Commentary on Rendell, L. & Whitehead, H. (2001) Culture in whales and dolphins. Behavioral and Brain Sciences 24 (2): XXX-XXX.
Abstract: 60 words
Main Text: 1000 words
References: 341 words
Total Text: 1482 words
Gottfried Mayer-Kress
mailto:gxm21@psu.edu
http://www.personal.psu.edu/faculty/g/x/gxm21/
Mason A. Porter Center for Applied Mathematics Cornell University Ithaca, NY 14850 USA mason@cam.cornell.edu http://www.cam.cornell.edu/~mason/index.html
The target article provides stimulating evidence for culture in cetaceans but does not provide a coherent theoretical framework. We argue that a complex, adaptive systems approach not only can provide such a framework but also can contribute advanced data analysis and simulation methods. For humpback whale songs, we suggest the framework of "small-world networks" to model the observed spatio-temporal dynamics.
Culture as emergent self-organized structure of a complex system
The authors give a list of published definitions and characterizations of the social phenomenon "culture" and argue that behavioral patterns observed in whale populations are best described by assuming that whales have developed cultures. It might prove useful for heuristic guidance to supplement elementary statistical analysis by theory-based numerical simulations--especially if the empirical data are as sparse as in the examples mentioned in the target article.
In the context of complex systems, cultures can be viewed as one manifestation of an emergent, self-organized structure of a complex, adaptive system (see for instance Haken, 1987, Strogatz, 1994). In this commentary we argue that the complex systems paradigm provides a coherent theoretical framework for data analysis and theory-building towards explaining the phenomena discussed in the target article.
Large-scale coherence of humpback whale song patterns
We pick as an example the singing behavior of humpback whales. Early claims that singers have reproductive advantages could not be confirmed in studies that clearly demonstrate that females are not attracted by singers (Mobley et al. 1988). Singers are also typically smaller than the male escorts who are believed to do the breeding (Spitz et al. 2000). Furthermore, there is evidence that singers do not optimize their depth for optimal transmission range (Mercado & Frazer, 1999).
Music as collective memory
In cultures without written language, songs play an important role in preserving the community's collective memory. Without speculating about the semantics of humpback whale songs, we nevertheless can analyze the songs with respect to their information content. For instance, Tom Lehrer's song "The Elements" lasts 86 sec and contains about 1 kb = 8000 bits of information (Lehrer, 1959). The upper limit of verbal information transmission for humans is of the order of 100 bits/sec. For the humpback whale songs, the stream of patterns distinguishable to us are significantly lower so that an upper limit of 200,000 bits for humpback whale songs seems reasonable. The mutual information content or redundancy between songs may be an appropriate statistic to track the spreading and evolution of the songs.
Work by K. Payne and others (see e.g. Payne, 1999) has identified recurrent structures and patterns in humpback whale songs that are similar to musical themes and motives in human songs. Therefore, the songs can be naturally mapped onto a symbolic representation with dynamics that evolve both in space and time. The similarity of songs is thereby potentially accessible to quantitative analysis with the help of symbolic dynamics, a tool from nonlinear dynamics that has been successfully applied to the study of human music, dance, and speech. A systematic study of song duration as a function of the time of the day or the day in the season has already revealed some fascinating regularities that can provide a rigorous foundation for a quantitative theory (Fristrup, 2000). We anticipate that a systematic analysis of spatio-temporal humpback whale song dynamics would reveal valuable information about their social learning and cultural evolution beyond the singing behavior itself.
Spreading of song patterns
The phenomenon of rapid spreading of humpback whale song patterns may be aptly described as exhibiting the so-called 'small-world' phenomenon (Milgram, 1967, Watts & Strogatz, 1998, Newman & Watts, 1999, Newman et al. 2000), whereby the network of singing whales is hypothesized to exhibit both local clustering (e.g. in the breeding grounds) and a small 'degree of separation' DS. For instance, if a singer has DS = 3, then this singer listened to a whale that had been listening to a singer that had been listening to any random humpback whale singer within the past season. As a comparison: For humans under the relation "is on a first-name basis with a person" the average degree of separation anywhere in the world is estimated to be no more than four. With this property, information travels very fast along the network---about as fast as on a random network if the degree of separation is small enough (i.e., there are enough shortcuts).
The theoretical challenge is to find an economical pathway connecting a singer in, say, breeding grounds in Hawaii with one in Japan and one in Mexico. Assuming social learning among singers, one asks how many degrees of separation exist between any two whales in any of the three Northern Pacific breeding grounds. A straight-forward statistical analysis could estimate the probability that singers visit new breeding grounds in consecutive seasons. In the small-world context, one would also expect to find "shortcuts" between clusters of singers concentrated in the three breeding grounds. . The extra shortcuts could potentially be identified as "traveling minstrel" whales who visit more than one breeding grounds within the same season (Salden et al. 1999).
A Back-of-the-Envelope Small-World Calculation
Suppose there are 6000 humpback whales, of which 1000-2000 are active singers. The five feeding grounds mentioned in the target article provide a potential location for traveling minstrels to act as shortcuts between the singers in the three clusters of breeding grounds.
In general, if the number of shortcuts is larger than a certain threshold, exponential transmission of information is expected because in this regime the DS is a logarithmic function of the number of whales. Below the threshold, the DS is a linear function of the number of whales, which implies a linear rate of information transmission.
If each singing whale has about 250 "listeners" among whales in the same breeding ground (i.e., before shortcuts are applied), then according to small-world models, the requisite number of shortcuts for exponentially fast information transmission could be as small as a few individuals.
Future Directions
The target article mentions examples of social learning between humans and cetaceans. We expect that modern computer and communication technology will lead to more efficient interaction between the two most intelligent terrestrial and maritime species and new forms of global self-organization that might help to solve upcoming global problems (Mayer-Kress & Barczys, 1995, Mayer-Kress, 1996, Mayer-Kress et al. 2000).
Fristrup, K. (2000) Private Communication
Haken, H. (1987) Advanced Synergetics, 2nd edition, Springer, Berlin
Lehrer, T. (1959) The Elements, Lehrer Records
Mayer-Kress, G. & Barczys, C. (1995) The Global Brain as an Emergent Structure from the Worldwide Computing Network, and its Implications for Modeling , The Information Society, Vol 11 No 1, 1-28
Mayer-Kress, G. (1996) Messy Futures and Global Brains. In: Predictability of Complex Dynamical Systems, Yu.A. Kravtsov, J.B. Kadtke (Eds.) Springer, Berlin
Mayer-Kress, G., Herman, L.M., Hoffmann-Kuhnt, M. & Pack, A.A. Video Tracking Interface for Dolphins: A New Approach to Interspecies Communication. In: Sciences of the Interface Symposium, H. Diebner (Ed.), ZKM Karlsruhe, May 18-21, 2000, to appear
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Mobley, J. R., Herman, L. M., & Frankel, A.S. (1988). Responses of wintering humpback whales (Megaptera novaeangliae) to playback recordings of winter and summer vocalizations and of synthetic sound. Behavioral Ecology and Sociobiology, 23, 221-223
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Payne, K. (1999) The Progressively Changing Songs of Humpback Whales: A Window on the Creative Process in a Wild Animal. In: Origins of Music, eds. Nils L. Wallin, Björn Merker, & Steven Brown, MIT Press
Salden, D. R., Herman, L. M., Yamaguchi, M., & Sato, F. (1999). Multiple visits of individual humpback whales (Megaptera novaeangliae) between the Hawaiian and Japanese winter grounds, Canadian Journal of Zoology, 77, 504-508
Spitz, S.S., Herman, L.M., & Pack, A.A. (2000). Measuring sizes of humpback whales (Megaptera novaeangliae) by underwater videogrammetry. Marine Mammal Science, 16, 664-676
Strogatz, S. H. (1994) Nonlinear Dynamics and Chaos Addison-Wesley.
Watts, D. J. & Strogatz, S. H. (1998) Collective dynamics of "small-world" networks. Nature 393: 440-442.
We gratefully acknowledge helpful discussions with Kurt Fristrup, Louis Herman, Katy Payne, and Mark Newman