Detecting social transmission in networks

Abstract

In recent years researchers have drawn attention to a need for new methods with which to identify the spread of behavioural innovations through social transmission in animal populations. Network-based analyses seek to recognise diffusions mediated by social learning by detecting a correspondence between patterns of association and the flow of information through groups. Here we introduce a new order of acquisition diffusion analysis (OADA) and develop established time of acquisition diffusion analysis (TADA) methods further. Through simulation we compare the merits of these and other approaches, demonstrating that OADA and TADA have greater power and lower Type I error rates than available alternatives, and specifying when each approach should be deployed. We illustrate the new methods by applying them to reanalyse an established dataset corresponding to the diffusion of foraging innovations in starlings, where OADA and TADA detect social transmission that hitherto had been missed. The methods are potentially widely applicable by researchers wishing to detect social learning in natural and captive populations of animals, and to facilitate this we provide code to implement OADA and TADA in the statistical package R.

Introduction

‘Social learning’ is broadly defined as learning that is influenced by observation of or interaction with a conspecific or its products (Heyes, 1994). Social learning can result in ‘social transmission’, which we define as occurring when the acquisition of information or a behavioural trait by one individual exerts a positive causal influence on the rate at which another acquires the same information or trait. Social learning appears widespread across both vertebrate and invertebrate taxa (Hoppitt and Laland, 2008; Leadbeater and Chittka, 2007), whilst experimental work has established that social transmission can result in the establishment of behavioural traditions (e.g. Galef and Allen, 1995; Whiten et al., 2005). This has lead to claims of animal cultures in natural populations of apes (McGrew, 1998; Whiten et al., 1999; van Schaik et al., 2003), cetaceans (Rendell and Whitehead, 2001; Krützen et al., 2005) and monkeys (Perry and Manson, 2003). However, such claims remain controversial because studies fail to adequately rule out alternative explanations for local differences in behaviour, such as local environmental differences, or genetic differences between populations (Laland and Hoppitt, 2003; Laland and Janik, 2006). There is concern that the current ‘ethnographic’ method, which infers social transmission only where the alternatives of genetic or environmental variation can be disregarded, will rule out genuine cases of social transmission that covary with these factors (Laland and Janik, 2006; Laland and Galef, 2009). Consequently, in recent years researchers have called for the development of quantitative methods for inferring social transmission from field and captive study data that can rule out alternative explanations for the observed effect (Laland and Janik, 2006; Laland and Galef, 2009, and chapters therein).

One type of data that has previously been used to infer social transmission in groups of animals is diffusion data, where researchers monitor the spread of a novel behavioural trait. For some time the shape of the ‘diffusion curve’ (the cumulative number of individuals seen to perform the novel behaviour plotted against time) was used to infer social learning (e.g. Lefebvre, 1995a, Lefebvre, 1995b). The assumption was that if learning were asocial, the rate of learning would be the same for all individuals, resulting in an r-shaped diffusion curve. In contrast, if there were social transmission, the rate of learning would increase as the number of demonstrators increased, resulting in an s-shaped curve (Reader, 2004). However, this approach has been somewhat discredited, since there are a number of situations in which we expect to see an s-shaped diffusion curve in the absence of social transmission (Laland and Kendal, 2003; Reader, 2004), or an r-shaped curve in the presence of social transmission (Franz and Nunn, 2009).

An alternative method is to use the order in which individuals acquire a behavioural trait to infer social transmission from diffusion data, on the assumption that if social transmission is operating we might expect the spread to follow the patterns of associations between individuals (Boogert et al., 2008; Morrell et al., 2008). The reasoning here is that individuals that are closely associated are more likely to learn from each other (Coussi-Korbel and Fragaszy, 1995). A randomisation approach has already been applied to test for such a pattern (Boogert et al., 2008; see also Morrell et al., 2008), but below we demonstrate that this approach is vulnerable to both Type I and Type II errors.

Here we propose an alternative method, which we call order of acquisition diffusion analysis, or OADA, where a model of social learning is fitted to the data by maximum likelihood, and tested against a model with no social transmission.¹ Our approach is similar to a method recently proposed by Franz and Nunn (2009), which they term ‘network-based diffusion analysis’ (or NBDA). Franz and Nunn's method exploits data on the time at which individuals acquire a behavioural trait, rather than the order in which they do so. However, as OADA and the randomisation approach of Boogert et al. (2008) are also network-based diffusion analyses, for clarity we rename Franz and Nunn's approach time of acquisition diffusion analysis (or TADA), and retain NBDA as the more general term for network-based approaches. We see the OADA and TADA approaches as complementary, and in later sections of this paper we introduce the OADA model, extend Franz and Nunn's TADA method, and provide a full comparison of OADA and TADA models. We end by illustrating the methods by applying them to a published data set: the diffusion of novel foraging traits in groups of starlings, Sturnus vulgaris (Boogert et al., 2008).