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The response threshold model explains the emergence of division of labor (i.e., task specialization) in an unstructured population by assuming that the individuals have different propensities to work on different tasks. The incentive to attend to a particular task increases when the task is left unattended and decreases when individuals work on it. Here we derive mean-field equations for the stimulus dynamics and show that they exhibit complex attractors through period-doubling bifurcation cascades when the noise disrupting the thresholds is small. In addition, we show how the fixed threshold can be set to ensure specialization in both the transient and equilibrium regimes of the stimulus dynamics. However, a complete explanation of the emergence of division of labor requires that we address the question of where the threshold variation comes from, starting from a homogeneous population. We then study a structured population scenario, where the population is divided into a large number of independent groups of equal size, and the fitness of a group is proportional to the weighted mean work performed on the tasks during a fixed period of time. Using a winner-take-all strategy to model group competition and assuming an initial homogeneous metapopulation, we find that a substantial fraction of workers specialize in each task, without the need to penalize task switching.

The fitness landscape metaphor plays a central role on the modeling of optimizing principles in many research fields, ranging from evolutionary biology, where it was first introduced, to management research. Here we consider the ensemble of trajectories of the imitative learning search, in which agents exchange information on their fitness and imitate the fittest agent in the population aiming at reaching the global maximum of the fitness landscape. We assess the degree to which the starting and ending points determine the learning trajectories using two measures, namely, the predictability that yields the probability that two randomly chosen trajectories are the same, and the mean path divergence that gauges the dissimilarity between two learning trajectories. We find that the predictability is greater in rugged landscapes than in smooth ones. The mean path divergence, however, is strongly affected by the search parameters -- population size and imitation propensity -- that obliterate the influence of the underlying landscape. The learning trajectories become more deterministic, in the sense that there are fewer distinct trajectories and those trajectories are more similar to each other, with increasing population size and imitation propensity. In addition, we find that the roughness of the learning trajectories, which measures the deviation from additivity of the fitness function, is always greater than the roughness estimated over the entire fitness landscape.

We study the emergence of cell differentiation under the assumption of the existence of a given number of tradeoffs between genes encoding different functions. In the model the viability of colonies is determined by the capability of their lower level units to perform different functions, which is implicitly determined by external chemical stimuli. Due to the existence of tradeoffs it can be evolutionarily advantageous to evolve the division of labor whereby the cells can suppress their contributions to some of the activities through the activation of regulatory genes, which in its turn inflicts a cost in terms of fitness. Our simulation results show that cell differentiation is more likely as the number of tradeoffs is increased but the outcome also depends on their strength. We observe the existence of critical values for the minimum number of tradeoffs and their strength beyond that maximum cell differentiation can be attained. Remarkably, we observe the occurrence of a maximum tradeoff strength beyond that the population is no longer viable imposing an upper tolerable level of constraint at the system. This tolerance is reduced as the number of tradeoffs grows., Comment: 6 pages, 5 figures

Understanding why strains with different metabolic pathways that compete for a single limiting resource coexist is a challenging issue within a theoretical perspective. Previous investigations rely on mechanisms such as group or spatial structuring to achieve a stable coexistence between competing metabolic strategies. Nevertheless, coexistence has been experimentally reported even in situations where it cannot be attributed to spatial effects [Heredity {\bf 100}, 471 (2008)]. According to that study a toxin expelled by one of the strains can be responsible for the stable maintenance of the two strain types. We propose a resource-based model in which an efficient strain with a slow metabolic rate competes with a second strain type which presents a fast but inefficient metabolism. Moreover, the model assumes that the inefficient strain produces a toxin as a byproduct. This toxin affects the growth rate of both strains with different strength. Through an extensive exploration of the parameter space we determine the situations at which the coexistence of the two strains is possible. Interestingly, we observe that the resource influx rate plays a key role in the maintenance of the two strain types. In a scenario of resource scarcity the inefficient is favored, though as the resource influx rate is augmented the coexistence becomes possible and its domain is enlarged., Comment: 9 pages, 4 figures

The interplay between energy efficiency and evolutionary mechanisms is addressed. One important question is how evolutionary mechanisms can select for the optimised usage of energy in situations where it does not lead to immediate advantage. For example, this problem is of great importance to improve our understanding about the major transition from unicellular to multicellular form of life. The immediate advantage of gathering efficient individuals in an energetic context is not clear. Although this process increases relatedness among individuals, it also increases local competition. To address this question, we propose a model of two competing metabolic strategies that makes explicit reference to the resource usage. We assume the existence of an efficient strain, which converts resource into energy at high efficiency but displays a low rate of resource consumption, and an inefficient strain, which consumes resource at a high rate with a low efficiency in converting it to energy. We explore the dynamics in both well-mixed and structured populations. The selection for optimised energy usage is measured by the likelihood of that an efficient strain can invade a population only comprised by inefficient strains. It is found that the region of the parameter space at which the efficient strain can thrive in structured populations is always larger than observed in well-mixed populations. In fact, in well-mixed populations the efficient strain is only evolutionarily stable in the domain whereupon there is no evolutionary dilemma. We also observe that small group sizes enhance the chance of invasion by the efficient strain in spite of increasing the competition among relatives. This outcome corroborates the key role played by kin selection and shows that the group dynamics relied on group expansion, overlapping generations and group split can balance the negative effects of local competition., Comment: 32 pages, 7 figures

When a simple excitable system is continuously stimulated by a Poissonian external source, the response function (mean activity versus stimulus rate) generally shows a linear saturating shape. This is experimentally verified in some classes of sensory neurons, which accordingly present a small dynamic range (defined as the interval of stimulus intensity which can be appropriately coded by the mean activity of the excitable element), usually about one or two decades only. The brain, on the other hand, can handle a significantly broader range of stimulus intensity, and a collective phenomenon involving the interaction among excitable neurons has been suggested to account for the enhancement of the dynamic range. Since the role of the pattern of such interactions is still unclear, here we investigate the performance of a scale-free (SF) network topology in this dynamic range problem. Specifically, we study the transfer function of disordered SF networks of excitable Greenberg-Hastings cellular automata. We observe that the dynamic range is maximum when the coupling among the elements is critical, corroborating a general reasoning recently proposed. Although the maximum dynamic range yielded by general SF networks is slightly worse than that of random networks, for special SF networks which lack loops the enhancement of the dynamic range can be dramatic, reaching nearly five decades. In order to understand the role of loops on the transfer function we propose a simple model in which the density of loops in the network can be gradually increased, and show that this is accompanied by a gradual decrease of dynamic range., Comment: 6 pages, 4 figures

A simple spatial computer simulation model was recently introduced to study the evolution of the linguistic diversity. The model considers processes of selective geographic colonization, linguistic anomalous diffusion and mutation. In the approach, we ascribe to each language a fitness function which depends on the number of people that speak that language. Here we extend the aforementioned model to examine the role of saturation of the fitness on the language dynamics. We found that the dependence of the linguistic diversity on the area after colonization displays a power law regime with a nontrivial exponent in very good agreement with the measured exponent associated with the actual distribution of languages on the Earth., Comment: 10 pages, 3 figures

We investigate the process of fixation of advantageous mutations in an asexual population. We assume that the effect of each beneficial mutation is exponentially distributed with mean value $\omega_{med}=1/\beta$. The model also considers that the effect of each new deleterious mutation reduces the fitness of the organism independent on the previous number of mutations. We use the branching process formulation and also extensive simulations to study the model. The agreement between the analytical predictions and the simulational data is quite satisfactory. Surprisingly, we observe that the dependence of the probability of fixation $P_{fix}$ on the parameter $\omega_{med}$ is precisely described by a power-law relation, $P_{fix} \sim \omega_{med}^{\gamma}$. The exponent $\gamma$ is an increase function of the rate of deleterious mutations $U$, whereas the probability $P_{fix}$ is a decreasing function of $U$. The mean value $\omega_{fix}$ of the beneficial mutations which reach ultimate fixation depends on $U$ and $\omega_{med}$. The ratio $\omega_{fix}/\omega_{med}$ increases as we consider higher values of mutation value $U$ in the region of intermediate to large values of $\omega_{med}$, whereas for low $\omega_{med}$ we observe the opposite behavior., Comment: 13 pages

We study the competition between several advantageous mutants in an asexual population (clonal interference) as a function of the time between the appearance of the mutants, their selective advantages, and the rate of deleterious mutations. We find that the overall probability of fixation (the probability that at least one of the mutants becomes the ancestor of the entire population) does not depend on the time interval between the appearance of these mutants, and equals the probability that a genotype bearing all of these mutations reaches fixation. This result holds also in the presence of deleterious mutations, and for an arbitrary number of competing mutants. We also show that if mutations interfere, an increase in the mean number of fixation events is associated with a decrease in the expected fitness gain of the population., Comment: 18 pages and 6 figures, requires svmult.cls. To appear in "Modeling in Molecular Biology" (Springer Series in Natural Computing), G. Ciobanu ed

We investigate the evolutionary dynamics of a finite population of sequences adapting to NK fitness landscapes. We find that, unlike in the case of an infinite population, the average fitness in a finite population is maximized at a small but finite, rather than vanishing, mutation rate. The highest local maxima in the landscape are visited for even larger mutation rates, close to a transition point at which the population delocalizes (i.e., leaves the fitness peak at which it was localized) and starts traversing the sequence space. If the mutation rate is increased even further, the population undergoes a second transition and loses all sensitivity to fitness peaks. This second transition corresponds to the standard error threshold transition first described by Eigen. We discuss the implications of our results for biological evolution and for evolutionary optimization techniques., Comment: 14 pages Latex, 5 figures. Uses Elsevier macros 'elsart.cls'. Submitted to Physica A