j - Dipartimento di Matematica - Politecnico di Torino

Applying the proposed LU identification methodology and deriving all the required parameters
needed to set up the mathematical model, this summarizing table can be obtained:
Total area (km 2 ) 475
High bio-potentiality area (km 2 ) 124
V 0 0.26
b T 0.1606
M max (Mcal/m 2 /year) 2.3 E+08
B max (Mcal/m 2 /year) 1.5 E+08
U 0 0.02
h 1.96
k 0.75
c 0.0374
V e 0.72
M e 0
Table 2.
The values in Table 2, have been entered in NetLogo model elaborating the proposed differential
system. In particular, b
T
, h, U
0
, M max , k and c seems to satisfy the inequality (II) so that the
equilibrium corresponding to he second scenario turns out to be stable and the system evolves
asymptotically to this equilibrium state. The system tends to keep areas with high value of biopotentiality
but they are isolated in landscape pattern and the fluxes of bio-energy between them
seem to be limited. As a consequence, the dynamic evolution of this environmental system shows a
trend toward a good production of bio-energy but with a limited diffusion of it, and, then, with
limited fluxes between LU. A low connectivity index (Table 2), discloses to this equilibrium state
as a solution of the differential equations system, since the lack of connectivity prejudices the
energy exchange between LU even containing high BTC values areas. The landscape fragmentation
provoked by a large urban sprawl phenomenon and by the rich and structured roads network is
reflected on the confined and obstructed energy fluxes between LU. The need of opportune
planning strategies and actions to reduce fragmentation favouring the energy fluxes between
ecosystems and preserving biodiversity, has to be underlined since the actual landscape pattern for
the study area shows a low response in terms of connectivity and energy fluxes.
Conclusions
If the ecological graph is a powerful tool to represent connections efficiency between LU and to
identify high ecological values areas to be protected and compromised ones limiting energy fluxes,
on the other side a mathematical model evaluating the potential effectiveness of natural resources
on the long term, is essential to assess the diachronic evolution of landscape as a unique system.
An integrated approach combining the ecological graph and the mathematical model, allows to face
the great challenge of planning and management under sustainable environmental and economical
conditions since it can represent a powerful decision system support to compare effects and impacts
of alternative scenarios and actions (evaluation of new roads and urban development plans).
Not only for a description of the available energy at LU scale but also as a tool for evaluating the
equilibrium trend in landscape evolution, this mathematical and GIS interfaced method can help in
understanding environment response and dynamic change in time to correctly manage and preserve
natural resources and ecosystems.