2 Landscape processes: Current approaches

Here, we choose to review the four main landscape types of continental areas, continuously interacting. In particular, the increasing human demography shows specific trends on present landscape dynamics (Lambin et al., 2001): forests landscapes are often replaced by agricultural or arid ones (Verburg and Veldkamp, 2004*), agricultural landscapes are often replaced by urban or arid, partly depending on anthropogenic or climatic conditions (Figure 1*). Yet, these transitions are not systematic at all. Only a few landscape transitions, such as forest shifting to agriculture, have been studied in depth up to now (Lambin, 1997*; Usher, 1981*), or shifts from rural to urban (Brown et al., 2013). No exhaustive description of individual models is given here, while model comparisons are helpful to emphasize their respective drawbacks and advantages (Agarwal et al., 2002; Haase and Schwarz, 2009; Mas et al., 2014*; Pontius Jr et al., 2008). Instead, we present a representative list of processes concerned by each landscape type. Additionally, we systematically focus on one specific feature of each landscape type and on implementations for typical models of the domain.
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Figure 1: Illustration of the two main landscape models. There are: process-explicit models, using specific processes (a), and neutral landscape models, using random functions (b). Process-explicit models often simulate landscape structure dynamics in terms of land cover (top-right), as well as bio-ecological and socio-economical processes (top-left) hosted by these structures. In addition, these processes are interacting (dashed arrows) through neighbouring fluxes that likely modify their dynamics (dashed curves). Neutral landscape models often simulate fixed landscape structures in raster mode (bottom-left), here adapted from Saura and Martínez-Millán (2000*). To study agricultural landscapes some patchy neutral models (bottom-right), associated to linear networks (in black), have recently been built on the basis of Voronoï diagrams. Colours are representing hypothetical land covers.

2.1 Agricultural landscape

Agricultural landscapes are very much human-driven landscapes. Such landscapes are often studied using Land-Use and Land-Cover Change (called LUCC) models and are modelled as a selection of socio-economic and biophysical variables that act as so-called “driving forces” of land-use changes (Barton et al., 2010*; Matthews et al., 2007; Verburg and Veldkamp, 2004*). Land uses are simultaneously at the origin and results of land covers. Many models have shown that agricultural land covers are mainly driven by multilevel land-use processes, involving on the one hand behaviours of individuals and the upscaling of these behaviours, and on the other hand the macro-economic processes and their downscaled effects on landscapes (Thenail et al., 2009*; Willemen et al., 2012*). Hence, micro-economic theory and general equilibrium modelling are often combined to model agricultural mosaics driven by isolated actors such as farmers and by regional or national economic incentives (Costanza and Voinov, 2004*; Lambin et al., 2000; Verburg and Veldkamp, 2004*). Although biophysical factors mostly do not “drive” land-use changes directly, they can participate in land-cover changes (e.g., through climate change) and they influence land-use allocation decisions (e.g., soil quality) (Viaud et al., 2010*).

Land-cover patterns are influenced at different scales of analysis by different driving forces. At the local level, this can be the local water policy or the presence of small ecologically valuable areas, whereas at the regional level the distance to a market or an airport might be the main determinant of the land-cover pattern. There are various ways to model such agricultural landscapes, depending on the interaction between biophysical and socio-economic factors that for example may influence farming practices (field and farm levels), as collective actions (community and village levels) or as governance systems (district and province levels). The wish to merge these scales in causal relationships has recently led to two broad classes of agricultural LM: the top-down approach, based on remote-sensing and other data such as the CLUE-S model (Verburg et al., 2002), and the bottom-up approach, based on local case-studies providing a refined understanding of human decisions such as the DYPAL model (Gaucherel et al., 2006b*, 2010*; Valbuena et al., 2010). However, we observed a limited understanding of the underlying mechanisms in the former approach and difficulties to generalize the findings due to the limited geographic coverage of the latter approach, thus justifying recent attempts to combine and even couple such approaches in landscape modelling (Brown and Castellazzi, 2014; Castella et al., 2007*; Houet et al., 2010*).

Many models have shown agricultural landscapes to be spatially driven by multi-level human decisions. We briefly illustrate this characteristic by highlighting a crop allocation system involving at least two successive organization levels (Castellazzi et al., 2010; Gaucherel et al., 2010*; Thenail et al., 2009*): the patch level and the farm level. Agricultural landscapes indeed are often composed of a wide variety of patches: crop fields, woodlots, hedgerows as well as roads, rivers and buildings, all influencing the farm property dynamics. Depending on the farm production system, the landscape is usually forced to follow a defined crop allocation at farm scale, which has been demonstrated to be the dominant driver of such human-based landscapes in temperate zones (Baudry et al., 2003*).

It may be relevant to focus on the pure temporal patterns observed within or between several farms that can be modelled by Markov chain models (Le Ber et al., 2006*; Usher, 1981*). Conversely, spatial properties such as neighbouring fields appear to have a strong influence on the central patch studied, thus suggesting to focus on spatial as well as temporal patterns. Agricultural models have highlighted the interest of working with patchy mosaics, i.e., formed by mainly uniform, autonomous and contiguous patches, exhibiting sharp boundaries with their neighbourhoods (Kotliar and Wiens, 1990*; Le Ber et al., 2006*). This new interest has furthermore focused modellers’ attention on the deep distinction between the landscape composition (land cover) and landscape configuration (land-cover shapes and spatial arrangements) (Li and Reynolds, 1994*).

2.2 Forest landscape

Forested landscapes proceed from different mechanisms. At large scales, modellers usually handle forest patches (woodlots), which exhibit very different types of vegetation cover, where forest would have been considered as a single land cover in an agricultural landscape for instance (Baker and Mladenoff, 1999; Perry and Enright, 2006; Scheller and Mladenoff, 2007*). Many of the first forest models were “gap models” that operate at the scale of individual trees or small forest gaps or patches (Shugart, 1984). Forest parameters under study here may be the woodlot biomass, the tree density or height, the species composition or forest age, etc.

Models may also help here to better understand the effects of fire on forests, and in particular the role of landscape connectivity on fire spread, of fuel moisture content, of time since last fire, etc. (Keane et al., 2013*). Other models explore logging processes, by adjusting succession stages and transitions between communities in order to reach a particular forest state. Fire and logging are usually considered as disturbances of the landscape. In the more recent forest models, spatial interactions at and beyond the first-order neighbourhood (of an individual tree or a woodlot) are increasingly being taken into account.

The atomic entity of forested landscapes is the tree, therefore modelled by a combination of various processes such as phenology, growth and ecophysiological processes, dispersion, competition (inter- and intra-species), disturbances that may be natural (fire Finney, 1999; Keane et al., 2013, herbivores Cousins et al., 2003, pests, etc.) or human-based in the case of pruning or harvesting (de Coligny, 2006*; Dufour-Kowalski et al., 2011*; Kurz et al., 2000). For this landscape type, natural and human drivers are combined in complex harvesting, land-use and climate interactions.

One typical example of such processes involved in forested LM concerns seed dispersal (Cousens et al., 2008; Wang and Smith, 2002). Attempts to model seed dispersal can be described by either phenomenological or mechanistic models. The former models mainly use Γ-function kernels describing installation probability at a certain distance to the mother-plant (Clark et al., 2001*; Saltré et al., 2013*). The latter dispersal models explicitly simulate grain (and pollen) dispersion depending on seed downfall velocity, of the height of seed release, of the structure of the local wind-field (in case of an anemochore species) or of animal movements (for zoochore species) that may promote long distance dispersal (Clark et al., 2001; Nathan et al., 2008). Models are particularly useful for highlighting the important role of long distance dispersal events to rapidly colonize new areas (Saltré et al., 2013*). LANDIS is a good example of the recent generation of forest models (Mladenoff, 2004), modelling dispersal as well as many other vegetation (either natural or anthropogenic) processes. Simpler models may help to analyze a more specific process (Seidl et al., 2012*; Usher, 1981*). Deforestation is the most dramatic forest landscape dynamic and is, in most cases, the result of a complex causality chain, which originates beyond the forestry sector.

2.3 Arid landscape

Arid and semi-arid landscapes are subject to dryland degradation and vegetation transition processes (Lambin, 1997*; Rietkerk and Van de Koppel, 2008*). Water availability and thus climate forcing is the main driver of such landscapes, while most studies focus on the vegetation response to water resources. Dryland degradation may start with agricultural, forestry or grazing land-use intensification and proceed with more severe degradation factors among which are found soil erosion and soil salinization (desertification). Hence, arid landscape dynamics rarely are purely natural dynamics.

Other processes linked to disturbance caused by herbivores or fires have been studied in depth to understand arid landscape dynamics and to help predict the unwanted transition from a vegetated to a desert state (Scheffer and Carpenter, 2003). Drivers here are climate change impacting primary production of vegetation (Sankaran et al., 2005*), as well as socio-political mechanisms leading to a “pressure of production on resources” (Barton et al., 2010; Krol and Bronstert, 2007). In most cases, we observe a somewhat complex interaction between natural and anthropogenic processes, such as in the desertification phenomenon (Lambin, 1997*; Lejeune et al., 2002*). Many models help to address the questions why, where and when such arid landscape changes take place.

Some recent studies have explored a specific case of arid landscape dynamics involving binary states (vegetated and non-vegetated states) and two opposing forces of landscape shaping. It has been shown in particular that regular patterns may be the result of a competition force slowing down the vegetation colonization and a facilitation force favouring the same colonization trend (Couteron and Lejeune, 2001*; Lejeune et al., 2002*). Competition for water resource through roots and facilitation against solar heat through the canopy act at different spatial scales, thus generating a wide panel of regular patterns (spotted or banded patterns, etc.).

Other studies at higher scales have shown that the size distribution of vegetation clusters in undisturbed plots follows a power law distribution (Scanlon et al., 2007*): most patches of vegetation have a small size, but a few of them have a very large size. Such self-organization pattern (i.e., landscape organization exhibiting a self-similar property, see Appendix A.2) seems to be the result of internal dynamic processes driven by local interactions, yet sometimes controlled by external factors such as precipitation (Rietkerk and Van de Koppel, 2008*; Sankaran et al., 2005). Such landscape functioning is still under debate and it is not yet clear how regular and self-similar patterns differ. As evidenced by the previous references, models in this landscape type are still often theoretical models.

2.4 Urban landscape

Similarly to agricultural landscapes, urban or periurban landscapes are mostly driven by humans (Berechman and Small, 1988*; Berling-Wolff and Wu, 2004*). The historical development of urban growth models are rooted in transportation and land-use planning. Early models postulated that the interaction between two cities and within a city varied directly with the size of the (two) city (cities), i.e., its demography, and inversely with the square of the distance between them (or the distance to its centre) (Foot, 1981; Lowry, 1964). The urban area was represented as a transport network and the flow and assignment of trips to the transport network modelled; later, more complex trips (home-work journeys) have been modelled and validated, even taking into account transport network congestion. In parallel, the idea emerged that trips and traffic in the city resulted mainly from decisions at the individual household level. At this stage, public policy impacts on household dispersion, employment constraints, urban agglomeration economics (and real-estate prices) and other land-use planning are analysed in various urban growth models (Gusdorf and Hallegatte, 2007; Gusdorf et al., 2008).

As a relevant process in urban LM, we would like to consider urban growth with two different models. Interestingly, some cellular automaton models have emphasized the way in which locally made decisions may lead to global self-organized urban patterns which are rarely, if ever, in equilibrium (Viguié et al., 2014). For example, diffusion-limited aggregation models have been developed to handle rapid disequilibrium growth often due to the emergence of suburbs (Batty et al., 1989; He et al., 2013*). Recent models focus on economics of agglomeration or ecological energetics, the flow of goods and resources in the city to better explain such disequilibrium. Cellular automata combining ideas of evolution, self-organization and fractal geometry enable to calculate transition potentials mimicking land-use changes by agents’ behaviours (White and Engelen, 1993). These models have been found in good agreement with observations. Similarly, the FRACTALYSE model extends Christaller’s Central Place theory according to a fractal (self-similar) principle, i.e., areas with smaller and smaller aggregated central places (Christaller, 1972; Thomas et al., 2008). Such an approach indeed, enables optimizing urbanization processes by minimizing the use of places and buildings nearby places already occupied.

The concept of urban systems (i.e., multi-city urban networks) is complementary to that of urban growth and several models have documented and interpreted this concept (Pumain, 1989). After early models based on the central place theory, a second period of landscape modelling made a more explicit use of the networks, both in analyzing communication or migration flows between cities and by suggesting that networks were more efficient and more democratic forms of organization than hierarchies (He et al., 2013*; Proulx et al., 2005*; Pumain, 2006*). Networks of innovation diffusion, inter-city migratory fluxes, urban competition, socio-economic trajectories of cities and comparative urban dynamics have become again implicit, but can help understand urban systems (Berling-Wolff and Wu, 2004*).

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