Some relevant model features

In Figure 5.3, we present a network of the major components of the three submodels and their interactions. All components are linked through nitrogen flows that ultimately define if farmer and lakesider incomes can be maintained above a threshold that makes their livelihood strategies and their resource managements sustainable.

Most of LINDISSIMA 1 has already been described above. N lixiviation and runoff during the (rainy) growth period is a linear function of N concentration in the soil, which depends on the pre-existing N stock in the soil and the balance between N fertilizer supply and N uptake by maize. Actual nitrogen uptake by maize plants depends on N demand and N available to their roots. Both depend on current maize ADM and the latter also on N concentration in the soil. Ecological thresholds are established for this latter variable: (1) a minimum N concentration value below which plant growth is arrested and irreversible

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erosion occurs due to lack of plant cover, and (2) a maximum value above which soil microbiota is severely affected.

Figure 5.3: Diagrammatic representation of submodels LINDISSIMA 1 (dark gray), 2 (light gray) and 3 (all the figure). Thick arrows represent N flows. Thin arrows represent direct (+) and inverse (-) relations. Some state variables are highlighted in rectangular boxes and some rates in hexagonal boxes. The three most important N management decisions (aside from maize and shrub densities, not shown) are in brackets. Nitrogen flows in the model ultimately affect the possibility of sustaining the maize-based and the eco-tourism based livelihoods of two different rural groups.

LINDISSIMA 2 draws heavily from a validated eutrophication model developed by Scheffer et al. (1993), which captures the basic dynamical features that produce bistability of microscopic algal populations in shallow lakes. As previously mentioned, when algae populations explode, the lake in our story becomes murky, tourists flee from the place and lakesiders have no other way of making a living. LINDISSIMA 2 describes microscopic algeae concentration in the lake as the major cause of water murkiness and as a direct and strongly nonlinear function of nitrogen lixiviated from maize fields (NL hereafter). This

“cusp catastrophe” function (Thom, 1989) arises from the following fact: macrophytic

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111 aquatic plants that live at the bottom of the lake compete strongly with algae for dissolved nitrogen. Under normal N concentrations, both populations coexist and low algeae populations are attracted to a clear-lake stable equilibrium. When algae concentration increases beyond a certain threshold, the lake becomes murky and the macrophytes are deprived of light and almost excluded, making most of the dissolved nitrogen available to the algae. As a consequence, the algal population at equilibrium becomes much higher for any given N lixiviation value as long as macrophytes are not reestablished; algea populations are now attracted to murky-lake stable equilibrium values. Macrophyte restoration is possible if algae concentration falls below the above-mentioned threshold but the latter will now occur at a much lower NL value. In short, if the algae population is currently attracted to equilibrium conditions producing a clear lake, then a threshold NL = X will cause the algae population to be attracted to a stable equilibrium condition producing a murky lake. To shift the population stable equilibrium back to the clear lake regime, NL has to be reduced to a value much lower than X. These two different thresholds define three NL intervals: (a) a low-value interval producing a stable clear lake irrespective of initial conditions; (b) an intermediate-value interval producing bi-stability such that the equilibrium state of the lake depends on initial conditions previous to lixiviation, and (c) a high value interval producing a stable murky lake irrespective of initial conditions. These behaviors are explained further in the program. A “cup and marble” (gradient analysis) representation of simulations is displayed in real time- coupled to a conventional time series graph of algae concentration- to help users understand how changes in NL move the system along these three stability regimes. This exercise stresses the fact that “the form of the cup is more important than the current position of the marble”, a notion commonly overlooked in NRM (Figure 5.4) (Carpenter and Gunderson, 2001).

Lakesiders confront three complications for establishing the maximum NL level they can accept: (a) during very warm years (occurring any specific year with a 10% probability) algal blooms occur at normal N concentration value in the lake during the dry season even in the absence of NL, but they reverse spontaneously at the beginning of the rainy season if there is no excess N to sustain them; (b) if such a natural algal bloom occurs, the NL value they can accept is much lower than X; (c) farmers do not accept an adaptive strategy where the NL value could be decided every year depending on (a), because government bureaucracy is slow in delivering the subsidized fertilizer and it has to be requested and paid many months before anybody knows if a natural algal bloom will occur. The stochasticity of algal blooms and their consequences are captured in this submodel.

LINDISSIMA 3 introduces a small leguminous shrub into the maize fields as an additive intercrop (i.e. maize density is not reduced to make room for it). This submodel is again very simple and it is inspired in more elaborate and realistic ecological and

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ecophysiological tree-crop models (reviewed in García-Barrios and Ong, 2004). Shrubs in our story can be sown at densities between 0 and 2 plants m^-2. As in real situations, they can have positive and negative effects on both maize production and NL: On the one hand, (a) shrubs can absorb excess N in the field; (b) when N is insufficient, they can fix atmospheric nitrogen (investing energy on it) and reduce the need of N fertilizer and its cost; (c) their shoot prunings cover the ground and reduce N runoff. On the other hand, (d) as prunings decay, their nitrogen is incorporated into the soil (no attempt is made in LINDISSIMA 3 to model N mineralization; we simply assume that all N coming from prunings is available to plants within one year); (e) shrub roots invade maize root zones to a certain extent and compete for nitrogen. Partition of available N at any given time between maize and shrubs is a function of their dry matter ratio, their respective N demands and the extent to which shrub roots invade the maize root zone.

LINDISSIMA 3 allows for a user-defined number of shoot prunings per year, as well as a user-defined % of annual root pruning, both at a cost to the farmer.

Figure 5.4: Cup and marble representation of the effect of NL on the stability regime of the lake.

When NL= 0 and 1.2, there is a single clear-lake stable equilibrium state were the marble rests, irrespective of where the marble starts. When NL = 1.5, 1.8 and 2.1, there are two possible stable equilibriums (clear to the right and murky to the left), depending on the initial position of the marble. When NL = 2.4 there is a single murky-lake stable equilibrium state were the marble rests,

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113 irrespective of where the marble starts. In the program, the movement for the cup and marbles is simulated for every NL value.