Multi-objective linear programming-based trade-off and optimization of the ecosystem services in Jiajiyu small watershed in the Loess Plateau, China

The Loess Plateau is one of the most serious soil-erosion areas with ecosystem service degradation in China. Small watersheds are the main place of soil erosion; therefore,it is important to evaluate various ecosystem services whenpromoting their water and soil conservation. This paper took Jiajiyu,a typical small watershed in the Loess Plateau,as the study area using 2012 as the base year and 2022 as the target year. Based on the Statistical Yearbook and investigation data,the ecosystem service values of different land-use types were evaluated by the methods of market value,shadow price,shadow project,alternative cost,and opportunity cost. The ecosystem services were evaluated and optimized based on the adjustment of land-use structure by multi-objective linear programming through adjusting land-use types. The supply service,water and soil conservation service,and other services values were taken as the trade-off sub-objectives and the total ecosystem service value as final objective,with 17 constraint equations developed by 35 decision variables. The constraint equations included the land-area control,grain and oil security,and suitability of land-use types on the slope.The results showed that the ecosystem service values of slope farmlands and waste grasslands were much lower than most of other land-use types,and both of them took a relatively higher proportion of small watershed area,which restricted the ecosystem service values of Jiajiyu. The land-use structure was obviously improved by the trade-off and optimization of ecosystem services,with most of the slope farmlands and waste grasslands adjusted to arbor forest or terrace,both of which have much higher ecosystem service values. The total ecosystem service value increased by 9.23%,and the value of supply service,water and soil conservation service, and other services also increased by 6. 24%,9. 81%, and 17. 35%,respectively. Increases in the three sub-objects of ecosystem service values were dominated by the total increase in ecosystem service values by 25.96%,54.42%,and 19.62%,respectively. Compared with the optimization results,which only took supply service,water and soil conservation service,other services or total ecosystem service values as the objective function,the optimization results of the three objective sub-functions were more coordinated,and all three benefits increased significantly. Significant differences were observed in the growth rates of ecosystem service values in different