Theory of Multiphase Sampling from a Finite or an Infinite Population on Successive Occasions 1, 2

1967 ◽  
Vol 35 (3) ◽  
pp. 247 ◽  
Author(s):  
B. D. Tikkiwal
Keyword(s):  
Infinite Population ◽  
Multiphase Sampling

Infinite-population approval voting: A proposal

Synthese ◽  
2021 ◽  
Author(s):  
Susumu Cato ◽  
Eric Rémila ◽  
Philippe Solal
Keyword(s):  
Approval Voting ◽  
Infinite Population

Comparing Mutational Variabilities

Genetics ◽  
1996 ◽  
Vol 143 (3) ◽  
pp. 1467-1483 ◽  
Author(s):  
David Houle ◽  
Bob Morikawa ◽  
Michael Lynch
Keyword(s):  
Life History ◽  
Morphological Traits ◽  
Life History Traits ◽  
Genetic Variance ◽  
Balance Model ◽  
Phenotypic Traits ◽  
Infinite Population ◽  
Persistence Time ◽  
Coefficients Of Variation ◽  
Balance Hypothesis

Abstract We have reviewed the available data on VM, the amount of genetic variation in phenotypic traits produced each generation by mutation. We use these data to make several qualitative tests of the mutation-selection balance hypothesis for the maintenance of genetic variance (MSB). To compare VM values, we use three dimensionless quantities: mutational heritability, the mutational coefficient of variation, CVM; and the ratio of the standing genetic variance to VM, VG/VM. Since genetic coefficients of variation for life history traits are larger than those for morphological traits, we predict that under MSB, life history traits should also have larger CVM. This is confirmed; life history traits have a median CVM value more than six times higher than that for morphological traits. VG/VM approximates the persistence time of mutations under MSB in an infinite population. In order for MSB to hold, VG/VM must be small, substantially less than 1000, and life history traits should have smaller values than morphological traits. VG/VM averages about 50 generations for life history traits and 100 generations for morphological traits. These observations are all consistent with the predictions of a mutation-selection balance model.

Genetic Drift in an Infinite Population: The Pseudohitchhiking Model

Genetics ◽  
2000 ◽  
Vol 155 (2) ◽  
pp. 909-919 ◽  
Author(s):  
John H Gillespie
Keyword(s):  
Genetic Drift ◽  
Stochastic Dynamics ◽  
Diffusion Theory ◽  
Stochastic Effects ◽  
Stochastic Force ◽  
Infinite Population ◽  
Sample Paths ◽  
Neutral Locus ◽  
Linked Selection ◽  
Number Of Branches

Abstract Selected substitutions at one locus can induce stochastic dynamics that resemble genetic drift at a closely linked neutral locus. The pseudohitchhiking model is a one-locus model that approximates these effects and can be used to describe the major consequences of linked selection. As the changes in neutral allele frequencies when hitchhiking are rapid, diffusion theory is not appropriate for studying neutral dynamics. A stationary distribution and some results on substitution processes are presented that use the theory of continuous-time Markov processes with discontinuous sample paths. The coalescent of the pseudohitchhiking model is shown to have a random number of branches at each node, which leads to a frequency spectrum that is different from that of the equilibrium neutral model. If genetic draft, the name given to these induced stochastic effects, is a more important stochastic force than genetic drift, then a number of paradoxes that have plagued population genetics disappear.

scholarly journals Applications of Queuing Theory in Quantitative Business Analysis

2020 ◽  
pp. 253-257
Keyword(s):  
Quantitative Analysis ◽  
Waiting Time ◽  
Queuing Theory ◽  
Single Channel ◽  
Analysis Approach ◽  
Single Server ◽  
Expected Number ◽  
Queuing Model ◽  
Infinite Population ◽  
Expected Waiting Time

Queuing Theory provides the system of applications in many sectors in life cycle. Queuing Structure and basic components determination is computed in queuing model simulation process. Distributions in Queuing Model can be extracted in quantitative analysis approach. Differences in Queuing Model Queue discipline, Single and Multiple service station with finite and infinite population is described in Quantitative analysis process. Basic expansions of probability density function, Expected waiting time in queue, Expected length of Queue, Expected size of system, probability of server being busy, and probability of system being empty conditions can be evaluated in this quantitative analysis approach. Probability of waiting ‘t’ minutes or more in queue and Expected number of customer served per busy period, Expected waiting time in System are also computed during the Analysis method. Single channel model with infinite population is used as most common case of queuing problems which involves the single channel or single server waiting line. Single Server model with finite population in test statistics provides the Relationships used in various applications like Expected time a customer spends in the system, Expected waiting time of a customer in the queue, Probability that there are n customers in the system objective case, Expected number of customers in the system

scholarly journals Incorporating genetic selection into individual-based models (IBMs) of malaria and other infectious diseases

2019 ◽  
Author(s):  
Ian M. Hastings ◽  
Raman Sharma
Keyword(s):  
Control Strategies ◽  
Genetic Parameter ◽  
Genetic Selection ◽  
Wait Time ◽  
Antimicrobial Drug Resistance ◽  
Infinite Population ◽  
Individual Based Models ◽  
Population Sizes ◽  
Human Infections ◽  
The Impact

AbstractOptimal control strategies for human infections are often investigated by computational approaches using individual-based models (IBMs). These typically track humans and evaluate the impact of control interventions in terms of human deaths, clinical cases averted, interruption of transmission etc. Genetic selection can be incorporated into these IBMs and used to track the spread of mutations whose origin and spread are often driven by the intervention, and which subsequently undermine the control strategy; for example, mutations which encode antimicrobial drug resistance or diagnosis- or vaccine-escape phenotypes. Basic population genetic descriptions of selection are based on infinite population sizes (so that chance fluctuations in allele frequency are absent) but IBMs track finite population sizes. We describe how the finite sizes of IBMs affect simulating the dynamics of genetic selection and how best to incorporate genetic selection into these models. We use the OpenMalaria IBM of malaria as an example, but the same principles apply to IBMs of other diseases. We identify four strategies to incorporate selection into IBMs and make the following four recommendations. Firstly, calculate and report the selection coefficients, s, of the advantageous allele as the key genetic parameter. Secondly, use these values of ‘s’ to calculate the wait-time until a mutation successful establishes itself in the population. The wait time for the mutation can be added to speed of selection, s, to calculate when the mutation will reach significant, operationally important levels. Thirdly, quantify the ability of the IBM to robustly estimate small selection coefficients. Fourthly, optimise computational efficacy: when ‘s’ is small it is plausible that fewer replicates of larger IBMs will be more efficient than a larger number of replicates of smaller size.

scholarly journals GENETIC VARIATION IN A HETEROGENEOUS ENVIRONMENT. I. TEMPORAL HETEROGENEITY AND THE ABSOLUTE DOMINANCE MODEL

Genetics ◽  
1974 ◽  
Vol 78 (2) ◽  
pp. 757-770
Author(s):  
Philip W Hedrick
Keyword(s):  
Genetic Variation ◽  
Temporal Variation ◽  
Gene Frequency ◽  
Environmental Heterogeneity ◽  
Finite Population ◽  
Environmental Variation ◽  
Dominance Model ◽  
Infinite Population ◽  
The Absolute ◽  
Absolute Dominance

ABSTRACT The conditions for a stable polymorphism and the equilibrium gene frequency in an infinite population are compared when there is spatial or temporal environmental heterogeneity for the absolute dominance model. For temporal variation the conditions for stability are more restrictive and the equilibrium gene frequency is often at a low gene frequency. In a finite population, temporal environmental heterogeneity for the absolute dominance model was found to be quite ineffective in maintaining genetic variation and is often less effective than no selection at all. For comparison, the maximum maintenance for temporal variation is related to the overdominant model. In general, cyclic environmental variation was found to be more effective at maintaining genetic variation than where the environment varies stochastically. The importance of temporal environmental variation and the maintenance of genetic variation is discussed.

Limit theorems for random mating in infinite populations

1966 ◽  
Vol 3 (01) ◽  
pp. 94-114 ◽  
Author(s):  
B. E. Ellison
Keyword(s):  
Limit Distribution ◽  
Limit Theorems ◽  
Random Mating ◽  
Limit Distributions ◽  
Infinite Population ◽  
The Law

This paper is concerned with the distribution of “types” of individuals in an infinite population after indefinitely many nonoverlapping generations of random mating. The absence of selection and mutation is assumed. The probabilistic law which governs the production of an offspring may be asymmetrical with respect to the “sexes” of the two parents, but the law is assumed to apply independently of the “sex” of the offspring. The question of the existence of a limit distribution of types, the rate at which a limit distribution is approached, and properties of limit distributions are treated.

scholarly journals A continuum of biological adaptations to environmental fluctuation

2019 ◽  
Vol 286 (1912) ◽  
pp. 20191623 ◽  
Author(s):  
Ming Liu ◽  
Dustin R. Rubenstein ◽  
Wei-Chung Liu ◽  
Sheng-Feng Shen
Keyword(s):  
Overlapping Generations ◽  
Bet Hedging ◽  
Environmental Fluctuation ◽  
Infinite Population ◽  
Biological Adaptation ◽  
Hedging Strategies ◽  
Wide Range ◽  
Population Sizes ◽  
Environmental Unpredictability ◽  
Per Capita

Bet-hedging—a strategy that reduces fitness variance at the expense of lower mean fitness among different generations—is thought to evolve as a biological adaptation to environmental unpredictability. Despite widespread use of the bet-hedging concept, most theoretical treatments have largely made unrealistic demographic assumptions, such as non-overlapping generations and fixed or infinite population sizes. Here, we extend the concept to consider overlapping generations by defining bet-hedging as a strategy with lower variance and mean per capita growth rate across different environments. We also define an opposing strategy—the rising-tide—that has higher mean but also higher variance in per capita growth. These alternative strategies lie along a continuum of biological adaptions to environmental fluctuation. Using stochastic Lotka–Volterra models to explore the evolution of the rising-tide versus bet-hedging strategies, we show that both the mean environmental conditions and the temporal scales of their fluctuations, as well as whether population dynamics are discrete or continuous, are crucial in shaping the type of strategy that evolves in fluctuating environments. Our model demonstrates that there are likely to be a wide range of ways that organisms with overlapping generations respond to environmental unpredictability beyond the classic bet-hedging concept.

scholarly journals A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems

2020 ◽  
Vol 28 (1) ◽  
pp. 55-85
Author(s):  
Bo Song ◽  
Victor O.K. Li
Keyword(s):  
Population Dynamics ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Analytical Framework ◽  
Population Models ◽  
Initial Population ◽  
Infinite Population ◽  
Continuous Optimization Problems

Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models are derived from Markov chains by exploiting symmetries between individuals in the population and analyzing the limit as the population size goes to infinity. In this article, we study the theoretical foundations of infinite population models of evolutionary algorithms on continuous optimization problems. First, we show that the convergence proofs in a widely cited study were in fact problematic and incomplete. We further show that the modeling assumption of exchangeability of individuals cannot yield the transition equation. Then, in order to analyze infinite population models, we build an analytical framework based on convergence in distribution of random elements which take values in the metric space of infinite sequences. The framework is concise and mathematically rigorous. It also provides an infrastructure for studying the convergence of the stacking of operators and of iterating the algorithm which previous studies failed to address. Finally, we use the framework to prove the convergence of infinite population models for the mutation operator and the [Formula: see text]-ary recombination operator. We show that these operators can provide accurate predictions for real population dynamics as the population size goes to infinity, provided that the initial population is identically and independently distributed.

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