# Self-contained Beta-with-Spikes Approximation for Inference Under a Wright-Fisher Model

arXiv: https://arxiv.org/abs/2303.04691 · HTML: https://mlsanity.com/paper/2303.04691/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 46 references that are in the map.
- First posted on arXiv 8 Mar 2023.

## Builds on (most cited first, 3 of 3)

- [Evolutionary forces in language change](https://mlsanity.com/paper/1608.00938/) (2016)
- [The Dynamics of Norm Change in the Cultural Evolution of Language](https://mlsanity.com/paper/1809.04328/) (2018)
- [How individuals change language](https://mlsanity.com/paper/2104.10210/) (2021)

## Built on by (most cited first, 1 of 1)

- [Reliable Detection and Quantification of Selective Forces in Language Change](https://mlsanity.com/paper/2305.15914/) (2023)

## Abstract (arXiv)

We construct a reliable estimation of evolutionary parameters within the Wright-Fisher model, which describes changes in allele frequencies due to selection and genetic drift, from time-series data. Such data exists for biological populations, for example via artificial evolution experiments, and for the cultural evolution of behavior, such as linguistic corpora that document historical usage of different words with similar meanings. Our method of analysis builds on a Beta-with-Spikes approximation to the distribution of allele frequencies predicted by the Wright-Fisher model. We introduce a self-contained scheme for estimating the parameters in the approximation, and demonstrate its robustness with synthetic data, especially in the strong-selection and near-extinction regimes where previous approaches fail. We further apply to allele frequency data for baker's yeast (Saccharomyces cerevisiae), finding a significant signal of selection in cases where independent evidence supports such a conclusion. We further demonstrate the possibility of detecting time-points at which evolutionary parameters change in the context of a historical spelling reform in the Spanish language.