Empirical likelihood confidence intervals for adaptive cluster sampling

Adaptive cluster sampling (ACS) is an efficient sampling design for estimating parameters of rare and clustered populations. It is widely used in ecological research. The modified Hansen-Hurwitz (HH) and Horvitz-Thompson (HT) estimators based on small samples under ACS have often highly skewed distributions. In such situations, confidence intervals based on traditional normal approximation can lead to unsatisfactory results, with poor coverage properties. Christman and Pontius (Biometrics 56:503–510, 2000) showed that bootstrap percentile methods are appropriate for constructing confidence intervals from the HH estimator. But Perez and Pontius (J Stat Comput Simul 76:755–764, 2006) showed that bootstrap confidence intervals from the HT estimator are even worse than the normal approximation confidence intervals. In this article, we consider two pseudo empirical likelihood functions under the ACS design. One leads to the HH estimator and the other leads to a HT type estimator known as the Hájek estimator. Based on these two empirical likelihood functions, we derive confidence intervals for the population mean. Using a simulation study, we show that the confidence intervals obtained from the first EL function perform as good as the bootstrap confidence intervals from the HH estimator but the confidence intervals obtained from the second EL function perform much better than the bootstrap confidence intervals from the HT estimator, in terms of coverage rate.     

Small queens in the ant Ectatomma tuberculatum: a new case of social parasitism

Social parasites exploit the worker force of colonies of other social insects to rear their own young. Social parasitism occurs in several Hymenoptera and is particularly common in several tribes of the ant subfamilies Myrmicinae and Formicinae. Here, we document the occurrence of miniaturized queens (microgynes) in colonies of Ectatomma tuberculatum, an ant belonging to the subfamily Ectatomminae. Behavioral observations and genetic analyses show that microgynes concentrate their reproductive efforts almost exclusively on the production of sexual offspring (microgynes and males), whereas the regular, large queens (macrogynes) produce workers in addition to sexuals. According to mitochondrial and nuclear markers, gene flow between microgynes and macrogynes is extremely limited. Whereas the co-occurrence of microgynes and macrogynes in the related species Ectatomma ruidum constitutes an intraspecific polymorphism associated with alternative dispersal tactics, microgynes found in colonies of E. tuberculatum appear to be a distinct species and to represent the first case of social parasitism in the poneromorph subfamilies of ants.