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A Critical Look at Directional Random Walk Modeling of Sparse Fossil Data
1University of South-Eastern Norway Notodden Norway.
Ecology and Evolution
|May 14, 2026
Summary
Estimating evolutionary step variances from fossil data is challenging due to measurement errors. Generalized least squares (GLS) provides a robust method for inferring directional evolution, especially with significant data uncertainties.
Area of Science:
- Paleontology
- Evolutionary Biology
- Statistical Modeling
Background:
- The general random walk (GRW) model is used to infer directional evolution in mean trait values from sparse fossil data.
- Estimating step variances in the GRW model is difficult, especially with realistic measurement errors in fossil data.
Purpose of the Study:
- To investigate the challenges in estimating step variances within the GRW model for fossil data.
- To compare the performance of GRW with generalized least squares (GLS) for inferring directional evolution.
Main Methods:
- Simulations were conducted to assess the estimation of mean step sizes and step variances.
- Four real fossil data cases were analyzed.
- Weighted mean square error (WMSE) was used for comparison.
Main Results:
- Mean step sizes are generally easier to estimate than step variances.
- Step variance estimation is unreliable with realistic measurement errors, often yielding negative values that must be set to zero.
- GRW with zeroed step variances can lead to under- or overestimation of directional evolution compared to GLS.
Conclusions:
- Generalized least squares (GLS) is the preferred method for inferring directional evolution, particularly in cases with large measurement errors.
- When step variances are set to zero, GLS simplifies to weighted least squares (WLS).
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