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Inference for Size Demography from Point Pattern Data using Integral Projection Models.

Souparno Ghosh1, Alan E Gelfand, James S Clark

  • 1S. Ghosh ( sg147@stat.duke.edu ) is a post-doctoral researcher and A.E. Gelfand ( alan@stat.duke.edu ) is a professor in the Department of Statistical Science at Duke University. J. S. Clark ( jimclark@duke.edu ) is a professor in the Nicholas School of Environment at Duke University.

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Summary
This summary is machine-generated.

This study introduces a new method for integral projection models (IPMs) to better project population trait distributions over time. By fitting models to population-level data, it improves accuracy compared to individual-level fitting.

Keywords:
Fourier transformLaplace approximationdensity dependencehierarchical modelintegro-difference equationnonhomogeneous Poisson processspectral domain

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Area of Science:

  • Ecology and Evolutionary Biology
  • Mathematical Biology
  • Population Genetics

Background:

  • Population dynamics and trait evolution are often studied using matrix projection models (MPMs) and integral projection models (IPMs).
  • Current IPM fitting relies on individual-level transition data, which can create a scale mismatch when projecting population-level trait distributions over time.
  • This mismatch hinders the alignment of projected distributions with observed temporal population benchmarks.

Purpose of the Study:

  • To address the scale mismatch in integral projection models (IPMs) by developing a novel fitting approach.
  • To improve the projection accuracy of population trait distributions, specifically focusing on size distributions.
  • To provide a method that aligns model projections with observed temporal population data.

Main Methods:

  • A three-stage hierarchical Bayesian model was developed to infer dynamic intensities from observed population size distributions viewed as point patterns.
  • The model incorporates a latent deterministic IPM, introducing uncertainty through variations in the operating IPM and point pattern realization.
  • Approximate Bayesian inference strategies were employed to manage computational challenges associated with exact fitting.

Main Results:

  • The proposed method effectively models population-level redistribution dynamics, providing mechanistic insights at the appropriate scale.
  • Fitting the model to temporal population data optimizes dynamic modeling for improved projection capabilities.
  • Illustrative examples with simulated and real tree growth data (Duke Forest, NC) demonstrate the approach's benefits over individual-level fitting.

Conclusions:

  • The developed hierarchical Bayesian approach offers a more mechanistically appropriate and accurate method for fitting and projecting IPMs.
  • This approach resolves the scale mismatch issue inherent in traditional individual-level fitting of IPMs.
  • The optimized dynamic modeling, fitted to temporal data, significantly enhances projection accuracy for population trait distributions.