Simulations in evolution. II. Relative fitness and the propagation of mutants.

In Neo-Darwinism, variation and natural selection are the two evolutionary mechanisms which propel biological evolution. Our previous article presented a histogram model [1] consisting in populations of individuals whose number changed under the influence of variation and/or fitness, the total population remaining constant. Individuals are classified into bins, and the content of each bin is calculated generation after generation by an Excel spreadsheet. Here, we apply the histogram model to a stable population with fitness F(1)=1.00 in which one or two fitter mutants emerge. In a first scenario, a single mutant emerged in the population whose fitness was greater than 1.00. The simulations ended when the original population was reduced to a single individual. The histogram model was validated by excellent agreement between its predictions and those of a classical continuous function (Eqn. 1) which predicts the number of generations needed for a favorable mutation to spread throughout a population. But in contrast to Eqn. 1, our histogram model is adaptable to more complex scenarios, as demonstrated here. In the second and third scenarios, the original population was present at time zero together with two mutants which differed from the original population by two higher and distinct fitness values. In the fourth scenario, the large original population was present at time zero together with one fitter mutant. After a number of generations, when the mutant offspring had multiplied, a second mutant was introduced whose fitness was even greater. The histogram model also allows Shannon entropy (SE) to be monitored continuously as the information content of the total population decreases or increases. The results of these simulations illustrate, in a graphically didactic manner, the influence of natural selection, operating through relative fitness, in the emergence and dominance of a fitter mutant.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Calcium reabsorption in the distal tubule: regulation by sodium, pH, and flow.

We developed a mathematical model of Ca transport along the late distal convoluted tubule (DCT2) and the connecting tubule (CNT) to investigate the mechanisms that regulate Ca reabsorption in the DCT2-CNT. The model accounts for apical Ca influx across transient receptor potential vanilloid 5 (TRPV5) channels and basolateral Ca efflux via plasma membrane Ca-ATPase pumps and type 1 Na/Ca exchangers (NCX1). Model simulations reproduce experimentally observed variations in Ca uptake as a function of extracellular pH, Na, and Mg concentration. Our results indicate that amiloride enhances Ca reabsorption in the DCT2-CNT predominantly by increasing the driving force across NCX1, thereby stimulating Ca efflux. They also suggest that because aldosterone upregulates both apical and basolateral Na transport pathways, it has a lesser impact on Ca reabsorption than amiloride. Conversely, the model predicts that full NCX1 inhibition and parathyroidectomy each augment the Ca load delivered to the collecting duct severalfold. In addition, our results suggest that regulation of TRPV5 activity by luminal pH has a small impact, per se, on transepithelial Ca fluxes; the reduction in Ca reabsorption induced by metabolic acidosis likely stems from decreases in TRPV5 expression. In contrast, elevations in luminal Ca are predicted to significantly decrease TRPV5 activity via the Ca-sensing receptor. Nevertheless, following the administration of furosemide, the calcium-sensing receptor-mediated increase in Ca reabsorption in the DCT2-CNT is calculated to be insufficient to prevent hypercalciuria. Altogether, our model predicts complex interactions between calcium and sodium reabsorption in the DCT2-CNT.

Comparison between molecular dynamics abd Monte Carlo simulations of an ordering process in a binary alloy

Ordering in a binary alloy is studied by means of a molecular-dynamics (MD) algorithm which allows to reach the domain growth regime. Results are compared with Monte Carlo simulations using a realistic vacancy-atom (MC-VA) mechanism. At low temperatures fast growth with a dynamical exponent x>1/2 is found for MD and MC-VA. The study of a nonequilibrium ordering process with the two methods shows the importance of the nonhomogeneity of the excitations in the system for determining its macroscopic kinetics.

Decay of unstable states in the presence of colored noise and random initial conditions. II. Analog experiments and digital simulations

The decay of an unstable state under the influence of external colored noise has been studied by means of analog experiments and digital simulations. For both fixed and random initial conditions, the time evolution of the second moment ¿x2(t)¿ of the system variable was determined and then used to evaluate the nonlinear relaxation time. The results obtained are found to be in excellent agreement with the theoretical predictions of the immediately preceding paper [Casademunt, Jiménez-Aquino, and Sancho, Phys. Rev. A 40, 5905 (1989)].

Simulations of electrophoretic collisions of DNA knots with gel obstacles

Gel electrophoresis can be used to separate nicked circular DNA molecules of equal length but forming different knot types. At low electric fields, complex knots drift faster than simpler knots. However, at high electric field the opposite is the case and simpler knots migrate faster than more complex knots. Using Monte Carlo simulations we investigate the reasons of this reversal of relative order of electrophoretic mobility of DNA molecules forming different knot types. We observe that at high electric fields the simulated knotted molecules tend to hang over the gel fibres and require passing over a substantial energy barrier to slip over the impeding gel fibre. At low electric field the interactions of drifting molecules with the gel fibres are weak and there are no significant energy barriers that oppose the detachment of knotted molecules from transverse gel fibres.

External fluctuations in a pattern-forming instability

The effect of external fluctuations on the formation of spatial patterns is analyzed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e., produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.

Colored noise in spatially extended systems

We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a time-dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled by both the correlation time and length of the noise. A Fokker-Planck equation and the steady probability density of the process are obtained by means of a theoretical approximation.

Magnetic structure of Li2CuO2: From ab initio calculations to macroscopic simulations

The magnetic structure of the edge-sharing cuprate compound Li2CuO2 has been investigated with highly correlated ab initio electronic structure calculations. The first- and second-neighbor in-chain magnetic interactions are calculated to be 142 and -22 K, respectively. The ratio between the two parameters is smaller than suggested previously in the literature. The interchain interactions are antiferromagnetic in nature and of the order of a few K only. Monte Carlo simulations using the ab initio parameters to define the spin model Hamiltonian result in a Nel temperature in good agreement with experiment. Spin population analysis situates the magnetic moment on the copper and oxygen ions between the completely localized picture derived from experiment and the more delocalized picture based on local-density calculations.