Evaluation of modeling strategies for assessing self-thinning behavior and carrying capacity.

Christian Salas‐Eljatib,Aaron R Weiskittel

doi:10.1002/ece3.4525

Christian Salas‐Eljatib, Aaron R Weiskittel

Open Access

https://doi.org/10.1002/ece3.4525

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Abstract

Self‐thinning and site maximum carrying capacity are key concepts for understanding and predicting ecosystem dynamics as they represent the outcome of several fundamental ecological processes (e.g., mortality and growth). Relationships are often derived using alternative modeling strategies, depending on the statistical approach, model formulation, and underlying data with unclear implications of these various assumptions. In this analysis, the influence of contrasting modeling strategies for estimating the self‐thinning relationship and maximum carrying capacity in long‐term, permanent plot data (n = 130) from the mixed Nothofagus forests in southern Chile was assessed and compared. Seven contrasting modeling strategies were used including ordinary least squares, quantile, and nonlinear regression that were formulated based on static (no remeasurements) or dynamic data (with remeasurements). Statistically distinct differences among these seven approaches were identified with mean maximum carrying capacity ranging from 1,050 to 1,912 stems/ha depending on the approach. The population‐level static approach based on quantile regression produced an estimate closest to the overall mean with site‐level carrying capacity depending on tree species diversity and climate. Synthesis and applications. Overall, the findings highlight strong variability within and between contrasting methods of determining self‐thinning and site maximum carry capacity, which may influence ecological inferences.

Highlights

Size–density relationships are essential for understanding and predicting core ecological processes
Defining this frontier relationship is difficult and, it has been derived using a variety of different approaches that depend upon the statistical approach, model formulation being used, and the actual data source
Where: SDImaxi is the predicted maximum stand density index at the i-plot; Xi is the predictor variables matrix at the i-plot; f() is a linear or non-lineal function; is a parameter vector of the model; ei is the random error term that follows a Gaussian distribution with zero mean and variance e2

Summary

| INTRODUCTION

Construction of maximum size–density relationships provides a basis for quantifying the ecological concepts of self-thinning and carrying capacity Defining this frontier relationship is difficult and, it has been derived using a variety of different approaches that depend upon the statistical approach, model formulation being used, and the actual data source. Weiskittel et al, (2009) used static data and SFR for estimating the self-thinning boundary line in different forest types in the Pacific Northwest, USA They found that site productivity and the proportion of basal area of the primary species being modeled were important predictor variables for the size–density relationship. We aimed to: (a) develop alternative strategies for constructing the maximum size– density relationship that explicitly account for hierarchical data; (b) compare implied estimates of site-level maximum carrying capacity;. (c) relate observed carrying capacity to various site-level and environmental variables

| METHODS

Findings

| DISCUSSION

| CONCLUDING REMARKS