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APPLYING NBDA
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We provide a computer script in R (NBDA_example_analyses.txt) and two example
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files (example_network_data.txt and example_diffusion_data.txt) so that others can
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apply NBDA to their own data. In the following we describe how to use this script. If
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you have problems applying NBDA or further questions, please contact the
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corresponding author.
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(a) To those inexperienced with R
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R is a free software that can be downloaded from the internet at
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http://www.r-project.org/.
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It is command line driven. One of the files included in the electronic supplementary
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material (NBDA_example_analyses.txt) includes the code for R to conduct NBDA.
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You can open this file using any text-editor (e.g. Word, Notepad etc.). From there
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you can copy the code to R, which will then run it.
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(b) Data preparation
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NBDA requires as input the structure of a social network and the timing at which the
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trait was acquired by individuals in the network (see in file
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NBDA_example_analyses.txt section ‘load data files’). The network structure must be
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given as a matrix. Each individual in the group is represented by a column and a row,
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and the values in the off-diagonal cells of this matrix equal the strength of a
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connection between two individuals. Zeros are entered along the diagonal. The order
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of the individuals should be the same for the rows and the columns, and values used
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for connection strength should be non-negative numbers.
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It is possible to use a non-symmetric matrix as input to NBDA. In this case it
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is assumed that the probability with which individual A learns from B can differ from
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the probability with which B learns from A. The network data must be entered in the
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way in which a column includes all values that impact the probability that the
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individual associated with this column is learning from other individuals in the rows
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(with a value of zero for where the row is equal to the column). For example, assume
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that all connection values associated with individual A are written in column and row
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one, and that all connection values associated with individual B are written in column
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and row two. The value that determines the probability that A will learn from B
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(provided that B is skilled) is written in column one, row two. The value that
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determines the probability that B will learn from A (when A is skilled) is written in
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column two, row one.
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The timing at which the individuals acquired the new trait should be coded in
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time steps that have been standardized to zero, with the first individual(s) acquiring
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the new trait at time step zero and all values scored as integers. These values should
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be written in a vector, in which the order of the corresponding individuals equals the
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order used in matrix that represents the social network structure. Examples for the
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required data formats can be found in files example_network_data.txt and
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example_diffusion_data.txt, which are included in the electronic supplementary
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material.
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Coding the observed diffusion data into discrete time steps requires choosing
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the length of a time step, e.g. one hour, one day, one month, or whatever is most
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appropriate for the data at hand. This choice should depend on the uncertainties that
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are associated with the observation conditions and the applied observation method.
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The length of a time step should be large enough to ensure a high certainty that every
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learning event actually occurred in the coded time step. In general it can be expected
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that the power to distinguish between social and asocial learning decreases if the
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number of individuals that learned in the same time step increases. If possible, the
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length of a time step should, therefore, kept short enough to avoid such cases.
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Preliminary analyses showed that results of NBDA do not depend on the specific
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choice of the length of a time step, as long as the length was not very large. However,
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this could vary among datasets, and we therefore suggest that users repeat NBDA
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with slightly different length of time steps to confirm that the results do not depend on
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the specific choice of this parameter.
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For cases in which the new behaviour did not spread through the entire group,
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it is necessary to also assign individuals who did not acquire the trait an ‘artificial’
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time step in which they learned. The assigned time step must be larger than any time
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step in which an individual was observed to acquire the new behaviour (a suitable
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value would be for instance one plus the largest observed time step). These data are
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not actually used in the calculations (see next section).
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(c) Changes required to be made in the code
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Some simple changes to the code will be required before running the analysis. First
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are changes in the section ‘Load data files,’ in which R is looking for the file to be
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opened. Here you have to specify the path and name of the file to be opened (note that
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paths are separated by a slash (“/”) rather than a backslash (“\”) as usual in Windows).
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Further changes might be required in two parameters that are set in section
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‘Set parameters’. The first parameter is tau_max, which determines the largest
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possible value of tau that is considered during maximum likelihood fitting of the
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social learning model (the smallest possible value is always zero, and for the asocial
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learning model the smallest and largest possible values for the asocial learning rate are
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always zero and one). Higher values of tau_max might be necessary if the mean
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connection strength is smaller than in the example files. In particular it is advised to
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increase tau_max if the estimated value for tau is close to tau_max. In any case the
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analysis should be repeated with different values of tau_max to ensure that the results
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are not affected by choosing values of tau_max that are too small (which might lead to
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the erroneous conclusion that the asocial learning model fits better).
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If a new behaviour did not spread through the entire group it is necessary to
manually set the parameter time_max. This parameter specifies the upper limit of the
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time frame which is used to calculate model likelihoods. The default value of this
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parameter is always set to the maximum value in the vector with learning times. In
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cases in which the new behaviour did not spread through the entire group, this
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maximum value will not correspond to the maximum time step in which an individual
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acquired the new behaviour (as described in the previous section). Therefore, the
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value of time_max has to be set to the truly observed maximum time step in which an
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individual acquired the new behaviour.
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(d) Results of NBDA
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A successful application of NBDA returns a table in which AIC, Akaike weights and
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estimated parameter values are reported for both models. Based on AIC values and/or
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Akaike weights, it is possible to identify which learning mechanism best explains the
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observed data (for further information on model selection see Burnham & Anderson
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2002).
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(e) Extended version of NBDA
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We also provide an R script in which an extended version of NBDA is implemented
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(NBDA_example_analyses.txt section ‘Extended network-based diffusion analysis’).
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In this analysis a model of pure asocial learning and a model of social and asocial
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learning are fit to the observed diffusion data. Fitting the model of social and asocial
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learning requires an additional optimization procedure. The new procedure does not
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require specifying a parameter tau_max, but initial values for tau (tau_i) and the
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asocial learning rate (alr_i) are needed. The user is advised to check robustness of the
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results relative to changes in these values.
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As noted in the main paper, this extended NBDA is able to analyze data that
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include time periods prior to the first occurrence of a new trait. Using such data, the
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time steps should not to be standardized to zero. Instead, the time step with value zero
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should correspond to the first time interval of the observation period and the time step
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at which the first individual(s) acquiring the new trait can be any integer that is equal
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or larger than zero.
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