*2.3. Methods*

### 2.3.1. Quantitative Evaluation Method

The standard deviation (*SD*) is the square of the deviation between the standard value of the fish pond size and the average area in each period. It was used to reflect the dispersion of the ponds within each period. Therefore, a larger *SD* indicates a greater difference in pond size. The coefficient of variation (*CV*) is the ratio of the standard deviation (*SD*) of the pond area to the corresponding average in each period. A larger *V* suggests a higher relative difference in pond size within each study unit [18].

The Theil coefficient (*T*) indicates the regional inequality and is used to quantify the degree of difference in individual pond sizes. A larger *T* indicates a larger inequality in pond size. In the formula, *xi* is the individual pond area; *x*0 is the mean value of the pond area. *N* is the total number of ponds.

$$SD = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} (\mathbf{x}\_i - \mathbf{x}\_0)} \tag{1}$$

$$CV = \frac{SD}{\chi\_0} \tag{2}$$

$$T = \frac{1}{N} \sum\_{i=1}^{N} \ln \frac{\mathbf{x}\_0}{\mathbf{x}\_i} \tag{3}$$

### 2.3.2. Water Area Change Index (*W*)

The water area change intensity index indicates the rate of the areal change of the ponds in a specific period.

$$W = 100\% \times \frac{S\_b - S\_d}{S\_a \times \Delta t'} \tag{4}$$

where, *Sa* and *Sb* represent the area of the ponds in the previous period a and the current period b, respectively, Δ*t* represents the timespan between periods a and b.

### 2.3.3. Expansion Coefficient (*E*)

Expansion Coefficient is an important quantitative indicator to measure the development and change in fish ponds:

$$E = \prod\_{i=1}^{3} e\_{i\prime} \tag{5}$$

where, *E* represents the expansion coefficient, which is obtained by multiplying the internal structure transition coefficient (*e*1), the spatial structure transition coefficient (*e*2) and the expansion coefficient (*e*3).

Internal structure transition coefficient: *e*1 = |*Pt* − *Pt*−<sup>1</sup>|, *e*1 in the formula represents the relative areal change of ponds. *Pt* represents the areal percentage of ponds in the total area in current period, and *Pt*−<sup>1</sup> represents the one in the previous period.

Spatial structure transition coefficient: *e*2 = |*St* − *St*−<sup>1</sup>|, *St* and *St*−<sup>1</sup> respectively represent the total fish pond area in the last and the first periods.

Expansion coefficient: *e*3 = √*t St*/*S*0 − 1. *e*3 is for the gradient change rate of fish ponds; *St*, and *S*0 respectively represent total pond area for the last and first periods. *T* is the research period.

In order to discriminate the patterns of the pond changes of each study unit, the 26 study units were generally divided into 4 patterns: fast growing (*E* > 40), weak growing (40 > *E* > 1), stable (1 > *E* > 0), and shrinking (*E* < 0) [19,20].
