scholarly journals Sustained fitness gains and variability in fitness trajectories in the long-term evolution experiment with Escherichia coli

2015 ◽  
Author(s):  
Richard E Lenski ◽  
Michael J Wiser ◽  
Noah Ribeck ◽  
Zachary D Blount ◽  
Joshua R Nahum ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Power Law ◽  
Hyperbolic Model ◽  
Significant Heterogeneity ◽  
Power Law Model ◽  
Constant Environment ◽  
Hard Limit ◽  
Evolution Experiment ◽  
Mean Fitness ◽  
Over Time

Many populations live in environments subject to frequent biotic and abiotic changes. Nonetheless, it is interesting to ask whether an evolving population's mean fitness can increase indefinitely, and potentially without any limit, even in a constant environment. A recent study showed that fitness trajectories of Escherichia coli populations over 50,000 generations were better described by a power-law model than by a hyperbolic model. According to the power-law model, the rate of fitness gain declines over time but fitness has no upper limit, whereas the hyperbolic model implies a hard limit. Here, we examine whether the previously estimated power-law model predicts the fitness trajectory for an additional 10,000 generations. To that end, we conducted more than 1100 new competitive fitness assays. Consistent with the previous study, the power-law model fits the new data better than the hyperbolic model. We also analysed the variability in fitness among populations, finding subtle, but significant, heterogeneity in mean fitness. Some, but not all, of this variation reflects differences in mutation rate that evolved over time. Taken together, our results imply that both adaptation and divergence can continue indefinitely-or at least for a long time-even in a constant environment.

scholarly journals Sustained fitness gains and variability in fitness trajectories in the long-term evolution experiment with Escherichia coli

2015 ◽  
Vol 282 (1821) ◽  
pp. 20152292 ◽  
Author(s):  
Richard E. Lenski ◽  
Michael J. Wiser ◽  
Noah Ribeck ◽  
Zachary D. Blount ◽  
Joshua R. Nahum ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Power Law ◽  
Hyperbolic Model ◽  
Significant Heterogeneity ◽  
Power Law Model ◽  
Constant Environment ◽  
Hard Limit ◽  
Evolution Experiment ◽  
Mean Fitness ◽  
Over Time

Many populations live in environments subject to frequent biotic and abiotic changes. Nonetheless, it is interesting to ask whether an evolving population's mean fitness can increase indefinitely, and potentially without any limit, even in a constant environment. A recent study showed that fitness trajectories of Escherichia coli populations over 50 000 generations were better described by a power-law model than by a hyperbolic model. According to the power-law model, the rate of fitness gain declines over time but fitness has no upper limit, whereas the hyperbolic model implies a hard limit. Here, we examine whether the previously estimated power-law model predicts the fitness trajectory for an additional 10 000 generations. To that end, we conducted more than 1100 new competitive fitness assays. Consistent with the previous study, the power-law model fits the new data better than the hyperbolic model. We also analysed the variability in fitness among populations, finding subtle, but significant, heterogeneity in mean fitness. Some, but not all, of this variation reflects differences in mutation rate that evolved over time. Taken together, our results imply that both adaptation and divergence can continue indefinitely—or at least for a long time—even in a constant environment.

scholarly journals A Comparison of Methods to Measure Fitness in Escherichia coli

2015 ◽  
Author(s):  
Michael J Wiser ◽  
Richard E Lenski
Keyword(s):  
Escherichia Coli ◽  
Traditional Method ◽  
Experimental Studies ◽  
Alternative Methods ◽  
Relative Fitness ◽  
Initial Population ◽  
Common Reference ◽  
Evolution Experiment ◽  
Mean Fitness ◽  
Changes Over Time

In order to characterize the dynamics of adaptation, it is important to be able to quantify how a population's mean fitness changes over time. Such measurements are especially important in experimental studies of evolution using microbes. The Long-Term Evolution Experiment (LTEE) with Escherichia coli provides one such system in which mean fitness has been measured by competing derived and ancestral populations. The traditional method used to measure fitness in the LTEE and many similar experiments, though, is subject to a potential limitation. As the relative fitness of the two competitors diverges, the measurement error increases because the less-fit population becomes increasingly small and cannot be enumerated as precisely. Here, we present and employ two alternatives to the traditional method. One is based on reducing the fitness differential between the competitors by using a common reference competitor from an intermediate generation that has intermediate fitness; the other alternative increases the initial population size of the less-fit, ancestral competitor. We performed a total of 480 competitions to compare the statistical properties of estimates obtained using these alternative methods with those obtained using the traditional method for samples taken over 50,000 generations from one of the LTEE populations. On balance, neither alternative method yielded measurements that were more precise than the traditional method.

scholarly journals Long-Term Experimental Evolution in Escherichia coli. VI. Environmental Constraints on Adaptation and Divergence

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 471-479 ◽  
Author(s):  
Michael Travisano
Keyword(s):  
Escherichia Coli ◽  
Genetic Variation ◽  
Experimental Evolution ◽  
Population Genetic ◽  
Environmental Constraints ◽  
Asymmetric Pattern ◽  
Nutrient Environment ◽  
Mean Fitness ◽  
Population Genetic Variation

The effect of environment on adaptation and divergence was examined in two sets of populations of Escherichia coli selected for 1000 generations in either maltose- or glucose-limited media. Twelve replicate populations selected in maltose-limited medium improved in fitness in the selected environment, by an average of 22.5%. Statistically significant among-population genetic variation for fitness was observed during the course of the propagation, but this variation was small relative to the fitness improvement. Mean fitness in a novel nutrient environment, glucose-limited medium, improved to the same extent as in the selected environment, with no statistically significant among-population genetic variation. In contrast, 12 replicate populations previously selected for 1000 generations in glucose-limited medium showed no improvement, as a group, in fitness in maltose-limited medium and substantial genetic variation. This asymmetric pattern of correlated responses suggests that small changes in the environment can have profound effects on adaptation and divergence.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals Unsteady thermal Maxwell power law nanofluid flow subject to forced thermal Marangoni Convection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Jawad ◽  
Anwar Saeed ◽  
Taza Gul ◽  
Zahir Shah ◽  
Poom Kumam
Keyword(s):  
Relaxation Time ◽  
Power Law ◽  
Marangoni Convection ◽  
Power Law Model ◽  
Analysis Method ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Welan Gum ◽  
Homotopy Analysis ◽  
Power Law Nanofluid

AbstractIn the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

scholarly journals X-ray Properties of 3C 111: Separation of Primary Nuclear Emission and Jet Continuum

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 219
Author(s):  
Elena Fedorova ◽  
B.I. Hnatyk ◽  
V.I. Zhdanov ◽  
A. Del Popolo
Keyword(s):  
Accretion Disk ◽  
Power Law ◽  
Line Emission ◽  
High Energy ◽  
Power Law Model ◽  
X Ray ◽  
Additional Information ◽  
Observational Dataset ◽  
Simple Power ◽  
Photon Index

3C111 is BLRG with signatures of both FSRQ and Sy1 in X-ray spectrum. The significant X-ray observational dataset was collected for it by INTEGRAL, XMM-Newton, SWIFT, Suzaku and others. The overall X-ray spectrum of 3C 111 shows signs of a peculiarity with the large value of the high-energy cut-off typical rather for RQ AGN, probably due to the jet contamination. Separating the jet counterpart in the X-ray spectrum of 3C 111 from the primary nuclear counterpart can answer the question is this nucleus truly peculiar or this is a fake “peculiarity” due to a significant jet contribution. In view of this question, our aim is to estimate separately the accretion disk/corona and non-thermal jet emission in the 3C 111 X-ray spectra within different observational periods. To separate the disk/corona and jet contributions in total continuum, we use the idea that radio and X-ray spectra of jet emission can be described by a simple power-law model with the same photon index. This additional information allows us to derive rather accurate values of these contributions. In order to test these results, we also consider relations between the nuclear continuum and the line emission.

Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface

1978 ◽  
Vol 45 (1) ◽  
pp. 19-24 ◽  
Author(s):  
V. Narayanamurthy ◽  
P. K. Sarma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Mathematical Formulation ◽  
Liquid Films ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Power Law Model ◽  
Falling Liquid Film ◽  
Falling Liquid Films ◽  
Special Case

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.

scholarly journals Erosion and Subsequent Transport State of Escherichia coli from Cowpats

2005 ◽  
Vol 71 (6) ◽  
pp. 2875-2879 ◽  
Author(s):  
Richard William Muirhead ◽  
Robert Peter Collins ◽  
Philip James Bremer
Keyword(s):  
Escherichia Coli ◽  
Surface Waters ◽  
Overland Flow ◽  
Single Cells ◽  
Rainfall Event ◽  
Buffer Strips ◽  
Simulated Rainfall ◽  
E Coli ◽  
Unattached Fraction ◽  
Over Time

ABSTRACT Processes by which fecal bacteria enter overland flow and their transportation state to surface waters are poorly understood, making the effectiveness of measures designed to intercept this pathway, such as vegetated buffer strips, difficult to predict. Freshly made and aged (up to 30 days) cowpats were exposed to simulated rainfall, and samples of the cowpat material and runoff were collected. Escherichia coli in the runoff samples were separated into attached (to particles) and unattached fractions, and the unattached fraction was analyzed to determine if the cells were clumped. Within cowpats, E. coli grew for 6 to 14 days, rather than following a typical logarithmic die-off curve. E. coli numbers in the runoff correlated with numbers inside the cowpat. Most of the E. coli organisms eroded from the cowpats were transported as single cells, and only a small percentage (about 8%) attached to particles. The erosion of E. coli from cowpats and the state in which the cells were transported did not vary with time within a single rainfall event or over time as the cowpats aged and dried out. These findings indicate that cowpats can remain a significant source of E. coli in overland flow for more than 30 days. As well, most of the E. coli organisms eroded from cowpats will occur as readily transportable single cells.

Validation of a Power Law Model in Upper Extremity Vessels: Potential Application in Ultrasound Bleed Detection

2012 ◽  
Vol 38 (4) ◽  
pp. 692-701 ◽  
Author(s):  
Aaron S. Wang ◽  
David H. Liang ◽  
Fritz Bech ◽  
Jason T. Lee ◽  
Christopher K. Zarins ◽  
...  
Keyword(s):  
Upper Extremity ◽  
Power Law ◽  
Potential Application ◽  
Power Law Model
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