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

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Abstract
Repeat measurement surveys of tree size are used in forests to estimate growth behaviour, 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. We 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. To 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 the root mean squared error (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 fourth 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. Overall, 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.

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