scholarly journals Dynamics of fitness distributions in the presence of a phenotypic optimum: an integro-differential approach

2018 ◽  
Author(s):  
M.-E. Gil ◽  
F. Hamel ◽  
G. Martin ◽  
L. Roques
Keyword(s):  
Sufficient Conditions ◽  
Geometrical Model ◽  
Nonlinear Transport ◽  
Asexual Population ◽  
Nonlinear Transport Equation ◽  
Fitness Value ◽  
Mean Fitness ◽  
Phenotype Space ◽  
Fitness Distribution ◽  
Concentration Phenomenon

AbstractWe propose an integro-differential description of the dynamics of the fitness distribution in an asexual population under mutation and selection, in the presence of a phenotype optimum. Due to the presence of this optimum, the distribution of mutation effects on fitness depends on the parent’s fitness, leading to a non-standard equation with “context-dependent" mutation kernels.Under general assumptions on the mutation kernels, which encompass the standardndimensional Gaussian Fisher’s geometrical model (FGM), we prove that the equation admits a unique time-global solution. Furthermore, we derive a nonlocal nonlinear transport equation satisfied by the cumulant generating function of the fitness distribution. As this equation is the same as the equation derived by Martin and Roques (2016) while studying stochastic Wright-Fisher-type models, this shows that the solution of the main integro-differential equation can be interpreted as the expected distribution of fitness corresponding to this type of microscopic models, in a deterministic limit. Additionally, we give simple sufficient conditions for the existence/non-existence of a concentration phenomenon at the optimal fitness value, i.e, of a Dirac mass at the optimum in the stationary fitness distribution. We show how it determines a phase transition, as mutation rates increase, in the value of the equilibrium mean fitness at mutation-selection balance. In the particular case of the FGM, consistently with previous studies based on other formalisms (Waxman and Peck, 1998, 2006), the condition for the existence of the concentration phenomenon simply requires that the dimensionnof the phenotype space be larger than or equal to 3 and the mutation rateUbe smaller than some explicit threshold.The accuracy of these deterministic approximations are further checked by stochastic individual-based simulations.

scholarly journals Segregation and the Evolution of Sex Under Overdominant Selection

Genetics ◽  
2003 ◽  
Vol 164 (3) ◽  
pp. 1119-1128 ◽  
Author(s):  
Elie S Dolgin ◽  
Sarah P Otto
Keyword(s):  
Correlated Response ◽  
Heterozygote Advantage ◽  
Genetic Associations ◽  
Asexual Population ◽  
Modifier Locus ◽  
Sexual And Asexual Reproduction ◽  
Overdominant Selection ◽  
Mean Fitness ◽  
Changes Over Time ◽  
Inbred Populations

AbstractThe segregation of alleles disrupts genetic associations at overdominant loci, causing a sexual population to experience a lower mean fitness compared to an asexual population. To investigate whether circumstances promoting increased sex exist within a population with heterozygote advantage, a model is constructed that monitors the frequency of alleles at a modifier locus that changes the relative allocation to sexual and asexual reproduction. The frequency of these modifier alleles changes over time as a correlated response to the dynamics at a fitness locus under overdominant selection. Increased sex can be favored in partially sexual populations that inbreed to some extent. This surprising finding results from the fact that inbred populations have an excess of homozygous individuals, for whom sex is always favorable. The conditions promoting increased levels of sex depend on the selection pressure against the homozygotes, the extent of sex and inbreeding in the population, and the dominance of the invading modifier allele.

scholarly journals PI Controllers for 1-D Nonlinear Transport Equation

2019 ◽  
Vol 64 (11) ◽  
pp. 4570-4582 ◽  
Author(s):  
Jean-Michel Coron ◽  
Amaury Hayat
Keyword(s):  
Transport Equation ◽  
Nonlinear Transport ◽  
Nonlinear Transport Equation ◽  
Pi Controllers

The nonlinear transport equation with delayed neutrons

1997 ◽  
Vol 26 (1-2) ◽  
pp. 153-165 ◽  
Author(s):  
Li Xuezhi ◽  
Hao Yong
Keyword(s):  
Transport Equation ◽  
Nonlinear Transport ◽  
Delayed Neutrons ◽  
Nonlinear Transport Equation

scholarly journals The relationship between robustness and evolution

2018 ◽  
Author(s):  
Pengyao Jiang ◽  
Martin Kreitman ◽  
John Reinitz
Keyword(s):  
Genetic Model ◽  
Initial Conditions ◽  
Genetic Locus ◽  
Genetic Mutation ◽  
Population Mean ◽  
Fitness Value ◽  
The Face ◽  
Evolutionary Trajectories ◽  
Mean Fitness ◽  
Developmental Noise

AbstractDevelopmental robustness (canalization) is a common attribute of traits in multi-cellular organisms. High robustness ensures the reproducibility of phenotypes in the face of environmental and developmental noise, but it also dampens the expression of genetic mutation, the fuel for adaptive evolution. A reduction in robustness may therefore be adaptive under certain evolutionary scenarios. To better understand how robustness influences phenotypic evolution, and to decipher conditions under which canalization itself evolves, a genetic model was constructed in which phenotype is explicitly represented as a collection of traits, calculated from genotype, and the degree of robustness can be explicitly controlled. The genes were sub jected to mutation, altering phenotype and fitness. We then simulated the dynamics of a population evolving under two classes of initial conditions, one in which the population is at a fitness optimum and one in which it is far away. The model is formulated with two robustness parameters in the genotype to phenotype map, controlling robustness over a tight (γ) or a broad (α) range of values. Within the robustness range determined by γ, high robustness results in a equilibrium population fitness closer to the optimal fitness value than low robustness. High robustness should be favored, therefore, under a constant optimal environment. This situation reverses when populations are challenged to evolve to a new phenotype optimum. In this situation, low robustness populations adapt faster than high robustness populations and reach higher equilibrium mean fitness. A larger set of phenotypes are accessable by mutation when robustness is low, in part explaining why low robustness is favored under this condition. A larger range of robustness could be sampled by varying α, revealing a complex relationship between robustness and both the initial rate of phenotypic adaptation as well as the final equilibrium population mean fitness. Intermediate values of α produced a bifurcation in evolutionary trajectories, with some populations remaining at low population mean fitness, and others escaping to achieve high population mean fitness. We then allowed robustness itself to be encoded by a mutable genetic locus that could co-evolve along with the phenotype under selection. Low robustness genotypes are initially favored when adapting to a new optimal phenotype. A high robustness genotype then replaces it, well before maximum fitness is achieved, and moreover appears to prevent further invasion into the population of a low-robustness genotype. This phenomenon was dependent on having tight linkage (and sufficiently low mutation rate) between the robustness locus and the loci encoding phenotype.

scholarly journals Stress-induced mutagenesis and complex adaptation

2014 ◽  
Vol 281 (1792) ◽  
pp. 20141025 ◽  
Author(s):  
Yoav Ram ◽  
Lilach Hadany
Keyword(s):  
Natural Selection ◽  
Deleterious Mutation ◽  
Raw Material ◽  
Mutation Rates ◽  
Asexual Population ◽  
Trade Off ◽  
Response To Stress ◽  
Mean Fitness ◽  
Induced Mutagenesis ◽  
Theoretical Results

Because mutations are mostly deleterious, mutation rates should be reduced by natural selection. However, mutations also provide the raw material for adaptation. Therefore, evolutionary theory suggests that the mutation rate must balance between adaptability —the ability to adapt—and adaptedness —the ability to remain adapted. We model an asexual population crossing a fitness valley and analyse the rate of complex adaptation with and without stress-induced mutagenesis (SIM)—the increase of mutation rates in response to stress or maladaptation. We show that SIM increases the rate of complex adaptation without reducing the population mean fitness, thus breaking the evolutionary trade-off between adaptability and adaptedness . Our theoretical results support the hypothesis that SIM promotes adaptation and provide quantitative predictions of the rate of complex adaptation with different mutational strategies.

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