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Likelihood ridges and multimodality in population growth rate models.
Leo Polansky1, Perry de Valpine, James O Lloyd-Smith
1Department of Environmental Science, Policy, and Management, University of California, 137 Mulford Hall, Berkeley, California 94720-3112, USA. leop@nature.berkeley.edu
Ecology
|September 11, 2009
Summary
Estimating density dependence in population ecology can create complex likelihood surfaces. Analyzing these surfaces, not just best-fit models, is crucial for robust biological interpretation.
Area of Science:
- Ecology
- Population Dynamics
- Statistical Modeling
Background:
- Estimating density dependence from time series data is a core challenge in population ecology.
- Phenomenological models like the theta-Ricker are commonly used for this purpose.
Purpose of the Study:
- To investigate the emergence of multimodality and ridges in likelihood surfaces during density dependence modeling.
- To provide guidance on interpreting complex likelihood surfaces for ecological data analysis.
Main Methods:
- Theoretical analysis and simulations using the theta-Ricker model.
- Fitting parametric and state-space models to ecological time series data.
- Detailed examination of likelihood surfaces, including ridges and multimodality.
Main Results:
- Multimodality and ridges can arise in likelihood surfaces even without model misspecification or observation error.
- Best-fit models for analyzed data were often biologically questionable outside the data range.
- Likelihood ratio confidence regions revealed a range of plausible alternative models.
Conclusions:
- Thorough examination of likelihood surfaces is essential for robust statistical analysis and biological interpretation in population ecology.
- Understanding likelihood surface features is critical for both frequentist and Bayesian approaches.
- Moving beyond single best-fit models enhances ecological inference.
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