Python code generating the data of figures 2, 3, 4, 5 and 6 of the manuscript: The evolution of cooperation in the unidirectional linear division of labour of finite roles

The evolution of cooperation is an unsolved mystery, which we see in many
social and biological systems. In the study titled "The evolution of
cooperation in the unidirectional linear division of labour of finite
roles", we investigate under which sanction systems and how the
evolution of cooperation happens in the linear division of
labour.  This python code has been used to produce the results of
Figures 2, 3, 4, 5, and 6 of the manuscript. This code shows the evolution
of cooperation among the population of various different groups which have
different roles to play in the linear division of labour, on the basis of
numerical analysis of a partial differential equation system, which
originates from the replicator equations used in the evolutionary game
theory.  We find the locally stable equilibria using this code,
which shows the ultimate results of the dynamics in the system under given
parameters. Figures 3, 5, and 6 are direct products of the code, showing
the dynamics of a system, and figures 2 and 4 are the end results of those
dynamics.  We found that in a social dilemma situation,
cooperation never evolves in the system without punishment. However, with
sanction systems by introducing a suitable amount of punishment, while
having a suitable findability of the defector, and a suitable initial
population structure, cooperation can evolve. These results can be found
with this code. We have no legal or ethical concerns regarding this data
as this is a numerical analysis based on theoretical equations.