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. 2017 Jun;14(131):20170215.
doi: 10.1098/rsif.2017.0215.

Modelling the spread of innovation in wild birds

Thomas R Shultz  1   2 , Marcel Montrey  3 , Lucy M Aplin  4
Affiliations

Modelling the spread of innovation in wild birds

Thomas R Shultz et al. J R Soc Interface. 2017 Jun.

Abstract

We apply three plausible algorithms in agent-based computer simulations to recent experiments on social learning in wild birds. Although some of the phenomena are simulated by all three learning algorithms, several manifestations of social conformity bias are simulated by only the approximate majority (AM) algorithm, which has roots in chemistry, molecular biology and theoretical computer science. The simulations generate testable predictions and provide several explanatory insights into the diffusion of innovation through a population. The AM algorithm's success raises the possibility of its usefulness in studying group dynamics more generally, in several different scientific domains. Our differential-equation model matches simulation results and provides mathematical insights into the dynamics of these algorithms.

Keywords: agent-based computer simulation; animal culture; conformity bias; differential equations; innovation diffusion; social learning.

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Conflict of interest statement

We declare we have no competing interests.

Figures

Figure 1.
Figure 1.
Mean cycles to reach consensus among non-Byzantine agents. (Online version in colour.)
Figure 2.
Figure 2.
Mean number of solvers for each algorithm at each cycle for treatment (black) and control (purple) conditions, with 95% CIs. (Online version in colour.)
Figure 3.
Figure 3.
Sigmoid and linear fits for the three learning algorithms in treatment conditions. (Online version in colour.)
Figure 4.
Figure 4.
Mean number of solvers for each algorithm at each cycle for original treatment (black) and naive joiner (purple) conditions, with 95% CIs. (Online version in colour.)
Figure 5.
Figure 5.
Mean reactions to joining a population having a different solution, with 95% CIs. (Online version in colour.)
Figure 6.
Figure 6.
Mean numbers of agents for each algorithm over cycles, with 95% CIs. (Online version in colour.)
Figure 7.
Figure 7.
Proportion of the seeded option for each algorithm over cycles. (Online version in colour.)
Figure 8.
Figure 8.
Mean per cent change in majority (x) and minority (y) agent-state counts across cycles for each of the three algorithms. (Online version in colour.)
Figure 9.
Figure 9.
Mean per cent changes in the x- and y-states, along with s.e. bars, from the first to the last (825th) cycle for the three algorithms. (Online version in colour.)
Figure 10.
Figure 10.
Per cent change in bird solutions of puzzle boxes over days for each of five sites. Data are newly calculated from [16]. (Online version in colour.)
Figure 11.
Figure 11.
Mean proportion (a) first learning, or (b) switching to, solution x as a function of the proportion of x in the population for each learning algorithm. All relations are linear except for AM switching, which is sigmoidal. (Online version in colour.)
Figure 12.
Figure 12.
Linear and sigmoid fits of the AM switching curve in figure 11. The better fit is sigmoidal. (Online version in colour.)
Figure 13.
Figure 13.
Mean numbers of agents for the BAM algorithm over cycles. Compare with AM in figure 6. (Online version in colour.)
Figure 14.
Figure 14.
Mean proportion first learning, or switching to, solution x as a function of the inclusive proportion of x in the population for BAM. First learning is linear, whereas switching is sigmoidal. Compare with AM switching (figure 11b). (Online version in colour.)
Figure 15.
Figure 15.
Linear and sigmoidal fits for the BAM switching curve in figure 14. The sigmoidal fit is superior. (Online version in colour.)
See this image and copyright information in PMC

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