Warton, D. | Search bioRxiv

bioRxiv2025

hmde: Hierarchical Methods for Differential Equations

AbstractRepeat observations of size are a common tool for understanding growth across taxa, and are used to estimate parameters for functions that describe growth rates. Recent advances in estimating differential equation parameters with a hierarchical longitudinal model have gone beyond available software. Custom implementation of such models is a barrier to use particularly for people who are not familiar with statistical programming. We introduce a new R package implementing a hierarchical Bayesian longitudinal model for repeat observation data with three growth models from ecological case studies. The package provides tools for model fitting and estimate extraction, example data, and case studies to demonstrate the use-case for each of the example models.

bioinformatics↗

bioRxiv2024

Yes, they're all individuals: Hierarchical models for repeat survey data improve estimates of tree growth and size

AbstractO_LIRepeat measurement surveys of tree size are used in forests to estimate growth be-haviour, biomass, and population dynamics. Although size is measured with error, and individuals vary in their growth trajectories, current size-based growth modelling approaches do not usually or fully account for both of these features, and therefore under-utilise available data. C_LIO_LIWe present a new method that leverages the auto-correlation structure of repeat surveys into a hierarchical Bayesian longitudinal growth model. This new structure allows users to correct for measurement error and capture individual-level variation in growth trajectories and parameters. C_LIO_LITo demonstrate the new method we applied it to a sample of tropical tree survey data from long-term monitoring sites at Barro Colorado Island. We were able to reduce estimated error in size and growth, and extract individual-and population-level growth parameter estimates. We used simulation to evaluate the ability of the new method to improve estimates of growth rate and size, and estimate individual and species-level parameters. Our method substantially improved RMSE for growth by an average of 61% compared to existing approaches using pairwise differences; and reduced RMSE in estimated size RMSE compared to observed values in simulated data. Better numerical integration methods (Runge-Kutta 4th order in comparison to Euler and midpoint) provided better estimates of parameters, but did not improve the estimation of size and growth. The choice of a positive growth function eliminated all negative increments without data exclusion. C_LIO_LIOverall, this study shows how we can gain new and improved insights on growth, using repeat forest surveys. Our new method offers improved biomass dynamics estimation through reduced error in sizes over time, coupled with novel information about within-species variation in growth behaviour that is inaccessible with species average models, such as individual parameters for the growth function which allows for relationships between parameters to be considered for the first time. C_LI

ecology↗