Abstract:

Aims Anand & Orlóci ( 1996) proposed a method measuring the total, disordered and organized complexity of community structure using the mean length of Huffman code, the 12th order of Rényi entropy, and the difference between these two measures, respectively. This method is quite different from measures based on community biodiversity and is potentially of great significance. Although some properties of the measures were discussed by Anand & Orlóci (1996), a thorough study has not been conducted, especially on their ecological meaning. The purpose of the paper is to reveal: 1) factors affecting the measures and their ecological meaning, 2) relationship between complexity and biodiversity, and 3) effect of species number on structural complexity.

Methods First, >4 000 000 simulated communities with different structures were constructed by two methods: evenly distributed mode and dominated mode. Then the three complexity measures were computed. Correlation analyses were conducted between these measures and potentially related factors such as Shannon-Wiener index, coefficient of variation and logarithmic proportion of most dominated species. Multiple linear regressions between the complexity measures and combination of these factors were carried out to explore the relationship between complexity and biodiversity. Communities with different species number were then constructed and tested to explore the effect of species number on complexity measures.

Important findings The three complexity measures are strongly correlated with the Shannon-Wiener index, coefficient of variation and logarithmic proportion of the most dominated species. For total complexity, the correlation coefficient between it and the Shannon-Wiener index is nearly 1 (0.996), so is that between the 12th order of Rényi entropy and logarithmic proportion of the most dominated species. The determining coefficient of multiple linear regression between organized complexity and Shannon-Wiener index and logarithmic proportion of the most dominated species is also near 1 (0.97). These findings suggest that all three measures of community structural complexity are affected by the Shannon-Wiener index, coefficient of variation and logarithmic proportion of the most dominated species. For organized structural complexity, it can be expressed as a linear combination of Shannon-Wiener index and logarithmic proportion of the most dominated species. Biodiversity can explain 41~46% of variation of organized structural complexity. Although the three complexity measures increase with number of species, they do not increase as much as described by Anand & Orlóci (1996), and it does not affect the relationship between the complexity measures and related factors.

Key words: complexity, structural complexity, Huffman code, Shannon-Wiener index, Rényi entropy, organized complexity, disordered complexity