Evolution by the birth-and-death process in multigene families of the vertebrate immune system

Concerted evolution is often invoked to explain the diversity and evolution of the multigene families of major histocompatibility complex (MHC) genes and immunoglobulin (Ig) genes. However, this hypothesis has been controversial because the member genes of these families from the same species are not necessarily more closely related to one another than to the genes from different species. To resolve this controversy, we conducted phylogenetic analyses of several multigene families of the MHC and Ig systems. The results show that the evolutionary pattern of these families is quite different from that of concerted evolution but is in agreement with the birth-and-death model of evolution in which new genes are created by repeated gene duplication and some duplicate genes are maintained in the genome for a long time but others are deleted or become nonfunctional by deleterious mutations. We found little evidence that interlocus gene conversion plays an important role in the evolution of MHC and Ig multigene families.

Generating Birth and Death Processes

Associated with an ordered sequence of an even number 2N of positive real numbers is a birth and death process (BDP) on {0, 1, 2,..., N} having these real numbers as its birth and death rates. We generate another birth and death process from this BDP on {0, 1, 2,..., 2N}. This can be further iterated. We illustrate with an example from tan(kz). In BDP, the decay parameter, viz., the largest non-zero eigenvalue is important in the study of convergence to stationarity. In this article, the smallest eigenvalue is found to be useful.

The 5S rDNA family evolves through concerted and birth-and-death evolution in fish genomes: an example from freshwater stingrays

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some Bounds for Almost Absorbing Birth and Death Processes with Catastrophes

2000 Mathematics Subject Classification: 60J27.

The pgip family in soybean and three other legume species: evidence for a birth-and-death model of evolution

Background Polygalacturonase-inhibiting proteins (PGIPs) are leucine-rich repeat (LRR) plant cell wall glycoproteins involved in plant immunity. They are typically encoded by gene families with a small number of gene copies whose evolutionary origin has been poorly investigated. Here we report the complete characterization of the full complement of the pgip family in soybean (Glycine max [L.] Merr.) and the characterization of the genomic region surrounding the pgip family in four legume species. Results BAC clone and genome sequence analyses showed that the soybean genome contains two pgip loci. Each locus is composed of three clustered genes that are induced following infection with the fungal pathogen Sclerotinia sclerotiorum (Lib.) de Bary, and remnant sequences of pgip genes. The analyzed homeologous soybean genomic regions (about 126 Kb) that include the pgip loci are strongly conserved and this conservation extends also to the genomes of the legume species Phaseolus vulgaris L., Medicago truncatula Gaertn. and Cicer arietinum L., each containing a single pgip locus. Maximum likelihood-based gene trees suggest that the genes within the pgip clusters have independently undergone tandem duplication in each species. Conclusions The paleopolyploid soybean genome contains two pgip loci comprised in large and highly conserved duplicated regions, which are also conserved in bean, M. truncatula and C. arietinum. The genomic features of these legume pgip families suggest that the forces driving the evolution of pgip genes follow the birth-and-death model, similar to that proposed for the evolution of resistance (R) genes of NBS-LRR-type.

Purifying selection and birth-and-death evolution in the ubiquitin gene family

Ubiquitin is a highly conserved protein that is encoded by a multigene family. It is generally believed that this gene family is subject to concerted evolution, which homogenizes the member genes of the family. However, protein homogeneity can be attained also by strong purifying selection. We therefore studied the proportion (pS) of synonymous nucleotide differences between members of the ubiquitin gene family from 28 species of fungi, plants, and animals. The results have shown that pS is generally very high and is often close to the saturation level, although the protein sequence is virtually identical for all ubiquitins from fungi, plants, and animals. A small proportion of species showed a low level of pS values, but these values appeared to be caused by recent gene duplication. It was also found that the number of repeat copies of the gene family varies considerably with species, and some species harbor pseudogenes. These observations suggest that the members of this gene family evolve almost independently by silent nucleotide substitution and are subjected to birth-and-death evolution at the DNA level.

First things and last : the story of birth and death certificates.

Cover title.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.

Independent origin of the growth hormone gene family in New World monkeys and Old World monkeys/hominoids

The growth hormone (GH) gene family represents an erratic and complex evolutionary pattern, involving many evolutionary events, such as multiple gene duplications, positive selection, the birth-and-death process and gene conversions. In the present study, we cloned and sequenced GH-like genes from three species of New World monkeys (NWM). Phylogenetic analysis strongly suggest monophyly for NWM GH-like genes with respect to those of Old World monkeys (OWM) and hominoids, indicating that independent gene duplications have occurred in NWM GH-like genes. There are three main clusters of genes in putatively functional NWM GH-like genes, according to our gene tree. Comparison of the ratios of nonsynonymous and synonymous substitutions revealed that these three clusters of genes evolved under different kinds of selective pressures. Detailed analysis of the evolution of pseudogenes showed that the evolutionary pattern of this gene family in platyrrhines is in agreement with the so-called birth-and-death process.

Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.

Study of Queuing Systems with a Generalized Departure Process

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.

On Queueinginventory Models – product form solution; reservation, Cancellation and common life time

Queueing theory is the mathematical study of ‘queue’ or ‘waiting lines’ where an item from inventory is provided to the customer on completion of service. A typical queueing system consists of a queue and a server. Customers arrive in the system from outside and join the queue in a certain way. The server picks up customers and serves them according to certain service discipline. Customers leave the system immediately after their service is completed. For queueing systems, queue length, waiting time and busy period are of primary interest to applications. The theory permits the derivation and calculation of several performance measures including the average waiting time in the queue or the system, mean queue length, traffic intensity, the expected number waiting or receiving service, mean busy period, distribution of queue length, and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.