Black swans in space: modeling spatiotemporal processes with extremes.

Area of Science:

• Ecology
• Ecological modeling
• Spatial statistics

Background:

• Ecological systems experience extreme events in time (e.g., population crashes) and space (e.g., range contractions).
• Existing spatiotemporal models may struggle with joint inference when extreme events occur.
• Accurate modeling of spatiotemporal extremes is crucial for understanding ecological dynamics.

Purpose of the Study:

• To develop a novel statistical model capable of handling simultaneous temporal and spatial extremes in ecological data.
• To assess the performance of the new model against traditional methods using simulated and real-world data.
• To provide an accessible R package for implementing advanced spatiotemporal generalized linear mixed-effects models (GLMMs).

Main Methods:

• A Bayesian predictive-process GLMM framework was employed.
• A multivariate-t distribution was utilized to model spatial random effects, allowing for extremes.
• The model was implemented in the R package 'glmmfields' for practical application.

Main Results:

• The new model successfully recaptured simulated spatiotemporal extremes and highlighted the limitations of models that ignore them.
• Predictions of mountain pine beetle-induced tree mortality in the Pacific Northwest were more accurate and precise compared to traditional models.
• The 'glmmfields' R package facilitates the application of these advanced models.

Conclusions:

• The developed Bayesian GLMM with a multivariate-t distribution effectively models simultaneous spatiotemporal extremes in ecological systems.
• This approach offers improved predictive accuracy for ecological processes influenced by extreme events.
• The 'glmmfields' package democratizes access to sophisticated spatiotemporal modeling techniques for researchers.