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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.

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m llerian mimicry an examination of fisher s theory of gradual evolutionary change

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

all things are not equally nice to eat
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

m llerian mimicry

Top row, Heliconius erato and bottom row, Heliconius melpomene

Müllerian mimicry
  • - Mimicry between unpalatable species
  • Shared signal dilutes predation risk
fritz m ller 1891

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

how does m llerian mimicry evolve
How does Müllerian mimicry evolve?

Saltational evolution

Purifying selection prevents most mutations from invading

Fisher 1930

Peak shift produces gradual evolution towards mimicry

slide6

Advergence

Coevolutionary convergence

Advergence or coevolutionary convergence ?

Saltational evolution gives only advergence

If evolution is gradual, both advergence and coevolutionary convergence seem possible

no empirical evidence for coevolution
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

testing fisher s process model
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
predators
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
survival and invasion fitness

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

fisher s process is possible individual based simulations

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)
the degree of advergence depends on the range of mutational increments
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.

conclusions
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
m llerian mimicry an examination of fisher s theory of gradual evolutionary change14

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