Empirical regression as a conditional expected value of a special distribution-mixture for a modelfree quantitative recording of stochastical relations

An “empirical” distribution function F?(x, y) is estimated from measured points (xi, yi), i =1(1)n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y). The density function F?(x, y) of F?(x, y) is a mixture of n two-dimensional normal densities. The first order moments of F?(x, y) are the sample means x and y, whilst the second order moments are only proportional to the sample variances and the sample covariance. This “empirical” distribution F?(x, y) is used for evaluation of an empirical regression curve where a free parameter has to be fixed by an optimality criterion. The procedure is demonstrated by an example from morphometrical research.     

Bivariate Modified Power Series Distribution Some Properties,Estimation and Applications

The class of bivariate modified power series probability distribution (BMPSD) has been defined by P(X = x, Y=y) =a(x, y) (g(?₁ ?₂))^x (h(?₁, ?₂))^xwhere a(x,y) is a sub-set of the Cartesian product of the set of non-negative integers and g(?₁, ?₂), h(?₁ ?₂) and f(?₁, (?₁, ?₂) are positive finite and successively differentiable functions of ?₁and ?₂. It includes a very large number of well known probability distributions. The recurrence relations for central moments and factorial moments have been determined. Also, the M.L. estimators for ?₁ and ?₂ and their asymptotic biases and variances are obtained. Some important properties are discussed. The results of an BMPSD have been applied to derive the corresponding results for the bivariate generalized negative bino-mial distribution and the bivariate Lagrangian Poisson distribution.     

On a restricted occupancy model and its applications

With the multivariate hypergeometric distribution as a background certain occupancy distributions useful in practical applications are derived. More specifically it is assumed that a sample of n individuals is drawn from a population consisting of m types with r individuals in each type, (i) without replacement and (ii) by returning the selected individual in the population and with it another individual of the same type. The distributions of the number Z of distinct types observed in the sample are obtained in both cases in terms of the numbers. Assuming, in addition to the m equiprobable types of individuals, the existence of a control type, say, with s individuals, the joint distribution of the number U of distinct types observed in the sample and the number V of individuals of the control type present in the sample is obtained in terms of the numbers C(n, k, r) and the marginal distribution of U in terms of the Gould-Hopper numbers. Using these distributions minimum variance unbiased estimators of the number m of types are derived. Moreover small sample tests based on the zero frequency are constructed.     

Outlier SNP markers reveal fine‐scale genetic structuring across European hake populations (Merluccius merluccius)

Shallow population structure is generally reported for most marine fish and explained as a consequence of high dispersal, connectivity and large population size. Targeted gene analyses and more recently genome‐wide studies have challenged such view, suggesting that adaptive divergence might occur even when neutral markers provide genetic homogeneity across populations. Here, 381 SNPs located in transcribed regions were used to assess large‐ and fine‐scale population structure in the European hake (Merluccius merluccius), a widely distributed demersal species of high priority for the European fishery. Analysis of 850 individuals from 19 locations across the entire distribution range showed evidence for several outlier loci, with significantly higher resolving power. While 299 putatively neutral SNPs confirmed the genetic break between basins (F_CT = 0.016) and weak differentiation within basins, outlier loci revealed a dramatic divergence between Atlantic and Mediterranean populations (F_CT range 0.275–0.705) and fine‐scale significant population structure. Outlier loci separated North Sea and Northern Portugal populations from all other Atlantic samples and revealed a strong differentiation among Western, Central and Eastern Mediterranean geographical samples. Significant correlation of allele frequencies at outlier loci with seawater surface temperature and salinity supported the hypothesis that populations might be adapted to local conditions. Such evidence highlights the importance of integrating information from neutral and adaptive evolutionary patterns towards a better assessment of genetic diversity. Accordingly, the generated outlier SNP data could be used for tackling illegal practices in hake fishing and commercialization as well as to develop explicit spatial models for defining management units and stock boundaries.     

Constitution and By-Laws of the American Association of Physical Anthropologists

From parent populations (N = 50,000) statistically generated, representing different levels of correlation (r) between the age at death and a hypothetical biological indicator (r = 0.8-0.98), reference samples and target demographic samples are randomly drawn. Two iterative techniques, proportional fitting procedure and Bayesian, are used to estimate from the reference samples the age distribution of the targets. Due to the random fluctuations of the pattern of aging, both in the reference and target samples, these techniques converge only in expectation toward the true value of a distribution, but not in practice for any particular realization. Nevertheless, these techniques allow the estimation of the average of an age distribution, even if its shape is unknown. Under the hypothesis that the target sample is drawn from a stationary population, this average represents the life expectancy at 20 years (plus 20 years). Using this mean age at death for the adults and the juvenility index at death (D5-14/D20-ω), a new set of paleodemographic estimators were derived from 40 archaic life tables. For a hypothesized stable population, they give the life expectancy at birth and at 20 years, and the probability of death at 1 and 5 years. © 1996 Wiley-Liss, Inc.     

Origin matters: Using a local reference genome improves measures in population genomics

Genome sequencing enables answering fundamental questions about the genetic basis of adaptation, population structure and epigenetic mechanisms. Yet, we usually need a suitable reference genome for mapping population-level resequencing data. In some model systems, multiple reference genomes are available, giving the challenging task of determining which reference genome best suits the data. Here, we compared the use of two different reference genomes for the three-spined stickleback (Gasterosteus aculeatus), one novel genome derived from a European gynogenetic individual and the published reference genome of a North American individual. Specifically, we investigated the impact of using a local reference versus one generated from a distinct lineage on several common population genomics analyses. Through mapping genome resequencing data of 60 sticklebacks from across Europe and North America, we demonstrate that genetic distance among samples and the reference genomes impacts downstream analyses. Using a local reference genome increased mapping efficiency and genotyping accuracy, effectively retaining more and better data. Despite comparable distributions of the metrics generated across the genome using SNP data (i.e. π, Tajima's D and F_ST), window-based statistics using different references resulted in different outlier genes and enriched gene functions. A marker-based analysis of DNA methylation distributions had a comparably high overlap in outlier genes and functions, yet with distinct differences depending on the reference genome. Overall, our results highlight how using a local reference genome decreases reference bias to increase confidence in downstream analyses of the data. Such results have significant implications in all reference-genome-based population genomic analyses.     

Estimation of Finite and Closed Population Size: An Inverse Sampling Approach with Unequal Recapture Probability

Based on capture-mark-recapture sampling methods the problem of estimating unknown population size was considered. The sampling started with the assumption that at the beginning of the experiment all the individuals were unmarked, and the unmarked individuals caught in each sample will be marked and returned to the original population before the next sample is drawn. It is also assumed that the population is closed by birth, death, emigration and immigration. Using a general inverse sampling approach, the unknown population size N is estimated by a maximum likelihood estimator (MLE), and a simple form for approximate MLE is obtained. The probability function for S (the minimum number of samples required to be drawn to have L (L ≥ 1) samples, each of which contains at least one marked individual) and the form for E[S] are also obtained. In addition, corrections and improvements of some previous works in this field are given.     

A sampling plan for population dynamics studies on currant clearwing,Synanthedon tipuliformis (Lepidoptera: Sesiidae)

Abstract

Sampling techniques for eggs, larvae, and pupae of the currant clearwing, Synanthedon tipuliformis (Clerck), attacking blackcurrant were developed, and their precision was evaluated. Reliable population estimates for the egg and early larval stages (standard error < 10%) were obtained by sampling one cane with at least two age groups of wood from the north and south halves of seven bushes in nine blocks. Similar precision was obtained for post-winter larvae from samples comprising three canes from each half of the bushes, but using this sampling scheme a lower precision (S.E.?25–30%) had to be accepted for overwintering mortality factors. The pupal population was estimated from the numbers of live larvae at the end of the post-winter feeding stage, and cross-checked from the number of emergence holes in the 1-year-old wood taken for egg sampling the following year. This procedure gave estimates of similar reliability to those for the egg and larval stages.     

Tree size structure of stands and each species in primary warm-temperate rain forests of Southern Japan

The frequency distribution of trunk diameter was analyzed for forest stands of various developmental stages and for each tree species population in primary warm-temperate evergreen rain forests, dominated byDistylium racemosum, on Yakushima Island of southern Kyushu, Japan. Trunk diameter distribution in stands showed the inverse J shape. A regression model, lnf(x)=b+b ₁x+b₂ lnx, expressed the distribution well, wherex is diameter andf(x) trunk density atx. Three coefficients of the model, calculated from the data in 20 stands, clearly showed linear relations to each other and they had high correlations with the basal area per stands. The result suggests thatb andb ₁ increase andb ₂ decreases with stand age. Fourteen populations of abundant tree species also showed inverse J-shaped diameter distribution, which can be well expressed by the above model. In both open sites (gaps) and closed stands, these species were abundant and their characteristics in diameter distribution were persistent.     

TETRASAT: a program for the population analysis of allotetraploid microsatellite data

Microsatellite markers are quite popular due to their degree of polymorphism and efficiency; however, the utility of such markers for analysing allotetraploid species is often hampered by an inability to determine allele copy number for partial heterozygotes. tetrasat is a program that uses an iterative substitution process to account for all probable combinations of allele copy numbers in populations with partial heterozygote samples. The program subsequently calculates allele frequencies, and mean Hardy–Weinberg expected heterozygosity (H_E), Shannon–Weiner Diversity Index (H′) and Nei's measure of population differentiation (G_ST) are reported for each locus and population. Of equal importance is the calculation of statistical variability generated by the missing data and allele substitution process, which allows for assessment of the strength of conclusions drawn from the statistics.     

Next‐generation sequencing for molecular ecology: a caveat regarding pooled samples

We develop a model based on the Dirichlet‐compound multinomial distribution (CMD) and Ewens sampling formula to predict the fraction of SNP loci that will appear fixed for alternate alleles between two pooled samples drawn from the same underlying population. We apply this model to next‐generation sequencing (NGS) data from Baltic Sea herring recently published by (Corander et al., 2013 , Molecular Ecology, 2931 –2940), and show that there are many more fixed loci than expected in the absence of genetic structure. However, we show through coalescent simulations that the degree of population structure required to explain the fraction of alternatively fixed SNPs is extraordinarily high and that the surplus of fixed loci is more likely a consequence of limited representation of individual gene copies in the pooled samples, than it is of population structure. Our analysis signals that the use of NGS on pooled samples to identify divergent SNPs warrants caution. With pooled samples, it is hard to diagnose when an NGS experiment has gone awry; especially when NGS data on pooled samples are of low read depth with a limited number of individuals, it may be worthwhile to temper claims of unexpected population differentiation from pooled samples, pending verification with more reliable methods or stricter adherence to recommended sampling designs for pooled sequencing e.g. Futschik & Schlötterer 2010 , Genetics, 186 , 207; Gautier et al., 2013a , Molecular Ecology, 3766 –3779). Analysis of the data and diagnosis of problems is easier and more reliable (and can be less costly) with individually barcoded samples. Consequently, for some scenarios, individual barcoding may be preferable to pooling of samples.     

Parameter Estimation for the Bateman Function via Moments of the Empirical Curve

The parameters of the function f(t)=c(e^?at-e^?bt) are related in a simple way to the moments ^∞ tⁿf(t)^dt(n=0, 1, 2). Using empirical values of f, the moments can be estimated by numerical integration. Therefrom estimates of the parameters are obtained by elementary algebra.     

Genomic scanning using AFLP to detect loci under selection in the moss Funaria hygrometrica along a climate gradient in the Sierra Nevada Mountains,Spain

The common cord moss Funaria hygrometrica has a worldwide distribution and thrives in a wide variety of environments. Here, we studied the genetic diversity in F. hygrometrica along an abiotic gradient in the Mediterranean high mountain of Sierra Nevada (Spain) using a genome scan method. Eighty‐four samples from 17 locations from 24 to 2700 m were fingerprinted based on their amplified fragment length polymorphism (AFLP) banding pattern. Using PCA and Bayesian inference we found that the genetic diversity was structured in three or four clusters, respectively. Using a genome scan method we identified 13 outlier loci, which showed a signature of positive selection. Partial Mantel tests were performed between the Euclidean distance matrices of geographic and climatic variables, versus the pair‐wise genetic distance of the AFLP dataset and AFLP‐positive outliers dataset. AFLP‐positive outlier data were significantly correlated with the gradient of the climatic variables, suggesting adaptive variation among populations of F. hygrometrica along the Sierra Nevada Mountains. We highlight the additional analyses necessary to identify the nature of these loci, and their biological role in the adaptation process.     

Distribution range and ecological niche of Primula marginata Curtis (Primulaceae)

The distribution range of Primula marginata Curtis (Primulaceae) has never been fully characterized. In the present study, authors did a revision of the distribution range using herbaria material, database records and in situ populations' check-up. P. marginata was confirmed extending from Cottian to Maritime and Ligurian Alps, with few outlier occurrences in the northern Apennines. The localities previously reported from northern Piedmont (Val d'Ossola) were not confirmed. Maximum entropy model (Maxent) was used to simulate the potential distribution of P. marginata under current climate conditions. According to the distribution modelling performed, the species prefers rocky calcareous habitats mainly at high elevations, with abundant precipitation, but low moisture retention at soil level and marked temperature range between winter and summer seasons. The potential distribution area drawn by Maxent seemed to describe P. marginata at its maximum extension, and any future climate changes might cause limitations for the survival of the species.     

Optimal Fixing of the Bandwidth-Parameter for the Empirical Regression1,2

The estimator ?₀(x) of the regression r(x) = E (Y | × = x) from measured points (x_i, y_i), i = 1(1) n, of a continuous two-dimensional random variable (X, Y) with unknown continuous density function f(x, y) and with moments up to the second order can be made with the help of a density estimation f?₀(x, y) (see e.g. SCHMERLING and PEIL, 1980). Here f?₀(x, y) still contains free parameters (so-called band-width-parameters), the values of which have to be optimally fixed in the concrete case. This fixing can be done by using a modification of the maximum-likelihood principle including jackknife techniques. The parameter values can be also found from the estimators for r(x). Here the cross-validation principle can be applied. Some numerical aspects of these possibilities for optimally fixing the bandwidth-parameter are discussed by means of examples. If ?₀(x) is used as a smoothing operator for time series the optimal choice of the parameter values is dependent on the purpose of application of the smoothed time series. The fixing will then be done by considering the so-called filter-characteristic of ?C₀(x).     

Sex differences in total body water in adolescent rhesus macaques estimated by ethanol dilution

Abstract: Non‐human primates are widely used in research, yet relatively few studies have addressed potential pharmacokinetic differences between males and females. The present study examined the relationship between total body water, sex, age, and weight in the rhesus macaque (Macaca mulatta). Ethanol‐naïve, adolescent rhesus macaques (n = 119) were administered ethanol (males, 2.1 g/kg; females, 2.0 g/kg) intravenously, and blood samples for blood ethanol concentration obtained at 5, 10, and 60 minutes following the end of the infusion. Non‐linear regression was used to compare and contrast a series of pharmacokinetic models examining the relationship between weight, sex, age, V_d and zero‐order elimination rate. V_d (mean ± SEM) for male rhesus was 0.771 ± 0.008 l/kg and for females was 0.730 ± 0.008 l/kg, different at P < 0.00001. There were no sex differences in the rate of zero‐order ethanol elimination, estimated to be 0.0032 ± 0.0004 g/kg/minute. The data reported here may be useful in designing and interpreting pharmacokinetic studies using rhesus monkeys.     

Population genomics meet Lagrangian simulations: Oceanographic patterns and long larval duration ensure connectivity among Paracentrotus lividus populations in the Adriatic and Ionian seas

Connectivity between populations influences both their dynamics and the genetic structuring of species. In this study, we explored connectivity patterns of a marine species with long‐distance dispersal, the edible common sea urchin Paracentrotus lividus, focusing mainly on the Adriatic–Ionian basins (Central Mediterranean). We applied a multidisciplinary approach integrating population genomics, based on 1,122 single nucleotide polymorphisms (SNPs) obtained from 2b‐RAD in 275 samples, with Lagrangian simulations performed with a biophysical model of larval dispersal. We detected genetic homogeneity among eight population samples collected in the focal Adriatic–Ionian area, whereas weak but significant differentiation was found with respect to two samples from the Western Mediterranean (France and Tunisia). This result was not affected by the few putative outlier loci identified in our dataset. Lagrangian simulations found a significant potential for larval exchange among the eight Adriatic–Ionian locations, supporting the hypothesis of connectivity of P. lividus populations in this area. A peculiar pattern emerged from the comparison of our results with those obtained from published P. lividus cytochrome b (cytb) sequences, the latter revealing genetic differentiation in the same geographic area despite a smaller sample size and a lower power to detect differences. The comparison with studies conducted using nuclear markers on other species with similar pelagic larval durations in the same Adriatic–Ionian locations indicates species‐specific differences in genetic connectivity patterns and warns against generalizing single‐species results to the entire community of rocky shore habitats.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

Polarized Photoacoustic Spectra of the Cyanobacterium Synechococcus Oriented in Polymer Film

Photoacoustic spectra (PAS) were obtained for the cyanobacterium Synechococcus (Anacystis nidulans) cells embedded in isotropic and stretched polyvinyl alcohol films. The polarized radiation with the electric vector changing in 30° intervals with respect to given direction in a sample plane was used. Two cyanobacterium strains, one with very low biliprotein content, second with normal amount of biliproteins were investigated. The polarized absorption and fluorescence spectra were also measured. Conclusions were drawn about the thermal deactivation occurring in differently oriented pools of chromophores and about mutual orientation of their transition moments. Thermal deactivation in carotenoids (Cars) of both strains was different. The ratio of Car thermal deactivation to the thermal deactivation of chlorophyll (Chl) was higher in cyanobacteria with lower content of biliproteins than in the strain with normal amount of these complexes. Hence biliproteins can play the role in excitation energy transfer from Cars to Chls. For complex biological samples, polarized PAS can be a more sensitive method to investigate the directions of the absorption transition moments than the widely used polarized absorption spectra.     

Bivariate POISSON Binomial Distributions

Three bivariate generalizations of the POISSON binomial distribution are introduced. The probabilities, moments, conditional distributions and regression functions for these distributions are obtained in terms of bipartitional polynomials. Recurrences for the probabilities and moments are also given. Parameter estimators are derived using the methods of moments and zero frequencies and the three distributions are fitted to some ecological data.