Network Based Diffusion Analysis Essay


A number of recent studies have used Network Based Diffusion Analysis (NBDA) to detect the role of social transmission in the spread of a novel behavior through a population. In this paper we present a unified framework for performing NBDA in a Bayesian setting, and demonstrate how the Watanabe Akaike Information Criteria (WAIC) can be used for model selection. We present a specific example of applying this method to Time to Acquisition Diffusion Analysis (TADA). To examine the robustness of this technique, we performed a large scale simulation study and found that NBDA using WAIC could recover the correct model of social transmission under a wide range of cases, including under the presence of random effects, individual level variables, and alternative models of social transmission. This work suggests that NBDA is an effective and widely applicable tool for uncovering whether social transmission underpins the spread of a novel behavior, and may still provide accurate results even when key model assumptions are relaxed.

It is frequently difficult to identify social learning in natural animal populations, or even in captive groups of animals. We are developing new mathematical and statistical methods to do this.

The Option Bias Method

The option-bias method is based on the well-established premise that social learning will generate greater homogeneity in behaviour between animals than expected in its absence. The procedure compares the observed level of homogeneity to a sampling distribution generated utilizing randomization and other procedures, allowing claims of social learning to be evaluated according to consensual standards. We have established that the method has higher statistical power than conventional inferential statistics, which is likely to be important in cases where sample size is small. We envisage that the method could be of value in both in assessing the validity of claims for culturally transmitted behaviour, and in enabling investigation of the social learning strategies deployed. For further details see:

Identifying social learning in animal populations: A new ‘option-bias’ method.
Kendal RL, Kendal JR, Hoppitt W & Laland KN. PLoS ONE, 2009 4:e6541[pdf]

To implement these analyses:

  1. Download the statistical package R, available free from
  2. Download Option Bias files “OB example” and “OB functions” in zip archive, and unzip.
  3. Cut and paste the code contained in the file “OB functions” into the R console.

The file “OB example” provides an example Option Bias analysis which can be used as a guide to using the functions.

The Boogert et al (2008) Randomisation Method

It is often assumed that social transmission tends to occur more rapidly between closely associated individuals in a population. Where this is the case we can test for social transmission by testing whether the order in which individuals acquire a behavioural trait is related to a matrix of measured associations between them. One way in which this can be done is by calculating an appropriate test statistic, and then generating a null distribution by randomising the order of acquisition a large number of times, calculating the test statistic each time. For further details see:

The origin and spread of innovations in starlings.
Boogert NJ, Reader SM, Hoppitt W & Laland KN. Animal Behavior, 2008 75:1509-1518[pdf]

To implement these analyses:

  1. Download the statistical package R, available free from
  2. Download Boogert Randomisation files zip archive and unzip.
  3. Cut and paste the code contained in the file “Boogert Randomisation” into the R console.

The file “Boogert Randomisation example” provides an example analysis that can be used as a guide to using the functions.

Network Based Diffusion Analysis (NBDA) Version 1.2

NBDA, first invented by Franz & Nunn (2009), infers social transmission when the pattern of acquisition of a novel behavioural trait follows the network of associations between individuals. In this respect, the method is similar to Boogert et al‘s randomisation method, but has a number of advantages that are discussed in Hoppitt et al (2010). Franz & Nunn’s original method requires data on the times at which individuals acquire a novel behavioural trait. In our paper (Hoppitt et al (2011)) we expand their method and introduce our own variant which requires data only on the order in which individuals acquire the trait. We call these methods Time of Acquisition Diffusion Analysis (TADA) and Order of Acquisition Diffusion Analysis (OADA) respectively. The relative advantages and disadvantages of each method are discussed in Hoppitt et al (2010). Here we provide R code to implement both OADA and our extended version of TADA.

Network-based diffusion analysis: a new method for detecting social learning.
Franz M & Nunn CL. Proceeding of the Royal Society B, 2009 doi:10.1098/rspb.2008.1824[pdf]

Detecting social transmission in networks.
Hoppitt W, Boogert NJ & Laland KN. Journal of Theoretical Biology, 2010 263:544-555[pdf]

Detecting social learning using networks: a users guide.
Hoppitt W & Laland KN. American Journal of Primatology, 2011 73:834-844[pdf]

To implement these analyses:

1. Download the statistical package R, available free from

2. Download NBDA files in zip archive and unzip:

  • R code: NBDA code 1.2.13.R
  • Instructions on how to use the code: NBDA User Guide V1.2.1.pdf
  • Example dataset: starlingSolve1.2 and stratDiffs
  • Example use of profLik functons.R

3. Cut and paste the code contained in the file “NBDA code 1.2.13.R” into the R console.

Bayesian NBDA

We have expanded NBDA to allow it to quantify the evidence for social transmission across a number of diffusions. To do this it is important to account for individual differences in asocial learning by fitting models with appropriate random effects. As random effects can be difficult to implement using maximum likelihood methods, here we take a Bayesian approach. See Nightingale et al (2015) for technical details.

Quantifying diffusion in social networks: a Bayesian approach.
Nightingale G, Boogert NJ, Laland KN & Hoppitt W. Animal Social Networks, chapter 5, 2015[pdf]

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