scholarly journals Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory

2019 ◽  
Vol 5 (7) ◽  
pp. eaav3842 ◽  
Author(s):  
Yipei Guo ◽  
Marija Vucelja ◽  
Ariel Amir
Keyword(s):  
Spin Glass ◽  
Fitness Landscape ◽  
Fitness Function ◽  
Metastable States ◽  
Hill Climbing ◽  
Type Model ◽  
Logarithmic Average ◽  
Glass Type ◽  
Average Fitness

Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hill-climbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect long-term fitness evolution. By using a spin-glass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.

scholarly journals Evolutionary Stability for Interactions among Kin under Quantitative Inheritance.

Genetics ◽  
1989 ◽  
Vol 121 (4) ◽  
pp. 877-889
Author(s):  
A B Harper
Keyword(s):  
Inclusive Fitness ◽  
Fitness Function ◽  
Quantitative Inheritance ◽  
Evolutionarily Stable Strategies ◽  
Environmental Variance ◽  
Pairwise Interactions ◽  
Simplifying Assumptions ◽  
Multilocus Model ◽  
Evolutionarily Stable

Abstract The theory of evolutionarily stable strategies (ESS) predicts the long-term evolutionary outcome of frequency-dependent selection by making a number of simplifying assumptions about the genetic basis of inheritance. I use a symmetrized multilocus model of quantitative inheritance without mutation to analyze the results of interactions between pairs of related individuals and compare the equilibria to those found by ESS analysis. It is assumed that the fitness changes due to interactions can be approximated by the exponential of a quadratic surface. The major results are the following. (1) The evolutionarily stable phenotypes found by ESS analysis are always equilibria of the model studied here. (2) When relatives interact, one of the two conditions for stability of equilibria differs between the two models; this can be accounted for by positing that the inclusive fitness function for quantitative characters is slightly different from the inclusive fitness function for characters determined by a single locus. (3) The inclusion of environmental variance will in general change the equilibrium phenotype, but the equilibria of ESS analysis are changed to the same extent by environmental variance. (4) A class of genetically polymorphic equilibria occur, which in the present model are always unstable. These results expand the range of conditions under which one can validly predict the evolution of pairwise interactions using ESS analysis.

scholarly journals Elevated nonlinearity as indicator of transition to overexploitation in fish stocks

2016 ◽  
Author(s):  
Vasilis Dakos ◽  
Sarah M. Glaser ◽  
Chih-hao Hsieh ◽  
George Sugihara
Keyword(s):  
Trophic Structure ◽  
Type Model ◽  
Western Atlantic ◽  
Economic Implications ◽  
Fish Stocks ◽  
As Species ◽  
Abrupt Changes ◽  
Risk Of Extinction ◽  
Statistical Metrics

AbstractEcosystems may experience abrupt changes such as species extinctions, reorganisations of trophic structure, or transitions from stable population dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we use a Ricker-type model to simulate the transition of a hypothetical stable fisheries population either to irregular boom-bust dynamics or to overexploitation. Our aim is to infer the risk of extinction in these two scenarios by comparing changes in variance, autocorrelation, and nonlinearity between unexploited and exploited populations. We find that changes in these statistical metrics reflect the risk of extinction but depend on the type of dynamical transition. Variance and nonlinearity increase similarly in magnitude along both transitions. In contrast, autocorrelation depends strongly on the presence of underlying oscillating dynamics. We also compare our theoretical expectations to indicators measured in long-term datasets of fish stocks from the California Cooperative Oceanic Fisheries Investigation in the Eastern Pacific and from the Northeast Shelf in the Western Atlantic. Our results suggest that elevated variance and nonlinearity could be potentially used to rank exploited fish populations according to their risk of extinction.

The shape of a defense-growth trade-off governs seasonal trait dynamics in natural phytoplankton

2018 ◽  
Author(s):  
Elias Ehrlich ◽  
Nadja J. Kath ◽  
Ursula Gaedke
Keyword(s):  
Fitness Landscape ◽  
Functional Trait ◽  
Grazing Pressure ◽  
Trait Variation ◽  
Trade Off ◽  
Community Persistence ◽  
Trade Offs ◽  
Combining Data ◽  
Persistence Theory

Functional trait compositions of communities can adapt to altered environmental conditions ensuring community persistence. Theory predicts that the shape of trade-offs between traits crucially affects these trait dynamics, but its empirical verification from the field is missing. Here, we show how the shape of a defense-growth trade-off governs seasonal trait dynamics of a natural community, using high-frequency, long-term measurements of phytoplankton from Lake Constance. As expected from the lab-derived concave trade-off curve, we observed an alternating dominance of several fast-growing species with intermediate defense levels and gradual changes of the biomass-trait distribution due to seasonally changing grazing pressure. By combining data and modelling, we obtain mechanistic insights on the underlying fitness landscape, and show that low fitness differences can maintain trait variation along the trade-off curve. We provide firm evidence for a frequently assumed trade-off and conclude that quantifying its shape allows to understand environmentally driven trait changes within communities.

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.

ChemInform Abstract: Spin-Glass-Type State in Complex Nonmagnetic Systems

ChemInform ◽  
2010 ◽  
Vol 41 (36) ◽  
pp. no-no
Author(s):  
E. E. Tareyeva ◽  
T. I. Schelkacheva ◽  
N. M. Chtchelkatchev
Keyword(s):  
Spin Glass ◽  
Glass Type

Metastable states of an asymmetric spin-glass with one stored pattern

1994 ◽  
Vol 94 (1-2) ◽  
pp. 187-193
Author(s):  
U. Geppert ◽  
M. Schreckenberg ◽  
J. Zittartz
Keyword(s):  
Spin Glass ◽  
Metastable States
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