Sea ice is the major constraint on human activities in the Southern Ocean. Depending on a vessel's ice class, human mobility may be restricted or even prevented altogether by sea-ice conditions. This may imply limited access to research or monitoring stations, preferred fishing grounds or attractive tourist sites. Here, we introduce a statistical model that evaluates the sea-ice cover with two measures: 1) accessibility (i.e. the probability that a given area is navigable by vessels at a given time) and 2) repeated accessibility (i.e. the probability that a given area is navigable by vessels at a given time and again at least once within a defined timespan). We use daily sea-ice concentration data from 2002 to 2020 to demonstrate this tool and its functioning regarding the spatiotemporal variability of sea-ice cover in the wider Weddell Sea region. These findings reflect known characteristics of sea-ice distribution and dynamics in the Weddell Sea, confirming the functionality of our simple tool for determining repeated accessibility of certain areas. Such a tool may facilitate the planning of research and monitoring activities in the Southern Ocean, as well as in Arctic seas.

Identifying optimal sampling designs for detecting population-level declines is critical for optimizing expenditures by research and monitoring programmes. The Tropical Ecology Assessment and Monitoring (TEAM) network is the most extensive tropical camera-trap monitoring programme, but the effectiveness of its sampling protocol has not been rigorously assessed. Here, we assess the power and sensitivity of the programme's camera-trap monitoring protocol for detecting occupancy changes in unmarked populations using the freely available application PowerSensor!. We found that the protocol is well suited to detect moderate (≥ 5%) population changes within 3–4 years for relatively common species that have medium to high detection probabilities (i.e. p > 0.2). The TEAM protocol cannot, however, detect typical changes in rare and evasive species, a category into which many tropical species and many species of conservation concern fall. Additional research is needed to build occupancy models for detecting change in rare and elusive species when individuals are unmarked.

We consider a piecewise-multilinear interpolation of a continuous random field on a d-dimensional cube. The approximation performance is measured using the integrated mean square error. Piecewise-multilinear interpolator is defined by N-field observations on a locations grid (or design). We investigate the class of locally stationary random fields whose local behavior is like a fractional Brownian field, in the mean square sense, and find the asymptotic approximation accuracy for a sequence of designs for large N. Moreover, for certain classes of continuous and continuously differentiable fields, we provide the upper bound for the approximation accuracy in the uniform mean square norm.

The Guadeloupe archipelago hosts nesting of the threatened hawksbill Eretmochelys imbricata, green Chelonia mydas and leatherback Dermochelys coriacea marine turtles. There is a need to monitor the nesting of these species but, with > 150 beaches in the archipelago, exhaustive monitoring is infeasible. Using a new monitoring design and a new statistical tool we have been able to monitor one-third of the beaches. Seasonality and level of nesting were described for the three species for 2 years on > 50 beaches. For each species beaches were categorized as A- or B-beaches, with high and low nest density, respectively. A-beaches were monitored on 6–7 days per month before and after the peak nesting period and on 7–15 days during the peak, and the B-beaches on 14–22 days during the peak. The monitoring design and statistical tool are described in detail as they could be applied to any migratory species. Hawksbill turtles at Trois Ilets beach have been monitored for 9 years and a positive trend in nesting has been detected.

Population genetic studies of lichen-forming fungi and their algae require appropriate sampling schemes that ensure representative sampling of the genetic variability. One question is whether mycobiont and photobiont populations require different sampling strategies. Here, I applied rarefaction methods to a dataset containing three microsatellite loci of Lobaria pulmonaria and three microsatellite loci of its green-algal photobiont, Dictyochloropsis reticulata. I analysed the sample sizes required for 1) the number of individuals per population, 2) the number of individuals required across a landscape and 3) the number of populations. The analyses were performed separately for the mycobiont and photobiont loci to detect any differences in the accumulation of genetic diversity among the symbionts that would require different sampling schemes. About 20 individuals were sufficient at the population level; within landscapes, 300–400 samples and about 25–30 populations covered most of the allelic diversity. The results indicated that a slightly higher sampling effort was required for the photobiont than for the mycobiont. The optimal sampling strategy strongly depends on the research question, the spatial scale of investigation, and the type of analysis to be performed with the data.

Diel, nocturnal and lunar input patterns of pre-settlement coral reef fish were described in Wallis, a typical high-island in the south-central Pacific, with a mid-size lagoon and a 2-m spring tidal range. Crest nets were set on the barrier reef to collect incoming pre-settlement fish. A diel input pattern was observed, with 82 to 99% of the larvae arriving at night. Nocturnal input of pre-settlement fish occurred throughout the night, at different times depending on the lunar phases. In contrast to studies done in other locations, the input was not higher during the first part of the night. The input level was related to moonlight and water level, but independent of tide direction. High input levels were recorded during all lunar phases, except the full moon. This lunar pattern differed from maximum settlement observed during the new moon in other locations. Consequently, a sampling strategy for studying temporal patterns of coral reef fish settlement in typical west Pacific high-islands should include new and quarter of the moon phases and should be extended to the entire night.

For a random closed set X and a compact observation window W the mean coverage fraction of W can be estimated by measuring the area of W covered by X. Jensen and Gundersen, and Baddeley and Cruz-Orive described cases where a point counting estimator is more efficient than area measurement. We give two other examples, where at first glance unnatural estimators are not only better than the area measurement but by Grenander's Theorem have minimal variance. Whittle's Theorem is used to show that the point counting estimator in the original Jensen-Gundersen paradox is optimal for large randomly translated discs.

We consider the problem of predicting integrals of second order processes whose covariances satisfy some Hölder regularity condition of order α > 0. When α is an odd integer, linear estimators based on regular sampling designs were constructed and asymptotic results for the approximation error were derived. We extend this result to any α > 0. When 2K < α ≤ 2K + 2, K a non-negative integer, we use an appropriate predictor based on the Euler-MacLaurin formula of order K with regular sampling designs. We give the corresponding result for the mean square error.