Birgit Müller, Anja Linstädter, Karin Frank, Michael Bollig, and Christian Wissel. 2007. Learning from local knowledge: modeling the pastoral-nomadic range management of the Himba, Namibia. Ecological Applications 17:1857–1875.

Appendix A. Calculation of required biomass and grazing pressure per pasture.

(i) Calculation of required biomass

The required biomass per pasture  is determined by livestock number n(t), demand of dry matter d, in tonnes, per TLU and year and the pasture part of total required biomass, :

The amount of dry matter d required to maintain the diet and to produce milk for one TLU per year depends on different factors (for instance on the nutritive value of the forage during the seasons, and on animal race). We assumed a constant requirement of d = 2.5 tonnes for one TLU per year (cf. 2.3-2.7 t/y – (de Leeuw and Tothill 1993, p.78; 2.3 t/y – Guevara et al. 1996).

In the following it is outlined in detail, how the pasture part of total required biomass  for the different pastures and strategies are determined (for a summary see Table A1). Have in mind the pasture part of total required biomass adds up to 1 for all pastures.

()

For the two strategies which include seasonal resting (T, A3),  depends on the length of the rainy season (4 mo, cf. Bollig 2002). Consequently for the traditional strategy T holds , since on rainy season pasture (RSP) lactating animals (portion pl(t) of cattle number) stay the whole year and non-lactating only during the rainy season. The non-lactating animals graze eight months on the dry season pastures (DSP)
(). The second and third dry season pastures are not used from the start.

For the two strategies with continuous grazing (A1, A2), the proportion  depends on the amount of available biomass on the considered pasture in relation to total available biomass on all used pastures. Hence for RSP and A1 (continuous grazing with retaining reserves for drought) holds  = . For the other pastures the pasture part of total required biomass can be calculated in the same way (cf. Table A1). Note all three DSP are used from the start applying A1 and A2.

Applying alternative strategy A3: The rainy season pasture is used in exactly the same manner as with the traditional strategy T. Hence, . The DSP and the reserve for drought (RFD) have to deliver fodder for eight months for non-lactating animals. In contrast to the traditional strategy, all three DSP and RFD (as fourth dry season pasture) are equally used here from the beginning of the dry season on. Hence  is prorated to the pastures used in the dry season according to the following rule: The allocation of animals depends on available biomass on this pasture in relation to all pastures used in the dry season ().

(ii) Classification of grazing pressure

The grazing pressure  depends on how much biomass is available,, compared to the required biomass . Hence, the ratio of both factors is calculated and compared to a threshold  (this procedure is applied in the same way independent of the strategy).

Three cases may occur:

 (1)  “heavy”,        if (2)  “moderate”,  if (3)  “no”,              if

In order to decide when the biomass on a pasture is insufficient and the cattle herd has to move to the next pasture, a second threshold , , is defined. Hence, if the ratio between available and required biomass falls below this threshold , an action is undertaken (cf. Table 6). In reality the level of milk production is used as an indicator. If insufficient milk is gained per cow a new grazing area is sought.

The required biomass on the next pasture is newly calculated by adding the amount of forage missing on the previous pasture. If the herd is already on the RFD, a certain portion  of the herd is assumed to die (or, seen equivalently, to be sold or to be hired out). That implies that a portion  of the cattle herd is able to cope with shortages of forage by other means (e.g., browsing seeds and leaves of trees and using fat reserves).

The state of variable grazing pressure is determined, apart from strength of grazing, by the time of grazing. If a pasture was already used in the rainy season, the status of grazing pressure is set to "grazing in rainy and dry season". This holds true, even if the time span for the use of the pasture during the rainy season is short.

If the pasture is grazed exclusively in the dry season, the status of grazing pressure is set to "grazing only in dry season". Hence, combined with the strength of grazing,   may take five values: (1) "no grazing pressure", (2) "moderate (only in dry season)", (3) "heavy  (only in dry season)", (4) "moderate (rainy + dry season)", (5) "heavy (rainy + dry season)". These five levels of grazing pressure involve different impacts on the dynamics of perennials and annuals.

TABLE A1.  Formula to calculate the part of fodder required   for each pasture (past=RSP, DSP1, DSP2, DSP3, RFD) and each grazing strategy (T- traditional, A1, A2, A3 alternatives), pl indicates the portion of lactating animals,  the biomass available on pasture past at time step t. For strategy T and A1, pastures initially not intended to be grazed (DSP2, DSP3, RFD) may be in need, if biomass on the prior used pastures is insufficient  (cf. Table 6). In this case, portion of fodder required   will take values different from 0 for these pastures.

 T A1 A2 A3 4/12*(1-pl(t)) + pl(t) 4/12*(1-pl(t)) + pl(t) 8/12*(1-pl(t)) 0 0 0 0

LITERATURE CITED

Bollig, M. 2002. Produktion und Austausch - Grundlagen der pastoralen Ökonomie Nordwest-Namibias. Kölner Geographische Arbeiten 77:189–206.

de Leeuw, P. N., and J. C. Tothill. 1993. Pages 77–88 in R. H. Behnke, Jr., I. Schoones, and C. Kerven, editors.The concept of rangeland carrying capacity in Sub-Saharan Africa - Myth or reality. Range ecology at disequilibrium. New models of natural variability and pastoral adaptation in African savannas.

Guevara, J. C., O. R. Estevez, and E. R. Torres. 1996. Utilization of the rain-use efficiency factor for determining potential cattle production in the Mendoza plain, Argentina. Journal of Arid Environments 33:347–353.

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