## 5 Conclusions  
This paper used the panel data from 40 SOFRs in Heilongjiang Province from 2001 to 2019 as the research sample. First, the individual fixed-effects model was used to determine a reasonable lag period, and then the panel threshold model was selected to investigate the increase in carbon sink efficiency and differences in FMI under different carbon sink levels. In addition, partially linear functional-coefficient panel data models were used to verify the law of the effect of FMI on increasing the carbon sink. The main conclusions of the study were as follows. (1) The aggregate carbon amount of SOFRs in Heilongjiang Province from 2001 to 2019 showed an overall upward trend, the total growth rate was 20.17%, and the overall fluctuation was large. In terms of space, the carbon sink showed a phenomenon of \"increasing as a whole and decreasing in a small area\". The SDE of the carbon sink presented a pattern of \"southeast-northwest\" and showed the characteristics of \"from southeast to northwest\" migration. In addition, the carbon sink of each forest region was quite different, showing the characteristics of \"more in the north and south, but less in the middle\". (2) The total FMI from 2001 to 2019 was approximately CNY 46.745 billion, showing an upward trend, but the amount of FMI varied greatly among forest regions. (3) The amount of carbon sink in each forest region significantly affected the efficiency of increasing the carbon sink by FMI. When the carbon sink was less than 5,327,211.8707 tons, the elasticity coefficient of the impact of FMI on the carbon sink was 0.00953. When the carbon sink was higher than 5,327,211.8707 tons, the elasticity coefficient of the impact of FMI on the carbon sink was 0.02175, and the latter's FMI efficiency was 128.23% higher than that of the former. (4) The increasing carbon sink effect of FMI showed the law of diminishing marginal benefits, but it has not yet reached the optimal investment scale. When the FMI reached CNY 100 million, the growth rate of the carbon sink remained at a low level.  
Overall, the government should reasonably increase the level of FMI in various forest regions and simultaneously strengthen the management and supervision of the use of forest management funds. Additionally, timely prevention of plant diseases and insect pests, drought prevention and moisture conservation, and timely implementation of forestry measures such as thinning and replanting should be implemented. The high-quality development of forests in the key SOFRs of Heilongjiang Province should be promoted and the realization of the \"dual carbon\" goal can be achieved.  
Conceptualization, S.L. and S.Y.; methodology, S.L.; software, S.L. and Z.D.; validation, Z.D., Y.L. and S.Y.; formal analysis, S.L. and Z.D.; investigation, S.L., Y.L. and Z.D.; resources, Y.L. and S.Y.; data curation, S.L.; writing--original draft preparation, S.L.; writing--review and editing, S.L.; visualization, S.L., Y.L. and Z.D.; supervision, S.Y. and Z.D.; project administration, S.Y.; funding acquisition, S.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Special Fund for Scientific Research of Forestry Commonwealth Industry, grant number 201504424 and the National Natural Science Foundation of China, grant number 71473195, 71773091.  
Not applicable.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The authors declare no conflict of interest.