Nonparametric mean estimation using partially ordered sets

In ranked-set sampling (RSS), the ranker must give a complete ranking of the units in each set. In this paper, we consider a modification of RSS that allows the ranker to declare ties. Our sampling method is simply to break the ties at random so that we obtain a standard ranked-set sample, but also to record the tie structure for use in estimation. We propose several different nonparametric mean estimators that incorporate the tie information, and we show that the best of these estimators is substantially more efficient than estimators that ignore the ties. As part of our comparison of estimators, we develop new results about models for ties in rankings. We also show that there are settings where, to achieve more efficient estimation, ties should be declared not just when the ranker is actually unsure about how units rank, but also when the ranker is sure about the ranking, but believes that the units are close.     

Density estimation using ranked-set sampling data

The ranked-set sampling (RSS) is applicable in practical problems where the variable of interest for an observed item is costly or time-consuming but the ranking of a set of items according to the variable can be easily done without actual measurement. In the context of RSS, the need for density estimation arises in certain statistical procedures. The density estimation also has its own interest. In this article, we develop a method for the density estimation using RSS data. We derive the properties of the resulted density estimate and compare it with its counterpart in simple random sampling (SRS). It is shown that the density estimate using RSS data provides a better estimate of the density than the usual density estimate using SRS data. The density estimate developed in this article can well serve various purposes in the context of RSS.     

Usefulness of the Umbrella Species Concept as a Conservation Tool

Abstract:  In the face of limited funding, knowledge, and time for action, conservation efforts often rely on shortcuts for the maintenance of biodiversity. The umbrella species concept—proposed as a way to use species requirements as a basis for conservation planning—has recently received growing attention. We reviewed the literature to evaluate the concept's general usefulness. An umbrella species is defined as a species whose conservation is expected to confer protection to a large number of naturally co-occurring species. This concept has been proposed as a tool for determining the minimum size for conservation areas, selecting sites to be included in reserve networks, and setting minimum standards for the composition, structure, and processes of ecosystems. Among the species suggested as potential umbrellas, most are large mammals and birds, but invertebrates are increasingly being considered. Eighteen research papers, most of which were based on hypothetical reserves or conservation networks, have provided evaluations of umbrella species schemes. These show that single-species umbrellas cannot ensure the conservation of all co-occurring species because some species are inevitably limited by ecological factors that are not relevant to the umbrella species. Moreover, they provide evidence that umbrella species from a given higher taxon may not necessarily confer protection to assemblages from other taxa. On the other hand, multi-species strategies based on systematic selection procedures (e.g., the focal species approach) offer more compelling evidence of the usefulness of the concept. Evaluations of umbrella species schemes could be improved by including measures of population viability and data from many years, as well as by comparing the efficiency of the proposed scheme with alternative management strategies.     

Nonparametric Ranked-set Sampling Confidence Intervals for Quantiles of a Finite Population

Ranked-set sampling from a finite population is considered in this paper. Three sampling protocols are described, and procedures for constructing nonparametric confidence intervals for a population quantile are developed. Algorithms for computing coverage probabilities for these confidence intervals are presented, and the use of interpolated confidence intervals is recommended as a means to approximately achieve coverage probabilities that cannot be achieved exactly. A simulation study based on finite populations of sizes 20, 30, 40, and 50 shows that the three sampling protocols follow a strict ordering in terms of the average lengths of the confidence intervals they produce. This study also shows that all three ranked-set sampling protocols tend to produce confidence intervals shorter than those produced by simple random sampling, with the difference being substantial for two of the protocols. The interpolated confidence intervals are shown to achieve coverage probabilities quite close to their nominal levels. Rankings done according to a highly correlated concomitant variable are shown to reduce the level of the confidence intervals only minimally. An example to illustrate the construction of confidence intervals according to this methodology is provided.     

Assessing the Value of the Umbrella‐Species Concept for Conservation Planning with Meta‐Analysis

Abstract: The umbrella‐species concept, which suggests that conservation strategies designed for one species may benefit co‐occurring species, has been promoted as a framework for conservation planning. Nevertheless, there has been considerable variation in the outcome of empirical tests of this concept that has led researchers to question its value, so we used data from 15 published studies in a meta‐analysis to evaluate whether conservation of putative umbrella species also conserves co‐occurring species. We tested the effectiveness of putative umbrella species categorized by taxonomic group, taxonomic similarity to co‐occurring species, body size, generality of resource use, and trophic level to evaluate criteria proposed to guide the selection of umbrella species. We compared species richness and number of individuals (by species and higher taxonomic group) between sites with and without putative umbrella species to test whether more co‐occurring species were present in greater abundances when the area or resource needs of umbrella species were met. Species richness and abundance of co‐occurring species were consistently higher in sites where umbrella species were present than where they were not and for conservation schemes with avian than with mammalian umbrella species. There were no differences in species richness or species abundance with resource generalist or specialist umbrella species or based on taxonomic similarity of umbrella and co‐occurring species. Taxonomic group abundance was higher in across‐taxonomic umbrella species schemes than when umbrella species were of the same taxon as co‐occurring species. Co‐occurring species had similar, or higher, species richness with small‐bodied umbrella species relative to larger‐bodied umbrella species. The only significant difference among umbrella species categorized by trophic level was that species richness was higher with omnivorous than it was with carnivorous avian umbrella species. Our results suggest there is merit to the umbrella‐species concept for conservation, but they do not support the use of the criteria we used to identify umbrella species.     

Use of surrogate species to cost-effectively prioritize conservation actions

Conservation efforts often focus on umbrella species whose distributions overlap with many other flora and fauna. However, because biodiversity is affected by different threats that are spatially variable, focusing only on the geographic range overlap of species may not be sufficient in allocating the necessary actions needed to efficiently abate threats. We developed a problem-based method for prioritizing conservation actions for umbrella species that maximizes the total number of flora and fauna benefiting from management while considering threats, actions, and costs. We tested our new method by assessing the performance of the Australian federal government's umbrella prioritization list, which identifies 73 umbrella species as priorities for conservation attention. Our results show that the federal government priority list benefits only 6% of all Australia's threatened terrestrial species. This could be increased to benefit nearly half (or 46%) of all threatened terrestrial species for the same budget of AU$550 million/year if more suitable umbrella species were chosen. This results in a 7-fold increase in management efficiency. We believe nations around the world can markedly improve the selection of prioritized umbrella species for conservation action with this transparent, quantitative, and objective prioritization approach.     

Selection of Multiple Umbrella Species for Functional and Taxonomic Diversity to Represent Urban Biodiversity

Surrogates, such as umbrella species, are commonly used to reduce the complexity of quantifying biodiversity for conservation purposes. The presence of umbrella species is often indicative of high taxonomic diversity; however, functional diversity is now recognized as an important metric for biodiversity and thus should be considered when choosing umbrella species. We identified umbrella species associated with high taxonomic and functional biodiversity in urban areas in Switzerland. We analyzed 39,752 individuals of 574 animal species from 96 study plots and 1397 presences of 262 plant species from 58 plots. Thirty‐one biodiversity measures of 7 taxonomic groups (plants, spiders, bees, ground beetles, lady bugs, weevils and birds) were included in within‐ and across‐taxa analyses. Sixteen measures were taxonomical (species richness and species diversity), whereas 15 were functional (species traits including mobility, resource use, and reproduction). We used indicator value analysis to identify umbrella species associated with single or multiple biodiversity measures. Many umbrella species were indicators of high biodiversity within their own taxonomic group (from 33.3% in weevils to 93.8% in birds), to a lesser extent they were indicators across taxa. Principal component analysis revealed that umbrella species for multiple measures of biodiversity represented different aspects of biodiversity, especially with respect to measures of taxonomic and functional diversity. Thus, even umbrella species for multiple measures of biodiversity were complementary in the biodiversity aspects they represented. Thus, the choice of umbrella species based solely on taxonomic diversity is questionable and may not represent biodiversity comprehensively. Our results suggest that, depending on conservation priorities, managers should choose multiple and complementary umbrella species to assess the state of biodiversity. Selección de Múltiples Especies Paraguas para la Diversidad Funcional y Taxonómica para Representar la Biodiversidad Urbana     

Evaluating the California Gnatcatcher as an Umbrella Species for Conservation of Southern California Coastal Sage Scrub

Abstract: Designing reserves that preserve the habitat of many coexisting and threatened species often involves use of conservation surrogates, such as umbrella species. Typically, animals with legal protection are used as umbrella species, and these selections are overwhelmingly vertebrates. The tacit assumption that vertebrates automatically serve as conservation umbrellas for invertebrates rarely has been justified. The California Gnatcatcher (   Polioptila californica, Muscicapidae ), is a federally listed and endangered species in the United States and has been used as an umbrella species for the conservation of coastal sage scrub in southern California. Conservation planning efforts for this community follow a general paradigm of using vertebrate-based reserve designs as de facto protection for invertebrate cohabitants. To test the effectiveness of this strategy, I surveyed 50 patches of coastal sage scrub in San Diego County for three species of Lepidoptera: Mormon metalmark ( Apodemia mormo, Riodinidae ), Bernardino blue, (   Euphilotes bernardino, Lycaenidae ), and Electra buckmoth (    Hemileuca electra, Saturniidae ). The presence of the gnatcatcher was a poor indicator of the presence of these insects. Only the largest or most recently separated habitat patches supported all three species of Lepidoptera, but the gnatcatcher was present on nearly every site, regardless of size. Results indicate that vertebrates do not automatically function as umbrella species for invertebrate cohabitants. Reserve designs based on vertebrate umbrella species, which assume invertebrates will be protected, may result in the loss of a large portion of invertebrate diversity.     

Enhancing Conservation,Ecosystem Services,and Local Livelihoods through a Wildlife Premium Mechanism

We propose the wildlife premium mechanism as an innovation to conserve endangered large vertebrates. The performance‐based payment scheme would allow stakeholders in lower‐income countries to generate revenue by recovering and maintaining threatened fauna that can also serve as umbrella species (i.e., species whose protection benefits other species with which they co‐occur). There are 3 possible options for applying the premium: option 1, embed premiums in a carbon payment; option 2, link premiums to a related carbon payment, but as independent and legally separate transactions; option 3, link premiums to noncarbon payments for conserving ecosystem services (PES). Each option presents advantages, such as incentive payments to improve livelihoods of rural poor who reside in or near areas harboring umbrella species, and challenges, such as the establishment of a subnational carbon credit scheme. In Kenya, Peru, and Nepal pilot premium projects are now underway or being finalized that largely follow option 1. The Kasigau (Kenya) project is the first voluntary carbon credit project to win approval from the 2 leading groups sanctioning such protocols and has already sold carbon credits totaling over $1.2 million since June 2011. A portion of the earnings is divided among community landowners and projects that support community members and has added over 350 jobs to the local economy. All 3 projects involve extensive community management because they occur on lands where locals hold the title or have a long‐term lease from the government. The monitoring, reporting, and verification required to make premium payments credible to investors include transparent methods for collecting data on key indices by trained community members and verification of their reporting by a biologist. A wildlife premium readiness fund would enable expansion of pilot programs needed to test options beyond those presented here. Mejora de la Conservación, Servicios del Ecosistema y Calidad de Vida Local Mediante un Mecanismo de Compensación de Vida Silvestre     

Lack-of-fit tests for assessing mean structures for continuous dose-response data

We review a range of lack-of-fit tests suitable for assessing the appropriateness of the mean function in dose-response models. The review encompasses both well-known tests and new tests based on recent developments in statistics, which we have extended to the dose-response case. We argue that the classical methods are inadequate in certain situations, where the new tests may be applied. Power comparisons are carried out by means of extensive simulation studies, covering both designs with and without replicates at small and large sample sizes. Three datasets from dose-response applications illustrate differences and similarities between the tests. The results suggest that the new tests perform better and exhibit a wider applicability.     

Structure and function of the locomotory system of the Scyphomedusa Cyanea capillata

The structure and function of the locomotory system of the jellyfish Cyanea capillata L. were studied by dissection, histology, photography and cinematography. The swimming muscle consists of a highly-folded subeptithelial-stratum of striated fibrils arranged on larger mesogleal folds. A proximal coronal muscle divided into 16 fields is anchored to the umbrella proper along the radial septa separating the fields. Sixteen distal couples of radial muscles are anchored to peripheral mesogleal buttresses. On the lower surface of the umbrellar mesoglea is a series of 16 deep radial grooves confluent with a coronal groove. These grooves (joints) are anchored to the exumbrellar surface of the umbrella by rows of large branching mesogleal fibers. During contraction, the muscles cause a folding of the umbrella around the system of joints. Sequences of swimming and turning were analyzed, and it was concluded that this swimming mechanism is much less refined than the hydrozoan mechanism.     

Defining and Evaluating the Umbrella Species Concept for Conserving and Restoring Landscape Connectivity

Conserving or restoring landscape connectivity between patches of breeding habitat is a common strategy to protect threatened species from habitat fragmentation. By managing connectivity for some species, usually charismatic vertebrates, it is often assumed that these species will serve as conservation umbrellas for other species. We tested this assumption by developing a quantitative method to measure overlap in dispersal habitat of 3 threatened species—a bird (the umbrella), a butterfly, and a frog—inhabiting the same fragmented landscape. Dispersal habitat was determined with Circuitscape, which was parameterized with movement data collected for each species. Despite differences in natural history and breeding habitat, we found substantial overlap in the spatial distributions of areas important for dispersal of this suite of taxa. However, the intuitive umbrella species (the bird) did not have the highest overlap with other species in terms of the areas that supported connectivity. Nevertheless, we contend that when there are no irreconcilable differences between the dispersal habitats of species that cohabitate on the landscape, managing for umbrella species can help conserve or restore connectivity simultaneously for multiple threatened species with different habitat requirements. Definición y Evaluación del Concepto de Especie Paraguas para Conservar y Restaurar la Conectividad de Paisajes     

A Mechanistic Approach to Evaluation of Umbrella Species as Conservation Surrogates

Abstract:  Although species with large area requirements are sometimes used as umbrella species, their general utility as conservation tools is uncertain. We surveyed the species diversity of birds, butterflies, carabids, and forest-floor plants in forest sites across an area (1600 km²) in which we delineated large breeding home ranges of Northern Goshawk ( Accipiter gentilis ). We tested whether protection of the home ranges could serve as an effective umbrella to protect sympatric species of the four taxa. We also used an empirical habitat model of occupancy of home range to examine mechanisms by which the Northern Goshawk acts as an umbrella species. Among species richness, abundance, and species composition of the four taxa, only abundance and species composition of birds differed between sites located inside and outside home ranges, which was due to greater abundance of bird species that were prey of Northern Goshawks inside the home ranges. Thus, although home range indicated areas with high abundance of certain bird prey species, it was not effective as an indicator of the species diversity of all four taxa. We also did not find any difference in species richness, abundance, and species composition between sites predicted as occupied and unoccupied using the habitat model. In contrast, when we selected sites on the basis of each habitat variable in the model, habitat variables that selected sites either in agricultural or forested landscapes encompassed sites with high species richness or particular species composition. This result suggests that the low performance of the Northern Goshawk as an umbrella species is due to this species' preference for habitat in both agricultural and forested landscapes. Species that can adjust to changes in habitat conditions may not act as effective umbrella species despite having large home ranges.     

Multivariate bootstrap confidence regions for abundance vector using

Abundance vector estimation is a well investigated problem in statistical ecology. The use of simple random sampling with replacement or replicated sampling ensures good asymptotic properties of the abundance vector estimators. However, real surveys are based on small sample sizes, and assuming any specific distribution of the abundance vector estimator may be hazardous.In this paper we focus our attention on situations where the population is not too large and the sample size is small. We propose bootstrap multivariate confidence regions based on data depth. Data depth is a geometrical concept of ordering data from the center outwardly in higher dimensions. The Simplicial depth, the Tukey's depth and the Mahalanobis depth are presented. In order to build confidence regions in the presence of a skewed distribution of the abundance vector estimator, the use of Tukey's depth is suggested. The proposed method has been applied to the benthic community of Lake Lesina. A comparison with Mahalanobis depth and standard existing methods is reported.     

Modeling misidentification errors that result from use of genetic tags in capture–recapture studies

Misidentification of animals is potentially important when naturally existing features (natural tags) such as DNA fingerprints (genetic tags) are used to identify individual animals. For example, when misidentification leads to multiple identities being assigned to an animal, traditional estimators tend to overestimate population size. Accounting for misidentification in capture–recapture models requires detailed understanding of the mechanism. Using genetic tags as an example, we outline a framework for modeling the effect of misidentification in closed population studies when individual identification is based on natural tags that are consistent over time (non-evolving natural tags). We first assume a single sample is obtained per animal for each capture event, and then generalize to the case where multiple samples (such as hair or scat samples) are collected per animal per capture occasion. We introduce methods for estimating population size and, using a simulation study, we show that our new estimators perform well for cases with moderately high capture probabilities or high misidentification rates. In contrast, conventional estimators can seriously overestimate population size when errors due to misidentification are ignored.     

Restoration of native biotic communities on land disturbed by metalliferous mining

The worldwide expansion of the metalliferous mining industry has caused increased attention to be directed at the reclamation of mine wastes. Until recently the majority of reclamation procedures were based on substrate amelioration with innocuous covering materials, the application of fertilisers and the sowing of non-indigenous species. Reinstatement of the native flora and fauna was rarely attempted. However, in several countries the mining legislation now requires reinstatement of at least the native vegetation as a reclamation objective. Many mines are located in natural ecosystems such as tropical and temperate forest, and arctic and alpine tundra where faithful reinstatement of the native flora and, if possible, the fauna is the prime objective.Despite the adverse physical and chemical properties of metal mine wastes, the requirements for the restoration of native floras and faunas are not impossible to meet. This paper reviews procedures for the restoration of native vegetation on land disturbed by metalliferous mining, and assesses the success of the procedures where appropriate evidence is available. Using these methods it has often been possible to create a permanent, self-perpetuating and relatively maintenance-free native vegetation which provides a diverse mosaic of habitats for native fauna to colonise. However, the development of methods for reinstatement of native biological communities on metalliferous mine wastes is in its infancy. Proper criteria have not yet been established for the assessment of the success of reinstatement and there is a paucity of published qualitative information on the success of restoration of native plant communities, particularly information covering a sufficient period of time to be ecologically meaningful.     

Comparison of a two-stage sampling design and its composite sample alternative: An application to soil studies

The objective of a long-term soil survey is to determine the mean concentrations of several chemical parameters for the pre-defined soil layers and to compare them with the corresponding values in the past. A two-stage random sampling procedure is used to achieve this goal. In the first step, n subplots are selected from N subplots by simple random sampling without replacement; in the second step, m sampling sites are chosen within each of the n selected subplots. Thus n · m soil samples are collected for each soil layer. The idea of the composite sample design comes from the challenge of reducing very expensive laboratory analyses: m laboratory samples from one subplot and one soil layer are physically mixed to form a composite sample. From each of the n selected subplots, one composite sample per soil layer is analyzed in the laboratory, thus n per soil layer in total. In this paper we show that the cost is reduced by the factor m — 1 when instead of the two-stage sampling its composite sample alternative is used; however, the variance of the composite sample mean is increased. In the case of positive intraclass correlation the increase is less than 12.5%; in the case of negative intraclass correlation the increase depends on the properties of the variable as well. For the univariate case we derive the optimal number of subplots and sampling sites. A case study is discussed at the end.     

Comparison of some homogeneity tests in analysis of over-dispersed binomial data

This paper compares the procedures based on the extended quasi-likelihood, pseudo-likelihood and quasi-likelihood approaches for testing homogeneity of several proportions for over-dispersed binomial data. The type I error of the Wald tests using the model-based and robust variance estimates, the score test, and the extended quasi-likelihood ratio test (deviance reduction test) were examined by simulation. The extended quasi-likelihood method performs less well when mean responses are close to 1 or 0. The model-based Wald test based on the quasi-likelihood performs the best in maintaining the nominal level. The score test performs less well when the intracluster correlations are large or heterogeneous. In summary: (i) both the quasilikelihood and pseudo-likelihood methods appear to be acceptable but care must be taken when overfitting a variance function with small sample sizes; (ii) the extended quasi-likelihood approach is the least favourable method because its nominal level is much too high; and (iii) the robust variance estimator performs poorly, particularly when the sample size is small.     

Estimating a distance dependent contagion function using point sample data

Natural events and human activities cause changes in landscape structure. Landscape metrics are used as a useful tool to study landscape trends and ecological processes related to the landscape structure. These metrics are commonly calculated on wall-to-wall raster data from remote sensing. A recent trend is to use sample data to estimate landscape metrics. In this study, point sampling was used to estimate a vector-based and distance dependent contagion metric. The metric is an extension of the established contagion. The statistical properties, for both unconditional and conditional contagions, were assessed by a point (point pairs) sampling experiment in maps from the National Inventory of landscapes in Sweden. Random and systematic sampling designs were tested for nine point distances and five sample sizes and for two classification systems. The systematic design showed slightly smaller root mean square error (RMSE) and bias than the random design. Both true and estimated values were calculated using computer programs in FORTRAN, which was specifically written for the purpose of the study. For a given sample size, RMSE and bias increased with increasing point distance. The estimator of unconditional contagion had acceptable RMSE and bias for moderate sample sizes, but in the conditional case the bias (and thus the RMSE) was unacceptably large. The main reason for this is that small classes (by area) affect both the true value of the contagion and are often missing in the sample. The method proposed can be adopted in gradient-based model of landscape structure where no distinct border is assumed between polygons. The method can also be applied in field-based inventories.     

Use made in marine ecology of methods for estimating demographic parameters from size/frequency data

Macdonald and Pitcher's method of decomposing a sizefrequency histogram into cohorts (mathematical optimization of the fit of the distribution function to the histogram) has been used to estimate the composition of random samples drawn from populations with known cohort structure. The large-sample behaviour of the method is in accordance with the results of asymptotic theory. With sample sizes typical of those used in many ecological studies, good estimates often could not be obtained without imposing constraints upon the estimation procedure, even when the number of age classes in the population was known. If the number of age classes was not known, it was frequently difficult to determine from small samples. When unconstrained solutions were obtainable, confidence limits about estimates were often very wide. Our results and information in the theoretical literature indicate that if the Petersen method (whereby several modes on a size-frequency histogram are taken to represent single age classes and all age classes to be present) does not work, accurate estimates of demographic parameters are unlikely to be obtainable using more rigorous methods. In view of these difficulties, we recommend that an iptimization method, such as that described by Macdonald and Pitcher, be used to estimate demographic parameters. Standard errors of estimates should be reported. Optimization methods give an indication when the data is inadequate to obtain accurate parameter estimates, either by failing to converge or by placing large standard errors about the estimates. Graphical methods do not give a clear warning of this, and should be avoided except where the modes on the size-frequency histogram are very well separated and sample sizes are large. Often, assumptions must be made about population parameters to enable their estimation. This may involve constraining some parameters to particular values, assuming a fixed relationship between cohort mean sizes and their standard deviations, or by assuming that individuals grow according to a von Bertalanffy curve. Any such assumptions need detailed justification in each case.