## The Probabilistic Model

Considering a landscape composed by a mosaic of units (patches), we can imagine that the ontogenetic processes appear according to a space/temporal caliber and that this caliber produces scaled effects.

We can imagine at least three ontogenetic levels based on a probabilistic typology. These are formally inserted into a hierarchy that is coupled in space and time.

Assuming an observer located away from the systems in a truly neutral position (this is never accomplished) and observing the phenomena that occur inside the system we can note at least three temporal occurrences with distinct frequencies and spatial orientation.

The most frequent and most space restricted occurrences are named "opportunities," and they are paired to the Greek letter a. The second is a stage of the events, p. Lastly there is a stage of the novelties, y, when the elements external to the system are dominant (Fig. 5.2).

These three states can be copied, maintaining the same sequence, across a broad range of scales. In terms of efficiency in processing energy, material, and organisms,

Fig. 5.2 Hierarchical relationship between the three typology of ontogenetic phenomena. Novelties of a lower level create conditions for opportunities at the superior level

Fig. 5.2 Hierarchical relationship between the three typology of ontogenetic phenomena. Novelties of a lower level create conditions for opportunities at the superior level

it is possible to characterize each state according to a mathematical metaphor: opportunities are like additive operators, events are multiplicative operators, and finally novelties are exponential operators. The energy and the speed of changes in a landscape can be easily understood for each state. The slowest changes occur at the y level, the fastest at the a level. It is intuitive that at each state different amounts of energy and information are involved.

The frequency of occurrence of these ontogenetic processes decreases moving from opportunities (a) to novelties (y). Conversely, the memory implicated in the processes decreases moving from novelties to opportunities. Few bits of memory are necessary for active opportunities, but for events and novelties the memory stock plays a central role. The stochasticity increases moving from opportunities to novelties. And finally new landscape configurations are expected in the novelty state.

Opportunities are the most common and frequent state created by the neighboring of different objects. Events are created by the combination of opportunities, but novelties require the contribution of some extra-system energy. The negative entropy level increases from the a state to the P state. This is a signal of increases in system complexity, but this also occurs in moving from P to y.

According to the amount of energy exchanged between the different levels, the intrasystemic energy prevails at the opportunities state with an increase of coalescence and an increase in interactions.

The event state is dominated by an exchange of intersystemic energy that is concentrated at the ecotones. In the novelty processes energy is supplied from the outside with a dramatic increase in entropy inside the system.

Opportunities can be produced by a disturbance that operates inside the system and determine an accumulation of memory with the possibility of a recursive loop. Also the events are produced by this disturbance process, but their emergent properties are represented by the formation of energetic gradients among the patches that compose the land mosaic and participate in the community's coalescence.

Finally, novelties are created by energy input from the outside that are so strong they create new spatial and energetic configurations. A formidable contribution to new configurations is done continuously by human activities that have the capacity to mobilize large amounts of energy in short time and that focus on sensitive targets.

All the three states have to be considered in a hierarchical framework in which opportunities occupy the lowest level and novelties the highest state.

The a, P, and y states have a sequence of occurrence that can't be inverted.