Speciation along Environmental Gradients Michael Doebeli and Ulf Dieckmann

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

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

Evolutionary Branching Branching point Convergence to disruptive selection

Sexual Cohesion Can Prevent Branching

Mating Character

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.

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

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

Spatial Evolutionary Branching Trait value Time Spatial location

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

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

Full Characterization

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

Peripheral Speciation? Optimal phenotype Species range Expected speciation zone?