A model to analyse the influence of resource management policies on the economic returns from a traditional African pastoral system

Agr&ultural Systems 33 (1990) 77-96

A Model to Analyse the Influence of Resource Management Policies on the Economic Returns from a

Traditional African Pastoral System

J. W. Hearne" & A. J. C. Buchan °

a Department of Mathematics and Applied Mathematics, b Institute of Natural Resources, University of Natal, Box 375, Pietermaritzburg, Republic of South Africa

(Received 29 September 1988; revised version received 30 August 1989; accepted 13 September 1989)

ABSTRACT

A mathematical model is presented of the subsistence pastoral system on the Makatini Flats surrounding the Pongola floodplain just south of the Mozambique border in north-eastern South Africa. The model takes into account the quality and quantity of the different vegetation types.

With the impoundment of the Pongola river a number of management issues have arisen relating to the use of land and water resources. The model is used to analyse the effects on the economic returns from the pastoral system of reductions in water and traditional grazing land. It is concluded that, at a regional level the expected returns from agriculture on irrigated land on the Makatini Flats will more than compensate for the consequential fall in returns .from the pastoral system. Whether the cultivation of maize on the floodplain should be encouraged or not is less conclusive.

I N T R O D U C T I O N

A large area of western Maputaland, South Africa, is inhabited by traditional subsistence pastoral farmers. Since the construction of the Pongolapoort dam in the region the pastoral system has come under increasing competit ion from agriculture for land and water resources. In this project we at tempt to evaluate the impact of these developments on the pastoral system and thus aid the various government departments (Water

77 Agricultural Systems 0308-52 ! X/90/$03.50 © 1990 Elsevier Science Publishers Ltd, England. Printed in Great Britain

78 J. W. Hearne, A. J. C. Buchan

Affairs, Development Aid, and others) who are responsible for managing the resources in the region.

THE STUDY AREA

The study area covers 60626 ha of grazeable land. Of this land about 7% lies on the Pongola floodplain and the rest comprises the the land adjacent to the floodplain known as the Makatini Flats. The land on the floodplain lies above the maximum retention level of the numerous shallow lakes in the area and is inundated during flood events.

Although representing only a small fraction of the total land in the study the floodplain is highly productive and has an impact on the pastoral system in the region disproportionate to its area. However, its productivity is dependent upon regular flooding and since the construction of the Pongolapoort Dam in 1972 flood releases have been largely under the control of man. The dam was constructed to irrigate about 30 000 ha of land on the Makatini Flats. As the irrigation scheme associated with the dam comes into operation the pastoral system is threatened in at least two ways:

(1) The increased demand for water from irrigated commercial farming might necessitate a reduction in the frequency of flood releases onto the floodplain and thus affect the productivity of this component of the system;

(2) The allocation of land for commercial agriculture will deprive the pastoral system of traditional grazing areas.

In addition to the above, the reduced probability of an untimely flood has led to an increasing tendency to cultivate maize on the floodplain and so further reduce available grazing resources.

OBJECTIVES

To facilitate the management of the land and water resources in the region answers to the following questions are sought:

(1) What fall in returns will the subsistence pastoral system suffer as a result of losses in grazing land:

(a) on the Makatini Flats; (b) on the floodplain'?

(2) What would be the effect on the performance of the pastoral system if the present policy of an annual flood release was not maintained?

Influence of resource management on African pastoral system 79

APPROACH

As any policy making concerning the welfare of people must address both transient and steady state effects, a dynamic mechanistic model was considered to be necessary with a time horizon of at least a decade--15 years was chosen. Furthermore, it was felt that the use of a deterministic model would be the most efficient way of comparing the mean effects on the pastoral system of different resource use policies.

A number of models have been developed which deal with the interaction between animal populations and the available forage and which are suitable for analysing management options for traditional African pastoral systems (Anderson & Trail, 1978; Sanders & Cartwright, 1979; Sere & Doppler, 1980; Sullivan et al., 1981; Cartwright et al., 1982; Uys et al., 1985). Some of these models deal only with the quantity of forage available (Uys et al., 1985) while others consider both the quantity and the quality of fodder (Sanders & Cartwright, 1979; Sullivan et al., 1981).

Although it was possible to draw from some of the ideas in these models it was not possible to utilise directly any existing model. The quality of pasture on the floodplain is far superior to that on the surrounding Makatini Flats. Furthermore, different pasture types respond differently to flooding--one of the decision variables. Therefore, in addition to quality and quantity of fodder, it was necessary to include different pasture types in this model.

The model comprises three components or sub-models relating to pasture, cattle and revenue. These three components are discussed below.

PASTURE

Based on the floristic descriptions of Furness (1981, 1989) and Furness & Breen (1980) and an analysis of the patterns of use of floodplain vegetation by stock (Buchan, 1988a) five important floodplain vegetation types/pasture areas can be identified. The Cynodon dactylon (L.) Pers. community forms extensive lawns around some lakes. Cyperus fastigiatus Rottb. and Echinochloa pyramidalis (Lam.) Hitch. & Chase communities occur in the low-lying marshy areas which remain wet for most of the year. Phragmites australis (Cav.) Trin. ex Steud. occurs on flat swampy areas and Phragmites mauritianus Kunth. occurs on river banks, pan margins and inlet-outlet channels where water level fluctuations are marked. Furness (1981) mapped floodplain fields and areas disturbed by agriculture as a separate vegetation type. These areas are characterised by genera such as Maytenus, Dichrostachys and Sesbania and include a wide range of herbs and grass species.


On the Flats there is mixed bushveld which includes sparse woodland with interspersed sweetveld grazing, and deciduous sand forest. (Acocks, 1953; Loxton & Hunting, 1969).

Hereafter the five pasture types identified on the floodplain and the pasture on the Flats will be referred to simply as: Echinochloa, Cynodon, Fastigiatus, Phragmites , Fields, and Flats pasture. For each of these pasture types the quantity of forage available for grazing at any time is represented byp~ (t ha- 1) for i = 1, 2, ..., 6, respectively. The quality of the forage is also important and although there are many ways of assessing forage quality (McDowell, 1985), digestibility is probably the most reliable single forage quality index (Mentis, 1981; Zacharias, 1986). The amount of digestible forage available at any time corresponding to the pasture types given above is represented by di (t ha-1), for i = 1, 2 . . . . . 6.

Production, grazing and decay determine changes in pasture, thus:

where

d p J d t = r 1,i - r2,i -- r3,i (1)

rl,i = production rate (t ha- 1 year- 1) r2, i ---- grazing rate (t ha - 1 year- 1) r3,i = decay rate (t ha- 1 year- 1)

Variations in Flats pasture are due mainly to rainfall (Danckwerts, 1982). The production rate of the Flats pasture is thus given by the equation:

rl ,6 = P 6 × al ,6 × r f ( t ) x (Pmax6 --P6)/[Pmax~( 1 + b l ) - P 6 ] (2(a))

where al. 6 (t t - 1 year- 1) is the specific annual production rate. The rainfall function, rf, allows production to vary seasonally with rainfall. The function is evaluated at time t by the equation:

r f = 12 × rain(t)/rav

where rain is a value determined by linear interpolation of the average monthly rainfall figures presented in Table 1, and ray is the average annual total rainfall (574 mm).

The last term in eqn (2(a)) causes production to be inhibited as pasture density approaches its maximum value, Pro,x6" The constant bl was chosen so

TABLE ! Average Monthly Rainfall (mm) as Supplied by Computer Centre for Water Research for

Ndumu (1916-1984) and Makhatini Agricultural Research Station (1956-1984)

Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

76 106 73 54 24 5 12 7 47 44 65 61


that production is reduced to half its normal rate when P6 attains 90% of its maximum value. Hence bl = 0.1 (dimensionless).

Production for the first five pasture types is zero during flooding. At other times, the production rate is influenced mainly by soil moisture which, in turn, is determined by either the rainfall or the time since the last flood (Hensley & Furness, 1985). Field observations indicate that in terms of its effect on soil moisture, rainfall at time t is equvalent to a flood that occurred at a time given by b 2 - b3 x rf(t), where r f was defined above b2 = 0.5 (year) and b3 = 0"18 (year) (Hensley & Furness, 1985; Buchan, unpublished data).

This means, for example, that if there had been no floods for some time, the heavy rains in February (see Table 1) would create the same conditions as if there had been a flood a little more than 5 weeks previously. In general, therefore, for soil moisture purposes, the effective cessation time, tf, of the last flood is given by:

t f = ( t a x { t - [ b 2 - b 3 × r f ( t ) ] , t f } flood off

flood on

The elapsed time since the last flood is given by:

z = t - - / f

The production rate of pasture on the floodplain is assumed to be an exponentially decreasing function of z. Inhibition of production at high densities as described above for the Flats pasture is also assumed to occur for the floodplain pastures. Thus, when there is no flood on and for i = 1, 2, . . . , 5 production is given by the following equation:

rl,i =Pi x al, i x exp(-a2 , i x z) x (Pmax,--Pi)/[Pm'~x, x (1 + bl) -P i ] (2(b))

where ai,i is the maximum specific production rate (t t-1 year-1) and a2, i (year-1) is an attenuation coefficient. The parameters al, i were calculated from field data (Furness, 1981; Buchan, 1988a, 1988b)and are presented in Table 2 together with the maximum attainable densities, Pmax,, of each pasture type.

Grazing

The amount of pasture consumed by cattle will vary depending on the density of the pasture (Ilavstad et al., 1983). Field observations (Buchan, unpublished data) indicate that one livestock unit (lsu) grazing on pasture of density 0.9 (t ha-~) will graze at a rate of 2.3 (t year-1 lsu - ~). Under these


TABLE 2 Pasture Parameters (see Eqns (2)-(6))

i Echinochloa Cynodon Fastigiatus Phragmites Fields Flats

al, i 25.60 18"25 25'60 14.00 10.00 2.50 a2. i 0'93 3"47 9-59 0"80 4"20 0-00 a3. i 2"8 1.7 2"1 3"6 1.7 1"7 a 4. i 1"0 10"0 3"0 1"0 10"0 1"0 as.i 0"69 2-13 2'50 1'50 1-80 2"40 a6. i 0'65 0'45 0-65 0'45 0'40 0-25 P .... 6'0 2"5 1"5 3"0 3"0 2"0 areal 827 443 208 173 2 675 56 300

reference conditions the total grazed 'normally', tgn ( tyear - l ) , by the regional herd is defined as follows:

t g n = Tlsu x b4 (3)

where Tlsu is the total livestock units (lsu) comprising the regional herd (see Table 3) and b4 = 2"3 (t yea r - 1 lsu- 1). The actual rate of grazing will change if the pasture density differs from 0.9 (t ha-1) so it is convenient to define a pasture density index, pdii (dimensionless), in the following way:

p d i i = p i / b 5

where b5 = 0.9 (t h a - 1). During a flood there is no grazing on the floodplain and grazing on the Flats is given by:

r2, 6 = tgn x f(b6, b7, b8, pdi6) (4a)

where f is an increasing function of pd i 6 with maximum value given by b6 = 2.0, minimum value given by b7 = 0.02 and slope at the point (1, 1) given by b8 = 2"5. The function (see appendix) is constructed so tha t f a s sumes the neutral value of one when pd i 6 = 1, i.e. when P6 = b5 grazing occurs at a rate of b4 (t yea r - 1 lsu- 1).

When there is no flood on it is assumed that the rate of grazing by the regional herd on a given pasture type is directly proportional to the total amount of digestible material of that pasture type compared with the total amount of digestible pasture of all types. Thus the rate of grazing per unit area during no flood for pasture type i ( i = 1, 2 . . . . . 6) is given by the following equation:

r2. i = tgn x f ( b6 , b7, b8, pdii) x dl / td (4b)


where t d is the total amount of digestible material available of all pasture types, i.e.

6

= ) ' a r e a / x d i td

i = 1

[Note: Eqn (4) gives the rate of grazing p e r un i t area . By multiplyin~ both sides of eqn (4b) by area~ the equation might be easier to understand.]

The area of each pasture type, area~ (ha), is given in Table 2.

Decay

The rate of loss of pasture through decay is assumed to be proportional to the pasture with proportionality constant a3, i. The decay process is accelerated by a factor a4, i during floods. Hence:

Ia3,i × Pi flood off r3, i = ( 5 )

{ a3, i X Pi x a4, i flood on

The values of the parameters in the above equation are given in Table 2. Note that the Flats are not affected by floods so that a4, 6 = l'0.

Digestible pasture

The amount of digestible pasture per unit area will deteriorate with time. Further losses to digestible material occur with losses in pasture due to grazing and decay. Increases in digestible material occur at a rate directly proportional to the rate of production of pasture, r~.i. Thus, the rate of change of digestible, material, di, is given by the differential equation:

d d i / d t = - a s , i x d i - - ( r 2 , i + r3,i) x dl /pi + a6,i x r l , i (6)

where as,i ( t t - l yea r -~) is the specific deterioration rate of digestible material and a6, i ( t t - 1) is the proportion of newly produced pasture that is digestible. Both these sets of parameters are given in Table 2.

CATTLE

Condition Index

Some of the rates determining cattle numbers are influenced by the condition of the cattle. To a large extent condition of the cattle in the study region is determined by the quantity and quality of the pasture grazed. The


quantity that is grazed under 'normal' conditions, tgn, was calculated earlier. Of this amount it has been estimated that 0.34 (t t - 1) is digestible (Buchan, 1988b). The rate of grazing of digestible material under 'normal' (reference) conditions, tdgn, is therefore calculated by the equation:

tdgn = tgn x b 10

where bl0 = 0.34 (t t - x). The rate of grazing of digestible material in general, tdg, is given by the following calculation:

6

"= ~ ' r2, i X areai x di/pi tdg

i = 1

A comparison of the amount of digestible material consumed with that consumed under 'normal' conditions yields the condition factor, cf, which is an important variable in the determination of an index of cattle condition. Thus c f is defined as follows:

c f = tdg/tdgn (7)

Note that under the reference ('normal') conditions the condition factor is equal to one. A condition factor less than one or greater than one will indicate a tendency towards a decline or improvement in the condition of the cattle compared with their condition under reference conditions. However, there is some delay before changes in the condition factor have a noticeable impact on the cattle condition. Hence, the condition index, cx, is defined by the following first order differential equation:

dcx/d t = (c f - cx)/b l 1 (8)

where bl 1 -- 0.2 (year).

Division of cattle

Cattle are divided into three age groups and the two older groups are further divided by sex as shown in Table 3. Also given in Table 3 is the LSU equivalent for animals in each group. The total livestock units (see eqn 3),

TABLE 3 Division of Cattle

Group Calves Heifers Cows Steers Bulls~Oxen

Symbol cl cz c3 c4 c5 Age (years) 0-1 1-3 3 + 1-3 3 + LSU equivalent 0.2 0.5 1-0 0.6 1.2


Tlsu, is calculated by summing over all groups the product of the number of animals in each group, q, and the LSU equivalent.

The rate of change in the number of animals in each group is determined by the birth rate sl,~, maturat ion rate s2.~, mortali ty rate s3,~ and sales rate s4, i. All these rates have units in terms of animals per year. With this notation the cattle numbers are determined from the following differential equations:

dc l /d t = sl, 1 - s2,1 - $3,1 - - $4,1 (9a)

dc2/dt = sr x s2.1 - s2,2 - s3,2 - s4.2 (9b)

dc3/dt = s2, 2 - $3, 3 - - $4, 3 (9C)

d c J d t = (1 - sr) x s2.1 - s2. 4 - $3, 4 - - $4, 4 (9d)

dcs/dt = s2,4 - s3,5 - s4,s (9e)

where sr = 0"52 (dimensionless) is the sex ratio which reflects the fact that offtake of male calves is slightly higher than that for females. The rates on the right-hand side of eqns (9) are calculated below.

Births

The birth rate, s1,1, is given by the equation:

Sl,1 = C3 X b12 x fro (10)

where b12=0.37 (calves cow -1 year -1) is the average annual specific fecundity rate under reference conditions. Fluctuations in fecundity occur due to changes in the condition of the cattle and this effect is represented by the fecundity multiplier, fm , calculated below.

Changes in the conception rate will occur with changes in the condition index, cx. Thus a multiplier is defined as follows:

ml = f ( b l 3, b14, bl 5, cx) (11)

where f ( see Appendix) is an increasing function of cx with maximum and minimum values given by b13 = 1.67 and b14 = 0.01, respectively, and slope at (1,1) given by b15=0 .06 (Uys et aL, 1985). The multiplier ml (dimensionless) assumes values greater than or less than unity depending on whether cx is greater than or less than unity. It is only after some delay (gestation period) that a boost in conception results in an increase in births. The multiplier, ml , is therefore subject to a third order delay to yield the fecundity multiplier, fm . Thus:

dm2/dt = (ml - rn2)/bl6

dm3/d t = (m2 - m3)/b16 (12)

dfm/d t = (m3 - fm) /b l 6


where m2, m3 are mathematical artifices of no physical significance and b 16 = 0-15 (year).

Ageing

The rate at which animals mature into the next age class at any time is simply propor t ional to the number of animals in that age class. Thus:

s2,i = ci x ql,i i = 1,2,4 (13)

where ql,~ is given in Table 4.

Deaths

The mortal i ty rate is determined as follows:

s3,i = Ci X q2,i x f ( q 3 , i , q4,i, qs,i, c x - 1 ) i = 1 ,2 , . . . , 5 (14)

where the specific mortal i ty rate, q2,i ( h e a d h e a d - 1 Y ea r - l ) is given in Table 4. The funct ionf(def ined in the Appendix) causes the mortal i ty rate to change according to the condit ion of the cattle. The parameter values are given in Table 4 and are the same as those used by Uys et a! (1985).

Sales

The rate of sale of stock is calculated as follows:

S4,i = Ci × q6.i i = 1, 2 , . . . , 5 (15)

where the parameters, q6.i, were obtained from field data (Buchan, 1988b) and are presented in Table 4. Included in this rate are animals sold for slaughter.

TABLE 4 Cattle Parameters (see eqns (13)-(15))

i Calves Heifers Cows Steers Bulls~Oxen

ql .i 1"00 0"67 - - 0"67 - - q2,i 0' 122 0"073 0'098 0'073 0"098 q3,i 1"65 1"55 1"40 1'55 1"35 q4.i 0"2 0"4 0"5 0'4 0"8 qs,i 0'9 0'9 0'8 0"9 0'4 q6.i 0"0 0"04 0'02 0"08 0'06


REVENUE

It is recognised that pastoral systems should be managed in relation to their economic value rather than technical efficiency (Wilson et al., 1987). In assessing the economic value of a system many programmes have only taken into account marketable utilities (Ayuko, 1981; Tapson & Rose, 1984). However, non-marketed utilities generally have a high value relative to marketable utilities (Colvin, 1983) and failure to recognise this is a common cause of programme failure (Horowitz, 1979; Baker, 1980; Colvin, 1985; Halderman, 1985). Therefore in defining a performance index for this analysis it is important to include all the economic benefits available from the pastoral system. These were identified during a 3 year intensive study in the field and are discussed in depth by Buchan (1988a). The corresponding model equations are given below.

Milk

The number of lactating cows, Lc, at any time can be determined by solving the differential equation:

d L c / d t = sl. 1 - L c / L p (16)

where sl. 1 is the birth rate (see eqn (10)) and Lp is the lactation period (0"67 year). The condition factor, ef(see eqn (7), of the cows has an immediate impact on milk yields so that rate of income from milk, my, is given by the equation:

my = Lc × c f × my × mp × h f (17)

where my is the milk yield (1328.6 litres year- 1 per lactating cow) and mp is the milk price (1-40 Rand litre- 1). The price of milk is based on the cost that would be incurred by a herdsman should he not have his own source of milk available. The health factor, h f = 0-8, reflects the loss of milk due to health factors such as mastitis.

Draught

The draught value, dr, of the regional herd is calculated by the equation:

dr=c5 x c f x dy x @ x hsf (18)

where c 5 is the number of bulls and oxen in the regional herd, dy is the draught yield (200 days year-1) and dp is the draught price (1-25 Rand per head day-1). The last factor in eqn (18) is the herd size factor, hsf, which represents the fact that only a proportion of the total bulls and oxen can be


used for draught. This is partly due to some individuals owning too few cattle to span a team. It is estimated that hsf= 0.62 (Buchan et al., 1989).

Income from sales

The rate of income from sales is given by:

5

sv = ~ s4,i x spi (19)

i = 1

where spi is the sales price of an animal in age/sex class i as given in Table 5.

TABLE 5 SalesPr iceofCat t le in Rand(seeeqns(19),(20))

i Calves He~brs Cows Steers BuHs/Oxen

spi 172 300 325 238 376 mpi 169 228 258 167 274

Value of carcass meat

Some meat is recovered from animals that have died. The value to the owners of this meat can be calculated as follows (Buchan, 1988b):

5

cv= ) i s3'i x mpi (20) / . . . . , d

i = 1

where mpl is the value of a carcass in class i as given in Table 5.

Increase in livestock assets

Increases in the value of the regional herd represent a further return to the owners. Increases arise from increase in cattle numbers and from increases in the price of cattle. However, a gain in the value of livestock in real terms is only realised if price increases exceed the inflation rate.

The rate of change in the value of livestock assets is given by:

5

=) ' (dc i /d t ) x spi x (1 + ix)+ assets x ix (21) a v

i = 1

Influence o f resource management on African pastoral system 89

where the sales prices, spi, are given in Table 5, 'assets' is simply the sales value of the cattle and ix is an index representing the amount by which cattle prices increase in real terms. The nominal value of ix was chosen as zero.

Return

The revenue from all the sources discussed in the preceding sections are summed to give the rate of 'return' (Rand year-1):

return = my + dv + sv + cv + av (22)

The percentage rate of return on livestock assets can be calculated by the equation:

%return = 100 x return/assets (23)

IMPLEMENTATION OF THE MODEL

Computer program

The model as given above comprises a system of first order differential equations. Due to the discontinuities in some of the rate equations, to keep computer time and memory requirements low and for ease of programming a simple Euler method was used to solve the system. The program was written in TURBO Pascal 4.0 and implemented on a 640K PC.

Reference solution

Beginning at the start of a year with the stated variables set to the values given in Table 6 and with a 2-week flood commencing in the eleventh week of each

TABLE 6 Initial Values

Echinochloa Cynodon Fastigiatus Phragmites Fields Flats

Pasture 1"20 0'89 0.32 0"94 0-59 0-57 Digestible

material 0.75 0-30 0"09 0"37 0" 15 0.07

Calves Heifers Con's Steers Bulls/Oxen

4 378 2 840 14 72 ! 2 496 10 063

cx f m m2 m3 Lc

0'62 0'99 0"86 0"96 3 346


Fig. I.

5 5 -

5

_.-. 4.5

'o 4 - E

c 3.5- 0

IJJ n,. D 2.5- f- J 09

2 - i

i V / / I -

0.5- ~ - - Ech lnoch lo ( I -- Ftotl

0 , i i

Y E A R S

Reference simulation: Periodic behaviour of Echinochloa on the floodplain and pasture on the Makatini Flats.

year the system exhibits periodic behaviour. As an example the periodic behaviour of the Echinochloa and Flats pastures is shown in Fig. 1.

The nature of the data available did not make it possible to do a thorough model validation. However, the annual average rates of mortality, fecundity, matter grazed and digestible matter grazed were calculated from the reference solution and found to be within 12% of the available field data (Furness, 1981; Buchan, 1988b).

Of primary interest in managing the region is the value of the returns yielded by the pastoral system. The reference solution shows this to be fluctuating around 6.8 million Rand per year. This represents a return on livestock assets of nearly 66%.

TABLE 7 Most Sensitive Parameters

Percentage change in

returns

Parameter Equation Description q/parameter

0.76 al, 6

0"74 b4

0-69 bl0

0.67 am, 1

0.62 Lp

0.62 In)'

2b Maximum specific production rate on Flats

3 Amount grazed per year by one livestock unit under reference conditions

(~7 Fraction of pasture that is digestible under reference conditions

2b Maximum specific production rate ofechinochloa

16 Lactation period

17 Milk yield


A sensitivity analysis was performed to ascertain to what extent inaccuracies in the parameter values affect the returns. One at a time each of the 107 parameters were perturbed by 1% and another simulation performed. Table 7 presents details of each perturbation that causes the percentage change in returns to differ from the reference solution by more than 0-5%. While parameter inaccuracies will have some influence on the results that follow in the next section the conclusions presented in the discussion are not affected.

POLICY ANALYSIS

Details of the objectives were given in an earlier section. In broad terms the objective is to assess the economic consequences of reducing the land and water available to the pastoral system.

Loss of grazing on the floodplain

A simulation was performed where 60% of'Fields' was placed out of bounds to cattle. All other parameter and initial values remained unchanged from the reference simulation.

Under these conditions the system settles down after about 10 years with a fall in returns from the pastoral system of 5.6%. This represents a fall in returns of 238 Rand per hectare lost to grazing. The size of the regional herd is also affected with a drop in the sales value of the cattle of 6'2%.

Loss of grazing on the Makatini Flats

The area of the grazing land on the Makatini Flats was reduced by 1000 ha. After 12 years the system settles down with a fall in returns of 42 Rand for every hectare no longer available for grazing.

Reduction in flood releases

A simulation was performed in which flooding occurred in alternate years only. Initially there is a fall in returns of nearly 11%. Figure 2 shows that as the system starts settling down there is a 6% fall in returns during years that a flood is missed and a much smaller fall in other years. The figure also shows a drop of about 4% in the sales value of the regional herd.

It is conceivable that the loss of a flood during drought might have more serious consequences than the scenario above. The rainfall was reduced to 10% of the long term average during the second year of the simulation


0 -

- 2 - IJJ t) -3 " z bJ n- -4 " t,t h bt. --5" ¢3 . , -6"

I- -7- Z uJ 0 - 8 - n.. n -9 -

- I O -

- I I

AAA!,, A . , I ; i~ , I / !1 /~

!,, VV A I/ 'J

V / I I

' ' 7 2 3 5 6

- - - R e t u r n s

- - A s s e t s

i v i i i i i i , i i ,

8 9 tO I t 12 13 14 15 16 17 18 19 2 0

YEARS

Fig. 2. The percentage fall in the pastoral system's annual 'returns' and livestock 'assets' after the imposition of a policy to restrict flood releases to alternate years only.

period. Two simulations were then performed. Simulation 1 had normal annual floods but in simulation 2 the flood was omitted during the 'drought' in the second year.

The percentage difference between the returns from the simulations is shown in Fig. 3. In the year of the drought the fall in returns in simulation 2 is 11% greater than the fall in simulation 1 (normal flooding). However, three years after the drought there is not much difference between the

~ ~ .i II 0 Z _2 j~ /

-41 / - 4 ~ 11 //

-64i /'

- 8 4 I /

- 9 4 i / / / ;

::1 - - R e l u r n s

- - A s s e t s

i 1 i i i i ~ i i i

I 2 3 4 5 6 7 8 9 I 0 I I t 2 13 14 15

YEARS

Fig. 3. The effect of a flood during a short drought in the second year of the simulation period. Shown are the percentage differences in 'returns' and livestock 'assets' between a simulation with normal flooding and a simulation without a flood during the drought year.


returns. In fact there are periods after the drought where the returns in simulation 2 are slightly greater than those in simulation 1.

DISCUSSION

It is expected that commercial agriculture will attain yields of around 500 Rand per hectare per year from irrigated land on the Makatini Flats. This should more than compensate for the fall in returns from the pastoral sector indicated by the simulations to be about 40 Rand per hectare per year. However, the irrigation scheme might necessitate the usual late summer flood to be missed on occasions but even if this should happen every alternate year this should not have a dramatic impact on the returns yielded by the pastoral system.

It is estimated that maize grown on the floodplain by subsistence farmers is worth about 125 Rand per hectare (pers. com., E. Pollet). This amount does not fully compensate for the consequent fall in returns from the pastoral system indicated by the simulations. This suggests that more study of the circumstances of subsistence farmers should be made before some groups continue with their present efforts to encourage maize cultivation on the floodplain.

The mathematical model and associated computer package have been shown to yield insight into some of the issues relating to land and water use in the region. As the need arises it can be used to assist in the decision making process for a much wider range of issues than have been dealt with here. For example, the model could be used to explore different cattle off-take strategies or different times for the annual flood. Furthermore, floodplains form an important part of many traditional African pastoral systems and with minimal modifications it should be possible to apply the model to resource management problems in these regions.

ACKNOWLEDGEMENTS

Partial funding of this project by the Inland Water Ecosystems Division of the FRD, CSIR is acknowledged. Professor C. M. Breen of the Institute of Natural Resources, University of Natal, is thanked for his advice and help.

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APPENDIX

The functionf(A, B, g, x) is used a number of times in the model (see eqns (4) and (14)). It is defined as follows (Uys, 1985):

For A > 1, 0 < B < 1, 0 < g

and independent variable x,

f (A, B, G, x) = A/[1 + E. exp(-- C. x')]

where E = ( A / B ) - 1, C = In [E/(A - 1)] and r = gA/[(A - 1) C]

96 J. w. Hearne, A. J. C. Buchan

This function has the following properties:

(a) f (A , B, g,x) = 1. (b) f (A , B,g,x) tends to the value A as x increases, i .e . fhas a horizontal

asymptote value of A. (c) f (A , B, g, x) tends to the value B as x decreases to O, and provided r > 1

this represents a horizontal asymptote. (d) d f ( A , B , g , x ) / d x = g , i.e. the gradient of f a t x = 1 is g.

Documents

A model to analyse the influence of resource management policies on the economic returns from a traditional African pastoral system