Inferring language dispersal patterns with velocity field estimation

The origins and dispersals of language families and groups worldwide are intricately linked to significant demic diffusions and cultural spreads over the past 10,000 years, particularly with the intensification of agricultural techniques. Advances in human genetics allow tracing the demographic dynamics of language-speaking populations, while linguistic history offers insights into cultural innovations not always reflected in archaeological records. Integrating linguistic, genetic, and archaeological evidence is crucial for a comprehensive understanding of prehistory, although aligning these often disparate sources presents a challenge. Phylogeographic approaches, frequently used to model language spatial evolution, rely on phylogenetic trees representing linguistic relatedness through vertical divergence. However, these trees often fail to account for horizontal contact like borrowing and areal diffusion, limiting their accuracy. This study introduces a novel method, Language Velocity Field Estimation (LVF), designed to overcome this limitation and provide a more robust inference of language dispersal patterns.

Previous research extensively used phylogeographic approaches to infer language dispersal patterns. These approaches utilize phylogenetic trees to represent linguistic relatedness, with branch lengths reflecting evolutionary trajectories. Geographic projection of the tree then yields dispersal trajectories. However, this method has limitations because phylogenetic trees primarily capture vertical divergence and neglect horizontal contact such as borrowing and areal diffusion, significant factors in many multilingual areas. Existing studies using these methods have yielded valuable insights but often present conflicting results, highlighting the need for approaches that consider both vertical and horizontal linguistic evolution. Recent advancements in velocity field estimation offer an alternative, enabling the modeling of spatiotemporal dynamics in various fields, including demic diffusions and cultural spreads.

The Language Velocity Field Estimation (LVF) method presented in this paper consists of two major steps. The first step establishes diachronic evolutionary trajectories of linguistic traits that shape linguistic relatedness without relying on phylogenetic trees. This involves: 1) Principal Component Analysis (PCA) to represent linguistic relatedness among language samples based on Euclidean distances in the PC space; 2) Development of a dynamic model using ordinary differential equations (similar to the covarion model) to reconstruct the past state of each linguistic trait for each language sample, yielding a high-dimensional velocity vector reflecting trait evolution; and 3) Projection of the high-dimensional velocity field into the two-dimensional PC space to visualize diachronic evolutionary trajectories. The second step transforms these trajectories into language dispersal trajectories using kernel projection, mapping velocity vectors from PC space to geographic space while maintaining the correlation between linguistic relatedness and language geography. The dispersal center is then inferred as the geographic location surrounded by velocity vectors that point radially outwards. The method's effectiveness and robustness were tested using 1000 simulated datasets with known dispersal patterns, varying parametric settings to assess sensitivity. Empirical application was performed on four agricultural language families: Indo-European, Sino-Tibetan, Bantu, and Arawak, using publicly available lexical datasets.

Simulated validations using 1000 datasets confirmed the LVF's high effectiveness and robustness in inferring dispersal centers under different parametric settings. The inferred centers were not significantly different from the known centers in the simulations. Empirical application of LVF to the four language families yielded dispersal trajectories largely consistent with previous linguistic studies and supported by archaeological and genetic evidence of demic diffusion and cultural spread. Inferred dispersal centers were geographically close to known ancient agricultural or Neolithic homelands: Indo-European in the Fertile Crescent, supporting the Anatolian origin hypothesis; Sino-Tibetan in the Gansu Province of China, consistent with the Northern origin hypothesis; Bantu in southern Cameroon, adjacent to the known African agricultural homeland; and Arawak in the northern lowlands of Bolivia, a key ancient agricultural area of South America. Comparisons with the phylogeographic approach showed similar performance when linguistic relatedness was well-represented by a family-tree model (as in simulated data). However, where horizontal contact significantly influenced linguistic relatedness (as in empirical data), LVF showed significant differences in inferred dispersal centers, especially for Sino-Tibetan and Arawak. These differences were correlated with the degree of deviation from tree-like topology, indicating LVF's superior performance when horizontal influences are substantial. Comparisons to three phylogeny-free baseline approaches (diversity, centroid, and minimal distance) also revealed significant differences in inferred dispersal centers, highlighting LVF’s unique contribution.

The LVF method provides a valuable advancement in inferring language dispersal patterns. Unlike phylogeographic approaches, it does not rely on phylogenetic trees, allowing for consideration of both vertical and horizontal evolutionary processes. This makes it particularly suitable for analyzing languages where horizontal contact has significantly shaped linguistic relatedness. Further, in contrast to phylogeny-free methods, LVF accounts for the complex interplay between linguistic relatedness and geographical distribution. The strong alignment of LVF results with interdisciplinary evidence, particularly in cases where the phylogenetic approach yields less consistent results, underscores its utility. Although the origins and dispersals of some language families remain controversial (e.g., Indo-European), LVF provides a robust approach that complements existing methodologies and offers new insights into the complex history of language evolution and its connection to cultural and demographic shifts.

This study presents Language Velocity Field Estimation (LVF), a novel computational approach for inferring language dispersal patterns that accounts for both vertical and horizontal linguistic evolution. Rigorous validations and empirical applications demonstrate its effectiveness and robustness. LVF offers a valuable addition to the methodological toolkit for investigating language evolution and its interplay with other aspects of human history. Future work should focus on incorporating temporal information to estimate dispersal periods more precisely and addressing biases introduced by uneven sampling of geographic distributions. The potential applications of LVF extend to various linguistic traits (lexicons, grammar, and sound) and interdisciplinary studies integrating linguistics, genetics, and archaeology.

While LVF provides a robust approach, limitations exist. The accuracy of the results depends on the quality and completeness of the linguistic datasets. Uneven sampling of geographic distributions can introduce biases, as acknowledged in the study. While the method addresses horizontal linguistic influences, the complexity of these interactions might not be fully captured. Future research should focus on refinements to mitigate these limitations, potentially by integrating Bayesian methods to incorporate uncertainty and incorporating weighting schemes to account for uneven sampling.