Supplementary Material:
The evolution of judgement-bias in indirect reciprocity
Daniel J. Rankin1,2,3 and Franziska Eggimann1
1) Division of Behavioural Ecology, Institute of Zoology, University of Bern,
Wohlenstrasse 50a, CH-3032 Hinterkappelen, Switzerland
2) Center for Systems Biology, Harvard University, Bauer Laboratory, 7 Divinity
Avenue, Cambridge, MA 02138, United States of America
3) Correspondence to: Dr Daniel J. Rankin, Department of Biochemistry, University
of Zurich, Building Y27, Winterthurstrasse 190, 8057 Zurich, Switzerland
Author E-mail addresses:
DJR: d.rankin@bioc.uzh.ch, FE: frency.eggimann@bluewin.ch
Figure S1. Effect of changing y (the propensity to discriminate) and z (the degree of
non-discriminate cooperation) on the evolution of judgement-bias x under scoring.
Both y and z are fixed (indicated by the values in the graph). The horizontal line at
x=1 indicates the threshold where good and bad acts are weighted in the same way.
The simulation was run for 25 rounds, and costs were set to c=1.
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Figure S2. Effect of changing y (the propensity to discriminate) and z (the degree of
non-discriminate cooperation) on the evolution of judgement-bias x under standing.
Both y and z are fixed (indicated by the values in the graph). All other details remain
the same as the simulations given in the methods. The horizontal line at x=1 indicates
the threshold where good and bad acts are weighted in the same way. The simulation
was run for 25 rounds, and costs were set to c=1.
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Figure S3. Evolution of judgement-bias when weight was put on good acts, rather
than bad acts. Here a value of x>1 corresponded to positive judgement-bias (i.e.
putting more weight on good acts) while a value of x<1 corresponded to negative
judgement-bias (i.e. putting more weight on bad acts). The left panels show the results
from the image-scoring simulation and the right panels show the results from the
standing simulation. Panels show judgement-bias (top), propensity to discriminate
(middle) and propensity to cooperate in the absence of discrimination (bottom). Solid
lines indicate results where judgement-bias could evolve and dashed lines indicate
results where judgement-bias did not evolve (classical indirect reciprocity, where x=1
for all members of the population). The horizontal line in the top two panels shows
the threshold where there is no judgement-bias (i.e. x=1). The costs were set to c=1.
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Figure S4. Evolution of judgement-bias when the number of rounds in each
generation was set to 5. The left panels show the results from the image-scoring
simulation and the right panels show the results from the standing simulation. Panels
show judgement-bias (top), propensity to discriminate (middle) and propensity to
cooperate in the absence of discrimination (bottom). Solid lines indicate results where
judgement-bias could evolve and dashed lines indicate results where judgement-bias
did not evolve (classical indirect reciprocity, where x=1 for all members of the
population). The horizontal line in the top two panels shows the threshold where there
is no judgement-bias (i.e. x=1). The costs were set to c=1.
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Figure S5. Evolution of judgement-bias when the number of rounds in each
generation was set to 50. The left panels show the results from the image-scoring
simulation and the right panels show the results from the standing simulation. Panels
show judgement-bias (top), propensity to discriminate (middle) and propensity to
cooperate in the absence of discrimination (bottom). Solid lines indicate results where
judgement-bias could evolve and dashed lines indicate results where judgement-bias
did not evolve (classical indirect reciprocity, where x=1 for all members of the
population). The horizontal line in the top two panels shows the threshold where there
is no judgement-bias (i.e. x=1). The costs were set to c=1.
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Figure S6. Evolution of judgement-bias when individuals could only observe 10% of
all interactions. The left panels show the results from the image-scoring simulation
and the right panels show the results from the standing simulation. Panels show
judgement-bias (top), propensity to discriminate (middle) and propensity to cooperate
in the absence of discrimination (bottom). Solid lines indicate results where
judgement-bias could evolve and dashed lines indicate results where judgement-bias
did not evolve (classical indirect reciprocity, where x=1 for all members of the
population). The horizontal line in the top two panels shows the threshold where there
is no judgement-bias (i.e. x=1). The costs were set to c=1 and the number of rounds in
each generation was 25.
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Figure S7. Evolution of judgement-bias when the population size consisted of only
25 individuals. The left panels show the results from the image-scoring simulation
and the right panels show results from the standing simulation. Panels show
judgement-bias (top), propensity to discriminate (middle) and propensity to cooperate
in the absence of discrimination (bottom). Solid lines indicate results where
judgement-bias could evolve and dashed lines indicate results where judgement-bias
did not evolve (classical indirect reciprocity, where x=1 for all members of the
population). The horizontal line in the top two panels shows the threshold where there
is no judgement-bias (i.e. x=1). The costs were set to c=1 and the number of rounds in
each generation was 25.
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Figure S8. The evolution of judgement-bias with random mutations. Here we started
off with a homogenous population where all individuals in each simulation started
with the same value for both discrimination (y) and non-discriminate cooperation (z).
These values were picked randomly. All individuals in the population always started
with a judgement-bias of x=1. We then ran the simulations as detailed in the methods,
but individuals could mutate to a different strategy of x, y or z with a probability 0.001
each generation. If a given trait in an individual mutated, the new value was
calculated as ’=exp(log() + v), where ’ was the mutated value of the trait,  was
the original value of the trait and v was a normally distributed random number (with
mean 0 and standard-deviation 0.1). This function was used to scale the new random
number so that negative values would not be chosen. We ran each simulation for
100,000 generations. All simulations were run 100 times. The mean +/- the standard
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error are plotted in the above figure. The left panels show the results from the scoring
simulation and the right panels show results from the standing simulation. Panels
show judgement-bias (top), propensity to discriminate (middle) and propensity to
cooperate in the absence of discrimination (bottom). Solid lines indicate results where
judgement-bias could evolve and dashed lines indicate results where judgement-bias
did not evolve (where x=1 for all members of the population). The horizontal line in
the top two panels represents the threshold where there is no judgement-bias (i.e.
x=1). The costs were set to c=1 and the number of rounds in each generation was 25.
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