Müllerian mimicry: An examination of Fisher’s theory of gradual evolutionary change

1. Top row, Heliconius erato and bottom row, Heliconius melpomene, Müllerian co-mimics. Müllerian mimicry: An examination of Fisher’s theory of gradual evolutionary change Alexandra Balogh and Olof Leimar Department of Zoology Stockholm University Sweden

2. All things are not equally nice to eat… Blue jay (Cyanocitta cristata) while eating monarch butterflies (Danaus plexippus) (left) and a few minutes later (right) - Aposematism is a way of signalling unprofitability to predators - Avoidance learning reduces predation on aposematic populations

3. Top row, Heliconius erato and bottom row, Heliconius melpomene Müllerian mimicry • - Mimicry between unpalatable species • Shared signal dilutes predation risk

4. Number of attacks (for separate populations) Survival gain when mimicry is attained Advantage from cooperation per capita The relative advantage is proportional to the relative population size squared Fritz Müller 1891 Resulting appearance will depend on the relative initial protection of the participants of the cooperation, like abundance and unpalatability

5. How does Müllerian mimicry evolve? Saltational evolution Purifying selection prevents most mutations from invading Fisher 1930 Peak shift produces gradual evolution towards mimicry

6. Advergence Coevolutionary convergence Advergence or coevolutionary convergence ? Saltational evolution gives only advergence If evolution is gradual, both advergence and coevolutionary convergence seem possible

7. No empirical evidence for coevolution • There seems to be a model and a mimic (Mallet 1999) • Typical model characters: higher abundance, larger geographical distribution, higher unpalatability, more ”original” appearance • Because of this, Müllerian mimicry is often believed have come about through saltations fake character original character Danaus plexippus Limenitis archippus Mimic and model in Batesian mimicry Müllerian mimics

8. Testing Fisher’s process: Model • Individual-based simulations of a community of two prey types and predators • Predator avoidance learning and generalization • Prey appearance is a one-dimensional quantitative trait • Given that a gradual process is possible, assess advergence through individual-based simulations and by solving the canonical equation

9. Predators • Predators accumulate inhibition • Next encounter: altered probability of attack q (h) = Probability of attack on a discovered prey depends on predator experience and on the trait of the encountered prey (predator generalization). Prey • Individual-based: survivors reproduce, mutations with a given distribution of effect sizes are produced • Canonical equation: invasion fitness of mutants computed, canonical equation integrated

10. Initially similar prey types Initially more distinct Two types of predators Invasion fitness Predator generalization Survival and invasion fitness Na = 1000, Nb = 5000, Np = 100

11. Fisher’s process is posible for traits sufficiently similar for predator generalization It is also possible for large trait differences when a predator spectrum is used Fisher’s process is possible(individual-based simulations)

12. The degree of advergence depends on the range of mutational increments Curves 1-3 correspond to succesively smaller ranges of mutational increments, 3 computed by solving the canonical equation.

13. Conclusions • Gradual evolution by peak shift towards Müllerian mimicry is possible also for large initial trait differences when a proportion of predators generalize broadly • The range of mutational increments affects the degree of advergence • The canonical equation approximates the evolutionary trajectory for very small mutational effects • For somewhat larger ranges of mutational effects, there is gradual evolution and more advergence than predicted by the canonical equation • The deviation from the canonical equation is related to the curvature of invasion fitness • Gradual evolution through Fisher’s process seems consistent with observations of advergence in Müllerian mimicry in nature

14. Top row, Heliconius erato and bottom row, Heliconius melpomene, Müllerian co-mimics. Müllerian mimicry: An examination of Fisher’s theory of gradual evolutionary change Alexandra Balogh and Olof Leimar Department of Zoology Stockholm University Sweden