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A mathematical model for predicting annual fertiliser requirements of kiwifruit vines
Scientia Itorticulturae, 37 (1988) 71-86 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
71
A M a t h e m a t i c a l Model for P r e d i c t i n g A n n u a l Fertiliser R e q u i r e m e n t s of K i w i f r u i t V i n e s J.G. BUWALDA and G.S. SMITH
Ruakura Agricultural Centre, MAFTech, Private Bag, Hamilton (New Zealand) (Accepted for publication 27 May 1988)
ABSTRACT Buwalda, J.G. and Smith, G.S., 1988. A mathematical model for predicting annual fertiliser requirements of kiwifruit vines. Scientia Hortic., 37: 71-86. A mathematical model for predicting fertiliser requirements in commercial kiwifruit orchards is presen';ed. The model assumes allometric distribution of dry weight amongst vine components for all levels of productivity, and uses a prediction of fruit yield to estimate vine dry weight, annual growth and hence nutrient uptake. The efficiency of nutrient recovery is used to estimate the total nutrient inputs to the soil required to maintain an equilibrium of the soil nutrient pools. Atmospheric inputs and nutrients cycled in senesced or pruned plant material are then deducted from the total :nutrientrequirement to calculate a nutrient deficit or fertiliser requirement. Leaf analysis is used to detect nutrient deficiencies or excesses that can be addressed in corrective fertiliser dressings. Sensitivity analysis showed that estimates of fruit yield and the efficiency of nutrient recovery had the ~eatest impact on predictions of fertiliser requirement. The validity of initial estimates of these parameters is discussed. Application of the model to a mature orchard and a developing orchard revealed that nitrogen fertiliser rates much less than those recommended did not lead to evidence of nitrogen deficiency, suggesting contributions to uptake from soil nitrogen reserves and/or incorrect assessment of the efficiency of nitrogen recovery. Potassium deficiency occurred in the mature orchard following low potassium fertiliser rates, and also in the developing orchard in spite of apparently high potassium fertiliser rates, highlighting the importance of this disorder for kiwifruit. For other nutrients, deficiencies or excesses followed fertiliser rates respectively lower or higher than those recommended. Keywords: Actinidia deliciosa; fertiliser requirements; kiwifruit; mathematical model; nutrition.
INTRODUCTION
Fert[liser inputs for kiwifruit (Actinidia deliciosa (A.Chev.) C.F. Liang et A.R. F erguson var. deliciosa 'Hayward') orchards normally constitute only about 2% of total production costs (MAF, 1987), but inappropriate fertiliser management can have disproportionately large effects on fruit yields (Smith 0304-4238/88/$03.50
© 1988 Elsevier Science Publishers B.V.
72 et al., 1987a). The widespread incidence of nutritional disorders, especially potassium deficiency (Smith et al., 1985), on commercial kiwifruit orchards has led to considerable interest in quantitative methods for calculating optim u m fertiliser rates. Response functions relating yield to fertiliser applications, used widely for annual crops, have limited value for perennial crops such as kiwifruit. The necessary field experiments would last several years before revealing significant responses to varying fertilisers, be very expensive to run, and probably test only a few possibilities. Dynamic models relating crop growth and development to soil and plant nutrient contents have also been developed for annual crops (Barnes et al., 1976; Thornley, 1978). However, solutions to these models normally depend on sophisticated inputs, so that practical application is usually limited, especially for perennial crops. In our previous paper (Smith et al., 1988), we discussed a budgetary method for estimating nutrient uptake for developing and mature kiwifruit vines. Allowances were made for expansion of the perennial framework (for developing vines), cycling or loss in deciduous and transient organs, and inefficiencies in the recovery of nutrients from the soil. This budgetary analysis highlighted the large potassium uptake requirements of kiwifruit. Estimates of nutrient uptake related to crop age and productivity may be used to develop fertiliser recommendations provided nutrient cycling, non-fertiliser nutrient inputs, and soil physical and chemical properties affecting nutrient recovery are understood. In this paper, we present a mathematical model incorporating nutrient budgets for predicting fertiliser requirements, coupled with monitoring of the plant nutrient status to detect nutritional disorders and define nutrient requirements for their correction. The model is based on empirical relationships rather than on a sophisticated mechanistic understanding of nutrient dynamics in the soil-plant system, but is intended for use with a minimum of sitespecific inputs. Sensitivity analysis is also presented to explore which factors most affect the accuracy of model predictions. Finally, the model is applied to a mature orchard and a developing orchard, and generalised fertiliser recommendations are compared with actual fertiliser use and leaf nutrient concentrations to provide a limited assessment of model performance. THE MODEL A schematic model summarising nutrient fluxes to, within and from kiwifruit vines is shown in Fig. 1. Nutrient uptake is determined by biomass production (current season growth), but may be limited by nutrient availability in the soil. For simplicity, total annual uptakes only are considered, so nutrient dynamics within a growing season are ignored. Nutrients taken up may be distributed in perennial (developing vines only), transient and deciduous components. Nutrients within transient components will ultimately be cycled (after pruning) under usual management, while those
73
SE.SON GROW,. I I f
~
l nutrient
pool
Uptake Atmospheric input Fertiiiser inpu|
Soil
Cycling
I~
l
Loss
Fig. 1. Schematicrepresentationof directionalflowsof nutrients within the kiwifruitecosystem. in deciduous organs may be exported from the orchard (in harvested fruit) or cycled i:a senesced plant material. The soil nutrient pool reflects the balance of additions (e.g. fertiliser and atmospheric inputs) and losses (e.g. leaching). Our mathematical model for predicting fertiliser requirements therefore defines n~£rient quantities required to maintain the soil nutrient pool at a level capable of supporting vine growth at desirable levels. Solution of the model require~,~ estimates of the nutrient fluxes described in Fig. 1. For convenience, the annual cycle of growth and nutrient uptake starts after fruit harvest. The symbols,; used hereafter are listed in Table 1. u p t a k e . - Annual nutrient uptake may be considered as the difference in the total nutrient content of the vines from one point in the growing season to the same point of the following season plus the quantity of nutrients lost from the vines during that year. This mass balance may be expressed as the sum of ~autrient quantities in current season growth and in expansion (if any) of the perennial framework minus recycling within the vine from leaves before senescence and from shoots retained at winter pruning. This may be described mathematically for developing vines as Nutrient
Uy = M ( c s g + p f + l t ) y - M ( p f + (sh.f) + R (lf))y-1
(1)
For mature vines without nutrient disorders, there is no net accumulation of nutriments in the perennial components, so annual uptake may be described more simply as U = M ( c s g + lt) - M ( ( s h . f ) + R (If))
(2)
SolulSons to these expressions of uptake depend on the definition of nutrient accumulation in component organs of the vine. As the nutrient concentrations of the various organs of kiwifruit vines at harvest are similar for vines of varying age and productivity (Buwalda and Smith, 1987), nutrient accumulation depends principally on biomass production. For vines aged 3 years or more, Buwalda ( 1987 ) showed an allometric distribution of incremental dry weight amongst component organs. Hence, biomass production can be estimated from
74 TABLE 1 List of symbols Symbol
Description
y
Vine age (years)
Plant components ft Fruit If Leaf sh Shoot It Lateral le Leader st Stem rs Structural root rf Fibrous root csg Current season growth; ft + lf+ sh + rf pf Perennial framework; le + st + rs Crop dimensions VD W Vine dry weight (t ha- 1) FY Estimated fruit yield (fresh weight) (t ha- 1 ) AFY Actual fruit yield (fresh weight) (t h a - l ) BN Bud numbers after winter pruning (m-~) TF Trunk factor (ratio of trunk circumference to allotted canopy area) (cm m -2) RY Relative yield, assuming yield-- 1 at optimum leaf nutrient concentration Nutrient dimensions Uptake (kg ha -1) U Nutrient quantity within plant or its components (kg ha -1) M Nutrient concentration in plant dry weight (g kg -1 ) N Nutrient quantity re-absorbed from vine organ between fruit harvest and senesR cence (kg h a - 1) Cycled nutrients (kg h a - 1) CN Atmospheric nutrient inputs (kg h a - ~) AI NI Nutrient inputs to soil from all sources (kg h a - ' ) Fertiliser requirements (kg h a - 1) FR NB Nutrient balance (deficit or surplus ) within plant (kg ha- i ) Target nutrient concentration (g kg-1 dry weight) TN Constants f k TVDW BB FS FW m g ER a,b,c
Fraction of shoots retained as laterals at winter pruning (0.625) Linear term in regression of vine dry weight against fruit yield (0.59) Treshold vine dry weight below which no fruit production occurs (3.8 t h a - 1) Proportion bud burst (0.40) Number of fruit harvested per shoot ( 3.0 ) Fruit weight at harvest (0.09 kg fruit- 1) Linear term in regression of fruit yield against logarithm of trunk factor (13.9 ) Constant term in regression of fruit yield against trunk factor (23.8) Efficiency of nutrient recovery by plant roots; value specific for each nutrient Quadratic, linear and constant terms in quadratic regression of relative yield against leaf nutrient concentration; values specific for each nutrient
75 a knowledge of fruit yield only, using the linear relationship (r 2= 0.89 ) derived from the data of Buwalda (1987),
VDW =: (FY.k) + T V D W
(3)
While recorded fruit yields may be used to describe vine dry weights and hence nutrient uptakes retrospectively, use of eqns. (1)-(3) to predict nutrient uptake and hence fertiliser requirements requires an advance estimate of fruit yield. A recent survey of kiwifruit vines in major growing areas of New Zealand (MAF, 1984) suggested that fruit yields may be related to parameters of vine size in the previous winter. One such relationship is that between bud number and fru:Ltyield,
FY=BN.BB.FS.FW
(4)
The lind burst proportion, fruit per shoot and fruit weight typically vary less than 20% with climatic and management factors (MAF, 1984), and general values Jbr these parameters may be considered (Table 1 ). Thus, vines with 28 buds m-2 after winter pruning would be expected to have a fruit yield of 30 t ha-1. For developing vines at least, fruit yield may be empirically related to the rat:io of trunk circumference at 0.6 m above the ground to the allotted canopy area (horizontal) per vine,
FY= (ln TF.m) + g
(5)
This linear regression shows a diminishing-returns-type response of fruit yield to the logarithm of trunk size. Vines with a fruit yield of 30 t ha-1 typically have a "trunk factor" of at least 1.6 cm m -2 (Buwalda and Smith, 1987), which is normally achieved 5-8 years after planting. The trunk circumference is more easily iaeasured than bud numbers. However, the relationship between trunk size and fruit yield breaks down as vines mature, as the trunk typically continues to expand while fruit yields reach a plateau (MAF, 1984). For mature vines, the yiei[d history for the previous 5 years should provide a reasonable estimate of fruit yield, assuming constant management. 2,--1
FYy= ~
AFY/5
(6)
.)--6
All these methods of estimating fruit yield ignore possible deleterious effects of the previous vine nutrient status or other cultural factors on growth and productivity, so that existing limitations such as potassium deficiency may be perpetuated. In some situations therefore, "target" rather than predicted fruit yields could be used to generate an estimate of vine dry weight and hence nutrient uptake. Typically kiwifruit vines under competent management should be expected to yield 10, 20 and 25 t ha - 1 at 3, 4 and 5 years of age, respectively, and at least 30 t ha-1 at maturity.
76 Once fruit yield and hence vine dry weight have been estimated, the model can calculate nutrient quantities accumulated in component organs, using reference data for vine nutrient composition, as presented in our previous paper (Smith et al., 1988). Annual nutrient uptake can then be predicted. Fertiliser requirement. - The fertiliser requirement in any year depends on nutrient uptake, the efficiency of nutrient recovery by plant roots, and nonfertiliser nutrient inputs. A major component of non-fertiliser inputs is the quantity of nutrients returned to the soil in cycled plant material, including senesced leaves, sloughed off fibrous roots and pruned shoots and laterals. Following the allometric relationship between fruit yield and the dry weight of component organs of the vines, this quantity may be estimated if the yield history data are available, CNy = M ( l f + r f + It + ( (1 - f ) - s h ) - R (lf))y-1
(7)
Atmospheric inputs to the soil nutrient pool include N fixation by the clover component of the sward beneath the kiwifruit canopy (Steele and Smith, 1988), which is assumed to be constant at all sites, and nutrients in rainfall and irrigation water (Smith et al., 1988). These inputs can be estimated for each orchard from reference to stored data. The model assumes that nutrients in fertiliser, atmospheric inputs and cycled plant material all enter the same pool in the soil, ignoring possible variations in the dynamics of chemical transformations for nutrients from different sources. This assumption should be valid for mature vines where fluxes of nutrients through the soil pool are in equilibrium. The possible absence of such an equilibrium for developing vines is not considered important, as nutrient uptake there normally depends principally on fertiliser inputs if soil nutrient reserves are maintained. The efficiency of nutrient recovery by the plant roots can then be described as ER=U/NI
(8)
Solution of this expression requires definition of all nutrient inputs (including fertiliser), and so must be based on historical data. Long-term nutrient recoveries in typical kiwifruit orchards were estimated in our previous paper (Smith et al., 1988). Those values may be used initially as parameters with constant value at all sites. It is likely that, for any nutrient, the relationship between uptake and nutrient inputs is not constant, as uptake normally shows a diminishing-returns-type of response to nutrient supply (Mengel and Kirkby, 1982). Hence, the efficiency of nutrient recovery will also vary, decreasing as the soil nutrient supply increases. This variation, coupled with expected sitevariability of recovery efficiency, can be accommodated where the model is used repeatedly at any site. The deficit between non-fertiliser inputs and the quantity of nutrients re-
77 quired to support uptake requirements of the vine then represents the fertiliser requirement,
FRy = (Uy/ER) - ( CNy + n I )
(9)
This es':imate of fertiliser requirement accounts only for nutrient removal from the soil in the current season, assuming a steady-state situation for soil nutrient levels, so does not redress existing nutrient imbalances.
Monitoring plant nutrient status. - A plant is essentially an integrator of many complex site (e.g. soil) factors. Reference by the model to an annual leaf analysis for monitoring the plant nutrient status thus checks the success of the fertiliser management, suggested previously, for providing adequate nutrients to the vines. It also partly overcomes the need to account for existing nutrient imbalances, complex site-specific variations in the size of the soil nutrient pools, fertiliser recovery, and uptake-yield relationships. The nutrient concentrations in sampled leaves are compared with reference data (Smith et al., 1987a). Samples may be taken at any stage of the growing season, although nutrient imbalances are probably detected most sensitively about 6 weeks after bud burst (Smith and Clark, 1987). Where the measured concemration of any nutrient in the leaf is outside the acceptable range, the effect on biomass production (current season growth) may be estimated from experimentally derived quadratic regressions between leaf nutrient concentration and vegetative growth for kiwifruit seedlings (G.S. Smith, unpublished results, 1987), RY=aN(lf)2+bN(lf)
+c
(10)
For nutrient deficiencies and excesses, the magnitude of the nutrient balance (deficit or surplus) within the vine may be estimated as
N B = ( 1 - (N(lf) "R Y / T N ( l f ) ) ). U
(11)
This nutrient quantity may be added or subtracted to the estimate of nutrient requirement in the following season. However, this should be considered to be a mininmm quantity for amendment, as the magnitude of the imbalance within the soil pool that resulted in the imbalance within the plant is not considered. SENSIT[VITYANALYSIS The effects of changing each of the major model parameters separately on estimated nitrogen and potassium fertiliser requirements, while the other parameters remain constant, are shown in Table 2. The efficiency of nutrient recovery (ER) was the parameter that most affected estimates of fertiliser requirement. As this efficiency is normally less than 1, any ratio of change will result in a larger proportional effect on the size of the total nutrient pool re-
78 TABLE 2 Effect of changing m a t h e m a t i c a l model parameters separately on estimated nitrogen and potassium requirements for a mature kiwifruit orchard, with a fruit yield (fresh weight) of 30 t h a - 1 Nutrient
Change ratio
P a r a m e t e r estimate FY ~
VDW
N
R
AI
ER
Nitrogen
0.66 0.80 1.00 1.20 1.33 1.50
116 147 192 236 265 303
138 158 192 215 234 258
116 147 192 236 265 303
204 199 192 185 181 175
203 198 192 186 182 177
351 269 192 140 115 88
Potassium
0.66 0.80 1.00 1.20 1.33 1.50
90 110 140 169 188 213
130 134 140 146 149 154
90 110 140 169 188 213
150 144 140 138 131 126
142 141 140 139 138 137
224 190 140 106 90 73
~See Table 1 for explanation of symbols.
quired to sustain uptake and, if other nutrient inputs (cycling, atmospheric) are unaltered, an even larger effect on the estimated nutrient deficit (fertiliser requirement). Changes in the nutrient concentrations of component organs of the vine or in total vine productivity have equal effects on nutrient uptake. Changes in all other parameters, influencing only part of the uptake equation or the nutrient inputs equation, have relatively small effects on the estimated fertiliser requirements. In usual situations, changing the size of one parameter may alter the size of another parameter. For example, the efficiency of nutrient recovery will depend partly on the extent of exploration of the soil by the roots, which in turn will depend on resource allocation to the roots. Nitrogen deficiency should alter the relationship between fruit yield and vine dry weight by altering the root: shoot ratio in favour of root growth (Drew and Saker, 1975), hence increasing the efficiency of nutrient recovery. Similarly, changes in the contribution of atmospheric nutrient inputs may alter root growth, the allometric distribution of dry matter within the vine and hence the efficiency of nutrient recovery. These interactions tend to buffer the magnitude of change in the overall soil-plant system resulting from a change in one component. Hence actual changes in the fertiliser requirement resulting from a change in any parameter are likely to be less than those indicated here. While the sensitivity analysis highlights the relative impact of changing the value of various parameters on estimated fertiliser requirements, it is also im-
79 portant to consider which parameters are presently poorly defined and/or show greatest variability. For example, the average nutrient concentration in component vines at harvest is relatively stable (Smith et al., 1987b) , and in the absence of nutrient disorders should vary little from the values assumed here. Deficiencies or excesses of macronutrients, at least, rarely result in tissue nutrient concentrations for kiwifruit differing more than 50% from those of healthy vines (G.S. Smith, unpublished results, 1987 ). Similarly, the extent of nutrient re-absorption from the leaves between leaf-fall and harvest is also unlikely to vary considerably in the absence of nutritional disorders. There is less certainty about the consistency of the relationship between fruit yield and vine dry weight. The linear regression used here is based largely on data from vines of various ages in one growing district (Buwalda, 1987). Ferguson and Bank ( 1986 ) reported, for a single mature vine with a fruit yield equivalent to 32 t ha-1, a total vine dry weight equivalent to 38 t ha-1; 65% higher than the dry weight that eqn. (3) would estimate. However, current season growth of that vine was not substantially greater than that estimated by the model. As the organs comprising the current season growth collectively represent the major sink for nutrients taken up anually (Smith et al., 1988), this inaccuracy in estimating total vine dry weight may not be of major significance in the subsequent estimates of uptake. The ipredicted fruit yield is a very sensitive parameter within the model, but accuracy in this prediction is sometimes difficult (MAF, 1984). We have considered four options for predicting fruit yield and thus allow subjective selection of one estimate that will drive subsequent equations. The most sensitive parameter in the fertiliser management model, the efficiency of nutrient recovery, is likely to vary considerably with factors such as soil type, rainfall and soil fertility. Repeated use of the model on any orchard will, as already mentioned, improve fertiliser recommendations following generation of site-specific estimates of the efficiency of nutrient recovery. MODELAPPLICATION o r c h a r d . - Estimated fertiliser requirements (from eqn. (9)) for a mature kiwifruit orchard were compared with actual fertiliser use and predicted nutrient uptakes during the period from 10 to 13 years from planting (Table 3). The yield estimate for the first year of this period was that recorded in the previous year, while subsequent yield predictions were based on average yields. Actual yields varied from 22 to 38 t h a - 1, in a biennial bearing pattern, while yields predicted on the basis of yield history declined steadily and, in 3 of 4 years examined, were greater than the actual yields. Predicted nutrient uptakes were broadly proportional to predicted yield, but were tempered by the effects of previous yields (and hence vine sizes) on nutrient reserves within the vine. Predicted uptakes were always high for nitrogen, potassium and calMature'
8O TABLE 3 Comparisons of model predictions of nutrient uptake (U), fertiliser requirement (FR) and actual fertiliser use (FU) on a mature kiwifruit orchard Fruit yield
Year1 U
N
Predicted (t ha -1 )
Actual
41
30
FR FU Year2 U
36
35
FR FU
32
,
Ca
Mg
S
(kg h a - 1)
C1 ,
168 214 78
22 59 21
182 184 140
165 153 1230
28 45 77
28 73 13
77 64 34
155 211 78
20 55 21
166 177 140
150 159 1230
25 45 77
25 68 13
69 53 34
148 189 84
20 52 27
160 163 75
145 139 1320
24 40 82
25 63 24
67 44 111
145 210 91
19 53 23
156 175 75
138 164 120
24 44 82
24 65 15
63 44 111
22
FR FU Year4 U
K
34
FR FU Year3 U
P
38
cium, intermediate for chlorine, and relatively low for phosphorus, magnesium and sulphur. Although not presented, predicted annual uptakes for sodium and the micronutrients were always less than 10 kg ha-1. Actual fertiliser use was considerably less than levels that would have been recommended by the model in every year for nitrogen, phosphorus, potassium and sulphur, and in 2 years for chlorine. In contrast, actual use of calcium (lime) and magnesium fertilisers was higher than the levels that would have been recommended by the model. Leaf nutrient analyses (Table 4) show potassium deficiency in each year, consistent with a low rate of potassium fertiliser application. Phosphorus deficiency was apparent in every second year only (coinciding with higher yields), in spite of low phosphorus fertiliser rates every year. There was no evidence of nitrogen or sulphur deficiency in any year, although actual nitrogen and sulphur fertiliser use was very low. Leaf calcium levels were all within the recommended range, while leaf magnesium concentrations were all very high. Leaf manganese and copper concentrations were generally very high, while leaf zinc was usually within the recommended range. On the other hand, leaf iron con-
81 TABLE 4 Comparison of nutrient concentrations of leaves sampled in February 1 from a mature kiwifruit orchard with recommended concentration ranges Recommended range ~ Macronctrients (g kg -1) N 20-23 P 2.3-2.5 K 20-24 Ca 34-44 Mg 3.7-4.5 S 4.0-5.0 Micronutrients (mg kg -~) Fe 70-95 Mn 120-170 Cu 7-10 Zn 18-30 B 50-60
Year 1
Year 2
Year 3
Year 4
25 2.4 18 43 6.1 6.5
20 2.1 15 41 5.4 5.6
23 2.4 15 48 5.6 7.9
22 2.0 19 38 5.2 4.8
96 240 14 33 41
64 170 11 23 31
75 235 11 18 32
61 154 8 22 46
~Until 1987, February was the recommended time for leaf sampling for nutrient analyses. 2Based on data of Smith et al. (1987a). TABLE 5 Nutrient dynamics and estimated efficiency of nutrient recovery over a 4-year period on a mature kiwifruit orchard
Uptake (kg h a - 1) Fertilise: use (kg h a - 1) Atmospheric inputs (kgha -~ } Cycled nutrients (kg h a - ~) Efficiency of recovery
N
P
K
527
70
572
517
331
92
430
124
1
28
364 0.64
39 0.53
223 0.84
Ca
S
C1
87
88
241
3900
318
65
290
28
16
48
464
76 0.21
73 0.47
190 0.26
485 0.12
Mg
centrations were low in years of high fruit yield, and leaf boron concentrations were low every year. The efficiency of nutrient recovery for this orchard may be estimated, assuming uptake and cycling calculated from a knowledge of actual fruit yield and using historic data for fertiliser and atmospheric nutrient inputs (Table 5). These estimates of recovery are higher than those assumed within the model for nit:cogen, phosphorus, potassium and sulphur (all applied at low rates), similar for chlorine, and lower for calcium and magnesium (applied at high
82
rates). These differences are consistent with the efficiency of nutrient recovery declining as soil fertility increases (Middleton and Smith, 1978) Model estimates of nutrient uptake and fertiliser requirements were compared with actual fertiliser use on a developing orchard, for the period from 3 to 5 years after planting (Table 6). The yield estimate derived from the linear regression between the logarithm of "trunk factor" and fruit yield (eqn. 5) was very similar for the 3-year-old vines, while estimates for the 4- and 5-year old vines were 20-25% less than actual production. Predicted nutrient uptakes for any year reflected the yield estimated for that year as well as the actual yield in the previous year (Table 6 ). Hence, predicted nitrogen uptake to support a fruit yield of 15.5 t ha -1 in Year 3 (following a fruit yield of 2.0 t ha -1 the previous year) was 22% higher than the predicted nitrogen uptake requirement to support a fruit yield of 22.8 t ha-1 in Year 5 (following an actual fruit yield of 24.3 t ha-1 the previous year). Estimated fertiliser requirements responded similarly to yield history. Fertiliser use on this orchard was considerably greater than the levels recommended by the model for phosphorus, potassium, sulphur and chlorine, while nitrogen fertiliser rates were much lower in the first year and subsequently similar to those recommended. No calcium or magnesium was applied during the period of orchard development examined. Leaf nutrient analyses (Table Developing orchard -
TABLE 6 Comparison of model predictions of nutrient uptake (U) and fertiliser requirement (FR) with actual fertiliser use (FU) on a developing kiwifruit orchard Fruit yield
3-year-old U
N
Predicted ( t h a -1 )
Actual
15.51
15.6
FR FU 4-year-old U
19.41
22.81
FU 1 Estimated using eqn. (5).
K
,
Ca
Mg
S
(kg h a - 1)
C1 ,
121 193 100
16 59 212
113 142 188
109 176 0
21 50 0
21 75 233
42 48 188
104 118 100
14 48 212
107 114 188
99 113 0
17 32 0
21 75 233
42 48 188
90 86 100
13 42 212
109 104 188
98 84 0
16 25 0
16 43 233
46 38 188
24.3
FR FU 5-year-old U FR
P
30.6
83 TABLE 7 Comparison of nutrient concentrations of leaves sampled in November for a developing kiwifruit orchard, with recommended concentration ranges Recommended range I
Vine age (years) 3
Macronutrients (g kg- l ) N 25-32 P 4.0-4.8 K 25-33 Ca 15-18 Mg 2.7-3.1 S 4.2-5.3 C1 7-15 Micronutrients (mgkg 1) Fe 90-110 Mn 90-110 Cu 15-18 Zn 30-40 B 40-50
31 4.6 19 15 2.8 5.4 12 144 160 16 29 38
4 28 4.8 20 16 2.6 5.7 10 131 140 19 28 49
5 3O 4.8 22 13 2.7 5.5 16 120 188 14 37 43
1Based cn data of Smith et al. (1987a).
7) show p o t a s s i u m deficiency in e a c h year, in spite of t h e high r a t e s of p o t a s s i u m a p p l i c a t i o n s , a n d m a r g i n a l c o n c e n t r a t i o n s of c a l c i u m a n d m a g n e s i u m . C o n c e n t r a t i o n s of all o t h e r n u t r i e n t s were w i t h i n or a b o v e t h e r e c o m m e n d e d range.
DISCUSSION
T h e m a t h e m a t i c a l model p r e s e n t e d here is a c o n v e n i e n t a n d objective m e t h o d for p r e d i c t i n g fertiliser r e q u i r e m e n t s a n d m o n i t o r i n g p l a n t n u t r i e n t s t a t u s for kiwifr[fit orchards. I n p u t s are simple, so t h a t users ( c o m m e r c i a l growers ) should h a v e little difficulty in u s i n g t h e model. W h i l e t h e o u t p u t h a s n o t b e e n discussed here, t h i s s h o u l d s i m i l a r l y be simple. C u r r e n t l y , 40% of all k i w i f r u i t vines in N e w Z e a l a n d are less t h a n 5 y e a r s old ( S m i t h et al., 1987a), a n d m a j o r n u t r i t i o n a l disorders, p a r t i c u l a r l y p o t a s s i u m deficiency, h a v e b e e n m o s t p r e v a l e n t in y o u n g o r c h a r d s ( S m i t h et al., 1985). H e n c e , use of t h e m o d e l for p r e d i c t i n g fertiliser r e q u i r e m e n t s will at
84 least initially be important for developing as well as mature orchards. Increasing annual fruit yields on such orchards may be difficult to predict. Over-estimating fruit yield is unlikely to result in dangerously high fertiliser rates, but it will be important to avoid underestimating yield and hence limiting yield by nutrient supply. The estimate of fruit yield was clearly an important parameter in the applications of this model to both the mature and developing orchards examined here. Annual fluctuations in fruit yield of the magnitude recorded in the mature orchard are not uncommon (Sale, 1985), and may result at least partly from nutritional disorders. Predictions of fruit yield based on yield history ignore such disorders and their effects on production. Hence, fertiliser recommendations following these predictions may perpetuate existing disorders. It would be prudent, therefore, to tend towards overestimates rather than underestimates of fruit yield. As the model, upon first contact with any orchard, assumes no nutritional disorders, initial fertiliser recommendations refer to macronutrients (nitrogen, phosphorus, potassium, calcium, magnesium, sulphur and chlorine) only. In practice, application of nitrogen as urea or calcium ammonium nitrate, phosphorus as superphosphate and potassium as KC1 will often supply adequate levels of nitrogen, phosphorus, potassium, calcium, sulphur and chlorine even when nitrogen, phosphorus and potassium requirements only are specifically addressed. In addition, regular dressings of agricultural lime should provide more than adequate quantities of calcium. Magnesium requirements, while relatively small, should be addressed regularly, as magnesium deficiency can be a significant disorder of kiwifruit (Clark and Smith, 1985). Micronutrient requirements are usually so small that soil reserves should normally be adequate. Fertiliser recommendations derived from the model therefore ignore micronutrients, except after leaf analysis has established a deficiency. Leaf analysis represents a vital check of the validity of fertiliser recommendations and detection of any need to correct nutritional disorders. This check also reduces the requirement to account precisely for all nutrient movements within the kiwifruit ecosystem. For the mature orchard examined here, the absence of any indication of nitrogen deficiency, in spite of nitrogen fertiliser rates much lower than those recommended by the model, could suggest that nitrogen recovery by the plant roots was very efficient or that nitrogen reserves in the soil, not considered within the model, were large. More information is clearly required on such aspects of nitrogen nutrition of kiwifruit. For the mature orchard, phosphorus and potassium fertiliser rates were obviously inadequate. However, potassium deficiency also occured within the developing orchard in spite of relatively high rates of potassium fertiliser, possibly as a consequence of initial soil potassium deficiencies. A strength of the model is that leaf analysis detects these anomalies and the need for corrective fertiliser dressings. However, the incidence of potassium deficiency in both these or-
85
chards further highlights the importance of this disorder for kiwifruit (Smith et al., 1985 ). It should also be noted that the potassium budget used here was based o:~ detailed data from a single orchard only (Buwalda and Smith, 1987 ), which was probably potassium-deficient. Hence potassium fertiliser requirements raay actually be higher than those presented here, and this may explain the incidence of potassium deficiency even where fertiliser rates were apparently adequate. While the efficiencies of nutrient recovery assumed in the model (Smith et al., 1988) are realistic when compared to those of other crops (Middleton and Smith, 1978; Haynes and Goh, 1980), they clearly varied from those calculated for the mature and developing orchards examined here. These differences can be attributed partly to fertiliser rates that were inadequate or excessive, resulting in higher and lower recoveries, respectively. The model's principal function is to describe external nutrient requirements to maintain the nutrient balance in the soil-plant system. The reliability of estimates of fertiliser requirement where nutrient deficiencies or excesses exist will depend strongly on the !Lmpactof such nutrient imbalances on the efficiency of nutrient recovery. Site-specific estimates of the efficiency of nutrient recovery may be obtained :~romthe data-base built up after repeated use of this model in situations where )~utrient deficiencies and excesses are not present and where fertiliser rates have generally been appropriate. Nevertheless, detection and estimation of nutrient deficiencies and excesses within the vine after leaf analysis will enable site-specific refinements of the fertiliser programme, which should largely overcome the impact of variable soil physical and chemical properties on model efficacy. The mathematical model presented here is now in commercial use in the New Zealand kiwifruit industry, as the basis of a kiwifruit nutrition management service. ACKNCWLEDGEMENTS
We are grateful to the New Zealand Kiwifruit Authority for financial support and to Bill Baldwin for use of fertiliser and yield records and leaf analysis data.
REFERENCES Barnes, A., Greenwood, D.J. and Cleaver, T.J., 1976. A dynamic model for the effects of potassium and nitrogen fertilisers on the growth and nutrient uptake of crops. J. Agric. Sci., 86: 225-244. Buwalda, J.G., 1987. Growth physiology of kiwifruit. Proc. Ruakura Hortic Conf., Kiwifruit, pp. 14-17. Buwalda, J.G. and Smith, G.S., 1987. Dry matter and nutrient accumulation and partitioning in deve::oping kiwifruit vines. Tree Physiol., 3: 295-307.
86 Clark, C.J. and Smith, G.S., 1985. Magnesium deficiency reduces fruit numbers. N.Z. Kiwifruit, Oct. 1985, p. 19. Drew, M.C. and Saker, L.R., 1975. Nutrient supply and the growth of the seminal root system in barley. II. Localised compensatory increases in lateral root growth and rates of nitrate uptake. J. Exp. Bot., 26: 79-90. Ferguson, A.R. and Bank, R.J., 1986. The great DSIR vine demolition derby. N.Z. Kiwifruit, March 1986, p. 25. Haynes, R.J. and Goh, K.M., 1980. Distribution and budget of nutrients in a commercial apple orchard. Plant Soil, 56: 445-457. MAF, 1984. Kiwifruit Vine Monitoring. Ministry of Agriculture and Fisheries Occasional Publication, 26 pp. MAF, 1987. Monitoring Report, Hamilton Region. Ministry of Agriculture and Fisheries Occasional Publication, 38 pp. Mengel, K. and Kirkby, E.A., 1982. Principles of Plant Nutrition. International Potash Institute, Bern, 655 pp. Middleton, K.R. and Smith, G.S., 1978. The concept of a climax in relation to the fertiliser input of a pastoral ecosystem. Plant Soil, 50: 595-614. Sale, P.R., 1985. Kiwifruit Culture. 2nd revised edition. Government Printer, Wellington, 96 pp. Smith, G.S. and Clark, C.J., 1987. Plant analysis - an essential management tool. Proc. Ruakura Hortic. Conf., Kiwifruit, pp. 7-9. Smith, G.S., Clark, C.J. and Buwalda, J.G., 1985. Potassium deficiency of kiwifruit, Proc. Ruakura Hortic. Conf., Kiwifruit, pp. 13-16. Smith, G.S., Asher, C.J. and Clark, C.J., 1987a. Kiwifruit Nutrition, Diagnosis of Nutritional Disorders. 2nd revised edition. Agress Communications, Wellington, 60 pp. Smith, G.S., Clark, C.J. and Henderson, H.V., 1987b. Seasonal accumulation of mineral nutrients by kiwifruit. I. Leaves. New Phytol., 106: 81-100. Smith, G.S., Buwalda, J.G. and Clark, C.J., 1988. Nutrient dynamics of a kiwifruit ecosystem. Scientia Hortic., 37:in press. Steele, K.W. and Smith, G.S., 1988. Clover makes a small contribution. N.Z. Kiwifruit, Feb. 1988, p. 19. Thornley, J.H.M., 1978. Crop response to fertilizers. Ann. Bot., 42: 817-826.
71
A M a t h e m a t i c a l Model for P r e d i c t i n g A n n u a l Fertiliser R e q u i r e m e n t s of K i w i f r u i t V i n e s J.G. BUWALDA and G.S. SMITH
Ruakura Agricultural Centre, MAFTech, Private Bag, Hamilton (New Zealand) (Accepted for publication 27 May 1988)
ABSTRACT Buwalda, J.G. and Smith, G.S., 1988. A mathematical model for predicting annual fertiliser requirements of kiwifruit vines. Scientia Hortic., 37: 71-86. A mathematical model for predicting fertiliser requirements in commercial kiwifruit orchards is presen';ed. The model assumes allometric distribution of dry weight amongst vine components for all levels of productivity, and uses a prediction of fruit yield to estimate vine dry weight, annual growth and hence nutrient uptake. The efficiency of nutrient recovery is used to estimate the total nutrient inputs to the soil required to maintain an equilibrium of the soil nutrient pools. Atmospheric inputs and nutrients cycled in senesced or pruned plant material are then deducted from the total :nutrientrequirement to calculate a nutrient deficit or fertiliser requirement. Leaf analysis is used to detect nutrient deficiencies or excesses that can be addressed in corrective fertiliser dressings. Sensitivity analysis showed that estimates of fruit yield and the efficiency of nutrient recovery had the ~eatest impact on predictions of fertiliser requirement. The validity of initial estimates of these parameters is discussed. Application of the model to a mature orchard and a developing orchard revealed that nitrogen fertiliser rates much less than those recommended did not lead to evidence of nitrogen deficiency, suggesting contributions to uptake from soil nitrogen reserves and/or incorrect assessment of the efficiency of nitrogen recovery. Potassium deficiency occurred in the mature orchard following low potassium fertiliser rates, and also in the developing orchard in spite of apparently high potassium fertiliser rates, highlighting the importance of this disorder for kiwifruit. For other nutrients, deficiencies or excesses followed fertiliser rates respectively lower or higher than those recommended. Keywords: Actinidia deliciosa; fertiliser requirements; kiwifruit; mathematical model; nutrition.
INTRODUCTION
Fert[liser inputs for kiwifruit (Actinidia deliciosa (A.Chev.) C.F. Liang et A.R. F erguson var. deliciosa 'Hayward') orchards normally constitute only about 2% of total production costs (MAF, 1987), but inappropriate fertiliser management can have disproportionately large effects on fruit yields (Smith 0304-4238/88/$03.50
© 1988 Elsevier Science Publishers B.V.
72 et al., 1987a). The widespread incidence of nutritional disorders, especially potassium deficiency (Smith et al., 1985), on commercial kiwifruit orchards has led to considerable interest in quantitative methods for calculating optim u m fertiliser rates. Response functions relating yield to fertiliser applications, used widely for annual crops, have limited value for perennial crops such as kiwifruit. The necessary field experiments would last several years before revealing significant responses to varying fertilisers, be very expensive to run, and probably test only a few possibilities. Dynamic models relating crop growth and development to soil and plant nutrient contents have also been developed for annual crops (Barnes et al., 1976; Thornley, 1978). However, solutions to these models normally depend on sophisticated inputs, so that practical application is usually limited, especially for perennial crops. In our previous paper (Smith et al., 1988), we discussed a budgetary method for estimating nutrient uptake for developing and mature kiwifruit vines. Allowances were made for expansion of the perennial framework (for developing vines), cycling or loss in deciduous and transient organs, and inefficiencies in the recovery of nutrients from the soil. This budgetary analysis highlighted the large potassium uptake requirements of kiwifruit. Estimates of nutrient uptake related to crop age and productivity may be used to develop fertiliser recommendations provided nutrient cycling, non-fertiliser nutrient inputs, and soil physical and chemical properties affecting nutrient recovery are understood. In this paper, we present a mathematical model incorporating nutrient budgets for predicting fertiliser requirements, coupled with monitoring of the plant nutrient status to detect nutritional disorders and define nutrient requirements for their correction. The model is based on empirical relationships rather than on a sophisticated mechanistic understanding of nutrient dynamics in the soil-plant system, but is intended for use with a minimum of sitespecific inputs. Sensitivity analysis is also presented to explore which factors most affect the accuracy of model predictions. Finally, the model is applied to a mature orchard and a developing orchard, and generalised fertiliser recommendations are compared with actual fertiliser use and leaf nutrient concentrations to provide a limited assessment of model performance. THE MODEL A schematic model summarising nutrient fluxes to, within and from kiwifruit vines is shown in Fig. 1. Nutrient uptake is determined by biomass production (current season growth), but may be limited by nutrient availability in the soil. For simplicity, total annual uptakes only are considered, so nutrient dynamics within a growing season are ignored. Nutrients taken up may be distributed in perennial (developing vines only), transient and deciduous components. Nutrients within transient components will ultimately be cycled (after pruning) under usual management, while those
73
SE.SON GROW,. I I f
~
l nutrient
pool
Uptake Atmospheric input Fertiiiser inpu|
Soil
Cycling
I~
l
Loss
Fig. 1. Schematicrepresentationof directionalflowsof nutrients within the kiwifruitecosystem. in deciduous organs may be exported from the orchard (in harvested fruit) or cycled i:a senesced plant material. The soil nutrient pool reflects the balance of additions (e.g. fertiliser and atmospheric inputs) and losses (e.g. leaching). Our mathematical model for predicting fertiliser requirements therefore defines n~£rient quantities required to maintain the soil nutrient pool at a level capable of supporting vine growth at desirable levels. Solution of the model require~,~ estimates of the nutrient fluxes described in Fig. 1. For convenience, the annual cycle of growth and nutrient uptake starts after fruit harvest. The symbols,; used hereafter are listed in Table 1. u p t a k e . - Annual nutrient uptake may be considered as the difference in the total nutrient content of the vines from one point in the growing season to the same point of the following season plus the quantity of nutrients lost from the vines during that year. This mass balance may be expressed as the sum of ~autrient quantities in current season growth and in expansion (if any) of the perennial framework minus recycling within the vine from leaves before senescence and from shoots retained at winter pruning. This may be described mathematically for developing vines as Nutrient
Uy = M ( c s g + p f + l t ) y - M ( p f + (sh.f) + R (lf))y-1
(1)
For mature vines without nutrient disorders, there is no net accumulation of nutriments in the perennial components, so annual uptake may be described more simply as U = M ( c s g + lt) - M ( ( s h . f ) + R (If))
(2)
SolulSons to these expressions of uptake depend on the definition of nutrient accumulation in component organs of the vine. As the nutrient concentrations of the various organs of kiwifruit vines at harvest are similar for vines of varying age and productivity (Buwalda and Smith, 1987), nutrient accumulation depends principally on biomass production. For vines aged 3 years or more, Buwalda ( 1987 ) showed an allometric distribution of incremental dry weight amongst component organs. Hence, biomass production can be estimated from
74 TABLE 1 List of symbols Symbol
Description
y
Vine age (years)
Plant components ft Fruit If Leaf sh Shoot It Lateral le Leader st Stem rs Structural root rf Fibrous root csg Current season growth; ft + lf+ sh + rf pf Perennial framework; le + st + rs Crop dimensions VD W Vine dry weight (t ha- 1) FY Estimated fruit yield (fresh weight) (t ha- 1 ) AFY Actual fruit yield (fresh weight) (t h a - l ) BN Bud numbers after winter pruning (m-~) TF Trunk factor (ratio of trunk circumference to allotted canopy area) (cm m -2) RY Relative yield, assuming yield-- 1 at optimum leaf nutrient concentration Nutrient dimensions Uptake (kg ha -1) U Nutrient quantity within plant or its components (kg ha -1) M Nutrient concentration in plant dry weight (g kg -1 ) N Nutrient quantity re-absorbed from vine organ between fruit harvest and senesR cence (kg h a - 1) Cycled nutrients (kg h a - 1) CN Atmospheric nutrient inputs (kg h a - ~) AI NI Nutrient inputs to soil from all sources (kg h a - ' ) Fertiliser requirements (kg h a - 1) FR NB Nutrient balance (deficit or surplus ) within plant (kg ha- i ) Target nutrient concentration (g kg-1 dry weight) TN Constants f k TVDW BB FS FW m g ER a,b,c
Fraction of shoots retained as laterals at winter pruning (0.625) Linear term in regression of vine dry weight against fruit yield (0.59) Treshold vine dry weight below which no fruit production occurs (3.8 t h a - 1) Proportion bud burst (0.40) Number of fruit harvested per shoot ( 3.0 ) Fruit weight at harvest (0.09 kg fruit- 1) Linear term in regression of fruit yield against logarithm of trunk factor (13.9 ) Constant term in regression of fruit yield against trunk factor (23.8) Efficiency of nutrient recovery by plant roots; value specific for each nutrient Quadratic, linear and constant terms in quadratic regression of relative yield against leaf nutrient concentration; values specific for each nutrient
75 a knowledge of fruit yield only, using the linear relationship (r 2= 0.89 ) derived from the data of Buwalda (1987),
VDW =: (FY.k) + T V D W
(3)
While recorded fruit yields may be used to describe vine dry weights and hence nutrient uptakes retrospectively, use of eqns. (1)-(3) to predict nutrient uptake and hence fertiliser requirements requires an advance estimate of fruit yield. A recent survey of kiwifruit vines in major growing areas of New Zealand (MAF, 1984) suggested that fruit yields may be related to parameters of vine size in the previous winter. One such relationship is that between bud number and fru:Ltyield,
FY=BN.BB.FS.FW
(4)
The lind burst proportion, fruit per shoot and fruit weight typically vary less than 20% with climatic and management factors (MAF, 1984), and general values Jbr these parameters may be considered (Table 1 ). Thus, vines with 28 buds m-2 after winter pruning would be expected to have a fruit yield of 30 t ha-1. For developing vines at least, fruit yield may be empirically related to the rat:io of trunk circumference at 0.6 m above the ground to the allotted canopy area (horizontal) per vine,
FY= (ln TF.m) + g
(5)
This linear regression shows a diminishing-returns-type response of fruit yield to the logarithm of trunk size. Vines with a fruit yield of 30 t ha-1 typically have a "trunk factor" of at least 1.6 cm m -2 (Buwalda and Smith, 1987), which is normally achieved 5-8 years after planting. The trunk circumference is more easily iaeasured than bud numbers. However, the relationship between trunk size and fruit yield breaks down as vines mature, as the trunk typically continues to expand while fruit yields reach a plateau (MAF, 1984). For mature vines, the yiei[d history for the previous 5 years should provide a reasonable estimate of fruit yield, assuming constant management. 2,--1
FYy= ~
AFY/5
(6)
.)--6
All these methods of estimating fruit yield ignore possible deleterious effects of the previous vine nutrient status or other cultural factors on growth and productivity, so that existing limitations such as potassium deficiency may be perpetuated. In some situations therefore, "target" rather than predicted fruit yields could be used to generate an estimate of vine dry weight and hence nutrient uptake. Typically kiwifruit vines under competent management should be expected to yield 10, 20 and 25 t ha - 1 at 3, 4 and 5 years of age, respectively, and at least 30 t ha-1 at maturity.
76 Once fruit yield and hence vine dry weight have been estimated, the model can calculate nutrient quantities accumulated in component organs, using reference data for vine nutrient composition, as presented in our previous paper (Smith et al., 1988). Annual nutrient uptake can then be predicted. Fertiliser requirement. - The fertiliser requirement in any year depends on nutrient uptake, the efficiency of nutrient recovery by plant roots, and nonfertiliser nutrient inputs. A major component of non-fertiliser inputs is the quantity of nutrients returned to the soil in cycled plant material, including senesced leaves, sloughed off fibrous roots and pruned shoots and laterals. Following the allometric relationship between fruit yield and the dry weight of component organs of the vines, this quantity may be estimated if the yield history data are available, CNy = M ( l f + r f + It + ( (1 - f ) - s h ) - R (lf))y-1
(7)
Atmospheric inputs to the soil nutrient pool include N fixation by the clover component of the sward beneath the kiwifruit canopy (Steele and Smith, 1988), which is assumed to be constant at all sites, and nutrients in rainfall and irrigation water (Smith et al., 1988). These inputs can be estimated for each orchard from reference to stored data. The model assumes that nutrients in fertiliser, atmospheric inputs and cycled plant material all enter the same pool in the soil, ignoring possible variations in the dynamics of chemical transformations for nutrients from different sources. This assumption should be valid for mature vines where fluxes of nutrients through the soil pool are in equilibrium. The possible absence of such an equilibrium for developing vines is not considered important, as nutrient uptake there normally depends principally on fertiliser inputs if soil nutrient reserves are maintained. The efficiency of nutrient recovery by the plant roots can then be described as ER=U/NI
(8)
Solution of this expression requires definition of all nutrient inputs (including fertiliser), and so must be based on historical data. Long-term nutrient recoveries in typical kiwifruit orchards were estimated in our previous paper (Smith et al., 1988). Those values may be used initially as parameters with constant value at all sites. It is likely that, for any nutrient, the relationship between uptake and nutrient inputs is not constant, as uptake normally shows a diminishing-returns-type of response to nutrient supply (Mengel and Kirkby, 1982). Hence, the efficiency of nutrient recovery will also vary, decreasing as the soil nutrient supply increases. This variation, coupled with expected sitevariability of recovery efficiency, can be accommodated where the model is used repeatedly at any site. The deficit between non-fertiliser inputs and the quantity of nutrients re-
77 quired to support uptake requirements of the vine then represents the fertiliser requirement,
FRy = (Uy/ER) - ( CNy + n I )
(9)
This es':imate of fertiliser requirement accounts only for nutrient removal from the soil in the current season, assuming a steady-state situation for soil nutrient levels, so does not redress existing nutrient imbalances.
Monitoring plant nutrient status. - A plant is essentially an integrator of many complex site (e.g. soil) factors. Reference by the model to an annual leaf analysis for monitoring the plant nutrient status thus checks the success of the fertiliser management, suggested previously, for providing adequate nutrients to the vines. It also partly overcomes the need to account for existing nutrient imbalances, complex site-specific variations in the size of the soil nutrient pools, fertiliser recovery, and uptake-yield relationships. The nutrient concentrations in sampled leaves are compared with reference data (Smith et al., 1987a). Samples may be taken at any stage of the growing season, although nutrient imbalances are probably detected most sensitively about 6 weeks after bud burst (Smith and Clark, 1987). Where the measured concemration of any nutrient in the leaf is outside the acceptable range, the effect on biomass production (current season growth) may be estimated from experimentally derived quadratic regressions between leaf nutrient concentration and vegetative growth for kiwifruit seedlings (G.S. Smith, unpublished results, 1987), RY=aN(lf)2+bN(lf)
+c
(10)
For nutrient deficiencies and excesses, the magnitude of the nutrient balance (deficit or surplus) within the vine may be estimated as
N B = ( 1 - (N(lf) "R Y / T N ( l f ) ) ). U
(11)
This nutrient quantity may be added or subtracted to the estimate of nutrient requirement in the following season. However, this should be considered to be a mininmm quantity for amendment, as the magnitude of the imbalance within the soil pool that resulted in the imbalance within the plant is not considered. SENSIT[VITYANALYSIS The effects of changing each of the major model parameters separately on estimated nitrogen and potassium fertiliser requirements, while the other parameters remain constant, are shown in Table 2. The efficiency of nutrient recovery (ER) was the parameter that most affected estimates of fertiliser requirement. As this efficiency is normally less than 1, any ratio of change will result in a larger proportional effect on the size of the total nutrient pool re-
78 TABLE 2 Effect of changing m a t h e m a t i c a l model parameters separately on estimated nitrogen and potassium requirements for a mature kiwifruit orchard, with a fruit yield (fresh weight) of 30 t h a - 1 Nutrient
Change ratio
P a r a m e t e r estimate FY ~
VDW
N
R
AI
ER
Nitrogen
0.66 0.80 1.00 1.20 1.33 1.50
116 147 192 236 265 303
138 158 192 215 234 258
116 147 192 236 265 303
204 199 192 185 181 175
203 198 192 186 182 177
351 269 192 140 115 88
Potassium
0.66 0.80 1.00 1.20 1.33 1.50
90 110 140 169 188 213
130 134 140 146 149 154
90 110 140 169 188 213
150 144 140 138 131 126
142 141 140 139 138 137
224 190 140 106 90 73
~See Table 1 for explanation of symbols.
quired to sustain uptake and, if other nutrient inputs (cycling, atmospheric) are unaltered, an even larger effect on the estimated nutrient deficit (fertiliser requirement). Changes in the nutrient concentrations of component organs of the vine or in total vine productivity have equal effects on nutrient uptake. Changes in all other parameters, influencing only part of the uptake equation or the nutrient inputs equation, have relatively small effects on the estimated fertiliser requirements. In usual situations, changing the size of one parameter may alter the size of another parameter. For example, the efficiency of nutrient recovery will depend partly on the extent of exploration of the soil by the roots, which in turn will depend on resource allocation to the roots. Nitrogen deficiency should alter the relationship between fruit yield and vine dry weight by altering the root: shoot ratio in favour of root growth (Drew and Saker, 1975), hence increasing the efficiency of nutrient recovery. Similarly, changes in the contribution of atmospheric nutrient inputs may alter root growth, the allometric distribution of dry matter within the vine and hence the efficiency of nutrient recovery. These interactions tend to buffer the magnitude of change in the overall soil-plant system resulting from a change in one component. Hence actual changes in the fertiliser requirement resulting from a change in any parameter are likely to be less than those indicated here. While the sensitivity analysis highlights the relative impact of changing the value of various parameters on estimated fertiliser requirements, it is also im-
79 portant to consider which parameters are presently poorly defined and/or show greatest variability. For example, the average nutrient concentration in component vines at harvest is relatively stable (Smith et al., 1987b) , and in the absence of nutrient disorders should vary little from the values assumed here. Deficiencies or excesses of macronutrients, at least, rarely result in tissue nutrient concentrations for kiwifruit differing more than 50% from those of healthy vines (G.S. Smith, unpublished results, 1987 ). Similarly, the extent of nutrient re-absorption from the leaves between leaf-fall and harvest is also unlikely to vary considerably in the absence of nutritional disorders. There is less certainty about the consistency of the relationship between fruit yield and vine dry weight. The linear regression used here is based largely on data from vines of various ages in one growing district (Buwalda, 1987). Ferguson and Bank ( 1986 ) reported, for a single mature vine with a fruit yield equivalent to 32 t ha-1, a total vine dry weight equivalent to 38 t ha-1; 65% higher than the dry weight that eqn. (3) would estimate. However, current season growth of that vine was not substantially greater than that estimated by the model. As the organs comprising the current season growth collectively represent the major sink for nutrients taken up anually (Smith et al., 1988), this inaccuracy in estimating total vine dry weight may not be of major significance in the subsequent estimates of uptake. The ipredicted fruit yield is a very sensitive parameter within the model, but accuracy in this prediction is sometimes difficult (MAF, 1984). We have considered four options for predicting fruit yield and thus allow subjective selection of one estimate that will drive subsequent equations. The most sensitive parameter in the fertiliser management model, the efficiency of nutrient recovery, is likely to vary considerably with factors such as soil type, rainfall and soil fertility. Repeated use of the model on any orchard will, as already mentioned, improve fertiliser recommendations following generation of site-specific estimates of the efficiency of nutrient recovery. MODELAPPLICATION o r c h a r d . - Estimated fertiliser requirements (from eqn. (9)) for a mature kiwifruit orchard were compared with actual fertiliser use and predicted nutrient uptakes during the period from 10 to 13 years from planting (Table 3). The yield estimate for the first year of this period was that recorded in the previous year, while subsequent yield predictions were based on average yields. Actual yields varied from 22 to 38 t h a - 1, in a biennial bearing pattern, while yields predicted on the basis of yield history declined steadily and, in 3 of 4 years examined, were greater than the actual yields. Predicted nutrient uptakes were broadly proportional to predicted yield, but were tempered by the effects of previous yields (and hence vine sizes) on nutrient reserves within the vine. Predicted uptakes were always high for nitrogen, potassium and calMature'
8O TABLE 3 Comparisons of model predictions of nutrient uptake (U), fertiliser requirement (FR) and actual fertiliser use (FU) on a mature kiwifruit orchard Fruit yield
Year1 U
N
Predicted (t ha -1 )
Actual
41
30
FR FU Year2 U
36
35
FR FU
32
,
Ca
Mg
S
(kg h a - 1)
C1 ,
168 214 78
22 59 21
182 184 140
165 153 1230
28 45 77
28 73 13
77 64 34
155 211 78
20 55 21
166 177 140
150 159 1230
25 45 77
25 68 13
69 53 34
148 189 84
20 52 27
160 163 75
145 139 1320
24 40 82
25 63 24
67 44 111
145 210 91
19 53 23
156 175 75
138 164 120
24 44 82
24 65 15
63 44 111
22
FR FU Year4 U
K
34
FR FU Year3 U
P
38
cium, intermediate for chlorine, and relatively low for phosphorus, magnesium and sulphur. Although not presented, predicted annual uptakes for sodium and the micronutrients were always less than 10 kg ha-1. Actual fertiliser use was considerably less than levels that would have been recommended by the model in every year for nitrogen, phosphorus, potassium and sulphur, and in 2 years for chlorine. In contrast, actual use of calcium (lime) and magnesium fertilisers was higher than the levels that would have been recommended by the model. Leaf nutrient analyses (Table 4) show potassium deficiency in each year, consistent with a low rate of potassium fertiliser application. Phosphorus deficiency was apparent in every second year only (coinciding with higher yields), in spite of low phosphorus fertiliser rates every year. There was no evidence of nitrogen or sulphur deficiency in any year, although actual nitrogen and sulphur fertiliser use was very low. Leaf calcium levels were all within the recommended range, while leaf magnesium concentrations were all very high. Leaf manganese and copper concentrations were generally very high, while leaf zinc was usually within the recommended range. On the other hand, leaf iron con-
81 TABLE 4 Comparison of nutrient concentrations of leaves sampled in February 1 from a mature kiwifruit orchard with recommended concentration ranges Recommended range ~ Macronctrients (g kg -1) N 20-23 P 2.3-2.5 K 20-24 Ca 34-44 Mg 3.7-4.5 S 4.0-5.0 Micronutrients (mg kg -~) Fe 70-95 Mn 120-170 Cu 7-10 Zn 18-30 B 50-60
Year 1
Year 2
Year 3
Year 4
25 2.4 18 43 6.1 6.5
20 2.1 15 41 5.4 5.6
23 2.4 15 48 5.6 7.9
22 2.0 19 38 5.2 4.8
96 240 14 33 41
64 170 11 23 31
75 235 11 18 32
61 154 8 22 46
~Until 1987, February was the recommended time for leaf sampling for nutrient analyses. 2Based on data of Smith et al. (1987a). TABLE 5 Nutrient dynamics and estimated efficiency of nutrient recovery over a 4-year period on a mature kiwifruit orchard
Uptake (kg h a - 1) Fertilise: use (kg h a - 1) Atmospheric inputs (kgha -~ } Cycled nutrients (kg h a - ~) Efficiency of recovery
N
P
K
527
70
572
517
331
92
430
124
1
28
364 0.64
39 0.53
223 0.84
Ca
S
C1
87
88
241
3900
318
65
290
28
16
48
464
76 0.21
73 0.47
190 0.26
485 0.12
Mg
centrations were low in years of high fruit yield, and leaf boron concentrations were low every year. The efficiency of nutrient recovery for this orchard may be estimated, assuming uptake and cycling calculated from a knowledge of actual fruit yield and using historic data for fertiliser and atmospheric nutrient inputs (Table 5). These estimates of recovery are higher than those assumed within the model for nit:cogen, phosphorus, potassium and sulphur (all applied at low rates), similar for chlorine, and lower for calcium and magnesium (applied at high
82
rates). These differences are consistent with the efficiency of nutrient recovery declining as soil fertility increases (Middleton and Smith, 1978) Model estimates of nutrient uptake and fertiliser requirements were compared with actual fertiliser use on a developing orchard, for the period from 3 to 5 years after planting (Table 6). The yield estimate derived from the linear regression between the logarithm of "trunk factor" and fruit yield (eqn. 5) was very similar for the 3-year-old vines, while estimates for the 4- and 5-year old vines were 20-25% less than actual production. Predicted nutrient uptakes for any year reflected the yield estimated for that year as well as the actual yield in the previous year (Table 6 ). Hence, predicted nitrogen uptake to support a fruit yield of 15.5 t ha -1 in Year 3 (following a fruit yield of 2.0 t ha -1 the previous year) was 22% higher than the predicted nitrogen uptake requirement to support a fruit yield of 22.8 t ha-1 in Year 5 (following an actual fruit yield of 24.3 t ha-1 the previous year). Estimated fertiliser requirements responded similarly to yield history. Fertiliser use on this orchard was considerably greater than the levels recommended by the model for phosphorus, potassium, sulphur and chlorine, while nitrogen fertiliser rates were much lower in the first year and subsequently similar to those recommended. No calcium or magnesium was applied during the period of orchard development examined. Leaf nutrient analyses (Table Developing orchard -
TABLE 6 Comparison of model predictions of nutrient uptake (U) and fertiliser requirement (FR) with actual fertiliser use (FU) on a developing kiwifruit orchard Fruit yield
3-year-old U
N
Predicted ( t h a -1 )
Actual
15.51
15.6
FR FU 4-year-old U
19.41
22.81
FU 1 Estimated using eqn. (5).
K
,
Ca
Mg
S
(kg h a - 1)
C1 ,
121 193 100
16 59 212
113 142 188
109 176 0
21 50 0
21 75 233
42 48 188
104 118 100
14 48 212
107 114 188
99 113 0
17 32 0
21 75 233
42 48 188
90 86 100
13 42 212
109 104 188
98 84 0
16 25 0
16 43 233
46 38 188
24.3
FR FU 5-year-old U FR
P
30.6
83 TABLE 7 Comparison of nutrient concentrations of leaves sampled in November for a developing kiwifruit orchard, with recommended concentration ranges Recommended range I
Vine age (years) 3
Macronutrients (g kg- l ) N 25-32 P 4.0-4.8 K 25-33 Ca 15-18 Mg 2.7-3.1 S 4.2-5.3 C1 7-15 Micronutrients (mgkg 1) Fe 90-110 Mn 90-110 Cu 15-18 Zn 30-40 B 40-50
31 4.6 19 15 2.8 5.4 12 144 160 16 29 38
4 28 4.8 20 16 2.6 5.7 10 131 140 19 28 49
5 3O 4.8 22 13 2.7 5.5 16 120 188 14 37 43
1Based cn data of Smith et al. (1987a).
7) show p o t a s s i u m deficiency in e a c h year, in spite of t h e high r a t e s of p o t a s s i u m a p p l i c a t i o n s , a n d m a r g i n a l c o n c e n t r a t i o n s of c a l c i u m a n d m a g n e s i u m . C o n c e n t r a t i o n s of all o t h e r n u t r i e n t s were w i t h i n or a b o v e t h e r e c o m m e n d e d range.
DISCUSSION
T h e m a t h e m a t i c a l model p r e s e n t e d here is a c o n v e n i e n t a n d objective m e t h o d for p r e d i c t i n g fertiliser r e q u i r e m e n t s a n d m o n i t o r i n g p l a n t n u t r i e n t s t a t u s for kiwifr[fit orchards. I n p u t s are simple, so t h a t users ( c o m m e r c i a l growers ) should h a v e little difficulty in u s i n g t h e model. W h i l e t h e o u t p u t h a s n o t b e e n discussed here, t h i s s h o u l d s i m i l a r l y be simple. C u r r e n t l y , 40% of all k i w i f r u i t vines in N e w Z e a l a n d are less t h a n 5 y e a r s old ( S m i t h et al., 1987a), a n d m a j o r n u t r i t i o n a l disorders, p a r t i c u l a r l y p o t a s s i u m deficiency, h a v e b e e n m o s t p r e v a l e n t in y o u n g o r c h a r d s ( S m i t h et al., 1985). H e n c e , use of t h e m o d e l for p r e d i c t i n g fertiliser r e q u i r e m e n t s will at
84 least initially be important for developing as well as mature orchards. Increasing annual fruit yields on such orchards may be difficult to predict. Over-estimating fruit yield is unlikely to result in dangerously high fertiliser rates, but it will be important to avoid underestimating yield and hence limiting yield by nutrient supply. The estimate of fruit yield was clearly an important parameter in the applications of this model to both the mature and developing orchards examined here. Annual fluctuations in fruit yield of the magnitude recorded in the mature orchard are not uncommon (Sale, 1985), and may result at least partly from nutritional disorders. Predictions of fruit yield based on yield history ignore such disorders and their effects on production. Hence, fertiliser recommendations following these predictions may perpetuate existing disorders. It would be prudent, therefore, to tend towards overestimates rather than underestimates of fruit yield. As the model, upon first contact with any orchard, assumes no nutritional disorders, initial fertiliser recommendations refer to macronutrients (nitrogen, phosphorus, potassium, calcium, magnesium, sulphur and chlorine) only. In practice, application of nitrogen as urea or calcium ammonium nitrate, phosphorus as superphosphate and potassium as KC1 will often supply adequate levels of nitrogen, phosphorus, potassium, calcium, sulphur and chlorine even when nitrogen, phosphorus and potassium requirements only are specifically addressed. In addition, regular dressings of agricultural lime should provide more than adequate quantities of calcium. Magnesium requirements, while relatively small, should be addressed regularly, as magnesium deficiency can be a significant disorder of kiwifruit (Clark and Smith, 1985). Micronutrient requirements are usually so small that soil reserves should normally be adequate. Fertiliser recommendations derived from the model therefore ignore micronutrients, except after leaf analysis has established a deficiency. Leaf analysis represents a vital check of the validity of fertiliser recommendations and detection of any need to correct nutritional disorders. This check also reduces the requirement to account precisely for all nutrient movements within the kiwifruit ecosystem. For the mature orchard examined here, the absence of any indication of nitrogen deficiency, in spite of nitrogen fertiliser rates much lower than those recommended by the model, could suggest that nitrogen recovery by the plant roots was very efficient or that nitrogen reserves in the soil, not considered within the model, were large. More information is clearly required on such aspects of nitrogen nutrition of kiwifruit. For the mature orchard, phosphorus and potassium fertiliser rates were obviously inadequate. However, potassium deficiency also occured within the developing orchard in spite of relatively high rates of potassium fertiliser, possibly as a consequence of initial soil potassium deficiencies. A strength of the model is that leaf analysis detects these anomalies and the need for corrective fertiliser dressings. However, the incidence of potassium deficiency in both these or-
85
chards further highlights the importance of this disorder for kiwifruit (Smith et al., 1985 ). It should also be noted that the potassium budget used here was based o:~ detailed data from a single orchard only (Buwalda and Smith, 1987 ), which was probably potassium-deficient. Hence potassium fertiliser requirements raay actually be higher than those presented here, and this may explain the incidence of potassium deficiency even where fertiliser rates were apparently adequate. While the efficiencies of nutrient recovery assumed in the model (Smith et al., 1988) are realistic when compared to those of other crops (Middleton and Smith, 1978; Haynes and Goh, 1980), they clearly varied from those calculated for the mature and developing orchards examined here. These differences can be attributed partly to fertiliser rates that were inadequate or excessive, resulting in higher and lower recoveries, respectively. The model's principal function is to describe external nutrient requirements to maintain the nutrient balance in the soil-plant system. The reliability of estimates of fertiliser requirement where nutrient deficiencies or excesses exist will depend strongly on the !Lmpactof such nutrient imbalances on the efficiency of nutrient recovery. Site-specific estimates of the efficiency of nutrient recovery may be obtained :~romthe data-base built up after repeated use of this model in situations where )~utrient deficiencies and excesses are not present and where fertiliser rates have generally been appropriate. Nevertheless, detection and estimation of nutrient deficiencies and excesses within the vine after leaf analysis will enable site-specific refinements of the fertiliser programme, which should largely overcome the impact of variable soil physical and chemical properties on model efficacy. The mathematical model presented here is now in commercial use in the New Zealand kiwifruit industry, as the basis of a kiwifruit nutrition management service. ACKNCWLEDGEMENTS
We are grateful to the New Zealand Kiwifruit Authority for financial support and to Bill Baldwin for use of fertiliser and yield records and leaf analysis data.
REFERENCES Barnes, A., Greenwood, D.J. and Cleaver, T.J., 1976. A dynamic model for the effects of potassium and nitrogen fertilisers on the growth and nutrient uptake of crops. J. Agric. Sci., 86: 225-244. Buwalda, J.G., 1987. Growth physiology of kiwifruit. Proc. Ruakura Hortic Conf., Kiwifruit, pp. 14-17. Buwalda, J.G. and Smith, G.S., 1987. Dry matter and nutrient accumulation and partitioning in deve::oping kiwifruit vines. Tree Physiol., 3: 295-307.
86 Clark, C.J. and Smith, G.S., 1985. Magnesium deficiency reduces fruit numbers. N.Z. Kiwifruit, Oct. 1985, p. 19. Drew, M.C. and Saker, L.R., 1975. Nutrient supply and the growth of the seminal root system in barley. II. Localised compensatory increases in lateral root growth and rates of nitrate uptake. J. Exp. Bot., 26: 79-90. Ferguson, A.R. and Bank, R.J., 1986. The great DSIR vine demolition derby. N.Z. Kiwifruit, March 1986, p. 25. Haynes, R.J. and Goh, K.M., 1980. Distribution and budget of nutrients in a commercial apple orchard. Plant Soil, 56: 445-457. MAF, 1984. Kiwifruit Vine Monitoring. Ministry of Agriculture and Fisheries Occasional Publication, 26 pp. MAF, 1987. Monitoring Report, Hamilton Region. Ministry of Agriculture and Fisheries Occasional Publication, 38 pp. Mengel, K. and Kirkby, E.A., 1982. Principles of Plant Nutrition. International Potash Institute, Bern, 655 pp. Middleton, K.R. and Smith, G.S., 1978. The concept of a climax in relation to the fertiliser input of a pastoral ecosystem. Plant Soil, 50: 595-614. Sale, P.R., 1985. Kiwifruit Culture. 2nd revised edition. Government Printer, Wellington, 96 pp. Smith, G.S. and Clark, C.J., 1987. Plant analysis - an essential management tool. Proc. Ruakura Hortic. Conf., Kiwifruit, pp. 7-9. Smith, G.S., Clark, C.J. and Buwalda, J.G., 1985. Potassium deficiency of kiwifruit, Proc. Ruakura Hortic. Conf., Kiwifruit, pp. 13-16. Smith, G.S., Asher, C.J. and Clark, C.J., 1987a. Kiwifruit Nutrition, Diagnosis of Nutritional Disorders. 2nd revised edition. Agress Communications, Wellington, 60 pp. Smith, G.S., Clark, C.J. and Henderson, H.V., 1987b. Seasonal accumulation of mineral nutrients by kiwifruit. I. Leaves. New Phytol., 106: 81-100. Smith, G.S., Buwalda, J.G. and Clark, C.J., 1988. Nutrient dynamics of a kiwifruit ecosystem. Scientia Hortic., 37:in press. Steele, K.W. and Smith, G.S., 1988. Clover makes a small contribution. N.Z. Kiwifruit, Feb. 1988, p. 19. Thornley, J.H.M., 1978. Crop response to fertilizers. Ann. Bot., 42: 817-826.