Thirty years of progeny from Chao’s inequality: Estimating and comparing richness with incidence data and incomplete sampling

In the context of capture-recapture studies, Chao (1987) derived an inequality among capture frequency counts to obtain a lower bound for the size of a population based on individuals’ capture/non-capture records for multiple capture occasions. The inequality has been applied to obtain a non-parametric lower bound of species richness of an assemblage based on species incidence (detection/non-detection) data in multiple sampling units. The inequality implies that the number of undetected species can be inferred from the species incidence frequency counts of the uniques (species detected in only one sampling unit) and duplicates (species detected in exactly two sampling units). In their pioneering paper, Colwell and Coddington (1994) gave the name “Chao2” to the estimator for the resulting species richness. (The “Chao1” estimator refers to a similar type of estimator based on species abundance data). Since then, the Chao2 estimator has been applied to many research fields and led to fruitful generalizations. Here, we first review Chao’s inequality under various models and discuss some related statistical inference questions: (1) Under what conditions is the Chao2 estimator an unbiased point estimator? (2) How many additional sampling units are needed to detect any arbitrary proportion (including 100%) of the Chao2 estimate of asymptotic species richness? (3) Can other incidence frequency counts be used to obtain similar lower bounds? We then show how the Chao2 estimator can be also used to guide a non-asymptotic analysis in which species richness estimators can be compared for equally-large or equally-complete samples via sample-size-based and coverage-based rarefaction and extrapolation. We also review the generalization of Chao’s inequality to estimate species richness under other sampling-without-replacement schemes (e.g. a set of quadrats, each surveyed only once), to obtain a lower bound of undetected species shared between two or multiple assemblages, and to allow inferences about undetected phylogenetic richness (the total length of undetected branches of a phylogenetic tree connecting all species), with associated rarefaction and extrapolation. A small empirical dataset for Australian birds is used for illustration, using online software SpadeR, iNEXT, and PhD

The flower mites of Trinidad III: The genus Rhinoseius (Acari: Ascidae)

http://deepblue.lib.umich.edu/bitstream/2027.42/56428/1/MP184.pd

Ecological and biogeographic null hypotheses for comparing rarefaction curves

The statistical framework of rarefaction curves and asymptotic estimators allows for an effective standardization of biodiversity measures. However, most statistical analyses still consist of point comparisons of diversity estimators for a particular sampling level. We introduce new randomization methods that incorporate sampling variability encompassing the entire length of the rarefaction curve and allow for statistical comparison of i ≥ 2 individual-based, sample-based, or coverage-based rarefaction curves. These methods distinguish between two distinct null hypotheses: the ecological null hypothesis (H0eco) and the biogeographical null hypothesis (H0biog). H0eco states that the i samples were drawn from a single assemblage, and any differences among them in species richness, composition, or relative abundance reflect only sampling effects. H0biog states that the i samples were drawn from assemblages that differ in their species composition but share similar species richness and species abundance distributions. To test H0eco, we created a composite rarefaction curve by summing the abundances of all species from the i samples. We then calculated a test statistic Zeco, the (cumulative) summed areas of difference between each of the i individual curves and the composite curve. For H0biog, the test statistic Zbiog was calculated by summing the area of difference between all possible pairs of the i individual curves. Bootstrap sampling from the composite curve (H0eco) or random sampling from different simulated assemblages using alternative abundance distributions (H0biog) was used to create the null distribution of Z, and to provide a frequentist test of ZjH0. Rejection of H0eco does not pinpoint whether the samples differ in species richness, species composition, and/or relative abundance. In benchmark comparisons, both tests performed satisfactorily against artificial data sets randomly drawn from a single assemblage (low Type I error). In benchmark comparisons with different species abundance distributions and richness, the tests had adequate power to detect differences among curves (low Type II error), although power diminished at small sample sizes and for small differences among underlying species rank abundances

Disentangling the exchange coupling of entangled donors in the Si quantum computer architecture

We develop a theory for micro-Raman scattering by single and coupled two-donor states in silicon. We find the Raman spectra to have significant dependence on the donor exchange splitting and the relative spatial positions of the two donor sites. In particular, we establish a strong correlation between the temperature dependence of the Raman peak intensity and the interdonor exchange coupling. Micro-Raman scattering can therefore potentially become a powerful tool to measure interqubit coupling in the development of a Si quantum computer architecture.Comment: Title changed. Other minor change

The Expanding Role of Natural History Collections

Museum specimens serve as the bedrock of systematic and taxonomic research and provide the basis for repeatability or reinterpretation of preserved aspects of phenotypes. Specimens are also fundamental to fields such as ecology, behavior, and development. Each specimen is a record of biodiversity and documents a particular species present at a particular place at a particular time. As such, specimens can provide key evidence for biodiversity and conservation initiatives. Four aspects of natural history collections and their use are discussed here: 1) collection, curation, and use of specimens, particularly non-traditional specimens; 2) the use of specimens and technological advances in morphology, ontogeny, systematics, and taxonomy; 3) specimen use in other fields of biology and ecology; and 4) specimen use in education and outreach. Collections, and their vitality, depend on both their continued roles in traditionally supported fields (e.g., taxonomy) as well as emerging arenas (e.g., epidemiology). Just as a library that ceases buying books becomes obsolete, or at least has diminished relevance, a natural history collection that does not continue to grow by adding new specimens ultimately will limit its utility. We discuss these roles of specimens and speak directly to the need to increase the visibility of the inherent value of natural history collections and the care of the specimens they protect for future generations

Identity Research and the Psychosocial Formation of One’s Sense of Spiritual Self: Implications for Religious Educators and Christian Institutions of Higher Education

Utilizing Erikson’s (1963) psychosocial ego identity development theory, 28 qualitative interviews with religiously devout Americans are analyzed to determine different patterns of adult spiritual identity. Following an integrationist approach, we provide response to the question, “What types of identity development are accommodated, promoted, or prohibited by particular models of Christian education and the educational communities that embody them?” Recognizing individual differences in (a) the social and contextual factors that affect identity formation, (b) the way religious doubts are resolved, and (c) what individuals seek from community, we offer important implications for religious educators and Christian institutions of higher education

Meter-Sized Moonlet Population in Saturn\u27s C Ring and Cassini Division

Stellar occultations observed by the Cassini Ultraviolet Imaging Spectrograph reveal the presence of transparent holes a few meters to a few tens of meters in radial extent in otherwise optically thick regions of the C ring and the Cassini Division. We attribute the holes to gravitational disturbances generated by a population of ~10 m boulders in the rings that is intermediate in size between the background ring particle size distribution and the previously observed ~100 m propeller moonlets in the A ring. The size distribution of these boulders is described by a shallower power-law than the one that describes the ring particle size distribution. The number and size distribution of these boulders could be explained by limited accretion processes deep within Saturn\u27s Roche zone

Use of ERTS-1 data in identification, classification, and mapping of salt-affected soils in California

There are no author-identified significant results in this report

Estimating the Richness of a Population When the Maximum Number of Classes Is Fixed: A Nonparametric Solution to an Archaeological Problem

Background: Estimating assemblage species or class richness from samples remains a challenging, but essential, goal. Though a variety of statistical tools for estimating species or class richness have been developed, they are all singly-bounded: assuming only a lower bound of species or classes. Nevertheless there are numerous situations, particularly in the cultural realm, where the maximum number of classes is fixed. For this reason, a new method is needed to estimate richness when both upper and lower bounds are known. Methodology/Principal Findings: Here, we introduce a new method for estimating class richness: doubly-bounded confidence intervals (both lower and upper bounds are known). We specifically illustrate our new method using the Chao1 estimator, rarefaction, and extrapolation, although any estimator of asymptotic richness can be used in our method. Using a case study of Clovis stone tools from the North American Lower Great Lakes region, we demonstrate that singly-bounded richness estimators can yield confidence intervals with upper bound estimates larger than the possible maximum number of classes, while our new method provides estimates that make empirical sense. Conclusions/Significance: Application of the new method for constructing doubly-bound richness estimates of Clovis stone tools permitted conclusions to be drawn that were not otherwise possible with singly-bounded richness estimates, namely, that Lower Great Lakes Clovis Paleoindians utilized a settlement pattern that was probably more logistical in nature than residential. However, our new method is not limited to archaeological applications. It can be applied to any set of data for which there is a fixed maximum number of classes, whether that be site occupancy models, commercial products (e.g. athletic shoes), or census information (e.g. nationality, religion, age, race)