scholarly journals A deterministic model of cyclical selection

1975 ◽  
Vol 25 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Rolf F. Hoekstra
Keyword(s):  
Deterministic Model ◽  
Fitness Function ◽  
Natural Populations ◽  
Sufficient Conditions ◽  
Selection Model ◽  
Property A ◽  
Order Of Magnitude ◽  
Protected Polymorphism ◽  
Mean Fitness ◽  
Special Case

SUMMARYA deterministic model of cyclical selection in randomly mating populations is studied. Sufficient conditions for a protected polymorphism, which are for the special case of alternating selection also necessary conditions, are obtained using a simple graphical approach. The most important condition requires ‘marginal overdominance’ (Wallace, 1968); the other conditions seem hard to satisfy in a natural situation. Furthermore it is shown that the cyclical selection model can be regarded as a special case of a frequency-dependent selection model (Cockerham et al. 1972). Using this property, a mean fitness function for the cyclical selection model is derived. Generally, the mean fitness will not be maximized under cyclical selection. The relevance of the model to the problem of the role of cyclical selection in the maintenance of genetic polymorphism in natural populations is discussed. It is concluded that this relevance is probably rather limited with regard to the creation of protected polymorphism, but that the influence of cyclical selection on transient polymorphisms might be more significant. An approximate formula for the time needed for a given change in gene frequency under cyclical selection is derived. It appears that cyclical selection can extend considerably the time during which a transient polymorphism persists, especially if the selective differences in the different environments are of the same order of magnitude and of opposite sign.

scholarly journals CHROMOSOME INTERACTIONS IN DROSOPHILA MELANOGASTER. II. TOTAL FITNESS

Genetics ◽  
1982 ◽  
Vol 102 (3) ◽  
pp. 485-502
Author(s):  
Robert D Seager ◽  
Francisco J Ayala ◽  
R William Marks
Keyword(s):  
Drosophila Melanogaster ◽  
Threshold Model ◽  
Fitness Function ◽  
Natural Populations ◽  
Genetic Load ◽  
Chromosome 2 ◽  
Synergistic Interactions ◽  
The Third ◽  
Mean Fitness ◽  
Selective Maintenance

ABSTRACT In a large experiment, using nearly 200 population cages, we have measured the fitness of Drosophila melanogaster homozygous (1) for the second chromosome, (2) for the third chromosome, and (3) for both chromosomes. Twentyfour second chromosomes and 24 third chromosomes sampled from a natural population were tested. The mean fitness of the homozygous flies is 0.081 ± 0.014 for the second chromosome, 0.080 ± 0.017 for the third chromosome, and 0.079 ± 0.024 for both chromosomes simultaneously. Assuming that fitnesses are multiplicative (the additive fitness model makes no sense in the present case because of the large selection coefficients involved), the expected mean fitness of the homozygotes for both chromosomes is 0.0066; their observed fitness is more than ten times greater. Thus, it appears that synergistic interactions between loci are considerable; and that, consequently, the fitness function substantially departs from linearity. Two models are tentatively suggested for the fitness function: a "threshold" model and a "synergistic" model.—The experiments reported here confirm previous results showing that the concealed genetic load present in natural populations of Drosophila is sufficient to account for the selective maintenance of numerous polymorphisms (of the order of 1000).

scholarly journals Sufficient conditions for polymorphism with cyclical selection in a subdivided population

1978 ◽  
Vol 31 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Rolf F. Hoekstra
Keyword(s):  
Deterministic Model ◽  
Sufficient Conditions ◽  
Combined Effect ◽  
Subdivided Population ◽  
Protected Polymorphism ◽  
Diploid Populations

SUMMARYThe combined effect of multi-niche selection and cyclical selection is studied in a deterministic model. Sufficient conditions for protected polymorphism are derived for diploid populations with and without dominance and for haploid populations. These conditions appear to be broader than in the cases of only multi-niche selection or only cyclical selection.

scholarly journals On the Rate and Linearity of Viability Declines in Drosophila Mutation-Accumulation Experiments: Genomic Mutation Rates and Synergistic Epistasis Revisited

Genetics ◽  
2004 ◽  
Vol 166 (2) ◽  
pp. 797-806 ◽  
Author(s):  
James D Fry
Keyword(s):  
Mutation Rate ◽  
Average Rate ◽  
Natural Populations ◽  
Mutation Accumulation ◽  
High Rate ◽  
Deleterious Mutations ◽  
Order Of Magnitude ◽  
Contamination Event ◽  
Genomic Mutation ◽  
The 1960S

Abstract High rates of deleterious mutations could severely reduce the fitness of populations, even endangering their persistence; these effects would be mitigated if mutations synergize each others’ effects. An experiment by Mukai in the 1960s gave evidence that in Drosophila melanogaster, viability-depressing mutations occur at the surprisingly high rate of around one per zygote and that the mutations interact synergistically. A later experiment by Ohnishi seemed to support the high mutation rate, but gave no evidence for synergistic epistasis. Both of these studies, however, were flawed by the lack of suitable controls for assessing viability declines of the mutation-accumulation (MA) lines. By comparing homozygous viability of the MA lines to simultaneously estimated heterozygous viability and using estimates of the dominance of mutations in the experiments, I estimate the viability declines relative to an appropriate control. This approach yields two unexpected conclusions. First, in Ohnishi’s experiment as well as in Mukai’s, MA lines showed faster-than-linear declines in viability, indicative of synergistic epistasis. Second, while Mukai’s estimate of the genomic mutation rate is supported, that from Ohnishi’s experiment is an order of magnitude lower. The different results of the experiments most likely resulted from differences in the starting genotypes; even within Mukai’s experiment, a subset of MA lines, which I argue probably resulted from a contamination event, showed much slower viability declines than did the majority of lines. Because different genotypes may show very different mutational behavior, only studies using many founding genotypes can determine the average rate and distribution of effects of mutations relevant to natural populations.

scholarly journals GENETIC LOAD IN NATURAL POPULATIONS: IS IT COMPATIBLE WITH THE HYPOTHESIS THAT MANY POLYMORPHISMS ARE MAINTAINED BY NATURAL SELECTION?

Genetics ◽  
1974 ◽  
Vol 77 (3) ◽  
pp. 569-589
Author(s):  
Martin L Tracey ◽  
Francisco J Ayala
Keyword(s):  
Drosophila Melanogaster ◽  
Natural Selection ◽  
Natural Population ◽  
Natural Populations ◽  
Genetic Load ◽  
Structural Genes ◽  
Invertebrate Species ◽  
Average Proportion ◽  
Mean Fitness ◽  
The Mean

ABSTRACT Recent studies of genetically controlled enzyme variation lead to an estimation that at least 30 to 60% of the structural genes are polymorphic in natural populations of many vertebrate and invertebrate species. Some authors have argued that a substantial proportion of these polymorphisms cannot be maintained by natural selection because this would result in an unbearable genetic load. If many polymorphisms are maintained by heterotic natural selection, individuals with much greater than average proportion of homozygous loci should have very low fitness. We have measured in Drosophila melanogaster the fitness of flies homozygous for a complete chromosome relative to normal wild flies. A total of 37 chromosomes from a natural population have been tested using 92 experimental populations. The mean fitness of homozygous flies is 0.12 for second chromosomes, and 0.13 for third chromosomes. These estimates are compatible with the hypothesis that many (more than one thousand) loci are maintained by heterotic selection in natural populations of D. melanogaster.

PBW deformations of quantum symmetric algebras and their group extensions

2016 ◽  
Vol 15 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Piyush Shroff ◽  
Sarah Witherspoon
Keyword(s):  
Finite Group ◽  
Lie Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group Extensions ◽  
Enveloping Algebra ◽  
Symmetric Algebras ◽  
Necessary And Sufficient ◽  
Special Case

We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the acting group is trivial, we determine conditions under which such a PBW deformation is a generalized enveloping algebra of a color Lie algebra; our PBW deformations include these algebras as a special case.

scholarly journals Quartic Rational Said-Ball-Like Basis with Tension Shape Parameters and Its Application

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Yuanpeng Zhu ◽  
Xuli Han ◽  
Shengjun Liu
Keyword(s):  
Error Estimate ◽  
Hermite Interpolation ◽  
Sufficient Conditions ◽  
Basis Functions ◽  
Shape Parameters ◽  
Interpolation Spline ◽  
Triangular Domain ◽  
Type Algorithm ◽  
Special Case ◽  
Monotonicity Preserving

Four new quartic rational Said-Ball-like basis functions, which include the cubic Said-Ball basis functions as a special case, are constructed in this paper. The new basis is applied to generate a class ofC1continuous quartic rational Hermite interpolation splines with local tension shape parameters. The error estimate expression of the proposed interpolant is given and the sufficient conditions are derived for constructing aC1positivity- or monotonicity- preserving interpolation spline. In addition, we extend the quartic rational Said-Ball-like basis to a triangular domain which has three tension shape parameters and includes the cubic triangular Said-Ball basis as a special case. In order to compute the corresponding patch stably and efficiently, a new de Casteljau-type algorithm is developed. Moreover, theG1continuous conditions are deduced for the joining of two patches.

scholarly journals Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

A model for interaction of a Poisson and a renewal process and its relation with queuing theory

1972 ◽  
Vol 9 (2) ◽  
pp. 451-456 ◽  
Author(s):  
Lennart Råde
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Queuing Theory ◽  
Random Number ◽  
Sufficient Conditions ◽  
Stieltjes Transform ◽  
Time Intervals ◽  
Response Process ◽  
Necessary And Sufficient ◽  
Special Case

This paper discusses the response process when a Poisson process interacts with a renewal process in such a way that one or more points of the Poisson process eliminate a random number of consecutive points of the renewal process. A queuing situation is devised such that the c.d.f. of the length of the busy period is the same as the c.d.f. of the length of time intervals of the renewal response process. The Laplace-Stieltjes transform is obtained and from this the expectation of the time intervals of the response process is derived. For a special case necessary and sufficient conditions for the response process to be a Poisson process are found.

scholarly journals Characterizations and Identities for Isosceles Triangular Numbers

2021 ◽  
Vol 14 (2) ◽  
pp. 380-395
Author(s):  
Jiramate Punpim ◽  
Somphong Jitman
Keyword(s):  
Positive Integer ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Triangular Numbers ◽  
Triangular Number ◽  
Recursive Formulas ◽  
Necessary And Sufficient ◽  
Positive Integers ◽  
Special Case

Triangular numbers have been of interest and continuously studied due to their beautiful representations, nice properties, and various links with other figurate numbers. For positive integers n and l, the nth l-isosceles triangular number is a generalization of triangular numbers defined to be the arithmetic sum of the formT(n, l) = 1 + (1 + l) + (1 + 2l) + · · · + (1 + (n − 1)l).In this paper, we focus on characterizations and identities for isosceles triangular numbers as well as their links with other figurate numbers. Recursive formulas for constructions of isosceles triangular numbers are given together with necessary and sufficient conditions for a positive integer to be a sum of isosceles triangular  numbers. Various identities for isosceles triangular numbers are established. Results on triangular numbers can be viewed as a special case.

Sign in / Sign up

Export Citation Format

Share Document