scholarly journals An extension of the Moran process using type-specific connection graphs

2022 ◽  
Vol 124 ◽  
pp. 77-96
Author(s):  
Themistoklis Melissourgos ◽  
Sotiris E. Nikoletseas ◽  
Christoforos L. Raptopoulos ◽  
Paul G. Spirakis
Keyword(s):  
Moran Process

scholarly journals Entropic Equilibria Selection of Stationary Extrema in Finite Populations

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 631
Author(s):  
Marc Harper ◽  
Dashiell Fryer
Keyword(s):  
Markov Process ◽  
Population Size ◽  
Mutation Rate ◽  
Stationary Distribution ◽  
Markov Processes ◽  
Local Maxima ◽  
Moran Process ◽  
The Stability ◽  
Definition Of ◽  
Selection Of

We propose the entropy of random Markov trajectories originating and terminating at the same state as a measure of the stability of a state of a Markov process. These entropies can be computed in terms of the entropy rates and stationary distributions of Markov processes. We apply this definition of stability to local maxima and minima of the stationary distribution of the Moran process with mutation and show that variations in population size, mutation rate, and strength of selection all affect the stability of the stationary extrema.

scholarly journals Evolution of kinship structures driven by marriage tie and competition

2020 ◽  
Vol 117 (5) ◽  
pp. 2378-2384 ◽  
Author(s):  
Kenji Itao ◽  
Kunihiko Kaneko
Keyword(s):  
Social Relationships ◽  
Mate Preference ◽  
Social Cooperation ◽  
Family Unit ◽  
Incest Taboo ◽  
Moran Process ◽  
Indirect Exchange ◽  
The Family ◽  
Group A ◽  
Generalized Exchange

The family unit and kinship structures form the basis of social relationships in indigenous societies. Families constitute a cultural group, a so-called clan, within which marriage is prohibited by the incest taboo. The clan attribution governs the mating preference and descent relationships by certain rules. Such rules form various kinship structures, including generalized exchange, an indirect exchange of brides among more than two clans, and restricted exchange, a direct exchange of brides with the flow of children to different clans. These structures are distributed in different areas and show different cultural consequences. However, it is still unknown how they emerge or what conditions determine different structures. Here, we build a model of communities consisting of lineages and family groups and introduce social cooperation among kin and mates and conflict over mating. Each lineage has parameters characterizing the trait and mate preference, which determines the possibility of marriage and the degree of cooperation and conflict among lineages. Lineages can cooperate with those having similar traits to their own or mates’, whereas lineages with similar preferences compete for brides. In addition, we introduce community-level selection by eliminating communities with smaller fitness and follow the so-called hierarchical Moran process. We numerically demonstrate that lineages are clustered in the space of traits and preferences, resulting in the emergence of clans with the incest taboo. Generalized exchange emerges when cooperation is strongly needed, whereas restricted exchange emerges when the mating conflict is strict. This may explain the geographical distribution of kinship structures in indigenous societies.

One-Mutation Model Can Explain Age Incidence in AML Carrying Nucleophosmin (NPM1) Mutations.

Blood ◽  
2007 ◽  
Vol 110 (11) ◽  
pp. 4312-4312
Author(s):  
Arcangelo Liso ◽  
Filippo Castiglione ◽  
Antonio Cappuccio ◽  
Fabrizio Stracci ◽  
Christian Thiede ◽  
...  
Keyword(s):  
Leukemic Cells ◽  
Specific Rate ◽  
Wild Type ◽  
Genetic Event ◽  
Knock Out ◽  
Incidence Data ◽  
Molecular Alterations ◽  
Moran Process ◽  
Mutation Model ◽  
Knock Out Mice

Abstract Acute myeloid leukemia (AML) carrying nucleophosmin (NPM1) mutations and cytoplasmic NPM (NPMc+ AML) accounts for about one-third of all AML patients, and exhibits distinctive biological and clinical features. The role of NPM1 mutations in leukemogenesis remains elusive. Mathematical models have been developed that, starting from cancer incidence data, allow to infer the somatic mutation rate, or the number of genetic events required to cause cancer. We collected data on age at diagnosis of AML patients from four centers in three different countries, and calculated age-specific rates of NPMc+ AML. A total of 4,155 AML patients were investigated. NPM1 mutations these were detected in 1288. Patients carrying NPM1 mutations with age below 20 years and above 59 years were excluded from the study because of the low number of younger cases and because older patients are not always referred to major institutions for diagnosis and treatment. To investigate NPMc+ AML we adapted one-mutation model published by Michor et al (PNAS, 2006; 103: 14931). The mathematical model consider a population of N (hemopoietic stem) cells that at beginning are wild-type. These cells proliferate according to the Moran process. The growth follows a logistic law with a saturation term. Our process follows the “classical” Moran process up to the appearance of a successful mutant. After that, the clone expands to a limiting population size. This is done to account for the dramatic expansion of the initial compartment peculiar of AML. Finally the rate of AML detection is proportional to the number of mutated cells. Experimental incidence curves of AML in Germany (Ge), Netherlands (Nl), and Italy (It) plotted simultaneously with predicted one-mutation model estimates are shown in Fig. 1. Linear regression of curves representing age-specific rate of diagnoses per year showed similar slopes (about 4 on a double-log scale) in different countries. The one-event model reproduces well the “exponential phenotype” of NPMc+ AML. In conclusion the model is in accordance with the hypothesis that NPM1 mutations by themselves are sufficient to cause NPMc+ AML. Alternatively, it is still possible that NPM1 mutations might cooperate with other molecular alterations to cause AML. In particular, since NPM1 mutations cause haploinsufficiency of wild-type NPM in leukemic cells and in knock-out mice NPM haploinsufficiency results in a MDS-like syndrome and given that the NPM1 mutant has oncogenic properties, these alterations could act in concert to cause AML. Indeed, the effect of these two alterations occurring simultaneously could be seen as a single genetic event. Figure Figure

scholarly journals Fitness dependence of the fixation-time distribution for evolutionary dynamics on graphs

2018 ◽  
Author(s):  
David Hathcock ◽  
Steven H. Strogatz
Keyword(s):  
Complete Graph ◽  
Time Distribution ◽  
Evolutionary Dynamics ◽  
Structured Populations ◽  
Relative Fitness ◽  
Death Process ◽  
Fixation Time ◽  
Large Network ◽  
Moran Process ◽  
Fitness Dependence

Evolutionary graph theory models the effects of natural selection and random drift on structured populations of mutant and non-mutant individuals. Recent studies have shown that fixation times, which determine the rate of evolution, often have right-skewed distributions. Little is known, however, about how these distributions and their skew depend on mutant fitness. Here we calculate the fitness dependence of the fixation-time distribution for the Moran Birth-death process in populations modeled by two extreme networks: the complete graph and the one-dimensional ring lattice, each of which admits an exact solution in the limit of large network size. We find that with non-neutral fitness, the Moran process on the ring has normally distributed fixation times, independent of the relative fitness of mutants and non-mutants. In contrast, on the complete graph, the fixation-time distribution is a weighted convolution of two Gumbel distributions, with a weight depending on the relative fitness. When fitness is neutral, however, the Moran process has a highly skewed fixation-time distribution on both the complete graph and the ring. In this sense, the case of neutral fitness is singular. Even on these simple network structures, the fixation-time distribution exhibits rich fitness dependence, with discontinuities and regions of universality. Applications of our methods to a multi-fitness Moran model, times to partial fixation, and evolution on random networks are discussed.

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