Comment on "Under-reported data analysis with INAR-hidden Markov chains"

In Fernandez-Fontelo et al (Statis. Med. 2016, DOI 10.1002/sim.7026) hidden integer-valued autoregressive (INAR) processes are used to estimate reporting probabilities for various diseases. In this comment it is demonstrated that the Poisson INAR(1) model with time-homogeneous underreporting can be expressed equivalently as a completely observed INAR(inf) model with a geometric lag structure. This implies that estimated reporting probabilities depend on the assumed lag structure of the latent process.Comment: This is the pre-reviewing version of a letter published in Statistics in Medicine 38(5), 893-898: https://onlinelibrary.wiley.com/doi/full/10.1002/sim.8032 Fernandez-Fontelo et al published a reply which raises some interesting further points: https://onlinelibrary.wiley.com/doi/10.1002/sim.8033 After a 12 month embargo period the accepted version will be made available on arxi

Convergence towards an asymptotic shape in first-passage percolation on cone-like subgraphs of the integer lattice

In first-passage percolation on the integer lattice, the Shape Theorem provides precise conditions for convergence of the set of sites reachable within a given time from the origin, once rescaled, to a compact and convex limiting shape. Here, we address convergence towards an asymptotic shape for cone-like subgraphs of the $\Z^d$ lattice, where $d\ge2$. In particular, we identify the asymptotic shapes associated to these graphs as restrictions of the asymptotic shape of the lattice. Apart from providing necessary and sufficient conditions for $L^p$- and almost sure convergence towards this shape, we investigate also stronger notions such as complete convergence and stability with respect to a dynamically evolving environment.Comment: 23 pages. Together with arXiv:1305.6260, this version replaces the old. The main results have been strengthened and an earlier error in the statement corrected. To appear in J. Theoret. Proba

A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments

Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating predation risk, and cooperative breeding and foraging. Individuals within these populations may differ in age, size, or geographic location and thereby structure these populations. Here, I study structured population models accounting for positive density-dependence and environmental stochasticity i.e. random fluctuations in the demographic rates of the population. Under an accessibility assumption (roughly, stochastic fluctuations can lead to populations getting small and large), these models are shown to exhibit a dynamical trichotomy: (i) for all initial conditions, the population goes asymptotically extinct with probability one, (ii) for all positive initial conditions, the population persists and asymptotically exhibits unbounded growth, and (iii) for all positive initial conditions, there is a positive probability of asymptotic extinction and a complementary positive probability of unbounded growth. The main results are illustrated with applications to spatially structured populations with an Allee effect and age-structured populations experiencing mate limitation

Dual random fragmentation and coagulation and an application to the genealogy of Yule processes

The purpose of this work is to describe a duality between a fragmentation associated to certain Dirichlet distributions and a natural random coagulation. The dual fragmentation and coalescent chains arising in this setting appear in the description of the genealogy of Yule processes.Comment: 14 page

Probability that a chromosome is lost without trace under the neutral Wright-Fisher model with recombination

I describe an analytical approximation for calculating the short-term probability of loss of a chromosome under the neutral Wright-Fisher model with recombination. I also present an upper and lower bound for this probability. Exact analytical calculation of this quantity is difficult and computationally expensive because the number of different ways in which a chromosome can be lost, grows very large in the presence of recombination. Simulations indicate that the probabilities obtained using my approximate formula are always comparable to the true expectations provided that the number of generations remains small. These results are useful in the context of an algorithm that we recently developed for simulating Wright-Fisher populations forward in time. C++ programs that can efficiently calculate these formulas are available on request.Comment: Additional Information, Padhukasahasram et al. 2008, Genetics, FORWSIM algorith

Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

Polymorphism Data Can Reveal the Origin of Species Abundance Statistics

What is the underlying mechanism behind the fat-tailed statistics observed for species abundance distributions? The two main hypotheses in the field are the adaptive (niche) theories, where species abundance reflects its fitness, and the neutral theory that assumes demographic stochasticity as the main factor determining community structure. Both explanations suggest quite similar species-abundance distributions, but very different histories: niche scenarios assume that a species population in the past was similar to the observed one, while neutral scenarios are characterized by strongly fluctuating populations. Since the genetic variations within a population depend on its abundance in the past, we present here a way to discriminate between the theories using the genetic diversity of noncoding DNA. A statistical test, based on the Fu-Li method, has been developed and enables such a differentiation. We have analyzed the results gathered from individual-based simulation of both types of histories and obtained clear distinction between the Fu-Li statistics of the neutral scenario and that of the niche scenario. Our results suggest that data for 10–50 species, with approximately 30 sequenced individuals for each species, may allow one to distinguish between these two theories

Analytical Framework for Identifying and Differentiating Recent Hitchhiking and Severe Bottleneck Effects from Multi-Locus DNA Sequence Data

Hitchhiking and severe bottleneck effects have impact on the dynamics of genetic diversity of a population by inducing homogenization at a single locus and at the genome-wide scale, respectively. As a result, identification and differentiation of the signatures of such events from DNA sequence data at a single locus is challenging. This paper develops an analytical framework for identifying and differentiating recent homogenization events at multiple neutral loci in low recombination regions. The dynamics of genetic diversity at a locus after a recent homogenization event is modeled according to the infinite-sites mutation model and the Wright-Fisher model of reproduction with constant population size. In this setting, I derive analytical expressions for the distribution, mean, and variance of the number of polymorphic sites in a random sample of DNA sequences from a locus affected by a recent homogenization event. Based on this framework, three likelihood-ratio based tests are presented for identifying and differentiating recent homogenization events at multiple loci. Lastly, I apply the framework to two data sets. First, I consider human DNA sequences from four non-coding loci on different chromosomes for inferring evolutionary history of modern human populations. The results suggest, in particular, that recent homogenization events at the loci are identifiable when the effective human population size is 50000 or greater in contrast to 10000, and the estimates of the recent homogenization events are agree with the “Out of Africa” hypothesis. Second, I use HIV DNA sequences from HIV-1-infected patients to infer the times of HIV seroconversions. The estimates are contrasted with other estimates derived as the mid-time point between the last HIV-negative and first HIV-positive screening tests. The results show that significant discrepancies can exist between the estimates

A System Dynamics Approach for Modeling Return on Quality for ECS Industry

The Electronic Components and Systems industry (ECS) is characterized by long lead times and high market volatility. Besides fast technological development within this industry, cyclic market up- and downturns are influencing the semiconductor market. Therefore, adequate capacity and inventory management as well as continuous process improvements are important success factors for semiconductor companies to be competitive. In this study, the authors focus on a manufacturing excellence approach to increase front-end supply reliability and the availability of inventory within the customer order decoupling point. Here, development and manufacturing processes must be designed in a way that highest levels of product quality, flexibility, time and costs are reached. The purpose of this study is to explore the impact of return on quality in manufacturing systems. Therefore, multimethod simulation modelling including discrete-event and system dynamics simulation is applied

Clades and clans: a comparison study of two evolutionary models

The Yule-Harding-Kingman (YHK) model and the proportional to distinguishable arrangements (PDA) model are two binary tree generating models that are widely used in evolutionary biology. Understanding the distributions of clade sizes under these two models provides valuable insights into macro-evolutionary processes, and is important in hypothesis testing and Bayesian analyses in phylogenetics. Here we show that these distributions are log-convex, which implies that very large clades or very small clades are more likely to occur under these two models. Moreover, we prove that there exists a critical value $\kappa(n)$ for each $n\geqslant 4$ such that for a given clade with size $k$, the probability that this clade is contained in a random tree with $n$ leaves generated under the YHK model is higher than that under the PDA model if $1<k<\kappa(n)$, and lower if $\kappa(n)<k<n$. Finally, we extend our results to binary unrooted trees, and obtain similar results for the distributions of clan sizes.Comment: 21page