| Abstract: |
| The ecological dynamics between elk and wolves in northern Yellowstone
have been a focal point of long-term research, particularly following
the reintroduction of wolves to the region. Although numerous studies
have explored this prey-predator interaction from ecological and
behavioral perspectives, there remains a lack of comprehensive analysis
using mathematical modeling approaches capable of uncovering underlying
dynamical patterns and system-level insights. In this study, we
investigate the prey-predator dynamics of the elk--wolf system in
northern Yellowstone National Park, USA, using a data-driven modeling
approach. We used yearly population data for elk and wolves from 1995 to
2022 (28 years) to construct a mathematical model using a sparse
regression modeling framework. To the best of our knowledge, no previous
work has applied this framework to capture elk--wolf interactions over
this time period. Our modeling pipeline integrates Gaussian process
regression for data smoothing, sparse identification of nonlinear
dynamics for model discovery, and model selection techniques to identify
the most suitable mathematical representation. The resulting model is
analyzed for its non-linear dynamics with ecologically meaningful
parameters. |
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