Yule Model Research Articles

Temporal Evolution of Bradford Curves in Academic Library Contexts

Bradford’s law of bibliographic scattering is a fundamental principle in bibliometrics, offering valuable guidance for academic libraries in literature search and procurement. However, Bradford curves can exhibit various shapes over time, and predicting these shapes remains a challenge due to a lack of causal explanation. This paper attributes the deviations from the theoretical J-shape to integer constraints on the number of journals and articles, extending Leimkuhler’s function to encompass highly productive core journals, where the theoretical journal number falls below one. Using the Simon–Yule model, key parameters of the extended formulas are identified and analyzed. The paper explains the reasons for the Groos droop and examines the critical points for shape changes. The proposed formulas are validated with empirical data from the literature, demonstrating that this method can effectively predict the evolution of Bradford curves, providing academic libraries with a valuable tool for evaluating journal coverage, optimizing resource allocation, and refining Collection Development Policies (CDP).

Clade size distribution under neutral evolutionary models

Given a labeled tree topology t, consider a population P of k leaves chosen among those of t. The clade of P is the minimal subtree of t containing P and its size is given by the number of leaves in the clade. When t is selected under the Yule or uniform distribution among the labeled topologies of size n, we study the “clade size” random variable determining closed formulas for its probability mass function, its mean, and its variance. Our calculations show that for large n the clade size tends to be smaller under the uniform model than under the Yule model, with a larger variability in the first scenario for values of k≥5. We apply our probability formulas to investigate set-theoretic relationships between the clades of two populations in a random tree, determining how likely one clade is contained in or it is equal to the other. Our study relates to earlier calculations for the probability that under the Yule model the clade size of P equals the size of P—that is, the population P forms a monophyletic group—and extends known results for the probability that the minimal (non-trivial) clade containing a random taxon has a given size.

The distributions under two species-tree models of the total number of ancestral configurations for matching gene trees and species trees

Given a gene-tree labeled topology G and a species tree S, the ancestral configurations at an internal node k of S represent the combinatorially different sets of gene lineages that can be present at k when all possible realizations of G in S are considered. Ancestral configurations have been introduced as a data structure for evaluating the conditional probability of a gene-tree labeled topology given a species tree, and their enumeration assists in describing the complexity of this computation. In the case that the gene-tree labeled topology G=t matches that of the species tree S, by techniques of analytic combinatorics, we study distributional properties of the total number of ancestral configurations measured across the different nodes of a random labeled topology t selected under the uniform and the Yule probability models. Under both of these probabilistic scenarios, we show that the total number Tn of ancestral configurations of a random labeled topology of n taxa asymptotically follows a lognormal distribution. Over uniformly distributed labeled topologies, the asymptotic growth of the mean and the variance of Tn are found to satisfy EU[Tn]∼2.449⋅1.333n and VU[Tn]∼5.050⋅1.822n, respectively. Under the Yule model, which assigns higher probabilities to more balanced labeled topologies, we obtain the mean EY[Tn]∼1.425n and the variance VY[Tn]∼2.045n.

Promotions and Team Building for Marketing Campaigns

The article analyzes in detail the main aspects of promotional marketing in team building. Team building is very important for marketing campaigns as it allows for the efficient completion of tasks and the achievement of set goals. The main purpose of the article is based on the evaluation of the effectiveness of marketing communications using the Yule model and the creation of a framework for the business modeling of the brand, since having a ready-made business model structure, one can describe the cost structure, which will reflect the key actions and all resources for investment in brand development. The article summarizes the main advantages and disadvantages of promotions and highlights the main consequences of the war for Ukrainian brands. The main reason for team building is that marketing campaigns usually require work with different specialists such as marketers, designers, copywriters, analysts, etc. Therefore, project teams secure necessary communication and coordination between project participants to avoid misunderstandings and ensure the successful implementation of the project. Moreover, project teams can secure efficient management of resources such as time, budget, and other resources. This is especially important for marketing campaigns since they often have limited resources and shorter deadlines. Each team member contributes and performs specific tasks to achieve the campaign goal. Team building is an essential element in the successful implementation of marketing campaigns. It allows for efficient communication and coordination among project participants, resource management, and the achievement of successful results. Effective promotions can provide a company with a competitive advantage. This article discusses the main types of promotions, such as advertising, discounts, gifts, contests, loyalty, etc. An important aspect is choosing the right type of promotion depending on the target audience and the company's marketing goals. The criteria for team building, including the abilities and skills of the participants, leadership, communication, and collaboration, are also considered. The concept of business management implies that the company's management should constantly work to improve business processes, optimize the use of resources, and efficiently utilize personnel. In addition, business management includes the development and implementation of the company's development strategy, as well as control over its financial results.

Spatial Yule Model for Urban Growth with Shared Resources

Spatial Yule Model for Urban Growth with Shared Resources

Distributions of cherries and pitchforks for the Ford model

Distributional properties of tree shape statistics under random phylogenetic tree models play an important role in investigating the evolutionary forces underlying the observed phylogenies. In this paper, we study two subtree counting statistics, the number of cherries and that of pitchforks for the Ford model, the alpha model introduced by Daniel Ford. It is a one-parameter family of random phylogenetic tree models which includes the proportional to distinguishable arrangement (PDA) and the Yule models, two tree models commonly used in phylogenetics. Based on a non-uniform version of the extended Pólya urn models in which negative entries are permitted for their replacement matrices, we obtain the strong law of large numbers and the central limit theorem for the joint distribution of these two statistics for the Ford model. Furthermore, we derive a recursive formula for computing the exact joint distribution of these two statistics. This leads to exact formulas for their means and higher order asymptotic expansions of their second moments, which allows us to identify a critical parameter value for the correlation between these two statistics. That is, when the number of tree leaves is sufficiently large, they are negatively correlated for 0≤α≤1/2 and positively correlated for 1/2<α<1.

Phylogeny, origin and diversification of the Dasylirion genus based on matK and rbcL sequences

AbstractThe Dasylirion genus is highly represented in the arid and semi-arid regions of Mexico and USA, playing important ecological and economical roles. Inferring the evolutionary patterns of this group will eventually facilitate understanding biological phenomena and outlining conservation and usage strategies. We performed a molecular phylogenetic analysis based on two chloroplast DNA regions: maturase-K gene (matK) and the large subunit of ribulose-1,5-bisphosphate carboxylase gene (rbcL). We constructed a phylogenetic tree by maximum likelihood with GTR as the sequence substitution model and a relaxed clock, inferred diversification patterns by lineage through time and explored the diversification rates of Dasylirion by the Yule model. The study included 11 species of the genus, which represent 50% of all its known species. We used two calibration points to date the tree, one based on fossil records of Acorus gramineus, and the other on the estimated stem age of the Yucca genus. The combined sequences of the two partial genes comprised 1455 bp and 18 polymorphic sites. We estimated an average substitution rate of 0.0005 nucleotide per million years for the concatenated DNA sequences. The molecular dating analysis estimated that the Dasylirion genus appeared more than 5.46 million years ago, with a rate of diversification of 0.0466 net speciation events per million years. The estimated age represents a lower bound, since not all Dasylirion species are included. These findings are consistent with other origin and diversification hypotheses for arid-land Asparagaceae in the Mexican highlands as a result of geomorphological events in North America.

Adaptation of stochastic model of economic cycles to empiric data

This paper deals with adaptation of the stochastic model of the economic cycle, represented by the values of the gross product. Establishing the statistical equivalence of the Yule series to discrete samples of income oscillations made it possible to determine analytical expressions between the coefficients of the Yule model and the parameters of economic cycle. This, the adaptation of the cycle model to empirical data is reduced to the linear problem of estimating the Yule model factors. The peculiarity of solution to this problem ensures the presence of an optimal discretization of the income function in the form of four samples for the cycle period. It is shown that with such discretization, the highest accuracy of calculated parameter estimates is ensured, that is, the efficiency of the estimates is obtained. The proposed procedure for adapting the cycle models considers the features of the economic data and provides: 1) recovery of the income function from values of the gross product estimates; 2) extraction of values of a cycle under interest from the recovered data; 3) determination of the time interval of cycle pseudo-stationarity; 4) parameter estimation of the cycle model; 5) accuracy analysis of parameter estimates. The procedure is formally (mathematically) described from the empirical values of the gross product to getting estimates of cycle parameters. It is applicable for econometric problems of estimating the parameters of systems described by ordinary differential and difference equations of the second order.

Spatial Yule Model for Urban Growth with Shared Resources

Spatial Yule Model for Urban Growth with Shared Resources

Extremal Values of the Sackin Tree Balance Index

Tree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are more likely than balanced ones. Also, concerning ordered search trees, more balanced ones allow for more efficient data structuring than imbalanced ones. Therefore, different methods to measure the balance of trees were introduced. The Sackin index is one of the most frequently used measures for this purpose. In many contexts, statements about the minimal and maximal values of this index have been discussed, but formal proofs have only been provided for some of them, and only in the context of ordered binary (search) trees, not for general rooted trees. Moreover, while the number of trees with maximal Sackin index as well as the number of trees with minimal Sackin index when the number of leaves is a power of 2 are relatively easy to understand, the number of trees with minimal Sackin index for all other numbers of leaves has been completely unknown. In this manuscript, we extend the findings on trees with minimal and maximal Sackin indices from the literature on ordered trees and subsequently use our results to provide formulas to explicitly calculate the numbers of such trees. We also extend previous studies by analyzing the case when the underlying trees need not be binary. Finally, we use our results to contribute both to the phylogenetic as well as the computer scientific literature using the new findings on Sackin minimal and maximal trees to derive formulas to calculate the number of both minimal and maximal phylogenetic trees as well as minimal and maximal ordered trees both in the binary and non-binary settings. All our results have been implemented in the Mathematica package SackinMinimizer, which has been made publicly available.

Phylogenetic Networks and Parameters Inferred from HIV Nucleotide Sequences of High-Risk and General Population Groups in Uganda: Implications for Epidemic Control.

Phylogenetic inference is useful in characterising HIV transmission networks and assessing where prevention is likely to have the greatest impact. However, estimating parameters that influence the network structure is still scarce, but important in evaluating determinants of HIV spread. We analyzed 2017 HIV pol sequences (728 Lake Victoria fisherfolk communities (FFCs), 592 female sex workers (FSWs) and 697 general population (GP)) to identify transmission networks on Maximum Likelihood (ML) phylogenetic trees and refined them using time-resolved phylogenies. Network generative models were fitted to the observed degree distributions and network parameters, and corrected Akaike Information Criteria and Bayesian Information Criteria values were estimated. 347 (17.2%) HIV sequences were linked on ML trees (maximum genetic distance ≤4.5%, ≥95% bootstrap support) and, of these, 303 (86.7%) that consisted of pure A1 (n = 168) and D (n = 135) subtypes were analyzed in BEAST v1.8.4. The majority of networks (at least 40%) were found at a time depth of ≤5 years. The waring and yule models fitted best networks of FFCs and FSWs respectively while the negative binomial model fitted best networks in the GP. The network structure in the HIV-hyperendemic FFCs is likely to be scale-free and shaped by preferential attachment, in contrast to the GP. The findings support the targeting of interventions for FFCs in a timely manner for effective epidemic control. Interventions ought to be tailored according to the dynamics of the HIV epidemic in the target population and understanding the network structure is critical in ensuring the success of HIV prevention programs.

On Sackin\u2019s original proposal: the variance of the leaves\u2019 depths as a phylogenetic balance index

BackgroundThe Sackin indexS of a rooted phylogenetic tree, defined as the sum of its leaves’ depths, is one of the most popular balance indices in phylogenetics, and Sackin’s paper (Syst Zool 21:225–6, 1972) is usually cited as the source for this index. However, what Sackin actually proposed in his paper as a measure of the imbalance of a rooted tree was not the sum of its leaves’ depths, but their “variation”. This proposal was later implemented as the variance of the leaves’ depths by Kirkpatrick and Slatkin in (Evolution 47:1171–81, 1993), where they also posed the problem of finding a closed formula for its expected value under the Yule model. Nowadays, Sackin’s original proposal seems to have passed into oblivion in the phylogenetics literature, replaced by the index bearing his name, which, in fact, was introduced a decade later by Sokal.ResultsIn this paper we study the properties of the variance of the leaves’ depths, V, as a balance index. Firstly, we prove that the rooted trees with n leaves and maximum V value are exactly the combs with n leaves. But although V achieves its minimum value on every space mathcal {BT}_{n} of bifurcating rooted phylogenetic trees with n≤183 leaves at the so-called “maximally balanced trees” with n leaves, this property fails for almost every n≥184. We provide then an algorithm that finds the trees in mathcal {BT}_{n} with minimum V value in time O(n log(n)). Secondly, we obtain closed formulas for the expected V value of a bifurcating rooted tree with any number n of leaves under the Yule and the uniform models and, as a by-product of the computations leading to these formulas, we also obtain closed formulas for the variance under the uniform model of the Sackin index and the total cophenetic index (Mir et al., Math Biosci 241:125–36, 2013) of a bifurcating rooted tree, as well as of their covariance, thus filling this gap in the literature.ConclusionThe phylogenetics community has been wise in preferring the sum S(T) of the leaves’ depths of a phylogenetic tree T over their variance V(T) as a balance index, because the latter does not seem to capture correctly the notion of balance of large bifurcating rooted trees. But it is still a valid and useful shape index.

On the continuous-time limit of the Barabási–Albert random graph

We prove that, via an appropriate scaling, the degree of a fixed vertex in the Barabási–Albert model appeared at a large enough time converges in distribution to a Yule process. Using this relation we explain why the limit degree distribution of a vertex chosen uniformly at random (as the number of vertices goes to infinity), coincides with the limit distribution of the number of species in a genus selected uniformly at random in a Yule model (as time goes to infinity). To prove this result we do not assume that the number of vertices increases exponentially over time (linear rates). On the contrary, we retain their natural growth with a constant rate superimposing to the overall graph structure a suitable set of processes that we call the planted model and introducing an ad-hoc sampling procedure.

Evolution equations and diffusion operators for demographic dynamics

ABSTRACT In this paper, we first review the related results of the evolution equations and operators in the parity theory of demographic evolution, and respectively establish differential equations and difference equations based on different initial states. In order to consider regional constraints, we modify the differential equation model to a stochastic Yule model and analyze the main features of the solution. Then, we add nonlinear terms to represent the limiting factors, transform the differential equation model into the initial value problem of nonlinear ordinary differential equations with parameters, and show the existence, stability and asymptotic behavior of global classical solutions in () spaces. Finally, we further study the demographic operator and the corresponding heat equation, and give the explicit structure of the singular geodesic of the associated Hamiltonian system and singular heat kernel of the operator.

A multi-epoch model for the number of species within genera

An early question in evolutionary theory asked why frequency distributions of taxonomic group sizes exhibit “hollow curves” so frequently. An answer to this question was provided by G. Udny Yule’s seminal contribution introducing a discrete model for those distributions. But Yule observed that the fit of his model to observed distributions was sometimes imperfect, in particular for the class of reptiles. The present study introduces a multi-epoch extension of the discrete Yule model that accounts for unobserved extinction of ancient lineages. The multi-epoch model is described as a Pòlya urn embedded in a continuous-time branching process with an harmonic sequence of diversification rates. The main results include equivalent descriptions of multi-epoch models, their probability distributions, expected values, tail behavior and a self-similarity property. As an illustration of the theory, the multi-epoch model is applied to study the taxonomic diversity of reptile species, and provides a much better fit to the observed distribution of species than the original discrete Yule model.

Studies on generalized Yule models

We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, in specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process.

Simulating the composition and structuration of coloring layers in historical painting from non-invasive spectral reflectance measurements

Reflectance spectroscopy is a powerful non-invasive technique for determining the material composition of historical polychromies, since the measurement is fast, simple, and contactless. However, reflectance spectra of complex color mixtures can sometimes be hard to interpret from a compositional point of view. In these cases, theoretical optical simulations can provide useful additional data. The main issue is the choice of the optical model that must be adapted to the measurement protocol and the material structure of the coloring layer, this latter being generally unknown. Simple models based on analytical formulas are preferred, as they can be easily inversed to deduce the optical and structural properties of the materials from the measured spectral reflectance of the object. In this paper, we address this issue to investigate the material composition of the colors of the Codex Borbonicus, a 16th-century Mesoamerican manuscript. Two models dedicated to two different types of material structures are presented: the Kubelka–Munk model with Saunderson correction, suitable for one homogenous layer, and the Clapper–Yule model used for continuous colorant layer, suitable when a weakly scattering paint is on top of a diffusing support. The results of the simulation provide new insights into the way the coloring materials were combined in the document, either as mechanical mixture before application or as superimposition. La spectroscopie de réflexion diffuse est une technique non invasive très pratique pour l'étude des polychromies historiques, puisque sa mise œuvre est rapide, simple et sans contact. Toutefois, les spectres de réflexion de mélanges colorés complexes peuvent parfois être difficiles à interpréter d'un point de vue compositionnel. Dans ces cas, des simulations optiques théoriques peuvent fournir des données supplémentaires pertinentes. La problématique principale concerne le choix du modèle optique, qui doit être adapté au protocole de mesure et à la structure matérielle (généralement inconnue) des couches colorées étudiées. Les modèles simples basés sur des formules analytiques sont préférés, puisqu'ils peuvent facilement être inversés pour déduire les propriétés optiques et la structure des matériaux à partir de leur réflectance spectrale. Dans cet article, cette problématique est abordée pour l'étude de la composition des peintures du Codex Borbonicus, un manuscrit mésoaméricain du XVIe siècle. Deux modèles sont appliqués pour deux types de structure matérielle : le modèle de Kubelka–Munk avec la correction de Saunderson, adapté à une couche colorée homogène, et le modèle de Clapper–Yule pour des couches continues de colorants, adapté à une peinture faiblement diffusante superposée à un support diffusant. Les simulations apportent une nouvelle compréhension quant à la façon dont les matériaux colorants ont été associés dans le document, soit par mélange mécanique avant application, soit par superposition.

Species Delimitation, Phylogenetic Relationships, and Temporal Divergence Model in the Genus Aeromonas.

The definition of species boundaries constitutes an important challenge in biodiversity studies. In this work we applied the Generalized Mixed Yule Coalescent (GMYC) method, which determines a divergence threshold to delimit species in a phylogenetic tree. Based on the tree branching pattern, the analysis fixes the transition threshold between speciation and the coalescent process associated with the intra-species diversification. This approach has been widely used to delineate eukaryote species and establish their diversification process from sequence data. Nevertheless, there are few examples in which this analysis has been applied to a bacterial population. Although the GMYC method was originally designed to assume a constant (Yule) model of diversification at between-species level, it was later evaluated simulating other conditions. Our aim was therefore to determine the species delineation in Aeromonas using the GMYC method and asses which model best explains the speciation process in this bacterial genus. The application of the GMYC method allowed us to clearly delineate the Aeromonas species boundaries, even in the controversial groups, such as the A. veronii or A. media species complexes.

The Probabilities of Trees and Cladograms under Ford's α-Model.

Ford's α-model is one of the most popular random parametric models of bifurcating phylogenetic tree growth, having as specific instances both the uniform and the Yule models. Its general properties have been used to study the behavior of phylogenetic tree shape indices under the probability distribution it defines. But the explicit formulas provided by Ford for the probabilities of unlabeled trees and phylogenetic trees fail in some cases. In this paper we give correct explicit formulas for these probabilities.

TreeSimGM: Simulating phylogenetic trees under general Bellman-Harris models with lineage-specific shifts of speciation and extinction in R.

Understanding macroevolutionary processes using phylogenetic trees is a challenging and complex process that draws on mathematics, computer science and biology. Given the development of complex mathematical models and the growing computational processing power, simulation tools are becoming increasingly popular.In order to simulate phylogenetic trees, most evolutionary biologists are forced to build their own algorithms or use existing tools built on different platforms and/or as standalone programmes. The absence of a simulation tool accommodating for user‐chosen model specifications limits, amongst others, model testing and pipelining with approximate Bayesian computation methods or other subsequent statistical analysis.We introduce “TreeSimGM,” an r‐package simulation tool for phylogenetic trees under a general Bellman and Harris model. This package allows the user to specify any desired probability distribution for the waiting times until speciation and extinction (e.g. age‐dependent speciation/extinction). Upon speciation, the user can specify whether one descendant species corresponds to the ancestor species inheriting its age or whether both descendant species are new species of age 0. Moreover, it is possible to scale the waiting time to speciation/extinction for newly formed species. Thus, “TreeSimGM” not only allows the user to simulate stochastic phylogenetic trees assuming several popular existing models, such as the Yule model, the constant‐rate birth–death model, and proportional to distinguishable arrangement models, but it also allows the user to formulate new models for exploration. A short explanation of the supported models and a few examples of how to use our package are presented here.As an r‐package, “TreeSimGM” allows flexible and powerful stochastic phylogenetic tree simulations. Moreover, it facilitates the pipelining of outputs or inputs with other functions in r. “TreeSimGM” contributes to the tools available to the r community in the fields of ecology and evolution, is freely available under the GPL‐2 licence and can be downloaded at https://cran.r-project.org/web/packages/TreeSimGM.