ONLINE APPENDIX
A.1. Objective function components:
The community is assumed to seek to maximize the following aggregate objective function:
Max NPV= (1+δ)-t (1)
where
NPV = the total discounted net income over the planning horizon
δ= real interest rate (6% per annum)
ut = total utility from all activities during the tth period measured as sum of incomes from crops (), goat rearing (), dairy production (),charcoal (), and non-farm activities () during the year. These activities are discussed in more detail in the following sub-sections.
A.1.1. Crop production: The income generated from crop cultivation, , was calculated as:
(1)
whereis the per hectare net returns from the jth crop (j = rain-fed barley, irrigated barley, rain-fed wheat, irrigated wheat, irrigated spring cucumber and irrigated autumn cucumber ) and is land area (ha) under the jthcrop at time t. For calculating , the price per kg, cost of production per kg and yield per hectare in kg/ha were used. The cost of production includesexpenditure incurred on all inputs, such as, seeds, fertilizers, pesticides, hired component of labour, machinery for ploughing and harvesting operations. Since community land and labour costs are not accounted for, the income so calculated represents returns to fixed farm resources.
A.1.2. Goat rearing: The income generated from goat rearing, ,was calculated as:
(2)
Where
pmeatand pmilk =the prices of meat and fresh milk per kg/litre
=average weight of a goat (kg) in the nthage class, n = {newly born kids, female yearlings, productive does, male yearlings and productive bucks}
= theannual production of goat milk (litre) in the nth age class
and are number of goats being rearedand those sold or slaughtered for community’s own consumption in the nth age class as computed by using equation 3.
= is the cost of hired labour and other costs (i.e. vaccination and medical costs) incurred on goat production.
Population of goats:In order to endogenously forecast goat populations and the number of goats sold or slaughtered, a density-dependent Leslie matrix model (1945)was embedded into the model with goats grouped in five age-gender groups. The general model for the goat population is given by equation (3). Note that vectors and matrices appear in bold letters.
Gt+1= Gt + dt (GM – I )Gt − St (3)
where,
Gt= Vector of number of goats in respective age class (n) at time t, with its elements gnt
dt=the density dependent function for goats computed as , where is the total population of goats and Ktis the carrying capacity for goats. The carrying capacity is computed based on the number of seedlings and sprouts available for browsing, the amount of barley available from cultivation plus the amount bought from the market, amount of farm residuals (wheat and barley) and grass (mainly from forests and fallow land). There is a feedback mechanism between wood harvesting and carrying capacity for goats in Zagrosian oak forests where sprouts are the main naturally occurring form of regeneration that develop after felling of trees or after natural mortality (Salehi and Eriksson 2010; Soltani et al.2014). Therefore, a large amount of wood harvested increases availability of sprouts leading to increased carrying capacity.Increased level of crop cultivation also adds to carrying capacity for goats.
GM = 5x5 Leslie matrix for goats with its elements representing transition of individuals from one age class to the next.
St= Column vector representing the number of goats sold, including animals slaughtered for home consumption with sn,t as its elements.
A.1.3. Dairy products:The income generated from goat based dairy production () was calculated as:
(4)
where
pcurdand pbutterarethe per unit (kg) prices of curd and butter,
andare the quantities of curd and butter produced at time t, and
isthe cost of production of curd and butter
The process of making curd requires the use of milkand firewood. Since these two inputs are considered intermediate products, they were not included as a cost of dairy production. The cost of purchasing milk from outside the community and the cost of hired labour in dairy production are considered in calculating dairy production cost. The quantities of curd and butter produced are calculated as follows:
(5)
(6)
andare the conversion coefficients for curd and butter from milk, is the litres of milk bought from outside the community at time t.
The dairy production is related to the forest resources by the following relation:
(7)
is volume of firewood required for producing curd at time t and is firewood required to produce one kg of curd.
A.1.4. Charcoal production: While the villagers use firewood for cooking, heating houses and in the production of dairy products, charcoal is almost entirely produced for sale. It accounts for the income generated from forests () and wascomputed as:
(8)
where,
= the ratio of conversion of one cubic meter of harvested wood to charcoal
hi,a,t = cubic meters of wood obtained from the harvested trees where subscripts iand arepresent diameter class and land unit as computed in equation 9
pchr= sale price of charcoal (per kg)
= the cost incurred in the production and transportation of charcoal in land unit “a” at time t. is the probability of villagers doing illegal harvest being caught by forest guards.If one is caught by forest guards, he will not only lose the charcoal made, but will also have to pay a fine determined in court. The probability of being caught is computed from the data obtained from the conducted village surveys using the relation , where Ωpenalty is the kg of charcoal found while making or/and transporting charcoal on which penalty is imposed by forest guards and Ωtotal is the kg of charcoal produced by the community. For the purpose of modelling, the area used by the community is divided into A1 and A2categories based on the distance to roads and settlements (see Figure 1). A1 is the forest area located near the roads and villages and A2 represents forests area farther from settlements and roads. The probability of being caught () is lower in A2 area but the transportation costs are higherdue to longer distance from settlement and roads.
Stand of trees: In order to project the number of trees and forest growth, a linear matrix model was incorporated in the overall economic model. The matrix model includes trees grouped by diameter classes. Harvesting of trees is dependent on the stand of trees, availability of labour, profitability of charcoal production and firewood requirement for community’s own energy consumption. The matrix model gives the total forest stock in each period (one year here), recruitments, mortality and harvest as follows:
Ft+1 = FM(Ft − Ht) + Rt−Bt (9)
where,
Ft =a vector of the number of live oak trees in year t with its elements as fi,a,twhere subscripts “i” and “a” represent diameter and land unit classes. The forest areas further from roads and settlements (A2) are characterized as higher value stocking parameters (such as, number of trees per hectare, biomass per hectare, number of seedlings and sprouts per hectare) than areas closer to settlement and roads (A1). Tree population is divided into ten diameter classes, starting from 5 cm (2.5-7.49 cm)
Ht= the column vector of trees harvested with its elements as hi,a,t
FM = the transition matrix for oak trees
Rt = the column vector of regeneration with ra,t as its elements accounting for the number of seedlings and sprouts at time t in land unit “a”
Bt= the column vector of trees browsed by goats with ba,t as its elements. It is a function of goat population at time t, length of browsing period and daily food requirement of goats.
A.1.5. Non-farm activities: Hiring out of labour is the most important non-farm activity, income from which () was computed as:
(10)
where,
= wage rate for hired labour
= the number of man-days hired out during xth the settlement and summer camp seasons during tth time period. It is computed by using equation 12.
A.2. Labour constrain:Since the villagers are semi-nomadic, the constraints on availability of labour are used for two seasons: settlement and summer camps. During the summer camp season, 50% of the human population will move to temporary camps away from the community along with their livestock herds. The remaining population takes charge of crop cultivation, firewood collection and production of charcoal. The following equation is used to calculate the availability of community labour during each season():
= Nt (11)
Where is the ratio of active human population (14- 64 years) to total population, are the average working days per season and Nt is the human population at time t.The sum of human labour used for crop production, goat rearing, dairy production, charcoal production and non-farm activities cannot exceed the total availability of human labour in the community plus the amount of labour hired from outside the community (equation 12).
(12)
, and are labour (man-days) required for crop cultivation, goat rearing, dairy production, charcoal production, firewood collection and non-farm activities during the xth season (settlement and summer camps ) and tth period. is the amount of hired labour from outside the community. It is assumed to be hired as long as it is profitable.
References:
Leslie, P.H., 1945. On the use of matrices in certain population mathemaatics. Biometrika. 3, 183-212.
Salehi, A., Eriksson, L. O., 2010. A model for management of mixed coppice stands in semiarid persian oak forests. Int. J. Math. Comput. For. Nat. Resour. Sci. 2, 20–29.
Soltani, A., Sankhayan, P. L., Hofstad, O., 2014. A dynamic bio-economic model for community management of goat and oak forests in Zagros, Iran. Ecol. Econ.106, 174-185.
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