scholarly journals Computer simulation for the growing probability of additional offspring with an advantageous reversal allele in the decoupled continuous-time mutation–selection model

2016 ◽  
Vol 27 (06) ◽  
pp. 1650070
Author(s):  
Wonpyong Gill
Keyword(s):  
Computer Simulation ◽  
Continuous Time ◽  
Selective Advantage ◽  
Selection Model ◽  
Sequence Length ◽  
Theoretical Formula ◽  
Fitness Parameters ◽  
Population Sizes ◽  
Fitness Parameter ◽  
Allele Model

This study calculated the growing probability of additional offspring with the advantageous reversal allele in an asymmetric sharply-peaked landscape using the decoupled continuous-time mutation–selection model. The growing probability was calculated for various population sizes, N, sequence lengths, L, selective advantages, s, fitness parameters, k and measuring parameters, C. The saturated growing probability in the stochastic region was approximately the effective selective advantage, [Formula: see text], when [Formula: see text] and [Formula: see text]. The present study suggests that the growing probability in the stochastic region in the decoupled continuous-time mutation–selection model can be described using the theoretical formula for the growing probability in the Moran two-allele model. The selective advantage ratio, which represents the ratio of the effective selective advantage to the selective advantage, does not depend on the population size, selective advantage, measuring parameter and fitness parameter; instead the selective advantage ratio decreases with the increasing sequence length.

COMPUTER SIMULATION FOR THE CROSSING TIME IN A DIPLOID, ASYMMETRIC, SHARPLY-PEAKED LANDSCAPE IN THE INFINITE POPULATION LIMIT

2013 ◽  
Vol 24 (01) ◽  
pp. 1250091 ◽  
Author(s):  
WONPYONG GILL
Keyword(s):  
Computer Simulation ◽  
Steady State ◽  
Selective Advantage ◽  
Sequence Length ◽  
Initial State ◽  
Infinite Population ◽  
Crossing Time ◽  
Increasing Function ◽  
Fitness Parameter ◽  
Extension Parameter

This study calculated the crossing time in the diploid mutation–selection model in an infinite population limit for various dominance parameters, h, and selective advantages, by switching on a diploid, asymmetric, sharply-peaked landscape, from an initial state which is the steady state in a diploid, sharply-peaked landscape. The crossing time for h < 1 was found to diverge at the critical fitness parameter, which increased with increasing selective advantage and decreased with increasing sequence length. When the sequence length was increased with a fixed extension parameter, there was no crossing time for h < 1 when the sequence length was longer than the critical sequence length, which increased with increasing selective advantage. The crossing time for h ≤ 1 was found to be an exponentially increasing function of the sequence length, and the crossing time for h > 1 became saturated at a long sequence length. The crossing time decreased with increasing selective advantage, mainly because the larger selective advantage caused the increase in relative density of the reversal allele to grow exponentially at an earlier time.

CALCULATION OF THE CROSSING TIME THROUGH THE FITNESS BARRIER IN A SYMMETRIC MULTIPLICATIVE LANDSCAPE

2005 ◽  
Vol 16 (01) ◽  
pp. 85-97 ◽  
Author(s):  
DOKYOON KIM ◽  
WONPYONG GILL
Keyword(s):  
Computer Simulation ◽  
Mutation Rate ◽  
Approximate Formula ◽  
Mutation Rates ◽  
Sequence Length ◽  
Crossing Time ◽  
Fitness Parameters ◽  
Time Region ◽  
Simulation Results ◽  
Fitness Parameter

The crossing time through fitness barrier in a symmetric multiplicative landscape is systematically calculated for various mutation rates, fitness parameters, and sequence lengths by using a computer simulation. It is found that the crossing time scales as a power law in the mutation rate and the fitness parameter. It is also found that the crossing time increases exponentially as the sequence length increases. We have obtained the approximate formula, which decribes the asymptotic behavior of the crossing time in the long-crossing-time region, and the improved approximate formula with the correction factor, which nicely fit computer simulation results even below the long-crossing-time region. From the comparison between the approximate formula in the multiplicative landscape and the approximate formula in the sharply-peaked landscape, it is found that both landscapes have the same scaling effect of fitness parameter and mutation rate on the crossing time in the long-crossing-time region.

CROSSING TIME THROUGH THE FITNESS BARRIER IN AN ASYMMETRIC MULTIPLICATIVE OR ADDITIVE LANDSCAPE IN THE MUTATION-SELECTION MODEL

2011 ◽  
Vol 22 (11) ◽  
pp. 1293-1307 ◽  
Author(s):  
WONPYONG GILL
Keyword(s):  
Continuous Time ◽  
Finite Population ◽  
Selection Model ◽  
Sequence Length ◽  
Continuous Time Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Infinite Population ◽  
Crossing Time ◽  
Extension Parameter

This study examines the dependence of crossing time on sequence length for a finite population in an asymmetric multiplicative, or additive, landscape with a positive asymmetric parameter and a fixed extension parameter in three types of mutation-selection model: the coupled discrete-time model, the coupled continuous-time model, and the decoupled continuous-time model. The crossing times for a finite population in the three types of mutation-selection model began to deviate from the crossing times for an infinite population at a critical sequence length. It then increased exponentially as a function of sequence length in the stochastic region where the sequence length was much longer than the critical sequence length. The exponentially increasing rates of the crossing times in the three types of mutation-selection model were similar to each other. These rates were decreased by increasing the asymmetric parameter. Once the asymmetric parameter reached a certain limit the crossing times for the three models in the stochastic region could not be decreased further by increasing the asymmetric parameter past this limit.

scholarly journals Recombination Can Evolve in Large Finite Populations Given Selection on Sufficient Loci

Genetics ◽  
2003 ◽  
Vol 165 (4) ◽  
pp. 2249-2258 ◽  
Author(s):  
Mark M Iles ◽  
Kevin Walters ◽  
Chris Cannings
Keyword(s):  
Experimental Evidence ◽  
Genetic Drift ◽  
Finite Population ◽  
Selective Advantage ◽  
Indirect Selection ◽  
Small Populations ◽  
Finite Populations ◽  
Population Sizes ◽  
Population Recombination

AbstractIt is well known that an allele causing increased recombination is expected to proliferate as a result of genetic drift in a finite population undergoing selection, without requiring other mechanisms. This is supported by recent simulations apparently demonstrating that, in small populations, drift is more important than epistasis in increasing recombination, with this effect disappearing in larger finite populations. However, recent experimental evidence finds a greater advantage for recombination in larger populations. These results are reconciled by demonstrating through simulation without epistasis that for m loci recombination has an appreciable selective advantage over a range of population sizes (am, bm). bm increases steadily with m while am remains fairly static. Thus, however large the finite population, if selection acts on sufficiently many loci, an allele that increases recombination is selected for. We show that as selection acts on our finite population, recombination increases the variance in expected log fitness, causing indirect selection on a recombination-modifying locus. This effect is enhanced in those populations with more loci because the variance in phenotypic fitnesses in relation to the possible range will be smaller. Thus fixation of a particular haplotype is less likely to occur, increasing the advantage of recombination.

scholarly journals The Optimal Portfolio Selection Model underg-Expectation

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li
Keyword(s):  
Prospect Theory ◽  
Decision Rule ◽  
Portfolio Selection ◽  
Continuous Time ◽  
Optimal Solution ◽  
Selection Model ◽  
Optimal Portfolio ◽  
Optimal Portfolio Selection ◽  
Choquet Expectation ◽  
Portfolio Selection Model

This paper solves the optimal portfolio selection model under the framework of the prospect theory proposed by Kahneman and Tversky in the 1970s with decision rule replaced by theg-expectation introduced by Peng. This model was established in the general continuous time setting and firstly adopted theg-expectation to replace Choquet expectation adopted in the work of Jin and Zhou, 2008. Using different S-shaped utility functions andg-functions to represent the investors' different uncertainty attitudes towards losses and gains makes the model not only more realistic but also more difficult to deal with. Although the models are mathematically complicated and sophisticated, the optimal solution turns out to be surprisingly simple, the payoff of a portfolio of two binary claims. Also I give the economic meaning of my model and the comparison with that one in the work of Jin and Zhou, 2008.

scholarly journals Microsatellite variation in honey bee (Apis mellifera L.) populations: hierarchical genetic structure and test of the infinite allele and stepwise mutation models.

Genetics ◽  
1995 ◽  
Vol 140 (2) ◽  
pp. 679-695 ◽  
Author(s):  
A Estoup ◽  
L Garnery ◽  
M Solignac ◽  
J M Cornuet
Keyword(s):  
Apis Mellifera ◽  
Phylogenetic Trees ◽  
Microsatellite Data ◽  
Effective Population ◽  
Average Heterozygosity ◽  
Microsatellite Variation ◽  
Infinite Allele Model ◽  
Population Sizes ◽  
Stepwise Mutation ◽  
Allele Model

Abstract Samples from nine populations belonging to three African (intermissa, scutellata and capensis) and four European (mellifera, ligustica, carnica and cecropia) Apis mellifera subspecies were scored for seven microsatellite loci. A large amount of genetic variation (between seven and 30 alleles per locus) was detected. Average heterozygosity and average number of alleles were significantly higher in African than in European subspecies, in agreement with larger effective population sizes in Africa. Microsatellite analyses confirmed that A. mellifera evolved in three distinct and deeply differentiated lineages previously detected by morphological and mitochondrial DNA studies. Dendrogram analysis of workers from a given population indicated that super-sisters cluster together when using a sufficient number of microsatellite data whereas half-sisters do not. An index of classification was derived to summarize the clustering of different taxonomic levels in large phylogenetic trees based on individual genotypes. Finally, individual population x loci data were used to test the adequacy of the two alternative mutation models, the infinite allele model (IAM) and the stepwise mutation models. The better fit overall of the IAM probably results from the majority of the microsatellites used including repeats of two or three different length motifs (compound microsatellites).

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