Population trend and spatio-temporal distribution of Greater White-fronted (Anser albifrons) and Bean Geese (Anser fabalis) in Korea

1.   Introduction

Recent anthropogenic impacts, such as climate change, habitat loss or habitat change, and hunting pressure, could have adversely affected various populations of birds, including those undertaking long-distance migration (Kirby et al., 2008; Knudsen et al., 2011; Bairlein, 2016). Notably, it is well documented that geese have encountered significant changes in their habitat, breeding in the Arctic (Madsen et al., 2023), where both indirect and direct drivers of climate change strongly operate (Rantanen et al., 2022), and wintering near the artificial regions susceptible to human disturbance (Béchet et al., 2004; Fox et al., 2005; Rosin et al., 2012; Panov et al., 2022). Over the last decades, their numbers in some species have notably increased due to climate-induced shifts and landscape change (Koons et al., 2014; Cunningham et al., 2021; Rozenfeld et al., 2021; Madsen et al., 2023; Ely et al., 2024), leading to the expansion of staging and breeding site (Tombre et al., 2019; Rozenfeld et al., 2021; Ely et al., 2024). However, the probability of fledgling success and winter survival has decreased due to density-dependent effects and increased abundance of predators, such as the Arctic Fox (Vulpes lagopus) (Layton-Matthews et al., 2020). Furthermore, habitat loss, landcover changes, and fragmentation of food resources caused by human activities (Fox et al., 2005; Desmonts et al., 2009; Clausen et al., 2012; He et al., 2022) make it challenging for geese to find suitable habitats, influencing the abundance and distribution of geese.

Understanding these variations in population size and distribution is not only vital for developing effective management and conservation measures but is also crucial for monitoring recently emerging infectious diseases, such as highly pathogenic avian influenza (HPAI). With the advancement of technology like tracking devices (e.g., Global Positioning System, GPS; Platform Transmitter Terminal, PTT), we can readily gather valuable insights into migration characteristics (Mitchell et al., 2016; Si et al., 2018; Zheng et al., 2018), local movements (Mitchell et al., 2016; Luukkonen et al., 2022), and changes in the distribution of geese (Lameris et al., 2023). Nevertheless, individual-based data may yield incorrect species-specific information at the population level due to the small sample size and limitations in non-random deployment in specific, easily accessible areas (Hebblewhite and Haydon, 2010; Meehan et al., 2022), including the relatively high cost compared to other methods (Gregory et al., 2023).

For these reasons, large-scale monitoring data (Fuentes et al., 2023) or various methods integrating telemetry or tracking data (Meehan et al., 2022; Gregory et al., 2023) have been implemented to track population changes. In cases where tracking data are insufficient, large-scale monitoring data such as census surveys and citizen science data could be utilized to understand the population movements (Fuentes et al., 2023). Census data, which counts all birds within the entire study area (Sutherland, 1996; Gregory et al., 2004), has the advantage of providing national population information when covering extensive regions, resolving the issues related to the representativeness of individual-based data. Moreover, when conducted at regular intervals over a long period, census data could unveil the trends in population size and population-scale migration movement through changes in distribution (Walker and Taylor, 2017; Fuentes et al., 2023). There is also the possibility of discovering the migration strategies of populations not confirmed in a limited number of tracking data.

The Greater White-fronted (Anser albifrons; GWFG) and Bean Geese (A. fabalis sensu lato; BEAG) are the dominant goose species in South Korea (the Republic of Korea) and representative long-distance migrants breeding in northeastern Russia. GWFG and BEAG populations in Korea are part of the East Asian population, divided into three populations based on their wintering countries: China, Japan, and Korea (Wetlands International, 2024b). Due to their extensive breeding range (BirdLife International, 2018, 2022) and the attributes of breeding area in Arctic Russia (GWFG: Northeast Russian Arctic; BEAG: from Central to Northeast Russian Arctic), primarily in remote, inaccessible, and uninhabited areas, accurately calculating the population size and trends of East Asian populations in the breeding sites is challenging compared to those of Europe and North America. Therefore, to gain a better understanding of the East Asian population of this species, the population information from winter counts is vital (Delany, 2005; Wetlands International, 2024a).

In this study, we aimed to document information about both GWFG and BEAG populations in South Korea. We utilized national census data to identify temporal (long-term and short-term) and spatial changes in the numbers of GWFG and BEAG during non-breeding periods. Therefore, we investigated how the population size in South Korea has changed over 24 years using the TRIM (TRends and Indices for Monitoring data) model. We also understood migration patterns from monthly patterns of population sizes, predicting if both species spend their non-breeding time in Korea, a highly peaked number would be observed in the main winter month (December of November). Lastly, we checked the distribution and primary wintering regions.

2.   Materials and methods

2.1   National census data

The Nationwide Winter Waterbird Census (NWWC) data are prepared and compiled by the Korean Ministry of Environment and associated institutes, namely the National Institute of Environmental Research (1999–2007) and the National Institute of Biological Resources (2008–present). Conducted annually every January since 1999, the NWWC covers important wintering habitats of migratory waterbirds, including lakes, wetlands, bays, and seashores. Beginning with 82 sites in 1999, the survey area has consistently expanded, reaching 200 sites by 2014. In addition, to meet the growing demand for data on the distribution status of migratory waterbirds, additional surveys have been conducted from October to March of the subsequent year since 2014 (NIBR, 2024). Nationwide censuses have been synchronously carried out over two consecutive days in the middle of each month. The census team for each region was composed of two experienced researchers, such as ornithologists and bird watchers. They moved through the survey area by vehicle, boat, and foot, recording all the species and number of birds observed at the target sites.

The Bean Geese in South Korea include two subspecies, the Tundra (Anser fabalis serrirostris, TDBG) and Taiga Bean Geese (A. f. middendorffii, TGBG), known to have differences in morphology, breeding distribution, and ecological characteristics (Kurechi et al., 1983; Burgers et al., 1991; Marjakangas et al., 2015; Heinicke, 2018; Fox et al., 2021; Wetlands International, 2024b). However, more recently, they have been recognized as different species based on mtDNA sequences (Ruokonen et al., 2008), but their taxonomical positions are still controversial.

Since NWWC was conducted without taxonomic splitting of the Bean Goose from the beginning, we tried to divide this species into two subspecies based on their main geographic distribution (Park, 2002; Jia et al., 2016). So, we considered BEAG observed in the Nakdong River watershed, Upo Wetland, and Junam Reservoir as TGBG.

2.2   Long-term population trends of GWFG, TDBG, and TGBG

In long-term monitoring, specific sites may not be counted in certain years, or new sites may be added while others vanish. One might attempt to address this issue by comparing only the sites monitored in all years, but such an approach would be inadequate for accurately identifying the population size and trends (Braak et al., 1994). The TRIM (TRends and Indices for Monitoring data) model is designed to analyze time series of counts with missing observations and is commonly used to estimate the growth and decline of animal populations (Pannekoek and van Strien, 2001). Thus, to understand the long-term population trend of GWFG and BEAG, we employed the TRIM method with winter census data collected every January from 1999 to 2023 using the rtrim package (Version 2.1.1; Bogaart et al., 2020), considering the variability in survey sites and missing values in our data.

2.3   Short-term spatial-temporal population trends

Given that the NWCC survey period included not only the main wintering season (December and January) but also migration seasons (spring: February and March; autumn: October and November), we expected that census data have sufficient potential to reflect population-scale migration information from changes in their distribution in South Korea. Therefore, we analyzed spatio-temporal population changes during winter using Generalized Additive Mixed Models (GAMMs; Wood, 2017) because the relationships between counts data and spatio-temporal variables could be nonlinear (Zhang et al., 2015; Knape, 2016).

The number of survey sites was not identical across survey months; 200 sites were surveyed during the main wintering season, January and February, while only 112 main areas were surveyed during the migration season. So, to control the effect of the varying number of survey sites, only sites surveyed consistently every month were selected for spatio-temporal analysis.

First, we estimated monthly patterns of population size for the entire wintering GWFG, TDBG, and TGBG using the following procedure. For our response variable, we filtered out the monthly count data of each survey site between 2014 and 2023, and we aggregated country-level monthly count data by merging each species’ abundances of all survey sites in each survey season; for example, the 2022–2023 season denoted the survey conducted from October 2022 to March 2023. In GAMMs, we included the intercept for survey seasons as a random effect and a smooth effect for survey months with a Poisson distribution. After comparing with the possible subset models based on the Akaike Information Criterion adjusted for small sample sizes (AICc; Burnham and Anderson, 2002), we selected the optimal model with the lowest AICc values. We assessed the significance of smooth effects for each group via p-values in the selected GAMMs and considered p < 0.05 to indicate statistically significant predictors. Predicted fitted values from the GAMMs were visualized to illustrate monthly changes in GWFG and BEAG, respectively.

Second, we examined whether monthly population changes were related to the latitudinal gradient. Because TGBG was distributed in restricted regions, we performed this analysis for BEAG (sensu lato). We used the site-level count data and calculated the centroid points to obtain the latitude of survey sites using QGIS (QGIS, 2023). Regarding site-level counts, as count data often include zero observations, a zero-inflated Poisson distribution was applied to GAMMs. The model for each species relating the site-level counts (response variables) to explanatory variables in interaction with survey sites’ latitude and month, including survey seasons as a random effect, was assessed and visualized using the same methods as above.

Population sizes were given as the means with standard deviations (SD). All analyses were conducted in R version 4.2.3 (R Core Team, 2023) to implement GAMMs using the mgcv package (Version 1.9.1; Wood, 2017), and the results were visualized through the ggplot2 package (Version 3.5.1; Wickham, 2016).

3.   Results

3.1   Long-term population trends of GWFG, TDBG, and TGBG

The TRIM model for GWFG in South Korea revealed a ‘moderate increase’ from 1999 to 2023 (p < 0.01). The GWFG population in January started at 61,328 in 1999 and rapidly increased after 2003 and 2016. In 2020, the population peaked at 182,608, three times larger than in 1999. The most recent survey in January 2023 recorded 127,843 GWFGs.

The Tundra Bean Goose's population showed a ‘moderate increase’ in the TRIM model (p < 0.01). A total of 34,177 individuals were recorded in January 1999, and the TDBG population also increased sharply around 2005. However, after that, January's TDBG population size fluctuated, reaching 95,344 in 2023. In contrast, Taiga Bean Goose's population trends fluctuated between 4000 and 10,000 over 24 years, not showing a clear increasing or decreasing trend in the TRIM Model (Fig. 1).

Figure  1.  The population trend of the wintering Greater White-fronted (GWFG, Anser albifrons; A), Tundra Anser fabalis serrirostris (TDBG; B) and Taiga Bean Geese A. f. middendorffii (TGBG; C) observed in January from 1999 to 2023 in South Korea. The red line and band represent the result of the TRIM (trends and indices for monitoring data) analysis with 95% confidence interval, and the black point shows the counted number of geese in the Nationwide Winter Waterbird Census.

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3.2   Short-term spatial-temporal population trends

We found strong spatiotemporal patterns in the monthly population trends of GWFG and BEAG based on the survey month and site's latitude, with high significance in the explanatory variables in GAMMs (p < 0.001; Table 1).

Table  1.  Results of the generalized additive mixed models (GAMMs) with temporal (month) and spatial (latitude) variables affecting Greater White-fronted (Anser albifrons; GWFG) and Bean Geese (Anser fabalis sensu lato; BEAG) population sizes in South Korea. Tundra Anser fabalis serrirostris (TDBG) and Taiga Bean Geese A. f. middend o r ffi i, (TGBG) were estimated based on their wintering distribution, not by census data.

Species	Model	Model term	Coeff.	SE	EDFa	F	t	p
GWFG	Monthly	Intercept	116810	7115			16.42	<0.001
		Month			3.57	29.79		<0.001
		Seasonb			6.18	3.40		<0.001
	Latitudinal	Intercept	1969.70	291.20			6.76	<0.001
		Latitudec × Month			474.37	20.25		<0.001
		Seasonb			7.48	3.19		<0.001
TDBG	Monthly	Intercept	61178	3003			20.37	<0.001
		Month			1.00	133.75		<0.001
		Seasonb			0.61	0.08		0.391
TGBG	Monthly	Intercept	4873.40	371.80			13.11	<0.001
		Month			3.97	29.23		<0.001
		Seasonb			4.65	1.39		<0.05
BEAG	Latitudinal	Intercept	1147.69	57.32			20.02	<0.001
		Latitudec × Month			412.27	21.04		<0.001
		Seasonb			1.76	0.27		0.274
a Number of the effective degrees of freedom. b Random effect. c Values from the centroid of each survey site.

 | Show Table

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The estimated monthly population trend of GWFG was right-skewed unimodal (Fig. 2), peaking in November and continuously decreasing afterward. The average GWFG counts and standard deviations (SD) during spring migration (February and March) were 77,016 ± 31,825, which was only half of the average population size during autumn migration (October and November; 158,879 ± 36,121) and significantly lower than in autumn (Tukey test: mean difference = −81,862.50, p < 0.001). In winter (December and January), the average counts were 114,534 ± 34,656, slightly lower than autumn migration counts (Tukey test: mean difference = −44,344.78, p < 0.001).

Figure  2.  Monthly population change of Greater White-fronted Geese (Anser albifrons; GWFG) in South Korea. The numbers of counted GWFG (points) and the trend, fitted values from the generalized additive mixed models (GAMMs; lines) with 95% confidence interval (bands), are displayed. Each color represents each season, from 2014 to 2015 to 2022–2023.

DownLoad: Full-Size Img PowerPoint

TDBG also showed the highest population counts, 100,965 ± 34,901, during the autumn migration season, steadily decreasing in winter to 59,894 ± 16,231 and in spring to 22,675 ± 14,504 (Dunn's test; autumn-spring: z = 6.22, p < 0.001; autumn-winter: z = 2.55, p < 0.05; spring-winter: z = −3.67, p < 0.001), similar to GWFG. However, the peak population of TDBG was observed in October, and the monthly trend showed a linear decrease rather than an unimodal pattern (Fig. 3A).

Figure  3.  Monthly population change of Tundra Anser fabalis serrirostris (TDBG; A) and Taiga Bean Goose A. f. middendorffii (TGBG; B) in South Korea. The numbers of counted TDBG and TGBG (points) and the trend, fitted values from the generalized additive mixed models (GAMMs; lines) with 95% confidence interval (bands), are displayed. Each color represents each season, from 2014 to 2015 to 2022–2023. Note the different scales between the two panels.

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Unlike GWFG and TDBG, TGBG showed a completely different trend, displaying a bell-shaped pattern with the highest population count in winter (7,623 ± 2,595; Fig. 3B). There was no difference in the counted numbers between autumn (3,205 ± 3,316) and spring (3,792 ± 2,478) migration seasons (Dunn's test; autumn-spring: z = −0.47, p = 0.64; autumn-winter: z = −3.89, p < 0.001; spring-winter: z = −3.42, p < 0.001).

From our GAMMs, which included interactions between latitude and survey month, we identified different monthly distributions of GWFG and BEAG along the Yellow Sea coast (Figs. 4 and 5). High populations of GWFG, about 100,000 and 80,000, were observed at 36.7° N and 38.3° N, respectively, during autumn migration. Although the GWFG's high population disappeared at 36.7° N afterward, it was still present at 38.3° N (Table 1; Fig. 4). A notable number of BEAG was also observed at 36.7° N and 37.9° N during the autumn migration season. As winter approached, the significant numbers observed at this latitude vanished. There were no specific latitudes where a significant number of individuals were observed in February and March (Fig. 5).

Figure  4.  The monthly observed Greater White-fronted Geese (Anser alfibrons; GWFG) numbers of survey sites (left) and the trend of numbers according to the latitudinal gradient (right). On the right graph, the color indicates the number of observed GWFG, the same color as the left graph's legend.

DownLoad: Full-Size Img PowerPoint

Figure  5.  The monthly observed Bean Goose (Anser fabalis sensu lato; BEAG) numbers of survey sites (left) and the trend of numbers according to the latitudinal gradient (right). On the right graph, the color indicates the number of observed BEAG, the same color as the left graph's legend.

DownLoad: Full-Size Img PowerPoint

4.   Discussion

4.1   Population sizes and trends

In this study, we aimed to understand trends in the population size and spatio-temporal distribution of GWFG and BEAG (TDBG and TGBG) in South Korea using the national-level census data from NWWC. We noted a substantial increase in the wintering population sizes of GWFG and TDBG in South Korea over 24 years. After the moderate increasing trends from 1999, the population has stabilized at about 150,000 for GWFG and 100,000 for TDBG over the past five years. Contrary to TDBG, TGBG in Korea has not experienced significant population size changes over time.

In Japan, Shimada et al. (2019) confirmed an increase in the Japanese GWFG population based on national-scale population data from the Japanese Ministry of Environment, indicating different population trends depending on latitude, mainly concentrated in Northern Japan (Miyagi Prefecture). On the other hand, Deng et al. (2020) reported a decrease in the GWFG population in China from 142,159 in 1992/93 to 54,223 in 2019/20, though this decrease was not statistically significant. The rise in the Korean population might imply a shift of Chinese populations to South Korea. Still, population changes in all three countries indicate an overall increase since 2014, when Korea's survey areas have not been changed. Moreover, the magnitude of the increase in South Korea (about 40,000 from 2014; NIBR, 2024) and Japan (about 70,000 from 2014; Shimada et al., 2019; Deng et al., 2020) is greater than the decrease in China's population (a reduction of 90,000 from 1993; Deng et al., 2020), suggesting the possibility of an overall growth in the East Asian GWFG population.

Li et al. (2020) confirmed the TDBG population has been increasing in all three East Asian countries (South Korea, China and Japan). While Japan showed only a slight increase (from 1500 to 8754 since the 1970s), China reported a remarkable nine-fold increase in population since the 1990s. With South Korea's current population size growing by an additional 20,000 individuals compared to Li et al. (2020), the East Asian population of TDBG will continue to grow constantly unless there are changes in population trends in other countries.

On the other hand, Li et al. (2020) described that the TGBG populations in Japan and Korea increased slightly, but considering the fluctuation range of the Japanese population over time is similar to ours and our TRIM results, it is believed that the East Asian population of TGBG has been maintained without any significant changes for a long time.

While our study relies solely on data collected in South Korea, insights into East Asian population variations can be derived from other research. Therefore, it is essential to compare not only Korea's data but also that of Japan and China to understand changes in the overall East Asian population trends comprehensively. However, the limited data on the Chinese population in the absence of regular nationwide surveys, unlike in South Korea and Japan, makes it difficult to grasp the population size trends. Therefore, for an accurate assessment of trends in the East Asian population and to compare population changes among countries, international cooperation among Korea, Japan, and China is essential to conduct census surveys with systematic methods, such as identical or similar survey periods and efforts.

4.2   Spatio-temporal distribution and migration strategy

Due to the survey intervals (once a month), it was not possible to capture detailed short-term temporal changes, but we were able to discern their migration strategies, which had not been confirmed previously. TGBG, consistent with our hypothesis, was observed in larger numbers during the main winter season, in December and January, than during the autumn and spring migration seasons, indicating that TGBG observed are true wintering individuals in Korea. However, we observed more individuals of GWFG and TDBG during the migration seasons, especially in autumn. Moreover, the high number detected near the Yellow Sea coast (36.7° N) in the early autumn migration season suggested the occurrence of a passage group that may stop over in Korea during their southward migration heading for wintering grounds in China (such as Poyang Lake and/or unconfirmed sites). Interestingly, the short-term decreasing trend in winter and the absence of a second peak in March provided a possible clue that GWFG and TDBG may use different routes, such as detouring South Korea to employ an elliptical migration pattern, during their northward spring migration.

One GWFG migration track in Movebank (https://www.movebank.org; movebank ID: 1614083125, GWFG ID: H129) displayed a southward migration from its breeding ground to China via northern South Korea and a subsequent northward migration detouring Korea, which supports the suggested migration pattern observed in our spatio-temporal data. Although the track represented only one individual, given their tendency to migrate in groups, some passage groups of GWFG in South Korea likely employ this elliptical migration strategy more broadly during their migration.

For TDBG, one individual wintering in Nantong, China, passed through Seoul, Korea, during its northward migration (movebank ID: 1614098614, BEAG ID: H1048). Additionally, among individuals tracked over multiple years, some utilized both Korea and China during the same winter season (Li et al., 2020). There was no evidence of an elliptical migration pattern proven by telemetry. However, the single peak only in autumn still suggests the pattern and the close migratory connectivity between Korea and China.

4.3   Increasing populations and pressures

The different latitudinal variations of counts in each month were linked to specific survey sites. The largest number near the Yellow Sea coast, occurring solely during the early autumn migration season, was from Cheonsu Bay (36.7° N, 126.4° E), consisting of 15,409 ha of agricultural land developed into reclaimed land as part of a national reclamation project. The northern region of South Korea includes the Cheorwon Plains (38.3° N, 127.2° E), characterized by high observations of GWFG counts during all survey periods, and the Imjin River (37.9° N, 126.8° E), where many TDBG are observed only in the autumn migration season. The variation in the geese population in wintering grounds is known to be primarily influenced by food availability (Zhao et al., 2010; Pearse et al., 2011; Cunningham et al., 2021) and mortality rates resulting from hunting (Lindberg and Malecki, 1994; Menu et al., 2002; Panov et al., 2022). With the strong regulation of wildlife hunting and poaching in South Korea since 1994 (Ministry of Government Legislation, 2011b, Ministry of Government Legislation, 1994), food availability has become the main factor for determining population size. Specifically, geese wintering in South Korea heavily depend on grains in rice paddies (Fujioka et al., 2010; Kim et al., 2016; Fox et al., 2017), making rice fields crucial habitats for sustaining goose populations as they offer a substantial amount of nutrition compared to natural wetlands and also serve as roosting and resting places (Czech and Parsons, 2002; Fujioka et al., 2010; Toral and Figuerola, 2010; Natuhara, 2013). Moreover, the conversion of saltmarshes and mudflats into rice fields, exemplified by the Saemangeum Seawall Project from 1991 to 2010 (Saemangeum Development Agency, 2024), has provided advantages for wintering geese by allowing them to forage on the remaining grain after harvest on the fields. Kim et al. (2016) confirmed that the increase in the population of geese overwintering in South Korea was closely related to the completion of the Saemangeum Project, suggesting that the geese may have utilized the newly reclaimed area near the west coast.

Nevertheless, the recent stable trends of geese in Korea may suggest that the geese populations might reach the carrying capacity for geese in Korea. Korean rice fields have been recently adopted bale silages for the collection of waste grains and straws to provide additional agricultural products and feed for livestock (Chung et al., 2021). Ongoing anthropogenic interference with urbanization continues to reduce the agricultural land, resulting in the decreased availability of grains in rice fields (Statistics Korea, 2023). Moreover, changes in agricultural policy due to reduced demand for rice (Jeong et al., 2021) and population decline in rural areas (Li et al., 2023) can make it hard to predict future changes in food availability for geese. Consequently, there could be a possibility that geese may need to move more within wintering grounds to find sufficient food or switch to less nutritious food. This could result in difficulties in obtaining enough energy for long-distance migration, negatively impacting the survival of wintering and migrating geese (Terrill, 1990; Owen et al., 1992; Harrison et al., 2013; Aharon-Rotman et al., 2017). Additionally, considering the density-dependent effects of the increasing population size, such as agricultural conflicts (Jensen et al., 2008; Mason et al., 2018) and intra- and interspecific competition for food and habitats (Schmutz and Laing, 2002; Zhao et al., 2020), appropriate management of key habitats is deemed necessary in South Korea to sustain the increasing trend or maintain the current population size.

5.   Conclusions

Our study holds great value in supporting the increase in the East Asian population of GWFG and BEAG and confirming a previously unobserved migration strategy, known as elliptical migration, through long-term census data. We believe further investigation is required to understand the reasons for using elliptical migration by linking it with external environmental factors and examining the ecological impacts of population growth along the complex migration network in the East Asian-Australasian Flyway. Additionally, collaborating with tracking data, long-term monitoring efforts could offer more detailed insights into population trends and migration strategies, contributing to the management and conservation of goose species in this region.

CRediT authorship contribution statement

Eun-Jeong Kim: Writing – original draft, Visualization, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Wee-Heang Hur: Writing – review & editing, Resources, Project administration. Hwa-Jung Kim: Writing – review & editing, Resources, Project administration. Yu-Seong Choi: Writing – review & editing, Resources, Project administration. Dongwon Kim: Writing – review & editing, Resources, Project administration. Who-Seung Lee: Writing – original draft, Project administration. Sejeong Han: Formal analysis. Hyerin Joo: Formal analysis. Chang-Yong Choi: Writing – review & editing, Supervision, Project administration, Data curation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.