Correcting Nesting-Success Estimates for Observer Effects: Maximum-Likelihood Estimates of Daily Survival Rates With Reduced Bias

Abstract

AbstractWe develop a statistical method that simultaneously estimates daily survival rate and observer effect. We used Monte Carlo simulation to (1) evaluate the performance of the model, (2) compare model performance with models that ignore observer effects, and (3) evaluate methods of choosing between competing models of survival. When observer effects were absent, all models produced unbiased estimates of daily survival rate. In the presence of observer effects, however, models that ignore these effects underestimated daily survival rate. In such cases, estimates of nesting success were strongly affected even when observer effects were relatively small. In contrast, estimates of daily survival rate and nesting success produced by the model that considers observer effects consistently had little bias. However, estimates of daily survival rate from this model were less precise than those from the simpler model. Objective criteria for choosing between competing models did not perform well with sample sizes of 150 to 600 because subtle but important observer effects are difficult to detect. Likelihood-ratio tests had low power for rejecting the null hypothesis of no observer effect over a wide range of levels of observer effect and with sample sizes of 150 to 600. Estimates of daily survival rate from models selected based on Akaike's Information Criterion (AIC) had higher bias than estimates from the model that estimates observer effect when observer effect was present. Estimates from AIC-selected models had lower mean squared error than estimates from the model that estimates observer effect when observer effects were small, but the pattern reversed as effects increased. We recommend that researchers estimate observer effects using the more complex model when observer effects are possible and decide whether to use estimates of daily survival from the simpler or more complex model based on analysis results and simulation or analytic results for relevant sample sizes, daily survival rates, and observer effects. To illustrate use of the analytical techniques, we analyzed field data from Dusky Flycatcher (Empidonax oberholseri) nests monitored during the nestling stage. The observer effect was estimated to be 1.003 (95% CI 0.866 to 1.162); thus, point estimates of daily survival were very similar from the simpler (0.971; 95% CI 0.957 to 0.985) and more complex model (0.970; 95% CI 0.925 to 1.000). In this case, analysis results and simulation results indicate that the simpler model is adequate and provides an estimate of daily survival rate with small potential bias and increased precision compared with an estimate from the more complex model.