A Sufficient Condition for Reducing Recursions in Hidden Markov Models

In hidden Markov models, the probability of observing a set of strings can be computed using recursion relations. We construct a sufficient condition for simplifying the recursion relations for a certain class of hidden Markov models. If the condition is satisfied, then one can construct a reduced recursion where the dependence on Markov states completely disappears. We discuss a specific example—namely, statistical multiple alignment based on the TKF-model—in which the sufficient condition is satisfied.     

植物空间分布格局中邻体距离的概率分布模型及参数估计

最近邻体法是一类有效的植物空间分布格局分析方法,邻体距离的概率分布模型用于描述邻体距离的统计特征,属于常用的最近邻体法之一。然而,聚集分布格局中邻体距离(个体到个体)的概率分布模型表达式复杂,参数估计的计算量大。根据该模型期望和方差的特性,提出了一种简化的参数估计方法,并利用遗传算法来实现参数优化,结果表明遗传算法可以有效地估计的该模型的两个参数。同时,利用该模型拟合了加拿大南温哥华岛3个寒温带树种的空间分布数据,结果显示:该概率分布模型可以很好地拟合美国花旗松(P.menziesii)和西部铁杉(T.heterophylla)的邻体距离分布,但由于西北红柏(T.plicata)存在高度聚集的团簇分布,拟合结果不理想;美国花旗松在样地中近似随机分布,空间聚集参数对空间尺度的依赖性不强,但西北红柏和西部铁杉空间聚集参数具有尺度依赖性,随邻体距离阶数增加而变大。最后,讨论了该模型以及参数估计方法的优势和限制。     

The graduation of secondary structure elements

A method of graduating (i.e., least-squares fitting) a smooth polynomial curve through long elements of protein secondary structure is described. It uses the Chebyshev polynomials of a discrete (integer) variable with several restraints to prevent artifactual curvatures. A new recursion formula is given which allows the evaluation of the polynomials on rational-number points as well as on the integer points. High-order splines suitable for interpolation between integer points are also discussed. The new method finds applications in graphics and in structural analysis.     

A model for the spread of an epidemic

A temporally continuous and spatially discrete stochastic model for the spread of an epidemic within some set of holdings is constructed. A recursion formula is given for the probability that a certain set of holdings is infected at a certain moment. Moreover, under an additional condition (which will always be satisfied in practice) a formula for the expected value and the variance of the moment when a certain holding is infected the first time is given.     

Inexpensive Computation of the Inverse of the Genomic Relationship Matrix in Populations with Small Effective Population Size

Many computations with SNP data including genomic evaluation, parameter estimation, and genome-wide association studies use an inverse of the genomic relationship matrix. The cost of a regular inversion is cubic and is prohibitively expensive for large matrices. Recent studies in cattle demonstrated that the inverse can be computed in almost linear time by recursion on any subset of ∼10,000 individuals. The purpose of this study is to present a theory of why such a recursion works and its implication for other populations. Assume that, because of a small effective population size, the additive information in a genotyped population has a small dimensionality, even with a very large number of SNP markers. That dimensionality is visible as a limited number of effective SNP effects, independent chromosome segments, or the rank of the genomic relationship matrix. Decompose a population arbitrarily into core and noncore individuals, with the number of core individuals equal to that dimensionality. Then, breeding values of noncore individuals can be derived by recursions on breeding values of core individuals, with coefficients of the recursion computed from the genomic relationship matrix. A resulting algorithm for the inversion called “algorithm for proven and young” (APY) has a linear computing and memory cost for noncore animals. Noninfinitesimal genetic architecture can be accommodated through a trait-specific genomic relationship matrix, possibly derived from Bayesian regressions. For populations with small effective population size, the inverse of the genomic relationship matrix can be computed inexpensively for a very large number of genotyped individuals.     

Sex predetermination: Its impact on fertility

Abstract

Genetic variability among seven Chilean Indian populations (Aymara, Atacameño, Diaguita, Pehuenche, Mapuche, Alacaluf, and Yagan) is measured in terms of net codon differences per locus from gene frequency data on seven serologic markers. Indices of cultural and linguistic differences are computed surveying the various ethnographic accounts of these tribal populations. Of the variables, culture, language, geography, and the degree of Caucasoid admixture, only geography seems to be the important factor in explaining the variabilities in genetic distances among these populations. An empirical relationship between geographic distance and gene identity is also established and shown graphically.     

Detecting spatial aggregation from distance sampling: a probability distribution model of nearest neighbor distance

Spatial point pattern is an important tool for describing the spatial distribution of species in ecology. Negative binomial distribution (NBD) is widely used to model spatial aggregation. In this paper, we derive the probability distribution model of event-to-event nearest neighbor distance (distance from a focal individual to its n-th nearest individual). Compared with the probability distribution model of point-to-event nearest neighbor distance (distance from a randomly distributed sampling point to the n-th nearest individual), the new probability distribution model is more flexible. We propose that spatial aggregation can be detected by fitting this probability distribution model to event-to-event nearest neighbor distances. The performance is evaluated using both simulated and empirical spatial point patterns.     

Graph theoretical methods for comparing phytosociological structures

This paper describes some methods that can be used to compare the phytosociological structure of plant communities using some graph theoretic properties of the directed graphs that represent them. In such a graph, the species are represented by points and the association of species A with species B is represented by a directed line segment going from B to A. Two communities can be compared using simple indices to measure the similarity of their species-lists (point similarity) and of the species associations in them (line similarity). A more sophisticated and informative measure of line similarity is the probability that, given the number of points shared by two graphs, they have at least as many lines in common as they are observed to have. A formula for calculating that probability is given here. The graphs of community structure can also be compared with respect to the homogeneity of the distribution of the lines among the points, a property related to the number of species that are important in determining the composition of the community. These techniques are illustrated using the graphs of the phytosociological structure of intertidal seaweed communities on the southeast coast of Nova Scotia.Nomenclature follows: South and Cardinal (1970)     

Statistics of RNA secondary structures

A statistical reference for RNA secondary structures with minimum free energies is computed by folding large ensembles of random RNA sequences. Four nucleotide alphabets are used: two binary alphabets, AU and GC, the biophysical AUGC and the synthetic GCXK alphabet. RNA secondary structures are made of structural elements, such as stacks, loops, joints, and free ends. Statistical properties of these elements are computed for small RNA molecules of chain lengths up to 100. The results of RNA structure statistics depend strongly on the particular alphabet chosen. The statistical reference is compared with the data derived from natural RNA molecules with similar base frequencies. Secondary structures are represented as trees. Tree editing provides a quantitative measure for the distance d_t, between two structures. We compute a structure density surface as the conditional probability of two structures having distance t given that their sequences have distance h. This surface indicates that the vast majority of possible minimum free energy secondary structures occur within a fairly small neighborhood of any typical (random) sequence. Correlation lengths for secondary structures in their tree representations are computed from probability densities. They are appropriate measures for the complexity of the sequence-structure relation. The correlation length also provides a quantitative estimate for the mean sensitivity of structures to point mutations. © 1993 John Wiley & Sons, Inc.     

Efficient Simulation of Multivariate Binomial and Poisson Distributions

Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the multivariate Poisson distribution are combined to obtain an algorithm for the quick implementation of its multivariate dependence structure. Simulation of the multivariate Poisson distribution then becomes feasible by first generating and then convoluting independent univariate Poisson variates with appropriate expectations. The latter can be computed via linear recursion formulae. Similar means for simulation are also considered for the binomial setting. In this scenario it turns out, however, that exact computation of the probability function is even easier to perform; therefore corresponding linear recursion formulae for the point probabilities of multivariate binomial distributions are presented, which only require information about the index parameter and the (simultaneous) success probabilities, that is the multivariate dependence structure among the binomial marginals.     

Sequence-specific responses of restriction endonucleases to bromodeoxyuridine substitution in mammalian DNA

Substitution of BrdU for dT in mammalian DNA alters the rates of DNA cleavage by restriction endonucleases in a manner that can be related to the specificity of cleavage. A formula is proposed that describes inhibitory and stimulatory contributions arising from the substitution of a Br atom for the CH3 group on T. The larger Br atom is postulated to sterically hinder the nuclease from binding to adjacent groups in the DNA cleavage site, while allowing a tighter binding to itself. The inhibition caused by steric hindrance is predicted to vary inversely with distance from the point of cleavage, whereas the stimulation caused by tighter binding is predicted to be independent of distance. The resultant formula gives a good fit to the data obtained for thirteen different restriction nucleases of known specificity. The parameters in the formula appear to be simple functions of ionic strength. This formula can be used to predict the effect of BrdU substitution on any endonuclease whose specificity of cleavage is known.     

Stereometric craniometry

A method is described whereby three-dimensional co-ordinates of points on a cranium can be recorded in terms of azimuth, elevation and radial distance from a selected point. These co-ordinates can be used to create two-dimensional representations of single crania, the differences between many crania or growth stages of individuals or series of individuals. The co-ordinates can be used in more conventional analytic ways in the same way as cartesian co-ordinates.     

The probability of obtaining complex kinetic curves for enzyme mechanisms with cubic terms in the pseudo-steady state rate equations

A number of details required for the classification of 3 : 3 double reciprocal plots are provided. It is shown that the ν(S) plot for a 3 : 3 function can have at most four inflexions and at most two inflexions adjacent to a turning point. Using this information, a classification of 3 : 3 ν(S) plots into ten main varieties with several subclasses is reported. The problem of defining the probability with which a given mechanism can give rise to specific curve shape features is considered. Applying this technique, the probability with which four simple enzyme mechanisms can give rise to 3 : 3 curve shapes is computed. It is shown that a 3 : 3 saturation function can have no turning points, at most two inflexions and at most one inflexion in double reciprocal space. The probability with which the available 3 : 3 shapes can arise is also computed. It is concluded that, with realistic values for rate constants, chemically reasonable enzyme mechanisms leading to rate equations of degree n : n can generate most of the kinetic profiles available to a rational function of degree n : n with positive coefficients. The probability of obtaining specific curve shapes is not so characteristic of the particular mechanism for 3:3 rate equations as it is for 2:2 rate equations. The probability of obtaining highly complex curves with several turning points or inflexions is rather lower for the enzyme mechanisms than with general 3 : 3 rational functions. There is a high probability that 3 : 3 mechanisms will generate kinetic curves that are geometrically similar to those possible for degree 2 : 2 but this is not so for binding isotherms. Hence differentiating 3 : 3 from 2 : 2 rate equations from experimental kinetic data is more likely to be successful by non-linear regression to the whole data set than by demonstrating a specific 3 : 3 feature. Binding curves, on the other hand, for three or more sites should give Scatchard plots with inflexions, features not possible with second degree equations which are conic sections in this space.     

Detection probability of Golden-winged Warblers during point counts with and without playback recordings

ABSTRACT Use of point‐count data to estimate population sizes of North American landbirds may be challenged by limitations on detection probability of particular species, thereby requiring correction factors to ensure accurate estimates. We estimated detection probability of Golden‐winged Warblers (Vermivora chrysoptera) during 3‐min point‐count surveys conducted both with and without use of playback recordings in a mixed shrubland‐forest habitat (clearcut area) and a 60‐m wide electric transmission line right‐of‐way (ROW) in central Pennsylvania from 20 May to 17 June 2002–2003. In addition, we assessed the value of playback with respect to response rates of warblers and distance within which warblers approached the observer. Without playback, detection probability was approximately 23% in the clearcut area and 61% in the ROW. Use of playback resulted in 7% and 19% net increases in probability at the clearcut area and the ROW, respectively; proportional increase was approximately 30% for both habitats. Warblers responded to playback 68% of the time, but response rate was greater within 100 m (72%) than beyond (53%). Most responses (85%) included approach of the warbler toward the observer, and most individuals approached within 10 m. We conclude that 3‐min point counts with playback do not yield detection probabilities sufficient to estimate population size of Golden‐winged Warblers without use of correction factors. Furthermore, detection probability in mixed shrubland‐forest habitats can be much lower than in linear habitats such as utility ROWs. Efforts to estimate population size of Golden‐winged Warblers from data of the North American Breeding Bird Survey should recognize that habitat structure has much influence on detection probability as it relates to distance at which an observer can hear (or see) warblers. Accordingly, we recommend that such efforts incorporate a maximum detection distance of 100–150 m in mixed shrubland‐forest habitats.     

Disentangling the drivers of Black-bellied Sandgrouse Pterocles orientalis nesting habitat use in a Mediterranean arid environment

ABSTRACT

Capsule: Nest site selection of Black-bellied Sandgrouse Pterocles orientalis in an Algerian arid environment is dictated by a combination of topography, human presence, landscape and space.

Aims: To disentangle the drivers affecting Black-bellied Sandgrouse nest habitat use in an Algerian arid environment.

Methods: We used data on a series of topographic, anthropogenic, landscape and space variables, to identify the predictors of the occurrence probability of Black-bellied Sandgrouse nests. These variables were measured at nests (n?=?33) and random points (n?=?33) within landscape plots of 250?m radius.

Results: The probability of a site being selected for nesting by Black-bellied Sandgrouse was negatively related to distance to the nearest cereal crops, but positively associated with the cover of natural water, cover of rocks, and distance to the nearest road. This probability was also high at elevations between 251 and 289?m.

Conclusion: From a practical perspective, it would be interesting to reproduce the same investigation in other Mediterranean arid environments to find out if this species follows a similar pattern of nesting habitat use. This would provide guidance for future conservation actions and inform appropriate habitat management for this species.     

Kinetics of amide proton exchange in helical peptides of varying chain lengths. Interpretation by the Lifson-Roig equation.

The kinetics of amide proton exchange (1H----2H) have been measured by proton nuclear magnetic resonance spectroscopy for a set of helical peptides with the generic formula Ac-(AAKAA)m Y-NH2 and with chain lengths varying from 6 to 51 residues. The integrated intensity of the amide resonances has been measured as a function of time in 2H2O at pH* 2.50. Exchange kinetics for these peptides can be modeled by applying the Lifson-Roig treatment for the helix-to-coil transition. The Lifson-Roig equation is used to compute the probability that each residue is helical, as defined by its backbone (phi, psi) angles. A recursion formula then is used to find the probability that the backbone amide proton of each residue is hydrogen bonded. The peptide helix can be treated as a homopolymer, and direct exchange from the helix can be neglected. The expression for the exchange kinetics contains only three unknown parameters: the rate constant for exchange of a non-hydrogen-bonded (random coil) backbone amide proton and the nucleation (v2) and propagation (w) parameters of the Lifson-Roig theory. The fit of the exchange curves to these three parameters is very good, and the values for v2 and w agree with those derived from circular dichroism studies of the thermally-induced unfolding of related peptides [Scholtz, J.M., Qian, H., York, E.J., Stewart, J.M., & Baldwin, R.L. (1991) Biopolymers (in press]).     

Neutral evolution in spatially continuous populations

We introduce a general recursion for the probability of identity in state of two individuals sampled from a population subject to mutation, migration, and random drift in a two-dimensional continuum. The recursion allows for the interactions induced by density-dependent regulation of the population, which are inevitable in a continuous population. We give explicit series expansions for large neighbourhood size and for low mutation rates respectively and investigate the accuracy of the classical Malécot formula for these general models. When neighbourhood size is small, this formula does not give the identity even over large scales. However, for large neighbourhood size, it is an accurate approximation which summarises the local population structure in terms of three quantities: the effective dispersal rate, sigma(e); the effective population density, rho(e); and a local scale, kappa, at which local interactions become significant. The results are illustrated by simulations.     

Automatic extraction and measurement of individual trees from mobile laser scanning point clouds of forests

Background and AimsIn addition to terrestrial laser scanning (TLS), mobile laser scanning (MLS) is increasingly arousing interest as a technique which provides valuable 3-D data for various applications in forest research. Using mobile platforms, the 3-D recording of large forest areas is carried out within a short space of time. Vegetation structure is described by millions of 3-D points which show an accuracy in the millimetre range and offer a powerful basis for automated vegetation modelling. The successful extraction of single trees from the point cloud is essential for further evaluations and modelling at the individual-tree level, such as volume determination, quantitative structure modelling or local neighbourhood analyses. However, high-precision automated tree segmentation is challenging, and has so far mostly been performed using elaborate interactive segmentation methods.MethodsHere, we present a novel segmentation algorithm to automatically segment trees in MLS point clouds, applying distance adaptivity as a function of trajectory. In addition, tree parameters are determined simultaneously. In our validation study, we used a total of 825 trees from ten sample plots to compare the data of trees segmented from MLS data with manual inventory parameters and parameters derived from semi-automatic TLS segmentation.Key ResultsThe tree detection rate reached 96 % on average for trees with distances up to 45 m from the trajectory. Trees were almost completely segmented up to a distance of about 30 m from the MLS trajectory. The accuracy of tree parameters was similar for MLS-segmented and TLS-segmented trees.ConclusionsBesides plot characteristics, the detection rate of trees in MLS data strongly depends on the distance to the travelled track. The algorithm presented here facilitates the acquisition of important tree parameters from MLS data, as an area-wide automated derivation can be accomplished in a very short time.     

Fast and Accurate Registration of the Proximal Femurs in Bilateral Hip Joint Images by Using the Random Sub-Sample Points

Background and ObjectiveAs is known, point clouds representing the objects are frequently used in object registration. Although the objects can be registered by using all the points in the corresponding point clouds of the objects, the registration process can also be achieved with a smaller number of the landmark points selected from the entire point clouds of the objects. This paper introduces a research study focusing on the fast and accurate rigid registration of the bilateral proximal femurs in bilateral hip joint images by using the random sub-sample points. For this purpose, Random Point Sub-sampling (RPS) was analyzed and the reduced point sets were used for an accurate registration of the bilateral proximal femurs in coronal hip joint magnetic resonance imaging (MRI) slices.MethodsIn registration, bilateral proximal femurs in MRI slices were registered rigidly by performing a process consisting of three main phases named as MR image preprocessing, proximal femur registration over the random sub-sample points and MR image postprocessing. In the stage of the MR image preprocessing, segmentation maps of the bilateral proximal femurs are obtained as region of interest (RoI) images from the entire MRI slices and then, the edge maps of the segmented proximal femurs are extracted. In the registration phase, the edge maps describing the proximal femur surfaces are represented as point clouds initially. Thereafter, the RPS is performed on the proximal femur point clouds and the number of points representing the proximal femurs is reduced at different ratios. For the registration of the point clouds, the Iterative Closest Point (ICP) algorithm is performed on the reduced sets of points. Finally, the registration procedures are completed by performing MR image postprocessing on the registered proximal femur images.ResultsIn performance evaluation tests performed on healthy and pathological proximal femurs in 13 bilateral coronal hip joint MRI slices of 13 Legg-Calve-Perthes disease (LCPD) patients, bilateral proximal femurs were successfully registered with very small error rates by using the reduced set of points obtained via the RPS and promising results were achieved. The minimum error rate was observed at RPS rate of 30% as the value of 0.41 (±0.31)% on all over the bilateral proximal femurs evaluated. When the range of RPS rate of 20-30% is considered as the reference, the elapsed time in registration can be reduced by almost 30-40% compared to the case where all the proximal femur points were included in registration. Additionally, it was observed that the RPS rate should be selected as at least 25% to achieve a successful registration with an error rate below 1%.ConclusionIt was concluded from the observed results that a more successful and faster registration can be accomplished by selecting fewer points randomly from the point sets of proximal femurs instead of using all the points describing the proximal femurs. Not only an accurate registration with low error rates was performed, but also a faster registration process was performed by means of the limited number of points that are sub-sampled randomly from the whole point sets.     

No Evidence of Coordination Between Different Subgroups in the Fission–Fusion Society of Spider Monkeys (<Emphasis Type="Italic">Ateles geoffroyi</Emphasis>)

Flexibility in spatial cohesion allows species with high fission–fusion dynamics to exploit variable habitats and decrease the costs of feeding competition. However, coordination among highly dispersed group members becomes problematic. In spider monkeys (Ateles spp.), individuals can spread over wide areas, forming several subgroups that appear to travel independently from each other. To explore their relative travel patterns, we compare the distance between different subgroups with the distance predicted by a null model of independent travel. Observations of distance between subgroups come from simultaneous follows of ≥2 subgroups in 2 different groups of spider monkeys in Punta Laguna, Mexico. We estimated space use using the kernel method, which produces areas with a given probability of presence of the subgroups, based on the frequency with which they were observed in each location. The null model consisted of the frequency distribution of distances between randomly chosen pairs of points within the home range, choosing each point independently with a probability proportional to the corresponding observed probability of presence. In all cases, the observed distances between subgroups were very close to those predicted by the null model, which suggests that subgroups do not coordinate their relative travel patterns. Also, the distance separating 2 individuals when in different subgroups was not affected by their sex or association index. These findings underscore the low cohesiveness between group members in species with high fission–fusion dynamics and challenge us to find the mechanisms by which groups maintain their social structure.