance (N) K dn dt dn dt ( ) = rn 1 N K ( = rn 1 N+C K ) Time (t)

13 Extending evolutionary rescue: competition Competition reduces the abundance of a species which must make extinction more likely. Maynard Smith (1989)

14 Extending evolutionary rescue: competition But, competition also influences selective pressures...

15 Competition and selection Fitness (isolated) Trait value (z) Fitness (in isolation):

16 Competition and selection Fitness (isolated) Competition (C) Trait value (z) Decreases selection strength Fitness (in isolation): Competition (C):

17 Competition and selection Fitness (isolated) Competition (C) Trait value (z) Decreases selection strength Fitness (in isolation): Competition (C): Trait value (z) Increases selection strength

18 Extending evolutionary rescue: competition But, competition also influences selective pressures and selection affects the rate of adaptation.

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

20 Adaptive dynamics Large asexual population All individuals have same phenotype Beneficial mutations rare and small

21 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

22 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

23 Competition and adaptation A Fitness (isolated) B Competition (C) Trait value (z) Decline in abundance: A>B Increased selection: A<B Rate of adaptation: A<B

24 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 overcome negative effect on abundance, competition can help evolutionary rescue

25 Circumstantial evidence Extinction rate (Er) of birds on islands increases with sqaure of species number, suggesting competition increases extinction Moulton & Pimm 1983 Fitness (isolated) Competition (C) Trait value (z)

26 Evidence Adaptation of algae to increased CO 2 slowed by competition Collins 2011 A high * 473 high * Fitness (isolated) Competition (C) 2699 high Trait value (z) 2137 high

27 Evidence for helpful competition? Fitness (isolated) Competition (C) Trait value (z)

28 Adaptive response znc z 0* K Abundance (n^) Trait value (z^) z n* Nc 0 0 tr t r ob s Time (t ) 50000

29 Time at risk influenced by: Time at risk (t r ) 0 0 z** z* Magnitude of change (z * 0 z * n ) 0Time at risk (t r) 0 1 Critical fraction of max abundance (N c K) K Time at risk (t r ) Original environment New environment N c 0 0 σ k * Environmental tolerance (σ k ) σ k ** K n 0 z 0 * z N c z n * Trait value (z^)

Warm Up. Explain how a mutation can be detrimental in one environmental context and beneficial in another.

Warm Up. Explain how a mutation can be detrimental in one environmental context and beneficial in another. Warm Up Explain how a mutation can be detrimental in one environmental context and beneficial in another. Last Picture 4B Evidence for Evolution 1A.4a: Scientific evidence of biological evolution uses