Much work in anthropology exhibits – or at least assumes – a significant degree of complex harmony or coherence between elements of culture within each society (e.g., Descola Reference Descola and Scott1994; Richerson et al. Reference Richerson, Boyd, Borgerhoff-Mulder, Durham, Weingart, Richerson, Mitchell and Maasen1997; Smelser Reference Smelser, Munch and Smelser1993). Whether there is as much coherence as some think, it is plausible that there are many cases in which adopting certain cultural variants affects the probability that others will be adopted (Henrich & McElreath Reference Henrich and McElreath2003; Sperber Reference Sperber1996; Thagard Reference Thagard and Sun2012; Wimsatt & Griesemer Reference Wimsatt, Griesemer, Sansom and Brandon2007). Such t ransmission probability interactions (TPIs) seem likely to play an important role in cultural transmission. For example, an individual may be more likely to adopt a belief suggested by someone else when she notices that it can be deduced from her existing beliefs, or that it has a high degree of plausibility given what she believes. More subtle kinds of inference may affect cultural transmission as well (cf. Sperber & Wilson Reference Sperber and Wilson1995). For example, in a previous paper (Abrams Reference Abrams2013), I suggest that cultural transmission might sometimes be biased by analogical relations between transmitted variants and existing beliefs (cf. Gentner et al. Reference Gentner, Holyoak and Kokinov2001; Hofstadter & Sander Reference Hofstadter and Sander2013; Holyoak & Thagard Reference Holyoak and Thagard1995; Thibodeau & Boroditsky Reference Thibodeau and Boroditsky2013). Although the ideas underlying the concept of transmission probability interactions are not new, I argue that a focus on TPIs as such can provide a useful enrichment to Kline's fruitful conceptualization of teaching types. Kline briefly discusses issues related to TPIs, for example, in her discussion of the role of relevance (Sperber & Wilson Reference Sperber and Wilson1995) in teaching, in section 5.

The explicit use of TPIs in modeling is illustrated in Abrams (forthcoming), which extends one of Enquist et al.'s (Reference Enquist, Strimling, Eriksson, Laland and Sjostrand2010) models. Enquist et al.'s results imply that cultural variants that are taught only by parents to same-sex children (e.g., Tehrani & Collard Reference Tehrani and Collard2009) would eventually disappear from a population. That result is correct when there are no TPIs, but I show that a cultural variant can be maintained by such “single parent” transmission if it can be inferred with the help of cultural variants taught by others. Earlier models that incorporate effects of interactions between cultural variants have produced significant insights (e.g., Boyd & Richerson Reference Boyd and Richerson1985; Reference Boyd and Richerson1987; Castro & Toro Reference Castro and Toro2014; Cavalli-Sforza & Feldman Reference Cavalli-Sforza and Feldman1981; Fogarty et al. Reference Fogarty, Strimling and Laland2011; McElreath et al. Reference McElreath, Boyd and Richerson2003; Mesoudi & O'Brien Reference Mesoudi and O'Brien2008). Those models were not formulated in terms of TPIs, but can be re-described in terms of them. However, building models using explicit representations of TPIs is useful because real-world transmission probability interactions are rooted in cognitive processes within particular physical and cultural contexts. The concept of a TPI thus provides a useful abstraction from cognitive processes involving cultural transmission, while preserving a natural mapping back to them. Sperberian attractors can also be understood as biases on probabilities of inferring internal states from transmitted representations.

Explicit focus on TPIs in empirical research would emphasize the ways in which different cultural variants affect each other's spread. For example, experimental methods in which some cultural variants are used as primes for others, such as in the studies by Dehghani et al. (Reference Dehghani, Sachdeva, Ekhtiari, Gentner, Forbus, Taatgen and van Rijn2009), Kashima (Reference Kashima2000), Mesoudi and Whiten (Reference Mesoudi and Whiten2004), and Thibodeau and Boroditsky (Reference Thibodeau and Boroditsky2013), could be applied in a broad range of populations. Field studies of the effects of social networks on transmission by Atran and Medin (Reference Atran and Medin2008) and Henrich and Broesch (Reference Henrich and Broesch2011) might be adapted to tease out distinctions between the effects of network structure and effects of TPIs, as well. It may also be possible to combine such analyses with studies of cultural phylogeny (e.g., Tehrani & Collard Reference Tehrani and Collard2009), to argue that the presence of certain cultural variants in some, but not all populations is likely to have been influenced by TPIs involving other cultural variants.

Fogarty et al. (Reference Fogarty, Strimling and Laland2011), and Castro and Toro (Reference Castro and Toro2014) argue that teaching is particularly advantageous for complex cumulative culture, and that this is a reason for its prevalence among humans. In many cases involving cumulative culture, successful teaching seems to depend partly on what other cultural variants the learner has already acquired (Bransford & National Research Council Reference Bransford2000; Wimsatt Reference Wimsatt, Caporael, Griesemer and Wimsatt2014; Wimsatt & Griesemer Reference Wimsatt, Griesemer, Sansom and Brandon2007), or on the presence of appropriate environmental features produced by human niche construction (Sterelny Reference Sterelny2012; Wimsatt Reference Wimsatt, Caporael, Griesemer and Wimsatt2014; Wimsatt & Griesemer Reference Wimsatt, Griesemer, Sansom and Brandon2007). Therefore, one role of teaching may be to organize the transmission of cultural variants so as to increase the chance of retention, for example, by encouraging the student to begin learning simpler or more fundamental ideas or methods before others, or by providing a supporting conceptual framework (Bransford & National Research Council Reference Bransford2000). In other words, some kinds of teaching can be viewed as methods for t ransmission probability coordination, that is, as methods for coordinating transmission of cultural variants in such a way that early acquisition of some variants increases the probability of later acquiring and retaining other variants. We can view the problem of communicating complex cumulative culture as an adaptive problem, even if it applies only to humans (Boyd et al. Reference Boyd, Richerson and Henrich2011). Transmission probability coordination then constitutes a partial solution to this problem. Its use overlaps with other methods listed by Kline, of course, but they overlap with each other as well.

Kline suggests that direct active teaching, in particular, aids transmission of cumulative culture. Direct active teaching is the method that most obviously allows control over transmission probability coordination. However, opportunity provisioning can serve this role as well, through the choice of what experiences to provide to pupils at different stages. Evaluative feedback may also sometimes be coordinated for the same purpose, providing feedback on only those mistakes that a pupil can be expected to be able to correct. Information provided through social tolerance and stimulus enhancement is parasitic on conditions that would exist regardless, but these methods nevertheless might be used to encourage a pupil to experience only those situations that are plausibly safe or comprehensible to her.

Finally, teaching methods may themselves constitute instances of complex cumulative culture. Conceptualizing differences between teaching strategies in terms of transmission probability coordination may provide a useful abstraction for understanding interactions between transmission of teaching strategies and transmission of the variants they are used to teach.