Elsevier

Environmental Modelling & Software

Volume 71, September 2015, Pages 15-29
Environmental Modelling & Software

Spatial neighborhood effect and scale issues in the calibration and validation of a dynamic model of Phragmites australis distribution – A cellular automata and machine learning approach

https://doi.org/10.1016/j.envsoft.2015.04.010Get rights and content

Highlights

  • We develop a dynamic model of Phragmites distribution using cellular automata.

  • We investigate patterns of distribution and spread at different scale settings.

  • We obtain cellular automata transition rules using boosted regression trees.

  • We present a model of neighborhood effect that captures directional influences.

Abstract

We developed a dynamic model of the distribution of Phragmites australis, a plant that has spread intensively on Finnish coasts. The model employs cellular automata and utilizes machine learning to provide the transition rules. We examined the effects that various cell sizes and neighborhood extents had on pattern detection and model behavior. We obtained the transition probabilities using boosted regression trees in a way that accounts for the spatial arrangement of the neighboring cells. The results show the influence of the scale settings on the ability to detect and simulate patterns of Phragmites dynamics. The introduced method of quantifying the neighborhood effect, based on the spatial arrangement of the neighboring cells, displayed potential for capturing directional influences within the neighborhood. Our study addresses the close-range effect on the distribution of Phragmites, and it can be linked with models of water quality to predict future distributions under various scenarios of land-cover change.

Introduction

Species distribution and dynamics are key subjects in ecological studies, and landscape management and conservation. For many decades, species distribution modeling (SDM) has proven useful for understanding species competition, response to external changes, equilibrium with the environment, and population dynamics under a projected future climate and land cover (e.g., Richardson et al., 2010). Important advancements have been achieved in the field of SDM during recent years (Zimmermann et al., 2010). Species distribution models have moved from being spatially implicit to spatially explicit (Sklar and Costanza, 1991, Hiebeler, 2000); from using conventional statistical methods to utilizing machine learning (ML) techniques; and from being static to including the dynamic elements of species’ interaction with their surroundings (Oborny et al., 2000). These trends in SDM are supported by enhanced data acquisition methods, the availability of increased computing power, and advancements in spatial analysis and software. Highlighting the progress and new trends in SDM, Zimmermann et al. (2010) emphasize the necessity of linking SDMs with dynamic models. Dynamic SDMs allow the prediction of future species distributions and provide useful tools for planning and management.

Dynamic spatial models have long been applied in landscape ecology and related fields (Sklar and Costanza, 1991). These models facilitate the quantitative description of processes in the landscape as well as the prediction of landscape changes. A plethora of dynamic spatial models have been introduced and applied for a wide range of ecological and environmental applications (Parker et al., 2003). The cellular automata (CA) approach is widely applied in dynamic modeling (Hogeweg, 1988; Balzter et al., 1998, Soares-Filho et al., 2002, Parker et al., 2003, Molofsky and Bever, 2004, Colasanti et al., 2007, Silva et al., 2008, Di Traglia et al., 2011). In CA, transition rules capturing local interactions are used to replicate the landscape processes in a bottom-up approach (Fonstad, 2006). In CA formalism, space is represented by a lattice of cells, each of which holds a state from a predefined finite set of states and evolves in discrete time steps. A cell evolves based on a set of transition rules that are functions of the state of the cell's neighborhood (Toffoli, 1984, Hogeweg, 1988, Balzter et al., 1998). One of the main reasons for the wide adoption of CA in modeling dynamic spatial processes is that CA are simple to define and implement while at the same time they are able to replicate processes in complex systems (Barredo et al., 2003). The utility of using CA as an approach for modeling vegetation dynamics is well established (Hogeweg, 1988, Balzter et al., 1998, Molofsky and Bever, 2004). CA have been employed in studies of species distribution to analyze and model species competition (Silvertown et al., 1992), clonal plant spreading (Inghe, 1989, Oborny et al., 2000), and forest succession (Alonso and Solé, 2000). The manifestation of populations on the mesoscale as a result of close-range interactions among individuals (Oborny et al., 2000) resembles species distributions observed in nature, particularly in plants and sessile organisms. The experimental potential of CA models makes them useful tools for both studying mechanisms causing the spread of species and for evaluating the different scenarios of planning and management (Barredo et al., 2003, Richardson et al., 2010). Finally, the representation of space in CA as a lattice grants the CA a number of advantages, such as the possibility for the multiple scale investigation of phenomena, computational efficiency, and compatibility with the GIS raster format (Itami, 1994, Drielsma et al., 2007). However, the usefulness of CA depends on their ability to characterize a process, which in turn depends on the definition of the CA transition rules and on the CA scale settings. While defining and implementing a CA model can be simple, the development of a realistic CA model for the process at hand is burdened with pitfalls (Mancy et al., 2013).

CA transition rules are a key determinant of the model behavior and its ability to yield realistic results. A probabilistic component needs to be incorporated in the transition rules due to the randomness inherent in natural processes and the incompleteness of knowledge of the relationships between processes and their driving forces (Couclelis, 1985, Phipps, 1992; cited in Balzter et al., 1998, Itami, 1994). CA transition rules also need to reflect the factors influencing species dynamics that cannot be abstracted in the neighborhood effect. While theoretical knowledge sheds light on the potential factors behind species distributions, quantifications of these relationships often need to be empirically derived. Data mining and ML methods were used in a number of studies to provide CA transition rules. Methods include, for instance, genetic algorithms (Jenerette and Wu, 2001), neural networks (Yeh and Li, 2003), naïve Bayes (Altartouri and Jolma, 2013), and support vector machines (Yang et al., 2008). ML methods have also gained popularity in SDM in recent years due to their ability to improve prediction (Elith et al., 2006) and model complex relationships in ecological data without the restricting assumptions often needed in the parametric approaches (Hochachka et al., 2007, Olden et al., 2008).

Other details of the CA have also been suggested to influence the ability of CA to model vegetation dynamics. These details include the spatial and temporal sequence with which states are updated (Ruxton and Saravia, 1998), the synchronous and asynchronous updating (Schönfisch and de Roos, 1999), and the discrete and continuous simulation of time (Mancy et al., 2013). In addition, the spatial scale at which data are analyzed can influence the derivation of transition rules as well as model behavior. The cell size and neighborhood extent have been found to affect the behavior of CA-based models of urban processes (Kocabas and Dragicevic, 2006) and land cover/use change (Ménard and Marceau, 2005, Pan et al., 2010). In addition, Chen and Mynett (2003) studied the effect of the cell and the neighborhood settings on the results of a CA-based prey–predator model and observed an influence of these settings on the resulting patterns of the two species. Despite the role of scale and its effect on landscape metrics (e.g., Parody and Milne, 2004, Wu, 2004), the model scale settings, such as the cell size, the neighborhood extent, and the time step, are often decided arbitrarily. There is a need for modeling the close-range effect in clonal species, such as Phragmites australis, at multiple scales and examining the effect of the transition rules and scale settings on the results of a dynamic SDM. The dynamic SDM needs to be confronted with observed distributions and evaluated based on the ability to correctly simulate the quantities and locations of changes in the species distribution.

In this study, we develop a dynamic model of clonal species distribution using CA with the aim of addressing two questions. The first question addresses the effect of the cell size and the neighborhood extent on the ability to detect distribution patterns and the ability to simulate the species dynamics. The second question is how the CA transition rules can be provided using ML techniques and what effect various neighborhood rules can have on the results of the model. The two questions are tightly linked because the transition rules of CA are functions of the state of a neighborhood that can take various sizes. The species subject for modeling in this study is the common reed, Phragmites australis.

The common reed, Phragmites australis (hereafter Phragmites), is a perennial vascular plant that spreads in wetlands and is distributed worldwide (Haslam, 1972, Lambertini et al., 2008). A native common helophyte around the Baltic Sea, Phragmites plays an important role in the ecosystem dynamics of shallow coastal areas (Meriste et al., 2012). Reed beds mitigate sediment-borne internal nutrient loading, form a buffer for catchment-borne external loading, and protect the shoreline from wave-induced bank erosion (Kaitaranta et al., 2013). Reed colonies also play a role in the ecology of coastal areas by providing spawning areas for fish (Härmä et al., 2008, Lappalainen et al., 2008) and nesting areas for birds (Huhta, 2009, Meriste et al., 2012). However, the rapid spread of Phragmites is claimed to have also had a negative effect on biodiversity because the reed is a strong competitor that shades other plant species (Munsterhjelm, 1997). In the coastal areas of Southern Finland, Phragmites has become substantially more abundant during the last few decades, blocking long segments of the shoreline and raising the concern of local people (IBAM, 2011).

The mechanisms of Phragmites dispersion include generative reproduction by seeds and seedlings, and vegetative expansion by rhizomes (Koppitz, 1999, Belzile et al., 2010). Seeds are produced in the autumn and are transported a distance of up to 10 km (Fér and Hroudová, 2009) by currents (in the ice-free period) and by wind (Baldwin et al., 2010). Three phases of Phragmites dispersion can be distinguished. In the settlement phase (Koppitz and Kühl, 2000) seeds establish new Phragmites patches if suitable environmental conditions exist (such as the optimum sediment property and moisture, and a lack of competing vegetation). Once established, Phragmites starts the propagation phase where it spreads vegetatively into suitable areas in the vicinity. In the last phase, various genotypes compete and the clones best adapted to the site prevail (Koppitz and Kühl, 2000). This results in a low genetic diversity in old reed beds – they typically consist of only a few of the best adapted rhizome-dispersed clones (Koppitz et al., 1997). Seed germination cannot occur under strong competition or in submerged conditions (Weisner and Ekstam, 1993, Weisner et al., 1993) and therefore close-range vegetative dispersion is said to be the major means of colonization (Koppitz et al., 1997, Mal and Narine, 2004, Fér and Hroudová, 2009, Kettenring and Mock, 2012).

The extensive expansion of Phragmites has been widely attributed to the anthropogenic disturbance in coastal areas (Burdick and Konisky, 2003, Silliman and Bertness, 2004, Bart et al., 2006, King et al., 2007, Chambers et al., 2008). In different regions, Phragmites is found to prevail on shorelines adjacent to developed urban areas (King et al., 2007) and agricultural land (Chambers et al., 2008), and along anthropogenic habitats such as drainage ditches (Maheu-Giroux and De Blois, 2007). The increased eutrophication due to excess nutrient runoff from catchments around the Baltic Sea, together with decreased grazing pressure, have been proposed to be the main reasons for the spread of Phragmites (Jutila, 2001, von Numers, 2011, Pitkänen et al., 2013). The topographic conditions have also been found to affect habitat suitability for Phragmites colonization. Sheltered areas with soft sediments in the Finnish archipelago have witnessed rapid expansion of Phragmites (Pitkänen et al., 2013). The area has also witnessed a seaward progression of Phragmites (von Numers, 2011) that exhibits more resistance to waves in shallow waters compared to other helophytes (Coops and Van der Velde, 1996). However, open shorelines and archipelago areas exposed to heavy waves are unfavorable habitats for Phragmites (Coops and Van der Velde, 1996, von Numers, 2011). Another physical barrier to the seaward propagation of Phragmites colonies is the depth of water (Meriste et al., 2012) because the transportation of oxygen to the roots becomes more difficult as the plant grows deeper (Huhta, 2009, Engloner and Major, 2011). These environmental factors, together with the dispersion mechanisms and causes, constitute the basis for the development of a dynamic model of Phragmites distribution.

Section snippets

Study area

Our study sites (Fig. 1) are located on the Finnish coast of the Gulf of Finland (GOF), the easternmost part of the Baltic Sea. The area has a jagged coastline forming many sheltered bays and inlets with shallow and brackish waters. The Finnish coasts of the GOF and the Archipelago Sea have witnessed a substantial increase in the Phragmites belt (von Numers, 2011, Pitkänen et al., 2013). The belt was estimated to cover an area of 28,000 ha in 2002 (Pitkänen, 2006).

The analyses were performed on

Methods

The developed model is shown in Fig. 2; the modules within the model are explained in subsections 3.1 The habitat suitability sub-model, 3.2 Neighborhood effect sub-models, 3.3 Rate of propagation, while the simulation procedure is described in Subsection 3.4. The scale settings and the various model runs are explained in 3.5 Spatial and temporal scale settings, 3.6 Model runs. Model validation is then explained in Subsection 3.7, followed by a description of the software used in this study (

Results

The distributions of the Phragmites-occupied and the unoccupied cells with respect to each predictor variable in Fig. 4 indicate the potential of these variables for assessment of the habitat suitability for Phragmites. At both sites, Phragmites prevails in sheltered areas with shallow waters and close proximity to river mouths where nutrient rich sediment can be found. The static SDM exhibited a good performance (0.7 < AUC < 0.9; Swets, 1988; cited in Bučas et al., 2013) in both interpolation

Discussion

The presented results help address a number of issues about the scale and the transition rules in the dynamic modeling of Phragmites distribution. The results demonstrate that the choice of the spatial scale, including the cell size and the neighborhood extent, is essential for both pattern detection and simulation. In addition, the results show the benefit of accounting for the spatial arrangement of the cells within the neighborhood in capturing directional influences and achieving an

Conclusion

In this study we presented a dynamic model of the Phragmites australis distribution in coastal areas Southern Finland, employing CA and ML. The transition probabilities were provided by BRT classifiers that take into account the location suitability and neighborhood conditions. We find the BRT method useful for providing the CA transition probabilities. Using BRT, we developed a method for modeling the neighborhood effect that accounts for the spatial arrangement of the neighboring cells in the

Acknowledgments

We would like to thank Hanna Piepponen and Meri Koskelainen from the Finnish Environment Institute (SYKE) for kindly providing the reed maps and the wave exposure data used in this study. Mapping the reed belt was conducted by SYKE as part of the Finnish Inventory Programme for the Underwater Marine Environment (VELMU). We also thank Robert Gilmore Pontius Jr. for commenting on the paper and Jaana Sorvari for helping in the revision. This study was initiated within the IBAM project (Integrated

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