Xia K. The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism.
BMC Ecol Evol 2021;
21:152. [PMID:
34348658 PMCID:
PMC8336419 DOI:
10.1186/s12862-021-01847-0]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 06/03/2021] [Indexed: 11/16/2022] Open
Abstract
BACKGROUND
In recent years, the average abundance function has attracted much attention as it reflects the degree of cooperation in the population. Then it is significant to analyse how average abundance functions can be increased to promote the proliferation of cooperative behaviour. However, further theoretical analysis for average abundance function with mutation under redistribution mechanism is still lacking. Furthermore, the theoretical basis for the corresponding numerical simulation is not sufficiently understood.
RESULTS
We have deduced the approximate expressions of average abundance function with mutation under redistribution mechanism on the basis of different levels of selection intensity [Formula: see text] (sufficiently small and large enough). In addition, we have analysed the influence of the size of group d, multiplication factor r, cost c, aspiration level [Formula: see text] on average abundance function from both quantitative and qualitative aspects.
CONCLUSIONS
(1) The approximate expression will become the linear equation related to selection intensity when [Formula: see text] is sufficiently small. (2) On one hand, approximation expression when [Formula: see text] is large enough is not available when r is small and m is large. On the other hand, this approximation expression will become more reliable when [Formula: see text] is larger. (3) On the basis of the expected payoff function [Formula: see text] and function [Formula: see text], the corresponding results for the effects of parameters (d,r,c,[Formula: see text]) on average abundance function [Formula: see text] have been explained.
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