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Statistical models for estimating absolute densities of field populations of animals have been widely used over the last century in both scientific studies and wildlife management programs. To date, two general classes of density estimation models have been developed: models that use data sets from capture-recapture or removal sampling techniques (often derived from trapping grids) from which separate estimates of population size$(\\hat N) and effective sampling area (\\hat A) are used to calculate density (\\hat D=\\hat N/\\hat A);$and models applicable to sampling regimes using distance-sampling theory (typically transect lines or trapping webs) to estimate detection functions and densities directly from the distance data. However, few studies have evaluated these respective models for accuracy, precision, and bias on known field populations, and no studies have been conducted that compare the two approaches under controlled field conditions. In this study, we evaluated both classes of density estimators on known densities of enclosed rodent populations. Test data sets (n = 11) were developed using nine rodent species from capture-recapture live-trapping on both trapping grids and trapping webs in four replicate 4.2-ha enclosures on the Sevilleta National Wildlife Refuge in central New Mexico, USA. Additional \"saturation\" trapping efforts resulted in an enumeration of the rodent populations in each enclosure, allowing the computation of true densities.$Density estimates (\\hat D) were calculated using program CAPTURE$for the grid data sets and program DISTANCE for the web data sets, and these results were compared to the known true densities (D) to evaluate each model's relative mean square error, accuracy, precision, and bias. In addition, we evaluated a variety of approaches to each data set's analysis by having a group of independent expert analysts calculate their best density estimates without a priori knowledge of the true densities; this \"blind\" test allowed us to evaluate the influence of expertise and experience in calculating density estimates in comparison to simply using default values in programs CAPTURE and DISTANCE. While the rodent sample sizes were considerably smaller than the recommended minimum for good model results, we found that several models performed well empirically, including the web-based uniform and half-normal models in program DISTANCE, and the grid-based models$M_b and M_{bh} in program CAPTURE (with \\hat A) adjusted by species-specific $full mean maximum distance moved (MMDM) values).$These models produced accurate \\hat D values $(with 95% confidence intervals that included the true D values) and exhibited acceptable bias but poor precision. However, in linear regression analyses$comparing each model's \\hat D values to the true D values$over the range of observed test densities, only the web-based uniform model exhibited a regression slope near 1.0; all other models showed substantial slope deviations, indicating biased estimates at higher or lower density values. In addition,$the grid-based \\hat D analyses using full MMDM values for \\hat W area adjustments$required a number of theoretical assumptions of uncertain validity, and we therefore viewed their empirical successes with caution. Finally, density estimates from the independent analysts were highly variable, but estimates from web-based approaches had smaller mean square errors and better achieved confidence-interval coverage of D than did grid-based approaches. Our results support the contention that web-based approaches for density estimation of small-mammal populations are both theoretically and empirically superior to grid-based approaches, even when sample size is far less than often recommended. In view of the increasing need for standardized environmental measures for comparisons among ecosystems and through time, analytical models based on distance sampling appear to offer accurate density estimation approaches for research studies involving small-mammal abundances.

Caridean shrimps (Caridea) are the dominant macroinvertebrates in most anchialine ecosystems. Hawaiian anchialine ecosystems, primarily composed of shallow surface pools connected to the ocean via hypogeal networks of cracks, tubes, and other voids, support 10 caridean shrimp species, including two federally listed as endangered. Little is known about most of these species. The objective of this study was to identify factors that affect the abundance and distribution of Metabetaeus lohena (Alpheidae), an uncommon species found across the Hawaiian Archipelago, at Kaloko-Honokōhau National Historical Park, Island of Hawai‘i. This park supports the highest concentration of anchialine pools in the State of Hawai‘i and is critical to protecting this threatened ecosystem. During 2017, we measured the density of M. lohena during nighttime surveys, as well as a variety of other biological, physical, and chemical parameters, in 130 pools. Metabetaeus lohena occupied 71.5% of the pools surveyed, with a mean density of 7.32 individuals/m2 (95% CI = 5.14–9.49). Invasive fish and the endemic shrimp Halocaridina rubra (Atyidae) had the strongest effects on M. lohena density, with negative and positive relations, respectively. In the first estimate of M. lohena density at this scale, our data indicate that Kaloko-Honokōhau supports about 11,480 shrimp (95% CI = 8,054–14,906) in the pools surveyed. Furthermore, our models predict that this park could support an additional 1,695 individuals (95% CI = 955–3,008) for a population of about 13,175 shrimp if fish were removed from 19 pools in which M. lohena are absent.

Let $\\mathfrak {F}_n$ be the set of all cuspidal automorphic representations $\\pi$ of $\\mathrm {GL}_n$ with unitary central character over a number field $F$. We prove the first unconditional zero density estimate for the set $\\mathcal {S}=\\{L(s,\\pi \\times \\pi ')\\colon \\pi \\in \\mathfrak {F}_n\\}$ of Rankin–Selberg $L$-functions, where $\\pi '\\in \\mathfrak {F}_{n'}$ is fixed. We use this density estimate to establish: (i) a hybrid-aspect subconvexity bound at $s=\\frac {1}{2}$ for almost all $L(s,\\pi \\times \\pi ')\\in \\mathcal {S}$; (ii) a strong on-average form of effective multiplicity one for almost all $\\pi \\in \\mathfrak {F}_n$; and (iii) a positive level of distribution for $L(s,\\pi \\times \\widetilde {\\pi })$, in the sense of Bombieri–Vinogradov, for each $\\pi \\in \\mathfrak {F}_n$.

We construct near-optimal coresets for kernel density estimates for points in Rd when the kernel is positive definite. Specifically we provide a polynomial time construction for a coreset of size O(d/ε·log1/ε), and we show a near-matching lower bound of size Ω(min{d/ε,1/ε2}). When d≥1/ε2, it is known that the size of coreset can be O(1/ε2). The upper bound is a polynomial-in-(1/ε) improvement when d∈[3,1/ε2) and the lower bound is the first known lower bound to depend on d for this problem. Moreover, the upper bound restriction that the kernel is positive definite is significant in that it applies to a wide variety of kernels, specifically those most important for machine learning. This includes kernels for information distances and the sinc kernel which can be negative.

The white-tailed deer (Odocoileus virginianus) is an ecologically important species in forests of North America. Effective management of forests requires accurate, precise estimates of deer population abundance to plan and justify management actions. Spotlight surveys in combination with distance sampling are a common method of estimating deer population abundance; however, spotlight surveys are known to have serious drawbacks such as high costs and sampling biases. Therefore, we tested the effectiveness of enumerating deer from unmanned aerial vehicle (UAV) flights, conducted 1 and 6 March 2018, to develop population and density estimates in 2 United States National Parks: Harpers Ferry National Historic Park (HAFE) and Monocacy National Battlefield (MONO). Concurrent spotlight surveys at MONO enabled us to compare estimates obtained by the 2 methods. Deer density estimates by 4 observers of UAV-obtained thermal imagery from HAFE were 94.5 ± 3.9 deer/km². Concurrent UAV and spotlight surveys at MONO found 19.7 ± 0.5 deer/km² and 6.4 ± 4.9 deer/km², respectively; suggesting that spotlight surveys may significantly underestimate deer densities. Despite the logistical challenges to UAV operation, our findings demonstrate that UAVs will become an invaluable tool for wildlife management as technology improves.

Data are currently being used, and reused, in ecological research at an unprecedented rate. To ensure appropriate reuse however, we need to ask the question: “Are aggregated databases currently providing the right information to enable effective and unbiased reuse?” We investigate this question, with a focus on designs that purposefully favor the selection of sampling locations (upweighting the probability of selection of some locations). These designs are common and examples are those designs that have uneven inclusion probabilities or are stratified. We perform a simulation experiment by creating data sets with progressively more uneven inclusion probabilities and examine the resulting estimates of the average number of individuals per unit area (density). The effect of ignoring the survey design can be profound, with biases of up to 250% in density estimates when naive analytical methods are used. This density estimation bias is not reduced by adding more data. Fortunately, the estimation bias can be mitigated by using an appropriate estimator or an appropriate model that incorporates the design information. These are only available however, when essential information about the survey design is available: the sample location selection process (e.g., inclusion probabilities), and/or covariates used in their specification. The results suggest that such information must be stored and served with the data to support meaningful inference and data reuse.

The Eurasian otter Lutra lutra is a territorial semi-aquatic carnivore usually found at low densities in rivers, coastal areas, and wetlands. Its diet is based on prey associated with aquatic environments. Mediterranean rivers are highly seasonal, and suffer reduced flow during the summer, resulting in isolated river sections (pools) that sometimes can be left with a minimal amount of water, leading to concentrations of food for otters. To our knowledge, this process, which was known to field naturalists, has not been accurately described, nor have otter densities been estimated under these conditions. In this study, we describe the population size and movements of an aggregation of otters in an isolated pool in the Guadiana River in the Tablas de Daimiel National Park (central Spain), which progressively dried out during the spring–summer of 2022, in a context of low connectivity due to the absence of circulating water in the Guadiana and Gigüela rivers. Using non-invasive genetic sampling of 120 spraints collected along 79.4 km of sampling transects and spatial capture-recapture methods, we estimated the otter density at 1.71 individuals/km of river channel length (4.21 individuals/km 2 ) in a progressively drying river pool, up to five times higher than previously described in the Iberian Peninsula. The movement patterns obtained with the spatial capture-recapture model are not quite different from those described in low density, which seems to indicate a wide home range overlap, with low signs of territoriality.

Lead isotope analysis has been used to provenance metals such as lead, silver and bronze for many decades. Different approaches to interpret lead isotope ratios were proposed, and various limitations of the method have been discussed and addressed. Overlap in composition between different possible ore sources is always mentioned as a major limitation in lead isotope studies. However, it has never been comprehensively studied using a multivariate statistical approach. In this paper, the kernel density estimation (KDE) approach previously proposed by the authors is applied to calculate overlap between possible ore source regions. Firstly, the copper and lead ores of the same regions are compared, to assess if they are consistent and thus can be combined to increase sample size for provenance studies. Secondly, the pair-wise overlap between all the mining regions is calculated to determine if the distinction can actually be made between those ore fields. The use of one-dimensional KDE’s is very effective for calculation and assessment of the overlap between ore sources. This study argues that merging the lead and copper ore data might increase the reliability of a region’s KDE’s in most cases, but the overlap should be assessed beforehand. Furthermore, the study provides useful tools to verify for every pair of possible ore sources if it is theoretically possible to discriminate between them, and to what extent.

We prove a version of the prime number theorem for arithmetic progressions that is uniform enough to deduce the Siegel–Walfisz theorem, Hoheisel’s asymptotic for intervals of length x 7 / 12 + ε , a Brun–Titchmarsh bound, and Linnik’s bound on the least prime in an arithmetic progression as corollaries. Our proof uses the Vinogradov–Korobov zero-free region, a log-free zero density estimate, and the Deuring–Heilbronn zero repulsion phenomenon. Improvements exist when the modulus is sufficiently powerful.