scholarly journals Making the most of potential: potential games and genotypic convergence

2021 ◽  
Vol 8 (8) ◽  
pp. 210309
Author(s):  
Omer Edhan ◽  
Ziv Hellman ◽  
Ilan Nehama
Keyword(s):  
Growth Rate ◽  
Sexual Reproduction ◽  
Genetic Linkage ◽  
Convergence Rates ◽  
Exponential Convergence ◽  
Basins Of Attraction ◽  
Single Locus ◽  
Potential Game ◽  
Unified Theory ◽  
Varying Environments

We consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even under genetic linkage between loci) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem. To analyse varying environments, we introduce the concept of ‘virtual convergence’, under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.

scholarly journals Making the Most of Potential: Potential Games and Genotypic Convergence

2020 ◽  
Author(s):  
Omer Edhan ◽  
Ziv Hellman ◽  
Ilan Nehama
Keyword(s):  
Growth Rate ◽  
Linkage Disequilibrium ◽  
Sexual Reproduction ◽  
Convergence Rates ◽  
Exponential Convergence ◽  
Basins Of Attraction ◽  
Single Locus ◽  
Potential Game ◽  
Underlying Theory ◽  
Varying Environments

AbstractWe consider genotypic convergence of populations and show that under fixed fitness asexual and haploid sexual populations attain monomorphic convergence (even with linkage disequilibrium) to basins of attraction with locally exponential convergence rates; the same convergence obtains in single locus diploid sexual reproduction but to polymorphic populations. Furthermore, we show that there is a unified underlying theory underlying these convergences: all of them can be interpreted as instantiations of players in a potential game implementing a multiplicative weights updating algorithm to converge to equilibrium, making use of the Baum–Eagon Theorem. To analyse varying environments, we introduce the concept of ‘virtual convergence’, under which, even if fixation is not attained, the population nevertheless achieves the fitness growth rate it would have had under convergence to an optimal genotype. Virtual convergence is attained by asexual, haploid sexual, and multi-locus diploid reproducing populations, even if environments vary arbitrarily. We also study conditions for true monomorphic convergence in asexually reproducing populations in varying environments.

Lack of an association between heterozygosity and growth rate in the wood frog, Rana sylvatica

1995 ◽  
Vol 73 (3) ◽  
pp. 569-575 ◽  
Author(s):  
Michael F. Wright ◽  
Sheldon I. Guttman
Keyword(s):  
Growth Rate ◽  
Multiple Regression ◽  
Rana Sylvatica ◽  
Developmental Period ◽  
Wood Frog ◽  
Single Locus ◽  
Regression Analyses ◽  
Enzyme Loci ◽  
Effect On Growth

The effect of both multilocus and single-locus heterozygosity on growth rate was examined in a cohort of larvae of the wood frog, Rana sylvatica, collected from a pond during the later stages of premetamorphic development. Seven electrophoretically detected enzyme loci were used to determine individual heterozygosity, whereas the growth rate was measured as wet mass. In all cases, no significant correlation was found between multilocus heterozygosity and mass among larvae collected at intervals during the developmental period. In addition, multiple regression analyses indicated that no single locus had a demonstrable effect on growth rate. The results of this study, therefore, provide no evidence for a link between enzyme heterozygosity and growth rate during the later stages of premetamorphic development in wood frog larvae.

scholarly journals IMMUNOGLOBULIN ISOANTIGENS (ALLOTYPES) IN THE MOUSE

1965 ◽  
Vol 121 (3) ◽  
pp. 415-438 ◽  
Author(s):  
Leonard A. Herzenberg ◽  
Noel L. Warner ◽  
Leonore A. Herzenberg
Keyword(s):  
Genetic Linkage ◽  
Soluble Proteins ◽  
Single Locus ◽  
Mouse Strains ◽  
Cross Reactions ◽  
Chromosome Markers ◽  
New Methods ◽  
Sensitive Method

Eight antigens of 7S γ2-immunoglobulins controlled by alleles at a single locus Ig-1, have been identified in mice. This locus has previously been shown to determine antigenic specificities on the F fragments of 7S γ2a-globulins. The reactions of these antigens with various isoantisera have shown that the antigens all cross react with one another. New methods for the analysis of antigenic specificities of soluble proteins are presented in detail. A sensitive method for detecting in the order of 0.01 µg of these isoantigens has been developed, based on the quantitative inhibition of precipitation of I125-labeled antigen. Cross-reactions of the antigens were analysed in inhibition assays and the data is compatible with the existence of a minimum of eight antigenic specificities. Each of the antigens is composed of different combinations of these specificities, with only one antigen having a specificity not present in any other. Sixty-eight mouse strains have been tested with specific isoantisera, and on the basis of the results, have been placed into the eight allele groups. Evidence for close genetic linkage of the Ig-1 locus and 11 chromosome markers has been sought and not found.

The Genetic Architecture of Plant Defense Trade-offs in a Common Monkeyflower

2020 ◽  
Author(s):  
Nicholas J Kooyers ◽  
Abigail Donofrio ◽  
Benjamin K Blackman ◽  
Liza M Holeski
Keyword(s):  
Growth Rate ◽  
Plant Defense ◽  
Genetic Linkage ◽  
Genetic Architecture ◽  
Life History Traits ◽  
Total Concentration ◽  
Defense Compounds ◽  
Genetic Constraints ◽  
Trade Offs ◽  
Phenylpropanoid Glycosides

Abstract Determining how adaptive combinations of traits arose requires understanding the prevalence and scope of genetic constraints. Frequently observed phenotypic correlations between plant growth, defenses, and/or reproductive timing have led researchers to suggest that pleiotropy or strong genetic linkage between variants affecting independent traits is pervasive. Alternatively, these correlations could arise via independent mutations in different genes for each trait and extensive correlational selection. Here we evaluate these alternatives by conducting a quantitative trait loci (QTL) mapping experiment involving a cross between 2 populations of common monkeyflower (Mimulus guttatus) that differ in growth rate as well as total concentration and arsenal composition of plant defense compounds, phenylpropanoid glycosides (PPGs). We find no evidence that pleiotropy underlies correlations between defense and growth rate. However, there is a strong genetic correlation between levels of total PPGs and flowering time that is largely attributable to a single shared QTL. While this result suggests a role for pleiotropy/close linkage, several other QTLs also contribute to variation in total PPGs. Additionally, divergent PPG arsenals are influenced by a number of smaller-effect QTLs that each underlie variation in 1 or 2 PPGs. This result indicates that chemical defense arsenals can be finely adapted to biotic environments despite sharing a common biochemical precursor. Together, our results show correlations between defense and life-history traits are influenced by pleiotropy or genetic linkage, but genetic constraints may have limited impact on future evolutionary responses, as a substantial proportion of variation in each trait is controlled by independent loci.

scholarly journals EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS

2005 ◽  
Vol 15 (04) ◽  
pp. 575-622 ◽  
Author(s):  
MARTIN COSTABEL ◽  
MONIQUE DAUGE ◽  
CHRISTOPH SCHWAB
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell Equations ◽  
Maxwell's Equations ◽  
Convergence Rates ◽  
Exponential Convergence ◽  
Polygonal Domains ◽  
Time Harmonic ◽  
Standard Tool ◽  
Optimal Convergence Rates

The time-harmonic Maxwell equations do not have an elliptic nature by themselves. Their regularization by a divergence term is a standard tool to obtain equivalent elliptic problems. Nodal finite element discretizations of Maxwell's equations obtained from such a regularization converge to wrong solutions in any non-convex polygon. Modification of the regularization term consisting in the introduction of a weight restores the convergence of nodal FEM, providing optimal convergence rates for the h version of finite elements. We prove exponential convergence of hp FEM for the weighted regularization of Maxwell's equations in plane polygonal domains provided the hp-FE spaces satisfy a series of axioms. We verify these axioms for several specific families of hp finite element spaces.

Exponential convergence rates for weighted sums in noncommutative probability space

2016 ◽  
Vol 19 (04) ◽  
pp. 1650027 ◽  
Author(s):  
Byoung Jin Choi ◽  
Un Cig Ji
Keyword(s):  
Probability Space ◽  
Von Neumann Algebra ◽  
Convergence Rates ◽  
Exponential Convergence ◽  
Large Deviation ◽  
Type Inequality ◽  
Independent Random Variables ◽  
Weighted Sums ◽  
Noncommutative Probability ◽  
Von Neumann

We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.

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