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.     

Biomass partitioning of benthic microbes in a Baltic inlet: relationships between bacteria, algae, heterotrophic flagellates and ciliates

 The structure of a benthic microbial food web and its seasonal changes were studied in the shallow brackish waters of the island of Hiddensee, northeastern Germany, at two sites in close proximity by monthly or bimonthly sampling from July 1995 to June 1996. Abundance and biomass of phototrophic and non-phototrophic bacteria, heterotrophic flagellates (HF) and ciliates as well as the biomass of microphytobenthos were determined in the upper 0.3 cm sediment layer. Abundance of organisms showed strong positive correlation with water temperature, with the exception of the bacteria. Non-phototrophic bacterial numbers ranged from 7 × 10⁸ to 6.7 × 10⁹ cells cm⁻³ and phototrophic bacterial abundance from 4 × 10⁷ to 2.7 × 10⁸. Heterotrophic protist abundance ranged from 8 × 10³ to 104 × 10³ ind cm⁻³ for HF and from 39 to 747 ind cm⁻³ for ciliates. The biomass partitioning demonstrated the primary importance of non-phototrophic bacteria (min. 0.83, max. 84.87 μg C cm⁻³), followed by the microphytobenthos (min. 1.32, max. 50.93 μg C cm⁻³). The heterotrophic protists contributed roughly the same fraction to the total microbial biomass, with the biomass of the HF being slightly higher (HF 0.23 to 1.76 μg C cm⁻³, ciliates 0.04 to 1.17 μg C cm⁻³). Taxonomic classification of the benthic HF revealed the euglenids to be the most important group in terms of abundance and biomass, followed by thaumatomastigids and kinetoplastids. Other important groups were apusomonads, cercomonads, pedinellids and cryptomonads. The structure of the HF assemblage showed strong seasonal changes with euglenids being the most abundant taxa in summer, while apusomonads and thaumatomastigids were predominant in winter. Similar to the pelagic microbial food web, benthic picophototrophic bacteria were occasionally abundant, and the feeding modes of heterotrophic protists exhibited a great variety (predominantly omnivores, bacterivores, herbivores or predators). Filter-feeding HF were of little importance. Contrary to the pelagic environment, a top-down control on total benthic bacterial numbers by HF seemed unlikely at the studied stations which were characterised by muddy sand. Received: 6 January 1999 / Accepted: 21 October 1999     

Esterase heterogeneity and an investigation into racial differences in the cirripede Balanus balanoides using acrylamide gel electrophoresis

Four groups of bands showing esterase activity were found after electrophoretic separation of extracts of Balanus balanoides (L.) prosoma on polyacrylamide gels. Each group was distinguishable from other groups by mobility, reaction with specific substrates, and susceptibility to various inhibitors. Groups designated BbEII and BbEIII showed cholinesterase activity, BbEIV showed carboxylesterase activity, and BbEI possible arylesterase activity. Polymorphisms were found within Groups BbEIII and BbEI. The frequency distribution of BbEIV polymorphs in a sample from the Menai Straits, UK, fitted the Hardy-Weinberg predicted values for 4 co-dominant alleles. A sample from St. Andrews, New Brunswick, Canada, however, did not fit the Hardy-Weinberg prediction. No variation between individuals was found when malate dehydrogenase (MDH) and lactate dehydrogenase (LDH) isozymes were examined. Hence, these systems are unsuitable for testing racial differences. The results for the cholinesterase and arylesterase isozymes substantiate the view, originally based on differences in reproductive phenology and egg size, that genetically separate races exist on either side of the Atlantic Ocean.     

Mitochondrial gene variation in Mercenaria clam sibling species reveals a relict secondary contact zone in the western Gulf of Mexico

We investigated phylogeographic relationships among American Mercenaria taxa by assessing variation in a 444 nucleotide fragment of the mitochondrial 16S ribosomal gene in clams sampled from four representative sites in January to November 1994. Three of these sites were in the Gulf of Mexico, one was on the Atlantic coast in South Carolina. Direct sequencing of this amplified gene fragment in 85 individuals revealed 21 haplotypes. Phylogenetic analyses consistently resolved this variation into three well supported clades, and within-clade genetic divergence levels were markedly lower than among-clade values. One of the clades, A, was taxon-specific, in that it solely and exclusively contained specimens of M. mercenaria (Linnaeus, 1758) sampled in South Carolina. The other two clades, B and C, were the most divergent and both encompassed specimens of M. campechiensis (Gmelin, 1791) and of M. campechiensis texana (Dall, 1902), sampled from the three Gulf of Mexico sites. Clade B was found at high frequencies at all three Gulf sites, whereas Clade C occurred at low frequencies at two western Gulf sites. We interpret this pattern as resulting from the secondary contact and introgression of two allopatrically differentiated Mercenaria taxa in the western Gulf of Mexico. Clade C haplotypes may represent relict mitochondrial lineages from original Gulf Mercenaria spp. populations that predate massive mitochondrial introgression by M. campechiensis. We further propose that the M. campechiensis texana nuclear genome is a mosaic, heavily weighted toward M. campechiensis, but containing some relict alleles inherited from the precontact population, especially those governing shell characteristics, which may be adaptive in cohesive sediments of bays and estuaries in the northwestern Gulf of Mexico.