scholarly journals Error thresholds and stationary mutant distributions in multi-locus diploid genetics models

1994 ◽  
Vol 63 (1) ◽  
pp. 63-78 ◽  
Author(s):  
Paul G. Higgs
Keyword(s):  
Sexual Reproduction ◽  
Fitness Landscape ◽  
Natural Populations ◽  
Error Threshold ◽  
Sharp Transition ◽  
Epistatic Interactions ◽  
Sexual Population ◽  
Mean Fitness ◽  
The Mean ◽  
Parameter Values

SummaryWe study multi-locus models for the accumulation of disadvantagenous mutant alleles in diploid populations. The theory used is closely related to the quasi-species theory of molecular evolution. The stationary mutant distribution may either be localized close to a peak in the fitness landscape or delocalized throughout sequence space. In some cases there is a sharp transition between these two cases known as an error threshold. We study a multiplicative fitness landscape where the fitness of an individual with j homozygous mutant loci and k heterozygous loci is wjk = (1 − s)j (1 − hs)k. For a sexual population in this landscape there are two types of solution separated by an error threshold. For a parthenogenetic population there may be three types of solution and two error thresholds for some values of h. For a population reproducing by selfing the solution is independent of h, since the frequency of heterozygous individuals is negligible. The mean fitnesses of the populations depend on the reproductive method even for the multiplicative landscape. The sexual may have a higher or lower fitness than the parthenogen, depending on the values of h and u/s. Selfing leads to a higher mean fitness than either sexual reproduction or parthenogenesis. We also study a fitness landscape with epistatic interactions with wjk = exp(− s(2j + k)α). The sexual population has a higher fitness than the parthenogen when α > 1. This confirms previous theories that sexual reproduction is advantageous in cases of synergistic epistasis. The mean fitness of a selfing population was found to be higher than both the sexual and the parthenogen over the range of parameter values studied. We discuss these results in relation to the theory of the evolution of sex. The fitness of the stationary distribution in cases where unfavourable mutations accumulation is one factor which could explain the observed prevalence of sexual reproduction in natural populations, although other factors may be more important in many cases.

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.

scholarly journals Adaptive fitness landscape for replicator systems: to maximize or not to maximize

2018 ◽  
Vol 13 (3) ◽  
pp. 25 ◽  
Author(s):  
Alexander S. Bratus ◽  
Yuri S. Semenov ◽  
Artem S. Novozhilov
Keyword(s):  
Natural Selection ◽  
Fitness Landscape ◽  
Evolutionary Process ◽  
Hill Climbing ◽  
Adaptive Landscape ◽  
Basic Model ◽  
Mean Fitness ◽  
The Mean ◽  
The Hill ◽  
Fisher’S Fundamental Theorem

Sewall Wright’s adaptive landscape metaphor penetrates a significant part of evolutionary thinking. Supplemented with Fisher’s fundamental theorem of natural selection and Kimura’s maximum principle, it provides a unifying and intuitive representation of the evolutionary process under the influence of natural selection as the hill climbing on the surface of mean population fitness. On the other hand, it is also well known that for many more or less realistic mathematical models this picture is a severe misrepresentation of what actually occurs. Therefore, we are faced with two questions. First, it is important to identify the cases in which adaptive landscape metaphor actually holds exactly in the models, that is, to identify the conditions under which system’s dynamics coincides with the process of searching for a (local) fitness maximum. Second, even if the mean fitness is not maximized in the process of evolution, it is still important to understand the structure of the mean fitness manifold and see the implications of this structure on the system’s dynamics. Using as a basic model the classical replicator equation, in this note we attempt to answer these two questions and illustrate our results with simple well studied systems.

scholarly journals On the environmental zero-point problem in microevolutionary climate response predictions

2022 ◽  
Author(s):  
Rolf Ergon
Keyword(s):  
Phenotypic Plasticity ◽  
Zero Point ◽  
Mean Value ◽  
Environmental Data ◽  
Global Maximum ◽  
Point Problem ◽  
Microevolutionary Change ◽  
Mean Fitness ◽  
The Mean ◽  
Parameter Values

It is well documented that populations adapt to climate change by means of phenotypic plasticity, but few reports on adaptation by means of genetically based microevolution caused by selection. Disentanglement of these separate effects requires that the environmental zero-point is defined, and this should not be done arbitrarily. Together with parameter values, the zero-point can be estimated from environmental, phenotypic and fitness data. A prediction error method for this purpose is described, with the feasibility shown by simulations. An estimated environmental zero-point may have large errors, especially for small populations, but may still be a better choice than use of an initial environmental value in a recorded time series, or the mean value, which is often used. Another alternative may be to use the mean value of a past and stationary stochastic environment, which the population is judged to have been fully adapted to, in the sense that the mean fitness was at a global maximum. An exception is here cases with constant phenotypic plasticity, where the microevolutionary change per generation follows directly from phenotypic and environmental data, independent of the chosen environmental zero-point.

scholarly journals Genotype-environment interactions and the maintenance of polygenic variation.

Genetics ◽  
1989 ◽  
Vol 121 (1) ◽  
pp. 129-138 ◽  
Author(s):  
J H Gillespie ◽  
M Turelli
Keyword(s):  
Genetic Variance ◽  
Balancing Selection ◽  
Additive Genetic Variance ◽  
Natural Populations ◽  
Extensive Literature ◽  
Multilocus Genotype ◽  
Polygenic Inheritance ◽  
Mean Fitness ◽  
The Mean ◽  
Polygenic Variation

Abstract Genotype-environment interactions may be a potent force maintaining genetic variation in quantitative traits in natural populations. This is shown by a simple model of additive polygenic inheritance in which the additive contributions of alleles vary with the environment. Under simplifying symmetry assumptions, the model implies that the variance of the phenotypes produced across environments by a multilocus genotype decreases as the number of heterozygous loci increases. In the region of an optimal phenotype, the mapping from the quantitative trait into fitness is concave, and the mean fitness of a genotype will increase with the number of heterozygous loci. This leads to balancing selection, polymorphism, and potentially high levels of additive genetic variance, even though all allelic effects remain additive within each specific environment. An important implication of the model is that the variation maintained by genotype-environment interactions is difficult to study with the restricted range of environments represented in typical experiments. In particular, if fluctuations in allelic effects are pervasive, as suggested by the extensive literature on genotype-environment interactions, efforts to estimate genetic parameters in a single environment may be of limited value.

scholarly journals Resampling the pool of genotypic possibilities: an adaptive function of sexual reproduction

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Donal A. Hickey ◽  
G. Brian Golding
Keyword(s):  
Genetic Variation ◽  
Natural Selection ◽  
Sexual Reproduction ◽  
Finite Population ◽  
Natural Populations ◽  
Initial Population ◽  
Adaptive Function ◽  
Asexual Population ◽  
Sexual Population ◽  
The Universe

Abstract Background Natural populations harbor significant levels of genetic variability. Because of this standing genetic variation, the number of possible genotypic combinations is many orders of magnitude greater than the population size. This means that any given population contains only a tiny fraction of all possible genotypic combinations. Results We show that recombination allows a finite population to resample the genotype pool, i.e., the universe of all possible genotypic combinations. Recombination, in combination with natural selection, enables an evolving sexual population to replace existing genotypes with new, higher-fitness genotypic combinations that did not previously exist in the population. This process allows the sexual population to gradually increase its fitness far beyond the range of fitnesses in the initial population. In contrast to this, an asexual population is limited to selection among existing lower fitness genotypes. Conclusions The results provide an explanation for the ubiquity of sexual reproduction in evolving natural populations, especially when natural selection is acting on the standing genetic variation.

scholarly journals Estimation of Deleterious-Mutation Parameters in Natural Populations

Genetics ◽  
1996 ◽  
Vol 144 (1) ◽  
pp. 349-360 ◽  
Author(s):  
Hong-Wen Deng ◽  
Michael Lynch
Keyword(s):  
Genetic Variance ◽  
Deleterious Mutation ◽  
Natural Populations ◽  
Breeding Systems ◽  
Deleterious Mutations ◽  
Empirical Estimates ◽  
Mean Fitness ◽  
The Mean ◽  
New Mutations

Abstract The rate and average effects of spontaneous deleterious mutations are important determinants of the evolution of breeding systems and of the vulnerability of small populations to extinction. Nevertheless, few attempts have been made to estimate the properties of such mutations, and those studies that have been performed have been extremely labor intensive, relying on long-term, laboratory mutation-accumulation experiments. We present an alternative to the latter approach. For populations in which the genetic variance for fitness is a consequence of selection-mutation balance, the mean fitness and genetic variance of fitness in outbred and inbred generations can be expressed as simple functions of the genomic mutation rate, average homozygous effect and average dominance coefficient of new mutations. Using empirical estimates for the mean and genetic variance of fitness, these expressions can then be solved to obtain joint estimates of the deleterious-mutation parameters. We employ computer simulations to evaluate the degree of bias of the estimators and present some general recommendations on the application of the technique. Our procedures provide some hope for obtaining estimates of the properties of deleterious mutations from a wide phylogenetic range of species as well as a mechanism for testing the validity of alternative models for the maintenance of genetic variance for fitness.

Estimation of Deleterious Genomic Mutation Parameters in Natural Populations by Accounting for Variable Mutation Effects Across Loci

Genetics ◽  
2002 ◽  
Vol 162 (3) ◽  
pp. 1487-1500 ◽  
Author(s):  
Hong-Wen Deng ◽  
Guimin Gao ◽  
Jin-Long Li
Keyword(s):  
Statistical Method ◽  
Mutation Rate ◽  
Genetic Variance ◽  
Natural Populations ◽  
Evolutionary Genetics ◽  
Simulation Studies ◽  
Fitness Effects ◽  
Mean Fitness ◽  
The Mean ◽  
Genomic Mutation

Abstract The genomes of all organisms are subject to continuous bombardment of deleterious genomic mutations (DGM). Our ability to accurately estimate various parameters of DGM has profound significance in population and evolutionary genetics. The Deng-Lynch method can estimate the parameters of DGM in natural selfing and outcrossing populations. This method assumes constant fitness effects of DGM and hence is biased under variable fitness effects of DGM. Here, we develop a statistical method to estimate DGM parameters by considering variable mutation effects across loci. Under variable mutation effects, the mean fitness and genetic variance for fitness of parental and progeny generations across selfing/outcrossing in outcrossing/selfing populations and the covariance between mean fitness of parents and that of their progeny are functions of DGM parameters: the genomic mutation rate U, average homozygous effect s, average dominance coefficient h, and covariance of selection and dominance coefficients cov(h, s). The DGM parameters can be estimated by the algorithms we developed herein, which may yield improved estimation of DGM parameters over the Deng-Lynch method as demonstrated by our simulation studies. Importantly, this method is the first one to characterize cov(h, s) for DGM.

scholarly journals Epistasis and the Mutation Load: A Measurement-Theoretical Approach

Genetics ◽  
2001 ◽  
Vol 158 (1) ◽  
pp. 477-485
Author(s):  
Thomas F Hansen ◽  
Günter P Wagner
Keyword(s):  
Epistatic Interaction ◽  
Gene Interaction ◽  
Gene Interactions ◽  
Mutation Load ◽  
Epistatic Interactions ◽  
Synergistic Interactions ◽  
Empirical Estimates ◽  
Selection Equilibrium ◽  
Mean Fitness ◽  
The Mean

Abstract An approximate solution for the mean fitness in mutation-selection balance with arbitrary order of epistatic interaction is derived. The solution is based on the assumptions of coupling equilibrium and that the interaction effects are multilinear. We find that the effect of m-order epistatic interactions (i.e., interactions among groups of m loci) on the load is dependent on the total genomic mutation rate, U, to the mth power. Thus, higher-order gene interactions are potentially important if U is large and the interaction density among loci is not too low. The solution suggests that synergistic epistasis will decrease the mutation load and that variation in epistatic effects will elevate the load. Both of these results, however, are strictly true only if they refer to epistatic interaction strengths measured in the optimal genotype. If gene interactions are measured at mutation-selection equilibrium, only synergistic interactions among even numbers of genes will reduce the load. Odd-ordered synergistic interactions will then elevate the load. There is no systematic relationship between variation in epistasis and load at equilibrium. We argue that empirical estimates of gene interaction must pay attention to the genetic background in which the effects are measured and that it may be advantageous to refer to average interaction intensities as measured in mutation-selection equilibrium. We derive a simple criterion for the strength of epistasis that is necessary to overcome the twofold disadvantage of sex.

scholarly journals Rapid review of available evidence on the serial interval and generation time of COVID-19

BMJ Open ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. e040263
Author(s):  
John Griffin ◽  
Miriam Casey ◽  
Áine Collins ◽  
Kevin Hunt ◽  
David McEvoy ◽  
...  
Keyword(s):  
Generation Time ◽  
Social Contact ◽  
Careful Consideration ◽  
Rapid Review ◽  
Eligibility Criteria ◽  
Reproduction Numbers ◽  
Serial Interval ◽  
Scientific Papers ◽  
The Mean ◽  
Parameter Values

The serial interval is the time between symptom onsets in an infector–infectee pair. The generation time, also known as the generation interval, is the time between infection events in an infector–infectee pair. The serial interval and the generation time are key parameters for assessing the dynamics of a disease. A number of scientific papers reported information pertaining to the serial interval and/or generation time for COVID-19. Objective Conduct a review of available evidence to advise on appropriate parameter values for serial interval and generation time in national COVID-19 transmission models for Ireland and on methodological issues relating to those parameters. Methods We conducted a rapid review of the literature covering the period 1 January 2020 and 21 August 2020, following predefined eligibility criteria. Forty scientific papers met our inclusion criteria and were included in the review. Results The mean of the serial interval ranged from 3.03 to 7.6 days, based on 38 estimates, and the median from 1.0 to 6.0 days (based on 15 estimates). Only three estimates were provided for the mean of the generation time. These ranged from 3.95 to 5.20 days. One estimate of 5.0 days was provided for the median of the generation time. Discussion Estimates of the serial interval and the generation time are very dependent on the specific factors that apply at the time that the data are collected, including the level of social contact. Consequently, the estimates may not be entirely relevant to other environments. Therefore, local estimates should be obtained as soon as possible. Careful consideration should be given to the methodology that is used. Real-time estimations of the serial interval/generation time, allowing for variations over time, may provide more accurate estimates of reproduction numbers than using conventionally fixed serial interval/generation time distributions.

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