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We consider a neutral dynamical model of biological diversity, where individuals live and reproduce independently. They have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at constant…
We propose a simple model to describe the dynamics of religious affiliation. For such purpose, we built a compartmental model with three distinct subpopulations, namely religious committed individuals, religious noncommitted individuals and…
Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most…
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual…
This paper develops a point-mutation model describing the evolutionary dynamics of a population of adult stem cells. Such a model may prove useful for quantitative studies of tissue aging and the emergence of cancer. We consider two modes…
When an infectious disease outbreak is of a relatively small size, describing the ancestry of a sample of infected individuals is difficult because most ancestral models assume large population sizes. Given a set of infected individuals, we…
We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing…
Nearest-neighbor(NN) free energy parameters for DNA are well studied and reliable values of these parameters exist in the literature. They have been found to be very useful in studying DNA melting and DNA stabilization studies. In this…
Gene expression is a complex and quantitative trait that is influenced by both genetic and non-genetic regulators including environmental factors. Evaluating the contribution of environment to gene expression regulation and identifying…
A theoretical study is presented to quantitatively analyze the transport experiment through individual DNA molecules reported recently by Porath {\it et al.} [Nature {\bf 403}, 635 (2000)]. A variety of valuable quantities are identified by…
In both criminal cases and civil cases there is an increasing demand for the analysis of DNA mixtures involving relationships. The goal might be, for example, to identify the contributors to a DNA mixture where the donors may be related, or…
How much information does a cell inherit from its ancestors beyond its genetic sequence? What are the epigenetic mechanisms that allow this? Despite the rise in available epigenetic data, how such information is inherited through the cell…
An adult human body is made up of some 30 to 40 trillion cells, all of which stem from a single fertilized egg cell. The process by which the right cells appear to arrive in their right numbers at the right time at the right place --…
Social interaction between microbes can be described at many levels of details, ranging from the biochemistry of cell-cell interactions to the ecological dynamics of populations. Choosing the best level to model microbial communities…
Long-range migrations and the resulting admixtures between populations have been important forces shaping human genetic diversity. Most existing methods for detecting and reconstructing historical admixture events are based on allele…
We study numerically a disordered version of the model for DNA denaturation transition (DSAW-DNA) consisting of two interacting SAWs in 3d, which undergoes a first order transition in the homogeneous case. The two possible values eAT and…
The effects of inbreeding on human health depend critically on the number and severity of recessive, deleterious mutations carried by individuals. In humans, existing estimates of these quantities are based on comparisons between…
Muller's ratchet is a paradigmatic model for the accumulation of deleterious mutations in a population of finite size. A click of the ratchet occurs when all individuals with the least number of deleterious mutations are lost irreversibly…
Maintenance of sexual reproduction and genetic recombination imposes physiological costs when compared to parthenogenic reproduction, most prominently: for maintaining the corresponding (molecular) machinery, for finding a mating partner,…
Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time $t$ have a most recent common ancestor (MRCA) who lived at time $A_t$, say. As time goes on, not only…