Dynamic simulation of Spartina alterniflora based on CA-Markov model — a case study of Xiangshan bay of Ningbo City , China

Biological invasions are a global environmental problem. They have resulted in enormous ecological and economic consequences worldwide, and they are among the greatest threats to biodiversity and ecosystem function. Spartina alterniflora, an invasive plant, has caused great ecological influence since it was introduced to China over 30 years ago. According to supervised classification and visual interpretation of three remote-sensing images (2002, 2006 and 2010), we attained the spatial population distribution of S. alterniflora in Xiangshan Bay, Ningbo, Zhejiang province. To explore the topic further, dynamic change processes were also analyzed using the IDRISI software and their spatial distributions in 2010 and 2014 predicted using a CA-Markov model. It was found that compared with remote-sensing image interpretation maps in 2010 and 2013, accuracy verification yielded overall Kappa coefficients of 81.99% and 85.57% respectively, indicating a good predictive result from the CA-Markov model. Therefore, the model can be used for long-term forecasting such as determining the dynamic change processes and evolution trends of S. alterniflora in the Xiangshan area over the next 20 years. This can in turn provide guidance for effective management and control of invasive plant populations such as S. alterniflora.


Introduction
Spartina alterniflora Loisel., a graminaceous perennial herbaceous plant with the characteristics of salt tolerance, submergence tolerance, fast growth, short breeding cycle, and wide ecological breadth, can facilitate sediment deposition, protect levees, and reconstruct shoals.It is native to the Atlantic coast of the Americas from Newfoundland, Canada, south to northern Argentina.It was introduced to China in 1979 by Professor Zhong Chongxin from Nanjing University in China and achieved positive effects when used for beach protection and siltation promotion (Tang and Zhang 2003;Chung 2006).However, as the area covered by S. alterniflora has expanded, it has had negative impacts on natural ecosystems and led to serious economic and social harm (Callaway and Josselyn 1992;Daehler and Strong 1996;Chen et al. 2004).
Originally, 16 m 2 of S. alterniflora was planted on a trial basis in the Wumen mudflat of Tongli, Yuhuan County of Zhejiang Province in 1983.After 30 years of invasion, the plant is distributed from the coast of Hangzhou bay in the north to southern Ao river, Cangnan county in the south, covering an area of 5092 ha, which has had some negative impacts on local natural ecosystems (Zhao and Lu 2007;Zhang and Lu 2010;Lu and Zhang 2013).For example: 1) S. alterniflora's dense growth clogs waterways, affecting boat traffic, preventing water exchange, and creating a risk of red tides (Yu et al. 2010); 2) some coastal species such as algae, shellfish, crabs, and fish populations decrease as rapid spread of S. alterniflora along the seaboard destroys their habitats, seriously threatening fisheries (Chung 2006); and 3) more seriously, competition with local coastal plants (e.g.Phragmites communis and Suaeda glauca) for growing space entails a threat to local biodiversity (Zhao and Lu 2007;Yu et al. 2010).Consequently, study of the temporal and spatial dynamics of S. alterniflora, including its diffusion time, processes, and development trends, has become very important.
Carefully selected models for predicting vegetation species spatial dynamic change have been widely used in biogeography, evolutionary biology, ecology, conservation biology, and management of invasive species and are demonstrated to be a useful tool (Fleishman et al. 2001;Peterson and Vieglais 2001;Fertig and Reiners 2002;Scott et al. 2002;Chen et al. 2008).Spatial dynamic change of S. alterniflora population studies in China have mainly focused on its temporal and spatial changes and associated mechanisms.Predicting the population dynamics of S. alterniflora is still not well understood and less frequently practiced.Few published studies have predicted the dynamics of S. alterniflora populations in China, and those which do concentrate on the Yangtze River estuary.For instance, Huang and Zhang (2007) investigated the population expansion pattern of S. alterniflora for 7 years in the Yangtze Estuary.In addition, a cellular automata (CA) model and a structurally dynamic model were built to simulate the vegetation changes (population expansion of S. alterniflora), also in the Yangtze River Estuary (Huang et al. 2008;Wang et al. 2013).Moreover, Ge et al. (2013Ge et al. ( , 2015) ) used a process-based grid model and a bio-physical processes model to simulate the range expansion of S. alterniflora and salt marsh vegetation in the same area.
In this study, we used a CA-Markov model to provide robust spatial and temporal dynamic modeling of land use changes.The advantages of the two models, i.e. the time series of the Markov and spatial predictions of the CA theory, enable it to be used for Spatial-Temporal Pattern stimulation (Torrens 2003;Mitsova et al. 2010;Sang et al. 2011;Hu et al. 2013;Yang et al. 2014).However, since the advent of the CA-Markov model, it has been used more for urban land-use change (Yang et al. 2007;Yikalo and Pedro 2010;Yang et al. 2012;Olga et al. 2014) and largescale land-cover change prediction (Till et al. 2005;Liu et al. 2008;Sanchayeeta and Jane 2012;Alexakis et al. 2014), and its direct use to study the spatial distribution of invasive species is less common.Therefore, based on the CA-Markov model we try to predict the spatial expansion trends of S. alterniflora for the next 20 years in the Xiangshan area by combining land-cover change transition matrices for 2002-2006 and 2006-2010, conditional probability data, and dynamic suitability maps of the S. alterniflora population, which can provide some suggestions for effective management and control of invasive species and for local beach development.

Study region
Xiangshan Bay is located in the southeastern part of Ningbo city, Zhejiang, China, and is bordered by Hangzhou Bay to the north, Sanmen Bay to the south, and the Pacific Ocean to the east.It is a semiclosed long and narrow gulf extending inland from northeast to southwest; the total sea area is 563 km 2 , the shoreline is 270 km, and the bay has a total of 59 islands (Figure 1).The study area is rich in marine resources, being the main aquaculture base in Zhejiang Province.Because of its unique geographical location and resource advantages, it has also become one of the most important natural resources for developing the marine economy in Ningbo.

Data sources and pre-treatment
To acquire a land-cover classification map of the Xiangshan area, four remote-sensing images were selected from the Landsat TM (Thematic Mapper) of 2002 and 2006, the Landsat ETM (Enhanced Thematic Mapper) of 2010, and the Landsat OLI (Operational Land Imager) of 2013.We chose these images based on the following criteria: 1) images taken between August and November when S. alterniflora flourish; 2) images must be taken during appropriate conditions, such as limited cloud cover; and 3) images must be taken at low tide such that the the intertidal area where S. alterniflora grows can be seen.Through pre-treatment by applying geometric correction, atmospheric correction, image mosaics, and band synthesis to the original image, a cropping profile of the Xiangshan area was obtained.Then, the resulting four images were classified using supervised classification, and the classification results were corrected by visual interpretation in ENVI.Moreover, DEM data of the Xiangshan area were imported into the IDRISI software, which generated a contour map and slope map for the multi-criteria evaluation module (MCE).The original data described above were attained through the Geospatial Data Cloud of International Services Centre of Science Data (www.gscloud.cn).

Methods
A cellular automaton is a local grid dynamic model of discrete time, space, and states which represents the interaction between space and causality over time.It has powerful spatial-operation capabilities which can be used to simulate complex multi-variable systems and are suitable for the study of temporal and spatial dynamics of plant communities (Li et al. 1999;Wu 2007;Cannas et al. 2004;Wang et al. 2007).A cellular automaton consists of the automaton itself, a cellular state, an area, and conversion rules, and its basic principle is that the state of a cellular automaton at time (t+1) is a function of its state at time (t).Its mathematical expression is as follows: where S is a cellular automaton collection of finite, discrete states; t represents time; f is the set of rules for local spatial cellular state transformation; and N indicates the cellular field.
The Markov dynamic model is used to predict the probability of an event at time t based on the theory of Markov processes.It can use the transition probability matrix between states to predict the status and development trend of incidents.The equation is as follows: where S is the system state, t is time, and P ij is the matrix of transition probabilities.CA and Markov are both discrete dynamic models of time state.Although the CA model has powerful spatial computation capability, it is not as good as the Markov model for quantitative calculations, and because the Markov model is focused mainly on forecasting the magnitude of changes, it cannot predict their spatial distribution (Zhang 2012).By combining the CA and Markov models, a CA-Markov model can be constructed which has both the ability of the CA model to simulate spatial variations of complex systems and the long-term numerical forecasting capabilities of the Markov model.
This research is based on the CA-Markov model using the IDRISI software.First, four images of the Xiangshan area in 2002, 2006, 2010, and 2013 were selected.Because S. alterniflora is a salt marsh plant growing in coastal wetlands, to reduce the effect of unrelated factors on classification accuracy and simulation precision, a region of interest was defined in ENVI by performing mask processing to exclude the outside sea area.After pre-treatment, supervised maximum likelihood classification was used to classify land-cover types and acquire remote-sensing classification images.Classification accuracy is an important indicator in remote-sensing image classification, and field validation is an important way to ensure this accuracy.The classification accuracy of the four remote-sensing images was verified using ENVI, taking the distribution of S. alterniflora in the published literature as a reference to verify the classification accuracy of images before 2010.Second, quantitative analysis (we gave the reasonable threshold to every driving factor and used the method of expert scoring to calculate the weight) of driving factors such as topography, slope, growth characteristics of S. alterniflora, and human impacts was performed.Spartina alterniflora survival is constrained to the wetlands of the seashore and limited by topography and slope.Additionally, recent human impacts, such as high rates of erosion, have destroyed many intertidal zones where S. alterniflora persists.Third, according to the MCE and Markov models, the landcover map, the land-cover transition matrix, and probability and suitability maps of land-cover change were obtained using the IDRISI software.Then a CA- Markov model was built to simulate the dynamic spatial pattern of the S. alterniflora community in Xiangshan Bay.Finally, simulation precision was verified using the Kappa coefficient (Pontius 2000;Pontius and Schneider 2001;Bu et al. 2005).The equation for this is: where P O is the correct analog ratio, P C is the expected simulation scale in stochastic cases, N is the total number of raster in the landscape pattern, n is the number of raster of correct analog, and A is the number of land-cover types.The result is usually between 0 and 1.A Kappa value less than 0.4 indicates less precision and less consistency; when 0.4 ≤ Kappa ≤ 0.75, accuracy is moderate; and when Kappa is greater than 0.75, there are small differences and high consistency between the two maps (Wu et al. 2008;Huang 2011).Figure 2 shows a detailed technical roadmap of this process.

Population spread of S. alterniflora in Xiangshan Bay
After similar processing of the three images for 2002, 2006, and 2010 and analysis of the forecast image for 2014 in Xiangshan Bay, spatial maps and data for population areas were calculated for the study years.By combining Figure 3 with     1 and Figure 3).

Transition matrix analysis of land-cover change in Xiangshan Bay
Quantitative analysis of land cover can provide only a preliminary analysis of the area changes in landcover patterns, whereas the transformation relationships between different land-cover types can be well displayed by the Markov transition matrix, but cannot be explained by it.By running the Markov model using the IDRISI software and entering the corresponding land-cover maps, the transition matrix of land-cover change can be obtained.From Table 2, it can be seen that: (1) the probability of other landcover types changing into S. alterniflora was not high overall during 2002-2006, 2006-2010, and 2002-2010.By contrast, the transformation of tideland into S. alterniflora had the highest probability, which shows that the plant is most suitable to growing in tidal flats.It cannot grow, or has only a small probability of growing, on the mainland and on islands, an observation which is consistent with the environmental growth characteristics of S. alterniflora.
(2) Comparing the two periods 2002-2006 and 2006-2010, the probability of conversion of tideland to S. alterniflora decreased, but that of S. alterniflora to tideland increased, which means that its rate of growth was slower later than in the early period.The probability of transforming seawater into tideland was also on the rise; this showed that tideland area was increasing and that some sea area was likely to convert to S. alterniflora.

Field validation and evaluation of classification accuracy
Classification accuracy is an important indicator in remote-sensing image classification, and field validation is an important way to ensure this accuracy.
The classification accuracy of remote-sensing images from 2002, 2006, 2010, and 2013 was verified using ENVI, taking the distribution of S. alterniflora in the published literature as a reference to verify the classification accuracy of images before 2010.The accuracy verification data for 2013 were based on a field survey from July to October in 2013.Overall classification accuracy for the four images was greater than 80%.

Forecasting and analysis of changes in invasive species population in Xiangshan bay
To predict land-cover change using the CA-Markov model, a land-cover map, a land-cover transition    Figure 4 and Table 3 can be summarized in the following conclusions: (1) Compared with the population in 2014, S. alterniflora will have increased by 4.50 km 2 in 2018 at an average annual rate of 1.125 km 2 .Compared with the past 12 years, its growth rate will be slower.From 2018 to 2030, growth rate will decrease by an average of 1 km 2 every four years.
(2) The most concentrated area of S. alterniflora is in Xihu Bay.Its proportion of total area has declined in the past 12 years, but it is still the highest, at more than 35%.(3) In the next 16 years, the total area of S. alterniflora in Xiangshan will rise, but a more complex trend with an initial decrease followed by an increase may occur in some small areas.Some areas may remain the same, depending on tideland area and human disturbance.
Precision verification is essential to ensure the accuracy and credibility of the simulated images and the predicted areas.In this study, real object classification maps for 2010 and 2013 were used to test the simulated images for 2010 and 2014 in Xiangshan Bay.The reason for verifying predicted maps for 2014 with real maps for 2013 is that the biomass of S. alterniflora reaches its maximum in October and November of each year (Xu et al. 2012), but the time of this study was earlier in the year, and the appropriate satellite images were unavailable.The validation module in IDRISI was used to calculate the value of Kappa, which gives the numerical position error between two thematic maps.This module was used to verify the accuracy of the predicted diagrams in 2010 and 2014.The overall Kappa coefficient of the simulated images was 81.99% in 2010 and 85.57% in 2014.
The projected area of S. alterniflora expanded rapidly during 2002-2030 in Xiangshan Bay; in particular, the population area grew exponentially from 2002 to 2014.The community area was also projected to increase in the next 16 years from 2014 to 2030, but the expected rate was much slower than before, amounting to slow but steady growth (Figure 5).
In Figure 6, the average annual growth rate of S. alterniflora appears to decline continuously overall in Xiangshan Bay during approximately 30 years.The 20% average annual growth rate before 2014 is expected to wither to less than 5% in the next four years.Moreover, it will decrease further to 1% per year in the next 16 years, a trend which may be related to the tideland area and the role of human disturbance.
According to analysis of the dynamic graph of S. alterniflora population in each small area in Xiangshan Bay, seven small areas grew rapidly in the early years and then gradually slowed down to reach a steady state, a trend which is consistent with their observed state of expansion (Figure 7).The most concentrated area of S. alterniflora among the seven small areas is in Xihu Bay; its proportion of the total area remained greater than 35% over the three decades from 2002 to 2030.The main reason for this may be that Xihu Bay contains the largest tideland among the seven regions, which is highly favorable for expansion of S. alterniflora.

Discussion
Invasive species have not only resulted in loss of biodiversity and ecosystem imbalance, but have also had negative effects on economic development (Li et al.  2006).Currently, effectively managing and controlling invasive species is a worrisome problem for the governments and scientists of every country in the world.Understanding the spatial distribution of invasive species and controlling their future expansion dynamics is undoubtedly an effective approach to their management and control.Ranking among the leading tourist centers in Ningbo, Zhejiang, Xiangshan Bay is rich in marine resources, is the main aquaculture base in Zhejiang Province, and is also an important marine economic zone (Zhao and Lu 2007;Zhang and Lu 2010).However, the invasion of S. alterniflora has had deleterious influences on local ecosystem balance and on marine economic development in recent years (Chung 2006;Lu and Zhang 2013).Huang et al. (2008) developed a Cellular Automata (CA) model to simulate the expanding process of S. alterniflora for a period of 8 years after being introduced to new shoals and predicted it would continue to expand at a high rate for a long period into the future.However, other research (Wang et al. 2013) established a structurally dynamic model using Stella software version 9.0 (Costanza and Voinov 2001) and predicted the area of S. alterniflora and Phragmites australis from 2011 to 2028 (Wang et al. 2013) and found that, after an initial rapid increase, S. alterniflora area remained stable, after which it decreased.For Phragmites australis area, the increasing rate was low during the initial years, but then maintained an increasing rate, eventually occupying more area on the Jiuduansha Zhongsha than S. alterniflora (Wang et al. 2013).
Our study was based on remote-sensing images and the CA-Markov model and predicted the spatial distribution and diffusion of S. alterniflora in coming years in Xiangshan Bay.The results of CA-Markov simulation showed that by 2030 the spatial distribution of S. alterniflora would further expand from its greatest concentration in Xihu Bay in 2002 to the east and west along the coast in Xiangshan Bay.However, the area of greatest concentration remains in Xihu Bay, highlighting where eradication efforts should begin.The average annual growth rate of the S. alterniflora community first increased and then slowed down in Xiangshan Bay over about 30 years.The 20% average annual growth rate before 2014 was expected to wither to less than 5% in the next four years and to decrease further by 1% in the next 16 years.
Simulation modelling is a key tool to integrate information and testing of hypotheses and has been of great importance in understanding the complex dynamics of ecosystems (Huang et al. 2008;Wang et al. 2013).However, different parameters used to build these models may yield different results.In this study we used the CA-Markov model to predict the spatial expansion trends of S. alterniflora in the next 20 years in the Xiangshan Bay by combining land-cover change transition matrices for 2002-2006 and 2006-2010, conditional probability data, and dynamic suitability maps of the S. alterniflora population in the hope that it can provide some suggestions for effective management, control of invasive species, and local economic development.

Figure 1 .
Figure 1.Location of Xiangshan Bay in Ningbo, China.A: The coast from Waigaoni to Xianchi, B: Xihu bay, C: the coast from Wusha to Jiangjiaao village, D: the coast from Jiangjiaao to Baishashu, E: the coast from Baishashu to Nansha island, F: the coast from Zhaojia to Changshawan.

Figure 2 .
Figure 2. Simplified schematic for remote sensing data processing and simulation modelling.
matrix, and suitability maps of land-cover change are needed.The data are acquired in three steps in the IDRISI software: (1) the Markov-based land-cover transition matrix; (2) the suitability maps of landcover change based on the multi-criteria evaluation module (MCE); (3) CA prediction based on the rules of numerical conversion, spatial transformation, and conversion of neighborhoods.By combining the land-cover map, the land-cover transition matrix, and the suitability maps of land-cover change for different years, it is possible to obtain simulated land-cover maps and a predictive map of the spatial distribution of S. alterniflora in Xiangshan Bay in the next 16 years.The spatial distribution and population areas in each small region of Xiangshan for2018, 2022, 2026,  and 2030 (i.e. at four-year intervals) were acquired.

Figure 7 .
Figure 7. Regional area statistics for S. alterniflora during 2002-2030 in Xiangshan bay.A: The coast from Waigaoni to Xianchi, B: Xihu bay, C: the coast from Wusha to Jiangjiaao village, D: the coast from Jiangjiaao to Baishashu, E: the coast from Baishashu to Nansha island, F: the coast from Zhaojia to Changshawan.

Table 1 .
Area and percentage of S. alterniflora population during 2002-2014 in Xiangshan bay.The coast from Waigaoni to Xianchi; B: Xihu bay; C: the coast from Wusha to Jiangjiaao village; D: the coast from Jiangjiaao to Baishashu; E: the coast from Baishashu to Nansha island; F: the coast from Zhaojia to Changshawan.
throughout the entire coastal area of Xiangshan.In particular (Figures1 and 3), from 2006 to 2010, it expanded from three small regions (A, B, and C) to six regions (A, B, C, D, E, and F).(4)The most concentrated area of S. alterniflora in all four years

Table 2 .
Markov transition probability matrix of Xiangshan bay land-cover types.The row is stand for the conversion rate of one kind of land type transform another four every four or eight years.
was Xihu Bay, which is part of Xiangshan Bay.From 2002 to 2014, the population in Xihu Bay was 0.3501 km 2 , 2.6890 km 2 , 4.6512 km 2 and 7.6450 km 2 , respectively.All of these areas are more than 39% of the total S. alterniflora area in Xiangshan Bay, which means that Xihu Bay is the focal distribution region of S. alterniflora in the Xiangshan Bay area (Table

Table 3 .
Area and percentage of S. alterniflora population during 2018-2030 in Xiangshan bay.The coast from Waigaoni to Xianchi, B: Xihu bay, C: the coast from Wusha to Jiangjiaao village, D: the coast from Jiangjiaao to Baishashu, E: the coast from Baishashu Nansha island, F: the coast from Zhaojia to Changshawan.