4 What model characteristics for what landscape type:
Research priorities

The appropriateness of model characteristics for modelling different landscape types has been rarely studied in detail. To combine the previous sections dedicated to landscape types and to LMs should help us to define research priorities in this field (Figure 1*). For example, we mentioned that patchy models simulate agricultural landscapes, that neutral models are used to study forested landscapes, that multiscale models are applied to arid landscapes, and that urban landscapes are often modelled by taking into account various networks. Such approaches are not exhaustive. We question here whether further developments of the previous model characteristics for new landscape types would open fruitful and complementary avenues to the field.

1. Neutral models – Neutral models, acting as null-hypothesis tests, are useful to identify mechanisms responsible for the observed landscape pattern or, rather, for refutation of absent mechanisms (Gardner and Urban, 2007; With and King, 1997*). It is often discussed how a specific process is able to generate a specific pattern, but it is more rarely tested how random or almost-random processes are not able to do the same.
2. Patchy models – A patchy approach is almost always possible to use, either according to some segmentation criteria or empirically and usually leads to a new conception of the studied landscape. Indeed, to use uniform patches with sharp boundaries between them is equivalent to discretize space in a specific way, radically different to that of more regular continuous or periodical representations (Gaucherel et al., 2006a*; Paudel and Yuan, 2012*). This is obviously the result of approximations within each patch, never perfectly uniform, but this approach also enables better taking into account various “singularities” observed in real landscapes. Singular presences are common in human-driven landscapes, as humans usually differentiate land covers and avoid managing fuzzy boundaries. It is also relevant for natural landscapes (Levin et al., 1993*), in particular at higher scales, when smoothed (geological, lithological or hydrographical) boundaries between land covers are progressively reduced to a narrow line (Moustakas et al., 2009; Viaud et al., 2010). Fluxes or organism movements can be stopped at or redirected along these lines of highly irregular (non-stationary) zones, thus leading to new behaviours of involved ecological processes (Forman and Godron, 1986*; Turner and Gardner, 1991*).
3. Multiscale models – Multilevel and multiscale LM are being increasingly studied, but could be further explored in new contexts. While it is often easier to work at only one or two scales to simulate a pattern, the frequent roles of lower and higher scales have been shown in these pattern generations (called emergent or immergent). When scales are considered as discrete levels, the hierarchy theory has proposed a heuristic approach for many ecological and environmental studies (O’Neill et al., 1986; Willemen et al., 2012). When scales are continuously successive, many concepts such as self-similarity (Pascual and Guichard, 2005*; Scanlon et al., 2007*; Solé and Bascompte, 2006*) or multifractality, and many tools such as geostatistics, wavelet transform (Grossman and Morlet, 1984), or local convolutions (Gaucherel et al., 2008) have been developed in order to describe and sometimes to model them. Hence, such multiscale LM can be expected to flourish in the future.
4. Network models – Finally, linear networks are of a great importance in landscape dynamics. There are several reasons why they have not been studied in a similar extent to that of other landscape features: i) they are rarely the central object of landscape studies, far behind crop fields or tree stands for example (Forman and Godron, 1986*); ii) reliable mathematical tools to handle networks such as graph theory have been considered only recently in environmental sciences (Strogatz, 2001); iii) many ecologists were not sufficiently aware of the role of these linear elements before some studies showed how landscape structures are constrained by them (Proulx et al., 2005*). Studying relationships between a landscape and the networks that inhabit it (e.g., green veins, blue veins, or roads) will probably lead to new discoveries. In case of urban or agricultural mosaics, landscapes may sometimes be reduced to the sole network that is carrying most of the landscape information (Thenail and Baudry, 2004*). Further, if we widen our considerations from linear networks to every kind of network, each landscape element can be considered as the node of a network, related to its neighbours by the network edges. Such topological network may be rich in information and interesting to study as such, opening new pathways to model landscapes (Gaucherel et al., 2012*).