Abstract:
A panel of polymorphisms associated with at least one disease state in multiple populations was constructed using a cut-off of 0.20 or greater confirmed minor allele frequency in a European Caucasian population. The fingerprinting assay was tested using the MALDI-TOF mass spectrometry method of allele determination on a Sequenom platform with a panel of 28 Caucasian HapMap samples; the results were compared with known genotypes to ensure accuracy. The frequencies of the alleles were compared to the expected frequencies from dbSNP and any genotype that did not achieve Hardy Weinberg equilibrium was excluded from the final assay.The final assay consisted of the AMG sex marker and 36 medically relevant polymorphisms with representation on each chromosome, encompassing polymorphisms on both the Illumina 550K bead array and the Affymetrix 6.0 chip (with over a million polymorphisms) platform. The validated assay has a P(ID) of 6.132 × 10-15 and a Psib(ID) of 3.077 × 10-8. This assay allows unique identification of our biorepository of 20,000 individuals as well and ensures that as we continue to recruit individuals they can be uniquely fingerprinted. In addition, diseases such as cancer, heart disease diabetes, obesity, and respiratory disease are well represented in the fingerprinting assay.The polymorphisms in this panel are currently represented on a number of common genotyping platforms making QA/QC flexible enough to accommodate a large number of studies. In addition, this panel can serve as a resource for investigators who are interested in the effects of disease in a population, particularly for common diseases.With the advent of genome wide association studies large bio-banks will become the stepping stones to tomorrow's medicine. The genome wide association study (GWAS) has recently proved its value with replicable findings for diseases such as coronary artery disease, prostate cancer, and diabetes [1], and many more discoveries are expected in the near future.

Abstract:
Spectral measures and transition probabilities of birth and death processes with 0= 0=0 are obtained as limite when 0 ￠ ’0+ of the corresponding quantities. In particular the case of finite population is discussed in full detail. Pure birth and death processes are used to derive an inequality for Dirichlet polynomials.

Abstract:
Many important stochastic counting models can be written as general birth-death processes (BDPs). BDPs are continuous-time Markov chains on the non-negative integers and can be used to easily parameterize a rich variety of probability distributions. Although the theoretical properties of general BDPs are well understood, traditionally statistical work on BDPs has been limited to the simple linear (Kendall) process, which arises in ecology and evolutionary applications. Aside from a few simple cases, it remains impossible to find analytic expressions for the likelihood of a discretely-observed BDP, and computational difficulties have hindered development of tools for statistical inference. But the gap between BDP theory and practical methods for estimation has narrowed in recent years. There are now robust methods for evaluating likelihoods for realizations of BDPs: finite-time transition, first passage, equilibrium probabilities, and distributions of summary statistics that arise commonly in applications. Recent work has also exploited the connection between continuously- and discretely-observed BDPs to derive EM algorithms for maximum likelihood estimation. Likelihood-based inference for previously intractable BDPs is much easier than previously thought and regression approaches analogous to Poisson regression are straightforward to derive. In this review, we outline the basic mathematical theory for BDPs and demonstrate new tools for statistical inference using data from BDPs. We give six examples of BDPs and derive EM algorithms to fit their parameters by maximum likelihood. We show how to compute the distribution of integral summary statistics and give an example application to the total cost of an epidemic. Finally, we suggest future directions for innovation in this important class of stochastic processes.

Abstract:
the genetic characterization of 117 peach and nectarine cultivars (prunus persica (l.) batsch) using microsatellite (ssr) markers is presented. analyzed genotypes include the complete list of cultivars under intellectual property (ip) protection in chile. one hundred and two out of the 117 cultivars under study could be identified using only 7 ssrs. other 5 cultivars were differentiated using 3 additional markers, but 5 pairs of genotypes were not differentiable. the average expected heterozygosity for the set of markers was 0.55, ranging from 0.28 in bppct-008 to 0.81 in cppct-022, with an f value of 0.37. a neighbor-joining dendrogram showed that, with few exceptions, peaches and nectarines clustered separately. these results are the basis for the development of a fingerprinting protocol for the unequivocal identification of most of the peach and nectarine cultivars officially registered in chile.

Abstract:
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable `matrix' quantum mechanics, which is recently proposed by Odake and the author. The ($q$-)Askey-scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of $q^x$ ($x$ being the population) corresponding to the $q$-Racah polynomial.

Abstract:
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth dynamics is mediated by the local, within a given distance, density of particles. Groups of individuals are formed in the system and in this paper we concentrate on the study of the properties of these clusters (lifetime, size, and collective diffusion). In particular, in the limit of the interaction distance approaching the system size, a unique cluster appears which helps to understand and characterize the clustering dynamics of the model.

Abstract:
Network models extend evolutionary game theory to settings with spatial or social structure and have provided key insights on the mechanisms underlying the evolution of cooperation. However, network models have also proven sensitive to seemingly small details of the model architecture. Here we investigate two popular biologically motivated models of evolution in finite populations: Death-Birth (DB) and Birth-Death (BD) processes. In both cases reproduction is proportional to fitness and death is random; the only difference is the order of the two events at each time step. Although superficially similar, under DB cooperation may be favoured in structured populations, while under BD it never is. This is especially troubling as natural populations do not follow a strict one birth then one death regimen (or vice versa); such constraints are introduced to make models more tractable. Whether structure can promote the evolution of cooperation should not hinge on a simplifying assumption. Here, we propose a mixed rule where in each time step DB is used with probability and BD is used with probability . We derive the conditions for selection favouring cooperation under the mixed rule for all social dilemmas. We find that the only qualitatively different outcome occurs when using just BD (). This case admits a natural interpretation in terms of kin competition counterbalancing the effect of kin selection. Finally we show that, for any mixed BD-DB update and under weak selection, cooperation is never inhibited by population structure for any social dilemma, including the Snowdrift Game.

Abstract:
We review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at the birth of particles or at a constant rate during their lives. In both models, we study the allelic partition of the population at time . We give closed-form formulae for the expected frequency spectrum at and prove a pathwise convergence to an explicit limit, as , of the relative numbers of types younger than some given age and carried by a given number of particles (small families). We also provide the convergences in distribution of the sizes or ages of the largest families and of the oldest families. In the case of exponential lifetimes, population dynamics are given by linear birth and death processes, and we can most of the time provide general formulations of our results unifying both models. 1. Introduction We consider a general branching model, where particles have i.i.d. (not necessarily exponential) life lengths and give birth at a constant rate during their lives to independent copies of themselves. The genealogical tree thus produced is called splitting tree [1–3]. The process that counts the number of the alive particles through time is a Crump-Mode-Jagers process (or general branching process) [4] which is binary (births occur singly) and homogeneous (constant birth rate). We enrich this genealogical model with mutations. In Model I, each child is a clone of her mother with probability and a mutant with probability . In Model II, independently of other particles, each particle undergoes mutations during her life at constant rate (and births are always clonal). For both models, we are working under the infinitely many alleles model; that is, a mutation yields a type, also called allele, which was never encountered before. Moreover, mutations are supposed to be neutral; that is, they do not modify the way particles die and reproduce. For any type and any time , we call family the set of all particles that share this type at time . Branching processes (and especially birth and death processes) with mutations have many applications in biology. In carcinogenesis [5–10], they can model the evolution of cancerous cells. In [11], Kendall modeled carcinogenesis by a birth and death process where mutations occur during life according to an inhomogeneous Poisson process. In [8, 10], cancerous cells are modeled by a multitype branching process where a cell is of type if it has undergone mutations and where the more a cell has undergone mutations, the faster it

Abstract:
The cosmic stellar birth rate can be measured by standard astronomical techniques. It can also be probed via the cosmic stellar death rate, though until recently, this was much less precise. However, recent results based on measured supernova rates, and importantly, also on the attendant diffuse fluxes of neutrinos and gamma rays, have become competitive, and a concordant history of stellar birth and death is emerging. The neutrino flux from all past core-collapse supernovae, while faint, is realistically within reach of detection in Super-Kamiokande, and a useful limit has already been set. I will discuss predictions for this flux, the prospects for neutrino detection, the implications for understanding core-collapse supernovae, and a new limit on the contribution of type-Ia supernovae to the diffuse gamma-ray background.

Abstract:
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant rate during their lives. In both models, we study the allelic partition of the population at time t. We give closed formulae for the expected frequency spectrum at t and prove pathwise convergence to an explicit limit, as t goes to infinity, of the relative numbers of types younger than some given age and carried by a given number of individuals (small families). We also provide convergences in distribution of the sizes or ages of the largest families and of the oldest families. In the case of exponential lifetimes, population dynamics are given by linear birth and death processes, and we can most of the time provide general formulations of our results unifying both models.