Learning from monitoring networks: Few-large vs. many-small plots and multi-scale analysis

Abstract

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In order to learn about broad scale ecological patterns, data from large-scale surveys must allow us to either estimate the correlations between the environment and an outcome and/or accurately predict ecological patterns. An important part of data collection is the sampling effort used to collect observations, which we decompose into two quantities: the number of observations or plots (n) and the per-observation/plot effort (E; e.g., area per plot). If we want to understand the relationships between predictors and a response variable, then lower model parameter uncertainty is desirable. If the goal is to predict a response variable, then lower prediction error is preferable. We aim to learn if and when aggregating data can help attain these goals. We find that a small sample size coupled with large observation effort coupled (few large) can yield better predictions when compared to a large number of observations with low observation effort (many small). We also show that the combination of the two values (n and E), rather than one alone, has an impact on parameter uncertainty. In an application to Forest Inventory and Analysis (FIA) data, we model the tree density of selected species at various amounts of aggregation using linear regression in order to compare the findings from simulated data to real data. The application supports the theoretical findings that increasing observational effort through aggregation can lead to improved predictions, conditional on the thoughtful aggregation of the observational plots. In particular, aggregations over extremely large and variable covariate space may lead to poor prediction and high parameter uncertainty. Analyses of large-range data can improve with aggregation, with implications for both model evaluation and sampling design: testing model prediction accuracy without an underlying knowledge of the datasets and the scale at which predictor variables operate can obscure meaningful results.

Keywords

• aggregation
• clustering
• Forest Inventory and Analysis (FIA)
• parameter uncertainty
• prediction performance
• sample design