Parrondo's games based on complex networks and the paradoxical effect

Influence analysis of network evolution on Parrondo effect

Parrondo's paradox is a scheme used to describe an interesting paradoxical situation that a losing Game A and a losing Game B played randomly or periodically will produce a winning result. Here, a dynamic process of network evolution of Link A + Game B is proposed to yield the Parrondo effect. Game B with two asymmetric branches depends on the relative comparison between the capital of the network node and the average capital of all its neighbors. Simulation results demonstrate that network structure evolution make the losing Game B produce a paradoxical effect of winning and would be advantageous to the development of the "ratcheting" mechanism in Game B. Furthermore, the underlying paradoxical mechanism is analyzed to illustrate the parameter space where the "strong" Parrondo effect occurs. Then influence of two types of network connection is analyzed, indicating that the "agitating" effect of the network is basically the same when a node connects to a neighbor's neighbor or randomly chooses a node other than its neighbors. Further, a higher frequency of network evolution yields a larger parameter region where the "strong" Parrondo effect emerges.

Does Cancer Biology Rely on Parrondo's Principles?

Simple Summary

Parrondo’s paradox, whereby losing strategies or deleterious effects can combine to provide a winning outcome, has been increasingly applied by biologists to explain complex adaptations in many living systems. Here, we suggest that considering this paradox in oncology, particularly in relation to the phenotypic diversity of malignant cells, could also be a promising approach to understand several puzzling aspects of cancer biology. For example, the high genetic and epigenetic instability of cancer cells, their metastatic behavior and their capacity to enter dormancy could be explained by Parrondo’s theory. We also discuss the relevance of Parrondo’s paradox in a therapeutical framework using different examples. This work provides a compelling argument that the traditional separation between medicine and other disciplines remains a fundamental limitation that needs to be overcome if complex processes, such as oncogenesis, are to be completely understood.

Abstract

Many aspects of cancer biology remain puzzling, including the proliferative and survival success of malignant cells in spite of their high genetic and epigenetic instability as well as their ability to express migrating phenotypes and/or enter dormancy despite possible fitness loss. Understanding the potential adaptive value of these phenotypic traits is confounded by the fact that, when considered separately, they seem to be rather detrimental at the cell level, at least in the short term. Here, we argue that cancer’s biology and success could frequently be governed by processes underlying Parrondo’s paradox, whereby combinations of intrinsically losing strategies may result in winning outcomes. Oncogenic selection would favor Parrondo’s dynamics because, given the environmental adversity in which malignant cells emerge and evolve, alternating between various less optimal strategies would represent the sole viable option to counteract the changing and deleterious environments cells are exposed to during tumorigenesis. We suggest that malignant processes could be viewed through this lens, and we discuss how Parrondo’s principles are also important when designing therapies against cancer.

Noise-induced polarization switching in complex networks

The combination of bistability and noise is ubiquitous in complex systems, from biology to social interactions, and has important implications for their functioning and resilience. Here we use a simple three-state dynamical process, in which nodes go from one pole to another through an intermediate state, to show that noise can induce polarization switching in bistable systems if dynamical correlations are significant. In large, fully connected networks, where dynamical correlations can be neglected, increasing noise yields a collapse of bistability to an unpolarized configuration where the three possible states of the nodes are equally likely. In contrast, increased noise induces abrupt and irreversible polarization switching in sparsely connected networks. In multiplexes, where each layer can have a different polarization tendency, one layer is dominant and progressively imposes its polarization state on the other, offsetting or promoting the ability of noise to switch its polarization. Overall, we show that the interplay of noise and dynamical correlations can yield discontinuous transitions between extremes, which cannot be explained by a simple mean-field description.

Effects of behavioral patterns and network topology structures on Parrondo's paradox

A multi-agent Parrondo's model based on complex networks is used in the current study. For Parrondo's game A, the individual interaction can be categorized into five types of behavioral patterns: the Matthew effect, harmony, cooperation, poor-competition-rich-cooperation and a random mode. The parameter space of Parrondo's paradox pertaining to each behavioral pattern, and the gradual change of the parameter space from a two-dimensional lattice to a random network and from a random network to a scale-free network was analyzed. The simulation results suggest that the size of the region of the parameter space that elicits Parrondo's paradox is positively correlated with the heterogeneity of the degree distribution of the network. For two distinct sets of probability parameters, the microcosmic reasons underlying the occurrence of the paradox under the scale-free network are elaborated. Common interaction mechanisms of the asymmetric structure of game B, behavioral patterns and network topology are also revealed.

A Paradoxical Evolutionary Mechanism in Stochastically Switching Environments

Organisms with environmental sensors that guide survival are considered more likely to be favored by natural selection if they possess more accurate sensors. In this paper, we develop a theoretical model which shows that under certain conditions of environmental stochasticity, selection actually favors sensors of lower accuracy. An analogy between this counter-intuitive phenomenon and the well-known Parrondo’s paradox is suggested.