3 Landscape-model properties: Current practices

Landscape models (LM) as defined here should not be confused with “landscape analysis models” aiming at analysing a spatial structure at landscape scales (Müller and Steinhardt, 2003). Instead, LM are dedicated to simulation of landscape change and dynamics. The previous section emphasises that many dynamic LM have been reviewed in the literature, concerning agricultural, forest, arid and urban landscapes (Berling-Wolff and Wu, 2004*; Scheller and Mladenoff, 2007; Verburg and Veldkamp, 2004*). LM mentioned in this paper are merely a sample selected to highlight some of the most important features of landscape modelling to explore some of the key challenges facing those who build and use LM. To be exhaustive, this section should also address considerations about the time management of models (Degenne et al., 2009*), about the 2D-3D representation of space in LMs (Gaucherel et al., 2010*), and many others. The time and spatial dimension challenges are urgent to improve our understanding of external needs such as biogeochemical processes, for example.

Scientific models pertain to various epistemological modes (Levins, 1966). They often serve an objective of comprehension through hypothesis tests and inference processes; they also help to define prospective objectives thanks to scenario elaboration and decision support tools; they finally offer a methodological objective by helping to define experiment protocols, by performing in silico experiments, by developing new algorithms and equations to fulfil a scientific questioning. In addition, another advantage of models is to integrate (to gather) knowledge into a coherent framework. We are not discussing here other topics concerning landscape modelling such as data calibration, validation, observation/simulation, comparison or sensitivity analyses. They are indeed critical in this debate about landscape modelling, but this would need another full-paper and has been well discussed in the literature (Jørgensen and Bendoricchio, 2001; Mas et al., 2014; Paegelow et al., 2013).

3.1 Explicit versus neutral landscape models: the “spirit” of models

The first and probably main dichotomy observed in LM concerns process-explicit versus neutral models. Process-explicit models simulate landscapes by implementing one or several specific processes, such as in most of the previously mentioned models (Costanza and Voinov, 2004*; Gustafson, 2013*; Seidl et al., 2012; Verburg et al., 2004) (Figure 1*a). Instead, neutral models are simulating landscapes with similar patterns and statistical properties without any process implementation (Gardner and Urban, 2007*; With and King, 1997*) (Figure 1*b). Such models are more or less neutral, depending on the more or less extensive use of random functions to generate the pattern (see Appendix A.1 for details). Neutral LM offer some kind of null-hypothesis tests translated into the landscape dynamics topics. They help to answer the generic question: Does a random (or almost random) function simulate observed patterns (or not) and, more rarely, observed dynamics (Caillault et al., 2013*)? If so, it is maybe not necessary to combine complex landscape generation processes to interpret observed landscapes (Gaucherel et al., 2006a*; Saura and Martínez-Millán, 2000*). Furthermore, if so, it becomes possible to model new virtual landscapes, dedicated to intrinsic as well as extrinsic needs already mentioned.

We have earlier detailed the kind of processes that are explicitly taken into account for LM, either of biophysical or socio-economical nature, and often both (Willemen et al., 2012*). A promising way of combining these various landscape processes certainly pertains to the use of model platforms in order to efficiently build models dedicated to landscape topics (de Coligny, 2006*; Dufour-Kowalski et al., 2011; Gaucherel et al., 2006b) (Figure 2*a). Another promising opportunity is that of Domain-Specific Language (DSL) (Degenne et al., 2009*; Fall and Fall, 2001*). DSL are languages adapted to a specific target, such as modelling a broad class of landscapes, and sharing various methods and knowledge for this goal. They are almost all process-explicit models, with the exception of the RULES platform dedicated to neutral models (Gardner, 1999*).

3.2 Raster versus patchy landscape models: the “space” of models

Another important dichotomy among LM, often mentioned but rarely discussed, concerns the type of spatial representation chosen to be implemented in the model. Most LM handle raster mode, i.e., grid-based or pixel-based, mosaics (Costanza and Voinov, 2004; Saura and Martínez-Millán, 2000*), because pixels are easier to manipulate than the various objects found in the vector mode (i.e., polygons, polylines, points…) (Degenne et al., 2009*; Gaucherel et al., 2006a*). Yet, most landscapes, if not all, are patchy in the sense that they are composed of patches (polygons) that are considered uniform relatively to their main attribute (often land cover), with sharp boundaries separating them from the contiguous neighbours (Forman and Godron, 1986*; Kotliar and Wiens, 1990*). Such landscapes are often called categorical, as they suppose land-cover categories, with discrete states of patches. In a sense, landscape modellers realize that landscapes are often discontinuous and may be less efficiently handled by the classical tools developed for several decades, such as point-pattern processes, interpolations as Geostatistics, etc. New surface-pattern analysis and modelling tools are now able to handle highly non-stationary spatial structures (i.e., with variable statistical moments) (Gustafson, 1998; Li and Reynolds, 1994*; Tischendorf, 2001). We list here a panel of advantages to model dynamic landscapes with patchy mosaics.

1. Realism – Among all advantages, the most convincing is certainly that patchy landscapes are more realistic. This argument is quite obvious for agricultural and urban mosaics, i.e., human-based landscapes (Forman and Godron, 1986*; Kotliar and Wiens, 1990*), but is still relevant for large forested and arid mosaics too, as we have seen that they often exhibit regular (and thus patchy) patterns, due to discrete soil, topography or climatic properties. Furthermore, this representation highlights existing boundaries between landscape elements. We argue here that the patchy representation, particularly suited for man-made landscapes, may suit well to most natural landscapes too, considering their natural boundaries (Henne et al., 2011; Moustakas et al., 2009*; Viaud et al., 2010*).
2. Complementarity – Patchy landscape simply is a new approach to study this object, thus offering an independent and potentially innovative way of studying the same object. Such independent ways of study have often been mentioned as useful to cross-check scientific interpretation. Manipulating polygons or polylines indeed suggests working with other unitary/single elements, computing and analytical methods, other topologies, etc. (Degenne et al., 2009*; Mackey, 2000*). For example, polygons have at least as many neighbours as their numbers of edges, while pixels always have eight neighbours, presenting the same directions. This difference partly explains difficulties to handle vector mode objects, but also highlights the richness of this approach.
3. Qualitative view – A patchy approach is often more intuitive and more rapid than pixel-based approach once implemented, because it handles a single object (e.g., a polygon) instead of handling a list of non autonomous and/or non independent pixels being linked to artificially create the uniform polygon studied. As a corollary, the patchy approach enables working with much larger landscape extents or much more rapidly for a similar extent. Yet, possible drawbacks concern the need to model landscapes in a more qualitative view that is not always easy to handle (e.g., distance related questions such as pollen or gene diffusions).
4. Property control – Interestingly, the patchy concept finally helps to understand the difference between the landscape composition (land cover) and the landscape configuration (patch arrangement) (Li and Reynolds, 1994). In a grid-based approach, both are mixed and handled in a simultaneous way, because changing a pixel state changes its land cover simultaneously to the land-cover pattern with its neighbours. While landscape composition and configuration are not fully independent in a patchy approach, they appear to be sufficiently differentiated to understand whether the studied landscape process concerns purely attributive changes, such as agricultural successions (Castellazzi et al., 2008; Verburg and Veldkamp, 2004), or is also modifying geometrical and/or topological changes, such as in urban systems for example (Pumain, 2006*).
5. Object-oriented view – Similarly to remote sensing transition between grid-based and object-based detection, it is relevant in LM to manipulate objects (Flanders et al., 2003). The patchy approach helps to dissociate objects within the landscape and to develop specific dynamical processes for them. Instead, a pixel is changing continuously from a crop field, a forest, a household, depending on probability transitions and thus is losing its nature all the time (Usher, 1981). Hence, patchy landscapes that are rather widespread and intuitive would possibly contribute to federate attempts directed towards the search for a general LM framework.

3.3 Mono- versus multi-scale models: the “scale” of models

LM often are multiscale, in a sense of including objects spreading over continuous scales or of including processes spread over several discrete organization levels. Multi-level models consider landscapes with two or more discrete organization levels such as temperate agricultural landscape processes mainly based on crop field rotations and farmer decisions. Other levels than farmers (villages, governments…) are often useful in modelling complex human-based landscapes. A more continuous view of scales, quite relevant in the case of natural landscapes (Pascual and Guichard, 2005*), would probably be less appropriate and more difficult to implement in human-driven landscapes, due to our perception of discrete levels of actors in landscapes. It has been shown that crop allocation at the farm scale is responsible for most agricultural landscape patterns (Benoît et al., 2012; Houet et al., 2010*; Rizzo et al., 2013; Thenail et al., 2009). Studying the sole crop rotation is a fruitful approach when computed with Markov chains (Le Ber et al., 2006*), although we cannot ignore the spatial autocorrelation caused by farm management (Baudry et al., 2003). This observation remains relevant for higher organization levels such as regional decisions, but today models rarely account for such multiscale/multilevel manipulations.

Vegetation cover in forested or arid ecosystems also shows various scaling behaviours. In particular, self-similar relationships between vegetation cluster size (scale) and their number (count) can define self-organized patterns of forested studied landscapes (Scanlon et al., 2007*). Several models such as in arid or forested areas have shown that local interactions may exhibit scaling laws over a wide range of conditions in arid areas, thus providing examples illustrating the criticality theory, i.e., discontinuous transitions between vegetated and non-vegetated zones (Pascual and Guichard, 2005*; Rietkerk and Van de Koppel, 2008*). Yet, such behaviours (Solé and Bascompte, 2006*) are not convincing: first, they are not robust over scales (they concern only few orders of magnitude); second, they are not fully understood (for example the scaling exponent cannot be predicted by the originated processes); third, they are phenomenological and should still be related to the ecological processes involved (Gustafson, 2013*); and fourth, if some processes (such as preferential attachment) have shown self-similar behaviours, it has not been proved that other processes would not succeed in doing so. In other words, this self-organization approach is close to a neutral model, but probably not fully appropriate for LM, as we think it will probably not provide in depth processes to understand landscape functioning.

3.4 Modelling networks or not: the “veins” of models

Agricultural and urban systems exhibit physical or more abstract linear networks in dynamic landscapes (Berling-Wolff and Wu, 2004; Turner and Gardner, 1991*). Agricultural areas are for example characterized by the so-called “blue veins” constituted by river networks, and by “green veins” such as hedgerows and other grass margin networks that all have strong effects in the landscape generation and functioning (Thenail and Baudry, 2004*). Fields and farms indeed are managed according to the islet they belong to, as farmers naturally follow these networks for defining their boundaries. Other networks (veins) are frequently found in rural areas, such as roads, dyke or ditch networks that may structure the landscape as well. Models have for example shown how a dyke network can influence the animal population viability it is hosting (Retho et al., 2008).

Above all, the field mosaic itself is sometimes modelled by the use of a network, considering that each patch is characterized by a gravity centre (or a summit of a graph) and is linked to its neighbours (with the edge of the same graph) (Gaucherel, 2008*; Le Ber et al., 2006*). Such linear networks can help to develop new analyses and to model tools as their objects have specific properties (Proulx et al., 2005*; Strogatz, 2001*). They grow or divide in specific patterns and topological dynamics that are very different from point-patterns or surface-patterns already mentioned. Urban landscapes highlight in particular the role of hidden networks such as communication and transport networks. Phone, electric or energy (e.g., gas) networks may strongly structure the emergence of new households in suburban areas (Berechman and Small, 1988; Pumain, 2006). Transport networks, such as roads, railroads or tracks are also a strong constraint in the landscape dynamics (Forman and Godron, 1986*).