1. Speciation along Environmental Gradients
Michael Doebeli and Ulf Dieckmann

2. Resource Competition Dynamics of population sizes ni of strategy si
distribution k(s)
competition
function a(s-s0)
resource
gradient s s0
Dynamics of population sizes ni of strategy si

3. Resultant Pairwise Invasibility Plots
With k = k0 N(0,σk) and a = N(0,σa) we obtain
for σa > σk for σa < σk – – + + + +
Mutant trait s‘
Mutant trait s‘ – –
Resident trait s
Resident trait s
 Evolutionary Stability
 Evolutionary Branching

4. Evolutionary Branching
Branching point
Convergence to disruptive selection

5. Sexual Cohesion Can Prevent Branching

6. Mating Character

7. Sexual Evolutionary Branching
Assortative Mating
Random Mating
Disassortative Mating
Evolutionary Branching Point
This mechanism also works when assortative mating is based on a marker character and when evolutionary branching is driven by interspecific interactions.

8. Spatial Gradient Maximum of carrying capacity varies with location
Trait value at maximum
Spatial location

9. Spatial Evolutionary Branching
Assortative
Mating
Random
Mating
Disassortative
Mating
Spatial Gradient
(vertical direction is ecologically neutral)
Evolutionary Branching Point

10. Spatial Evolutionary Branching
Trait value
Time
Spatial location

11. Spatial Gradient Facilitates Branching
Branching range for non-spatial model
Extra branching range due to gradient
Migration scale
σa / σk 1

12. Intermediate Slopes Are Most Speciation-Prone
No branching expected for non-spatial model
σa = 
Extra branching range due to gradient
Migration scale
g σs / σk 1

13. Full Characterization

14. Summary Spatial gradients can greatly facilitate branching
Sympatric speciation processes may lead to patterns of species abutment
The responsible mechanism is not isolation by distance but instead local adaptation leading to frequency-dependent disruptive selection
Intermediate slopes appear to be most speciation-prone
Sympatric speciation processes may lead to patterns of peripheral speciation

15. Peripheral Speciation?
Optimal
phenotype
Species
range
Expected speciation zone?