128 results on '"Birth–death process"'
Search Results
2. Some mechanisms leading to underdispersion: Old and new proposals.
- Author
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Puig, Pedro, Valero, Jordi, and Fernández‐Fontelo, Amanda
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POISSON distribution , *STATISTICAL models - Abstract
In statistical modeling, it is important to know the mechanisms that cause underdispersion. Several mechanisms that lead to underdispersed count distributions are revisited from new perspectives, and new ones are introduced. These include procedures based on the number of arrivals in arrival processes, such as renewal and pure birth processes and steady‐state distributions of birth‐death processes, like queues with state‐dependent service rates. Weighted Poisson and other well‐known underdispersed distributions are also related to birth‐death processes. Classical and variable binomial thinning mechanisms are also viewed as important procedures for generating underdispersed distributions, which can also generate bivariate count distributions with negative correlation. Some example applications are shown, one of which is related to Biodosimetry. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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3. Fixation probability in evolutionary dynamics on switching temporal networks.
- Author
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Bhaumik, Jnanajyoti and Masuda, Naoki
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TIME-varying networks , *SWITCHING systems (Telecommunication) , *PROBABILITY theory , *GRAPH theory - Abstract
Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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4. Numerical Computation of Distributions in Finite-State Inhomogeneous Continuous Time Markov Chains, Based on Ergodicity Bounds and Piecewise Constant Approximation.
- Author
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Satin, Yacov, Razumchik, Rostislav, Usov, Ilya, and Zeifman, Alexander
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PIECEWISE constant approximation , *MARKOV processes , *DISTRIBUTION (Probability theory) , *PERTURBATION theory , *MARKOV chain Monte Carlo , *APPROXIMATION error , *CONTINUOUS time models - Abstract
In this paper it is shown, that if a possibly inhomogeneous Markov chain with continuous time and finite state space is weakly ergodic and all the entries of its intensity matrix are locally integrable, then, using available results from the perturbation theory, its time-dependent probability characteristics can be approximately obtained from another Markov chain, having piecewise constant intensities and the same state space. The approximation error (the taxicab distance between the state probability distributions) is provided. It is shown how the Cauchy operator and the state probability distribution for an arbitrary initial condition can be calculated. The findings are illustrated with the numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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5. Temporal network modeling with online and hidden vertices based on the birth and death process.
- Author
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Zeng, Ziyan, Feng, Minyu, and Kurths, Jürgen
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TIME-varying networks , *DISTRIBUTION (Probability theory) , *PHASE transitions , *MARKOV processes , *SOCIAL interaction - Abstract
• We propose a temporal network model considering the stochastic phase transition of vertices. • Theoretical analysis is derived based on the continuous Markov chain method and confirmed by simulations. • Application in fitting the real network is discussed. Complex networks have played an important role in describing real complex systems since the end of the last century. Recently, research on real-world data sets reports intermittent interaction among social individuals. In this paper, we pay attention to this typical phenomenon of intermittent interaction by considering the state transition of network vertices between online and hidden based on the birth and death process. By continuous-time Markov theory, we show that both the number of each vertex's online neighbors and the online network size are stable and follow the homogeneous probability distribution in a similar form, inducing similar statistics as well. In addition, all propositions are verified via simulations. Moreover, we also present the degree distributions based on small-world and scale-free networks and find some regular patterns by simulations. The application in fitting real networks is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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6. Probability Distribution of Tree Age for the Simple Birth–Death Process, with Applications to Distributions of Number of Ancestral Lineages and Divergence Times for Pairs of Taxa in a Yule Tree.
- Author
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Mulder, Willem H.
- Abstract
In this contribution, a general expression is derived for the probability density of the time to the most recent common ancestor (TMRCA) of a simple birth–death tree, a widely used stochastic null-model of biological speciation and extinction, conditioned on the constant birth and death rates and number of extant lineages. This density is contrasted with a previous result which was obtained using a uniform prior for the time of origin. The new distribution is applied to two problems of phylogenetic interest. First, that of the probability of the number of taxa existing at any time in the past in a tree of a known number of extant species, and given birth and death rates, and second, that of determining the TMRCA of two randomly selected taxa in an unobserved tree that is produced by a simple birth-only, or Yule, process. In the latter case, it is assumed that only the rate of bifurcation (speciation) and the size, or number of tips, are known. This is shown to lead to a closed-form analytical expression for the probability distribution of this parameter, which is arrived at based on the known mathematical form of the age distribution of Yule trees of a given size and branching rate, which is derived here de novo, and a similar distribution which additionally is conditioned on tree age. The new distribution is the exact Yule prior for divergence times of pairs of taxa under the stated conditions and is potentially useful in statistical (Bayesian) inference studies of phylogenies. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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7. Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer's Impatience.
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Satin, Yacov, Razumchik, Rostislav, Kovalev, Ivan, and Zeifman, Alexander
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PATIENCE , *CONSUMERS , *DISTRIBUTION (Probability theory) , *NUMBER systems - Abstract
We consider a non-standard class of Markovian time: varying infinite capacity queues with possibly heterogeneous servers and impatience. We assume that during service time, a customer may switch to the faster server (with no delay), when such a server becomes available and no other customers are waiting. As a result, customers in the queue may become impatient and leave it. Under this setting and with certain restrictions on the intensity functions, the quantity of interest, the total number of customers in the system, is the level-dependent birth-and-death process (BPD). In this paper, for the first time in the literature, explicit upper bounds for the distance between two probability distributions of this BDP are obtained. Using the obtained ergodicity bounds in combination with the sensitivity bounds, we assess the stability of BDP under perturbations. Truncation bounds are also given, which allow for numerical solutions with guaranteed truncation errors. Finally, we provide numerical results to support the findings. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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8. Sufficient conditions for regularity, positive recurrence, and absorption in level‐dependent QBD processes and related block‐structured Markov chains.
- Author
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Gómez‐Corral, Antonio, Langwade, Joshua, López‐García, Martín, and Molina‐París, Carmen
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MARKOV processes , *T cell receptors , *T cells , *CELLULAR signal transduction , *ABSORPTION , *CELL communication - Abstract
This paper is concerned with level‐dependent quasi‐birth‐death (LD‐QBD) processes, i.e., multi‐variate Markov chains with a block‐tridiagonal q$$ q $$‐matrix, and a more general class of block‐structured Markov chains, which can be seen as LD‐QBD processes with total catastrophes. Arguments from univariate birth‐death processes are combined with existing matrix‐analytic formulations to obtain sufficient conditions for these block‐structured processes to be regular, positive recurrent, and absorbed with certainty in a finite mean time. Specifically, it is our purpose to show that, as is the case for competition processes, these sufficient conditions are inherently linked to a suitably defined birth‐death process. Our results are exemplified with two Markov chain models: a study of target cells and viral dynamics and one of kinetic proof‐reading in T cell receptor signal transduction. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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9. On the stochastic engine of contagious diseases in exponentially growing populations.
- Author
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Lindström, Torsten
- Subjects
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COMMUNICABLE diseases , *BIOLOGICAL extinction , *STOCHASTIC models , *BIRTH rate , *DEATH rate - Abstract
The purpose of this paper is to analyze the mechanism for the interplay of deterministic and stochastic models for contagious diseases. Deterministic models for contagious diseases are prone to predict global stability. Small natural birth and death rates in comparison to disease parameters like the contact rate and the removal rate ensures that the globally stable endemic equilibrium corresponds to a tiny average proportion of infected individuals. Asymptotic equilibrium levels corresponding to low numbers of individuals invalidate the deterministic results. Diffusion effects force probability mass functions of the stochastic model to possess similar stability properties as the deterministic model. Particular simulations of the stochastic model predict, however, oscillatory patterns. Small and isolated populations show longer periods, more violent oscillations, and larger probabilities of extinction. We prove that evolution maximizes the infectiousness of the disease as measured by the ability to increase the proportion of infected individuals. This holds provided the stochastic oscillations are moderate enough to keep the proportion of susceptible individuals near a deterministic equilibrium. We close our paper with a discussion of the herd-immunity concept and stress its close relation to vaccination-programs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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10. Time Series Path Integral Expansions for Stochastic Processes.
- Author
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Greenman, Chris D.
- Abstract
A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. All methods rely on finding a suitable reproducing kernel associated with an underlying representative algebra to perform the expansion. Birth–death processes can be analysed with these techniques, using either standard Doi-Peliti coherent states, or the s u (1 , 1) Lie algebra. These result in simplest expansions for processes with linear or quadratic rates, respectively. The techniques are also adapted to diffusion processes. The resulting series differ from those found in standard Dyson time series field theory techniques. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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11. The Birth–death Processes with Regular Boundary: Stationarity and Quasi-stationarity.
- Author
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Gao, Wu Jun, Mao, Yong Hua, and Zhang, Chi
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EIGENVALUES - Abstract
For the birth—death Q-matrix with regular boundary, its minimal process and its maximal process are closely related. In this paper, we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process. And via the construction theory, we mainly derive the eigentime identity and the distribution of the fastest strong stationary time (FSST) for the maximal process. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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12. A three-term recurrence relation for accurate evaluation of transition probabilities of the simple birth-and-death process.
- Author
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Pessia, Alberto and Tang, Jing
- Subjects
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GAUSSIAN function , *PROBABILITY theory , *HYPERGEOMETRIC functions , *POPULATION dynamics , *EXPECTATION-maximization algorithms , *STOCHASTIC models , *HYPERGEOMETRIC series - Abstract
The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is known about formal estimator properties. Here we will show that its application to observed data is further complicated by the fact that numerical evaluation of the well-known transition probability is an ill-conditioned problem. To overcome this difficulty we will rewrite the transition probability in terms of a Gaussian hypergeometric function and subsequently obtain a three-term recurrence relation for its accurate evaluation. We will also study the properties of the hypergeometric function as a solution to the three-term recurrence relation. We will then provide formulas for the gradient and Hessian of the log-likelihood function and conclude the article by applying our methods for numerically computing maximum likelihood estimates in both simulated and real dataset. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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13. Modelling and solving resource allocation problems via a dynamic programming approach.
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Forootani, Ali, Tipaldi, Massimo, Ghaniee Zarch, Majid, Liuzza, Davide, and Glielmo, Luigi
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DYNAMIC programming , *RESOURCE allocation , *STOCHASTIC programming , *REVENUE management , *MARKOV processes , *DISCRETE choice models - Abstract
In this paper, resource allocation problems are formulated via a set of parallel birth–death processes (BDP). This way, we can model the fact that resources can be allocated to customers at different prices, and that customers can hold them as long as they like. More specifically, a discretisation approach is applied to model resource allocation problems as a set of discrete-time BDPs, which are then integrated into one Markov decision process. The stochastic dynamics of the resulting system are also investigated. As a result, revenue management becomes a stochastic decision-making problem, where price managers can propose suitable prices to the allocation requests such that the maximum expected total revenue is obtained at the end of a predefined finite time horizon. Stochastic Dynamic Programming is employed to solve the related optimisation problem with the support of an ad-hoc Matlab-based application. Several simulations are performed to prove the effectiveness of the proposed model and the optimisation approach. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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14. Success probability for selectively neutral invading species in the line model with a random fitness landscape.
- Author
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Farhang‐Sardroodi, Suzan, Komarova, Natalia L., Michelen, Marcus, and Pemantle, Robin
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PROBABILITY theory , *SUCCESS , *SPECIES , *SIZE - Abstract
We consider a spatial (line) model for invasion of a population by a single mutant with a stochastically selectively neutral fitness landscape, independent from the fitness landscape for nonmutants. This model is similar to those considered earlier. We show that the probability of mutant fixation in a population of size N, starting from a single mutant, is greater than 1/N, which would be the case if there were no variation in fitness whatsoever. In the small variation regime, we recover precise asymptotics for the success probability of the mutant. This demonstrates that the introduction of randomness provides an advantage to minority mutations in this model, and shows that the advantage increases with the system size. We further demonstrate that the mutants have an advantage in this setting only because they are better at exploiting unusually favorable environments when they arise, and not because they are any better at exploiting pockets of favorability in an environment that is selectively neutral overall. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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15. 5G 隧道环境非平稳宽带双散射簇 V2V 信道建模.
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周文轩, 周 杰, and 刘少云
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POWER spectra , *POWER density , *5G networks , *TUNNELS - Abstract
This paper proposed a general 3D non-stationary wideband two-cluster channel model for 5G V2V tunnel communication environments. In the proposed model, the received signal consists of a sum of the components with line-of-sight ( LoS ) propagations and the components via the two-cluster model, i. e., non-line-of-sight ( NLoS) propagations. This paper introduced a birth-death algorithm to model the appearance and disappearance of clusters on both the array and time axes to investigate the non-stationary properties of clusters. The impacts of the non-stationary properties of clusters on the multiple-input and multipleoutput ( MIMO) channels we re investigated via statistical properties, including spatial cross-correlation functions ( CCF), temporal spatial auto-correlation functions( ACF), and Doppler power spectrum densities ( PSD ) . Numerical results of the proposed propagation properties fit the simulation results and prior measured results very well, which demonstrate that the proposed 3D model is able to describe the real 5G V2V communications in tunnel environments. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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16. Bio-Inspired Quorum Sensing-Based Nanonetwork Synchronization Using Birth-Death Growth Model.
- Author
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Tissera, Ponsuge Surani Shalika and Choe, Sangho
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SYNCHRONIZATION , *QUORUM sensing , *BACTERIAL growth , *COLLECTIVE behavior , *GAUSSIAN processes - Abstract
We construct a bio-inspired nanomachine network via the quorum sensing (QS) mechanism and analyze that nanonetwork from the perspective of global synchronization time and channel capacity. We propose a realistic (stochastic) approach using birth-death-process-based bacterial growth model and compare it to a conventional ideal (deterministic) approach using exponentially-increased bacterial growth model. For the comparative study, we first define a diffusion-based molecular communication channel between bacterial density and autoinducer (AI) concentration as an approximated Gaussian process, and then analyze the presented QS behavior model numerically as well as theoretically. Increases in the bacterial density augment the diffused AI concentration. When the AI concentration satisfies a specified threshold indicating gene expression, almost all bacteria in that colony represent a collective QS behavior such as biofilm formation. Compared to the ideal approach that is simple but not feasible in real life given the limited resources (e.g., food), the realistic approach is complex but better at representing real and probabilistic QS nature, less sensitive at gene expression, and so more suitable for global synchronization analysis. Via simulation, we evaluate the proposed model in terms of AI concentration versus bacterial density, synchronization time, and information sensing capacity, and demonstrate its superiority over the traditional model. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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17. Wald's martingale and the conditional distributions of absorption time in the Moran process.
- Author
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Monk, Travis and van Schaik, André
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MARTINGALES (Mathematics) , *CHARACTERISTIC functions , *STOCHASTIC processes , *ABSORPTION , *EVOLUTIONARY models , *CONDITIONAL probability - Abstract
Many models of evolution are stochastic processes, where some quantity of interest fluctuates randomly in time. One classic example is the Moranbirth–death process, where that quantity is the number of mutants in a population. In such processes, we are often interested in their absorption (i.e. fixation) probabilities and the conditional distributions of absorption time. Those conditional time distributions can be very difficult to calculate, even for relatively simple processes like the Moran birth–death model. Instead of considering the time to absorption, we consider a closely related quantity: the number of mutant population size changes before absorption. We use Wald's martingale to obtain the conditional characteristic functions of that quantity in the Moran process. Our expressions are novel, analytical and exact, and their parameter dependence is explicit. We use our results to approximate the conditional characteristic functions of absorption time. We state the conditions under which that approximation is particularly accurate. Martingales are an elegant framework to solve principal problems of evolutionary stochastic processes. They do not require us to evaluate recursion relations, so when they are applicable, we can quickly and tractably obtain absorption probabilities and times of evolutionary models. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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18. Continuous-Time Birth-Death MCMC for Bayesian Regression Tree Models.
- Author
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Mohammadi, Reza, Pratola, Matthew, and Kaptein, Maurits
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REGRESSION trees , *MARKOV chain Monte Carlo , *REGRESSION analysis , *POISSON processes , *ALGORITHMS - Abstract
Decision trees are flexible models that are well suited for many statistical regression problems. In the Bayesian framework for regression trees, Markov Chain Monte Carlo (MCMC) search algorithms are required to generate samples of tree models according to their posterior probabilities. The critical component of such MCMC algorithms is to construct "good" Metropolis-Hastings steps to update the tree topology. Such algorithms frequently suffer from poor mixing and local mode stickiness; therefore, the algorithms are slow to converge. Hitherto, authors have primarily used discrete-time birth/death mechanisms for Bayesian (sums of) regression tree models to explore the tree-model space. These algorithms are efficient, in terms of computation and convergence, only if the rejection rate is low which is not always the case. We overcome this issue by developing a novel search algorithm which is based on a continuous-time birth-death Markov process. The search algorithm explores the tree-model space by jumping between parameter spaces corresponding to different tree structures. The jumps occur in continuous time corresponding to the birth-death events which are modeled as independent Poisson processes. In the proposed algorithm, the moves between models are always accepted which can dramatically improve the convergence and mixing properties of the search algorithm. We provide theoretical support of the algorithm for Bayesian regression tree models and demonstrate its performance in a simulated example. [ABSTRACT FROM AUTHOR]
- Published
- 2020
19. Additional Analytical Support for a New Method to Compute the Likelihood of Diversification Models.
- Author
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Laudanno, Giovanni, Haegeman, Bart, and Etienne, Rampal S.
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MACROEVOLUTION , *INFORMATION resources - Abstract
Molecular phylogenies have been increasingly recognized as an important source of information on species diversification. For many models of macroevolution, analytical likelihood formulas have been derived to infer macroevolutionary parameters from phylogenies. A few years ago, a general framework to numerically compute such likelihood formulas was proposed, which accommodates models that allow speciation and/or extinction rates to depend on diversity. This framework calculates the likelihood as the probability of the diversification process being consistent with the phylogeny from the root to the tips. However, while some readers found the framework presented in Etienne et al. (Proc R Soc Lond B Biol Sci 279(1732):1300–1309, 2012) convincing, others still questioned it (personal communication), despite numerical evidence that for special cases the framework yields the same (i.e., within double precision) numerical value for the likelihood as analytical formulas do that were independently derived for these special cases. Here we prove analytically that the likelihoods calculated in the new framework are correct for all special cases with known analytical likelihood formula. Our results thus add substantial mathematical support for the overall coherence of the general framework. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
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20. Contact-dependent infection and mobility in the metapopulation SIR model from a birth–death process perspective.
- Author
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Xie, Meiling, Li, Yuhan, Feng, Minyu, and Kurths, Jürgen
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BASIC reproduction number , *POISSON processes , *REPRODUCTION , *COVID-19 , *INFECTION - Abstract
Given the widespread impact of COVID-19, modeling and analysis of epidemic propagation has been critical to epidemic prevention and control. However, previous studies have overlooked the significant influence of individual heterogeneity in behavior and physiology, including contact-dependent infection and migration on epidemic propagation. In this paper, we propose two metapopulation SIR models from individual and population perspectives. The first individual model introduces individual contact-dependent infection considering activity potential and infection rate, which leads to the derivation of the basic reproduction number R 0 of our model. The birth–death process, used in the second population model, is represented by a compound Poisson process flow and Poisson process decomposition, respectively, to depict population mobility among subpopulations. In simulations, the number of individuals in each state and the converged number are illustrated to demonstrate the impact of various parameters. The relationship between the basic reproduction number R 0 and various parameters is also demonstrated. Furthermore, the validity of our model is also confirmed on a real clinical report dataset of COVID-19 disease. • A metapopulation SIR model with individual heterogeneity and population mobility is proposed. • Individual model considers contact-dependent infection, leading to R 0 derivation. • Population model uses a birth–death process with compound Poisson flow and decomposition. • Simulations illustrate the impact of parameters and validate R 0 correlations. • Model demonstrates on real COVID-19 dataset in Shanghai. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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21. Stochastic models in seed dispersals: random walks and birth–death processes.
- Author
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Abdullahi, A., Shohaimi, S., Kilicman, A., and Ibrahim, M. H.
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SEED dispersal , *RANDOM walks , *STOCHASTIC models , *GERMINATION , *PLANT species , *LARVAL dispersal - Abstract
Seed dispersals deal with complex systems through which the data collected using advanced seed tracking facilities pose challenges to conventional approaches, such as empirical and deterministic models. The use of stochastic models in current seed dispersal studies is encouraged. This review describes three existing stochastic models: the birth–death process (BDP), a 2 dimensional ( 2 D ) symmetric random walks and a 2 D intermittent walks. The three models possess Markovian property, which make them flexible for studying natural phenomena. Only a few of applications in ecology are found in seed dispersals. The review illustrates how the models are to be used in seed dispersals context. Using the nonlinear BDP, we formulate the individual-based models for two competing plant species while the cover time model is formulated by the symmetric and intermittent random walks. We also show that these three stochastic models can be formulated using the Gillespie algorithm. The full cover time obtained by the symmetric random walks can approximate the Gumbel distribution pattern as the other searching strategies do. We suggest that the applications of these models in seed dispersals may lead to understanding of many complex systems, such as the seed removal experiments and behaviour of foraging agents, among others. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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22. On a property of random walk polynomials involving Christoffel functions.
- Author
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van Doorn, Erik A. and Szwarc, Ryszard
- Abstract
Discrete-time birth-death processes may or may not have certain properties known as asymptotic aperiodicity and the strong ratio limit property. In all cases known to us a suitably normalized process having one property also possesses the other, suggesting equivalence of the two properties for a normalized process. We show that equivalence may be translated into a property involving Christoffel functions for a type of orthogonal polynomials known as random walk polynomials. The prevalence of this property – and thus the equivalence of asymptotic aperiodicity and the strong ratio limit property for a normalized birth-death process – is proven under mild regularity conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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23. Proximity inheritance explains the evolution of cooperation under natural selection and mutation.
- Author
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Tan, Shaolin
- Subjects
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PUNISHMENT , *NATURAL selection , *ATTRIBUTION (Social psychology) , *PRISONER'S dilemma game , *COOPERATION - Abstract
In this paper, a mechanism called proximity inheritance is introduced in the birth–death process of a networked population involving the Prisoner's Dilemma game. Different from the traditional birth–death process, in the proposed model, players are distributed in a spatial space and offspring is distributed in the neighbourhood of its parents. That is, offspring inherits not only the strategy but also the proximity of its parents. In this coevolutionary game model, a cooperative neighbourhood gives more neighbouring cooperative offspring and a defective neighbourhood gives more neighbouring defective offspring, leading to positive feedback among cooperative interactions. It is shown that with the help of proximity inheritance, natural selection will favour cooperation over defection under various conditions, even in the presence of mutation. Furthermore, the coevolutionary dynamics could lead to self-organized substantial network clustering, which promotes an assortment of cooperative interactions. This study provides a new insight into the evolutionary mechanism of cooperation in the absence of social attributions such as reputation and punishment. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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24. Leader formation with mean-field birth and death models.
- Author
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Albi, Giacomo, Bongini, Mattia, Rossi, Francesco, and Solombrino, Francesco
- Subjects
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JUMP processes , *MASS transfer , *EQUATIONS of state , *STOCHASTIC processes , *LABOR (Obstetrics) , *SOCIAL dynamics - Abstract
We provide a mean-field description for a leader–follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending nonlinearly on the global state of the system at each time. We first prove the existence and uniqueness of solutions for the leader–follower dynamics, under suitable assumptions. We then establish, for an appropriate choice of the initial datum, the equivalence of the system with a PDE–ODE system, that consists of a continuity equation over the state space and an ODE for the transition from leader to follower or vice versa. We further introduce a stochastic process approximating the PDE, together with a jump process that models the switch between the two populations. Using a propagation of chaos argument, we show that the particle system generated by these two processes converges in probability to a solution of the PDE–ODE system. Finally, several numerical simulations of social interactions dynamics modeled by our system are discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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25. A MULTIVARIATE LOG-NORMAL MOMENT CLOSURE TECHNIQUE FOR THE STOCHASTIC PREDATOR-PREY MODEL.
- Author
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TRAKOOLTHAI, TANAWAT, CURTIS, DIANA, and SWITKES, JENNIFER
- Subjects
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LOGNORMAL distribution , *BIOLOGIC predation models , *LOTKA-Volterra equations , *STOCHASTIC models , *COVARIANCE matrices - Abstract
The deterministic Lotka-Volterra model is a simple predator-prey model that classically portrays the interaction between two species, leading to closed curves in the predatorprey phase plane. Using the probability generating function, we develop a corresponding stochastic version of this model, which has the form of a simple birth-death process. This stochastic model involves the expected values of the populations, which are governed by a system of differential equations almost identical in form to the deterministic system. However, we find that the stochastic model is no longer a closed system. To gain a more intuitive understanding of this model, we turn to a moment closure approximation technique, which captures the main features of the stochastic model. Assuming that the distribution of the two populations is approximately multivariate log-normal, we use a moment closure technique to obtain a closed system of differential equations for the expected values, multiplicative variances, and multiplicative covariance of the populations. [ABSTRACT FROM AUTHOR]
- Published
- 2018
26. How big is a genus? Towards a nomothetic systematics.
- Author
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Sigwart, Julia D, Sutton, Mark D, and Bennett, K D
- Subjects
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PHYLOGENY , *ANIMAL classification , *MACROEVOLUTION , *TAXONOMY , *SPECIES diversity - Abstract
A genus is a taxonomic unit that may contain one species (monotypic) or thousands. Yet counts of genera or families are used to quantify diversity where species-level data are not available. High frequencies of monotypic genera (~30% of animals) have previously been scrutinized as an artefact of human classification. To test whether Linnean taxonomy conflicts with phylogeny, we compared idealized phylogenetic systematics
in silico with real-world data. We generated highly replicated, simulated phylogenies under a variety of fixed speciation/extinction rates, imposed three independent taxonomic sorting algorithms on these clades (2.65 × 108 simulated species) and compared the resulting genus size data with quality-controlled taxonomy of animal groups (2.8 × 105 species). 'Perfect' phylogenetic systematics arrives at similar distributions to real-world taxonomy, regardless of the taxonomic algorithm. Rapid radiations occasionally produce a large genus when speciation rates are favourable; however, small genera can arise in many different ways, from individual lineage persistence and/or extinctions creating subdivisions within a clade. The consistency of this skew distribution in simulation and real-world data, at sufficiently large samples, indicates that specific aspects of its mathematical behaviour could be developed into generalized or nomothetic principles of the global frequency distributions of higher taxa. Importantly, Linnean taxonomy is a better-than-expected reflection of underlying evolutionary patterns. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
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27. Some properties of the conditioned reconstructed process with Bernoulli sampling.
- Author
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Wiuf, Carsten
- Subjects
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BERNOULLI numbers , *GENETICS , *MARKOV processes , *GENETIC mutation , *SAMPLING (Process) - Abstract
In many areas of genetics it is of relevance to consider a population of individuals that is founded by a single individual in the past. One model for such a scenario is the conditioned reconstructed process with Bernoulli sampling that describes the evolution of a population of individuals that originates from a single individual. Several aspects of this reconstructed process are studied, in particular the Markov structure of the process. It is shown that at any given time in the past, the conditioned reconstructed process behaves as the original conditioned reconstructed process after a suitable time-dependent change of the sampling probability. Additionally, it is discussed how mutations accumulate in a sample of particles. It is shown that random sampling of particles at the present time has the effect of making the mutation rate look time-dependent. Conditions are given under which this sampling effect is negligible. A possible extension of the reconstructed process that allows for multiple founding particles is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
28. The coalescent of a sample from a binary branching process.
- Author
-
Lambert, Amaury
- Subjects
- *
COALESCENCE (Chemistry) , *TREES , *BERNOULLI numbers , *GENEALOGY , *RANDOM variables - Abstract
At time 0, start a time-continuous binary branching process, where particles give birth to a single particle independently (at a possibly time-dependent rate) and die independently (at a possibly time-dependent and age-dependent rate). A particular case is the classical birth–death process. Stop this process at time T > 0 . It is known that the tree spanned by the N tips alive at time T of the tree thus obtained (called a reduced tree or coalescent tree) is a coalescent point process (CPP), which basically means that the depths of interior nodes are independent and identically distributed (iid). Now select each of the N tips independently with probability y (Bernoulli sample). It is known that the tree generated by the selected tips, which we will call the Bernoulli sampled CPP, is again a CPP. Now instead, select exactly k tips uniformly at random among the N tips (a k -sample). We show that the tree generated by the selected tips is a mixture of Bernoulli sampled CPPs with the same parent CPP, over some explicit distribution of the sampling probability y . An immediate consequence is that the genealogy of a k -sample can be obtained by the realization of k random variables, first the random sampling probability Y and then the k − 1 node depths which are iid conditional on Y = y . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
29. Counting statistics based on the analytic solutions of the differential-difference equation for birth-death processes.
- Author
-
Park, Seong Jun and Choi, M.Y.
- Subjects
- *
DIFFERENTIAL-difference equations , *BIRTH rate , *BIRTH size , *DEATH rate , *STATISTICS - Abstract
Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every time birth or death occurs, which makes fluctuations in the rates inevitable. The differential-difference equation governing the time evolution of such a birth-death process is well established, but it resists solving for a non-asymptotic solution. In this work, we present the analytic solution of the differential-difference equation for birth-death processes without approximation. The time-dependent solution we obtain leads to an analytical expression for counting statistics of products (or customers). We further examine the relationship between the system size fluctuations and the birth and death rates, and find that statistical properties (variance subtracted by mean) of the system size are determined by the mean death rate as well as the covariance of the system size and the net growth rate (i.e., the birth rate minus the death rate). This work suggests a promising new direction for quantitative investigations into birth-death processes. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
30. The fossilized birth-death model for the analysis of stratigraphic range data under different speciation modes.
- Author
-
Stadler, Tanja, Gavryushkina, Alexandra, Warnock, Rachel C.M., Drummond, Alexei J., and Heath, Tracy A.
- Subjects
- *
FOSSIL trees , *BIOSTRATIGRAPHY , *GENETIC speciation , *PLANT phylogeny , *PLANT classification - Abstract
A birth-death-sampling model gives rise to phylogenetic trees with samples from the past and the present. Interpreting “birth” as branching speciation, “death” as extinction, and “sampling” as fossil preservation and recovery, this model – also referred to as the fossilized birth-death (FBD) model – gives rise to phylogenetic trees on extant and fossil samples. The model has been mathematically analyzed and successfully applied to a range of datasets on different taxonomic levels, such as penguins, plants, and insects. However, the current mathematical treatment of this model does not allow for a group of temporally distinct fossil specimens to be assigned to the same species. In this paper, we provide a general mathematical FBD modeling framework that explicitly takes “stratigraphic ranges” into account, with a stratigraphic range being defined as the lineage interval associated with a single species, ranging through time from the first to the last fossil appearance of the species. To assign a sequence of fossil samples in the phylogenetic tree to the same species, i.e. , to specify a stratigraphic range, we need to define the mode of speciation. We provide expressions to account for three common speciation modes: budding (or asymmetric) speciation, bifurcating (or symmetric) speciation, and anagenetic speciation. Our equations allow for flexible joint Bayesian analysis of paleontological and neontological data. Furthermore, our framework is directly applicable to epidemiology, where a stratigraphic range is the observed duration of infection of a single patient, “birth” via budding is transmission, “death” is recovery, and “sampling” is sequencing the pathogen of a patient. Thus, we present a model that allows for incorporation of multiple observations through time from a single patient. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
31. Integral-type functionals of first hitting times for continuous-time Markov chains.
- Author
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Liu, Yuanyuan and Song, Yanhong
- Subjects
- *
INTEGRALS , *FUNCTIONALS , *CONTINUOUS functions , *MARKOV processes , *POLYNOMIAL operators - Abstract
We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. How big is a genus? Towards a nomothetic systematics.
- Author
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SIGWART, JULIA D., SUTTON, MARK D., and BENNETT, K. D.
- Subjects
- *
CLADISTIC analysis , *GENETIC speciation , *MACROEVOLUTION , *SPECIES diversity , *BIOLOGICAL classification - Abstract
A genus is a taxonomic unit that may contain one species (monotypic) or thousands. Yet counts of genera or families are used to quantify diversity where species-level data are not available. High frequencies of monotypic genera (~30% of animals) have previously been scrutinized as an artefact of human classification. To test whether Linnean taxonomy conflicts with phylogeny, we compared idealized phylogenetic systematics in silico with real-world data. We generated highly replicated, simulated phylogenies under a variety of fixed speciation/extinction rates, imposed three independent taxonomic sorting algorithms on these clades (2.65 × 108 simulated species) and compared the resulting genus size data with quality-controlled taxonomy of animal groups (2.8 × 105 species). 'Perfect' phylogenetic systematics arrives at similar distributions to real-world taxonomy, regardless of the taxonomic algorithm. Rapid radiations occasionally produce a large genus when speciation rates are favourable; however, small genera can arise in many different ways, from individual lineage persistence and/or extinctions creating subdivisions within a clade. The consistency of this skew distribution in simulation and real-world data, at sufficiently large samples, indicates that specific aspects of its mathematical behaviour could be developed into generalized or nomothetic principles of the global frequency distributions of higher taxa. Importantly, Linnean taxonomy is a better-than-expected reflection of underlying evolutionary patterns. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
33. Birth/birth-death processes and their computable transition probabilities with biological applications.
- Author
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Ho, Lam Si Tung, Xu, Jason, Crawford, Forrest W., Minin, Vladimir N., and Suchard, Marc A.
- Subjects
- *
MOLECULAR epidemiology , *INFECTIOUS disease transmission , *MONTE Carlo method , *BAYESIAN analysis , *LAPLACE transformation - Abstract
Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the
birth/birth-death process , a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution. [ABSTRACT FROM AUTHOR]- Published
- 2018
- Full Text
- View/download PDF
34. Optimizing web server RAM performance using birth-death process queuing system: scalable memory issue.
- Author
-
Salmanian, Zolfaghar, Izadkhah, Habib, and Isazadeh, Ayaz
- Subjects
- *
QUEUEING networks , *INFORMATION retrieval , *COMPUTER security , *COMPUTER architecture , *CLIENT/SERVER computing , *CLOUD computing , *INTERNET servers - Abstract
Planning a powerful server imposes an enormous cost for providing ideal performance. Given that a server responding for web requests is more likely to consume RAM memory than other resources, it is desirable to provide an appropriate RAM capacity for optimal performance of server in congested situations. This can be done through RAM usage modeling and its performance evaluation. In the literature, modeling of RAM usage is not provided with mathematical modeling. We propose an approach to model RAM usage of such a server, based on birth-death process in this article. The model can be used to figure out an operation research problem of finding minimum RAM capacity covering intended constraints elicited from birth-death queuing system. We show how optimal RAM capacity can be obtained using our approach with an illustrative example. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
35. A MOMENT CLOSURE TECHNIQUE FOR A STOCHASTIC PREDATOR-PREY MODEL.
- Author
-
CURTIS, DIANA and SWITKES, JENNIFER
- Subjects
- *
MATHEMATICAL models , *LOTKA-Volterra equations , *NUMERICAL analysis , *PROBABILITY theory , *COMPUTER simulation - Abstract
The classical deterministic Lotka-Volterra predator-prey model famously leads to closed curves in the predator-prey phase plane. A stochastic version of this model has the form of a simple birth-death process, with the expected values governed by a system of differential equations almost identical in form to the deterministic system, the difference in rate function for each species being proportional to the time-dependent covariance of the populations of the two species. We explore the impact of this covariance term. Assuming that the distribution of the two populations is roughly multivariate normal, we use a moment closure technique to obtain a closed system of differential equations for the expected values, variances, and covariance of the populations. [ABSTRACT FROM AUTHOR]
- Published
- 2017
36. A rate balance principle and its application to queueing models.
- Author
-
Oz, Binyamin, Adan, Ivo, and Haviv, Moshe
- Subjects
- *
BIRTH rate , *DEATH rate , *QUEUEING networks , *APPLICATION servers (Computer software) , *STOCHASTIC processes - Abstract
We introduce a rate balance principle for general (not necessarily Markovian) stochastic processes. Special attention is given to processes with birth-and-death-like transitions, for which it is shown that for any state n, the rate of two consecutive transitions from $$n-1$$ to $$n+1$$ coincides with the corresponding rate from $$n+1$$ to $$n-1$$ . We demonstrate how useful this observation is by deriving well-known, as well as new, results for non-memoryless queues with state-dependent arrival and service processes. We also use the rate balance principle to derive new results for a state-dependent queue with batch arrivals, which is a model with non-birth-and-death-like transitions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
37. The Evolutionary Dynamics of the Odorant Receptor Gene Family in Corbiculate Bees.
- Author
-
Brand, Philipp and Ramírez, Santiago R.
- Subjects
- *
OLFACTORY receptor genes , *OLFACTORY receptors , *BEE behavior , *SMELL , *CHEMORECEPTORS , *CHROMOSOME duplication , *BIODIVERSITY , *INSECTS - Abstract
Insects rely on chemical information to locate food, choose mates, and detect potential predators. It has been hypothesized that adaptive changes in the olfactory system facilitated the diversification of numerous insect lineages. For instance, evolutionary changes of Odorant Receptor (OR) genes often occur in parallel with modifications in life history strategies. Corbiculate bees display a diverse array of behaviors that are controlled through olfaction, including varying degrees of social organization, and manifold associations with floral resources. Here we investigated the molecular mechanisms driving the evolution of the OR gene family in corbiculate bees in comparison to other chemosensory gene families. Our results indicate that the genomic organization of the OR gene family has remained highly conserved for ~80 Myr, despite exhibiting major changes in repertoire size among bee lineages. Moreover, the evolution of OR genes appears to be drivenmostly by lineage-specific gene duplications in few genomic regions that harbor large numbers of OR genes. A selection analysis revealed that OR genes evolve under positive selection, with the strongest signals detected in recently duplicated copies. Our results indicate that chromosomal translocations had a minimal impact on OR evolution, and instead local molecular mechanisms appear to be main drivers of OR repertoire size. Our results provide empirical support to the longstanding hypothesis that positive selection shaped the diversification of the OR gene family. Together, our results shed new light on the molecular mechanisms underlying the evolution of olfaction in insects. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
38. On the quasi-ergodic distribution of absorbing Markov processes.
- Author
-
He, Guoman, Zhang, Hanjun, and Zhu, Yixia
- Subjects
- *
MARKOV processes , *ORDER picking systems , *INTEGERS - Abstract
In this paper, we give a sufficient condition for the existence of a quasi-ergodic distribution for absorbing Markov processes. Using an orthogonal-polynomial approach, we prove that the previous main result is valid for the birth–death process on the nonnegative integers with 0 an absorbing boundary and ∞ an entrance boundary. We also show that the quasi-ergodic distribution is stochastically larger than the unique quasi-stationary distribution in the sense of monotone likelihood-ratio ordering for the birth–death process. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
39. Ergodicity Bounds for Birth-Death Processes with Particularities.
- Author
-
Zeifman, Alexander I., Satin, Yacov, Korotysheva, Anna, Shilova, Galina, Kiseleva, Ksenia, Korolev, Victor Yu., Bening, Vladimir E., and Shorgin, Sergey Ya.
- Subjects
- *
BIRTH rate , *DEATH rate , *MATHEMATICAL bounds , *MATHEMATICS , *REGRET bounds (Mathematics) - Abstract
We introduce an inhomogeneous birth-death process with birth rates αk(t), death rates μk(t), and possible transitions to/from zero with rates βk(t), rk(t) respectively, and obtain ergodicity bounds for this process. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
40. Bayesian Total-Evidence Dating Reveals the Recent Crown Radiation of Penguins.
- Author
-
GAVRYUSHKINA, ALEXANDRA, HEATH, TRACY A., KSEPKA, DANIEL T., STADLER, TANJA, WELCH, DAVID, and DRUMMOND, ALEXEI J.
- Subjects
- *
BIOLOGICAL divergence , *FOSSILS , *FOSSILIZATION , *BAYESIAN analysis , *MACROEVOLUTION , *STATISTICAL methods in evolution - Abstract
The total-evidence approach to divergence time dating uses molecular and morphological data from extant and fossil species to infer phylogenetic relationships, species divergence times, and macroevolutionary parameters in a single coherent framework. Current model-based implementations of this approach lack an appropriate model for the tree describing the diversification and fossilization process and can produce estimates that lead to erroneous conclusions. We address this shortcoming by providing a total-evidence method implemented in a Bayesian framework. This approach uses a mechanistic tree prior to describe the underlying diversification process that generated the tree of extant and fossil taxa. Previous attempts to apply the total-evidence approach have used tree priors that do not account for the possibility that fossil samples may be direct ancestors of other samples, that is, ancestors of fossil or extant species or of clades. The fossilized birth-death (FBD) process explicitly models the diversification, fossilization, and sampling processes and naturally allows for sampled ancestors. This model was recently applied to estimate divergence times based on molecular data and fossil occurrence dates. We incorporate the FBD model and amodel of morphological trait evolution into a Bayesian total-evidence approach to dating species phylogenies. We apply this method to extant and fossil penguins and show that the modern penguins radiated much more recently than has been previously estimated, with the basal divergence in the crown clade occurring at ∼12.7 Ma and most splits leading to extant species occurring in the last 2 myr. Our results demonstrate that including stem-fossil diversity can greatly improve the estimates of the divergence times of crown taxa. The method is available in BEAST2 (version 2.4) software www.beast2.org with packages SA (version at least 1.1.4) and morph-models (version at least 1.0.4) installed. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
41. An Evolutionary Model of Tumor Cell Kinetics and the Emergence of Molecular Heterogeneity Driving Gompertzian Growth.
- Author
-
West, Jeffrey, Hasnain, Zaki, Macklin, Paul, and Newton, Paul K.
- Subjects
- *
TUMOR growth , *CANCER cells , *CELL populations , *CANCER treatment - Abstract
We describe a cell-molecular-based evolutionary mathematical model of tumor development driven by a stochastic Moran birth-death process. The cells in the tumor carry molecular information in the form of a numerical genome which we represent as a four-digit binary string used to differentiate cells into 16 molecular types. The binary string is able to undergo stochastic point mutations that are passed to a daughter cell after each birth event. The value of the binary string determines the cell fitness, with lower fit cells (e.g., 0000) defined as healthy phenotypes, and higher fit cells (e.g., 1111) defined as malignant phenotypes. At each step of the birth-death process, the two phenotypic subpopulations compete in a prisoner's dilemma evolutionary game with the healthy cells playing the role of cooperators, and the cancer cells playing the role of defectors. Fitness, birth-death rates of the cell populations, and overall tumor fitness are defined via the prisoner's dilemma payoff matrix. Mutation parameters include passenger mutations (mutations conferring no fitness advantage) and driver mutations (mutations which increase cell fitness). The model is used to explore key emergent features associated with tumor development, including tumor growth rates as it relates to intratumor molecular heterogeneity. The tumor growth equation states that the growth rate is proportional to the logarithm of cellular diversity/heterogeneity. The Shannon entropy from information theory is used as a quantitative measure of heterogeneity and tumor complexity based on the distribution of the four-digit binary sequences produced by the cell population. To track the development of heterogeneity from an initial population of healthy cells (0000), we use dynamic phylogenetic trees which show clonal and subclonal expansions of cancer cell subpopulations from an initial malignant cell. We show that tumor growth rates are not constant throughout tumor development and are generally much higher in the subclinical range than in later stages of development, which leads to a Gompertzian growth curve. We explain the early exponential growth of the tumor and the later saturation associated with the Gompertzian curve which results from our evolutionary simulations using simple statistical mechanics principles related to the degree of functional coupling of the cell states. We then compare dosing strategies at early stage development, midstage (clinical stage), and late-stage development of the tumor. If used early during tumor development in the subclinical stage, well before the cancer cell population is selected for growth, therapy is most effective at disrupting key emergent features of tumor development. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
42. A multispecies birth–death–immigration process and its diffusion approximation.
- Author
-
Di Crescenzo, Antonio, Martinucci, Barbara, and Rhandi, Abdelaziz
- Subjects
- *
EMIGRATION & immigration , *DIFFUSION , *APPROXIMATION theory , *LATTICE theory , *INTEGERS , *PROBABILITY theory - Abstract
We consider an extended birth–death–immigration process defined on a lattice formed by the integers of d semiaxes joined at the origin. When the process reaches the origin, then it may jump toward any semiaxis with the same rate. The dynamics on each ray evolves according to a one-dimensional linear birth–death process with immigration. We investigate the transient and asymptotic behavior of the process via its probability generating function. The stationary distribution, when existing, is a zero-modified negative binomial distribution. We also study a diffusive approximation of the process, which involves a diffusion process with linear drift and infinitesimal variance on each ray. It possesses a gamma-type transient density admitting a stationary limit. As a byproduct of our study, we obtain a closed form of the number of permutations with a fixed number of components, and a new series form of the polylogarithm function expressed in terms of the Gauss hypergeometric function. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
43. Notes on the birth-death prior with fossil calibrations for Bayesian estimation of species divergence times.
- Author
-
dos Reis, Mario
- Subjects
- *
BIOLOGICAL divergence , *PHYLOGENY , *BAYESIAN analysis , *MOLECULAR clock , *BIOLOGY - Abstract
Constructing a multi-dimensional prior on the times of divergence (the node ages) of species in a phylogeny is not a trivial task, in particular, if the prior density is the result of combining different sources of information such as a speciation process with fossil calibration densities. Yang & Rannala (2006 Mol. Biol. Evol. 23, 212-226. (doi:10.1093/molbev/msj024)) laid out the general approach to combine the birth-death process with arbitrary fossil-based densities to construct a prior on divergence times. They achieved this by calculating the density of node ages without calibrations conditioned on the ages of the calibrated nodes. Here, I show that the conditional density obtained by Yang & Rannala is misspecified. The misspecified density can sometimes be quite strange-looking and can lead to unintentionally informative priors on node ages without fossil calibrations. I derive the correct density and provide a few illustrative examples. Calculation of the density involves a sum over a large set of labelled histories, and so obtaining the density in a computer program seems hard at the moment. A general algorithm that may provide a way forward is given. This article is part of the themed issue 'Dating species divergences using rocks and clocks'. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
44. Nonlinear diffusion for chemotaxis and birth-death process for Keller-Segel model.
- Author
-
Dokuyucu, Mustafa Ali and Celik, Ercan
- Subjects
- *
NONLINEAR analysis , *BIRTH & death processes (Stochastic processes) , *REACTION-diffusion equations - Abstract
This paper seeks to establish the stability of the birth-death process in relation to the Keller-Segel Model. As well, it attempts to describe the stability of non-linear diffusion for chemotaxis. Attention will be on mass criticality results applying to the chemotaxis model. Afterwards, the analysis of the relative stability that stationary states exhibit is undertaken using the Keller-Segel system for the chemotaxis having linear diffusion. Standard linearization and separation of variables are the techniques employed in the analysis. The stability or instability of the analysed cases is demonstrated by the graphics. By using the critical results obtained for the models, the graphics are then compared with the rest. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
45. A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations.
- Author
-
Chou, Tom and Greenman, Chris
- Subjects
- *
AGE-structured populations , *STATISTICAL methods in population biology , *PROBABILITY theory , *HIERARCHIES , *GENERALIZATION - Abstract
We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
46. Does Gene Tree Discordance Explain the Mismatch between Macroevolutionary Models and Empirical Patterns of Tree Shape and Branching Times?
- Author
-
STADLER, TANJA, DEGNAN, JAMES H., and ROSENBERG, NOAH A.
- Subjects
- *
TREE declines , *PHYLOGENETIC models , *TREE mortality , *BRANCHING (Botany) , *TREES , *PLANT health - Abstract
Classic null models for speciation and extinction give rise to phylogenies that differ in distribution from empirical phylogenies. In particular, empirical phylogenies are less balanced and have branching times closer to the root compared to phylogenies predicted by common null models. This difference might be due to null models of the speciation and extinction process being too simplistic, or due to the empirical datasets not being representative of random phylogenies. A third possibility arises because phylogenetic reconstruction methods often infer gene trees rather than species trees, producing an incongruity between models that predict species tree patterns and empirical analyses that consider gene trees. We investigate the extent to which the difference between gene trees and species trees under a combined birth-death and multispecies coalescent model can explain the difference in empirical trees and birth-death species trees. We simulate gene trees embedded in simulated species trees and investigate their difference with respect to tree balance and branching times. We observe that the gene trees are less balanced and typically have branching times closer to the root than the species trees. Empirical trees from Tree Base are also less balanced than our simulated species trees, and model gene trees can explain an imbalance increase of up to 8% compared to species trees. However, we see a much larger imbalance increase in empirical trees, about 100%, meaning that additional features must also be causing imbalance in empirical trees. This simulation study highlights the necessity of revisiting the assumptions made in phylogenetic analyses, as these assumptions, such as equating the gene tree with the species tree, might lead to a biased conclusion. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
47. On Ergodicity Bounds for an Inhomogeneous Birth-death Process.
- Author
-
Zeifman, Alexander I., Korolev, Victor Yu., Chertok, Andrey V., and Shorgin, Sergey Ya.
- Subjects
- *
ERGODIC theory , *BIRTH & death processes (Stochastic processes) , *MATHEMATICAL bounds , *STOCHASTIC convergence , *STATIONARY processes , *ORDER flow (Securities) - Abstract
We obtain the conditions of weak ergodicity and explicit bounds on the rate of convergence for a model of stock order flows with nonstationary intensities. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
48. Collective Activity of Many Bistable Assemblies Reproduces Characteristic Dynamics of Multistable Perception.
- Author
-
Cao, Robin, Pastukhov, Alexander, Mattia, Maurizio, and Braun, Jochen
- Subjects
- *
MULTISTABLE visual perception , *PSYCHOMETRICS , *STOCHASTIC analysis , *NEURAL circuitry , *NEOCORTEX - Abstract
The timing of perceptual decisions depends on both deterministic and stochastic factors, as the gradual accumulation of sensory evidence (deterministic) is contaminated by sensory and/or internal noise (stochastic). When human observers view multistable visual displays, successive episodes of stochastic accumulation culminate in repeated reversals of visual appearance. Treating reversal timing as a "first-passage time" problem, we ask how the observed timing densities constrain the underlying stochastic accumulation. Importantly, mean reversal times (i.e., deterministic factors) differ enormously between displays/observers/stimulation levels, whereas the variance and skewness of reversal times (i.e., stochastic factors) keep characteristic proportions of the mean. What sort of stochastic process could reproduce this highly consistent "scaling property?" Here we show that the collective activity of a finite population of bistable units (i.e., a generalized Ehrenfest process) quantitatively reproduces all aspects of the scaling property of multistable phenomena, in contrast to other processes under consideration (Poisson, Wiener, or Ornstein-Uhlenbeck process). The postulated units express the spontaneous dynamics of attractor assemblies transitioning between distinct activity states. Plausible candidates are cortical columns, or clusters of columns, as they are preferentially connected and spontaneously explore a restricted repertoire of activity states. Our findings suggests that perceptual representations are granular, probabilistic, and operate far from equilibrium, thereby offering a suitable substrate for statistical inference. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
49. Anomalous Growth of Aging Populations.
- Author
-
Grebenkov, Denis
- Subjects
- *
POPULATION aging , *POPULATION dynamics , *MARKOV processes , *AGING , *MONTE Carlo method - Abstract
We consider a discrete-time population dynamics with age-dependent structure. At every time step, one of the alive individuals from the population is chosen randomly and removed with probability $$q_k$$ depending on its age, whereas a new individual of age 1 is born with probability r. The model can also describe a single queue in which the service order is random while the service efficiency depends on a customer's 'age' in the queue. We propose a mean field approximation to investigate the long-time asymptotic behavior of the mean population size. The age dependence is shown to lead to anomalous power-law growth of the population at the critical regime. The scaling exponent is determined by the asymptotic behavior of the probabilities $$q_k$$ at large k. The mean field approximation is validated by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
50. Models for gene duplication when dosage balance works as a transition state to subsequent neo-or sub-functionalization.
- Author
-
Teufel, Ashley I., Liang Liu, and Liberles, David A.
- Subjects
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DOSAGE forms of drugs , *CHROMOSOME duplication , *COMPUTATIONAL complexity , *DNA , *MOLECULAR genetics - Abstract
Background: Dosage balance has been described as an important process for the retention of duplicate genes after whole genome duplication events. However, dosage balance is only a temporary mechanism for duplicate gene retention, as it ceases to function following the stochastic loss of interacting partners, as dosage balance itself is lost with this event. With the prolonged period of retention, on the other hand, there is the potential for the accumulation of substitutions which upon release from dosage balance constraints, can lead to either subsequent neo-functionalization or sub-functionalization. Mechanistic models developed to date for duplicate gene retention treat these processes independently, but do not describe dosage balance as a transition state to eventual functional change. Results: Here a model for these processes (dosage plus neofunctionalization and dosage plus subfunctionalization) has been built within an existing framework. Because of the computational complexity of these models, a simpler modeling framework that captures the same information is also proposed. This model is integrated into a phylogenetic birth-death model, expanding the range of available models. Conclusions: Including further levels of biological reality in methods for gene tree/species tree reconciliation should not only increase the accuracy of estimates of the timing and evolutionary history of genes but can also offer insight into how genes and genomes evolve. These new models add to the tool box for characterizing mechanisms of duplicate gene retention probabilistically. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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