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.     

Life history costs of olfactory status signalling in mice

Large body size confers a competitive advantage in animal contests but does not always determine the outcome. Here we explore the trade-off between short-term achievement of high social status and longer-term life history costs in animals which vary in competitive ability. Using laboratory mice, Mus musculus, as a model system, we show that small competitors can initially maintain dominance over larger males by increasing investment in olfactory status signalling (scent-marking), but only at the cost of reduced growth rate and body size. As a result they become more vulnerable to dominance reversals later in life. Our results also provide the first empirical information about life history costs of olfactory status signals. Received: 15 December 1999 / Revised: 6 June 2000 / Accepted: 24 June 2000     

Growth of plankton algae as a function of N-concentration,measured by means of batch technique

Employing a special batch technique which involves extremely low concentrations of the alga Selenastrum capricornutum, it is shown that a growth rate of ca. 75% of optimum growth occurs at a concentration of 0.02 g-at N(NH₄ ⁺) l^-1. The low concentrations of this N-source in the oligotrophic parts of the oceans (ca. 0.06 g-at l^-1) thus give rise to a borderline deficiency. As the half-saturation constant (K _S) for growth was recorded at 0.05 g-at N(NO₃ ^-), this ion can hardly be of much importance at the low concentrations present in these parts of the oceans. It is wrong to assert that N is the primary limiting nutrient. Phosphate also is found at concentrations giving rise to a borderline deficiency.