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In this work, we consider a gradostat made up of several chemostats coupled by migrations of substrates and products between them. We seek maximum product synthesis or maximum sustainable yield by optimizing with the dilution rate. The mathematical study of the complete model is carried out by searching equilibrium points and stability. We compare the overall maximal synthesis of the system of coupled chemostats to the sum of the maximal syntheses of isolated chemostats. We show that in the homogeneous case where all the chemostats are identical, the difference between the maximum synthesis of the system of coupled chemostats and the sum of the maximum syntheses of the isolated chemostats or excess yield cannot be positive. We show that the excess yield can be positive only in the heterogeneous case. In these cases, under some conditions, the coupling of chemostats can make it possible to obtain a higher productivity compared to the case of isolated chemostats. We illustrate our theoretical results with numerical simulations with various examples corresponding to slow and fast migrations.

Color plays a key role in human vision but the neural machinery that underlies the transformation from stimulus to perception is not well understood. Here, we implemented a two-dimensional network model of the first stages in the primate parvocellular pathway (retina, lateral geniculate nucleus and layer 4C$\beta$ in V1) consisting of conductance-based point neurons. Model parameters were tuned based on physiological and anatomical data from the primate foveal and parafoveal vision, the most relevant visual field areas for color vision. We exhaustively benchmarked the model against well-established chromatic and achromatic visual stimuli, showing spatial and temporal responses of the model to disk- and ring-shaped light flashes, spatially uniform squares and sine-wave gratings of varying spatial frequency. The spatiotemporal patterns of parvocellular cells and cortical cells are consistent with their classification into chromatically single-opponent and double-opponent groups, and nonopponent cells selective for luminance stimuli. The model was implemented in the widely used neural simulation tool NEST and released as open source software. The aim of our modeling is to provide a biologically realistic framework within which a broad range of neuronal interactions can be examined at several different levels, with a focus on understanding how color information is processed.

We present a dynamic model of a population under selection pressure and in a changing habitat. Two kinds of changes are considered: In the first climate changes in one direction only, like in coming of the glacial era; in the second, the changes are randomly fluctuating. We compare four evolutionary strategies: First: evolution without any external influence; second: evolution where ill-fitted individuals are eliminated; third: where the phenotypes of the progeny are improved to make them better fit to the existing conditions, and finally evolution where the last two procedures are applied together. We show that the systematic phenotype improvement is the most successful strategy in the long run and the elimination of the ill-fitted almost always leads to a disaster.

We derive catastrophic senescence of the Pacific salmon from an aging model which was recently proposed by Stauffer. The model is based on the postulates of a minimum reproduction age and a maximal genetic lifespan. It allows for self-organization of a typical age of first reproduction and a typical age of death. Our Monte Carlo simulations of the population dynamics show that the model leads to catastrophic senescence for semelparous reproduction as it occurs in the case of salmon, to a more gradually increase of senescence for iteroparous reproduction.

Inspired by the work of Ray et al., we study a model of predator-prey dynamics that incorporates the effects of a discrete genotype. We thoroughly analyze the many features of the model, and show that the system seems to reach a critical state in the genotype space, with some evidence of self-organization. Our results present the effects of natural selection at work in genotype space. The presence of the discrete genotype seems to make the model more robust to small variations of the main parameters, when compared to the bare Lotka–Volterra dynamics.

It is shown that if the computer model of biological aging proposed by Stauffer is modified such that the late reproduction is privileged, then the Gompertz law of exponential increase of mortality can be retrieved.

Using a bit string model, we show that asexual reproduction for diploids is more efficient than for haploids: it improves genetic material producing new individuals with less deleterious mutations. We also see that in a system where competition is present, diploids dominate, even though we consider some dominant loci.

The social effects of wolf pack survival are simulated by combining the Makowiec model with Stauffer's simple aging model.

We use a simple model for biological aging to study the mortality of the population, obtaining a good agreement with the Gompertz law. We also simulate the same model on a square lattice, considering different strategies of parental care. The results are in agreement with those obtained earlier with the more complicated Penna model for biological aging. Finally, we present the sexual version of this simple model.

Complementarity is one of the main features underlying the interactions in biological and biochemical systems. Inspired by those systems we propose a model for the dynamical evolution of a system composed of agents that interact due to their complementary attributes rather than their similarities. Each agent is represented by a bit-string and has an activity associated to it; the coupling among complementary peers depends on their activity. The connectivity of the system changes in time respecting the constraint of complementarity. We observe the formation of a network of active agents whose stability depends on the rate at which activity of agents diffuses in the system. The model exhibits a nonequilibrium phase transition between the ordered phase, where a stable network is generated, and a disordered phase characterized by the absence of correlation among the agents. The ordered phase exhibits multi-modal distributions of connectivity and activity, indicating a hierarchy of interaction among different populations characterized by different degrees of activity. This model may be used to study the hierarchy observed in social organizations.

In this work, we study the critical behavior of an epidemic propagation model that considers individuals that can develop drug resistance. In our lattice model, each site can be found in one of the four states: empty, healthy, normally infected (not drug resistant) and strain infected (drug resistant) states. The most relevant parameters in our model are related to the mortality, cure and mutation rates. This model presents two distinct stationary active phases: a phase with co-existing normal and drug resistant infected individuals, and an intermediate active phase with only drug resistant individuals. We employed a finite-size scaling analysis to compute the critical points and the critical exponents, β/ν and 1/ν, governing the phase transitions between these active states and the absorbing inactive state. Our results are consistent with the hypothesis that these transitions belong to the directed percolation universality class.

We consider the spreading and competition of languages that are spoken by a population of individuals. The individuals can change their mother tongue during their lifespan, pass on their language to their offspring and finally die. The languages are described by bitstrings, their mutual difference is expressed in terms of their Hamming distance. Language evolution is determined by mutation and adaptation rates. In particular we consider the case where the replacement of a language by another one is determined by their mutual Hamming distance. As a function of the mutation rate we find a sharp transition between a scenario with one dominant language and fragmentation into many language clusters. The transition is also reflected in the Hamming distance between the two languages with the largest and second to largest number of speakers. We also consider the case where the population is localized on a square lattice and the interaction of individuals is restricted to a certain geometrical domain. Here it is again the Hamming distance that plays an essential role in the final fate of a language of either surviving or being extinct.

Biological genomes are divided into coding and non-coding regions. Introns are non-coding parts within genes, while the remaining non-coding parts are intergenic sequences. To study evolutionary significance of the inside intron recombination we have used two models based on the Monte Carlo method. In our computer simulations we have implemented the internal structure of genes by declaring the probability of recombination between exons. One situation when inside intron recombination is advantageous is recovering functional genes by combining proper exons dispersed in the genetic pool of the population after a long period without selection for the function of the gene. Populations have to pass through the bottleneck, then. These events are rather rare and we have expected that there should be other phenomena giving profits from the inside intron recombination. In fact we have found that inside intron recombination is advantageous only in the case when after recombination, besides the recombinant forms, parental haplotypes are available and selection is set already on gametes.

A model of dynamics of three interacting species is presented. Two of the species are prey and one is predator, which feeds on both prey, however with some preference to one type. Prey compete for space (breeding) although they always have access to food. Predators in order to survive and reproduce must catch prey, otherwise they die of hunger. The dynamics of the model is found via differential equations in the mean-field like approach and through computer simulations for agent-based method. We show that the coexistence of the three species is possible in the mean-field model, provided the preference of the predators is small, whereas from simulation it follows that the stochastic fluctuations drive, generally, one of the prey populations into extinction. We have found a different type of behavior for small and large systems and a rather unexpected dependence of the coexistence chance of the preference parameter in bigger lattices.

We present a simple model of pseudo-speciation driven only by selective mating. Using Monte Carlo simulation on a lattice we show that even without considering the genetic structure of the individuals a population living in a homogeneous habitat will divide into two, spatially separated, groups having different values of their trait. After some time one group (species) will change their trait and will be absorbed into the winning species.

We present a simple model of a population of individuals characterized by their genetic structure in the form of a double string of bits and the phenotype following from it. The population is living in an unchanging habitat preferring a certain type of phenotype (optimum). Individuals are unisex, however a pair is necessary for breeding. An individual rejects a mate if the latter's phenotype contains too many bad, i.e. different from the optimum, genes in the same places as the individual's. We show that such strategy, analogous to disassortative mating based on the major histocompatibility complex, avoiding inbreeding and incest, could be beneficial for the population and could reduce considerably the extinction risk, especially in small populations.

It is argued that the present log-normal distribution of language sizes is, to a large extent, a consequence of demographic dynamics within the population of speakers of each language. A two-parameter stochastic multiplicative process is proposed as a model for the population dynamics of individual languages, and applied over a period spanning the last ten centuries. The model disregards language birth and death. A straightforward fitting of the two parameters, which statistically characterize the population growth rate, predicts a distribution of language sizes in excellent agreement with empirical data. Numerical simulations, and the study of the size distribution within language families, validate the assumptions at the basis of the model.

We assess the Lattice Boltzmann (LB) method versus centered finite-difference schemes for the solution of the advection–diffusion–reaction (ADR) Fisher's equation. It is found that the LB method performs significantly better than centered finite-difference schemes, a property we attribute to the near absence of dispersion errors.

We propose a nonlinear age-structured model of tumor cell population with proliferating and quiescent phases. We apply the discontinuous Galerkin (DG) method to study its dynamical behavior. The DG numerical approximation is used for the spatial discretization and then the strong-stability-preserving explicit Runge–Kutta (SSPERK) method is performed for the temporal discretization. This paper aims to establish more efficient results in the sense of computational approach and compare these with analogous estimates for Weighted Essentially and Non-Oscillatory (WENO) scheme. Finally, some test examples and numerical simulations are given to illustrate theoretical results and to examine the behavior of the solution.

We discuss the effects of spatial interference between two infectious hotspots as a function of the mobility of individuals (wind speed) between the two and their relative degree of infectivity. As long as the upstream hotspot is less contagious than the downstream one, increasing the wind speed leads to a monotonic decrease of the infection peak in the downstream hotspot. Once the upstream hotspot becomes about between twice and five times more infectious than the downstream one, an optimal wind speed emerges, whereby a local minimum peak intensity is attained in the downstream hotspot, along with a local maximum beyond which the beneficial effect of the wind is restored. Since this nonmonotonic trend is reminiscent of the equation of state of nonideal fluids, we dub the above phenomena “epidemic condensation”. When the relative infectivity of the upstream hotspot exceeds about a factor five, the beneficial effect of the wind above the optimal speed is completely lost: any wind speed above the optimal one leads to a higher infection peak. It is also found that spatial correlation between the two hotspots decay much more slowly than their inverse distance. It is hoped that the above findings may offer a qualitative clue for optimal confinement policies between different cities and urban agglomerates.