Complex networks generated by the Penna bit-string model: Emergence of small-world and assortative mixing

Abstract

The Penna bit-string model successfully encompasses many phenomena of population evolution, including inheritance, mutation, evolution, and aging. If we consider social interactions among individuals in the Penna model, the population will form a complex network. In this paper, we first modify the Verhulst factor to control only the birth rate, and introduce activity-based preferential reproduction of offspring in the Penna model. The social interactions among individuals are generated by both inheritance and activity-based preferential increase. Then we study the properties of the complex network generated by the modified Penna model. We find that the resulting complex network has a small-world effect and the assortative mixing property.

A Price Paid for Our Internal Strife: Escalated Intragroup Aggression and the Evolution of Ingroup Derogation

“…This model is able to reproduce many features observed in real populations (e.g., the Eve effect; all alive individuals are descendants from one common ancestor), and it is the only Monte Carlo simulation technique that can fits the Gompertz law and the Azbel theory based on real demographic data ( de Oliveira, 1998 ). Researchers have employed this model in numerous theoretical and empirical studies in biology and ecology, including the study of aging (e.g., Biecek and Cebrat, 2006 ; Periwal, 2013 ), the phenomenon of sympatric speciation (e.g., Sousa, 2004 ), the influence of medical care ( Niewczas et al, 2000 ), the spreading of epidemics ( He et al, 2005 ), the evolution of intelligence (e.g., Pan et al, 2005 ; He et al, 2007 ), social networks (e.g., Li and Maini, 2005 ), and language ( Schwammle, 2007 ), and in the studies of the evolution of population dynamics of organisms (e.g., insects, fishes, wolves, and humans) in the laboratory or in the field (e.g., Makowiec, 1996 ; Penna and Stauffer, 1996 ; Giarola et al, 2006 ; de Oliveira et al, 2008 , 2013 ; de Souza et al, 2012 ; dos Santos et al, 2012 ; Periwal, 2013 ), and so on (for a small review, see Stauffer, 2007 ). Due its success and validity in evolution modeling, we utilized the sexual Penna model to simulate the evolution of ingroup derogation in order to test our hypothesis in Study 1.…”

Network analysis of human heartbeat dynamics

“…A network is considered as assortative mixing if the high-degree nodes in the network tend to be connected to other high-degree nodes, otherwise disassortative mixing is shown when high-degree nodes attach to low-degree ones. [17][18][19] Assortative mixing may have profound effect on the properties of a network. For example, it is found that assortative networks are more robust to remove their highest degree nodes than the disassortative ones.…”

“…For example, it is found that assortative networks are more robust to remove their highest degree nodes than the disassortative ones. [17][18][19] The assortative property of a network can be measured by the assortative coefficient. For mixing by node degree in an undirected network, the assortative coefficient is 17…”

Transmission of sexually transmitted disease in complex network of the Penna model

“…Assortative mixing is also a significant property, which means that the vertices in networks that have many connections can be connected to other vertices with many connections with high probability [9,10]. In [11], the authors made some modifications on the standard Penna model and considered social interactions among individuals. They found that the population can form a complex network, which exhibits some interesting properties, such as small-world and assortative mixing.…”

“…But we consider that the standard Verhulst factor is too severe in the Penna model. We use a modified form of Verhulst factor as mentioned in [11,16]. We assume that, at each time step, the mature individuals will produce int(N(1−N/N max )) offspring, where N max is the maximum population size allowed by the environment and N is the current population size.…”