Precision of the mean and the design of benthos sampling programmes: caution revised

Normative variance functions can be used to accurately predict sampling exigencies, but such empirically derived formulae are continuous functions that can predict levels of sampling precision that cannot logically occur in discrete population samples. General formulae are presented that allow calculation of upper and lower boundary constraints on levels of sampling precision. These boundary constraints would only have a significant influence on sampling design where populations are so sparse that samples consist mainly of presence-absence data. A previously published empirical equation for the prediction of requisite sample number for the estimation of a freshwater benthos population correctly shows that using a small sampler can result in an up to 50-fold reduction in the amount of sediment processed, regardless of these constraints. A previously published empirical equation for the prediction of sampling variance, based on over 3000 sets of replicate samples of marine benthos populations, suggests that the use of small samplers over large ones requires the processing of between one-half and one-twentieth of the sediment for the same level of precision. It is concluded that discussions of sampling optimization should be based on knowledge of real sampling costs.     

Importance of biotic and abiotic regulators of abundance of the intertidal amphipod Calliopius laeviusculus (Amphipoda: Gammaridae) and assessment of the accuracy and precision of sampling methods for detecting abundance changes

We examined seasonal patterns of abundance for the intertidal amphipod Calliopius laeviusculus (Amphipoda: Gammaridae). Amphipods were sampled with an epibenthic sled during the daytime high tide period from 18 May to 8 August 1988. Amphipod density increased from May to June and reached maxima in both late June and early August. Amphipod density was unrelated to any abiotic component measured in the intertidal community. These variables included sampling location, wave height, water column height, water temperature, salinity and cloud cover. Changes in abundance were related with sampling date and with the onset of capelin (Mallotus villosus) spawning activity in the intertidal. Capelin eggs are an important food item for amphipods. The accuracy of density estimates obtained with the epibenthic sled was assessed through comparison with densities obtained with a more efficient quadrat sampler. Sled samples consistently sampled ca. 1% of the amphipod population. We found that a large portion of the amphipod population burrowed into the sediment and was not effectively sampled by the sled. Sled sampler precision was roughly equivalent to that of quadrats with D (precision) ranging from 0.26 to 0.42 for sled samples and D=0.29 for quadrat samples. Although sample collection with the epibenthic sled was achieved more quickly and under a wider range of weather conditions than was possible with the quadrat sampler, the serious underestimate of amphipod density based on sled samples alone indicates that both sled and quadrat samples, obtained in concert, are required to obtain accurate measures of daily variation in C. laeviusculus abundance.Contribution to the program of GIROQ (Groupe interuniversitaire de recherches oceanographique du Quebec)     

Sampling biological characteristics of krill: Effect of heterogeneous nature of swarms

An effect of the very patchy distribution of Antarctic krill (Euphausia superba Dana) in various forms of aggregation is that a single swarm may not provide an unbiased estimate of population parameters such as mean length of krill in the local area. Here, we analyse the number of samples required to estimate the characteristics of a local population as precisely as if there were no differences between krill swarms in terms of their biological composition. Krill were intensively sampled over different spatial and temporal scales around South Georgia in 1981 and 1982, and in the Bransfield Strait in 1985. These varied from replicate hauls at a single station over 24 h and repeat sampling in restricted areas over periods of 6 to 14 d to regional surveys around South Georgia and in the Bransfield Strait. Various biological characteristics were measured such as length, maturity, moult stage and feeding state. Depending upon the biological characteristic examined and the area covered by the sampling programme, the number of samples needed to obtain the same degree of precision as would be found in the absence of heterogeneity varied from 3 to > 80 samples. This has important implications for the design of net-sampling programme for monitoring krill populations.     

Bayesian predictive inference for the proportion of eroded land in a small area in Iowa

There is an increasing interest in the quality of soil, especially for small geographical areas. We present a method to estimate the percent of the area in a county or hydrological basin that is eroded. There are sample data (for several counties in eastern Iowa) from the National Resources Inventory and population data on land use, land capability class, rainfall and slope length and steepness. Using the Gibbs sampler we perform Bayesian predictive inference to obtain estimates for the non-sampled units. These estimates, together with the sample data, provide an estimate of the proportion of the total area that is eroded. We assess the quality of fit of our model using two cross-validation exercises and graphical methods.     

Method of estimating the standing stock of Trochus niloticus incorporating Landsat satellite data,with application to the trochus resources of the Bourke Isles,Torres Strait,Australia

The habitat of Trochus niloticus in the Bourke Isles, Torres Strait, was classified into areas of a Landsat image, using high-ratio values of green (Band 2) to red (Band 3) light, along the windward reef margins. These shallow-water (< 15 m) areas have a coral and rubble/algal pavement cover, which constitutes the optimal habitat for this gastropod. The habitat was sampled to estimate the abundance of T. niloticus. The proportion of commercial-sized individuals was estimated by measuring the basal width of all individuals in a sample. A multistage sample design incorporating three spatial scales -100 m² (transect), 1500 m² (site) and 1 km² (reef) — was used to provide variance estimates for sample-design optimisation and to provide data on the spatial variation of abundance. Most variation (68%) in abundance was within reefs and was attributable to differences in reef cover. Variations in abundance and time costs for sampling 2 and 4 m transects were compared; the 2 m transect was more efficient than the 4 m transect. The abundance estimates were combined with habitat-area estimates and the proportion of commerical-sized individuals was estimated at a standing stock of 186000 (24% precision), or 14 t of commerical-sized T. niloticus.     

Large-scale estimate of somatic growth in Amphiura filiformis (Echinodermata: Ophiuroidea)

Quantitative data on size structure of the ophiuroid Amphiura filiformis (O.F. Müller) from 35 benthic stations in the Kattegat sampled twice with a 143 d interval, June and October 1991, were used to estimate somatic growth. The material was objectively divided into cohorts, and cohorts, from the two occasions were paired to give estimates of growth. The growth constant, K, in the Von Bertalanffy equation, was estimated from a Ford-Walford plot to 0.54 yr^-1. Results were in agreement with previous estimates from a few single sites, and suggest that the main part of dise growth occurs within the first 5 to 7 yr of living. Size specific growth in oral width was density independent despite high densities of A. filiformis (>3000 ind m^-2) and high total benthic biomass (up to 1000 g wet wt m^-2) in some areas. Growth was uncorrelated with plant pigment concentrations in the sediment and showed weak positive correlation with sediment carbon and nitrogen, as well as water depth. Growth was higher in fine sediments. This is the first attempt to estimate growth in this important species over a large area and to relate growth in the field to environmental factors.     

Differences between swarms of Antarctic krill and some implications for sampling krill populations

Antarctic krill, Euphausia superba Dana, were sampled from 28 discrete swarms in a small area south west of Elphant Island, South Shetlands, over a period of 14 d (24 February-9 March 1985). Four biological characteristics of the krill (length, sex, moult, gut fullness) were examined in a study of variation between swarms. Analysis of these characteristics indicated extensive differences between swarms and no single characteristic, or combination of characteristics, emerged as consistently accounting for the observed heterogeneity. There was no relationship between the degree of heterogeneity and the physical or temporal proximity of swarms. The variability between even close swarms strongly suggests that swarms are the basic unit of organization of krill populations. This conclusion has important implications for sampling programmes aimed at estimating population parameters. Thus, in the population studied here, we calculate that it was necessary to sample 23 swarms to estimate mean length and 10 swarms to establish a reliable estimate for the proportion of females in the population.     

Adaptive two-stage one-per-stratum sampling

We briefly describe adaptive cluster sampling designs in which the initial sample is taken according to a Markov chain one-per-stratum design (Breidt, 1995) and one or more secondary samples are taken within strata if units in the initial sample satisfy a given condition C. An empirical study of the behavior of the estimation procedure is conducted for three small artificial populations for which adaptive sampling is appropriate. The specific sampling strategy used in the empirical study was a single random-start systematic sample with predefined systematic samples within strata when the initially sampled unit in that stratum satisfies C. The bias of the Horvitz-Thompson estimator for this design is usually very small when adaptive sampling is conducted in a population for which it is suited. In addition, we compare the behavior of several alternative estimators of the standard error of the Horvitz-Thompson estimator of the population total. The best estimator of the standard error is population-dependent but it is not unreasonable to use the Horvitz-Thompson estimator of the variance. Unfortunately, the distribution of the estimator is highly skewed hence the usual approach of constructing confidence intervals assuming normality cannot be used here.     

Molecular and morphometric variation in European populations of the articulate brachiopod Terebratulina retusa

Molecular and morphometric variation within and between population samples of the articulate brachiopod Terebratulina spp., collected in 1985–1987 from a Norwegian fjord, sea-lochs and coastal sites in western Scotland, the southern English Channel (Brittany) and the western Mediterranean, were measured by the analysis of variation in the lengths of mitochondrial DNA (mtDNA) fragments produced by digestion with nine restriction endonucleases and by multivariate statistical analysis of six selected morphometric parameters. Nucleotide difference within each population sample was high. Nucleotide difference between population samples from the Scottish sites, both those that are tidally contiguous and those that appear to be geographically isolated, were not significantly different from zero. Nucleotide differences between the population samples from Norway, Brittany, Scotland and the western Mediterranean were also very low. Morphometric analysis confirmed the absence of substantial differentiation.     

Two neighborhood-free plot designs for adaptive sampling of forests

Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.     

Microphytobenthos of the Dogger Bank: a comparison between shallow and deep areas using phytopigment composition of the sediment

The surface sediment characteristics related to benthic microalgae primary production were studied at the Dogger Bank, North Sea, in order to evaluate the potential role of microphytobenthos as a food source for the macrobenthic fauna. Twenty-one stations were sampled in July 2001 and May 2002, with water depth ranging from 16.3 to 68.5 m. High-performance liquid chromatography pigment analyses revealed that concentrations of chlorophyll a, chlorophyll c and fucoxanthin are mainly associated with benthic diatom flora at most parts of the Dogger Bank. High percentage of phytopigments (>50%) was firmly attached to sand grains at the stations shallower than 40 m water depth. The deeper stations were characterized by a phytopigment composition originating from pelagic phytoplankton settled on the sea floor. Qualitative microscopy showed that the benthic microflora on top of the Bank mainly consists of small diatoms (5–10 μm), such as e.g., Diploneis spp., living attached to the sand grains. The results are discussed concerning possible implications for ecology and biogeochemistry of the Dogger Bank area.     

Growth and production of<Emphasis Type="Italic"> Ophiocten gracilis</Emphasis> (Ophiuroidea: Echinodermata) on the Scottish continental slope

Growth and production of the bathyal ophiurid brittle star Ophiocten gracilis was studied from skeletal growth bands and disc size frequencies of specimens collected in sled and trawl samples taken on the continental slope off Scotland. Growth bands showed up in SEM examination as ring-like zones in surface relief and texture of the stereom microstructure of the intervertebral muscle insertions on the arm ossicles. Seasonal variability in somatic growth, presumed to underlie this growth pattern, may reflect reproduction and/or a possible non-feeding period during gonad maturation. Disc size-at-age was back-calculated from size-at-age interpreted from growth-band series on the vertebral ossicles from arms of O. gracilis. Pooled growth-band frequency data and normal-distribution mixtures based on size-at-age data were used to test for overgrowth of early growth bands on the ossicles from larger individuals. Von Bertalanffy and Gompertz growth models were fitted to the finalised back-calculated disc size-at-age data. These were used along with the modal structure of the observed disc size frequencies to develop a demographic model based on normal-distribution mixtures constrained by the growth model. These and other defining parameters were fitted by non-linear regression to size structure observed in a sample of the breeding population from 997 m depth on the Hebrides Terrace. Recruitment was estimated according to available data from sediment-trap time series. A ratio of somatic production/biomass, P_S/B, in the range of 0.43–0.54 was estimated using a fitted size/mass relationship and the increment summation method (ISM) applied to the fitted growth models. A narrower, but otherwise similar, range in estimated P_S/B ratios (0.48–0.49) was obtained in a parallel approach using the mass-specific growth rate method (MSGRM), whereby the same size/mass relationship was applied to the observed frequencies and growth parameters fitted to growth banding. Using previously obtained data on population density, a standing crop of 4.8 g wet weight (~0.58 mg AFDW) m^?2 would provide annual wet weight production in the range of 1.9–2.4 g (~0.23–0.29 mg AFDW) m^?2 in the population between ca. 700–1000 m depth. Somewhat greater production estimates (P_S/B=0.73–0.98) were obtained from MSGRM by pooling the sample with size frequencies from other large samples in which postlarval sizes were more numerous, but larger sizes less numerous. Similarly high production was estimated by MSGRM from a box corer sample from the Wyville-Thomson Ridge. Explanations for variability in size structure are discussed, but even the lower estimates are comparable to boreal shallow-water brittle stars. The high rate of growth and production by accepted deep-sea standards may be related to a capability for interface feeding.     

Hierarchical spatial modeling for estimation of population size

Estimation of population size has traditionally been viewed from a finite population sampling perspective. Typically, the objective is to obtain an estimate of the total population count of individuals within some region. Often, some stratification scheme is used to estimate counts on subregions, whereby the total count is obtained by aggregation with weights, say, proportional to the areas of the subregions. We offer an alternative to the finite population sampling approach for estimating population size. The method does not require that the subregions on which counts are available form a complete partition of the region of interest. In fact, we envision counts coming from areal units that are small relative to the entire study region and that the total area sampled is a very small proportion of the total study area. In extrapolating to the entire region, we might benefit from assuming that there is spatial structure to the counts. We implement this by modeling the intensity surface as a realization from a spatially correlated random process. In the case of multiple population or species counts, we use the linear model of coregionalization to specify a multivariate process which provides associated intensity surfaces hence association between counts within and across areal units. We illustrate the method of population size estimation with simulated data and with tree counts from a Southwestern pinyon-juniper woodland data set.     

Methods for measurement of community structure in deep-sea macrobenthos

Methods are compiled and developed for the analysis of community structure in the deep-sea benthos. These methods are tailored to the conditions of high species diversity and low standing crop. A new modification of the 0.25-m² box corer is described. Fisher's index of dispersion is adapted by using each species as a replicate. When the resultant summary statistic is partitioned in the illustrated manner, it is possible to determine whether species indeed behave as homegeneous replicates of a single dispersion pattern, or, alternatively, whether habitat partitioning is indicated. Species are also used as replicates in a modification of Pielou's “joins” technique of determining whether high-density and low-density areas of given species are randomly mingled. An indirect analytical approach is developed which proposes that, if an environmental grain of relatively small dimensions has been important in structuring the community, species which have smaller ambits will be more diverse than species having larger ambits.     

Surface area in ecological analysis: Quantification of benthic coral-reef algae

The surface area of organisms and substrata is shown to be a significant ecological parameter because of its functional importance in the system. Quantification of surface area can be of particular value in morphologically complex environments such as coral reefs. The amount of surface in a reef habitat can be estimated by direct measurements and theoretical approximations, using a surface index (SI) for the amount of surface increase over that of a similarly bounded plane. SI values for a section of the British Honduran barrier reef ranged up to 15 in the reef-crest area at scales significant to macro-organisms. By combining substrate-area measurements with estimates of percent coverage of the major benthic algal components, a reef transect with a horizontal area of 300 m² was shown to have over 300 m² covered by benthic macroalgae. The potential for the further development of surface estimation techniques is discussed.     

Deep distributions of oceanic cirripede larvae in the Sargasso Sea and surrounding North Atlantic Ocean

From deep ( 1000 m), multi-depth zooplankton samples taken in the Azores frontal region from November 1980 to June 1981, high numbers of the two larval forms ofLepas pectinata, the commonest lepadid cirripede in this area, were sampled. The nauplii and cyprid larvae are large and long-lived. Nauplii were sampled where they feed, in the upper 150 m, closely associated with the fluorescence maximum. The cyprids were mainly sampled between 300 and 400 m, with a sharp cut-off in numbers just below the distribution peak. This deep distribution is intriguing, as the cyprids, which were not migrating diurnally, are non-feeding. To complete their life cycle they must settle on floating debris at the surface, where very few were sampled. They are negatively buoyant and there is no apparent physical reason for this deep distribution. There was no obvious pattern of changes in individual length or length/dry weight distribution with depth, the population appeared homogeneous. There was also no accumulation of other zooplankton at the same depth, or evidence from gut contents of large carnivores that the distribution pattern was caused by selective predation. A close association exists betweenL. pectinata andSargassum spp. weed, the cyprids preferentially settling on small fragments of weathered weed, the supply of which may be enhanced after winter. During winter, the harsh environment at the surface of the northern Sargasso Sea may discourage cyprid settlement. The deep distribution may be an ontogenetic migration conferring some survival advantage and saving energy due to the lower temperature and oxygen levels at depth. If it is a behavioural mechanism, duration of the cyprid stage will be extended until a more clement time of year, allowing them to settle over a longer period. The cyprids of other species were also sampled at depth, so the phenomenon appears to be widespread. If subsequent research confirms these observations as an ontogenetic migration, our current understanding of the fouling behaviour of oceanic lepadid cirripedes would be considerably modified.     

Productivity of bacteria and microalgae and the effect of grazing by holothurians in sediments on a coral reef flat

Bacterial productivity in sandy sediments on reef flats at Lizard Island, Great Barrier Reef was determined from the rate of incorporation of tritiated thymidine into DNA. The study was conducted during January 1982 and July 1983. A small diurnal increase occurred in sediments having a dense population of microalgae. Bacterial production was 120 to 370 mg C m^-2 d^-1 in summer on reef flats, which was equivalent to 30–40% of primary production by benthic microalgae. In winter, rates of primary production by benthic microalgae and secondary production by bacteria were about one-half to one-fifth of those in summer. There was much variation in production, due to patchiness in the distribution of benthic microbes, especially microalgae. Doubling times for the bacteria in surface sediment were 1 to 2 d in summer and 4 to 16 d in winter on the reef flats. These high productivity values for bacteria indicated that a net input of organic matter to the sediment was needed to support the growth of bacteria. Sediment bacteria thus have a very important role in transforming organic matter on the reef flats. Grazing by Holothuria atra depressed both primary production and bacterial production. It was estimated that these holothurians ate about 10 to 40% of bacterial carbon produced each day in summer, and thus have an important role in the carbon cycle. Harpacticoid copepods were numerically important components of the benthic meiofaunal community and probably had a significant impact on bacterial density as grazers.     

Benthic community structure, diversity, and productivity in the shallow Barents Sea bank (Svalbard Bank)

The Barents Sea is among the most productive areas in the world oceans, and its shallow banks exhibit particularly high rates of primary productivity reaching over 300 g C m^?2year^?1. Our study focused on the Svalbard Bank, an important feeding area for fishes and whales. In order to investigate how benthic community structure and benthic secondary production vary across environmental gradients and through time, we sampled across the bank and compared results with a similar study conducted 85 years ago. Considerable variability in community structure and function across bank corresponded with differences in the physical structure of the habitat, including currents, sedimentation regimes and sediment type, and overlying water masses. Despite an intensive scallop fishery and climatic shifts that have taken place since the last survey in the 1920s, benthic community structure was very similar to that from the previous survey, suggesting strong system resilience. Primary and secondary production over shallow banks plays a large role in the Barents Sea and may act as a carbon subsidy to surrounding fish populations, of which many are of commercial importance.     

Geographical variations in the trophic ecology of Japanese anchovy, Engraulis japonicus, inferred from carbon and nitrogen stable isotope ratios

Carbon and nitrogen stable isotope ratios of Japanese anchovy (Engraulis japonicus) and their stomach contents were examined and compared among various regions around Japan. Geographical variations in the isotope ratios were found between inshore and Pacific offshore regions. While most of the anchovy samples had isotope ratios around −17.6‰ for δ¹³C and 10.0‰ for δ¹⁵N as median values, higher (more enriched) isotope values were found in the anchovy sampled from inshore regions. On the contrary, lower (more depleted) values were found mostly in the anchovy from the Pacific offshore region including the Kuroshio Extension and Kuroshio-Oyashio transition zones. Higher carbon isotope ratios in the inshore regions may reflect a carbon source from benthic primary producers in addition to phytoplankton possibly through the consumption of the larvae of benthic organisms such as bivalves or decapods, which were found in the stomach contents of the inshore anchovy. Variations in the nitrogen isotope ratio may reflect not only differences in the trophic level of prey species, but also variations in the baseline level of food webs. Stable isotope ratios are potentially a useful tool for understanding the stock/population structure and migration of anchovy. The present findings indicate the potential importance of the “inshore–offshore” variations in the biology of Japanese anchovy populations in the northwestern Pacific waters.     

Method for comparing the capture efficiency of benthic sampling devices

Traditional comparisons between the capture efficiency of sampling devices have generally looked at the absolute differences between devices. We recommend that the signal-to-noise ratio be used when comparing the capture efficiency of benthic sampling devices. Using the signal-to-noise ratio rather than the absolute difference has the advantages that the variance is taken into account when determining how important the difference is, the hypothesis and minimum detectable difference can be made identical for all taxa, it is independent of the units used for measurement, and the sample-size calculation is independent of the variance. This new technique is illustrated by comparing the capture efficiency of a 0.05 m² van Veen grab and an airlift suction device, using samples taken from Heron and One Tree lagoons, Australia.