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This paper uses Landsat TM/OLI images from 1987, 1993, 1999, 2005, 2011 and 2017 by the weight vector AdaBoost (WV AdaBoost) multi-classification algorithm extracting LULC data sets, and the spatiotemporal patterns of LULC over these periods were analysed. The spatiotemporal change patterns and driving force of ESV was estimated. The effect of LULC dynamics on the ESV was evaluated. The flow chart is shown in Fig. 1.
Figure 1

The framework of this paper.

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Study area
Guangzhou is located at 112° 57′ ~ 114° 3′ E, 22° 26′ ~ 23° 56′ N in the southeast part of Guangdong Province in the northern margin of the Pearl River Delta. It has a total land area of 7434.40 km2. The topography is high in the northeast and low in the southwest, with low mountains and hills in the north and plains in the south and a rich geomorphology. The level of urbanization is high, the land use structure is complex and the land use pattern is changing rapidly. Regional public infrastructure, commercial service land and external transportation land is increasing. Export-oriented industrial agglomeration areas are developing continuously, and the characteristics of export-oriented land use are obvious. Guangzhou has a subtropical oceanic monsoon climate, with an annual average temperature of 20–22 °C and an annual rainfall of about 1720 mm. Guangzhou includes eleven districts (Fig. 2a). This paper focuses on the main urban area of Guangzhou as the research object, a decision based on the city government’s overall urban development strategy for Guangzhou (2010–2020), the main urban area of Guangzhou includes five districts—Liwan, Yuexiu, Haizhu, Baiyun and Tianhe (Fig. 2a). In 2017, the per capita GDP will exceed 136,100 yuan for the first time (Fig. 2b). The population density is large, and the intensity of development is extraordinary. The population has increased from 2.73 million in 1987 to 8.05 million in 2017 (Fig. 2c). The industrial structure has been constantly optimized and improved. The proportion of secondary industries decreased from 31.46% in 1987 to 11.28% in 2017, while the proportion of tertiary industries increased from 61.9% in 1987 to 89.61% in 2017.
Figure 2

Location of study area and GDP and population. (a) location, (b) GDP, (c) population. (Software: Arc Map 10.5.0, http://www.esri.com. OriginPro 2017C SR2, https://www.originlab.com/).

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Data and data processing
Data
The data used include Landsat series images, an administrative zoning map of Guangzhou, a local historical land use map and social and economic statistics from 1987 to 2017. To explore the socio-economic and natural factors driving the ESV change for different land use types, we examined ten factors—the normalized vegetation index (NDVI), year-end population, elevation, slope, distance from roads, distance from railways, land cover types, GDP, secondary industry GDP and investment in fixed assets.
The Landsat images were taken from the United States Geological Survey website (http://glovis.usgs.gov/), and we downloaded cloud-free Landsat 5 TM and Landsat 8 OLI images (path 122, row 44). Images taken in the dry season (October, November and December) were selected because there was less cloud cover, the change in surface reflectance was much smaller than in other seasons and the image quality was higher. The spatial resolution of imaging is 30 m, and the data of Landsat 5 TM (8 December 1987, 24 December 1993, 25 December 1999, 23 November 2005, 19 November 2011) and Landsat 8 OLI (23 October 2017) were collected.
The elevation data are provided by the Japan Aerospace Exploration Agency (http://www.eorc.jaxa.jp/ALOS/en/aw3d30/data/index.htm); the horizontal resolution is 30 m, and the elevation accuracy is 5 m. The road and railway data are provided by Openstreetmap (download.geofabrik.de/), and the distance between roads and railways were calculated. The land use types are provided by Tsinghua University (http://data.ess.tsinghua.edu.cn/) with a resolution of 10 m. GDP, secondary industry GDP and investment in fixed assets were provided by Guangzhou Statistics Bureau28.
Considering the size of the study area and the resolution of the data, we used Fishnet in ArcGIS10.5 to establish a 500 × 500 m grid covering the study area. The values of ten factors were extracted to the grid centre points, and 3915 points were obtained.
Remote sensing extraction of LULC types
To obtain high-precision LULC data, the surface features based on the original remote sensing image were enhanced using the index model (the Index-based Built-up Index (IBI)29, the modified normalized difference water index (MNDWI)30 and the soil-adjusted vegetation index (SAVI)). The humidity, brightness and green chroma indices were transformed using the tasselled-cap method23. Using the six indices, six images were calculated and superposed into a new multi-band image in the order of IBI, SAVI, MNDWI, brightness, green chroma and humidity (referred to as the six-index image). This was superposed with the original image (band 1, 2, 3, 4, 5, 7) to create an enhanced 12-band image as the data source for LULC classification. The image stretching function was then used to stretch the composite image to better distinguish the characteristics of land use types. After feature enhancement, the LULC types in the main urban area of Guangzhou could be divided into seven types—forest, water body, grassland, cultivated land, high reflectivity building, low reflectivity building and bare land. Of these, high reflectance buildings and low reflectance buildings are sub-categories of the built-up area category. The spectrum of high reflectivity buildings is similar to that of bare land; therefore, they are classified separately to avoid erroneous classification31. Based on Google Earth and TM/OLI images, the interpretation marks of LULC types were established (Table 1). To obtain pure and representative samples, the K-means method of unsupervised classification was utilized to cluster the pixels of the ISM image into seven unlabelled classes and to eliminate abnormal clustering. We then selected uniform points and drew polygons on them. Each polygon contains more than 100 pixels, and each class contains between five and seven polygons. All polygons were saved in a shape file as a mask file, which is utilized to extract pure pixels as training samples.
Table 1 Interpretation mark of land cover types.
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Dou and Chen31 suggest using the weight vector AdaBoost (WV AdaBoost) multi-classification algorithm for LULC classification. Compared with AdaBoost, it provides higher classification accuracy and stability. WV AdaBoost includes a C4.5 decision tree, a Naïve Bayes neural network and an artificial neural network. In this study, we use Naïve Bayes-based WV AdaBoost to classify LULC based on Landsat-enhanced images. To obtain a highly accurate LULC classification, it is necessary to post-process the image after classification, overlay the early land use map during the research period, check the incorrectly classified area, and filter and correct some segments. After image classification, the random selection of 200 pixels in each class was checked, and the correctness of the classification and the evaluated accuracy were confirmed.
The average classification accuracy of WV AdaBoost based on Naïve Bayes on the original image is 85.02%, and the kappa coefficient is 0.839. The WV AdaBoost algorithm is based on Naïve Bayes processes for the 12-band images of the new combination (enhanced 12-band image). The average classification accuracy is 88.86%, and the kappa coefficient is 0.871. The classification results still need to be strengthened by post-processing, which achieves good classification accuracy. The final average classification accuracy is 91.97%. The kappa coefficient is 0.907. These classification results agree with the ensuing analysis of LULC.
Methods
Based on Landsat TM/OLI data from 1987 to 2017, a transfer matrix, a land use change index, an ESV evaluation index, a sensitivity model (CS) and a geo-detector (P) were used to analyze the response of ESVs to LULC evolution.
Transfer matrix
The transfer matrix reflects the dynamic process information about mutual transformation LULC types at the beginning (T) and the end (T + 1) of a specified period of time in a certain region (Fig. 3). The general form is:

$${S}_{ij}=left[begin{array}{c}{s}_{11} {s}_{12}dots {s}_{1n}\ {s}_{21} {s}_{22}dots {s}_{2n}\ dots dots dots dots \ { s}_{n1} {s}_{n2}dots {s}_{nn}end{array}right]$$
(1)

where S stands for area, and i,j (i,j = 1,2,…, n) represents LULC types before and after the transfer.
Figure 3

Land use transfer process. T the beginning of land use types, T + 1 the end of land use types; A, B, C, D, E, F: different land use types.

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The LULC analyzing indices
(1)
Land use dynamics (RS)
Land use dynamics describe the rate and magnitude of LUCC. The general form is:

$$RS=frac{{U}_{b}-{U}_{a}}{{U}_{a}}times frac{1}{T}times 100mathrm{%},$$
(2)

where ({U}_{a}) is the area of a certain land class at the beginning (km2), ({U}_{b}) is the area of a certain land class at the end (km2), and T is the study period.

(2)
Spatial dynamics of land use (RSS)
Spatial dynamics of land use describe the degree of spatial change in a certain land use type. The general form is:

$$RSS=frac{{U}_{in}-{U}_{out}}{{U}_{a}}times frac{1}{T}times 100mathrm{%},$$
(3)

where ({U}_{in}) is the sum area of other types converted to this type in study period T, and ({U}_{out}) is the sum area of a certain type converted to other types in study period T. ({U}_{a}) is the area of a certain type at the beginning.

(3)
Land use change state index (PS)

The land use change state index represents the trend and state of LUCC. The general form is:

$$PS=frac{{U}_{in}-{U}_{out}}{{U}_{in}+{U}_{out}},$$
(4)

where ({U}_{in}) is the sum area of other types converted to this type in study period T, and ({U}_{out}) is the sum area of a certain type converted to other types in study period T.
Calculation of ecosystem service value
In this paper, the improved ecosystem services valuation method based on the unit area value equivalent factor proposed by Xie et al.2 is employed to evaluate ESV. Therefore, the LULC types of the main urban area of Guangzhou were associated to the corresponding representative biomes (Table 2). The most representative biomes used as a proxy for each LULC type are: (1) cropland for cultivated land, (2) tropical forest for forest, (3) grassland for grassland, and (4) water system and wetland for water body. (5) bare land for bare land.
Table 2 Parameters of ESV for different land use types in the main urban area of Guangzhou.
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The LULC types are not exactly identical with the representative biomes. For example, cultivated land in this study accounts areas used for paddy fields and dry land. Therefore, the ESV index of cultivated land is calculated by weighting the area ratio of paddy field and dry land in the statistical yearbook. The average value of the ESV index of the water system and wetland is adopted for water body. The ESV index of build-up area is 0. the ESV index of land use types is shown in Table 2. The value of the universal equivalent factor ESV (D value) of the improved ESV method is 340.65 thousand yuan/km2.
In this study, the ESV of each land use unit area is based on the research methods of Costanza3 and Xie et al.2. The calculation formula is:

$$ESV=sum {A}_{i}times {VC}_{i}$$
(5)

$${ESV}_{f}=sum {A}_{i}times {VC}_{fi},$$
(6)

where ESV is the total value (yuan) of ecosystem services, ({A}_{i}) (km2) is the area of class i, and VCi is the ESV coefficient (yuan/km· year) corresponding to class i. ESVf is the single ESV, and VCfi is the value coefficient of the single service function.
Sensitivity analysis model
The sensitivity model is used to calculate the response of ESV to the change of value coefficient (VC)14 by adjusting the 50% of the ESV coefficient of each land use type up and down and determining the change in ESV over time and the degree of dependence on the value coefficient. The calculation formula is as follows:

$$CS=frac{{(ESV}_{j}-{ESV}_{i})/{ESV}_{i}}{{(VC}_{jk}-{VC}_{ik})/{VC}_{ik}},$$
(7)

where ESV is the estimated ESV, VC is the value coefficient, i and j are the initial value and adjusted value (50% up and down adjustment) and K is the land use type. When CS ≥ 1, ESV is elastic relative to VC; when CS ≤ 1, ESV is inelastic. The larger the CS value is, the more critical the accuracy of the ESV index.
Grid analysis method
Grid analysis method is used to divided the study area into regular grid matrixes with the same size and no overlap, and takes grid as the research object to express and statistical unit in geospatial space9. It uses regular square grid as ESV’s spatial statistical unit instead of irregular land-use map spots to ensure the capacity invariance within the unit, which not only highlights the spatial distribution characteristics of ESV, but also facilitates the spatial quantitative statistics of ESV.
The premise of calculating ESV spatial differentiation is to determine the size of grid cell. In this study, based on ArcGIS10.5 software, the area of each land use type in four grid units with side length of 0.5 km, 1 km, 2 km and 3 km was extracted respectively, and then compare the degree of area change, namely the coefficient of variation. The grid of this scale is the optimal grid unit size for the spatial differentiation of ESV in the study area. Finally, the grid analysis method is introduced to construct a (0.5 × 0.5) km square grid as a geospatial statistical unit. By using the equal spacing system sampling method, the study area is divided into 2024 square grids that do not overlap each other (0.5 × 0.5) km, and the grid matrix is composed of these grids. Through the intersection operation of grid matrix and land use data of each research year, the area of various land use types in each grid is counted, and the spatial heterogeneity of land use types and ESV is analyzed.
Geo-detector
Combined with GIS spatial superposition technology and set theory, a statistical method proposed by Wang et al.32 can detect spatial heterogeneity and reveal the driving force to identify the interaction between multiple factors. This model is widely used to analyze the influence mechanism of social economic factors and natural environmental factors. The geo-detector consists of four detectors—a differentiation and factor detector, an interaction detector, a risk area detector and an ecological detector. In this paper, factor detection and interaction detection are utilized to detect and analyze the driving force of ESVs in the main urban area of Guangzhou.
(1) Factor detector: Factor detection can identify the explanatory power of each spatial driving factor in landscape type change, and its model is as follows:

$$P=1-frac{1}{{ndelta }^{2}}sum_{i=1}^{m}{n}_{i}{{delta }^{2}}_{i},$$
(8)

where P is the explanatory power index of ESV influencing factors; ni is the number of samples in the secondary area; n is the total number of samples; m is the number of samples in the secondary area; ({delta }^{2}) is the variance in land use type change in the whole area; and ({{delta }^{2}}_{i}) is the variance in land use type in the secondary area. Thus, the model is established, assuming ({{delta }^{2}}_{i}) ≠ 0.
The range of values for P is [0,1]. When P = 0, it shows that the spatial distribution of ESV changes is random. The larger the P value is, the greater the impact of longitudinal driving factors on ESV changes.
(2) Interactive detector: Interaction detection can be used to identify the interaction between different spatial drivers. When detecting the interaction of X1 and X2, the explanatory power of the dependent variable Y will increase or decrease. The evaluation method is used to calculate the q value of two factors, X1 and X2, for Y, respectively, q (X1) and q (X2); to calculate the q value of their interaction, q (X1 ∩ X2); and to compare q (X1), q (X2) and q (X1 ∩ X2). The five results of the interactive detector are given in Table 3.
Table 3 Types of interactions between two covariates.
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In this study, we used the black garden ant Lasius niger to investigate the benefits and factors of pleometrosis, the transitory association between founding queens. The monitoring of colonies founded by one or two queens showed that pleometrosis increased and accelerated offspring production. Then, the experimental pairing of L. niger founding queens revealed that in pairs of queens of different fecundity but similar size, the most fecund queen was more likely to survive. Our experiment could not detect a similar effect of size when controlling for fecundity. Finally, we found that queens associated preferentially with less fecund queens.
Our findings of pleometrosis benefiting offspring production are in line with the literature for this, and other ant species3,7,9,10,12,22,23. Interestingly, we only detected these benefits at the colony level, as pleometrosis had either no effect or a negative influence on the per capita offspring production9,12,22. However, colony-level measurements are more relevant in the case of pleometrosis, as the queen that survives the association inherits all the offspring produced during colony foundation. In the field, colonies with a faster, more efficient worker production would have a competitive advantage over neighbouring founding colonies3,4. This is especially true for L. niger, which shows high density of founding colonies that compete for limiting resources and raid the brood of other colonies10. Thus, the competitive advantage provided by pleometrosis likely enhances colony growth and survival.
The increased and faster production of workers in colonies with two queens may stem from a nutritional boost for the larvae. L. niger founding queens do not forage, and produce the first cohort of workers from their own metabolic reserves. Larvae have been observed to cannibalize both viable and non-viable (trophic) eggs24. We found that colonies with two queens produced more eggs, but that this did not translate in them having more larvae. However, more of these larvae became pupae—and ultimately workers. In addition, while the time to produce the first egg and larva did not differ between colonies with one and two queens, the first pupa and worker were produced faster when two queens were present, consistent with a shorter larval stage. We propose that larvae in pleometrotic colonies developed faster and were more likely to reach pupation because they had more eggs that provided nutrients, boosting the development rate of the first workers.
These benefits of pleometrosis are only inherited by the queens that survive, it is thus important to understand the factors that determine queen survival in pleometrotic associations. Although this question has been relatively well studied3,16,17,18,19,20,21, it has remained challenging to disentangle the effects of correlated factors. For example, we found that size, which has been reported to predict queen survival16,19, correlated with fecundity, which would itself be confounded with the parentage of workers in the first cohort produced. To address this issue, we disentangled size and fecundity experimentally, and used foreign workers that developed from pupae collected in field colonies to prevent any potential nepotistic behaviour.
We found that fecundity, but not size, determined queen survival. The finding that, despite being of similar size, more fecund queens are more likely to survive indicates that the outcome of pleometrosis is not the mere consequence of physical dominance. The higher fecundity could reflect a better health condition, which may give the advantage to the more fecund queen in direct fights3,15, or if workers initiate the fights. Natural selection may have favoured workers that skew aggression toward the less fecund queen, both because this queen would be less efficient at building a colony, and because the workers would be more likely to be the offspring of the more fecund queen. The latter would not necessarily involve direct nepotistic behaviours (the workers would not behave according to parentage, but to fecundity), which have remained elusive in social insects in general25,26,27, and in pleometrotic associations in particular16,17,20. Despite regular behavioural observations, we did not observe who initiated aggression in our experiments, and it remains unclear whether the queens and/or the workers are responsible for the onset of fights. Consistently with previous studies16,23, we found that a certain proportion of queen death occurred before worker emergence, suggesting that worker presence is not required for queen execution. Finally, we cannot rule out that the least fecund queens were more likely to die because of a weaker health status, possibly combined with the stress of being associated with another, healthier queen.
Although it has not been directly reported before, our finding that fecundity determines queen survival is consistent with previous reports of weight being associated with queen survival17, more fecund queens being more aggressive28, cuticular hydrocarbon profiles differing between surviving and culled queens21, and between more and less fecund queens28. We could not directly support previous reports of size correlating with survival16,19. This could be because in those studies, size could have been confounded with fecundity, and/or because we lacked the statistical power to detect such effect in our experiment.
Pleometrosis provides clear benefits, but these benefits are only inherited by the surviving queens, and the losing queens pay the great cost of dying without contributing to the next generation. Natural selection should thus favour queens that decide whether or not to join a pleometrotic association based on the relative benefits compared to individual foundation—these may differ across ecological contexts29—and the likelihood of surviving the association. As fecundity appears to determine queen survival in L. niger, queens may have evolved the ability to choose among potential partners according to their fecundity. Our results are consistent with this hypothesis, as queens preferentially associated with partners that would later produce fewer eggs, possibly because they were less fecund, and therefore less healthy and easier to eliminate. This suggests that founding queens may assess the fecundity of potential partners, possibly via their cuticular hydrocarbon profile28. This result further supports our finding that fecundity plays an important role in pleometrotic associations. It is important to note that this difference in egg production could have alternative explanations. First, it could stem from more fecund queens having no interest in forming an association because they are able to start a competitive colony alone. Second, it could be a consequence, rather than a cause, of the outcome of the choice experiment. We cannot rule out that entering an association with another queen and/or leaving this association prematurely at the end of the choice experiment may have been stressful for the chosen queens, and affected their later production of eggs. We could not detect any difference between chosen and not chosen queens in the number of larvae and pupae produced, which are likely influenced by factors other than fecundity (e.g., brood care behaviour). Interestingly, we did not find that queens chose according to size, consistent with our finding that size may not affect which queen survives the pleometrotic association.
Our study informs on the benefits and factors of pleometrosis, and highlights the role of fecundity in the decision to associate with another queen, and in determining which queen survives the association. As such, it contributes to a better understanding of the onset and outcome of pleometrosis, a classic case of cooperation between unrelated animals. More

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