shape of the model world and the location of thefirst followers in the model
world will also influence the exact pattern of growth. This is, however, exactly
what happens at the expansion of actual religious movements. Note that
interactions in the real world involve even more complex network structures,
which could be built into a more advanced version of the model. Already this
very simple scenario shows that agent-based models capture aspects of real-life
phenomena that are lost in mathematical models.
We can now adjust the values of different parameters to examine their effect
on the spread of the movement in the model (see Table 9.1). For example,
lowering the conversion-rate will increase the number of days needed until
every household is converted substantially; increasing the conversion-rate
decreases the number of days needed. The effect (which could be expected
intuitively) is not linear: changing the conversion-rate from 0.1 to 1 (tenfold
increase) results in a change of the number of days from around 140 to less
than 10 days (fourteen-fold decrease).^13 What happens if we add an apostle to
the movement? Apostles are followers that move around freely (represented as
“turtles”in NetLogo); we can thus expect that they speed up the spread of the
movement. As a few runs of the model show, however, this effect depends on a
variety of circumstances. If we lower the conversion-rate to 0.1, adding ten
itinerants reduces the number of days needed for all households to convert by
Table 9.1.Number of days needed until all households are converted at different
conversion rates, with and without apostles^12
Apostles Days at
conversion
rate = 1
Days at
conversion
rate = 0.5Days at conversion
rate = 0.1Days at conversion
rate = 0.010 8.08 22.67 139.23 1485.19
1 8.15 22.77 134.77 1326.74
2 8.13 22.4 130.63 1249.42
3 8.09 21.85 131.99 1175.85
4 7.96 21.92 128.8 1102.07
5 8.01 21.75 127.2 1082.91
6 7.97 21.98 122.96 1095.94
7 8 21.61 121.59 1062.59
8 7.95 21.72 122.35 1016.14
9 7.92 21.42 118.67 1030.8
10 7.91 21.04 117.74 1008.13
same day. If we rewrite the model to remove all randomness and set the conversion rate to one,
the innovation will spread in a wave-like fashion at every run.
(^12) The values in the“Days at conversion rate...”columns represent the mean of the results
from a hundred runs of the model in each condition.
(^13) Such an impact of the conversion-rate is predicted by its role in the logistic function, see
our discussion of the growth of the movement in a single day above.
Social Networks and Computer Models 199