Integral Projection Models: Simulation Studies and Sensitivity Analyses
Integral projection model (IPM) is an important tool to study population dynamics and demography in ecology. Traditional IPMs are handled first with a fitting stage at individual-level transitions, then with a projection stage at population-level distributions. Here we adopt a new IPM framework that coherently focusing on population-level size distributions using point pattern theory.
We conduct simulation studies and sensitivity analyses to explore the properties of this new IPM framework. Under certain settings of demographic functions and parameters, we conduct two simulation studies by deterministically projecting population dynamics and stochastically generating point patterns. Assuming stationarity at equilibrium state, we then derive analytical solutions for the sensitivity of stable stage size distribution to kernel demographic parameters. We implement the sensitivity analyses to the two simulation studies. Demography, population dynamics, prior vs. posterior parameters, and sensitivities are compared among parameter settings and simulations.
For two simulation studies, we find that parameter recovery is challenging except under tight priors, suggesting possible parameter identification problems. Issues could somewhat be resolved by sensitivity analyses, which identify parameters that are most sensitive to the stable stage size distributions. In summary, we find population-level only data may be limited to infer demography, and we will integrate both individual- and population-level data in the future.
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