Evaluating Dependence Among Mule Deer Siblings in Fetal and Neonatal Survival Analyses

Abstract

: The assumption of independent sample units is potentially violated in survival analyses where siblings comprise a high proportion of the sample. Violation of the independence assumption causes sample data to be overdispersed relative to a binomial model, which leads to underestimates of sampling variances. A variance inflation factor, c, is therefore required to obtain appropriate estimates of variances. We evaluated overdispersion in fetal and neonatal mule deer (Odocoileus hemionus) datasets where more than half of the sample units were comprised of siblings. We developed a likelihood function for estimating fetal survival when the fates of some fetuses are unknown, and we used several variations of the binomial model to estimate neonatal survival. We compared theoretical variance estimates obtained from these analyses with empirical variance estimates obtained from data‐bootstrap analyses to estimate the overdispersion parameter, c. Our estimates of c for fetal survival ranged from 0.678 to 1.118, which indicate little to no evidence of overdispersion. For neonatal survival, 3 different models indicated that ĉ ranged from 1.1 to 1.4 and averaged 1.24–1.26, providing evidence of limited overdispersion (i.e., limited sibling dependence). Our results indicate that fates of sibling mule deer fetuses and neonates may often be independent even though they have the same dam. Predation tends to act independently on sibling neonates because of dam‐neonate behavioral adaptations. The effect of maternal characteristics on sibling fate dependence is less straightforward and may vary by circumstance. We recommend that future neonatal survival studies incorporate additional sampling intensity to accommodate modest overdispersion (i.e., ĉ = 1.25), which would facilitate a corresponding ĉ adjustment in a model selection analysis using quasi‐likelihood without a reduction in power. Our computational approach could be used to evaluate sample unit dependence in other studies where fates of individually marked siblings are monitored.

Declining recruitment of Gunnison Sage-Grouse highlights the need to monitor juvenile survival

“…We followed methodologies described by Bishop et al (2008) and implemented in Program MARK (White and Burnham 1999). Each bootstrap analysis consisted of 2,000 replicates.…”

“…Burnham and Anderson (2002) suggest that estimates of the overdispersion parameter (ĉ) that are just above 1.0 show only slight overdispersion and that judgment should be used for interpretation. We interpreted estimates ofĉ , 1.2 to indicate weak support for overdispersion in the chick survival and juvenile survival analyses (Bishop et al 2008). If the resultingĉ estimate was above the cutoff of 1.2, then the estimatedĉ was incorporated into Program MARK and model estimates were compared using Quasi-Akaike's Information Criterion (QAIC c ; Burnham and Anderson 2002).…”

Differential investment in twin offspring by female pronghorns (Antilocapra americana)

“…The explanation for this difference is obscure, but it may be related to the temporal pattern of mortality in twin littermates. In ungulates, neonatal co-twins often are both killed at the same predation event, but sometimes survival of co-twins is substantially independent (Bishop et al 2008;Panzacchi et al 2009;Testa et al 2000). Our results indicate that most mortality events involved only 1 co-twin, and the few sameday events were concentrated in the 1st few days after birth.…”

An experimental study of fledging success in American Coots (Fulica americana): Effects of brood size, food availability, and hatching asynchrony

“…I ran this global model 1,000 times. sampling entire broods with replacement to achieve sample sizes of 99 broods for each analysis (Bishop et al 2008). 1 retained estimates of real parameters (i.e., five estimates each of age-specific resighting and survival probabilities) and calculated SD over 1,000 simulations.…”

“…1 retained estimates of real parameters (i.e., five estimates each of age-specific resighting and survival probabilities) and calculated SD over 1,000 simulations. I estimated overdispersion (c) for each parameter as the ratio of the empirical variance versus the theoretical variance (SD^:SE^; Bishop et al 2008). This provided an estimate of overdispersion (c ± SE= 1.90 ± 0.20, range: 0.93-2.91), which 1 used to adjust model rankings by use of QAIC^ and to inflate standard errors (Burnham and Anderson 2002).…”