Multinomial N-mixture models for removal sampling

Multinomial $N$-mixture models are commonly used to fit data from a removal sampling protocol. If the mixing distribution is negative binomial, the distribution of the counts does not appear to have been identified, and practitioners approximate the requisite likelihood by placing an upper bound on the embedded infinite sum. In this paper, the distribution which underpins the multinomial $N$-mixture model with a negative binomial mixing distribution is shown to belong to the broad class of multivariate negative binomial distributions. Specifically, the likelihood can be expressed in closed form as the product of conditional and marginal likelihoods and the information matrix shown to be block diagonal. As a consequence, the nature of the maximum likelihood estimates of the unknown parameters and their attendant standard errors can be examined and tests of the hypothesis of the Poisson against the negative binomial mixing distribution formulated. In addition, appropriate multinomial $N$-mixture models for data sets which include zero site totals can also be constructed. Two illustrative examples are provided.     

On the two-locus sampling distribution

Two methods are discussed for evaluating the distribution of the configuration of unlabeled gametic types in a random sample of size n from the two-locus infinitely-many-neutral-alleles diffusion model at stationarity. Both involve finding systems of linear equations satisfied by the desired probabilities. The first approach, which is due to Golding, is to include additional probabilities in the system that allow some members of the sample to be specified at only one locus. The second approach, which is new, considers the joint distribution of the sample configuration and the number of recombination events since the time of the most recent common ancestor. The first approach is used for numerical computation, whereas the second approach is used to derive a two-locus version of Hoppe's urn model. The latter permits efficient simulation of the two-locus sampling distribution, provided the recombination parameter is not too large.Supported in part by NSF grants DMS-8704369 and DMS-8902991     

Partition structures, Polya urns, the Ewens sampling formula, and the ages of alleles

It has recently been shown that the Ewens sampling formula may be generated by a Polya-like urn model. A genealogical proof of this result equates the labelling of balls in the urn to the partition by age of alleles in the sample. This urn construction is shown to be equivalent to the construction of Kingman (Proc. Roy. Soc. London Ser. A 361 (1978), 1-20) using a Poisson-Dirichlet "paintbox" and as a consequence, the partition by ages is seen to be equivalent to the size biased permutation of the Poisson-Dirichlet distribution. This approach unifies and extends many results on ages of alleles, the Polya urn, and the Poisson-Dirichlet distribution. Furthermore the Ewens sampling formula is characterized as being the only partition structure which may be generated by an urn-like mechanism.     

A randomized test for the conditional odds ratio of matched pairs in an inverse binomial sampling design

Matched case‐control paired data are commonly used to study the association between a disease and an exposure of interest. This work provides a consistent test for this association with respect to the conditional odds ratio (), which is a measure of association that is also valid in prospective studies. We formulate the test from the maximum likelihood (ML) estimate of by using data under inverse binomial sampling, in which individuals are selected sequentially to form matched pairs until for the first time one obtains either a prefixed number of index pairs with the case unexposed but the control exposed or with the case exposed but the control unexposed. We discuss the situation of possible early stopping. We compare numerically the performance of our procedure with a competitor proposed by Lui ( 1996 ) in terms of type I error rate, power, average sample number (ASN) and the corresponding standard error. Our numerical study shows a gain in sample size without loss in power as compared to the competitor. Finally, we use the data taken from a case‐control study on the use of X‐rays and the risk of childhood acute myeloid leukemia for illustration.     

Effects of distance on detectability of Arctic waterfowl using double‐observer sampling during helicopter surveys

Aerial survey is an important, widely employed approach for estimating free‐ranging wildlife over large or inaccessible study areas. We studied how a distance covariate influenced probability of double‐observer detections for birds counted during a helicopter survey in Canada’s central Arctic. Two observers, one behind the other but visually obscured from each other, counted birds in an incompletely shared field of view to a distance of 200 m. Each observer assigned detections to one of five 40‐m distance bins, guided by semi‐transparent marks on aircraft windows. Detections were recorded with distance bin, taxonomic group, wing‐flapping behavior, and group size. We compared two general model‐based estimation approaches pertinent to sampling wildlife under such situations. One was based on double‐observer methods without distance information, that provide sampling analogous to that required for mark–recapture (MR) estimation of detection probability, , and group abundance, , along a fixed‐width strip transect. The other method incorporated double‐observer MR with a categorical distance covariate (MRD). A priori, we were concerned that estimators from MR models were compromised by heterogeneity in due to un‐modeled distance information; that is, more distant birds are less likely to be detected by both observers, with the predicted effect that would be biased high, and biased low. We found that, despite increased complexity, MRD models (ΔAICc range: 0–16) fit data far better than MR models (ΔAICc range: 204–258). However, contrary to expectation, the more naïve MR estimators of were biased low in all cases, but only by 2%–5% in most cases. We suspect that this apparently anomalous finding was the result of specific limitations to, and trade‐offs in, visibility by observers on the survey platform used. While MR models provided acceptable point estimates of group abundance, their far higher stranded errors (0%–40%) compared to MRD estimates would compromise ability to detect temporal or spatial differences in abundance. Given improved precision of MRD models relative to MR models, and the possibility of bias when using MR methods from other survey platforms, we recommend avian ecologists use MRD protocols and estimation procedures when surveying Arctic bird populations.     

Novel redistribution of myosin-containing filaments in cultured keratinocytes identified by a human monoclonal autoantibody

Summary A time-dependent redistribution of microfilaments was observed in cultured human keratinocytes using a human monoclonal autoantibody specific for myosin. Immunofluorescent staining revealed that 5 days after plating keratinocytes in either 0.1 mM or 2.0 mM Ca⁺⁺, myosin was distributed uniformly throughout the cytoplasm. At day 6, parallel arrays of myosin-containing microfilaments were prominent in the cell peripheries. At day 7 the microfilaments formed circumferential rings. The distribution of the microfilaments was disrupted by cytochalasin but not by colchicine, indicating that this novel distribution of myosin was not dependent on colchicine-sensitive vimentin intermediate filaments. The time-dependent redistribution of myosin was not influenced by cell population density, cell shape or cell cycle phase, except for mitotic cells in which myosin was distributed diffusely through the cytoplasm. If, as suggested by Kolega (9), microfilaments align parallel to the direction of applied tension, the redistribution of myosin-containing microfilaments in cultured keratinocytes may reflect the increased tension between cells resulting from increasing strength of cell-cell junctions over time. In sectioned human skin, myosin was localized in the peripheral cytoplasm of stratified epidermal cells. Tensions arising from the numerous desmosomal junctions between cellsin vivo could account for this distribution of myosin. Supported by grant NS-23537 (V. A. L.) from the National Institutes of Health, Bethesda, MD, and by the Mayo Foundation. C. L. W. is recipient of the Kermit E. Osserman and Blanche McClure Fellowship, 1987, National Myasthenia Gravis Foundation.     

Pólya-like urns and the Ewens' sampling formula

A Markov process of partitions of the natural numbers is constructed by defining a Pólya-like urn model. The marginal distributions of this process are the Ewens' sampling distributions of population genetics.Research supported in part by NSF Grant MCS-8108689     

Application of the\mathop m\limits^* - m method to the analysis of spatial patterns by changing the quadrat sizemethod to the analysis of spatial patterns by changing the quadrat size

A method for the analysis of spatial pattern using quadrats of different sizes is developed on the basis of the relationship of mean crowding () to mean density (m). The -on-m regression obtained by successive changes in quadrat size in a single population (unit-size relation) shows a characteristic pattern according to the type of distribution. By aid of the ρ-index proposed here, we can distinguish the random, aggregated and uniform distributions of the basic components (individual or group of individuals). The ρ serves as an index of spatial correlation between neighbouring quadrats, and it also provides information on the approximate area occupied by clump (colony), distribution pattern of individuals within clumps, and possibly the distribution pattern of clumps themselves. Even in a specified type of distribution, the unit-size relation is not necessarily identical with the relation for a series of populations at a particular quadrat size (series relation). The changes in the series relationship with successive changes of quadrat sizes are also considered for some basic patterns of distributions. The combined use of the unit-size and the series relations for a set of populations of the species under study may provide a satisfactory picture of the spatial pattern characteristic of the species. Application of the method is illustrated by using distribution data of several species of animals and plants. The advantage of the present method over other methods are discussed, and the formulae for determining the optimum quadrat unit in sampling surveys are given.     

Population dynamics of the chestnut gall-wasp,Dryocosmus kuriphilus Yasumatsu (Hymenoptera: Cynipidae) IV. Further analysis of the distribution of eggs and young larvae in buds using the truncated negative binomial series

Distribution pattern of eggs and the first instar larvae of the chestnut gall-wasp, Dryocosmus kuriphilus, per bud of the chestnut tree was re-examined using the truncatedPoisson and the truncated negative binomial series. The results are as follows:

1. About sixty percent of the distribution are approximated by the truncated negative binomial and another thirty percent by the truncatedPoisson . When the distribution has been approximated by the truncated negative binomial, the show scattered values, some of which are near thePoisson , but the mean value of is about 4 both in eggs and in the first instar larvae.
2. The number of buds which have not been infested by gall-wasps is resulted from various factors as follows: (a) Buds formed after the laying activity of gall-wasps has ceased; (b) Old and shrunk buds which were avoided in laying; (c) Buds in which eggs have died by the time of sampling; and (d) Buds escaping ovipositions by chance. Most of the gall-wasp-free buds located in the middle part of the shoot are accounted for the zero-class expected by the negative binomial series.
3. Brass (1958) moment method for estimating parameters of the truncated negative binomial give good precision within the range of from 1 to 10 and of from 1 to 6.
4. It is concluded that the truncated distributions used are useful for the purpose of analysis of the distribution pattern of the chestnut gall-wasp.

     

Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles

Ewens' sampling formula, the probability distribution of a configuration of alleles in a sample of genes under the infinitely-many-alleles model of mutation, is proved by a direct combinatorial argument. The distribution is extended to a model where the population size may vary back in time. The distribution of age-ordered frequencies in the population is also derived in the model, extending the GEM distribution of age-ordered frequencies in a model with a constant-sized population. The genealogy of a rare allele is studied using a combinatorial approach. A connection is explored between the distribution of age-ordered frequencies and ladder indices and heights in a sequence of random variables. In a sample of n genes the connection is with ladder heights and indices in a sequence of draws from an urn containing balls labelled 1,2,...,n; and in the population the connection is with ladder heights and indices in a sequence of independent uniform random variables.     

Analysis of spatial association between two species based on the interspecies mean crowding

The measurement of spatial association between two species is considered on the basis of interspecies mean crowding. Two indices of overlapping, γ and C_p, are derived as geometric and weighted arithmetic means of the same component ratios related to inter-and intraspecies mean crowdings. Both indices behave in a similar way, ranging from 1 when the distributions of two species are completely overlapped to 0 when they are completely exclusive with each other. The former is essentially identical with indices proposed byKuno (1968) andPianka (1973), and the latter is a modified form ofMorisita's (1959)C_σ index. Indices to measure the degree of spatial correlation between species, Ω and R_μ, are then derived for both kinds of overlapping indices, which vary from 1 in complete overlapping, through 0 in independent occurrence, to −1 in complete exclusion. Various kinds of interspecies association are analyzed using these indices and an extended form of the regression graph which provides a convenient way of indicating the spatial interrelation between two species as well as distribution patterns of respective species. The method presented in this paper may also be applicable to compare temporal distribution patterns between species, similarity between communities, etc. For such a wider application which includes continuous as well as discrete distributions, the interpretation of intra-and interspecies mean crowdings is not necessarily appropriate, and hence the concept of mean concentration with the symbols and for intraspecies relation and and for interspecies relation is suggested.     

Estimating the distribution of heterogeneous treatment effects from treatment responses and from a predictive biomarker in a parallel-group RCT: A structural model approach

When the objective is to administer the best of two treatments to an individual, it is necessary to know his or her individual treatment effects (ITEs) and the correlation between the potential responses (PRs) and under treatments 1 and 0. Data that are generated in a parallel-group design RCT does not allow the ITE to be determined because only two samples from the marginal distributions of these PRs are observed and not the corresponding joint distribution. This is due to the “fundamental problem of causal inference.” Here, we present a counterfactual approach for estimating the joint distribution of two normally distributed responses to two treatments. This joint distribution of the PRs and can be estimated by assuming a bivariate normal distribution for the PRs and by using a normally distributed baseline biomarker functionally related to the sum . Such a functional relationship is plausible since a biomarker and the sum encode for the same information in an RCT, namely the variation between subjects. The estimation of the joint trivariate distribution is subjected to some constraints. These constraints can be framed in the context of linear regressions with regard to the proportions of variances in the responses explained and with regard to the residual variation. This presents new insights on the presence of treatment–biomarker interactions. We applied our approach to example data on exercise and heart rate and extended the approach to survival data.     

Non-linear compartmental systems: extensions of S. R. Bernard's urn model

One of the limitations of stochastic, linear compartmental systems is the small degree of variability in the contents of compartments. S. R. Bernard's (1981) urn model (S. R. Bernardet al., Bull. math. Biol. 43, 33–45.) which allows for bulk arrivals and departures from a one-compartment system, was suggested as a way of increasing content variability. In this paper, we show how the probability distribution of the contents of an urn model may be simply derived by studying an appropriate set of exchangeable random variables. In addition, we show how further increases in variability may be modeled by allowing the size of arrivals and departures to be random. Supported by NSF Grant No. MCS 8102215-01.     

Important role of genetic drift in rapid polygenic adaptation

We analyzed a model to determine the factors that facilitate or limit rapid polygenic adaptation. This model includes population genetic terms of mutation and both directional and stabilizing selection on a highly polygenic trait in a diploid population of finite size. First, we derived the equilibrium distribution of the allele frequencies of the multilocus model by diffusion approximation. This formula describing the equilibrium allele frequencies as a mutation‐selection‐drift balance was examined by computer simulation using parameter values inferred for human height, a well‐studied polygenic trait. Second, assuming that a sudden environmental shift of the fitness optimum occurs while the population is in equilibrium, we analyzed the adaptation of the trait to the new optimum. The speed at which the trait mean approaches the new optimum increases with the equilibrium genetic variance. Thus, large population size and/or large mutation rate may facilitate rapid adaptation. Third, the contribution of an individual locus i to polygenic adaptation depends on the compound parameter , where is the effect size, the equilibrium frequency of the trait‐increasing allele of this locus, and . Thus, only loci with large values of this parameter contribute coherently to polygenic adaptation. Given that mutation rates are relatively small, this is more likely in large populations, in which the effects of drift are limited.     

An index of spatial distribution

The index , which takes the value of −1 for a perfectly regular distribution, +1 for a highly aggregated distribution and 0 for the distribution implied by the theoretical varianceσ², is proposed and a significance table provided.     

Five new species of Dicerapanorpa Zhong & Hua (Mecoptera,Panorpidae) from Yunnan,China

Five new scorpionfly species of the genus Dicerapanorpa Zhong and Hua, 2013 are described and illustrated from Yunnan Province, China. Dicerapanorpa macula sp. n. can be readily recognized by all branches of paramere parallel, basal and mesal branches extending well beyond basal process of gonostylus in male, and posterior arm of medigynium short and stout in female. Dicerapanorpa deqenensis sp. n. is characterized by basal branch of paramere as long as lateral branch and ventral valve of aedeagus nearly reaching apex of gonocoxite in male, and medigynium with paired auricular lateral processes in female. Dicerapanorpa tanae sp. n. is unique by genital bulb broad and spherical, basal branch of paramere short, and lateral branches curved convergently and parallel apically in male, and main plate of medigynium rounded in female. Dicerapanorpa tenuis sp. n. is distinguishable by hypovalve with largely expanded and inward curved apex and all branches of paramere reaching or exceeding apex of gonocoxite in male, and medigynium slender in female. Dicerapanorpa zhongdianensis sp. n. is characterized by basal branches of paramere parallel and mesal branches curved convergently in male, and main plate of medigynium subtriangular with a pair of auricular lateral processes in female. The species number of Dicerapanorpa is increased to thirteen.LSID: www.zoobank.org/urn:lsid:zoobank.org:pub:A4490511-C475-4C5B-9E89-4BF4EBAA2137     

New species of Nanomis Lugo-Ortiz and McCafferty, 1999 (Ephemeroptera: Baetidae) from Venezuela

As the first taxonomic and faunistic report of Nanomis Lugo-Ortiz and McCafferty, 1999 for Venezuela, we describe a new species, N. rasmusseni sp. n., based on material from Andean streams. Comparisons of the nymphal and imaginal stages of N. rasmusseni with those of N. galera Lugo-Ortiz and McCafferty, 1999 – the only species currently known for this genus – are done in detail. Further, additional morphological characters are discussed to delineate the genus from the other baetid genera. Likewise, ecological data and distribution of N. rasmusseni in the Andean highlands of Venezuela are provided, which improves knowledge of the richness and distribution of the genus in South America.

http://www.zoobank.org/urn:lsid:zoobank.org:pub:C9DF3936-101F-4240-B067-AC5DF394C805     

Four-urn catenary model for excretion

A chain-like arrangement of four urns (a catenary system) into which different color balls (white, corresponding to radio atoms, and black, corresponding to stable atoms) are being transferred is used to simulate the transport of atoms down the GI tract of man and animals. Into the first urn (stomach) are placedw _o white balls andr black balls while in the 2nd (small intestines) and 3rd (large intestines) urn, onlyr blacks are put in, with no whites. A sample of sizer is transferred from the 1st, 2nd and 3rd urns to the 2nd, 3rd and 4th (infinite universe) urns. From the random variable difference equations the first and second moments for the distribution of the number of radio atoms present in each urn are obtained. The variance of the contents of radioatoms in the excretion urn is Research sponsored by the Office of Health and Environmental Research, U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.     

烟草潜叶蛾幼虫空间分布型及其应用研究

本文就烟草潜叶蛾幼虫空间分布型及其垂直分布规律进行了探讨,结果表明：烟草潜叶蛾幼虫在田间呈聚集分布,聚集强度不因种群密度的改变而改变,幼虫主要聚集分布在烟草下部第一段（4片叶）上;降集或随机分布在第二段上;随机分布在第三段上,此外,应用虫株率进行田间种群密度的估计,其中Wilson模型和Gerrard模型所配理论曲线的预测值与实测值显著适合,但Gerrard模型的抽样估计误差较Wilson模型的小,最后本文用Taylor式中的参数a,b确定理论抽样数及序贯抽样,其模型分别为。     

On the distribution of the time required to remove white balls from an URN

Balls are removed one-at-a-time at equal time intervals from an urn initially containingw ₀ white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw ₁ from the urn. We then find the mean and variance of this distribution and also look at the special case whenw ₁ =w ₀.