Agroforestry: An economic appraisal of the benefits of intercropping trees with grassland in Lowland Britain

Agricultural Systems 21 (1986) 1-32

Agroforestry: An Economic Appraisal of the Benefits of Intercropping Trees with Grassland in Lowland Britain C. J. D o y l e , a J. E v a n s b & J. R o s s i t e r a "The Animal and Grassland Research Institute, Hurley, Berkshire SL6 5LR, Great Britain bThe Forestry Commission Research Station, Alice Holt Lodge, Wrecclesham, Surrey GUI0 4LH, Great Britain

S UMMA R Y A mathematical model simulating the effect ofintercropping trees (ash) with grassland on wood production, grass yields and output of sheepmeat is described. Using the model, an assessment has been made of the implications of varying the density and the planting pattern of the trees on the combined income from the sale of wood and livestock over a number of years. The resultant incomes have been compared with that from an equivalent unafforested area to assess the likely economic implications of intercropping trees with grass. At a discount rate of 5°//o, the indications are that combining wood and sheepmeat production on the same area could be financially attractive. At higher discount rates, the economic attraction of growing trees is more dependent on an increase in timber prices relative to those prevailing at present. However, given the large number of assumptions necessitated by the limited availability of data and in the absence of any means of validating the model, extreme care is needed in interpreting the results. Confident economic projections of the value of intercropping trees with grass await further experimental work on appropriate growth models for open-grown trees, light interception, tree rooting patterns and water uptake of tree roots.

INTRODUCTION The objective of the study is to assess the economic implications of combining grassland management with open plantations of trees on the 1

Agricultural Systems 0308-521X/86/$03.50 ~ Elsevier Applied Science Publishers Ltd, England, 1986. Printed in Great Britain.

2

c.J. Doyle, J. Evans, J. Rossiter

same area. To do this, the combined income from the sale of wood and livestock over a number of years is compared with the income from an equivalent unafforested area, using a simplified mathematical model. Within the model plant growth is described in terms of a limited number of key processes: light interception, photosynthesis, respiration, grazing, litterfall, assimilate partitioning, nutrient uptake and water use. Following McMurtrie & Wolf (1983b), competition is presumed to occur between the trees and grass for light, nutrients and water. Growth and economic assumptions have been made specifically for ash (Fraxinus excelsior) on a yield class 10 site, although cherry, sycamore and southern beech would have been equally suitable trees.

THE M O D E L The model may be divided conveniently into five submodels concerned with: (i) the ground area covered by the woodland canopy; (ii) competition for light; (iii) competition for water and nutrients: (iv) the dry matter production of grass and utilisable timber and (v) the estimation of the economic returns from forestry and livestock farming. Within the model, time (t) is divided into years. At any time the biomass of the trees can be described in terms of the dry weight of foliage, Lw(t ), of the fine roots, Rw(t) and of the stem, S~,(t). Following McMurtie & Wolf (1983b), the dry weight of the stem is equated with the weight of stem wood, branches, stump and large roots. Similarly, the grass biomass is divided into the dry weight of the roots, Rg(t), and the leaves, Lg(t). In each case the weights are expressed in kilograms per square metre. All symbols employed in the model are listed in the Appendix, while a schematic representation of the basic model is shown in Fig. 1. Spatial extent of woodland canopy

The area of ground shaded by the canopy of the trees is considered to be a function of the average size of the individual trees, the density of trees and the planting configuration. For an individual tree the area of ground covered by its canopy (CA, m 2) can be related to the diameter of its trunk (D, m) by a relationship of the following form (White, 1981): log CA(t) = log :~o + ~1 log D(t)

(1)

The economic benefits of intercropping trees with grassland

-- ~ . . . . . -..i

Nutrients,N -Wa te r. W . . . . . .

I," . . . . . . . . .

L I

Light, Io

I~

3

I

-Z~Partition of

!

"~ light

I

~

I

bygrass . g I

Oralsphotasnt,o s[ IIOross tas °t' s s by,rees. Pw r / respi ration by roots, shoots ~" & leaves

j

I[byg~.~ respiration by ~eaves & roots

/~ l

lNet photosynthesis by trees, Pnw J

"Nel ~hotosynthesis I by grass Png I

Partltlon of

'tree CA canopy ~

t"

JPartition oi:

.~ass ~ I {bioml I Rw

.

b'l~.gmass

.

1 i~/o0d p;o,ductic~n I

pt°ckingrate'STRl

Net financial returns, CNPV

I

Fig. 1. A schematic representation of the basic modal.

4

C . J . Doyle, J. Erans, J. Rossiter

where % and :t I are constants. In turn, a fairly constant relationship appears to exist between the trunk diameter and the above-ground biomass of the tree (B, kg dry matter (DM)). From observations by White (1981), the tbrm of the relationship is as follows: log D(t) = log ~2 + x3 log B(t)

(2)

where ~z and :~3 are constants. Combining eqns (1) and (2) gives: tog C A ( t ) = a o + a 1 log B(t)

(3)

where a o = log:% + s t log~ 2 and a t = ~t~3. Assuming that, at a given time after planting, all the trees are identical, the average above-ground biomass of each tree is simply given by: B(t) = [Lw(t) + Sw(t)]/dw

(4)

where L w and Sw, as previously defined, are the average dry weights of foliage and stem, in kilograms per square metre of ground and dw is the average density of the trees in plants per square metre of ground. Where the trees are distributed uniformly across the land area, the proportion of the ground covered by the woodland canopy (p) at any time (t) is given by: (5)

p ( t ) = d w C A (t)

where 0 < p ( t ) < 1. On the other hand, where the trees are planted in rows or blocks, with intervening areas of open grassland, the proportion of ground shaded by the trees will be less than that suggested by eqn (5) due to overlapping canopies. Let 6 represent the distance in metres between any tree and its neighbours. Assuming that the canopy of each tree can be represented by a circle of radius, p, in metres, then, for p greater than 0.56, the proportion of the tree's canopy overlapping with that of a neighbouring tree (l) can be shown to be: 2 0 -2 C O S - t ( d / 2 p )

/=

-

c~(p 2 -

7zp 2

6 2 / 4 ) 0.5

(6)

where p is less than 0-56, there is no overlap a n d / e q u a l s 0. Thus. for trees planted in rows at a constant distance (6) apart, the proportion of the ground area collectively shaded by their canopies becomes: p(t) = d w C A ( t ) ( 1 - / )

(7)

The economic benefits of intercropping trees with grassland

5

Competition for light The light transmission, T, through a discontinuous canopy may conveniently be regarded as comprising two discrete and additive components (Jackson & Palmer, 1979): T = Tb + L

(8)

where T b is the fraction of light that reaches the ground when the canopy is completely non-transmitting and Tc is the fraction of the light that has passed through the canopy (see Fig. 2). The proportion Tc will have a maximum value of 1 - T b if the canopy is transparent and, in general, T~ is given by: T~ = (1 - Tb) x attenuation by the canopy

(9)

The degree of light attenuation by the canopy will depend on its leaf area. If LA I(t) is the leaf area index of the canopy----defined as the leaf area per unit of total ground a r e a - - t h e n the effective leaf area index, L A I ' ( t ) , is given by: L A I ' ( t ) = L A I ( t ) / ( 1 - T b)

(10)

In turn, LA I is assumed to be a function of the foliage dry weight of the trees (Lw, kilograms of dry matter per square metre), so: (11)

L A I( t) = s w L w ( t )

where sw is the specific leaf area in square metres per kilogram of dry

q

.

"*--Tc

,1

~,

1-Tb--.-,~-rb~

"

Fig. 2. Light transmission through a discontinuous canopy of trees, illustrated for vertical radiation Io. Per unit area, a fraction, Tb,reaches the gound without traversingthe canopy of the trees. The remaining fraction, 1- Tb, passes through the canopy, where it is attenuated and.;of this, T~reaches the ground. (Adapted from France & Thornley, 1984.)

6

C.J. Doyle, J. Evans. J. Rossiter

weight of foliage. Assuming that the relationship between light penetration and leaf area is described by Beer's Law (Monsi & Saeki, 1953), the attenuation by the canopy is given by: exp [ - k w L A I ' ( t ) ]

(12)

where kw is the light extinction coetficient. Accordingly, combining eqns (8) to (12) gives: T = Tb + (1 - Tb) exp [-- kwswLw(t)/(l - Tb)]

(13)

Assuming that light is falling vertically on the tree canopy, the proportion 1 Tb may be equated with the proportion of the ground area shaded by the trees, p(t). Hence, eqn (13) may be rewritten as: T = [1 - p ( t ) ] +p(t) exp [-kwswLw(t)/p(t) ]

(14)

Let Io(t ) represent the average daily light received by a horizontal plane above the tree canopy in J m -2 d a y - t of photosynthetically active radiation, then the light intercepted by the trees (lw,J m - 2 day- ~) is given by: Iw(t ) = (1 - T)Io(t ) (15) The incident radiation received by the grass is then TIo(t). While the radiation received by the grass is not uniformly distributed, with lower light levels immediately under the canopy of the trees, it is considered that, in lowland Britain, with diffuse radiation accounting for a significant proportion of all radiation received by the grass, the errors involved in assuming uniform light levels at the top of the grass canopy are small. Assuming that the proportion of incident radiation penetrating the grass canopy obeys Beer's Law, then the light intercepted by the grass canopy (I s, J m - 2 d a y -1) is given by:

Is(t ) = [1 - exp(-k~ssLs(t)]Tlo(t)

(16)

Where ks, s s and L s are, respectively, the light extinction coefficient, the specific leaf area and the leaf dry weight of the grass. Given the amount of light intercepted by the trees and the grass, following Thornley (1976) the average daily gross photosynthetic rate of the trees (Pw) and of the grass (Ps), measured in kilograms of CO 2 per square metre per day, are assumed to be approximated by:

Pw(t) = [bwIw(t)PMAXw]/[bwIw(t) + PMAXw] Ps(t) = [bjs(t)PMA.J(s]/[bsls(t) + PAtA Xs]

(17) (18)

The economic benefits of intercropping trees with grassland

7

where bw and bg are constants, expressed in kg CO_, J- ~. and P M A X w and PMAXg (kilograms of CO 2 per square metre per day) are the respective maximum daily rates of gross photosynthesis for the trees and the grass at saturating light levels (I o ~ ~:~). In turn, the maximum daily rates of gross photosynthesis are assumed to be a function of the leaf area index of the crop (France & Thornley, 1984). Thus: P M A X w =a z + a3(swLw(t)/p) P M A X 9 = a,~ + as(soLo(t))

(19) (20)

The effect of increasing the proportion of the grounded area shaded by the trees, p(t), for a woodland with a given foliage dry weight, Lw(t), is to decrease the average daily gross photosynthetic rate of the trees. This can be shown by substituting eqn (14) into eqn (15) and differentiating I w with respect to p, giving: dI w = dp[1 - (1 + kwswLw/p) exp( - l%.swLw/p)]lo

(21)

The term ( l + k w s w L w @ ) e x p ( - k w s w L w / p ) is always less than 1. Accordingly, a decrease in p will produce a decrease in the amount of light intercepted by the trees for a given foliage dry weight. From eqn (17) this will result in a decrease in Pw. Thus, where the canopy of individual trees overlaps, competition for light between the trees will decrease the rate of photosynthesis and, in turn, the rate of biomass production compared with an identical group of trees in which canopies do not overlap. Competition for nutrients and water

Following McMurtrie & Wolf (1983b), competition tbr water and nutrients is considered to affect the rate of gross photosynthesis, either by reducing photosynthetic efficiency or reducing the length of the growing period. Relative to the situation where water and nutrients are nonlimiting, let fw and fg represent the proportionate rates of gross photosynthesis by the trees and grass, respectively. Thus, eqns (17) and (18) may be re-written as: Pw(t) =Jw[bwlw(t)PmAXw]/[bwiw(t) + PMAXw] Pg(t) =fo[bjo(t)PMAX~l/[bjo(t) + PMAXg]

(22) (23)

Where the availability of water and nutrients are such that there is no competition between the grass and the trees, the fw =fg = 1.

8

C . J . Doyle, J. Evans, J. Rossiter

Let Ww(t) and Wg(t) represent the average daily quantities of water available to the trees and the grass, respectively, in cubic metres per square metre of ground per day. Similarly, assuming that phosphate and potash are adequate, nitrogen is the principal nutrient limiting growth. Let Nw(t) and Ng(t) denote the corresponding quantities of nitrogen available in kilograms per square metre of ground per day. The dependence offw andJ~ upon water and nitrogen is then presumed to be as follows: Jw = I. [K,/Nw(t) + K,~./Ww(t) + K,~/Nw(t)Ww(t)] fo =

+ K' /W tt) + K;w/G(t)W

(O]

(24)

(25)

where K,, Kw, K,~.. K;, K'w and K,~ware constants. Where nitrogen and water are present in saturation quantities f w and fg tend to unity. There are several possible justifications for eqns (24) and (25), although none is rigorous. First, fertiliser responses of this type have been widely observed (Greenwood et al.. 1974). Secondly, Thornley (1976) has shown that twosubstrate biochemical reactions can be represented by equations of this form. In respect of the trees, the quantities of water and nitrogen per square metre of ground at which growth is not limited will be expected to vary with both the density and the size of the trees. Accordingly, the parameters K,, K,,. and K,w in eqn (24) are considered to be linear functions of the above-ground biomass of trees per square metre, so that: K, = G{Sw(t) + Lw(t)]

(26)

K w = Kw{Sw(t) + Lw(t)]

(27)

K.w = Ko.[Swtt) +

G-(t)]

(28)

where Sw(t) and Lw(t) are, respectively, the dry weights of tree stem and foliage in year t and G, ~, and Gw are constants. The actual availability of water and nitrogen to the trees and the grass is presumed to depend on their relative root masses and the distribution of the roots within the soil in relation to the water and nitrogen. The soil, or rooting zone, of depth s (m) is arbitrarily presumed to be divided into six equal layers. Within the rooting zone water is presumed to be uniformly distributed. Thus. let W (cubic metres per square metre of ground per day) equal the average daily quantity of water available in the entire

The economic benefits of intercropping trees with grassland

9

rooting zone. Then the proportion of this water to be found in layerj (q~) is: rt~ = 0-167

(29)

Nitrogen, on the other hand, is assumed to be concentrated in the upper layers. Accordingly, let N(kilograms per square metre of ground per day) equal the average daily quantity of nitrogen available in the soil, then the proportion of this nitrogen to be found in layer j (/~j) is presumed to be described by the following relationship: /at = (2 ~-J)/2

(30)

where j = 1 for the top soil layer and j = 6 for the bottom layer. Given the availability of water and nitrogen in each layer, the proportions available to the trees and and the grass are presumed to depend on the relative root masses in each layer. Thus, let 0r and ~bjdenote the proportion of the tree and grass root masses in layer j, then the average daily quantities of water and nitrogen available to the trees and grass are given by: j=6

Ww(t) =

{ewOjRw(t)/[ewOjRw(t ) + 0jRg(t)] ~,.qjW(t)

(3 l)

{4~Ro(t)/[ewOjRw(t) + q~Ro(t)] }r/jW(t)

(32)

{ewOjRw(t)/[ewOjRw(t ) + c~iRg(t)]}l~jN(t )

(33)

{(pjRg(t)/[ewOjR,~(t ) + q~jRg(t)] }/~jN(t)

(34)

j=l j=6

W~(t)

=

j=t j=6

Nw(t) = j=l j=6

j=l

where Rs(t) and Rw(t) are the respective root masses of the grass and trees in kilograms of dry matter per square metre of ground and ew is the relative efficiency with which tree roots take up water compared with grass roots. The inclusion of the term ew allows for the fact that, for a given root mass, trees may take up less water than grass.

C. J. Doyle, J. Evans, J. Rossiter

l0

The distribution of grass roots, ~j, between each layer is presumed to be described by the vector ~, following Garwood (1965) =

. . . . .

= [0"80, 0-15, 0"05, 0, 0, 0]

(35)

In contrast, the distribution of tree roots is presumed to alter with the age (t) of the trees. In the establishment year (t = 0), all tree roots are presumed to be in the top layer. In subsequent years the proportion of tree roots in layerj is presumed to be described by the following relationship:

Oj(t) = ( I - h ) O ~ ( t - 1) +hO~_l(t- 1)

j = 2 to 6

(36)

where h is a constant which determines how rapidly the distribution of the root mass changes with time. The effect ofeqn (36) is to increase, with the age of the trees, the proportion of the tree root mass in the lower soil layers. The average daily quantity of water available, W, is presumed to be a function of the summer (April-September) rainfall (SR, cubic metres per square metre of ground) and the soil's available water capacity (A WC, cubic metres per square metre of ground). For a presumed growing season of 180 days W is given by:

W(t) = [SR(t) + A WC(t)]/180

(37)

However, to allow for the fact that about 20 ~ of the water falling on the canopy of the trees between April and September will be intercepted and lost through evaporation before it reaches the ground, eqn (37~ must be re-written as:

W(t) = [1 - 0.2p(t)][SR(t) + A WC(t)], 180

(38)

where p(t) is the proportion of the ground area covered by the canopy of the trees. Finally, the nitrogen available to the trees and grass, N, is presumed to consist of soil nitrogen (SN, kilograms per square metre of ground per year), fertiliser nitrogen (FN, kilograms per square metre of ground per year) and nitrogen released from decaying leaf litter (RN, kilograms per square metre of ground per year). Assuming that the N content of leaf litter is 2 ° o, then. for a 180-day growing season. Nis given by:

Nit) = [SN(t) + FN(t) + O.02Lw(t - 1)]/180

(39)

where L w ( t - l) is the foliage dry weight of the trees in the preceding year.

The economic benefits of intercropping trees with grassland

11

Dry matter production The model treats growth as a process which occurs when the available photosynthate is surplus to requirements for tissue maintenance and respiration (McMurtrie & Wolf, 1983b). Given the lbliage dry weight of the trees (Lw, kilograms of dry matter per square metre of ground), the average rate of photosynthesis by the trees, net of respiration ( P n w , kilograms of CO, per square metre per day) is given by: Pnw(t) = Pw(t) - rLLw(t)

(40)

where r L is the rate of leaf dark respiration in kilograms of CO,, per foliage dry weight per day. The products of photosynthesis are then partitioned between the foliage, stem and roots of the trees in the proportions A L, As and AR, respectively, where A L + A s + AR = 1. The rate of tissue production in each biomass component is then considered to be proportional to the difference between the amount of photosynthate available for its growth and that lost through respiration, senescence, etc. Let the maintenance requirements of the trees" roots (M R, kilograms of CO_, per kilogram of dry weight per day) and the stem (M s, kilograms of CO, per kilogram of dry weight per day) be proportional to their respective dry weights, R w and S w (kilograms of dry matter per square metre of ground), then: LI~IR(t) = r R R w ( t ) (41) Ms(t ) = rsSw(t)

(42)

where r R and r s are the respiration rates of the roots and the stem in kilograms of CO 2 per kilogram of dry weight per day. Let the rates of loss of leaf, trunk and fine roots through litterfall, senescence, etc., be denoted by F t, F s and F R (expressed per unit of standing dry weight), then the annual growths of leaf, stem and fine root over a 180-day growing season in kilograms of dry matter per square metre of ground per year are given by: d L w (t) = 1 8 0 Y A L P n w ( t ) dt

FLLw(t)

d Ww d----t- (t) = 1 8 0 Y ( A s P n w ( t ) - M s ( t ) ) - F~Sw(t)

dRy, dt

(t) = 1 8 0 Y ( A R P n w ( t ) - M R ( t ) ) -- [-RRw(t)

(43) 144) (45)

12

C. J. Doy&, J. Evans, J. Rossiter

where Y is a conversion efficiency parameter (dry matter production per unit CO.,). In reality, the partitioning of the products of photosynthesis between leaf, stem and root is likely to vary with time in the case of trees. Thus, At, A s and A R are time-dependent. In general, with time, a decreasing proportion of photosynthate will be partitioned to root and leaf. Accordingly, the partition coefficients are presumed to be described by the following relationships: At. - Aot.( 1 - qL t)

(46)

A R = AoR(1 -- qRt)

(47)

A s-- 1 - A L - A R

(48)

where Aor and AoR are the proportions of photosynthate partitioned to leaves and roots the establishment year (t = 0) and qt and qR are constants which determine the rate of decrease of A L and A R with time. In a similar fashion it is possible to derive the average rate of photosynthesis by the grass, net of respiration (Png, kilograms o f C O 2 per square metre per day), the maintenance requirements of the grass roots (M~, kilograms of CO., per kilogram of dry weight per day) and the annual growth of leaf (dL~/dt, kilograms of dry matter per square metre of ground per year) and roots (dR~/dt, kilograms of dry matter per square metre of ground per year) as follows:

Png(t) = Py(t) - r'Lio(t )

(49)

M'R(t ) = r'RRg(t )

(50)

dLy(t) _ 180V).LPng(t ) _ 7LLo (t) dt

(51)

dR0(t) dt = 180y().RPn~(t)- M ~ ( t ) ) - TaRg(t)

(52)

L~(t) and R~(t) are, respectively, the dry weights of the grass leaf and roots (kilograms of dry matter per square metre of ground), r;. and r~ are the respective respiration rates for the leaves and roots, ;.t- and ';-R are the coefficients determining the partitioning of photosynthate to leaves and roots (;'L + f"R = 1), 7L and 7R are rates of leaf and root loss through litterfall and senescence and 1' is a conversion efficiency parameter (dry matter production per unit CO2). In contrast to the trees, the products of

The economic benefits of intercropping trees with grassland

13

photosynthesis are assumed to be partitioned in fixed proportions, so that )-L and ~-R are taken to be constant from year to year. Economic returns

Let Cw(t) represent the costs incurred in establishing and maintaining the open plantation in year t in £ per tree and Vw(n) represent the value of the timber at felling in year n in £ (per kilogram of dry matter) of saleable timber. Assuming that the density of planting is d w (trees per square metre of ground) and the crop rotation is n years, then, at a discount rate, ~, the net present value of the returns from the timber ( N P V w, £ per square metre of ground) is given by: i=tl

N P V w = Vw(n)UwSw(n)

(1 +

V

Cw(i)

(s3)

i=0

where u w is the proportion of the stem dry weight (Sw), which includes branches and the large roots, which is utilisable. However, eqn /53) ignores the fact that the value of the timber extracted (Vw) is likely to be related to the diameter of the trunk (D, m) at felling. From eqns (2) and (3) the average diameter of the trees can be related to the leaf (Lw) and stem (Sw) dry weights in kilograms of dry matter per square metre of ground, namely: log D(n) = log 3~2 -'~ ~3 log {[Lw(n) + Sw(n)]/dw}

(54)

Assuming that the value of the timber for trees sold standing increases linearly with the diameter, Vw becomes: Vw(n ) = z o + zlD(n)

(55)

where z o and z~ are constants. In reality, the relationship between vw and D is likely to be more complex. However, because of the limited available information on the price-size curves for ash, this simplification has been adopted. The economic output from grassland is presumed to be a function of the potential stocking rate (STR, animals per square metre of ground). Let I T K (kilograms of dry matter per head per year) equal the average annual grass intake requirements per animal, then, given the annual

14

C. J. Doyle, J. Et'ans, J. Rossiter

herbage production (dLg/dt, kilograms of dr.', matter per square metre of ground per year), STR is given by:

STR(t) - dLe(t) /:ITK(t) dt

(56)

Let vg represent the net returns after costs in £ per head, then the net present value of the returns from grazing the land (NPVg, £ per square metre of ground) over a period of n years is given by: i=n

NPV~

=y L.._a

vgSTR(i) (1 + ~z)~

(57)

i=0

where rc is the discount rate--for a discussion of discounting see Ritson (1978, pp. 206-8 and 286-92) and Nix (1984, pp. 126-9). Specifically, % is equated with the "gross margin' less "fixed costs other than rent'--see Ministry of Agriculture, Fisheries and Food (1978) for a definition of these terms. The combined net present value of returns from forestry and farming (CNPV, £ (per square metre of ground)) is then:

CNPV = NPV w + NPVy

(58)

PARAMETER VALUES AND INITIAL CONDITIONS Solution of the equations requires specification of five initial values, L~, Rg, L~, and S w, at time t = 0 and values for 45 parameters. A survey of the literature, including Bunce (1968), Garwood (1965), Kramer (1969), Woledge (1971), Jobling & Pearce (1977), de Wit et al. (1978), Mohler et al. (1978), Charles-Edwards (1981), Johnson & Thornley (1983), McMurtrie & Wolf (1983a, b) and France & Thornley (1984), yielded estimates of some parameter values. The remaining parameter values were then derived by fitting the output from the model to a set of experimental observations. In the case of grass, the data used for fitting the parameters were taken from Corrall et al. (1982). This study gives the annual dr,,, matter production of a perennial ryegrass sward at sites with different rainfall and soil conditions and receiving differing rates of fertiliser nitrogen. For estimating those parameters controlling tree growth, data were taken from unpublished surveys of ash planted at low densities. At these

The economic benefits o f intercropping trees with grassland

15

densities the growth rate of individual trees was assumed not to be constrained by competition between the trees. The resultant parameter values are shown in Table 1. Two possible management strategies for the woodland have been considered:first, the trees are felled when the diameter (D) of the trunk at breast-height (1.3 m above ground) reaches 15 cm, and sold for firewood; secondly, felling is delayed until the trees reach a trunk diameter of 45 cm

TABLE

1

Initial Conditions and Parameter Values State variables at t = 0 Lo = 0.15 k g m - - ' L w = 0.000 125 k g m - - ' R~ = 0.67 kg m - -' R w = 0.000 250 kg m - z S w = 0-000 125 kg m - : Parameters

a o = 1-250 a~ =0-528 a., =0-025 a 3 = 0"025 a~ = 0'025 a 5 =0'025 b~ = 8 . 0 0 x 10 -9 kilograms of C O , per joule b w = 5.50 x 10 -9 kilograms of C O , per joule dw = 0"005 trees per square m e t r e ew = 0.1 h =0.05 K,, = 0-000 15 K,. = 0.75 K,~. = 0-000 15 k~ = 0 . 6 kw =0"6 qL = 0"01

qr =0"0125 r a = 0'0028 kilograms of C O , per kilogram dry matter per clay r~_ = O.Ol kilograms o f C O z per kilogram dry matter per day

r R = 0-005 6 kilograms o f CO_, per kilogram dry matter per day r~ = 0.01 kilograms of CO_, per kilogram dry matter per day r s = 0.001 kilograms of C O 2 per kilogram dry matter per day s~ = 35 square metres per kilogram of leaf dry matter sw = 35 square metres per kilogram o f leaf dry matter u w = 0.70 v = 0.72 kilograms of dry matter per kilogram of C O , F = 0-72 kilograms o f dry matter per kilogram of C O , F t = 0"33 F R = 0"45 F s = 0"01 "& = 1"0

7r 6 ~'. ~.

= 0.5 = 14.14m = 0'0 = 0065 G,,. = 0"0 AOL =0-25 :\or = 0"50 ;-L = 0-5 ;-r = 0-5 n =0.05

16

C. J. Doyle, J. Evans, J. Rossiter TABLE 2

Costs, Values and Animal Grass Requirements for Two Different Agro-forestry Strategies Felling diameter (cm) Timber value (£ per kilogram dry matter) Livestock net returns (£ per head) Costs (£ per tree) Establishment (year 0} Tree protection (year 0) Pruning (year 10) Weeding tyears l-5) Annual grass requirements for sheep (kilograms of dry matter per ewe)a

15 0"015 18

45 0"100 18

10

1'0

1.5 0-0 0.2

1.5 0.5 0.2

450

450

Assuming a grass utilisation efficiencyof 75 °o. when they are then felled for timber. These management strategies may not be optimal from the economic viewpoint, but, in the absence of sufficient information on the price-size curves for ash, it has not been possible to determine those rotations which would maximise discounted revenues. In each case the tree crop is presumed to be combined with sheep grazing. The corresponding costs (Cw), values (v w and t') and animal grass requirements ( I T K ) are summarized in Table 2. For the two management strategies, the effects of varying the density of trees, the rate of fertiliser nitrogen and the soil and rainfall conditions have been investigated. F o u r planting densities of 0, 50, 100 and 200 stems per hectare (dw = 0 , 0.005, 0.01 and 0.02 trees per square metre, respectively), three fertiliser nitrogen levels (FN) of 0, 150 and 300 kg N h a - ~ y e a r - ~ and two sites have been evaluated. At the first site the average summer rainfall (SR) is assumed to be 440 mm and the soil available water capacity (A WC) is fixed at 100ram. The corresponding figures at the second site are 270 mm and 60 ram. In both instances, the mean daily radiation level (1 o) is presumed to be 7 M J , which is reasonably typical of light levels in southern England (France & Thornley, 1984). RESULTS S i m u l a t e d g r o w t h o f trees and grass

The projected trunk diameter and the volume of saleable timber per hectare for trees of a given age are shown in Fig. 3. The results are

The economic benefits of intercropping trees with grassland

]

50 i

(a)

L

40 )

.

,,

17

,"',""

Trunk diameter at breast- height tom)

10 20 30 Age of tree (yearsl

500

40

50

(bl

400

300

.."" ..." zJ ..." /

Volume of saleable timbe( m-3 ha'l~ 200

." ..."

10

20

30

/ ,,

40

50

Age of trees(years)

Fig. 3. Projected relationships between age of tree and (a) trunk diameter and (b) volume of saleable timber per hectare for planting densities of 50 ( ), 1 0 0 ( - - - ) and 200 ( . . . . . ) stems per hectare.

presented for three different planting densities. In each case the trees are presumed to be planted in a regular matrix or chequer-board pattern, while the grass is assumed to receive no fertiliser nitrogen. Rainfall and soil conditions are taken to be favourable to growth, with a mean summer rainfall of 440 mm year- ~ and a soil A WC of 100 ram. It is evident from Fig. 3(a) that at planting densities of 50 and 100 stems per hectare the trees will attain trunk diameters of 25 cm and 45 cm at 19 and 36 years of age, respectively. These projections accord reasonably

18

C. J. Doyle, J. Et'ans, J. Rossiter

well with the estimated diameter-age relationships derived from unpublished surveys of open-grown ash. At a density of 200 stems per hectare, compared with 50 stems per hectare, tree growth rates are projected to decline from about age 30, so that a trunk diameter of 45 cm is only reached at age 45. This may not be unreasonable, since some competition between the trees themselves for water, nutrients and light in the later years of the rotation might be expected at higher planting densities. Even so, the projected annual growth rate of the trees at a density of 200 stems per hectare is higher than that attained by ash grown at conventional plantation densities (Forestry Commission, 1980). The simulated volumes of saleable timber per hectare at different tree ages are shown in Fig. 3(b). To estimate these figures the shoot dry weight (S,.) was converted to a volume by assuming a density for ash wood of 0.68 g cm 3 (Bunce. 1968; Weast & Astle, 1980). Since S~ comprises not only the trunk but also the branches, stump and large roots, it is presumed that only 70 °/o of the shoot dry weight is saleable. At a planting density of 50 stems per hectare the harvestable yields are projected to be 24 and 90 m 3 ha-~ at 20 and 36 years after planting, respectively. Again, these projections accord reasonably well with estimates of harvestable yield prepared from surveys of open-grown ash. Doubling the planting density to 100 stems per hectare is calculated to double the harvestable yield for trees of a given age. However, arising from the projected slower annual growth rate, at a density of 200 stems per hectare the yield of saleable timber is only about half as much again by the time the trees have reached 36 years of age. The effect of the trees on annual grass production over time is depicted in Fig. 4. At 150 kg ha - ~ year - t of fertiliser nitrogen, net annual herbage production is projected to be 7 tonnes of dry matter per hectare in the absence of trees. This grass yield figure is consistent with those estimated by Corrall et al. (1982) for a site with a mean summer rainfall in excess of 400 ram. At a planting density of 50 stems per hectare, annual grass production is projected to decline to 5.4 tonnes of dry matter 36 years after planting. At a density of 100 stems per hectare, the decline in annual grass production is appreciably increased, so that it has declined to 5.4 tonnes of dry matter per hectare by year 19 and by the date of felling (t = 36) grass production has virtually ceased. Finally, at a planting density of 200 stems per hectare the projection is that grass production will be negligible by year 19. Comparison of the projected decline in grass production over time with the predicted effect from trials conducted in

The economic benefits of intercropping trees with grassland

Annual grass oroduction f t D M ha'%

19

\

\

\ .

,\

x\

\ 10

20

30

~,O

Age oF trees(years}

Fig. 4. Changes in the annual dry matter yield of grass per hectare over time at planting densities of 50 ( ), 100 ( - - - ) and 200 ( . . . . . ) stems per hectare. Grassland receiving 150 kg h a - t year- ~ of fertiliser nitrogen.

New Zealand with Pinus radiata (Percival & Knowles. 1983) indicated reasonable agreement. In particular, Percival and Knowles projected that doubling the planting density from 100 to 200 stems per hectare would virtually double the rate of decline in annual grass production. Effect of planting density on economic returns Since simulated growth of the trees and the grass conforms reasonably to observations, the model may be used to determine the likely economic returns from combining sheep rearing with forestry on the same land. Accordingly, for three tree planting densities and three levels of fertiliser nitrogen, the net present value (CNPV) of the returns from forestry and farming per hectare are compared with the equivalent returns from the land where it is solely devoted to sheep rearing. In all cases the mean summer rainfall and soil A WC are presumed to be 400 mm and 100 mm per year, respectively. Independent of the level of fertiliser nitrogen applied the trees are projected to attain a trunk diameter of 45 cm 36 years after planting, at densities of 50 and 100 stems per hectare. The corresponding age at 200 stems per hectare is 45 years. Since economic comparisons are only valid where the time period under consideration is identical, the economic benefits must be evaluated over a constant number of years. Accordingly, the economic evaluations have been conducted over a fixed time period: namely 45 years. Where the trees are projected to be cut before this time, it is assumed that the entire area reverts to sheep production. Thus, at 50 stems per hectare the economic benefits are evaluated for 36 years of

20

C. J. Doyle, J. Evans, J. Rossiter

combined forestry and farming, followed by 9 years of livestock rearing. This procedure will bias the results to the extent that, for the few years during which the land is solely devoted to livestock, sheep rearing is more or less profitable than a combination of livestock and trees. Assuming a discount rate of 5 °~0 ( r: = 0.05), the net present values for each of the forestry options are shown in Table 3. These figures are compared with the situation where the grassland is entirely given over to sheep rearing; namely, at a planting density of 0 stems per hectare. It is apparent from Table 3 that where the grassland receives little or no TABLE 3

Net Present Value (£ ha-~) of Combining Forestry with Sheepmeat Production at Different Tree Planting Densities and Different Levels of Fertiliser Nitrogen (Results presented for the case where trees are felled at a trunk diameter of 45cm, at a site with a mean summer rainfall of 440 mm year- t and a soil ,4 WC of 100mm. Discount rate (~) of 5 "o employed.) Planting density (stems per hectare)

0 50 100 200

Fertiliser ,V usage (kg ha- t year -1) on grass O

150

300

I 493 2238 3051 2 980

5 226 5 775 5974 4 752

8 585 8 515 8314 6 182

fertiliser nitrogen, a combination of forestry plus sheep rearing is likely to be economically more b e n e f i c i a l than sheep rearing alone. It would also appear that the highest economic benefits are attained at a planting density of 100 stems per hectare. The same holds true at a fertiliser N rate of 150 kg per hectare, although the comparative benefits are smaller. However, at high levels of fertiliser application (300 kilograms of N per hectare), the highest net present value is realised where the land is solely devoted to sheepmeat production. Where the trees are felled for firewood, rather than timber, at a trunk diameter of 15 cm, Table 4 shows the comparative net present values for the three planting densities and three fertiliser levels considered in Table 3. In each case tree felling is projected to occur in year 10, which is 2-3 years earlier than is actually observed. It is apparent from Table 4 that, without exception, d e v o t i n g the land solely to sheep production is likely

The economic benefits of intercropping trees with grassland

21

TABLE 4 Net Present Value (£ ha-~) of Combining Forestry with Sheepmeat Production at Different Tree Planting Densities and Different Levels of Fertiliser Nitrogen (Results presented for the case where trees are felled at a trunk diameter of 15 cm, at a site with a mean summer rainfall of 440ram year -1 and a soil AWC of 100mm. Discount rate (r0 of 5 % employed.) Planting density (stems per hectare)

0 50 100 200

Fertiliser N usage (kg ha- I )'ear- t) on grass 0

150

300

649 373 312 95

2270 2039 1 874 1469

3 730 3368 3 139 2616

to offer better economic returns than a combination of forestry with farming. Effect of growing conditions on economic returns

It is interesting to speculate how changes in soil and rainfall conditions may affect the growth rate of the trees and, in turn, the relative economics of combining forestry with farming. At a site with a mean summer rainfall of 270 mm per year and a soil A W C of 60 mm it is projected that, at tree planting densities of 50 and 100 stems per hectare, there is no appreciable increase in the age at which trees attain a trunk diameter of 45 cm, relative to the previously considered site with higher summer rainfalll and soil A WC. On the other hand, at 200 stems per hectare the age at which trees attain a trunk diameter of 45 cm is increased from 45 to 48 years as a result of less favourable moisture conditions. However, as far as the management options considered in Table 3 are concerned, the comparative net present values are unaltered, although, due to lower annual grass production, the general absolute level of discounted returns is reduced by £1000 to £2000 per hectare. Likewise, for strategies involving the felling of the trees for firewood at a trunk diameter of 15 cm, the general observations based on Table 4 still apply. Effect of planting configuration on economic returns

So far attention has been confined to the situation where the trees are planted in a regular matrix. An alternative would be to plant the trees in

C. J. Doyle. J. Erans. J. Rossiter

22

rows with a closer spacing of 4 m between trees. One of the benefits of this would be less shading of the grass and, consequently, a less rapid decline in annual grass production over time. At a planting density of 100 stems per hectare, annual grass production on a sward receiving 250 kg of N per hectare per year is projected to have declined by nearly 50 °/o over the 20 years subsequent to tree planting, where the trees are planted in a regular matrix. Where the same density of trees are planted in widely spaced rows, annual grass production 50 years later is still 80 ° o of that at planting. However, the price is a slower growth rate of the trees. Whereas, at densities of 50 and 100 stems per hectare, trees attain a trunk diameter of 45cm after 36 ,,ears when planted in a regular matrix, they are not projected to attain an equivalent size until 54 years when planted in tight rows. At 200 stems per hectare, the effect of planting trees in tight rows instead of in a chequer-board pattern is to increase the corresponding age for felling from 45 to 60 years. The comparative net present values of the returns for the two planting configurations at three different planting densities are shown in Table 5. In each case, the fertiliser nitrogen, mean summer rainfall and soil A WC are presumed to be 150 kilograms of N per hectare per year. 440mm and 100 mm per year, respectively. As previously, to facilitate comparison the economic evaluations have been conducted over a fixed time period of 60 years, the choice of the time period being determined by the planting regime with the longest rotation. It would appear from Table 5 that there is unlikely to be any long-term economic benefit from planting trees in rows as against in a chequer-board pattern. TABLE 5 Net Present Value (£ h a - 1 ) of Planting Trees in Rows a n d in a Regular Matrix at Different Planting Densities (Results presented for the case where trees are felled at t r u n k diameter of 45 cm, at a site with a mean s u m m e r rainfall of 440 m m ,,ear- ' and a soil .4WC of 100ram. Fertiliser nitrogen applied at rate of 150kg N h a - ~ and a discount rate of 5°o is assumed.)

Planting density Istems per hectare) 50 100 200

Planting configuration Regular matrix

Rows

6117 63[6 4914

5617 5711 4844

The economic benefits of intercropping trees with grassland

23

Sensitivit)' to initial conditions and parameters The sensitivity of the results to changes in the parameter values needs to be investigated. Obviously, it is impractical to evaluate the effect on output of changes in all 45 parameters. Instead, attention has been confined to two key parameters which might be expected to influence the ability of trees to compete for light and water: namely, the light extinction coefficient of the tree canopy, k w, and the relative efficiency with which tree roots take up water, e w. The effect of altering the values of these two parameters has been investigated at a site with a mean summer rainfall of 440 mm per year, a fertiliser nitrogen rate of 150 kilograms per hectare per year and a tree density of 200 stems per hectare. As regards changes in k w, this was found to have no effect on the projected growth rate of the trees. Thus, for values of kw ranging from 0-3 to 0.9. the projected discounted benefits from sheep farming and forestry were found to be virtually identical. On the other hand, an improvement in e w was found to influence the projected discounted benefits. However, unexpectedly, the effect of increasing e w was to adversely affect economic returns. Thus, the comparative net present values of the returns from forestry and sheep farming at values for e w of 0.10, 0.25 and 0.50, were £4844, £3900 and £3299 per hectare, respectively. The reason for this was that an increase in e w did not accelerate the growth rate of the trees, but rather reduced the water available to the grass. As a consequence, grass yields and, in turn, the stock-carrying capacity of the land, were lowered. Increasing ew from 0.1 to 0-5 brought f o ~ a r d the year at which annual grass production effectively ceased from year 20 to year 10. Thus, the choice of the value of e w is likely to significantly affect the apparent benefits of combining forestry with farming relative to using the land solely for sheep production. The apparent economic attraction of combining wood production with livestock farming is also greatly influenced by the choice of discount rate. Conventionally. a discount rate of 5°o (7z=0.05) is employed in evaluations of forestry projects (Jobling & Pearce, 1977; Centre for Agricultural Strategy, 1980), although the Treasury only requires the Forestry Commission to use a discount rate of 3°/o in evaluating woodland investments. The impact on the projected net present values at planting densities of 0. 50, 100 and 200 stems per hectare of using the discount rates of 3['o, 7°0 and 10 % /O is shown in Table 6. The mean

C. J. Doyle, J. Evans, J. Rossiter

24

TABLE 6 Effect of Changes in the Discount Rate on the Comparative Net Present Values (£ h a - ~) from Combining Trees with Sheep Production at Various Planting Densities (Fertiliser nitrogen usage is fixed at 150 kg N ha - ~ y e a r - ~ and the mean summer rainfall is assumed to be 440 mm year-*) Planting density (stems per hectare)

0 50 I00 200

Discount rate (°o) 3

5

7

10

7071 8490 9345 8 921

5226 5775 5974 4 752

4076 4190 4099 2 828

3038 2837 2613 1 644

summer rainfall and the fertiliser nitrogen usage are presumed to be 440 mm per year and 150 kilograms N per hectare per year, respectively. The trees are felled at 45 years of age. Examining Table 6, it is evident that, at discount rates of 7 °,o and 10 °Jo, a combination of forestry with sheep farming is unlikely to be competitive with farming on its own. On the other hand, at a discount rate of 3 °;o. combining livestock farming with timber production is apparently very worth while. Finally, the relative economic advantage of combining wood production with sheep rearing is sensitive to the relative price of timber. In the long-term prices for timber are expected to rise due to a growing TABLE 7 Comparative Net Present Values (£ ha - ~) from Combining Trees with Sheep Production at Various Planting Densities and Discount Rates Following a Doubling of the Real Prices for Timber IFertiliser nitrogen usage and mean summer rainfall are. respectively, 150kg N h a - : year- ~ and 440 mm y e a r - ~) Planting density (stems per hectare)

0 50 100 200

Discount rate (°o) 3

5

7

lO

707l 10660 13560 15 769

5226 6 532 7718 7719

4076 4 762 5618 4109

3038 3054 3008 2023

The economic benefits of intercropping trees with grassland

25

imbalance on the world market between supply and demand (Centre for Agricultural Strategy, 1980); moreover, the present real prices for wood are well below the historic long-term averages. As a result it is reasonable to assume that, by the year 2030, prices of timber will have doubled in real terms compared with the present, as was projected by the Centre for Agricultural Strategy (1980). Assuming prices for agricultural products remain constant, the impact of doubling timber values on the net present values for the agro-forestry options considered in Table 6 is shown in Table 7. Comparison with Table 6 reveals that, at a 10 ~o discount rate. the effect of doubling timber prices is very small. On the other hand, at discount rates of 3 o/ /o, 5~o and 7/o, o~, the effect is appreciable, so that combinations of forestry with sheep farming now appear economic at a discount rate as high as 7 %o.

DISCUSSION AND CONCLUSIONS Care is required in the interpretation of the results from the model. First, difficulty has been encountered in finding reliable estimates for many of the parameters in the model from a review of the literature. As a result, only limited confidence can be attached to the projected responses to changes in rainfall, fertiliser nitrogen and tree density. Secondly. it has not been possible to validate satisfactorily the results from the model. Thirdly, the conclusions concerning the benefits of combining forestry with sheep farming are extremely sensitive to assumptions about the discount rate and the future real prices for timber. In addition, what is not indicated by the relative net present values for the different land management strategies is the timing of the benefits. Thus, compared with using the land solely for sheep rearing which will give a constant annual income, a strategy of combining trees with livestock will give a much more uneven cash flow. In particular, at a density of around 200 stems per hectare, the annual income may be very low in the second half of the rotation (years 20-40). This could have a considerable influence on the attractiveness of agroforestry to farmers. Nonetheless, the results from the model give some indication of the likely economic implications of combining sheep farming with the open plantation of trees on the same grassland area. First, at current prices a policy of planting trees at densities of 50 to 200 stems per hectare and telling them for firewood as soon as they have reached a trunk diameter of

26

C. J. Doyle, J. Ecans, J. Rossiter

15cm is unlikely to be worth while. In such situations the discounted returns from the sale of timber will not compensate for the loss of livestock earnings, when compared with equivalent land solely under sheep production. On the other hand, where felling is delayed until the trees reach maturity at a trunk diameter of 45 cm, at a discount rate of 5 3o a combination of farming with forestry may yield higher discounted benefits than using the land solely for livestock production, especially on land receiving less than 150 kilograms of N per hectare per year. Maximum discounted benefits were found to occur at a planting density of 100 stems per hectare. At discount rates of 7 °/o and 10 o,..o,the economic attraction of growing trees is more dependent on an increase in timber prices relative to those prevailing at present. Accepting that the model is a first attempt to simulate the effect of intercropping trees with grassland on livestock production per hectare, it would be unwise to draw any more detailed conclusions from the study. Before greater confidence can be attached to the projections further experimental work is required on five major areas. First. a better understanding is needed of the growth patterns and the stem wood -crown wood partitioning for trees grown in the open, as distinct from trees grown in dense stands. Secondly, more detailed knowledge is required of light interception and the light environment between trees grown in the open. Thirdly, in the absence of information on how well established trees and grass compete for moisture, information is needed on the rooting patterns and water uptake of tree roots. Fourthly, more needs to be known about how the presence of animals may affect both the establishment and growth rates of trees. Fifthly, the financial implications of agroforestry require closer study. In particular, the implications of uneven cash flows associated with such systems need closer scrutiny.

ACKNOWLEDGEMENTS We are grateful to John Thornley and Roger Wilkins of the Animal and Grassland Research Institute and David Burdekin, Richard Crowther and Diana Mitlin of the Forestry Commission for constructively commenting on an earlier version of this paper. The Animal and Grassland Research Institute is financed through the Agricultural and Food Research Council. This work is in part commissioned by the Ministry of Agriculture, Fisheries and Food.

The economic benefits of intercropping trees with grassland

27

REFERENCES Bunce, R. G. H. (1968). Biomass and production of trees in mixed deciduous woodland. 1. Girth and height as parameters for the estimation of tree dry weight. Journal of Ecology, 56, 759-75. Centre for Agricultural Strategy (1980). Strategy for the U Kjorest industry. CA S report 6, Centre for Agricultural Strategy, Reading, 347. Charles-Edwards, D. A. (1981). The mathematics of photosynthesis and productivity. Academic Press, London, 127. Corrall, A. J., Morrison, J. & Young, J. W. O. (L982). Grass production. In: Milk from grass (Thomas, C. & Young, J. W. O. (Eds)). Imperial Chemical Industries and Grassland Research Institute, Hurley, L04. Forestry Commission (L980). Published yield tables jot plantation crops, Table R46a. HMSO. London. France, J. & Thornley, J. H. M. (1984). Mathematical models in agriculture. Butterworths, London, 335. Gardwood, E. A. (1965). Some factors which b~uence the root growth. MSc thesis, University of Reading. Greenwood, D. J., Cleaver, T. J. & Turner, M. K. (1974). Fertiliser requiremer,,ts of vegetable crops. Proceedings of the Fertiliser Society No. 145. Jackson, J. E. & Palmer, J. W. (1979). A simple model of light transmission and interception by discontinuous canopies. Annals of Botany, 44.38 I-3. Jobling, J. & Pearce, M. L. (1977). Free growth o/oak. Foresto' Commission Leaflet 113. HMSO, London, 16. Johnson, I. R. & Thornley. J. H. M. (1983). Vegetative crop growth model incorporating leaf area expansion and senescence and applied to grass. Plant, Cell and Enrironment, 6, 72l-9. Kramer, P. J. (1969). Plant and soil water relationships: A modern ©'nthesis. McGraw-Hill, New York. McMurtrie, R. & Wolf, L. (1983a). Above- and below-ground growth of forest stands: A carbon budget model. Annals of Botany, 52, 437-48. McMurtrie, R. & Wolf, L. (1983b). A model of competition between trees and grass for radiation, water and nutrients. Annals of Botany, 52, 449-58. Ministry of Agriculture, Fisheries and Food (1978). Definition of terms used in agricultural business management. MAFF Booklet GFM 21, MAFF (Publications), Pinner, 39. Mohler. C. L., Marks, P. L. & Sprugel, D. G. (1978). Stand, structure and allometry of trees during self-thinning of pure stands. Journal of Ecology. 66, 599-614. Monsi. M. & Saeki, T. (1953). Uber den Lichffaktor in den PflanzengeselIschaften und seine Bedeutung ftir die Stoff produktion. Japanese Journal of Botany, 14. 22-52. Nix. J. (1984). Farm management pocketbook (15th edn) (1985). Farm Business Unit, Wye College. Kent, 177. Percival, N. S. & Knowles, R. L. (1983). Agro-forestry: Expanding horizons. Proceedings of 1983 Ruakura Farmers" Conference, Hamilton, New Zealand, 37-45.

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C. J. Doyle, J. Evans, J. Rossiter

Ritson, C. (1978). Agricultural economics. Principles and policy. Granada Publishing, London, 409. Thornley, J. H. M. (1976). Mathematical models m plant physiology. Academic Press, London. 317. Weast, R. C. & Astle. M. J. (1980). CRChandbook of chemistry and physics. CRC Press, Boca Ratan. White, J. (I 981), The allometric interpretation of the self-thinning rule. Journal of Theoretical Biology, 89, 475-500. Wit, de C. T. et al. (1978). Simulation of assimilation, respiration and transpiration of crops. Pudoc, Wageningen. Woledge, J. ( 1971). Effect of light intensity during growth on the subsequent rate of photosynthesis of leaves of tall rescue (Festuca arundinacea). Annals of Botany, 55, 3l 1-22.

A P P E N D I X : D E F I N I T I O N OF SYMBOLS Independent variables t = time (years) j = soil layer State variables Ly = weight of grass leaves (kilograms of dry matter per square metre of ground) Lw = weight of foliage of trees (kilograms of dry matter per square metre of ground) R~ = weight of grass roots (kilograms of dry matter per square metre of ground) Rw = weight of fine roots of trees (kilograms of dry matter per square metre of ground) Sw = weight of stem wood, branches, stumps and larger roots of trees (kilograms of dry matter per square metre of ground) Other variables A WC = available water capacity of soil (cubic metres of water per square metre of ground) B = above-ground biomass of an individual tree (kilograms of dry matter per tree) CA = area of ground covered by the canopy of an individual tree

(m=) C N P V = combined net present value of returns from forestry and farming (£ per square metre of ground)

The economic benefits o f intercropping trees with grassland

29

diameter of trunk of individual tree (m) F N = fertilizer nitrogen applied (kilograms of N per square metre of ground per year) [o = average daily light received by a horizontal plane above the tree canopy (J per square metre of ground per day) light intercepted by grass canopy (J per square metre of ground per day) light intercepted by tree canopy (J per square metre of ground per day) I T K = average annual grass requirements per livestock unit (kilograms of dry matter per head per year) L A I = leaf area index (square metres of leaf per square metre of ground) M R = maintenance requirements of tree foliage (kilograms of CO_, per kilogram dry matter per day) ,.Vfs = maintenance requirements of tree stem (kilograms of CO, per kilogram dry matter per day) M ' R = maintenance requirements of grass leaves (kilograms of CO_, per kilogram dry matter per day) N = average daily quantity of nitrogen available (kilograms per square metre of ground per day) :\: = average daily quantity of nitrogen available to the grass (kilograms per square metre of ground per day) N w = average daily quantity of nitrogen available to the trees (kilograms per square metre of ground per day) N P V g = net present value of returns from grassland farming (£ per square metre of ground) N P V w = net present value of returns from forestry (£ per square metre of ground) average daily gross photosynthetic rate of the grass (kilograms of CO_, per square metre of ground per day) average daily gross photosynthetic rate of the tree PW (kilograms of CO 2 per square metre of ground per day) Pn~ = the average daily net photosynthetic rate of the grass (kilograms of CO, per square metre of ground per day) P n W ~. the average daily net photosynthetic rate of the trees (kilograms of CO 2 per square metre of ground per day) S N = soil nitrogen (kilograms of nitrogen per square metre of ground per year) O

C. J. Doyle, J. Evans. J. Rossiter

30

S R = summer (April-September) rainfall (cubic metres of water STR =

W=

%= W~v =

per square metre of ground) stocking rate (head of livestock per square metre of ground) average daily quantity of water available (cubic metres per square metre of ground per day) average daily quantity of water available to the p a s s (cubic metres per square metres of ground per day) average daily quantity of water available to the trees (cubic metres per square metre of ground per day)

Parameters = constant in eqn (3) = c o n s t a n t in eqn (3) a 2 = constant in eqn (19) a 3 = c o n s t a n t in eqn (19) aa. = constant in eqn (20) 0 5 = constant in eqn (20) b~ = initial slope of response curve for leaf photosynthesis to light for the grass crop (kilograms of C O , per Joule) = initial slope of response curve for leaf photosynthesis to /5,W light for the tree crop (kilograms of CO_, per Joule) CW = annual cost of maintaining trees (£ per tree) d w = density of trees (trees per square metre of ground) ew = relative efficiency with which tree roots take up water compared to grass roots = L proportionate rate of gross photosynthesis bv the grass where water and nitrogen are limiting = /w proportionate rate of gross photosynthesis by the trees where water and nitrogen are limiting = light extinction coefficient for the grass canopy kw = light extinction coefiqcient for the tree canopy / = proportion of tree's canopy overlapping canopy of a neighbouring tree = P proportion of ground area covered by the canopy of the trees = maximum daily gross photosynthetic rate of the grass at saturating light levels (kilograms of C O , per square metre per day) P M A X w = maximum daily gross photosynthetic rate of tke trees at a0 01

The economic benefits o f intercropping trees with grassland

31

saturating light levels (kilograms per CO2 per square metre per day) factor determining the rate of decrease in the proportion of qL photosynthate partitioned to the leaves of trees with time qR = factor determining the rate of decrease in the proportion of photosynthate partitioned to the roots of trees with time rate of leaf dark respiration for trees (kilograms of CO: per rL kilogram of dry matter per day) r'L= rate of leaf dark respiration for grass Ikilograms of CO, per kilogram of dry matter per day) r R = respiration rate of tree roots (kilograms of CO, per kilogram of dry matter per day) FR = respiration rate of grass roots (kilograms of CO 2 per kilogram of dry matter per day) ?'S = respiration rate of tree stems (kilograms of CO2 per kilogram of dry matter per day) Sg = specific leaf area of grass leaves (square metres per kilogram of leaf dry matter) S W = specific leaf area of tree foliage (square metre per kilogram of leaf dry matter) T = proportion of light tailing on tree canopy reaching top of grass canopy L= proportion of light reaching grass canopy where tree canopy is non-transmitting L= proportion of light passing through tree canopy It W = proportion of stem wood, branches, stumps and large tree roots which are utilisable % = net returns per head of livestock (£ per head) t'w = net returns from saleable timber where trees sold standing (£ per cubic metre) v =conversion factor from CO: to dry weight for grass (kilograms of dry matter per kilogram of CO2) Y=conversion factor from CO2 to dry weight for trees (kilograms of dry matter per kilogram of CO 2) :% = constant in eqn (1) :~ =constant in eqn (1) a 2 constant in eqn (2) :t 3 = constant in eqn (2) F;_ = proportionate rate of leaf loss in trees p

=

C. J. Doyle, J. Evans, J. Rossiter

32

proportionate rate of root loss in trees proportionate rate of stem loss in trees 1-s = 7L = proportionate rate of leaf loss in grass 7R = proportionate rate of root loss in grass 6 = distance between trees (m) r/j= proportion of soil water in layer j Oj = proportion of tree roots in layer j ~,~ = constant in eqn (24) ~-~.= constant in eqn (24) ~%w= constant in eqn (24) A L = proportion of photosynthate going to tree foliage :\R = proportion of photosynthate going to tree roots A s = proportion of photosynthate going to tree stem AoL = proportion of photosynthate going to tree foliage in year t=0 AoR = proportion of photosynthate going to tree roots in year t=0 ';'L = proportion of photosynthate going to grass leaves ;-R = proportion of photosynthate going to grass roots ].tj = proportion of available nitrogen in layer j. O radius of canopy of individual tree (m) proportionate rate of discount 40a proportion of grass roots in layer j 1" R =