How to construct the statistic network? An association network of herbaceous plants constructed from field sampling

In present study I defined a new type of network, the statistic network. The statistic network is a weighted and non-deterministic network. In the statistic network, a connection value, i.e., connection weight, represents connection strength and connection likelihood between two nodes and its absolute value falls in the interval (0, 1]. The connection value is expressed as a statistical measure such as correlation coefficient, association coefficient, or Jaccard coefficient, etc. In addition, all connections of the statistic network can be statistically tested for their validity. A connection is true if the connection value is statistically significant. If all connection values of a node are not statistically significant, it is an isolated node. An isolated node has not any connection to other nodes in the statistic network. Positive and negative connection values denote distinct connection types (positive or negative association or interaction). In the statistic network, two nodes with the greater connection value will show more similar trend in the change of their states. At any time we can obtain a sample network of the statistic network. A sample network is a non-weighted and deterministic network. The statistic network, in particular the plant association network that constructed from field sampling, is mostly an information network. Most of the interspecific relationships in plant community are competition and cooperation. Therefore in comparison to animal networks, the methodology of statistic network is more suitable to construct plant association networks. Some conclusions were drawn from this study: (1) in the plant association network, most connections are weak and positive interactions. The association network constructed from Spearman rank correlation has most connections and isolated taxa are fewer. From net linear correlation, linear correlation, to Spearman rank correlation, the practical number of connections and connectance in the constructed network increases. Network compactness also follows the trend. In addition, as the increase of network compactness and connectance, the portion and number of negative association declines dramatically. (2) In an association (interaction) network, only a few connections follow the linear relationship. Most connections follow the quasi-linear or non-linear relationships. (3) The association networks constructed from partial linear correlation and linear correlation measures are generally scale-free complex networks. The degree of these networks is power low distributed. (4) Isolated species (families, etc.) are likely important in the statistic network. They are the sink species for shaping new network after a community is seriously disturbed. (5) Beween-taxa connections at higher taxonomic level are generally weaker than that at lower taxonomic level.