scholarly journals Strategies for increasing fixation probabilities of recessive mutations

1991 ◽  
Vol 58 (2) ◽  
pp. 129-138 ◽  
Author(s):  
A. Caballero ◽  
P. D. Keightley ◽  
W. G. Hill
Keyword(s):  
Breeding Systems ◽  
Fixation Probability ◽  
Selection Intensity ◽  
Gene Effects ◽  
Recessive Mutations ◽  
Sib Mating ◽  
Population Structures ◽  
Recessive Genes ◽  
Fixation Probabilities ◽  
Close Inbreeding

SummaryFixation probabilities and mean times to fixation of new mutant alleles in an isogenic population having an effect on a quantitative trait under truncation selection were computed using stochastic simulation. A variety of population structures and breeding systems were studied in order to find an optimal design for maximizing the fixation probability for recessive genes without impairing that for non-recessives or delaying times to fixation. Circular mating or cycles with repeated generations of close inbreeding alternating with combination of the families proved to be very inefficient. The most successful scheme found, considering fixation probabilities and times to fixation jointly, was to practise individual selection and mate full sibs whenever possible, otherwise mate at random. The benefit was directly proportional to the number of full-sib matings performed, which, in turn, almost exclusively depended on the number of selected individuals with very little effect of selection intensity or magnitude of gene effects. Fixation rates could be well approximated by diffusion methods. When selection was practised in only one sex and, therefore, the proportion of full-sib matings could be varied from zero to one, maximizing the amount of full-sib mating was found to maximize fixation probability, at least for single mutants.

scholarly journals Evolution of cooperation in an epithelium

2019 ◽  
Vol 16 (152) ◽  
pp. 20180918 ◽  
Author(s):  
Jessie Renton ◽  
Karen M. Page
Keyword(s):  
Social Interactions ◽  
Voronoi Tessellation ◽  
Evolutionary Game ◽  
Cellular Level ◽  
Structured Populations ◽  
Evolution Of Cooperation ◽  
Animal Kingdom ◽  
Population Structures ◽  
Fixation Probabilities ◽  
Evolutionary Graph Theory

Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom but also on the cellular level. In cancer, for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory (EGT). The population structures arising due to cellular arrangement in tissues, however, are dynamic and thus cannot be accurately represented by either of these frameworks. In this work, we compare the conditions for cooperative success in an epithelium modelled using EGT, to those in a mechanical model of an epithelium—the Voronoi tessellation (VT) model. Crucially, in this latter model, cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the VT model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the EGT model.

scholarly journals Amplifiers of selection

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150114 ◽  
Author(s):  
B. Adlam ◽  
K. Chatterjee ◽  
M. A. Nowak
Keyword(s):  
Population Structure ◽  
Probability Distribution ◽  
Initial Conditions ◽  
Large Population ◽  
Fixation Probability ◽  
Population Structures ◽  
The Difference ◽  
Large Population Limit

When a new mutant arises in a population, there is a probability it outcompetes the residents and fixes. The structure of the population can affect this fixation probability. Suppressing population structures reduce the difference between two competing variants, while amplifying population structures enhance the difference. Suppressors are ubiquitous and easy to construct, but amplifiers for the large population limit are more elusive and only a few examples have been discovered. Whether or not a population structure is an amplifier of selection depends on the probability distribution for the placement of the invading mutant. First, we prove that there exist only bounded amplifiers for adversarial placement—that is, for arbitrary initial conditions. Next, we show that the Star population structure, which is known to amplify for mutants placed uniformly at random, does not amplify for mutants that arise through reproduction and are therefore placed proportional to the temperatures of the vertices. Finally, we construct population structures that amplify for all mutational events that arise through reproduction, uniformly at random, or through some combination of the two.

scholarly journals Can chromosomal heterosis in Drosophila be explained by deleterious recessive genes? Negative results from a dichromosomal population test

1989 ◽  
Vol 53 (2) ◽  
pp. 129-140 ◽  
Author(s):  
Alan N. Wilton ◽  
Michael G. Joseph ◽  
John A. Sved
Keyword(s):  
Selection Intensity ◽  
Wild Type ◽  
Partial Dominance ◽  
Negative Results ◽  
Rate Of Increase ◽  
Recessive Genes ◽  
Set Up ◽  
Expected Increase ◽  
Balancer Chromosome ◽  
Rule Out

SummaryHigh levels of chromosomal heterosis have previously been detected in Drosophila using the balancer chromosome equilibration (BE) technique, in which single wild-type chromosomes are introduced into population cages along with a dominant/lethal balancer chromosome. The balancer chromosome is rarely eliminated in such populations, showing that the fitness of chromosome homozygotes must be low by comparison with chromosomal heterozygotes. As with all cases of chromosomal heterosis, the underlying cause could either be deleterious recessives at various loci or generalized overdominance. The experiment of the present paper examines the first of these explanations. Population cages containing just two wild-type chromosomes (dichromosomal populations) were set up and allowed to run for many generations. Single chromosomes were then re-extracted from these populations, and their fitness measured using the BE technique. Our expectation was that the gradual elimination of recessive genes from the dichromosomal populations ought to result in an increase in the fitness of such re-extracted chromosome homozygotes. Yet in two replicated experiments we were unable to demonstrate an; unequivocal increase in fitness. We have estimated the rate of increase of fitness under multiple locus dominance and partial dominance models. The principal unknown parameter in these calculations is the selection intensity per locus, s. The expected increase is approximately proportional to s, and we estimate that values of s around 1/64 should be detectable in our experiments. However linkage is expected to reduce the efficiency of the dichromosomal procedure We show by computer simulation that this reduction is by a factor of approximately 2, thus increasing the detectable level of s to approximately 1/32. Consideration of mutation-selection balance models shows that this is a feasible selection intensity only if dominance is nearly complete. Thus we are unable to rule out the notion that the genes responsible for heterosis are maintained by a simple mutation-selection balance, but the experimental results constrain the parameters of such a model to a narrow range.

scholarly journals The effect of population structure on the rate of evolution

2013 ◽  
Vol 280 (1762) ◽  
pp. 20130211 ◽  
Author(s):  
Marcus Frean ◽  
Paul B. Rainey ◽  
Arne Traulsen
Keyword(s):  
Population Structure ◽  
Evolutionary Process ◽  
Ecological Factors ◽  
Structured Populations ◽  
Fixation Time ◽  
Fixation Probability ◽  
Star Graphs ◽  
Rate Of Evolution ◽  
Population Structures ◽  
Evolution Proceeds

Ecological factors exert a range of effects on the dynamics of the evolutionary process. A particularly marked effect comes from population structure, which can affect the probability that new mutations reach fixation. Our interest is in population structures, such as those depicted by ‘star graphs’, that amplify the effects of selection by further increasing the fixation probability of advantageous mutants and decreasing the fixation probability of disadvantageous mutants. The fact that star graphs increase the fixation probability of beneficial mutations has lead to the conclusion that evolution proceeds more rapidly in star-structured populations, compared with mixed (unstructured) populations. Here, we show that the effects of population structure on the rate of evolution are more complex and subtle than previously recognized and draw attention to the importance of fixation time. By comparing population structures that amplify selection with other population structures, both analytically and numerically, we show that evolution can slow down substantially even in populations where selection is amplified.

scholarly journals Fixation probabilities for simple digraphs

2013 ◽  
Vol 469 (2154) ◽  
pp. 20120676 ◽  
Author(s):  
Burton Voorhees ◽  
Alex Murray
Keyword(s):  
Complete Bipartite Graph ◽  
Directed Graphs ◽  
Closed Form Solution ◽  
Form Solution ◽  
Upper And Lower Bounds ◽  
Death Process ◽  
Fixation Probability ◽  
Single Vertex ◽  
Fixation Probabilities ◽  
Birth Death

The problem of finding birth–death fixation probabilities for configurations of normal and mutants on an N -vertex graph is formulated in terms of a Markov process on the 2 N -dimensional state space of possible configurations. Upper and lower bounds on the fixation probability after any given number of iterations of the birth–death process are derived in terms of the transition matrix of this process. Consideration is then specialized to a family of graphs called circular flows, and we present a summation formula for the complete bipartite graph, giving the fixation probability for an arbitrary configuration of mutants in terms of a weighted sum of the single-vertex fixation probabilities. This also yields a closed-form solution for the fixation probability of bipartite graphs. Three entropy measures are introduced, providing information about graph structure. Finally, a number of examples are presented, illustrating cases of graphs that enhance or suppress fixation probability for fitness r >1 as well as graphs that enhance fixation probability for only a limited range of fitness. Results are compared with recent results reported in the literature, where a positive correlation is observed between vertex degree variance and fixation probability for undirected graphs. We show a similar correlation for directed graphs, with correlation not directly to fixation probability but to the difference between fixation probability for a given graph and a complete graph.

scholarly journals Fixation Probabilities of Evolutionary Graphs Based on the Positions of New Appearing Mutants

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Pei-ai Zhang
Keyword(s):  
Markov Chain ◽  
Graph Theory ◽  
Evolutionary Dynamics ◽  
Chain Process ◽  
Fixation Probability ◽  
Spatial Structures ◽  
Single Level ◽  
Fixation Probabilities ◽  
Evolutionary Graph Theory

Evolutionary graph theory is a nice measure to implement evolutionary dynamics on spatial structures of populations. To calculate the fixation probability is usually regarded as a Markov chain process, which is affected by the number of the individuals, the fitness of the mutant, the game strategy, and the structure of the population. However the position of the new mutant is important to its fixation probability. Here the position of the new mutant is laid emphasis on. The method is put forward to calculate the fixation probability of an evolutionary graph (EG) of single level. Then for a class of bilevel EGs, their fixation probabilities are calculated and some propositions are discussed. The conclusion is obtained showing that the bilevel EG is more stable than the corresponding one-rooted EG.

scholarly journals The effect of initial reverse selection upon total selection response

1964 ◽  
Vol 5 (1) ◽  
pp. 68-79 ◽  
Author(s):  
J. S. Allan ◽  
Alan Robertson
Keyword(s):  
Population Size ◽  
Gene Frequency ◽  
Initial Period ◽  
Low Frequency ◽  
Selection Response ◽  
Selection Intensity ◽  
Forward Selection ◽  
Frequency Distributions ◽  
Gene Effect ◽  
Recessive Genes

A computer has been used to investigate the effect of an initial period of reverse selection on the subsequent response of a population to renewed forward selection with the same population size and selection intensity. As the computer was used to derive gene frequency distributions, there was no random element in the results obtained. A theoretical solution to the problem was obtained for genes with small effects.The process can be adequately described by the duration of the reverse selection (expressed in terms of the population size N), the product of population size and gene effect, Ns, and the initial gene frequency. If the duration of reverse selection, t, is less than N/2, the loss in selection advance due to the reverse selection is roughly t/N, though slightly greater than this for genes with low frequency. The ‘point of no return’ after which it is impossible, with the same population size and selection intensity, to return even to the starting frequency is 1·4N generations for genes with small effect and this declines as the gene effect increases.Some extension of results to recessive genes is also given.

Design and evaluation of progeny testing in open-nucleus breeding systems

1984 ◽  
Vol 38 (1) ◽  
pp. 1-8 ◽  
Author(s):  
J. P. Mueller ◽  
J. W. James
Keyword(s):  
Relative Efficiency ◽  
Individual Performance ◽  
Breeding Systems ◽  
High Fertility ◽  
Progeny Testing ◽  
Small Magnitude ◽  
Genetic Gains ◽  
Population Structures ◽  
Selection Intensities ◽  
Open Nucleus

ABSTRACTWhen comparing progeny-testing schemes with individual performance selection, one should use equivalent selection intensities and population structures in the two systems. Adapting formulae from open-nucleus theory, the relative efficiency of progeny testing has been tested for a range of heritabilities, fertility levels, upward gene-transfer rates, mating ratios and numbers of sires selected. In sheep and beef cattle breeding, the heritability of the trait under consideration has usually to be very low to make progeny testing worth-while. High fertility increases genetic gains but does not change the relative efficiency of progeny testing. Opening the nucleus to females from the base increases genetic gains and reduces relative efficiency of progeny testing, both effects being of small magnitude. For fixed mating ratios, only a small fraction of females should be in the nucleus, but for fixed sire numbers approximately one-third of the population should be mated to proven sires. In these analyses, variances were adjusted for the effects of repeated selection and for the effects due to mixing groups with different means. This adjustment did reduce absolute genetic gains, but did not change conclusions on progeny testing efficiency and optimum design.

The comparison of wheat-rye and wheat-Aegilops amphidiploids

1957 ◽  
Vol 49 (2) ◽  
pp. 246-250 ◽  
Author(s):  
Ralph Riley ◽  
Victor Chapman
Keyword(s):  
Chromosome Number ◽  
Breeding System ◽  
Diploid Species ◽  
The Self ◽  
Breeding Systems ◽  
Diploid Parent ◽  
Seed Fertility ◽  
Triticum Vulgare ◽  
Aegilops Longissima ◽  
Recessive Genes

1. The diploid species Secale cereale (2n= 14) is self-incompatible, Aegilops longissima (2n = 14) and A. caudata (2n = 14) are self-compatible. A. longissitna is usually self-pollinated and A. caudata is usually out-pollinated.2. Meiotic behaviour, constancy of chromosome number and seed fertility have been examined in the three octoploid amphidiploids derived from crosses of Triticum vulgare variety Holdfast (2n = 42) with S. cereale A. longissima and A. caudata respectively.3. All the amphidiploids had cells in which some chromosomes were unpaired at first metaphase of meiosis. This meiotic irregularity is not, therefore, related to the breeding system of the diploid parent.4. The fertility of the amphidiploids was not related to their meiotic regularity.5. The least fertile amphidiploid was derived from the self-incompatible diploid S. cereale. The most fertile amphidiploid was derived from the selfcompatible, self-pollinating diploid, A. longissima.6. It is suggested that the infertility of the wheatrye amphidiploid may result from interactions between genotypes adapted to different breeding systems, rather than from the homozygosity in the amphidiploid of deleterious recessive genes derived from the outbreeding rye parent.7. The demonstration of the independence of meiotic regularity and fertility will complicate selection work on wheat-rye amphidiploid material.

Open nucleus breeding systems

1977 ◽  
Vol 24 (3) ◽  
pp. 287-305 ◽  
Author(s):  
J. W. James
Keyword(s):  
Numerical Analysis ◽  
Genetic Gain ◽  
Breeding Systems ◽  
Generation Model ◽  
Selection Intensity ◽  
Base Population ◽  
Cattle Breeding ◽  
Discrete Generation ◽  
Nucleus Breeding ◽  
Open Nucleus

SUMMARYA theoretical analysis of open nucleus breeding systems, in which there is some introduction of breeding females to the sire breeding nucleus, is presented. Numerical analysis of a discrete generation model shows that the rate of genetic gain may be increased by 10 to 15% by opening the nucleus when selection intensity in females is low. In sheep and beef cattle breeding the optimal structure would be to have about 10% of the population in the nucleus, to get half of the nucleus female replacements from the base population, and to use all nucleus-born females not needed as nucleus replacements for breeding in the base population. The genetic gain, however, is not very sensitive to variation in these parameters. The rate of inbreeding in such an open nucleus would be about half that in a closed nucleus of the same size.

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