Confidence intervals for the mean of the delta-lognormal distribution

Data that are skewed and contain a relatively high proportion of zeros can often be modelled using a delta-lognormal distribution. We consider three methods of calculating a 95% confidence interval for the mean of this distribution, and use simulation to compare the methods, across a range of realistic scenarios. The best method, in terms of coverage, is that based on the profile-likelihood. This gives error rates that are within 1% (lower limit) or 3% (upper limit) of the nominal level, unless the sample size is small and the level of skewness is moderate to high. Our results will also apply to the delta-lognormal linear model, when we wish to calculate a confidence interval for the expected value of the response variable, given the value of one or more explanatory variables. We illustrate the three methods using data on red cod densities, taken from a fisheries trawl survey in New Zealand.

Effects of water-body characteristics other than temperature and salinity on respiration in Euphausia pacifica

Ample evidence exists that many planktonic species are limited in their distribution to a given water mass. It has been suggested that the temperature-salinity values which define a given water mass are in themselves limiting these species' distribution. Other workers have suggested that other unique properties of a water mass may be involved. Euphausia pacifica is distributed throughout the Pacific subarctic water mass; its distribution also extends into British Columbia coastal waters. Experiments have shown that E. pacifica can withstand temperature changes of up to 15 C°; it can also withstand salinity changes of up to 10. Coastal E. pacifica appear to be able to better withstand stress from changes in temperature and salinity in water from some sources than in water from others. These differences are thought to result from differences in the past history of the water in question.Contribution No. 75008 from the Bigelow Laboratory for Ocean Sciences.     

Misspecification of within-area exposure distribution in ecological Poisson models

Ecological studies enable investigation of geographic variations in exposure to environmental variables, across groups, in relation to health outcomes measured on a geographic scale. Such studies are subject to ecological biases, including pure specification bias which arises when a nonlinear individual exposure-risk model is assumed to apply at the area level. Introduction of the within-area variance of exposure should induce a marked reduction in this source of ecological bias. Assuming several measurements per area of exposure and no confounding risk factors, we study the model including the within-area exposure variability when Gaussian within-area exposure distribution is assumed. The robustness is assessed when the within-area exposure distribution is misspecified. Two underlying exposure distributions are studied: the Gamma distribution and an unimodal mixture of two Gaussian distributions. In case of strong ecological association, this model can reduce the bias and improve the precision of the individual parameter estimates when the within-area exposure means and variances are correlated. These different models are applied to analyze the ecological association between radon concentration and childhood acute leukemia in France.

Delayed recovery of giant kelp near its southern range limit in the North Pacific following El Niño

The northern distribution limit of giant kelp, Macrocystis pyrifera (Agardh), along the Pacific coast of North America is relatively stable near Point Año Nuevo, California, but its southern limit has varied over hundreds of kilometers along the Baja California peninsula during the past 20 years. The factors that drive this variability in the southern limit were examined by: (1) quantifying the abundances of M. pyrifera and the subsurface stipitate kelp, Eisenia arborea (Areschoug), near M. pyriferas then southern limit at Punta San Roque (27°15N; 114°42W) on ten occasions between August 1997 and June 2002 (prior to and following the 1997/1998 El Niño Southern Oscillation); (2) initiating a field manipulation at Punta San Roque in June 2000 to examine competition between these two kelp species; and (3) surveying 20 additional sites near Punta San Hipólito (27°01N; 114°00W) in June 2002 to determine whether M. pyrifera populations had recovered to their pre-1982/1983 El Niño southern range limit after ~20 years of absence. These observations and the experimental results suggest that M. pyrifera is removed from its southern limit by the high temperatures and large waves associated with El Niños, while E. arborea is able to survive and recruit in high densities and thereby delay or even prevent M. pyriferas recovery. An inverse relationship was observed between these two species over the 5-year study. The field experiment showed that at both 4 months and 1 year after areas occupied by E. arborea were cleared, substantial recruitment of M. pyrifera occurred, while recruitment was negligible in uncleared areas. This study suggests that the southern range limit of M. pyrifera is determined by increased mortality and recruitment failure following the warm temperatures and low nutrient conditions associated with El Niños, limited substrate availability, and by competition with the more persistent populations of E. arborea.Communicated by J.P. Grassle, New Brunswick     

Photosynthetic acclimation and biochemical responses ofGelidium sesquipedale cultured in chemostats under different qualities of light

The red algaGelidium sesquipedale (Clem.) Born. et Thur. has been cultured in chemostats to assess the effects of light quality and photon-fluence rate (PFR) on growth, photosynthesis and biochemical composition. Plants under blue and red light (BL and RL) showed higher growth rates than under white light (WL) of the same PFR (40 mol m^–2 s^–1). The light-saturated rate of photosynthesis was higher for algae grown under BL and RL than for algae grown under WL. When algae were transferred to WL of moderate PFR (100 mol m^–2 s^–1), the light-saturated rate of photosynthesis decreased, being higher in previously RL-grown algae than in previously BL- and WL-grown algae. The initial slope of photosynthesis-irradiance (PI) curves () was affected by PFR but not by light quality. Pigment content was little affected by light quality. Light-quality treatments also affected the biochemical composition of the alga; previous exposure to various light treatments activate or repress several metabolical pathways that are fully expressed in the subsequent phase of WL of moderate PFR. Thus, phycobiliproteins and soluble proteins increased for previously BL- and RL-grown algae, whereas insoluble carbohydrate concentration was reduced, indicating a change of the C-partitioning between carbon compounds and organic nitrogen compounds. Inorganic nitrogen metabolism was also affected by light: under WL of moderate PFR, NO₃ ^– was totally depleted from sea water, and maximal values of NO₃ ^– uptake were recorded. In addition, neither NO₂ ^– nor NH₄ ⁺ was released. However, when algae were transferred to a low PFR, there was a drastic reduction of NO₃ ^– uptake under WL, which only partially recovered over time. It was accompanied by the release of NO₂ ^–, but not NH₄ ⁺, to the culture medium. Under BL and RL, however, there was a transient enhancement of NO₃ ^– uptake that was followed by a net release of NO₂ ^– and NH₄ ^–. Growth rates were not correlated with PFR. This could be due to the the dynamics of internal carbon mobilization and accumulation in the algae. When algae were exposed to a moderate PFR of WL, carbon requirements for growth were satisfied by photosynthesis. Thus, there was a net accumulation of carbon in the tissue. In contrast, when algae were exposed to low PFRs of either WL, BL or RL, observed growth rates could not be maintained by photosynthesis and carbon was mobilized.     

A Geochemical Survey of Topsoil in the City of Oslo, Norway

The city of Oslo is situated centrally in the Oslo-graben, which is a Permian rift basin consisting of different kinds of volcanic and sedimentary rocks. In the summer of 1998, approximately 300 samples of surface soil (2–3cm) were taken systematically, 1km^–2. The investigated area covers about 500km². Samples were dissolved in 7M HNO₃ and analysed for 29 elements with ICP-AES, mercury with cold-vapour technique (CV-AAS) and arsenic and cadmium with a graphite furnace (GF-AAS). A factor analysis is frequently used to identify relationships among sets of interrelated variables. To describe the covariant relationships among the elements, a factor analysis has been completed. The first factor contains the elements Sc, Fe, Li, Co, Al, Cr, Be, K, Ni, V, Mg, Y, Ba, Zr, Mn and As (listed with decreasing communality). These elements are typical for the minerals in the area and most of these elements have a near normal distribution. Sources for this factor are probably geological. The second factor contains Cd, Hg, P, Zn, Cu, Ba and Pb. They have a log-normal distribution. Road traffic is probably one of the sources contributing to this factor. In Norway studded tyres are used frequently in the winter season which results in large amounts of road dust. Leaded petrol has been a major source for Pb but is not in use any more. Wear and tear of tyres and brakes contribute also to this factor. Other sources contributing to this factor are probably industry, rubbish incineration, crematoria and release of some of these elements from structural material by fire. Factors 3, 4 and 6 with elements such as Ca, Na, La, Ti and Sr probably have geological sources. They are associated with minerals like amphiboles, pyroxenes and feldspars and some of the elements are from sea aerosols. Factor 5 contains Mn, Cd, Zn, As and Pb. Manganese may be derived from many different sources such as rock weathering, windblown dust, agriculture and traffic. Since As and Mn are placed in both factor 1 and 5 they probably have both geological and anthropogenic sources. Concentrations of the elements in the second factor are much higher in the central parts of Oslo, than in the rest of Oslo. The median value of Hg in the centre is 0.48mgkg^–1, which is 8 times higher than that in the rest of the city. Also, the other elements have much higher levels in the centre. The industrial district north-east of the centre also has high values. The distribution of arsenic is regular throughout the whole city, but has a slightly higher level in the centre. Norm values for contaminated land used by the Norwegian authorities are 2mg As kg^–1 and 25mg Cr kg^–1. Of 297 samples, 61% contain more than 25mg Cr kg^–1 and 79% more than 3mg As kg^–1, which is the detection limit of the analysis. These samples will therefore be regarded as contaminated. Factor analysis places these elements in the geological factor. The Norm value of zinc is 150mgkg^–1, and 40% of the samples contain more than this. The Norm value of lead is 150mgkg^–1, and 35% of the samples contain. Road traffic is probably the major source for these elements.     

Hierarchical Bayesian space-time models

Space-time data are ubiquitous in the environmental sciences. Often, as is the case with atmo- spheric and oceanographic processes, these data contain many different scales of spatial and temporal variability. Such data are often non-stationary in space and time and may involve many observation/prediction locations. These factors can limit the effectiveness of traditional space- time statistical models and methods. In this article, we propose the use of hierarchical space-time models to achieve more flexible models and methods for the analysis of environmental data distributed in space and time. The first stage of the hierarchical model specifies a measurement- error process for the observational data in terms of some 'state' process. The second stage allows for site-specific time series models for this state variable. This stage includes large-scale (e.g. seasonal) variability plus a space-time dynamic process for the anomalies'. Much of our interest is with this anomaly proc ess. In the third stage, the parameters of these time series models, which are distributed in space, are themselves given a joint distribution with spatial dependence (Markov random fields). The Bayesian formulation is completed in the last two stages by speci- fying priors on parameters. We implement the model in a Markov chain Monte Carlo framework and apply it to an atmospheric data set of monthly maximum temperature.     

Diurnal migration and vertical distribution of phyllosoma larvae of the western rock lobster Panulirus cygnus

Studies off the west coast of Australia showed that the phyllosoma larvae of Panulirus cygnus George undergo a diurnal vertical migration, with light as an important factor influencing the depth distribution of all 9 phyllosoma stages. The early stages (I to III) occurred at the surface at night regardless of moonlight intensity, whereas late stages (VI to IX) concentrated at the surface only on nights with less than 5% of full moonlight. Midday peak densities of early-stage larvae occurred in the 30 to 60 m depth range while those of mid (IV to VI) and late stages were in the 50 to 120 m range. Depths of peak densities of larvae increased with distance offshore. The limits of vertical distribution of the phyllosoma remained within ranges of illuminance which were estimated to be in the order of 50 to 250 E m^-2 sec^-1 for early stages, 20 to 200 E m^-2 sec^-1 for mid stages and 5 to 50 E m^-2 sec^-1 for late stages. Minimal rates of net vertical movement were estimated for the larvae. Early stages exhibited mean net rates of ascent and descent of 13.7 and 13.0 m h^-1, respectively, while the rates for mid stages were 16.0 and 16.6 m h^-1 and for late stages 19.4 and 20.1 m h^-1. Diurnal migrations and vertical distribution are shown to have a vital role in the relationships between circulation in the south-eastern Indian Ocean and the transport and dispersal of the phyllosoma larvae. The diurnal migrations of early stages place them at the surface at night, when offshore vectors of wind-driven ocean-surface transport dominate, and below the depth of wind-induced transport during the day, when offshore vectors are small or negative, thus accounting for their offshore displacement. Mid and late stages, because of their deeper daytime distribution and absence from the surface on moonlight nights, are predominantly subject to circulation features underlying the immediate surface layer. This is hypothesized to account for the return of the phyllosoma to areas near the continental shelf edge by subjecting them to a coastward mass transport of water which underlies the immediate surface layer.The western rock lobster is referred to as P. longipes or P. longipes cygnus in some of the literature quoted; these are synonymous with P. cygnus.     

Distribution et synécologie des fonds à Gryphus vitreus (Brachiopoda) en Corse

In the Mediterranean Sea, the brachiopod Gryphus vitreus (Born) was collected off Corsica by dredging and trawling during three cruises (June 1983; April and July 1984) and from along the French continental coast by dredging during many cruises (1975–1985). The upper limit of its bathymetric distribution lies between 115 and 125 m (rarely, from 90 m), the lower limit between 140 and 200 m depth, forming a belt along the edge of the continental shelf. The horizontal distribution of G. vitreus varies from 250 m to >4 km, and is directly related to geomorphological and hydrodynamic variations resulting from local topography and/or geographical location. The G. vitreus bottoms are bounded on the continental slope by the bathyal mud biocoenosis and on the shelf by the coastal detritic or shelf-edge detritic biocoenosis, both circalittoral. The bottoms correspond to a bathylittoral ecosystem characterized by (1) prevailing environmental conditions which result in a biotope characterized by coarse detritic sediment clogged by fine sand and mud with a high content of small hard substrates, by constant moderate bottom-currents which become weaker with increasing depth, and by small annual variations in temperature and salinity; the occurrence of an ostreobium sp. alga in the shell of G. vitreus indicates the involvement of the phytal system, as defined by Pérès (1982); (2) the G. vitreus biocoenosis, comprised of characteristic macrobenthic stocks (particularly polychaetes, mollusks, and epifaunal species on small hard substrates). Whatever the geomorphology, neighbouring circalittoral and bathyal biocoenoses have little influence on the G. vitreus biocoenosis, which displays a comparatively greater species richness and density. However, immigration of circalittoral species is encouraged by detrital sediments and water currents. The occurrence of this ecosystem as a distinct belt intercalated between circalittoral and bathyal zones is discussed. The ecosystem is considered to be bathylittoral.     

Fish from Missouri's lead belt: To eat or not to eat

Data collected over the past four years indicate that filets of suckers and some species of sunfish taken from certain sites in Missouri's Old Lead Belt consistently contain elevated lead concentrations which exceed the limit of 0.3 g/g suggested by the World Health Organization. The problem exists in bottom-feeding species taken from some sites along the Big River affected by erosion from abandoned lead tailings piles. Fish from many other sites within the Old Lead Belt and the New Lead Belt, including current wastewater treatment systems, are within the acceptable limits for lead in food. Public health implications are discussed relative to observed lead concentrations and available data regarding lead toxicity to humans.     

Fitting the truncated negative binomial distribution to count data

Modeling empirical distributions of repeated counts with parametric probability distributions is a frequent problem when studying species abundance. One must choose a family of distributions which is flexible enough to take into account very diverse patterns and possess parameters with clear biological/ecological interpretations. The negative binomial distribution fulfills these criteria and was selected for modeling counts of marine fish and invertebrates. This distribution depends on a vector \(\left( K,\mathfrak {P}\right) \) of parameters, and ranges from the Poisson distribution (when \(K\rightarrow +\infty \)) to Fisher’s log-series, when \(K\rightarrow 0\). Moreover, these parameters have biological/ecological interpretations which are detailed in the literature and in this study. We compared three estimators of K, \(\mathfrak {P}\) and the parameter \(\alpha \) of Fisher’s log-series, following the work of Rao CR (Statistical ecology. Pennsylvania State University Press, University Park, 1971) on a three-parameter unstandardized variant of the negative binomial distribution. We further investigated the coherence underlying parameter values resulting from the different estimators, using both real count data collected in the Mauritanian Exclusive Economic Zone (MEEZ) during the period 1987–2010 and realistic simulations of these data. In the case of the MEEZ, we first built homogeneous lists of counts (replicates), by gathering observations of each species with respect to “typical environments” obtained by clustering the sampled stations. The best estimation of \(\left( K,\mathfrak {P}\right) \) was generally obtained by penalized minimum Hellinger distance estimation. Interestingly, the parameters of most of the correctly sampled species seem compatible with the classical birth-and-dead model of population growth with immigration by Kendall (Biometrika 35:6–15, 1948).     

Stepwise acclimation—a method for estimating the potential euryhalinity of the gastropod Hydrobia ulvae

The White Sea gastropod Hydrobia ulvae (Pennant) was exposed to step-wise lowering or increase of the habitat salinity. The time allowed for acclimatization to the successive salinity levels was sufficient to complete non-genetic adaptation. In this way, the lower and upper salinity limits were extended. The tolerance limits obtained are assumed to be indicative of the capacity for non-genetic adaptation and to serve as a genotypical characteristic. The tolerance of specimens colleced from in situ conditions (mid littoral, 20 S) ranged between 14 and 34 S. After non-genetic adaptation, the lower tolerance value shifted to 6 S (adaptation limit), and the upper value to 76 S (final limit not reached). There is no reason for considering White Sea H. ulvae to represent a special physiological race of specimens from those on the coast of Great Britain.     

Optimal allocation procedure in ranked set sampling for unimodal and multi-modal distributions

This paper presents a ranked set sample allocation procedure that is optimal for a number of nonparametric test procedures. We define a function that measures the amount of information provided by each observation given the actual joint ranking of all the units in a set. The optimal ranked set sample allocates order statistics by maximizing this information function. This paper shows that the optimal allocation of order statistics in a ranked set sample is determined by the location of the mode(s) of the underlying distribution. For unimodal, symmetric distributions, optimal allocation always quantifies the middle observation(s). If the underlying distribution with cdf F is a multi-modal distribution with modes , then the optimal allocation procedure quantifies observations at in a set of size m. We provide similar results for unimodal, asymmetric distributions. We also propose a new sign test which considers the relative positions of the quantified observations from the same cycle in a ranked set sample. The proposed sign test provides improvement in the Pitman efficiency over the ranked set sample sign test of Hettmansperger (1995). It is shown that the information optimal allocation procedure induced by Pitman efficiency is equivalent to the optimal allocation procedure induced by the information criteria. We show that the finite sample distribution of the proposed test based on this optimal design is binomial.     

Assessment of distubance in Mediterranean lagoons: An evaluation of methods

A number of methods were applied to assess disturbance in macrozoobenthic communities in three Mediterranean lagoons with different levels of stress. Tsopeli, Ionian Sea, with no obvious source of stress, harbours a fauna typical of brackish-water lagoons. Vivari, Aegean Sea, also without apparent source of disturbance, is characterised by a few typical lagoonal species and some species characteristic of perturbation. Goro lagoon, in the northern Adriatic, is much larger and more open to the sea. At the centre of the lagoon, where anoxia is known to occur in the summer (Goro polluted), the fauna is dominated by species typical of disturbance and a few lagoonal species. A dredged area closer to the sea (Goro dredged) is totally dominated by species characteristic of disturbance. The species diversity in all lagoons ranges from low to very low. According to the distribution of individuals in geometric abundance classes, all the lagoons are characterised as stressed. The distribution of individuals in geometric size classes shows dominance of larger specimens in the least disturbed Tsopeli and exclusively small sizes in the greatly disturbed dredged area of Goro. The abundance/biomass comparison curves characterise Tsopeli as undisturbed, Vivari and Goro polluted stations as moderately disturbed and Goro dredged station as disturbed. The last two methods agree with the characterisation derived by examining the dominant species. It is concluded that methods based on size changes of the fauna are more sensitive than those based on relative abundance in assessing disturbance in coastal brackish-water lagoons.     

Performance of IUCN proxies for generation length

One of the criteria used by the International Union for Conservation of Nature (IUCN) to assess threat status is the rate of decline in abundance over 3 generations or 10 years, whichever is longer. The traditional method for calculating generation length (T) uses age‐specific survival and fecundity, but these data are rarely available. Consequently, proxies that require less information are often used, which introduces potential biases. The IUCN recommends 2 proxies based on adult mortality rate, = α + 1/d, and reproductive life span, = α + z^*RL, where α is age at first reproduction, d is adult mortality rate, RL is reproductive life span, and z is a coefficient derived from data for comparable species. We used published life tables for 78 animal and plant populations to evaluate precision and bias of these proxies by comparing and with true generation length. Mean error rates in estimating T were 31% for and 20% for , but error rates for were 16% when we subtracted 1 year ( ), as suggested by theory; also provided largely unbiased estimates regardless of the true generation length. Performance of depends on compilation of detailed data for comparable species, but our results suggest taxonomy is not a reliable indicator of comparability. All 3 proxies depend heavily on a reliable estimate of age at first reproduction, as we illustrated with 2 test species. The relatively large mean errors for all proxies emphasized the importance of collecting the detailed life‐history information necessary to calculate true generation length. Unfortunately, publication of such data is less common than it was decades ago. We identified generic patterns of age‐specific change in vital rates that can be used to predict expected patterns of bias from applying .     

Optimal foraging: Some simple stochastic models

Summary Some simple stochastic models of optimal foraging are considered. Firstly, mathematical renewal theory is used to make a general model of the combined processes of search, encounter, capture and handling. In the case where patches or prey items are encountered according to a Poisson process the limiting probability distribution of energy gain is found. This distribution is found to be normal and its mean and variance are specified. This result supports the use of Holling's disc equation to specify the rate of energy intake in foraging models. Secondly, a model based on minimization of the probability of death due to an energetic shortfall is presented. The model gives a graphical solution to the problem of optimal choices when mean and variance are related. Thirdly, a worked example using these results is presented. This example suggests that there may be natural relationships between mean and variance which make solutions to the problems of energy maximization and minimization of the probability of starvation similar. Finally, current trends in stochastic modeling of foraging behavior are critically discussed.     

Changes in blood lead and water lead in Edinburgh. An eight year follow-up to the Edinburgh lead study

This study aimed to measure changes in household water lead and blood lead in young people living in Edinburgh over a period of 8 years. Two hundred and twenty-three families were eligible and 207 (93%) agreed to participate. A half-hour stagnation sample of kitchen cold water was taken from each household, and 171 young people (aged 14–17 years) provided a blood sample for lead analysis. Information on plumbing changes, exposure to other sources of lead and factors which might influence blood lead was collected by questionnaire. Edinburgh is supplied with water treated in one of two treatment plants. There was a different programme of water treatment in each plant. In one (A) lime and orthophosphate was introduced in the interval between the original and follow-up studies. In the other (F) lime treatment began before the original study and orthophosphate was introduced subsequently. In water from treatment plant A, mean water lead levels fell from 34 to 4.3 gL-1 (87%). In water supplied from treatment plant F the corresponding values were 9.3 to 3.6 gL-1 (61%). These reductions were due to both water treatment and removal of lead plumbing. Houses with no lead plumbing have water lead levels 89% lower than houses with lead tanks, and 47% lower than houses with lead pipes. About one-third of households with lead tanks are predicted to have water lead levels above the current EC limit of 50 gL- 1, though only 3% or less of the remaining households would exceed this limit. If the proposed 10 gL-1 limit were introduced, 34% of households supplied from plant A and 25% from plant F would breach the limit. Blood lead levels fell from an average of 11.0 gdL-1 to 4.0 gdL-1. Males had higher values than females and the main factors influencing levels were water lead and age of house. Our results show substantial reductions in household water lead and blood lead in our sample over a period of 8 years and represent an important achievement in public health. However, more progress will be required if the proposed new limit of 10 gL-1 for water lead is to be met. There is a need for the continuing surveillance of household water lead and blood lead levels in representative samples of the population.     

Population characteristics of the deep-sea lobsters Polycheles typhlops and Stereomastis sculpta (Decapoda: Polychelidae) in a bathyal mud community of the Mediterranean Sea

Distribution and abundance as a function of depth, and population parameters such as sex and size structure of the population and aspects of reproductive biology have been studied in the deep-sea polychelid lobsters Polycheles typhlops and Stereomastis sculpta. Samples were taken by otter trawl in the Balearic Sea, a deepsea basin in the northwestern Mediterranean Sea from 1985 to 1989. In both species the largest size classes were dominated by females. In S. sculpta, male and female sizes were very similar. In P. typhlops, ovigerous females and those with external spermatophores were 23 and 25 mm in carapace length (CL), respectively; males with external spermatophores were 17 mm in CL. In S. sculpta, ovigerous females and those with external spermatophores were 24 and 19 mm CL, respectively, and males with external spermatophores 19 mm CL. Highest densities of P. typhlops occurred along the middle slope at depths between 500 and 1000 m. Only small-sized individuals were found at the deepest depths sampled; some recruitment must therefore occur in waters much deeper than those usually inhabited by the adult population. The sex-ratio was 1:1 in most samples, but in some of the shallowest samples females predominated. The depth distribution range of S. sculpta was 981 to 2253 m: densities clearly increased with increasing depth. There were no apparent variations in size distribution as a function of depth. Since very few adult males and females were captured, the population in the survey area would seem to be comprised mainly of juveniles. As a function of depth, females were numerically dominant only in some of the shallowest samples taken in the distribution range of this species. There is strict habitat partitioning between the two species. In both species, the variation in the sex-ratio as a function of depth suggests differential migration between the sexes, probably related to egg incubation and hatching.     

Spatial and temporal patterns of recuruitment of juvenile coral reef fishes to coral habitats within “One Tree Lagoon”, great barrier reef

Recruitment of juvenile fishes to coral grids, each comprising 4 colonies of 3 species of coral (Acropora formosa, Seriatopora hystrix and Pocillopora damicornis), was examined at 4 widely separated sites within the lagoon of One Tree Reef over two successive summers and intervening months (November 1976–January 1978). Recruitment was highly seasonal, with most recruitment occurring during summer. For many species, numbers settling differed greatly from year to year with total numbers (over all sites) differing as much as an order of magnitude between summers. Many fish species demonstrated marked preference among the three coral species as settling sites. The distribution of each of the 20 commonest species across the 4 lagoon sites differed significantly from a random pattern. Differences of an order of magnitude were common in the numbers of a given species recruited to different sites. Each site was preferred by at least one species. In each of 5 cases examined, the pattern of settlement of the species across the 4 sites changed significantly from one summer to the next. The distribution of recruits of a number of species corresponded to the distribution of adults, but for other species there was no correspondence. It is concluded that, at the spatial scale examined, patterns of recruitment of some taxa are consistently more variable than those of other taxa. The implications of spatial variability of recruitment for the distribution of adult fish is discussed and the importance of being able to discriminate such natural variability from other kinds of change is stressed.     

Comparison of distribution function estimators for forestry applications following variable probability sampling

Practical considerations often motivate employing variable probability sampling designs when estimating characteristics of forest populations. Three distribution function estimators, the Horvitz-Thompson estimator, a difference estimator, and a ratio estimator, are compared following variable probability sampling in which the inclusion probabilities are proportional to an auxiliary variable, X. Relative performance of the estimators is affected by several factors, including the distribution of the inclusion probabilities, the correlation () between X and the response Y, and the position along the distribution function being estimated. Both the ratio and difference estimators are superior to the Horvitz-Thompson estimator. The difference estimator gains better precision than the ratio estimator toward the upper portion of the distribution function, but the ratio estimator is superior toward the lower end of the distribution function. The point along the distribution function at which the difference estimator becomes more precise than the ratio estimator depends on the sampling design, as well as the coefficient of variation of X and . A simple confidence interval procedure provides close to nominal coverage for intervals constructed from both the difference and ratio estimators, with the exception that coverage may be poor for the lower tail of the distribution function when using the ratio estimator.