Evolution of music by public choice

As EP1 evolved, it seemed to us that the loops were becoming more pleasing to listen to, and that we were, in fact, evolving music from noise (audio examples have been archived at doi:10.5061/dryad.h0228 and can be heard at http://soundcloud.com/uncoolbob/sets/darwintunes/). To test this objectively, we carried out a new experiment. We randomly sampled 2,000 of the 50,480 loops produced at any time during EP1’s evolution and, via a Web interface, asked public consumers to rate them as before. Because consumers heard and rated loops sampled from the entire evolutionary trajectory in this experiment, their ratings can be used to estimate the mean absolute musical appeal, M, of the population at any time. This is analogous to bacterial experiments in which the fitness of an evolved strain is compared directly with that of its ancestor (10). Fig. 1B shows that M increased rapidly for the first 500–600 generations but then came to equilibrium. Thus, in our system, musical quality evolves, but it seems that it does not do so indefinitely.

What makes the loops of later generations so much more pleasing? The aesthetic value of a given piece of music depends on many different features, such as consonance, rhythm, and melody (23). In recent years, music information retrieval (MIR) technology has permitted the automatic detection of some of these features (24 –26); reasoning that our raters listen to, and like, Western popular music, we measured the phenotypes of our loops using two MIR algorithms designed to detect features in this music. The first, Chordino, detects the presence of chords commonly used in the Western repertoire (27). The fit of a loop to Chordino’s canonical chord models is given by a log-likelihood value and is an estimate of the clarity of the chordal structure. The second, Rhythm Patterns (28), extracts a rhythmic signature, from which we derive a complexity measure, R. To validate these algorithms, we tested them on a standardized test set of specifically generated loops (SI Appendix, A.3 ).

To examine the evolution of musical qualities in EP1, we measured and R for every loop. We found that, like musical appeal, these traits increased rapidly over the first 500–600 generations but then appear to fluctuate around a long-term mean (Fig. 2 A and B). Given these dynamics, and because and R are measured without error, we are able to model their evolution using a discrete version of the Ornstein–Uhlenbeck (O-U) process, according to which the change in the mean of a character from one generation to the next is anticorrelated to how far it is from a long-term mean:

where is the difference between the means of each offspring and parental generation, ; a is a constant such that ; ; u is the long-term mean; and ε is a normally distributed random variable with a mean = 0. For both and R, the confidence limits on the long-term mean do not include the initial values ( and , respectively), confirming the visual impression that and R increased significantly over the course of the experiment (Fig. 2 A and B and SI Appendix, Table S6 ).

Because musical appeal and its components all increase, they are probably being selected. However, the trajectory of a DarwinTunes population, like that of any evolving population, depends not only on selection but on stochastic sampling, the analog of genetic drift. In experimental evolution, replicable responses are a signature of selection (10, 29). Hence, to determine whether the increases in chordality and rhythmicity are idiosyncratic to the preferences of the particular set of consumers contributing to EP1, or perhaps are attributable to chance correlations between these characters and other characters that were the true targets of selection, we repeated the experiment in a more controlled setting. To do this, we cloned additional populations from the same base population that EP1 started with and asked undergraduates to rate them. These populations, designated EP2 and EP3, were allowed to evolve independently for about 400 generations and received an average of 10,683 ratings. We found that and R also increased rapidly in these populations, again to a plateau (SI Appendix, B.1 and SI Appendix, Fig. S5 ). As controls, we generated 1,000 additional populations with the same origin as the experimental populations and subject to the same variational processes and demography for 400 generations but differing from them in that ratings were assigned randomly rather than by consumers. We found that mean and R of the selected populations were significantly higher than those of the unselected control populations by generation 100 (Fig. 2 C and D and SI Appendix, B.2 ). We also used the control populations to examine whether and R are intrinsically related to each other and found that they are weakly correlated, [mean (±95% confidence interval)] (SI Appendix, B.3 ). Thus, although selection on one of these features may influence the evolution of the other, they are largely independent. We cannot, however, preclude the possibility that either feature is highly correlated with unmeasured traits that are more direct targets of selection.

The increase in and R implies that selection is directional. Thus, why do our populations stop evolving? Remarkably, it is not merely that these traits cease to evolve: Musical appeal itself does also. This pattern of fast-slow evolution or even stasis is often seen in biological populations, whether in the laboratory, wild, or fossil record. Stasis can result from several different population genetic forces; however, it has often been difficult to distinguish among them (10, 30 –32). Because we know the complete histories of the DarwinTunes populations, we can study the forces driving their evolutionary dynamics in detail. We first considered the possibility that DarwinTunes populations have arrived at an adaptive peak, such that selection, which was previously directional, now stabilizes the population means. To investigate this, we estimated selective surfaces using multivariate cubic-spline regression (33) and plotted adaptive walks on them. Fig. 3A shows that EP1 has a single adaptive peak near high R and and that although it walks erratically up the slope toward the peak, it does not reach it. Very rhythmic loops (very high R) may be less fit than slightly less rhythmic ones; even so, it is clear that EP1 has stopped evolving at least 1 SD in each dimension away from its adaptive peak; thus, stasis is not attributable to an absence of selection. Interestingly, the topology of the EP1 adaptive landscape suggests that R and have a synergistic effect on fitness: high loops are especially fit when they have a high R as well; a model with interaction explains significantly more of the variation than one without it. A similar interaction is found in EP2 but not EP3 (SI Appendix, B.4 ).

We next considered the possibility that the populations have simply run out of genetic variation and that they have become fixed for all beneficial variants. Fig. 3 B and C show the frequency distributions of and R over the evolution of EP1. The rapid progress of the population before generation 1,000 is associated with a decrease in frequency of loops with the lowest chordal clarity and rhythmic complexity, likely attributable to selection. However, as the population continues to evolve, new low and R loops are reintroduced by mutation or recombination, and throughout the evolution of the populations, many loops have higher and R values than the long-term O-U mean. Thus, the lack of progressive evolution after about generation 500 is not attributable to fixation of high and R variants and complete exhaustion of genetic variation. This is also true for EP2 and EP3 (SI Appendix, Fig. S8 ).

To probe the forces acting on these populations further, we made use of the Price equation (34 –37). The Price equation, a general description of all evolutionary processes, decomposes the mean response to selection in a given generation, , into a covariance term that describes the effect of selection and a transmission term that describes the effect of inheritance:

where z is the phenotype of an individual, is the mean phenotype of the population; w is the fitness of an individual (how many offspring it has); is the mean fitness of the population; , where is the phenotype of an individual and is the mean phenotype of its offspring; and has been defined previously. The covariance term in any generation is the product of the population variance, , and the strength of directional selection, which, in turn, can be estimated as the slope of a linear regression of the fitness of parents on a phenotype, . The transmission term is based on the phenotypic similarity of parents to their offspring, and thus estimates the fidelity of transmission: When it is zero, inheritance is perfect; when it is negative, offspring have a lower phenotype than their parents; and when it is positive, offspring have a greater phenotype than their parents.

At evolutionary equilibrium, , the covariance and transmission terms must be equal in magnitude but opposite in sign. Given that our populations appear to be at equilibrium, one or both of these terms must have changed during their evolution. However, which term changed? As noted above, in an O-U process, the expected change from one generation to the next is a linear function of the current value with a negative slope (i.e., changes are expected to be positive when the current value is below the long-term mean and negative when it is above the long-term mean). We now decompose into covariance and transmission terms, and we test whether either changes as a function of the mean, . Considering only the first 400 generations, before and R approach equilibrium, the change in trait value attributable to selection (i.e., the covariance term) is independent of the current value in all cases but the amount by which offspring differ from their parents (i.e., the transmission term) becomes increasingly negative as the current value increases (Fig. 3D and SI Appendix, B.6 ). This indicates that the fidelity of transmission becomes an increasing impediment to progress as adaptation proceeds. It is this factor that causes evolution to slow down as and R increase over the first 400 generations.

In organisms, a decrease in the fidelity of transmission could be attributable to an increase in environmental variance, recombination pressure, or mutation pressure (38). Because the genome for any DarwinTunes loop produces an identical sound file on all computers, there is no environmental variance; a decrease in the fidelity of transmission must therefore be attributable to an increase in recombination, mutation pressure, or both. Because the genomic rates of recombination and mutation were constant throughout the experiment, this increase cannot be attributable to an increase in the frequency of recombination or mutation but must be attributable to increasingly deleterious phenotypic effects. Recombination could have increasingly deleterious effects if, as the population evolves, high fitness comes to depend on particular genomic configurations that can be broken up by sex; in other words, fitness epistasis increases (39). If so, this explanation would be analogous to the epistatic effects that Dobzhansky and Muller thought were responsible for hybrid sterility and lethality (40). As noted above, there is some evidence for synergistic fitness epistasis between R and . Perhaps loops with pleasing combinations of R and are selected but then quickly broken up by recombination. If so, this would imply that these traits are controlled by different regions of the loops’ genomes, but we do not know this, and rhythm and chordal clarity may themselves be influenced by multiple interacting loci. Alternatively, mutations may become increasingly deleterious as the populations become more adapted for the same reasons that R. A. Fisher inferred they do in organisms: the increasing vulnerability of complex, fine-tuned structures to change (41, 42). We cannot distinguish between these explanations for decrease in transmission fidelity in our populations, but further experiments may do so.

Curiously, if we consider all 2,513 generations of EP1, we get a different picture in which the transmission term is no longer significant for and the covariance terms for both and R show a significant decline (Fig. 3D). To investigate this further, we decomposed the covariance term into the strength of selection, , and the variance of the trait, . The slopes and are significantly positive in all cases, showing directly that both and R were under directional selection (SI Appendix, B.6 ). As the population mean increases, remains constant, whereas increases significantly; thus, consistent with our impression from the adaptive landscapes, the long-term stasis of neither trait is attributable to a decline in the strength of directional selection. By contrast, both and decline as the population mean increases, implying that the long-term stasis of this population is at least partly attributable to a decrease in the amount of phenotypic variance present (SI Appendix, B.6 ). Thus, although recombination or mutation pressure limits adaptive evolution in the short term, in the longer term, even a subtle decline in the amount of genetic variation can do so as well.

Because and R have increased as a result of selection, they must be contributing to the overall increase in musical appeal (M) (Fig. 1). However, music has many dimensions, and we only measured two. We used single and multiple linear regression analysis to estimate how much of the overall increase in M is attributable to the features we measured. We find that alone is responsible for 3.0% of the increase in M and R alone is responsible for 2.8%, whereas, together, they account for 4.2%, leaving 95.8% unexplained (SI Appendix, B.7 ); thus, other features must also contribute to the evolution of appealing music in these populations. In the future, we will be able to examine these with an expanded MIR toolkit.