Finding confidence limits on population growth rates: bootstrap and analytic methods.

Area of Science:

• Ecology
• Population Dynamics
• Mathematical Biology

Background:

• Population dynamics are often predicted using matrix models, which rely on vital rates.
• Accurate predictions necessitate confidence intervals that encompass all error sources, from observations to model parameters and predictions.
• Understanding the impact of observational variability on vital rates and subsequent predictions is crucial.

Purpose of the Study:

• To assess how observation variability affects vital rates and population model predictions.
• To compare three distinct methods for calculating confidence intervals for matrix model predictions.
• To evaluate the reliability of these methods for ecological forecasting.

Main Methods:

• Employed Usher matrix models to predict the asymptotic stock recovery rate for three timber species.
• Utilized bootstrap methods to estimate standard errors of vital rates.
• Applied an analytic method approximating standard errors using asymptotic variance.
• Developed a hybrid method combining bootstrap and analytic approaches for prediction error estimation.

Main Results:

• Little difference was observed between the hybrid and analytic methods for confidence interval calculation.
• Both hybrid and analytic methods' bias and standard error estimates converged with bootstrap estimates as vital rate errors decreased.
• Sufficient data (over 5000 observations) minimized vital rate errors, aligning analytic/hybrid results with bootstrap.

Conclusions:

• Analytic and hybrid methods provide reliable confidence intervals for population predictions, comparable to bootstrap.
• The accuracy of these methods improves with larger sample sizes, reducing observational error.
• Confidence intervals are essential for robust population dynamics forecasting in ecological studies.