Ecological diffusion models are still useful in ecology

Context

Connecting animal movement across scales—both among spatial scales and between individual and population level processes—is a central theme in ecology, including the sub-fields of movement and landscape ecology. However, most modeling frameworks operate at either the individual (Lagrangian) or population (Eulerian) level.

Objectives

We aimed to review how a partial differential equation (PDE) known as the ecological diffusion equation (EDE) offers connections among the scales of animal movement and how it can be embedded in commonly used statistical frameworks (e.g., hierarchical models) and fit to multiple types of data, such as count, presence-only, presence-absence, and telemetry data. In doing so, we also highlight emerging and promising avenues of research related to statistical EDE models.

Methods

We present how the EDE is derived from a simple set of first principles, can be used to represent both individual animal movement and spatiotemporal population dynamics, and can be fit to data by being applied in a hierarchical statistical framework. Finally, we review literature on recent applications and advances related to EDE models.

Results

In presenting the derivation of the EDE and reviewing recent advances and applications of EDE models, we established that the EDE can enable a mechanistic understanding of animal movement across scales, as well as the integration of multiple types of data. We also identified a number of topics where EDE models can be advanced to gain additional ecological insight.

Conclusions

Ecological diffusion is a process that emerges naturally from first principles governing animal movement and can be used to model both individual and population-level spatiotemporal dynamics. Statistical EDE models are related to other modeling frameworks, such as species distribution models, occupancy models, and step-selection analysis. The flexibility of hierarchical statistical modeling allows combining different types of data collected on movement and population dynamics, and the theoretical underpinnings of the EDE allow it to connect ecological processes occurring at fine and coarse spatial scales, as well as individual animal movement and population dynamics.