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Inference of the marginal likelihood of sample allele configurations using backward algorithms yields identical results with the Kingman coalescent, the Moran model, and the diffusion model (up to a scaling of time). For inference of…
Variability of a galaxy's core radio source can be a significant consequence of AGN accretion. However, this variability has not been well studied, particularly at high radio frequencies. As such, we report on a campaign monitoring the high…
It has been a puzzling question why some organisms reproduce sexually. Fisher and Muller hypothesized that reproducing by sex can speed up the evolution. They explained that in the sexual reproduction, recombination can combine beneficial…
The common understanding of protein evolution has been that neutral or slightly deleterious mutations are fixed by random drift, and evolutionary rate is determined primarily by the proportion of neutral mutations. However, recent studies…
Despite initial success, cancer therapies often fail due to the emergence of drug-resistant cells. In this study, we use a mathematical model to investigate how cancer evolves over time, specifically focusing on the state of the tumor when…
The growing probabilities of additional offspring with the beneficial reversal allele for various population sizes, $N$, sequence lengths, $L$, selective advantages, $s$, fitness parameters, $k$, and measuring parameters, $C$, were…
A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of…
Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy…
The neutral mutation rate is known to vary widely along human chromosomes, leading to mutational hot and cold regions. We provide evidence that categories of functionally-related genes reside preferentially in mutationally hot or cold…
Consider an advantageous allele that arises in a haploid population of size $N$ evolving in continuous time according to a skewed reproduction mechanism, which generates under neutrality genealogies lying in the domain of attraction of a…
Cancer cells evolve through random somatic mutations. "Beneficial" mutations which disrupt key pathways (e.g. cell cycle regulation) are subject to natural selection. Multiple mutations may lead to the same "beneficial" effect, in which…
The purpose of this article is to study some asymptotic properties of the \Lambda-Wright-Fisher process with selection. This process represents the frequency of a disadvantaged allele. The resampling mechanism is governed by a finite…
The mother-dependent neutral mutations model describes the evolution of a population across discrete generations, where neutral mutations occur among a finite set of possible alleles. In this model, each mutant child acquires a type…
Sex difference in allele frequency is an emerging topic that is critical to our understanding of ascertainment bias, as well as data quality particularly of the largely overlooked X chromosome. To detect sex difference in allele frequency…
Genomic evolution can be viewed as string-editing processes driven by mutations. An understanding of the statistical properties resulting from these mutation processes is of value in a variety of tasks related to biological sequence data,…
In this paper we study the evolution of the mutation rate for simple organisms in dynamic environments. A model with multiple fitness coding loci tracking a moving fitness peak is developed and an analytical expression for the optimal…
We study the evolution of mutation rates for an asexual population living on a static fitness landscape, consisting of multiple peaks forming an evolutionary staircase. The optimal mutation rate is found by maximizing the diffusion towards…
Recent experimental evidence suggests that acute myeloid leukemias may originate from multiple clones of malignant cells. Nevertheless it is not known how the observed clones may differ with respect to cell properties such as proliferation…
Integrating experimental data into ecological models plays a central role in understanding biological mechanisms that drive tumor progression where such knowledge can be used to develop new therapeutic strategies. While the current studies…
We deal with the study of the evolution of the allelic frequencies, at a single locus, for a population distributed continuously over a bounded habitat. We consider evolution which occurs under the joint action of selection and arbitrary…