Exploring inbreeding dynamics by considering reproductive bound and polygyny.

Inbreeding is a clinically significant measure of a population dependent on human social structures including the population size or the cultural traits. Here, we propose an expanded and elaborate model to analyze the inbreeding within a population where explicit polygyny and inbreeding bounds are taken into account. Unlike the models presented so far, we implemented biologically realistic assumptions that there is the disproportionate probability of males to reproduce (polygyny) and female reproduction is bounded. Using the proposed model equations, we changed the parameters that represent the polygyny degree, the female reproductive bound correlated to the mutation rate, and the total population size. The disappearance of the polygyny that numerous human societies experienced results in the long-lasting effect of the decreasing inbreeding coefficient. Decreased female reproductive bound correlated with a higher mutation rate reveals similar results. After the effect of each factor is analyzed, we modeled the dynamics of the inbreeding coefficient throughout an imaginary human population where polygyny disappears and late marriage becomes prevalent. In this group, the population size gradually and exponentially increases reflecting the traits of prehistoric human society and rising agricultural productivity. To observe how late and less marriage, the feature of the modern developed society, affects the inbreeding dynamics, the female reproductive bound and the population size were assumed to decrease after the population upsurge. The model can explain the decreasing trend of the prehistoric inbreeding coefficient of the actual human population and predict how the trend will be shifted when traits of modern societies continue.

Spatial simulation of autologous cell defection for cancer treatment.

Cancer cells are highly cooperative in a nepotistic way and evolutionarily dynamic. Present cancer treatments often overlook these aspects, inducing the selection of resistant cancer cells and the corresponding relapse. As an alternative method of cancer elimination, autologous cell defection (ACD) was suggested by which modified cancer cells parasitically reliant on other cancer cells are implemented to the cancer cluster. Specifically, modified cancer cells should not produce costly growth factors that promote the growth of other cancer cells while receiving the benefit of exposure to such growth factors. Analytical models and rudimentary experiments up to date provide the medical feasibility of this method. In this study, I built comprehensive spatial simulation models by embracing the effects of the multiple growth factors, the Warburg effect, mutations and immunity. The simulation results based on planar spatial structures indicate that implementation of the defective modified tumours may replace the existing cancer cluster and defective cells would later collapse by themselves. Furthermore, I built a mathematical model that compares the fitness of the cells adjacent to the hypertumour-cancer interface. I also calculated whether anticancer drugs that reduce the effects of the growth factors promote or demote the utility of ACD under diverse fitness functions. The computational examination implies that anticancer drugs may impede the therapeutic effect of ACD when there is a strong concavity in the fitness function. The analysis results could work as a general guidance for effective ACD that may expand the paradigm of cancer treatment.

The role of recognition error in the stability of green-beard genes.

The empirical examples of the green-beard genes, once a conundrum of evolutionary biology, are accumulating, while theoretical analyses of this topic are occasional compared to those concerning (narrow-sense) kin selection. In particular, the recognition error of the green-beard effect that the cooperator fails to accurately recognize the other cooperators or defectors is readily found in numerous green-beard genes. To our knowledge, however, no model up to date has taken that effect into account. In this article, we investigated the effect of recognition error on the fitness of the green-beard gene. By employing theories of evolutionary games, our mathematical model predicts that the fitness of the green-beard gene is frequency dependent (frequency of the green-beard gene), which was corroborated by experiments performed with yeast FLO1. The experiment also shows that the cells with the green-beard gene (FLO1) are sturdier under severe stress. We conclude that the low recognition error among the cooperators, the higher reward of cooperation, and the higher cost of defection confer an advantage to the green-beard gene under certain conditions, confirmed by numerical simulation as well. Interestingly, we expect that the recognition error to the defectors may promote the cooperator fitness if the cooperator frequency is low and mutual defection is detrimental. Our ternary approach of mathematical analysis, experiments, and simulation lays the groundwork of the standard model for the green-beard gene that can be generalized to other species.

Reformulation of Trivers-Willard hypothesis for parental investment.

The Trivers-Willard hypothesis (TWH) plays a central role in understanding the optimal investment strategies to male and female offspring. Empirical studies of TWH, however, yielded conflicting results. Here, we present models to predict optimal comprehensive multi-element parental strategies composed of primary sex ratio, brood size, resource allocation among offspring, and the resultant secondary sex ratio. Our results reveal that the optimal strategy depends on sex differences in the shape of offspring fitness function rather than in fitness variance. Also, the slope of the tangent line (through the origin) to the offspring fitness function can be used to predict the preferred offspring sex. We also briefly discuss links between the model and the empirical research. This comprehensive reformulation of TWH will offer a thorough understanding of multi-element parental investment strategies beyond the classical TWH.

Trails of ants converge or diverge through lens-shaped impediments, resembling principles of optics.

Analogies across disciplines often indicate the existence of universal principles such as optimization, while the underlying proximate mechanisms may differ. It was reported recently that trails of ants refract at the border of substrates, on which walking speeds differ. This phenomenon is analogous to the travel-time-minimizing routes of light refracting at the borders between different media. Here, we further demonstrate that ant tracks converge or diverge across lens-shaped impediments similar to light rays through concave or convex optical lenses. The results suggest that the optical principle of travel time reduction may apply to ants. We propose a simple mathematical model that assumes nonlinear positive feedback in pheromone accumulation. It provides a possible explanation of the observed similarity between ant behavior and optics, and it is the first quantitative theoretical demonstration that pheromone-based proximate mechanisms of trail formation may produce this similarity. However, the future detailed empirical observations of ant behavior on impediment edges during the process of pheromone trail formation are needed in order to evaluate alternative explanations for this similarity.