Tourists’ Behavioral Characteristics Regarding Island-Based Tourism Destinations through the Perspective of Spatial Constraints: A Case Study of Yangma Island in China

: The factors affecting tourist behavior are complex and diverse, but research on its effect from a purely spatial perspective is still limited. The aim of this paper is to explore the dichotomous interaction between tourists and islands: the behavioral patterns of tourists in island destinations and the mechanisms by which island spaces constrain tourist behavior. This study uses ﬁne-grained global positioning system (GPS) tracking data actively authorized and released by tourists. We empirically studied tourist behavior from a spatial constraint perspective and discovered the following: island space has a strong inﬂuence and constraining effect on tourist behavior; different spatial attributes have different constraining effects on tourist behavior; and people with different identities interact with different attributes of space to produce different spatial properties, resulting in a ‘harmony-contradiction’ model of spatial interaction. These ﬁndings are of great value in expanding the perspective of spatial constraints and exploring the interactions between people and land. They are also of great practical signiﬁcance in promoting spatial planning synergy, facilitating the construction of high-quality island-based tourism destinations, and building a harmonious relationship between people and land. negative impacts to the vegetation on the island and vegetation growth. The water-related area refers to activities such as pebble picking, oyster collecting and sea anemone collecting in the offshore area. To a certain extent, it adversely affects the local original ecology. In this regard, Yangma Island should pay attention to re-optimizing the layout of the island’s tourism service zone, based on the tourist’s activity demand. Simultaneously, they should strengthen the environmental protection of the island’s ecological protection zone, continue to build and improve the service facilities in the tourist-intensive area, and most importantly pay attention to improving the coastal landscape protection and sightseeing services within the island’s ring area. Therefore, different subjects and objects and their activities have formed diverse spatial interaction patterns within the island. Summarizing the above spatial types and their attributes is of great signiﬁcance to further optimize the harmonious spatial state and solve contradictory spatial problems.


Introduction
In the 21st century, with the rise of mass tourism in China and the economic development of coastal areas, island tourism has become a core pillar in the industrial structure of China's marine economy [1]. The booming development of island tourism has attracted the attention of many scholars. It has become a hotspot for tourism research in China, mainly in the areas of island resources and development, human earth relations and social impacts, and coordinated development of island economies [2]. Although it displays diversified development, most of these focus on the island itself, while the main activity of island tourism (i.e., the tourists) is relatively lacking in studies.
As a dichotomy between tourists and islands, what are the patterns of tourists' activities in terms of attraction selection, route planning, and human flow distribution within the islands? How does the closed and independent island space influence and constrain tourist behavior? Based on the perspective of spatial constraint, this paper analyzes the behavioral characteristics of tourists in island destinations, which differ from those of general land-based destinations, using kernel density, standard deviation ellipse, on-track rate, and the restriction involvement index. It further refines the spatial constraint mechanism and interaction model that affect tourists' behavior. The study has a theoretical and empirical value, and can enrich and expand the content and boundaries on the behavior of island tourists in terms of spatial constraints. In addition, the study also significantly promotes spatial synergy in island planning and the construction of high-quality island-based ISPRS Int. J. Geo-Inf. 2022, 11, 14 2 of 18 tourism destinations, and building a harmonious relationship between people and land. This study will be analyzed and discussed through the following six sections: Section 2 is composed of the literature related to tourism constraints. It introduces the literature on tourism behavior research from the perspective of the methodological development of acquiring data. Section 3 introduces the case land of the study, describing the data crawled from the trajectory sharing platform and the specific geographic analysis method. Section 4 summarizes and explores the characteristics of tourist behavior and spatial constraints under the interaction of mechanisms. Section 5 further explores the relationship between the tourists and the island space, condensed into two parts: the spatial constraint mechanism and the spatial interaction model. Finally, Sections 6 and 7 highlights innovations in the study such as perspectives and models, describes the theoretical and practical implications of the study, and illustrates the limitations and future vision.

Tourism Behavior
One of the main tasks of tourism geography is to study tourism activities and spatial patterns of people in relation to the natural and built environment [3]. Related studies focus on explaining spatial patterns of tourism activities at different scales, such as global, national, regional, and local scales [4,5]. They often focus on larger scale patterns of movement between destinations [6][7][8][9][10]. Influenced by humanism and postmodernism, research in human geography has begun to focus on explaining human geographic phenomena from the perspective of micro-individual behaviors [11]; thus, individual tourist behaviors that conduct activities within smaller-scale destinations have begun to receive attention, but related research is still relatively limited [12].
Advances in the study of tourist behavior within destinations are not limited to advances in ideology, but depend largely on the level of development of recording and tracking methods [13]. Initially, scholars used non-participatory observations to record tourist behavior; Hartmann [14] used remote observation of tourists, while Sasaki and Keul [15] and Keul and Kiheberger [16] used field methods to track tourists, but such methods record limited data on the range of tourist activities and movement information. Therefore, in the next phase, spatio-temporal budgeting techniques became the mainstream method. These take the form of spatio-temporal diaries that record detailed information about the sequence and timing of tourist activities. They have contributed largely to the global studies of tourist behavior, while improving the overall chain of tourist behavior [17][18][19][20][21][22]. However, the time-consuming and labour-intensive questionnaire format used in this method has discouraged certain tourists. Even if they agree to complete it, the accuracy of the information collected is difficult to guarantee, due to the subjects' ability to recall past events [17], and a rapid decline in the quantity and quality of data collected during the completion process [23].
With the development of satellite positioning technology, the global positioning system (GPS) tracking and recording method has made up for the shortcomings of tracking and questionnaire methods [24,25], which predominantly provides data records of the density, flow and distribution of human movement by capturing ground travel patterns [26]. GPS has been proven to collect relatively accurate, detailed, and complete spatial and temporal data [27][28][29][30]. Both GPS and the GPS survey method have made a significant contribution to the study of behavior within national parks [25,31]. Nevertheless, GPS survey methods also involve cost issues, such as purchasing instruments, issuing equipment, and retrieving equipment. There is also instability in individual areas where equipment trajectories can cause interference and jamming. Although advanced Bluetooth technology [32][33][34], radio frequency identification [35], and hybrid technology [36] have emerged as current tourism supplements to travel behavior tracking methods, with the advent of the mobile internet era, the popularity of smartphones brought an unprecedentedly strong impetus to travel behavior research [24,33]. Among them, geolocation-based travel sharing media platforms (such as Weibo, Twitter, and Flickr) [37][38][39], tourist experience-based evaluation platforms (such as TripAdvisor and Ctrip) [40][41][42][43][44], and tourist-formed travel journal sharing platforms (such as Mafengwo) [45,46] provide a new, enriched, and expanded source of data for research on tourist behavior. However, unlike the media above, the rise of outdoor GPS track sharing platforms provides a new way of looking at travel behavior research. Unlike Flickr and Weibo, outdoor GPS track sharing applications can provide more granular and more complete GPS tracks of tourists. This data is not only proactively authorized and shared by the users, but guarantees satisfactory results for mobile phone location functions. Furthermore, platform users use their cell phones to actively record the trajectories of their travel activities and authorize their release to the public platform, which alleviates the concern of whether the insecurity of outsider tracking devices will change or deflect the itinerary, while avoiding the violation of the user's willingness to voluntarily disclose information. This protects the user's privacy in a better way. Thus, the adoption of a shared outdoor track recording platform not only alleviates the cost of money and time for researchers, but also enables the use of more granular data to understand how tourists move within a destination and the factors influencing their movement, which is important for improving island facilities, innovative product development and marketing [3].

Tourism Constraints
Häagerstrand's temporal geography does not attempt to predict human spatial behavior. Rather, it focuses on the spatial and temporal constraints on human activity. It is mainly used to study individual activity patterns under various constraints in a spatio-temporal context [47]. This conceptual framework has been used in tourism behavior research. It also played a continuous and important role in the study of tourism behavior. Although tourists' behavior is constrained by a variety of internal and external factors [6,12,47,48], the two spatiol-temporal dimensions provided by Häagerstrand [47] remain the most influential constraints. The influence of spatio-temporal factors is reflected not only in the movement patterns of individual behaviors in the spatio-temporal prism, but also in the constraints on human behavior within the prism [49].
Mobility is becoming increasingly important in highly urbanised societies and complex urban spatial structures [50]. The temporal model constructed by Häagerstrand has gradually been replaced by a more diverse model of intra-city mobility [51]. As a result, there is a growing interest in time and urban space [52], and a new way of thinking about time in public policy and planning. As a result, some governments have introduced time policies that intervene in scheduling and organizing to reconcile the problem of spatiotemporal correlations by regulating the rhythms of cities and people [51,53], ultimately allowing for the adaptation to a spatio-temporally diverse city and a human society with more accessible spatio-temporal choices [52]. Tourism now has an important place in many urban industrial systems, which has profoundly affected the use of time and space for tourism in cities. However, time has recently and increasingly been mentioned and explored as a constraint on tourism activity [20][21][22][54][55][56][57]. However, Pearce [5] argues that the absence of an explicit study of space in tourism research makes temporal studies fragmented at best. Therefore, analyzing the tourist flow under spatial constraints will not only have the theoretical value of compensating for the lack of individual tourist flow and improving the tourist flow constraint mechanism, but it will also have a strong practical value that enhances the tourist experience, improves the construction of scenic spots and achieves economic benefits.
Every human being is in the given space, all social activities are carried out in a specific space, and human beings simultaneously construct this space and are bound to the given and human-initiated constructed space. Thus, the binding of space is expressed through the order and structure of activities within this space. Tourism spatial constraints often refer to the tourist's behavior and activities in the tourism process, from spatial properties, spatial relations, and other aspects of constraints. This means that it is difficult to achieve specific tourist space that is in a state of freedom of movement. At present, spatial constraints are mainly applied in urban planning, spatial optimization and other related fields [58][59][60], while the results on tourism destinations are applied to less. The focus is on the accessibility factors [61][62][63][64], spatial distance decay of source markets [62,65] and theme park layout [66,67]. Few microscopic spatial constraint mechanisms are explored within their destinations. Therefore, we explore the feasibility of spatial constraints based on and in conjunction with actual case lands [67,68]. Four analytical dimensions of spatial distance, shape, pattern, and zone [60] were selected to research the mobility behavior of tourists within island-based tourism destinations, which not only helps to expand the depth and breadth of spatial constraints in tourism research application fields, but also uses quantitative and qualitative methods to analyze and summarize these concepts. This expands the depth and breadth of the application of spatial constraints in tourism research. Importantly, this also analyzes and summarizes the flow characteristics of tourists in islandtype tourism destinations, using the quantitative and qualitative methods, and realizes the analysis of future scenarios on this basis, to promote the research progress of tourism spatial constraints and micro-scale island-type tourism destinations. This can help achieve the goal of spatial optimization of Yangma Island.

Data Source and Description
Yangma Island is located in the Yellow Sea in Yantai, Shandong Province, China. With a total area of 13.52 sq. km, a coastline of 19.5 km, and shaped like an oval in the north-east-south-west direction, the island is known as the 'Maldives of China' because of its beautiful scenery, abundant seafood, and pleasant climate. Emperor Qin Shi Huang (the first emperor of feudal China) apparently used to raise horses in this area during his eastern tour. There are many popular scenic spots on the island, such as Tianma Square, Qinfeng Cliff, Zhang Island, and the Racecourse, most of them located in the coastal area. Yangma Island is close to the mainland's cities and main consumer markets, and its tourism and fishing industries are quite developed. There is a high degree of integration between the living zones of the villages in the south of the island and the tourist space. A large number of fishers' houses with special characteristics are offered to tourists to provide them with food, accommodation, leisure and entertainment services, as an added attraction for tourists to experience. In recent years, with the spread of new media (such as the Douyin App, the Chinese version of Tik Tok, and Kuaishou app), the daily average number of tourists received at Yangma Island during the peak season has been as high as 50,000, indicating a rapid growth for its tourism industry.
The enclosed and relatively independent internal spatial structure of Yangma Island is relatively simple, with routes that are clear, which makes it easy to identify the behavior trajectory of its tourists. The southern periphery of the island is a city and there are more residential areas within it, with more base stations and better cell phone reception signals. Within the destination, and especially the coastal area, the space is relatively open. The tour route is basically free of trees and buildings that block the GPS signal received by cell phones, so the signal reception strength is relatively high and the trajectory records are relatively accurate. Therefore, it is highly feasible to use it as a case study of spatial constraints and tourists' behavior.

Data Sources
The data used to study the interaction between spatial constraints and tourist behavior are often divided into two parts: one is the basic geographic information data from sky maps and geospatial data clouds, which are predominantly used to extract island boundaries, build road networks, classify land types, and analyze spatial patterns; the other part is the GPS trajectory data of tourists with geographic attributes, which are automatically recorded by GPS devices based on fixed time intervals. The original data are track points that are presented as lines and can reflect the activity range and travel pattern of individual tourists and groups in estimation [69]. The trajectory data were obtained from Six Feet and Two Steps, two website platforms that specialize in recording outdoor athletes' trajectories.
These are sharing and exchange platforms for tourists to record, browse, and share routes. The platforms rely on smartphones with GPS chips to collect and share activity trajectories of tourists' outdoor behavior [70].
As of 28 September 2020, a search was conducted with the keyword 'Yangma Island', and the collected data were cut to fit the research requirements, as per the scope of the study. Through the analysis and evaluation of each track, the invalid tracks (e.g., nontourist tracks, incorrect positioning, repeated records, and trips that were too short) were screened and deleted. Finally, 160 tracks were obtained. The actual effective trajectories were also obtained, with an efficiency rate of 50.63% and a total length of 2140.64 km. This included basic information (e.g., username, latitude and longitude, time, speed, elevation, etc.), which assisted in judging tour behavior and tourists' status. The six-foot platform uses a frequency of 4 s/time to record the data of point and line trajectories for tourists. The Two Step platform uses a frequency of 2 s/time to record only the line trajectories. Hence, there is a certain data difference between the two and all the trajectory data files are standardized. The 160 KML files are imported into ArcGIS 10.2 and a suitable fishing net is established within the range of Yangma Island. Through repeated testing, it was concluded that the fishing net grid size of 5 × 5 m not only ensured substantial data accuracy, but also ensured the smooth operation of all subsequent operations, so that the computer was able to operate and run. Finally, 544,508 trajectory points were obtained through the intersection of the trajectory line and fishing net turning points, which provided strong data support for feature quantification and subsequent research.

Research Methodology
Space is not a container filled with objects, but a dwelling place for human consciousness [71], where people move around constantly and are always under its constraints. Tourism space, while providing a certain length of travel, morphological range, road network pattern and functional zones for tourists' behavior, also influences the subjective initiative of tourists through distance, shape, pattern, and zone, which constrains their behavioral activities. To verify the existence of different forms of spatial constraints in a more targeted manner, different geographic processing and analysis methods are used to verify accordingly: in terms of distance constraint, the kernel density calculation method is used to reflect the hot and cold conditions of the intra-island distribution of tourists visually. Thereafter, the profile analysis is conducted along the traffic circle, with the help of three-dimensional (3D) lines, to verify the decay of intra-island distance and its characteristics. In terms of shape constraint, the standard deviation ellipse is used to reflect the influence of island shape. It falls onto the specific distribution of tourists. In terms of pattern constraint, the trajectory in on-track analysis method is used to establish a buffer zone based on the existing road width of Yangma Island. The trajectory of tourists is superimposed with the road range, and then reflected by the on-track rate. In terms of zone constraint, the number, length and area of trajectories within different functional areas are taken into account for comprehensive statistics to reflect the level of constraint on tourist involvement in that functional zone.

Distance Constraint
Kernel density estimation is applied as a nonparametric technique to the spatial distribution of tourist behavior trajectory data. Through quantitative calculations, point features are transformed into smooth surface features, to analyze the spatial distribution trends of point features of tourist trajectories. Influenced by geographic elements, tourists' activities have characteristics that are evolving, such as core polarization and edge diffusion [72]. This presents a gradient change pattern of activity intensity with distance decay [73]. Profile analysis along the traffic circle (with the help of 3D lines in ArcGIS 10.2) can visually reflect the hot and cold conditions of the intra-island distribution of tourists, which can then be used to verify the intra-island distance decay and its characteristics. The specific formula is is called the kernel function, which is based on the quadratic kernel function described in Silverman ( ; n is the number of track points; (x − x i ) is the distance from the estimated point to sample x i ; h is the bandwidth, and an appropriate KDE bandwidth can be determined to equal the smaller of the length or width of a study area, divided by between 30 and 50 [75]. Comparing the results with bandwidth values in reasonable intervals revealed that the density raster generated using the ArcGIS 10.2 default bandwidth (divided by 30, h = 218.225368) was smoother and more generalized, clearly representing the distribution and mobility characteristics of tourist trajectories.

Shape Constraint
The standard deviation ellipse is a classical statistical measure that can summarize spatial characteristics (e.g., central tendency, dispersion and direction of a series of GPS track points) in a more visual and concrete way, by measuring the distribution of these track points [76,77]. The overall distribution of the behavioral activities of tourists on the island is presented in the form of a standard deviation ellipse. The results of the area and rotation angle of the resulting standard deviation ellipse reflect the influence of the island's shape on the specific distribution of tourists. The specific formula is as follows.
Ellipse rotation angle: x, y represent the deviation of each element's coordinates from the mean center. x-axis and y-axis standard deviation.

Pattern Constraint
Based on the existing road width of Yangma Island, a buffer zone is established. The trajectory of tourists is overlaid with the road range. The on-track rate reflects the degree of constraint of tourist trajectory in the island by the road pattern. The specific formula is where P reflects the probability of on-track distribution of tourist trajectory points, n is the number of trajectory points within the road buffer, and N is the total number of trajectory points [70]. In addition, while roads constrain tourist behavior paths, they also influence tourist mobility patterns through the road network pattern. A question worth exploring is how the road network pattern within the island affects tourist mobility and thus, what behavior patterns are formed. Therefore, this study adopts the trajectory overlay method [78,79] which is often used to visualize the clustering of tourist trajectories. To do so, it sets the GPS trajectories of tourists to a positive red colour and projects the transparency to 95% into the base map of Yangma Island and road network in ArcGIS10.2. Finally, the clustering analysis of the results were presented as the flow trajectory patterns of tourists on Yangma Island. This allows for further exploration of the road network pattern and its influence on behavioral patterns.

Zone Constraint
The land of Yangma Island is divided into three functional zones: ecological protection zone, residential living zone and tourism service zone. By calculating the number, length and area of tourists' trajectories, we can determine the distribution area and flow range of tourists [70], so as to verify whether the functional zones have an impact on the overall activity range of tourists on the island. The number of trajectories and the length of trajectories are used to visually express the frequency and distances of tourists' wandering behavior. A grid-based spatial measurement is used to consolidate the area of the trajectories in the corresponding functional zones, to reflect the degree of constraint of tourists' wandering in the functional zones. The restriction involvement index is a quantitative measure of the extent to which the range of tourist behavior is restricted and is designed for trajectory data to act as a corroboration in welcoming or restricting tourists to different functional zones. The specific formula is where, for track number index A: the ratio of the number of tracks in this functional zone to the total number of tracks. Involvement length index B: the ratio of the length of tracks in this functional zone to the total length of tracks. Involvement zone index C: the ratio of the number of grids 5 m × 5 m within this functional zone, which are involved by tourists to the total area of the corresponding functional zone. i is the type of functional zone, which are tourism service zone, ecological protection zone, and residential living zone. To eliminate the influence of data outlined in different regions, the data are standardized and the index is kept within a fixed range, from 0 to 1. R is the final restriction involvement index; the larger the value, the more binding the region is in restricting tourist activities.

Distance Constraint
From the results of kernel density analysis (Figure 1), the behavior trajectory of tourists on the island show obvious 'traffic circle fever' characteristics. The traffic circle road is the road with the highest kernel density value. Taking the entrance of the traffic circle as the starting point, the kernel density value shows a decreasing trend in fluctuation when tourists travel along the traffic circle road. The east west road also has a certain amount of heat, but it is predominantly used by tourists in the western section, as the island exit, so the heat decreases from west to east. In addition to following the law of distance decay, the nuclear density value profile of the round island ( Figure 2) shows that there are also two major peak areas (i.e., the two major wave peaks of Qinfeng Cliff and Zhang Island). These two areas, as the main thermal cores, have an obvious role in clustering and driving the surrounding areas, especially around Zhang Island, which forms the overall high value range area of the island. This indicates that the closer the hotspot area is, the higher the number of corresponding tourists will be, while the heat of the areas farther away from the hotspot scenic spots, or those that lack attractions, are relatively lower.

Distance Constraint
From the results of kernel density analysis (Figure 1), the behavior trajectory of tourists on the island show obvious 'traffic circle fever' characteristics. The traffic circle road is the road with the highest kernel density value. Taking the entrance of the traffic circle as the starting point, the kernel density value shows a decreasing trend in fluctuation when tourists travel along the traffic circle road. The east west road also has a certain amount of heat, but it is predominantly used by tourists in the western section, as the island exit, so the heat decreases from west to east. In addition to following the law of distance decay, the nuclear density value profile of the round island ( Figure 2) shows that there are also two major peak areas (i.e., the two major wave peaks of Qinfeng Cliff and Zhang Island). These two areas, as the main thermal cores, have an obvious role in clustering and driving the surrounding areas, especially around Zhang Island, which forms the overall high value range area of the island. This indicates that the closer the hotspot area is, the higher the number of corresponding tourists will be, while the heat of the areas farther away from the hotspot scenic spots, or those that lack attractions, are relatively lower.

Shape Constraint
The standard deviation ellipse generated from tourists' GPS trajectories can summarize the actual range of tourists' activities on the island. Despite the differences in preference, time, and energy of tourists in the tour process which led to different characteristics of the tour itineraries the results of the standard deviation ellipses (Figure 3) show that

Shape Constraint
The standard deviation ellipse generated from tourists' GPS trajectories can summarize the actual range of tourists' activities on the island. Despite the differences in preference, time, and energy of tourists in the tour process which led to different characteristics of the tour itineraries the results of the standard deviation ellipses (Figure 3) show that there are large common features among the tourists' trajectories. The overall standard deviation ellipse generated by the itinerary trajectories of all tourists is basically the same in direction and shape as that of Yangma Island. This implies that tourists are deeply constrained by the shape of the island during their excursions within the island-based tourist destinations. At the same time, the island-type tourist destination is surrounded by seawater, which limits the possibility for most tourists to explore further, beyond the boundaries of the island shape. Hence, the land within the island and the beach, which is formed by the intertidal zone, are the feasible activities for tourists. The resulting standard deviation ellipse has a noteworthy similarity to the overall shape of the island.

Pattern Constraint
The travel of the tourists through space is seen as an expression of programmatic 'modes of movement' [80]. The tourist trajectory under the spatial constraint of road pattern is essentially a linear combination of the tourists' rational choice of roads and other spatial elements within the destination area [81]. The results found that the tourist trajectories fit with the existing road network pattern significantly. The actual tour routes are constrained by the island traffic pattern that have strong clustering of main roads. Among them, 448,200 trajectory points were located within the road buffer zone, with an on-track rate of 82.32%. Off-track activities predominantly occurred in the offshore beach area (Figure 4). According to the trajectory overlay clustering results, the behavioral paths among tourists are significantly similarity. The round-island tour is the most widely chosen by tourists and the trajectory overlay effect is the most prominent. In addition, the route design of the northern one-way route and the recommended counter-clockwise island loop has a more compulsory flow constraint, resulting in a clear one-way flow characteristic of tourists during the tour process.

Pattern Constraint
The travel of the tourists through space is seen as an expression of programmatic 'modes of movement' [80]. The tourist trajectory under the spatial constraint of road pattern is essentially a linear combination of the tourists' rational choice of roads and other spatial elements within the destination area [81]. The results found that the tourist trajectories fit with the existing road network pattern significantly. The actual tour routes are constrained by the island traffic pattern that have strong clustering of main roads. Among them, 448,200 trajectory points were located within the road buffer zone, with an on-track rate of 82.32%. Off-track activities predominantly occurred in the offshore beach area (Figure 4). According to the trajectory overlay clustering results, the behavioral paths among tourists are significantly similarity. The round-island tour is the most widely chosen by tourists and the trajectory overlay effect is the most prominent. In addition, the route design of the northern one-way route and the recommended counter-clockwise island loop has a more compulsory flow constraint, resulting in a clear one-way flow characteristic of tourists during the tour process.

Zone Constraint
The planning scheme of Yangma Island divides it into three functional zones-residential living zone, tourism service zone, and ecological protection zone-for differentiated utilization, management, and protection, respectively. These constrain and regulate the content and range of activities for tourists. The tourist service zone is mainly the areas where tourists can go sight-seeing, and are provided with services and related facilities. The residential living zone is mainly where the islanders live, although some of the residents have switched from fishing to other professions. Thus, while some of the space has some overlap between tourism services and residential living, the zone is still within the village and mainly serves as the islanders' living area. The ecological protection zone is an area in the woodlands created by the local government for environment protection, with boundaries of protective fences and other devices to prevent disturbance and damage from humans, and therefore does not serve tourism activities such as excursions. The nature and function of the different zones regulate tourist activities on the island.
For tourists, the sea is not only an important landscape, but also the biggest regional constraint unit of activities. Specifically, the coastal area of Yangma Island is the aquacultural base of local fishermen. Due to the existence of problems such as unclear delineation of regional boundaries, fishermen are prone to certain conflicts of interest with shallow sea fishing for seafood for tourists. This intensifies the conflicts between fishermen and tourists. Due to the blockage of hardware facilities and the protective behavior of the policy, only 9.38% of the tourists involved in the ecological protection zone and the zone involved is extremely limited. The manifestation of restricting the proliferation and mobility of tourists within this area is more obvious (see Figure 5 and Table 1), so the northern ecological protection zone is less affected by the activities of tourists. Although the residential living zone is relatively open, they lack the tourism elements that attract tourists. Therefore, they are relatively less involved. The traffic circle area, on the other hand, is planned as a tourism service zone, with the highest degree of openness to the outside world. It possesses beautiful coastal scenery and relatively sound tourist service facilities; therefore, it has become the main area, with the highest concentration of tourist activities.

Zone Constraint
The planning scheme of Yangma Island divides it into three functional zones-residential living zone, tourism service zone, and ecological protection zone-for differentiated utilization, management, and protection, respectively. These constrain and regulate the content and range of activities for tourists. The tourist service zone is mainly the areas where tourists can go sight-seeing, and are provided with services and related facilities. The residential living zone is mainly where the islanders live, although some of the residents have switched from fishing to other professions. Thus, while some of the space has some overlap between tourism services and residential living, the zone is still within the village and mainly serves as the islanders' living area. The ecological protection zone is an area in the woodlands created by the local government for environment protection, with boundaries of protective fences and other devices to prevent disturbance and damage from humans, and therefore does not serve tourism activities such as excursions. The nature and function of the different zones regulate tourist activities on the island.
For tourists, the sea is not only an important landscape, but also the biggest regional constraint unit of activities. Specifically, the coastal area of Yangma Island is the aquacultural base of local fishermen. Due to the existence of problems such as unclear delineation of regional boundaries, fishermen are prone to certain conflicts of interest with shallow sea fishing for seafood for tourists. This intensifies the conflicts between fishermen and tourists. Due to the blockage of hardware facilities and the protective behavior of the policy, only 9.38% of the tourists involved in the ecological protection zone and the zone involved is extremely limited. The manifestation of restricting the proliferation and mobility of tourists within this area is more obvious (see Figure 5 and Table 1), so the northern ecological protection zone is less affected by the activities of tourists. Although the residential living zone is relatively open, they lack the tourism elements that attract tourists. Therefore, they are relatively less involved. The traffic circle area, on the other hand, is planned as a tourism service zone, with the highest degree of openness to the outside world. It possesses beautiful coastal scenery and relatively sound tourist service facilities; therefore, it has become the main area, with the highest concentration of tourist activities.

Spatial Constraint Mechanism
From the abovementioned analysis, we can find that: (1) with the increase of the distance around the island, the frequency of tourists is decreasing, showing an obvious negative correlation; (2) the overall distribution of tourists has a greater similarity to the shape and contour of Yangma Island, in line with the 'northeast-southwest' pattern; (3) the path of tourists who visit the island is consistent with the existing road network pattern, and the overall tour pattern is relatively similar; (4) the functional zones of the island restricts the scope of tourists' behavior, and the scope constraints on the trajectory of tourists are more obvious. Furthermore, we condensed the spatial constraints on the behavior of island tourists into the following four points ( Figure 6): spatial distance constraint affect its flow length; spatial shape constraint affect its flow distribution; spatial pattern constraint affect its flow path; spatial zone constraint affect its flow range. The four constraints summarized above interact and influence each other, acting together on the tourist flow behavior in island-type tourist destinations, which forms a holistic constraint mechanism.

Spatial Constraint Mechanism
From the abovementioned analysis, we can find that: (1) with the increase of the distance around the island, the frequency of tourists is decreasing, showing an obvious negative correlation; (2) the overall distribution of tourists has a greater similarity to the shape and contour of Yangma Island, in line with the 'northeast-southwest' pattern; (3) the path of tourists who visit the island is consistent with the existing road network pattern, and the overall tour pattern is relatively similar; (4) the functional zones of the island restricts the scope of tourists' behavior, and the scope constraints on the trajectory of tourists are more obvious. Furthermore, we condensed the spatial constraints on the behavior of island tourists into the following four points ( Figure 6): spatial distance constraint affect its flow length; spatial shape constraint affect its flow distribution; spatial pattern constraint affect its flow path; spatial zone constraint affect its flow range. The four constraints summarized above interact and influence each other, acting together on the tourist flow behavior in island-type tourist destinations, which forms a holistic constraint mechanism. ISPRS Int. J. Geo-Inf. 2022, 11, x FOR PEER REVIEW 13 of 19 Figure 6. Spatial constraint mechanism of tourists' behavior.

Spatial Interaction Model
Based on the profit loss relationship between tourists, island residents and producers in different areas, and further exploring the human land relationship in Yangma Island by combining tourists' behavior trajectory and spatial constraint mechanism, the spatial interaction pattern of Yangma Island is qualitatively divided into two spatial attributes: harmony and contradiction, according to their main profit loss relationship. The harmonious and contradictory spaces are further divided into specific and different spatial types, according to different human land interactions (see Figure 7).
Among them, harmonious space is a type of space where the tourist is the main body. After interacting with related people and places on the island, they have a high evaluation of tourism services and experiences, which is conducive to the sustainable development of tourism on the island. These include common space and consumption space, which is defined as follows: 'common space' is a type of space formed by the interaction of two main bodies (the tourist and the residents engaged in tourism production) from which both benefit. The consumption space is the type of space formed by the interaction between tourists and foreign businesses engaged in tourism production. These include tourists who buy tickets to watch equestrian shows at the racecourse, invested by companies outside the island. Conflict space is the type of space formed by tourists as the main body, after interacting with related people and places on the island, which produces a lower evaluation of tourism services and experiences or causes negative impacts on the livelihood of local people, native culture, and ecologically sustainable development of the island. These include conflict space, interference space, invasion space, and water-related space. Conflict space mainly refers to the type of space where tourists and producers have certain conflicts of interest in the marine space. This includes tourists who rush to the sea to pick up the aquatic products of local farmers and are expelled by the farmers. Interference space refers to the type of space where tourists use undeveloped villages or those less willing to open, as one of the island tour destinations. This causes certain interferences in the daily life and native culture of residents. Invasion space refers to the type of space where tourists enter the protected forests and other vegetation protection zones in the Figure 6. Spatial constraint mechanism of tourists' behavior.

Spatial Interaction Model
Based on the profit loss relationship between tourists, island residents and producers in different areas, and further exploring the human land relationship in Yangma Island by combining tourists' behavior trajectory and spatial constraint mechanism, the spatial interaction pattern of Yangma Island is qualitatively divided into two spatial attributes: harmony and contradiction, according to their main profit loss relationship. The harmonious and contradictory spaces are further divided into specific and different spatial types, according to different human land interactions (see Figure 7).
Among them, harmonious space is a type of space where the tourist is the main body. After interacting with related people and places on the island, they have a high evaluation of tourism services and experiences, which is conducive to the sustainable development of tourism on the island. These include common space and consumption space, which is defined as follows: 'common space' is a type of space formed by the interaction of two main bodies (the tourist and the residents engaged in tourism production) from which both benefit. The consumption space is the type of space formed by the interaction between tourists and foreign businesses engaged in tourism production. These include tourists who buy tickets to watch equestrian shows at the racecourse, invested by companies outside the island. Conflict space is the type of space formed by tourists as the main body, after interacting with related people and places on the island, which produces a lower evaluation of tourism services and experiences or causes negative impacts on the livelihood of local people, native culture, and ecologically sustainable development of the island. These include conflict space, interference space, invasion space, and water-related space. Conflict space mainly refers to the type of space where tourists and producers have certain conflicts of interest in the marine space. This includes tourists who rush to the sea to pick up the aquatic products of local farmers and are expelled by the farmers. Interference space refers to the type of space where tourists use undeveloped villages or those less willing to open, as one of the island tour destinations. This causes certain interferences in the daily life and native culture of residents. Invasion space refers to the type of space where tourists enter the protected forests and other vegetation protection zones in the island illegally, causing negative impacts to the vegetation on the island and vegetation growth. The water-related area refers to activities such as pebble picking, oyster collecting and sea anemone collecting in the offshore area. To a certain extent, it adversely affects the local original ecology. In this regard, Yangma Island should pay attention to re-optimizing the layout of the island's tourism service zone, based on the tourist's activity demand. Simultaneously, they should strengthen the environmental protection of the island's ecological protection zone, continue to build and improve the service facilities in the tourist-intensive area, and most importantly pay attention to improving the coastal landscape protection and sightseeing services within the island's ring area. Therefore, different subjects and objects and their activities have formed diverse spatial interaction patterns within the island. Summarizing the above spatial types and their attributes is of great significance to further optimize the harmonious spatial state and solve contradictory spatial problems.
ISPRS Int. J. Geo-Inf. 2022, 11, x FOR PEER REVIEW 14 island illegally, causing negative impacts to the vegetation on the island and veget growth. The water-related area refers to activities such as pebble picking, oyster colle and sea anemone collecting in the offshore area. To a certain extent, it adversely af the local original ecology. In this regard, Yangma Island should pay attention to remizing the layout of the island's tourism service zone, based on the tourist's activit mand. Simultaneously, they should strengthen the environmental protection of th land's ecological protection zone, continue to build and improve the service faciliti the tourist-intensive area, and most importantly pay attention to improving the co landscape protection and sightseeing services within the island's ring area. Therefore ferent subjects and objects and their activities have formed diverse spatial interaction terns within the island. Summarizing the above spatial types and their attributes is of significance to further optimize the harmonious spatial state and solve contradictory tial problems.

Discussion
Although some scholars have explored the spatial influence mechanisms, they focused on a single aspect of distance decay. This study goes a step further by ref space into attributes such as shape, pattern, and partition in addition to distance. expands the boundaries of spatial analysis dimensions in the study of tourist beha Furthermore, data sources and research case sites are also a highlight of this study shared track recording platform provides us with accurate, effective, and user-autho public GPS track data, which alleviates the concern and interference of the insecuri external tracking devices, on the basis of avoiding privacy infringement and furthe ducing the cost of researchers' money, time, and effort.
By using a series of geographic analysis methods to analyze and explore the Yan Island and its tourist behavior, it was further confirmed that space is an important f that influences and constrains the behavioral activities of tourists within the tourist d

Discussion
Although some scholars have explored the spatial influence mechanisms, they have focused on a single aspect of distance decay. This study goes a step further by refining space into attributes such as shape, pattern, and partition in addition to distance. This expands the boundaries of spatial analysis dimensions in the study of tourist behavior. Furthermore, data sources and research case sites are also a highlight of this study. The shared track recording platform provides us with accurate, effective, and user-authorized public GPS track data, which alleviates the concern and interference of the insecurity of external tracking devices, on the basis of avoiding privacy infringement and further reducing the cost of researchers' money, time, and effort.
By using a series of geographic analysis methods to analyze and explore the Yangma Island and its tourist behavior, it was further confirmed that space is an important factor that influences and constrains the behavioral activities of tourists within the tourist destination. Initially, we envisioned four types of spatial constraints: distance, shape, pattern and zone constraints. We verified the trajectories of tourist activities within the island through four methods corresponding to different constraint types: kernel density, standard deviation ellipse, in-track rate and trajectory superposition. We also restricted involvement index, which finally confirmed the assumption of the existence of four spatial constraints. We further confirmed that different spatial attributes do have different effects and constraints on tourist behaviors. We expressed this as 'distance constrains behavior length, shape constrains behavior distribution, pattern constrains behavior path and zone constrains behavior range.
On this basis, understanding the spatial interactions of tourists within and between destinations also plays a crucial role in conducting investigations of tourism phenomena [82]. Previous research has focused on the location, identification, and delineation of tourism areas [83]. However, many players are changing and shaping tourism spaces due to their growing mobility, plasticity, fickleness, and difficulty of definition. Tourists and other owners of space define their own spaces [84], and create more complex spatial states and types during the interaction. This study constructs a model of the interaction results between tourist activity spaces and other spaces. It generalizes the space of tourist activity to tourist space. It interacts with local production, living, and natural spaces, resulting in various spatial types of human terrestrial interactions, and emphasizing outcomes that arise from such interactions [82][83][84].
The tourism development on the island has had some negative ecological and cultural impacts [85][86][87][88][89] while achieving economic benefits [88,90,91]. The effects also apply to developed and more established island destinations like the Mediterranean and Oceania [92][93][94]. This is inextricably linked to the behavioral activities of tourists on islands. Although the spatial movement of tourists affects policymaking, transport planning, and development trends in tourism, this topic has received relatively little attention in tourism research [82]. Therefore, a comprehensive understanding of tourist behavioral patterns and the factors that influence them can help island destinations to become more aware of the spatial areas and types that tourists are likely to prefer and visit. This will enable them to plan spatially and collaboratively in a sustainable manner and ensure that the range of tourism services needed is adequately organized [95][96][97].

Conclusions
The aim of this paper is to explore the dichotomous interaction between tourists and islands: the behavioral patterns of tourists in island destinations and the mechanisms by which island spaces constrain tourist behavior. In this study, with Yantai Yangma Island as a case study, through the collection of field information and the mining of trajectory data on the network platform, we innovatively explore the flow characteristics of tourists under the state of spatial constraints, from the perspective of spatial constraints, and refine the constraint mechanism and spatial relationship of tourists' intra-island flow to obtain useful conclusions. As a small piece of land surrounded by seawater, the flow trajectory of tourists in island-type tourism destinations show strong dependence on the ocean. It is deeply influenced by the ocean scenery, tidal ebb and flow, and the type of coast. This is manifested in the hydrophilic nature of attraction selection, the traffic circle nature of route planning, and the dynamic change of human flow distribution. At the same time, island space has a strong influence and constraint on tourist behavior. The four spatial constraints of distance, shape, pattern, and zone that we propose in this regard, act on tourist flow behavior of island-type tourist destinations to varying degrees and produce different but interrelated constraint mechanisms.
In addition to confirming the role of island spaces in expressing and constraining tourist behavior, we have identified and summarized the results based on different identities of people interacting with spaces with different attributes. The spatial interaction patterns between people and places on Yangma Island are qualitatively classified into two spatial attributes--harmony and contradiction--based on their main profit-and-loss relationships. A model of spatial interactions on island tourism destinations was formed. The spatial interaction model further expands the boundaries of spatial analysis on the study of tourist behavior. At the same time, it enhances the cognition of the spatial aspects of tourists, which is conducive to promoting spatial synergy and building harmonious relationships between people and places.
The study has some limitations that require further attention. For example, although tourism spatial constraints can be interpreted by using a single constraint tourist mobility phenomenon and its characteristics, it should be noted that these constraint behaviors are not solely caused by a single element of distance, shape, pattern, and zone. Although it constrains the time of tourists, it does not necessarily determine them [98], and behavioral patterns are presented as a result of a complex combination of economic, cultural, and personality preference choices that are included in the tourism space [82]. Therefore, the behavior of tourists in different types of islands may show different characteristics and patterns. This paper focuses on the tourist type or the sightseeing type of islands, but the cultural and holiday types of islands are also worthy of further exploration. Second, the two-dimensional (2D) perspective of the plane analysis largely ignored the 3D space, due to factors such as the altitude brought about by the flow rate changes and anomalous activities. It is important to note that the tidally influenced island space is in a state of constant dynamic change, which has a significant impact on the generation of the island landscape and tourism activities and their content. Therefore, future research processes can verify it by combining questionnaires, and constructing attractiveness models and 3D spatial data, to further expand and refine the factors influencing tourism behavior, enrich and enhance the research on tourists' behavior, make tourism destination planning respond to the tourists' real needs, and further realize high-quality development of tourism destinations.
Author Contributions: Conceptualization, methodology, software, formal analysis, investigation, resources, data curation, writing-original draft, visualization, Xintao Ma; Methodology, software, formal analysis, Yongwei Liu; Writing-review and editing, validation, Yuna Hu. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by the National Natural Science Foundation of China (no. 41901171).

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.

Data Availability Statement:
The data that support the findings of this study are available on reasonable request from the corresponding author.