Code and supplementary information for the speed of neutral evolution on graphs

The speed of evolution on structured populations is crucial for biological and social systems. The likelihood of invasion is key for evolutionary stability, but it makes little sense if it takes long. It is far from known what population structure slows down evolution. We investigate the absorption time of a single neutral mutant for all the 112 non-isomorphic undirected graphs of size 6. We find that about three-quarters of the graphs have an absorption time close to that of the complete graph, less than one-third are accelerators, and more than two-thirds are decelerators. Surprisingly, determining whether a graph has a long absorption time is too complicated to be captured by the joint degree distribution. Via the largest sojourn time, we find that echo-chamber-like graphs, which consist of two homogeneous graphs connected by few sparse links, are likely to slow down absorption. These results are robust for large graphs, mutation patterns as well as evolutionary processes. This work ..., , , # Code and supplementary information for the speed of neutral evolution on graphs

[https://doi.org/10.5061/dryad.0p2ngf27x](https://doi.org/10.5061/dryad.0p2ngf27x)

## Description of the data and code

* Data

1. graphs.RData:

This file contains the adjacency matrices of 112 undirected graphs with 6 nodes. These adjacency matrices represent the connectivity patterns of the graphs and can be utilized for generating an Atlas of all the undirected graphs of size 6. For generating Atlases of graphs with larger node sizes, please refer to NetworkX or other graph analysis libraries.
2. `all_state_112_graph.zip`

The file contains visual representations of the 64 states for each of the 112 graphs. These states comprise 2 absorbing states and 62 transient states.
* code

1. DB_six_nodes_random_initial.R:

This script file is designed to compute simulation results for Death-Birth process under neutral selection for each graph included in the graphs.R...

结构化种群的演化速率对于生物与社会系统而言至关重要。入侵概率是演化稳定性的核心判据，但倘若演化耗时过长，该判据便失去了实际意义。目前学界仍未明确何种种群结构会延缓演化进程。我们针对全部112个规模为6的非同构无向图，研究了单个中性突变体（neutral mutant）的吸收时间（absorption time）。我们发现，约四分之三的图的吸收时间与完全图（complete graph）相近，不足三分之一的图为演化加速结构，超过三分之二的图为演化延缓结构。令人意外的是，判断一张图是否拥有较长吸收时间的问题过于复杂，无法通过联合度分布（joint degree distribution）加以刻画。借助最大逗留时间（sojourn time），我们发现由少量稀疏连接边绑定两个同质图所构成的回音室类图，大概率会延缓吸收过程。上述结论在大规模图、不同突变模式以及各类演化过程中均具有稳健性。本研究……

# 针对图上中性演化速率的代码与补充信息
[https://doi.org/10.5061/dryad.0p2ngf27x](https://doi.org/10.5061/dryad.0p2ngf27x)

## 数据与代码说明
* 数据
1. graphs.RData：
该文件包含112个6节点无向图的邻接矩阵（adjacency matrices）。这些邻接矩阵表征了图的连通模式，可用于生成规模为6的全部无向图图集。如需生成更大节点规模的图图集，请参考NetworkX或其他图分析库。
2. `all_state_112_graph.zip`：
该文件包含112张图各自的64种状态的可视化结果。这些状态包含2个吸收态与62个暂态。
* 代码
1. DB_six_nodes_random_initial.R：
该脚本文件用于计算graphs.R中包含的每张图在中性选择下的死亡-出生（Death-Birth）过程的仿真结果。