A Bayesian multinomial logistic exposure model for estimating probabilities of competing sources of nest failure

Abstract

Understanding causes of nest loss is critical for the management of endangered bird populations. Available methods for estimating nest loss probabilities to competing sources do not allow for random effects and covariation among sources, and there are few data simulation methods or goodness-of-fit (GOF) tests for such models. We developed a Bayesian multinomial extension of the widely used logistic exposure (LE) nest survival model which can incorporate multiple random effects and fixed-effect covariates for each nest loss category. We investigated the performance of this model and the accompanying GOF test by analysing simulated nest fate datasets with and without age-biased discovery probability, and by comparing the estimates with those of traditional fixed-effects estimators. We then exemplify the use of the multinomial LE model and GOF test by analysing Piping Plover Charadrius melodus nest fate data (n = 443) to explore the effects of wire cages (exclosures) constructed around nests, which are used to protect nests from predation but can lead to increased nest abandonment rates. Mean parameter estimates of the randomeffects multinomial LE model were all within 1 sd of the true values used to simulate the datasets. Age-biased discovery probability did not result in biased parameter estimates. Traditional fixed-effects models provided estimates with a high bias of up to 43% with a mean of 71% smaller standard deviations. The GOF test identified models that were a poor fit to the simulated data. For the Piping Plover dataset, the fixed-effects model was less well-supported than the random-effects model and underestimated the risk of exclosure use by 16%. The random-effects model estimated a range of 1-6% probability of abandonment for nests not protected by exclosures across sites and 5-41% probability of abandonment for nests with exclosures, suggesting that the magnitude of exclosure-related abandonment is site-specific. Our results demonstrate that unmodelled heterogeneity can result in biased estimates potentially leading to incorrect management recommendations. The Bayesian multinomial LE model offers a flexible method of incorporating random effects into an analysis of nest failure and is robust to age-biased nest discovery probability. This model can be generalized to other staggered-entry, time-to-hazard situations.

Life‐history tradeoffs revealed by seasonal declines in reproductive traits of Arctic‐breeding shorebirds

“…We expanded the Bayesian DSR model to explicitly estimate cause-specific rates of nest failure so that we could test for seasonality in competing risks as well as DSR. We followed the conceptual approach of a risk-partitioning nest survival model previously developed in a maximum-likelihood framework (Etterson et al 2007), which has recently been demonstrated in a Bayesian framework that allows the inclusion of random effects (Darrah et al 2017). Our model differed from that of Darrah et al (2017) in that we used a DSR model rather than a logistic-exposure model.…”

“…We followed the conceptual approach of a risk-partitioning nest survival model previously developed in a maximum-likelihood framework (Etterson et al 2007), which has recently been demonstrated in a Bayesian framework that allows the inclusion of random effects (Darrah et al 2017). Our model differed from that of Darrah et al (2017) in that we used a DSR model rather than a logistic-exposure model. Unlike Etterson et al (2007) and Darrah et al (2017), we also assessed the probability of each risk as conditional on failure; that is, the survival process was evaluated first (whether the nest survived or failed), and for nests that failed, the probability of each cause of failure was then evaluated.…”

“…Our model differed from that of Darrah et al (2017) in that we used a DSR model rather than a logistic-exposure model. Unlike Etterson et al (2007) and Darrah et al (2017), we also assessed the probability of each risk as conditional on failure; that is, the survival process was evaluated first (whether the nest survived or failed), and for nests that failed, the probability of each cause of failure was then evaluated. Our approach allowed us to assess whether a covariate had an effect on the overall survival rate (survived versus failed) as well as whether any covariate of interest affected each competing risk for nests that failed (depredated versus abandoned versus failed to other causes).…”

Exclosure fences around nests of imperiled Florida Grasshopper Sparrows reduce rates of predation by mammals

“…We tested the effect of fences, cameras, and ordinal date of nest visit on nest fates (species pooled) at Three Lakes (2015–2018) by constructing a Bayesian multinomial logistic exposure model (Darrah et al. ). This allows simultaneous modeling of multiple sources of nest failure using a unique set of covariates for each response level.…”

Video documentation of predators and nest defense at Bachman’s Sparrow nests

“…We used a Bayesian formulation of a logistic-exposure, multinomial nest mortality model to estimate daily survival for all nests, as well as daily probability of mortality from different predator types (Darrah et al 2018). We chose to present multinomial nest mortality rates because they can be compared across studies to infer larger scale patterns, which is a limitation of presenting only counts.…”