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Population Ecology of Tunes

John M. McBride, Armand. M. Leroi

arXiv:2609.09501v1q-bio.PEcs.SDphysics.soc-ph

TL;DR

Cultural evolution research asks how selection shapes cultural repertoires and how diversity persists. Using weekly tunebook data for Irish traditional tunes, the study finds tune-specific fitness alongside rising diversity driven by new compositions.

  • Problem

    Cultural evolution asks whether change is neutral or selective, what determines relative fitness, and what maintains diversity under selection.

    Source: INTRODUCTION · p. 1

  • Method

    The study models weekly tune-popularity data from The Session with ecological birth processes under neutral, frequency-dependent, and tune-specific fitness hypotheses.

    Source: INTRODUCTION · p. 1

  • Results

    Tune-specific fitness best explains popularity dynamics, while new compositions drive increasing repertoire diversity.

    Source: INTRODUCTION · p. 1, DISCUSSION · p. 4

  • Takeaways & Limitations

    Directional selection and stable or increasing cultural diversity can coexist in this musical ecosystem.

    Source: DISCUSSION · p. 4

    The findings cover roughly thirteen years of an already-established tradition and may not capture earlier or slower homogenizing effects.

    Source: DISCUSSION · p. 4

Abstract

from arXiv · show

How cultural repertoires maintain diversity under selection is a fundamental question in cultural evolution. We address this using thirteen years of weekly popularity data for approximately 20,000 Irish traditional tunes, fitting ecological birth-process models under neutral, frequency-dependent, and per-tune selection hypotheses. We find strong evidence that tunes differ in intrinsic fitness - some are systematically more likely to be learned than others. We find that 29% of the variance in fitness can be explained by a mixture of social and melodic features. Some tunes appear to be carried along via linkage due to the tradition of playing tunes in sets, analogous to selective sweeps in genetics. By measuring changes in fitness over time and comparing this with recordings we precisely identify the mechanism by which a long-dormant tune can become fit through a popular recording. Despite the directional selection, repertoire diversity increases, driven by the continual arrival of new compositions. These results demonstrate that selection and diversity can coexist in a cultural ecosystem, and establish Irish traditional music as a quantitatively tractable system for studying the evolution of cultural variants and understanding what makes a tune stand out.

INTRODUCTION

The study uses Irish traditional music to test how selection shapes tune popularity and whether diversity can persist as repertoires change. Weekly tunebook data and models of tune popularity support tune-specific fitness and increasing diversity through new compositions.

INTRODUCTION

  • The central questions are whether cultural change is neutral or selective, what determines relative fitness, and what maintains diversity under selection.Earlier empirical tests often used truncated, aggregated, or poorly delimited populations, making selection difficult to distinguish from drift.Source: INTRODUCTION · p. 1
  • At sessions, musicians encounter tunes, decide whether to learn them, and may add them to their active repertoires, providing a clear transmission mechanism.Tunes are commonly passed orally and played together in sets.Source: INTRODUCTION · p. 1
  • The Session provides weekly records of users’ personal tunebook additions across more than thirteen years and approximately 20,000 tunes.The platform is the largest online tune repository described in the passage.Source: INTRODUCTION · p. 1
  • Cultural models distinguish neutral copying, frequency-dependent social selection, and selection for intrinsic properties; without new variants, most reduce diversity in finite populations.Negative frequency dependence is the exception identified as maintaining diversity without new variants.Source: INTRODUCTION · p. 1
  • Tune popularity is best explained by tune-specific fitness rather than neutral or frequency-dependent change, while new compositions drive increasing repertoire diversity.The study reports that social and melodic features explain 29% of fitness variance.Source: INTRODUCTION · p. 1

RESULTS

Per-tune directional selection best explains tune popularity, while social and melodic features account for part of the differences in fitness. Sets can link tunes’ fortunes, but new compositions more than offset selection’s erosion of diversity.

Selection on tunes

  • For the 11,791 retained tunes, the per-tune model strongly beat neutrality (ΔAIC = −57700), with βᵢ ranging from −0.84 to 1.60.Tunes that never reached a tunebook count of 10 were excluded because their selection-coefficient standard errors were very large.Source: Selection on tunes · p. 1, Figure 1 · p. 2
  • Frequency-dependent selection was weak: βf was 0.024, or 0.048 after saturation, and its ΔAIC was about 3% of the per-tune model’s.Tunes averaging fewer than about 60 tunebook entries had a small disadvantage, while more popular tunes had a small advantage.Source: Selection on tunes · p. 2, Figure 1 · p. 2

Predicting tune success

  • The predictor model reached held-out R2 = 0.29; social popularity, mean frequency, and melodic variables uniquely explained 16%, 1%, and 3% of βᵢ variance, respectively.The three feature groups carried largely non-overlapping information.Source: Predicting tune success · p. 2, Figure 2 · p. 3
  • Positive selection increased with recording count and maximum Spotify popularity, while more complex tunes were less successful on average.Complexity was measured using chroma entropy and melodic note density; this contrasts with a previously reported inverted-U relationship for this dataset.Source: Predicting tune success · pp. 2–3, Figure 2 · p. 3
  • After six years averaging 3.2 adds, Maids of Selma’s βᵢ rose from slightly negative to ≥0.7 after an October 2020 YouTube video; the rise appeared driven by that video.The analysis estimated approximately one new tunebook add per 500 views.Source: Predicting tune success · p. 2, Figure 2 · p. 3
  • The predictors are probably proxies for true sources and targets of selection, and the analysis assumes each tune’s fitness depends only on its own properties.Tunes played in stereotyped sets could violate that assumption.Source: Predicting tune success · p. 3

Musical linkage

  • Sets were not assembled at random, and Maids of Selma may have hitchhiked with Lisnagun, whose βᵢ was 0.89 and which was paired with it in the video.The pair appeared in 18 user-contributed sets as an exact pair, ranked 134th among 22,982 distinct pairs.Source: Musical linkage · p. 3, Figure 2 · p. 3

Innovation dominates diversity

  • Popularity entropy rose by 0.37 bits as active tunes more than doubled from roughly 9,000 to over 22,000, while entropy declined among the 8,808 tunes present at Week 0.Continual arrival of new tunes more than compensated for directional selection’s erosion of diversity among the initially active tunes.Source: Innovation dominates diversity · p. 3, Figure 3 · p. 3

DISCUSSION

Tune popularity reflects directional selection, yet repertoire diversity rises as new tunes enter fast enough to offset concentration on fitter tunes. In the observed digital ecosystem, technology’s effects operate mainly through prestige rather than conformity.

DISCUSSION

  • The number of active tunes more than doubled as innovation drove an increase in repertoire entropy despite selection favoring fitter tunes.New tunes enter at a sufficient rate to offset the concentration of popularity into fitter existing tunes.Source: DISCUSSION · p. 4
  • Most tunes have fitness near zero, while other proposed diversity mechanisms—including niches, network structure, and changing tastes—remain untested directly.The observation window is too short to detect long-period fluctuations in fitness.Source: DISCUSSION · p. 4
  • Frequency-dependent selection is weak (β ≈0.05), and observed technology effects act primarily through prestige bias rather than conformity.The authors caution against generalizing beyond roughly thirteen years of a well-established tradition; homogenizing effects could predate the data or unfold too slowly to detect.Source: DISCUSSION · p. 4
  • Case studies contrast a prestige-backed tune with low fitness and a high-fitness tune whose growth predates its video.The model accommodates recordings as affecting both exposure and attractiveness through the per-tune fitness parameter.Source: DISCUSSION · p. 4
  • Fitness inference is limited by a single-platform dataset, tunebook adds as an indirect measure, and coarse covariates that explain 29% of fitness variance.The authors cannot yet explain why tunes differ in fitness or quantify how intrinsic properties determine whether a prestige boost is sustained.Source: DISCUSSION · p. 4
  • Irish music offers a constrained, testable system with bounded melodic forms, concrete transmission steps, and historical collections extending beyond the digital record.Proposed next steps include richer melodic representations, controlled learning and recall experiments, and finer-grained transmission tracking.Source: DISCUSSION · pp. 4–5

METHODS

The methods combine weekly tunebook-add records with reconstructed tune frequencies, then fit birth-process models that compare neutral, frequency-dependent, and per-tune selection. The analysis also checks burst events and tests robustness to removals using a second dataset.

Data

  • The main dataset contains 820,752 add events for 22,216 tunes from December 2012 to March 2026, aggregated into 695 weekly bins.The main analyses retain 11,791 tunes after excluding those never reaching 10 members and week–tune cells below 10.Source: Data · p. 5

Data Cleaning

  • Six tunes had at least half their add events in rapid-fire bursts, so 63 burst events were removed before interval aggregation.The number flagged was insensitive to ε from 30–300 seconds when min_samples was at least 3.Source: Data Cleaning · p. 5

Overview

  • DS2 analyses using a Skellam process confirm robust results, with tune removals having negligible effects.DS2 includes weekly totals that account for adds and removals.Source: Overview · p. 5
  • Add events are modeled as independent categorical draws over active tunes, with weights normalized into selection probabilities.The likelihood uses adjacent weekly transitions; inactive tune cells are skipped.Source: Overview · p. 5
  • The three models assign weights by current frequency alone, frequency-dependent selection, or a tune-specific fitness offset.For the frequency-dependent model, positive β favors popular tunes and negative β favors novelty.Source: Overview · p. 5
  • The neutral baseline treats new adds as sampled with replacement from the previous period’s tunebook entries.The model equates encounter probability with relative popularity, while new-tune inception is included only after a tune appears.Source: Overview · p. 5
  • Per-tune weights are multiplied by a saturation factor because each user can add a given tune only once.The fitted saturation parameter implies an effective user pool of approximately 22,500; the saturated model is the default for reported fitness estimates.Source: Overview · p. 5

Ridge Regularisation

The models use independent Gaussian ridge priors on free selection parameters, and the prior regularizes estimates when add-event data are sparse.

Ridge Regularisation

  • A Gaussian ridge prior is placed independently on each free selection parameter, with default standard deviation σ = 0.2.For saturation models, the prior is placed on s rather than γ.Source: Ridge Regularisation · pp. 5–6
  • The optimization objective is the negative log-posterior, combining the log-likelihood with the prior.Source: Ridge Regularisation · p. 6
  • The ridge prior prevents overfitting when a tune has few add events.A sensitivity analysis of inferred β is reported in Supplementary Figure S5.Source: Ridge Regularisation · p. 6

Optimisation

The objective is optimized with L-BFGS using analytic gradients and a gradient-norm convergence criterion.

Optimisation

  • L-BFGS optimization uses analytic gradients and stops at convergence when the gradient norm falls below 10^-2, with a maximum of 500 iterations.A strong Wolfe line-search condition is used.Source: Optimisation · p. 6

Uncertainty Quantification

Uncertainty in the parameter estimates is quantified with a Laplace approximation, followed by Wald tests and false-discovery-rate correction for per-tune selection.

Uncertainty Quantification

  • Parameter standard errors use a Laplace approximation with covariance given by the inverse Hessian of the objective at the MAP estimate.Only diagonal Hessian elements are computed, using central finite differences.Source: Uncertainty Quantification · p. 6
  • When a diagonal Hessian element is non-positive, its standard error falls back to the prior standard deviation as a conservative upper bound.The finite-difference step defaults to 10^-4.Source: Uncertainty Quantification · p. 6
  • Wald z-statistics and two-tailed p-values are computed for parameters, with Benjamini-Hochberg correction applied to per-tune selection p-values.Source: Uncertainty Quantification · p. 6

Model Comparison

The models are compared by AIC, while overlapping time windows track changes in per-tune fitness. Recording data from TheSession.org, Discogs, and Spotify supply tune-level proxies for recording prominence.

Model Comparison

  • AIC compares models using the number of free parameters and ridge-free log-likelihood at the MAP estimate.The neutral model has no free parameters; the frequency-dependent model has one, the per-tune model has one per tune, and saturated variants add one global parameter.Source: Model Comparison · p. 6

Sliding-Window Fitness Trajectories

  • Per-tune fitness is re-estimated in 23 overlapping windows, each spanning two years and advanced by six months.The fits use the full-data ridge prior and optimizer; tunes without add events in a window are held at βi = 0, and standard errors are not computed.Source: Sliding-Window Fitness Trajectories · p. 6

Recording Prestige Proxies

  • The recording proxies are assembled by mapping TheSession.org user-contributed tune-to-track data to Discogs and Spotify information.Discogs wish-list counts and mean or median Spotify scores were excluded after preliminary screening because they were highly collinear with retained proxies.Source: Recording Prestige Proxies · p. 6
  • TheSession.org track counts and Discogs recording have-counts are log1p-transformed and used as tune-level predictive features.TheSession counts tracks on which a tune appears; Discogs sums user have-counts across matched recordings, assigning zero to unmatched recordings.Source: Recording Prestige Proxies · p. 6
  • Spotify popularity is the maximum 0–100 score among matched tracks for each tune, with unmatched tracks assigned zero before log1p transformation.Tracks are matched through album-name similarity and track-count agreement; this track-level measure is described as more precise than the recording-level Discogs measure.Source: Recording Prestige Proxies · p. 6

Intrinsic Melodic Features

The analysis derives five melodic-structure measures from ABC notation for each tune setting, then uses the median across settings to represent each tune. A wider set of descriptors was screened out before the headline analysis.

Intrinsic Melodic Features

  • Five melodic measures are computed from each setting’s ABC notation and aggregated to the tune level by taking the median across settings.The retained measures are pitch-class entropy, note density, LZ76 complexity, mean absolute interval size, and contour complexity.Source: Intrinsic Melodic Features · p. 6
  • Pitch-class entropy summarizes the pitch-class sequence, while note density counts note onsets per quarter-note-length unit and excludes unison intervals.The text treats long notes and unison pairs or triplets as exchangeable and essentially uninformative in the Irish tradition.Source: Intrinsic Melodic Features · p. 6
  • LZ76 complexity is normalized by sequence length and a fixed 12-pitch-class alphabet, approaching 1 for uniform i.i.d. sequences and falling below 1 for repetitive sequences.It uses the greedy exhaustive parsing phrase count.Source: Intrinsic Melodic Features · p. 6
  • Mean absolute interval size measures non-zero melodic intervals, while contour complexity measures direction changes among consecutive non-zero intervals.Contour complexity ranges from 0 for a monotonic melody to 1 for alternating up-down motion.Source: Intrinsic Melodic Features · p. 6
  • Additional melodic descriptors were excluded after screening because they were highly collinear with retained measures and added negligibly to predictive accuracy.The excluded set included pitch and interval descriptors, tune length, note counts, and pitch range.Source: Intrinsic Melodic Features · p. 6

XGBoost predictor of βi

The predictor models per-tune fitness as a nonlinear function of three recording-prestige proxies, five melodic features, and a popularity baseline. It uses a conservative gradient-boosted tree ensemble and five-fold cross-validation.

XGBoost predictor of βi

  • Fitness βi is modeled as a nonlinear function of nine covariates: three prestige proxies, five melodic features, and one popularity baseline.Prestige and melodic covariates are z-scored; analyses retain tunes with average tunebook counts of at least 10 and complete covariates, yielding 8,051 matched tunes.Source: XGBoost predictor of βi · p. 6
  • A gradient-boosted decision-tree ensemble is fitted by weighted squared error, with per-tune weights set to the inverse squared standard error from the Laplace approximation.The specified tree depth, child-weight, learning-rate, estimator-count, subsampling, and regularization settings are deliberately conservative.Source: XGBoost predictor of βi · p. 6
  • The model’s in-sample R2 is 0.42 and its five-fold cross-validation R2 is 0.29, a gap of 0.13.Out-of-fold predictions use a fixed fold assignment.Source: XGBoost predictor of βi · p. 6

Variance Partitioning

The analysis compares covariate groups using consistent XGBoost fits and fold assignments. It reports each group’s standalone predictive signal and the performance change when that group is removed from the full model.

Variance Partitioning

  • Each covariate group is evaluated both in isolation and by removing it from the full model using the same XGBoost configuration.The fold assignment is held constant across fits so the two cross-validation R2 values are directly comparable.Source: Variance Partitioning · p. 6
  • The group-only CV R2 measures its total signal, while the leave-one-group-out CV R2 isolates signal not redundant with other groups.The full model’s five-fold CV R2 is the reference for the leave-one-group-out comparison.Source: Variance Partitioning · pp. 6–7
  • All R2 values in the group comparisons are sample-weighted by wi.The weights are those used for the predictor fits.Source: Variance Partitioning · p. 7

GAM Partial Effects

The additive GAM smooths make covariate associations with tune fitness directly interpretable, while observed two-tune sets recur more often than a popularity-only null predicts.

GAM Partial Effects

  • A GAM fitted with one penalized spline per covariate estimates marginal effects, and its partial-effect curves show the same qualitative pattern as XGBoost.The four plotted predictors span their 1st–99th percentiles with 95% confidence intervals.Source: GAM Partial Effects · p. 7

Set Co-occurrence Analysis

  • Irish traditional music is typically performed in sets: sequences of two or more tunes played consecutively.TheSession records user-submitted sets in its GitHub data repository, dating from 2016.Source: Set Co-occurrence Analysis · p. 7

Frequency of Recorded Sets

Null Model

  • 22,982 distinct two-tune combinations were observed, versus an average of 40,788 under the popularity-only null; the observed maximum was 134 recordings versus 8.The null averages results across 20 simulated corpora.Source: Null Model · p. 7
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