## The Landscape as a Matrix

A very popular vision of landscape is a matrix of processes and related patterns. Most of the actual research in landscape ecology focuses on this perspective. The described objects in this matrix, or background, have their domain inside such a matrix. But a dual problem arises when we follow this vision. The first is how to distinguish a matrix, and the second is how to distinguish the patches inside. This approach has further complications. In Fig. 2.4 the problem is represented in geometrical form. If a patch is localized inside a matrix, the relationship with other patches is not a simple case of absolute distance but a matter of matrix localization. Matrix can be considered background, but, according to the delineation of a part of the matrix that we require to describe any phenomenon, the position of patches depends on the size and localization of the matrix window. Matrix concepts are

Fig. 2.4 According to the position of the describing window a matrix can describe different objects (A,B) in the same domain

Fig. 2.4 According to the position of the describing window a matrix can describe different objects (A,B) in the same domain

implicitly undetermined although we believe the contrary. A possible way to bypass this uncertainty is to consider a domain and assume contemporarily that such a domain has heterogeneous characteristics, but still the choice of the observing window is not determined by objective characters. In modern landscape ecology, we assume that the landscape is a heterogeneous entity and that in such an entity we can observe a patch that is distinct from the background. According to this view, it would be possible to distinguish one patch at a time and not all the patches of a matrix, because in this case the matrix would be coincident with the background and, as a consequence, invisible. The matrix concept can be considered a first approximation that is not the product of observations but the result of an anticipated vision of the environmental context. It is a matter of sequential scanning of the background and the assemblage a posteriori of the different units detected one at a time.

When we try to attribute a function to a matrix, we assume a different role for the neighboring patches as though they were at the same time real. In effect every patch that we can distinguish pertains to different domains, or if you prefer every patch is the result of a distinct process (Fig. 2.5). That they are neighbors is a matter of observation, but they are false neighbors. Maintaining this assumption we are obliged to reject most of the interpretations that we have accumulated especially in landscape ecology.

The next step is to recognize a composite unity, a unity in which it is possible to distinguish different components. In this case the heterogeneous nature of such unity develops solitary characteristics and thus enters into the domain of the unit.

Fig. 2.5 Most of the processes that we can observe pertain to different domains (a, b, c, d, e, f) but are perceived by our sensors as contemporary and topologically related. This vision often is responsible for the bias that we introduce in the management of natural and human resources

In the case of the matrix, the composite nature is probably not real, but is an effect of accumulated observations distinguishing each unit at a time, and we are exploring different domains at one time. A residual possibility is that a matrix defined in such a way has a true character if the patchiness pertains to a meta-domain. Our capacity to distinguish and to accumulate such distinction, such as in a scanning process, raises problems of interpretation of reality. This capacity must not be considered a gestalt capacity, but a multidomain scanning that often swindles the observer who believes observed entities pertain to the same domain. The heterogeneous character of the landscape that represents the major attribute used in landscape ecology to process complexity could be a matter of human capacity to scan unities from a background using a multiresolution sensor. This hypothesis is extremely unpopular at present because scientists do not pay attention to the reality but seek to find evidences to a "pre-ordinato" mental model. We assume the heterogeneous character of the landscape, and we don't pay attention to other possibilities. In Fig. 2.6 the procedure that we use to scan a matrix is represented.

The problematic linked to the matrix bias affects most of our information on the real world and produces a great epistemological confusion. We discuss this later in the mosaic theory and for the moment we try to clarify the relationships between the different domains, a matter that we solve by adopting the ecotone paradigm in landscape ecology.

We have to assume that heterogeneity is represented by an asynchronous perception of separate unities recombined in our mind. Several problems in interpreting the reality of our surroundings are due to this distorted vision of reality.

A duality of problems must be discussed now that, for the first time, we have rejected the assumption of the universal value of heterogeneity. However, the heterogeneity does not exist at all; it is a product of the observer. We have to distinguish between a simple entity and a composite entity. The first is composed of a simple structure. It could be a strand of thread of a unique color and material (like wool). A composite entity is composed of several parts that are associated into the functional whole.

Fig. 2.6 The scanning capacity of the observer agency can produce a false mosaic of patches that pertains to different domains. The relationship between the different entities are not direct but are mediated by meta-domain filters ABCD

Fig. 2.6 The scanning capacity of the observer agency can produce a false mosaic of patches that pertains to different domains. The relationship between the different entities are not direct but are mediated by meta-domain filters ABCD

When woodland is in contact with an agricultural field, the two entities interact with each other in a special location that we call an ecotone. This is correct from a formal point of view and especially if we adopt the paradigm of geographical heterogeneity. But if we observe the processes that create and maintain these two entities it is clear that the processes responsible for a woodland growth are quite different from the ones that produce a crop field. The exchange of information between the two systems is quite low; order is produced inside the separate systems and not between. The domain in which a forest grows and develops is different from the domain of the human being. At this point we have to reconsider carefully the ecotone paradigm that is not a simple juxtaposition of patches but areas of contact between different systems or domains.

In regard to the typology of different ecotones, it is necessary to introduce a differentiation between intradomain and interdomain ecotones. In the first case the flux of material and energy might be higher than in the second.

For example, such intra and interdomain ecotones can be represented in moving outward from the center of a city along a gradient of "naturalness."