Uncovering state-dependent relationships in shallow lakes using Bayesian latent variable regression.

Area of Science:

• Ecology
• Environmental Science
• Statistical Modeling

Background:

• Ecosystems can exhibit alternative stable states, such as clear or turbid shallow lakes.
• Identifying critical thresholds is crucial for effective ecosystem management.
• Previous methods lacked the ability to simultaneously classify states and estimate thresholds.

Purpose of the Study:

• To develop an integrated framework for classifying ecosystem states and identifying critical thresholds.
• To estimate state-dependent relationships between driving variables and key system features.
• To provide tools for managers to prioritize ecosystems for rehabilitation.

Main Methods:

• Bayesian latent variable regression (BLR) was developed to classify lake states and estimate total phosphorus (TP) thresholds.
• The framework was evaluated using simulated data from a stochastic differential equation model and compared to k-means clustering with regression (KMR).
• The BLR model was applied to cross-sectional data from 130 shallow lakes over three years.

Main Results:

• BLR demonstrated high state classification accuracy (>97%) and accurately estimated TP thresholds and TP-chlorophyll a (chl a) relationships for simulated data.
• BLR outperformed KMR in classification accuracy and threshold estimation.
• The framework successfully applied to empirical data, providing bifurcation diagrams for management prioritization.

Conclusions:

• The BLR framework offers a robust method for classifying ecosystem states and identifying critical thresholds in systems with alternative stable states.
• This approach improves upon existing methods by simultaneously classifying states and estimating thresholds, providing uncertainty estimates.
• The BLR framework is broadly applicable to other ecosystems exhibiting alternative stable states, aiding in effective environmental management and rehabilitation efforts.