Journal Article•
Nonparametric estimation of the number of classes in a population
TL;DR: On applique la methode d'Efron (1981, 1982) a la construction d'intervalles de confiance bases sur des distributions du bootstrap as discussed by the authors.
Abstract: On applique la methode d'Efron (1981, 1982) a la construction d'intervalles de confiance bases sur des distributions du bootstrap
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TL;DR: The importance of using 'reference' sites to assess the true richness and composition of species assemblages, to measure ecologically significant ratios between unrelated taxa, toMeasure taxon/sub-taxon (hierarchical) ratios, and to 'calibrate' standardized sampling methods is discussed.
Abstract: Both the magnitude and the urgency of the task of assessing global biodiversity require that we make the most of what we know through the use of estimation and extrapolation. Likewise, future biodiversity inventories need to be designed around the use of effective sampling and estimation procedures, especially for 'hyperdiverse' groups of terrestrial organisms, such as arthropods, nematodes, fungi, and microorganisms. The challenge of estimating patterns of species richness from samples can be separated into (i) the problem of estimating local species richness, and (ii) the problem of estimating the distinctness, or complementarity, of species assemblages. These concepts apply on a wide range of spatial, temporal, and functional scales. Local richness can be estimated by extrapolating species accumulation curves, fitting parametric distributions of relative abundance, or using non-parametric techniques based on the distribution of individuals among species or of species among samples. We present several of these methods and examine their effectiveness for an example data set. We present a simple measure of complementarity, with some biogeographic examples, and outline the difficult problem of estimating complementarity from samples. Finally, we discuss the importance of using 'reference' sites (or sub-sites) to assess the true richness and composition of species assemblages, to measure ecologically significant ratios between unrelated taxa, to measure taxon/sub-taxon (hierarchical) ratios, and to 'calibrate' standardized sampling methods. This information can then be applied to the rapid, approximate assessment of species richness and faunal or floral composition at 'comparative' sites.
4,245 citations
TL;DR: Over 1.2 million previously unknown genes represented in these samples, including more than 782 new rhodopsin-like photoreceptors are identified, suggesting substantial oceanic microbial diversity.
Abstract: We have applied “whole-genome shotgun sequencing” to microbial populations collected en masse on tangential flow and impact filters from seawater samples collected from the Sargasso Sea near Bermuda. A total of 1.045 billion base pairs of nonredundant sequence was generated, annotated, and analyzed to elucidate the gene content, diversity, and relative abundance of the organisms within these environmental samples. These data are estimated to derive from at least 1800 genomic species based on sequence relatedness, including 148 previously unknown bacterial phylotypes. We have identified over 1.2 million previously unknown genes represented in these samples, including more than 782 new rhodopsin-like photoreceptors. Variation in species present and stoichiometry suggests substantial oceanic microbial diversity. Microorganisms are responsible for most of the biogeochemical cycles that shape the environment of Earth and its oceans. Yet, these organisms are the least well understood on Earth, as the ability to study and understand the metabolic potential of microorganisms has been hampered by the inability to generate pure cultures. Recent studies have begun to explore environ
4,210 citations
TL;DR: Patient stratification by GI microbiota provides further evidence that CD represents a spectrum of disease states and suggests that treatment of some forms of IBD may be facilitated by redress of the detected microbiological imbalances.
Abstract: The two primary human inflammatory bowel diseases, Crohn's disease (CD) and ulcerative colitis (UC), are idiopathic relapsing disorders characterized by chronic inflammation of the intestinal tract. Although several lines of reasoning suggest that gastrointestinal (GI) microbes influence inflammatory bowel disease (IBD) pathogenesis, the types of microbes involved have not been adequately described. Here we report the results of a culture-independent rRNA sequence analysis of GI tissue samples obtained from CD and UC patients, as well as non-IBD controls. Specimens were obtained through surgery from a variety of intestinal sites and included both pathologically normal and abnormal states. Our results provide comprehensive molecular-based analysis of the microbiota of the human small intestine. Comparison of clone libraries reveals statistically significant differences between the microbiotas of CD and UC patients and those of non-IBD controls. Significantly, our results indicate that a subset of CD and UC samples contained abnormal GI microbiotas, characterized by depletion of commensal bacteria, notably members of the phyla Firmicutes and Bacteroidetes. Patient stratification by GI microbiota provides further evidence that CD represents a spectrum of disease states and suggests that treatment of some forms of IBD may be facilitated by redress of the detected microbiological imbalances.
3,967 citations
TL;DR: It is shown that bacterial communities of deep water masses of the North Atlantic and diffuse flow hydrothermal vents are one to two orders of magnitude more complex than previously reported for any microbial environment.
Abstract: The evolution of marine microbes over billions of years predicts that the composition of microbial communities should be much greater than the published estimates of a few thousand distinct kinds of microbes per liter of seawater. By adopting a massively parallel tag sequencing strategy, we show that bacterial communities of deep water masses of the North Atlantic and diffuse flow hydrothermal vents are one to two orders of magnitude more complex than previously reported for any microbial environment. A relatively small number of different populations dominate all samples, but thousands of low-abundance populations account for most of the observed phylogenetic diversity. This "rare biosphere" is very ancient and may represent a nearly inexhaustible source of genomic innovation. Members of the rare biosphere are highly divergent from each other and, at different times in earth's history, may have had a profound impact on shaping planetary processes.
3,535 citations
TL;DR: Examination of the oral and gut microbiome of melanoma patients undergoing anti-programmed cell death 1 protein (PD-1) immunotherapy suggested enhanced systemic and antitumor immunity in responding patients with a favorable gut microbiome as well as in germ-free mice receiving fecal transplants from responding patients.
Abstract: Preclinical mouse models suggest that the gut microbiome modulates tumor response to checkpoint blockade immunotherapy; however, this has not been well-characterized in human cancer patients. Here we examined the oral and gut microbiome of melanoma patients undergoing anti-programmed cell death 1 protein (PD-1) immunotherapy (n = 112). Significant differences were observed in the diversity and composition of the patient gut microbiome of responders versus nonresponders. Analysis of patient fecal microbiome samples (n = 43, 30 responders, 13 nonresponders) showed significantly higher alpha diversity (P < 0.01) and relative abundance of bacteria of the Ruminococcaceae family (P < 0.01) in responding patients. Metagenomic studies revealed functional differences in gut bacteria in responders, including enrichment of anabolic pathways. Immune profiling suggested enhanced systemic and antitumor immunity in responding patients with a favorable gut microbiome as well as in germ-free mice receiving fecal transplants from responding patients. Together, these data have important implications for the treatment of melanoma patients with immune checkpoint inhibitors.
2,791 citations
References
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Book•
01 Jan 1987
TL;DR: The Delta Method and the Influence Function Cross-Validation, Jackknife and Bootstrap Balanced Repeated Replication (half-sampling) Random Subsampling Nonparametric Confidence Intervals as mentioned in this paper.
Abstract: The Jackknife Estimate of Bias The Jackknife Estimate of Variance Bias of the Jackknife Variance Estimate The Bootstrap The Infinitesimal Jackknife The Delta Method and the Influence Function Cross-Validation, Jackknife and Bootstrap Balanced Repeated Replications (Half-Sampling) Random Subsampling Nonparametric Confidence Intervals.
7,007 citations
TL;DR: It is shown that in a large collection of Lepidoptera captured in Malaya the frequency of the number of species represented by different numbers of individuals fitted somewhat closely to a hyperbola type of curve, so long as only the rarer species were considered.
Abstract: Part 1. It is shown that in a large collection of Lepidoptera captured in Malaya the frequency of the number of species represented by different numbers of individuals fitted somewhat closely to a hyperbola type of curve, so long as only the rarer species were considered. The data for the commoner species was not so strictly `randomized', but the whole series could be closely fitted by a series of the logarithmic type as described by Fisher in Part 3. Other data for random collections of insects in the field were also shown to fit fairly well to this series. Part 2. Extensive data on the capture of about 1500 Macrolepidoptera of about 240 species in a light-trap at Harpenden is analysed in relation to Fisher's mathematical theory and is shown to fit extremely closely to the calculations. The calculations are applied first to the frequency of occurrence of species represented by different numbers of individuals--and secondly to the number of species in samples of different sizes from the same population. The parameter ` alpha ', which it is suggested should be called the `index of diversity', is shown to have a regular seasonal change in the case of the Macrolepidoptera in the trap. In addition, samples from two traps which overlooked somewhat different vegetation are shown to have ` alpha ' values which are significantly different. It is shown that, provided the samples are not small, ` alpha ' is the increase in the number of species obtained by increasing the size of a sample by e (2.718). A diagram is given (Fig. 8) from which any one of the values, total number of species, total number of individuals and index of diversity (alpha), can be obtained approximately if the other two are known. The standard error of alpha is also indicated on the same diagram. Part 3. A theoretical distribution is developed which appears to be suitable for the frequencies with which different species occur in a random collection, in the common case in which many species are so rare that their chance of inclusion is small. The relationships of the new distribution with the negative binomial and the Poisson series are established. Numerical processes are exhibited for fitting the series to observations containing given numbers of species and individuals, and for estimating the parameter alpha representing the richness in species of the material sampled; secondly, for calculating the standard error of alpha, and thirdly, for testing whether the series exhibits a significant deviation from the limiting form used. Special tables are presented for facilitating these calculations.
3,121 citations
"Nonparametric estimation of the num..." refers methods in this paper
...When the hypothesis of equiprobability is false or in doubt, most previous approaches were to adopt specific parametric models, see Fisher et al. (1943), McNeil (1973), Engen (1974, 1978), Efron & Thisted (1976) and many others....
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TL;DR: A model is given for multiple recapture studies on closed populations which allows capture probabilities to vary among individuals and a nonparametric estimation procedure for population size is given that is robust to moderate variations in individual capture probabilities which may occur in commonly used short—term livetrapping studies.
Abstract: A model is given for multiple recapture studies on closed populations which allows capture probabilities to vary among individuals. The capture probability of each individual is assumed to be constant over time. Based on this model we give a nonparametric estimation procedure for population size. The estimator involves selecting one of a sequence of estimators which are each linear combinations of the capture frequencies. The individual estimators are derived from the generalized jackknife method. We also give a goodness of fit test for the model's assumption that individual capture probabilities do not change during the study. The robustness of this estimation procedure is investigated with a simulation study. By virtue of this study, and the theoretical nature of the estimator, it is judged to be robust to moderate variations in individual capture probabilities which may occur in commonly used short—term livetrapping studies. See full-text article at JSTOR
840 citations
"Nonparametric estimation of the num..." refers background or methods or result in this paper
...For practical examples, see Goodman (1949), Efron & Thisted (1976), Burnham & Overton (1978, 1979) and Holst (1981)....
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...(1) Burnham & Overton (1979) also provided a testing procedure to select an appropriate k....
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...On the other hand, Burnham & Overton (1978, 1979) suggested to use the jackknife estimate 63= 159 with the interval of (116, 202)....
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...The form of the jackknife estimator developed by Burnham & Overton (1978, 1979) for multiple recapture studies is slightly different from that given in (1)....
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...Applying the generalized jackknife technique to the naive estimator d, Burnham & Overton (1978, 1979) have developed nonparametric estimators under the assumption that the bias of d is expressible in a power series in N-1....
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TL;DR: In this article, a model which allows capture probabilities to vary by individuals is introduced for multiple recapture studies on closed populations, where the set of individual capture probabilities is modelled as a random sample from an arbitrary probability distribution over the unit interval.
Abstract: SUMMARY A model which allows capture probabilities to vary by individuals is introduced for multiple recapture studies on closed populations. The set of individual capture probabilities is modelled as a random sample from an arbitrary probability distribution over the unit interval. We show that the capture frequencies are a sufficient statistic. A nonparametric estimator of population size is developed based on the generalized jackknife; this estimator is found to be a linear combination of the capture frequencies. Finally, tests of underlying assumptions are presented.
770 citations
"Nonparametric estimation of the num..." refers background or methods or result in this paper
...The form of the jackknife estimator developed by Burnham & Overton (1978, 1979) for multiple recapture studies is slightly different from that given in (1)....
[...]
...Applying the generalized jackknife technique to the naive estimator d, Burnham & Overton (1978, 1979) have developed nonparametric estimators under the assumption that the bias of d is expressible in a power series in N-1....
[...]
...On the other hand, Burnham & Overton (1978, 1979) suggested to use the jackknife estimate 63= 159 with the interval of (116, 202)....
[...]
...For practical examples, see Goodman (1949), Efron & Thisted (1976), Burnham & Overton (1978, 1979) and Holst (1981)....
[...]
TL;DR: In this paper, the authors investigate several nonparametric methods, such as the bootstrap, the jackknife, the delta method, and other related techniques, to assign non-parametric standard errors to a real-valued statistic.
Abstract: We investigate several nonparametric methods; the bootstrap, the jackknife, the delta method, and other related techniques. The first and simplest goal is the assignment of nonparametric standard errors to a real-valued statistic. More ambitiously, we consider setting nonparametric confidence intervals for a real-valued parameter. Building on the well understood case of confidence intervals for the median, some hopeful evidence is presented that such a theory may be possible.
693 citations
"Nonparametric estimation of the num..." refers background or methods in this paper
...Efron (1981, 1982) introduced the percentile method using bootstrap distributions to set confidence intervals in general nonparametric situations, and justified it from various theoretical points of view....
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...Then Efron's percentile method (Efron 1981, 1982) is applied as follows: (i) Draw a bootstrap sample of size N from the "pseudo population" and compute 0* based on this sample....
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...For practical examples, see Goodman (1949), Efron & Thisted (1976), Burnham & Overton (1978, 1979) and Holst (1981)....
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