3.4.1. Symbiosis Model

Symbiosis can describe the correlation degree of the variation of quality parameters between two symbiosis units or systems and reflect the correlation degree of their mutual influence [55]. This paper took tourism's carbon emission efficiency (TCEE) and the tourism economy's high-quality development (TEHQD) as symbiotic units and selected the added value of the comprehensive score of TCEE and TEHQD as the main quality parameters. Then, the symbiotic degree of TCEE and TEHQD is:

$$
\delta\_{CE} = \frac{dv\_{\mathbb{C}}/v\_{\mathbb{C}}}{dv\_{\mathbb{E}}/v\_{\mathbb{E}}} = \frac{v\_{\mathbb{E}}}{v\_{\mathbb{C}}} \frac{dv\_{\mathbb{C}}}{dv\_{\mathbb{E}}} \tag{6}
$$

Similarly, the symbiosis degree between TEHQD and TCEE is:

$$
\delta\_{\rm EC} = \frac{d\upsilon\_{\rm E}/\upsilon\_{\rm E}}{d\upsilon\_{\rm C}/\upsilon\_{\rm C}} = \frac{\upsilon\_{\rm C}}{\upsilon\_{\rm E}} \frac{d\upsilon\_{\rm E}}{d\upsilon\_{\rm C}} \tag{7}
$$

If δ*CE* = δ*EC* > 0, it indicates that TCEE and TEHQD are in a positive symbiotic state. If δ*CE* = δ*EC* > 0, then the two parties are in a positive asymmetric symbiosis. If δ*CE* = δ*EC* < 0, it indicates that TCEE and TEHQD are in a state of reverse symmetry symbiosis. If δ*CE* = δ*EC* < 0, it indicates that both parties are in a state of reverse asymmetric symbiosis. If δ*CE* > 0 (=0, <0), δ*EC* < 0 (=0, >0), it indicates that the two parties are in the parasitic, coexisting, and parasitic states, respectively.
