scholarly journals THE AGE OF A NEUTRAL MUTANT PERSISTING IN A FINITE POPULATION

Genetics ◽  
1973 ◽  
Vol 75 (1) ◽  
pp. 199-212
Author(s):  
Motoo Kimura ◽  
Tomoko Ohta
Keyword(s):  
Arrival Time ◽  
Finite Population ◽  
Low Frequency ◽  
Effective Population ◽  
Random Drift ◽  
Current Frequency ◽  
Very Low Frequency ◽  
First Arrival ◽  
The Mean ◽  
First Arrival Time

ABSTRACT Formulae for the mean and the mean square age of a neutral allele which is segregating with frequency x in a population of effective size Ne have been obtained using the diffusion equation method, for the case of 4Nev<1 where v is the mutation rate. It has been shown that the average ages of neutral alleles, even if their frequencies are relatively low, are quite old. For example, a neutral mutant whose current frequency is 10% has the expected age roughly equal to the effective population size Ne and the standard deviation 1.4Ne (in generations), assuming that this mutant has increased by random drift from a very low frequency. Also, formulae for the mean "first arrival time" of a neutral mutant to a certain frequency x have been presented. In addition, a new, approximate method has been developed which enables us to obtain the condition under which frequencies of "rare" polymorphic alleles among local populations are expected to be uniform if the alleles are selectively neutral.—It was concluded that exchange of only a few individuals on the average between adjacent colonies per generation is enough to bring about such a uniformity of frequencies.

scholarly journals ANALYSES OF THE AGE OF GENES AND THE FIRST ARRIVAL TIMES IN A FINITE POPULATION

Genetics ◽  
1983 ◽  
Vol 105 (4) ◽  
pp. 1041-1059
Author(s):  
Takeo Maruyama ◽  
Paul A Fuerst
Keyword(s):  
Arrival Time ◽  
Mutant Gene ◽  
Intermediate Frequency ◽  
Lag Phase ◽  
Reversal Theory ◽  
Infinite Allele Model ◽  
First Arrival ◽  
Mean And Variance ◽  
The Mean ◽  
First Arrival Time

ABSTRACT The age of a mutant gene is studied using the infinite allele model in which every mutant is new and selectively neutral. Based on a time reversal theory of Markov processes, we develop a method of mathematical analysis that is considerably simpler for calculating the various statistics of the age than previous methods. Formulas for the mean and variance and for the distribution of age are presented together with some examples of relevance to cases in natural populations.—Theoretical studies of the first arrival time of an allele to a specified frequency, given an initially monomorphic condition of the locus, are presented. It is shown that, beginning with an allele that has frequency p = 1 or an allele with frequency p = 1/2N, there is an initial lag phase in which there is virtually no chance of an allele with a specified intermediate frequency appearing in the population. The distribution of the first arrival time is also presented. The distribution shows several characteristics that are not immediately obvious from a consideration of only the mean and variance of first arrival time. Especially noteworthy is the existence of a very long tail to the distribution. We have also studied the distribution of the age of an allele in the population. Again, the distribution of this measure is shown to be more informative for several questions than are the mean and variance alone.

scholarly journals Moth Mating: Modeling Female Pheromone Calling and Male Navigational Strategies to Optimize Reproductive Success

2020 ◽  
Vol 10 (18) ◽  
pp. 6543
Author(s):  
Tracy L. Stepien ◽  
Cole Zmurchok ◽  
James B. Hengenius ◽  
Rocío Marilyn Caja Rivera ◽  
Maria R. D’Orsogna ◽  
...  
Keyword(s):  
Arrival Time ◽  
Mathematical Framework ◽  
Reproductive Process ◽  
Mating Period ◽  
Agent Based ◽  
First Arrival ◽  
The Mean ◽  
First Arrival Time ◽  
Over Time

Male and female moths communicate in complex ways to search for and to select a mate. In a process termed calling, females emit small quantities of pheromones, generating plumes that spread in the environment. Males detect the plume through their antennae and navigate toward the female. The reproductive process is marked by female choice and male–male competition, since multiple males aim to reach the female but only the first can mate with her. This provides an opportunity for female selection on male traits such as chemosensitivity to pheromone molecules and mobility. We develop a mathematical framework to investigate the overall mating likelihood, the mean first arrival time, and the quality of the first male to reach the female for four experimentally observed female calling strategies unfolding over a typical one-week mating period. We present both analytical solutions of a simplified model as well as results from agent-based numerical simulations. Our findings suggest that, by adjusting call times and the amount of released pheromone, females can optimize the mating process. In particular, shorter calling times and lower pheromone titers at onset of the mating period that gradually increase over time allow females to aim for higher-quality males while still ensuring that mating occurs by the end of the mating period.

scholarly journals The interaction between effective population size and linkage intensity under artificial selection

1966 ◽  
Vol 7 (3) ◽  
pp. 313-323 ◽  
Author(s):  
B. D. H. Latter
Keyword(s):  
Population Size ◽  
Finite Population ◽  
Low Frequency ◽  
Selection Response ◽  
Appreciable Effect ◽  
Effective Population ◽  
Mean Waiting Time ◽  
Tight Linkage ◽  
The Mean ◽  
Total Selection

The effects of tight linkage on the total response due to pairs of identical additive loci, segregating in a population initially in linkage equilibrium, have been studied both algebraically and by means of computer simulation. Particular attention has been given to the effects of finite population size on the probabilities of (a) the elimination from the population of the gamete carrying both ‘plus’ alleles; (b) the joint preservation of the two types of repulsion gametes; (c) the recovery of the desired combination of plus alleles through crossing-over; and (d) the fixation of the gamete in the population following its recovery.The study is restricted to situations in which linkage is known to have an appreciable effect on total selection response, i.e. to the case of genes of large effect initially at low frequency. A comparison of regimes with the same expected response under free recombination has shown the probability of (a) to be high, and the probability of (b) to be very nearly the same for all regimes tested. Provided that the recovery of the gamete carrying both plus alleles is an unlikely event at any given point in time, the probability of the fixation of the gamete, once reconstituted, is expected to be independent of population size for genes of large effect. In this context, approximate algebraic expressions have been derived for the probability of effective recovery of the required gamete, and for the mean waiting time involved.

First arrival time picking for microseismic data based on DWSW algorithm

2018 ◽  
Vol 22 (4) ◽  
pp. 833-840 ◽  
Author(s):  
Yue Li ◽  
Yue Wang ◽  
Hongbo Lin ◽  
Tie Zhong
Keyword(s):  
Arrival Time ◽  
Microseismic Data ◽  
First Arrival ◽  
First Arrival Time ◽  
Arrival Time Picking

scholarly journals A European lightning density analysis using 5 years of ATDnet data

2014 ◽  
Vol 14 (4) ◽  
pp. 815-829 ◽  
Author(s):  
G. Anderson ◽  
D. Klugmann
Keyword(s):  
Detailed Analysis ◽  
Arrival Time ◽  
Detection Efficiency ◽  
Low Frequency ◽  
Continuous Data ◽  
Data Sets ◽  
Current Form ◽  
Very Low Frequency ◽  
Density Analysis ◽  
Using Data

Abstract. The Met Office has operated a very low frequency (VLF) lightning location network since 1987. The long-range capabilities of this network, referred to in its current form as ATDnet, allow for relatively continuous detection efficiency across Europe with only a limited number of sensors. The wide coverage and continuous data obtained by Arrival Time Differing NETwork (ATDnet) are here used to create data sets of lightning density across Europe. Results of annual and monthly detected lightning density using data from 2008–2012 are presented, along with more detailed analysis of statistics and features of interest. No adjustment has been made to the data for regional variations in detection efficiency.

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