1 INTRODUCTION

The geographical distribution pattern of species and utilizing species distribution models (SDMs) to predict the potential geographical distribution of species are one of the hot research issues in the fields of biogeography and biodiversity conservation (Gaston, 2000; Zhang & Ma, 2008; Ning et al., 2018; Tripathi et al., 2019a). Studying the geographical distribution pattern and predicting the potential geographical distribution of species are of great significance for developing effective biodiversity conservation strategies (Zhang et al., 2019; Lazo-Cancino et al., 2020), preventing and managing the spread of invasive alien species (IAS) diffusion (Fernandes et al., 2019) and assessing the impact of climate change on species distribution (Lazo-Cancino et al., 2020), and they are also an effective means of protecting and managing some rare, endangered and/or threatened species.
The maximum entropy (MaxEnt) model is a species distribution model based on the environmental factors matching method, and is often used to predict the potential geographical distribution of species. The MaxEnt model employs the data of species distribution locations and environmental variables to jointly simulate the potential geographical distribution of species and has many advantages over other species distribution models, including easy operation and use, high simulation precision, good performance with incomplete datasets (Li et al., 2020). Currently, the MaxEnt is the most widely used species distribution model (Merow et al., 2013; Gong et al., 2015; Ning et al., 2018). The research results of Hernandez et al. (2006) and Deb et al. (2017) both showed that in the case of few geographical locations (< 10), even as low as 4 or 5, the MaxEnt model can still produce effective prediction results with high precision. At present, the model has been applied to simulate and predict the potential geographical distribution of endemic species (e.g.,Impatiens hainanensis ; Ning et al., 2018), national protected species (e.g., Phellodendron amurense ; Huang et al., 2018) and many other key species.
It is helpful to improve the scientific understanding of the spatial relationship between species and environment by studying the impact of different types of environmental factors on the potential geographical distribution of species. The spatial distribution pattern of species diversity is related to variations in environmental factors (e.g., Latitude, elevation and climate) (Tripathi et al., 2019a). However, the relationship between them often has spatial non-stationarity (i.e., Relationship between independent and dependent variables will change with geographical location) (Gouveia et al., 2013). Geographically weighted regression (GWR) model, which is an extension of traditional regression model (e.g., Ordinary least squares, OLS) (Ștefănescu et al., 2017; Tripathi et al., 2019a; Tripathi et al., 2019b; Xue et al., 2020), has become one of the crucial spatial heterogeneity modeling tools (Lu et al., 2020). In recent years, many domestic and foreign scholars have carried out in-depth and extensive research in various fields by using GWR model, including social environmental factors and regional economy, regional house prices and pollution (McCord et al., 2018; Xu et al., 2019), the impacts of environmental heterogeneity and land use change on wild animal distribution (Liu et al., 2019; Wang et al., 2020; Xue et al., 2020), vegetation activity and climate change (Gao et al., 2019). However, there are few studies that in combination MaxEnt with GWR models to analyze the potential geographical distribution and explore environmental explanations for some key species, especially in biodiversity hotspot areas.
According to the Living Planet Report 2020 (https://www.wwf.org.uk/press-release/living-planet-report-2020), published by World Wide Fund for Nature (WWF) and Zoological Society of London (ZSL), population sizes of mammals, birds, fish, amphibians and reptiles have fallen an average of 68% globally. Northwest Yunnan of China is one of the global biodiversity hotspots (Myers et al., 2000; Ye et al., 2020a; Ye et al., 2020b). Plenty of rare, endangered, threatened and endemic species that need critical conservation are distributed in this area (Yang et al., 2017). In recent decades, due to the interference of human activities (e.g., Mining and collecting herbs) and the influence of the external natural environment, especially climate change, the populations and distribution area of some rare, endangered and threatened species have been decreasing (Yu et al., 2014). Living Planet Report 2020 also stated that from 2000 to 2018, the species habitat index dropped by 2%, which indicated that the habitat quality of species shows a general trend of rapid decline. In addition, some species have the characteristics of geographical isolation and narrow distribution (Wang et al., 2013), as a result, their survival and development are faced with severe threats. Therefore, it is urgent to protect these key species and their suitable habitats in this area. In order to protect these key species reasonably and effectively, their geographical distribution must be clear first. However, at present, we are still unclear about the potential geographical distribution and main limited environmental factors for these key species in Northwest Yunnan.
Therefore, in this study, 25 key species were the focus of analysis, including some rare, endangered and/or national protected key higher plant species in Northwest Yunnan. Initially, we adopted the method of combining the MaxEnt model together with GWR model to predict the potential geographical distribution of each species on the grid map with a resolution of 0.05° × 0.05° (for more details about resolution, see Ye et al., 2020a). Then, we overlaid the potential geographical distribution of each species, and obtained the potential geographical distribution pattern of species richness on the spatial scale of the ecological niche model with a resolution of 0.05° × 0.05°. Ultimately, we analyzed the explanation capabilities of various environmental factors on the potential geographical distribution patterns of these key species, and explored the main restrictive environmental factors. These research results would contribute to a more comprehensive understanding of the potential geographical distribution pattern of some key higher plant species in Northwest Yunnan, and would provide a scientific basis for the conservation and management of suitable habitat for rare, endangered and many other key species in this region.