D. Zoebl Agriculture, Ecosystems and Environment 79 2000 233–244 235
increasing rate of concentrate feeds the production without concentrates has value b at x=0.
Function -2: I Crop production with irrigation in a
desert area. II Pork and egg output in the bio-industry at an increasing rate of feeds the maintenance feed
being mainly responsible for the ca intercept. In this graph, there is no place for diminishing
returns to increasing inputs. In scientific trials and agricultural practice, diminishing returns will invari-
ably occur as soon as inputs can no longer be applied or taken up by animals in balanced rations, or where
growth factors such as water or radiation become limiting Janssen and Guiking, 1990. However, the
following examples will be shown to be within the trajectory where balanced or counterbalanced bound-
ary conditions reign.
3. Four cases of input use efficiency, and the virtual point Q
The unsophisticated mathematical expressions as given lie at the core of most production functions in
agriculture and other ecosystems, whether in the nat- ural or the human realm. Their nature may remain ob-
scure, however, because agricultural research results or statistical tables are often presented in a trajectory
beyond the intercept values. Such a presentation can be inevitable, because these intercepts are often ob-
tained by extrapolation beyond practical reality. More often than not, paradoxical, or even conflicting views
are the result, as will be shown.
3.1. Nitrogen use efficiency in leaf canopies Nitrogen is essential for the photosynthetic assim-
ilation of plants. Leaf nitrogen content per unit area, therefore, often reflects the potential for photosyn-
thetic leaf assimilation per unit area Sinclair and Horie, 1989. The ratio between these physiological
characteristics is a case of nitrogen use efficiency, an important growth parameter Lüttge, 1997. Plants
and plant parts have long been known to have the plasticity of adapting their photosynthetic potential in
a functional way. Givnish 1988 considers that leaf and canopy traits can only be understood in terms of
their effect on whole-plant carbon gain, not on leaf level assimilation alone. To use the phraseology of
Field 1988, whose work on N use efficiency in Piper spp. is extensively cited by Lüttge, the following
general mechanism is now ‘conceptually reasonable’. Where growth conditions are expected to be good,
single leaves invest heavily in N-content and photo- synthetic capacity at a certain ontogenetic stage. With
favourable growth conditions, these investments are paid for. However, where these optimal conditions
are not met, assimilation and N use efficiency would have been better with lower N contents in leaf tissue.
This low level of nitrogen can be realized by a mod- erate investment during the period of leaf formation
Field, 1988, or by a retranslocation in senescent or shade leaves Givnish, 1988. Therefore, early crop
simulation models such as ELCROS de Wit et al., 1970 had only limited predictive value, because they
were based on rigid single leaf assimilation functions Zoebl, 1972.
Lüttge 1997 noticed that the curves representing the N use efficiency of single leaves of some Ama-
zonian forest species, measured at a set of ecological conditions, often do not appear to extrapolate through
the origin, thus showing reduced N use efficiency at the lower N levels. Concurrently, increased efficiency
occurs at the higher levels, and this appears to apply especially where intercepts, thus N levels, are high,
as in plants grown in habitats with high light intensi- ties or resource acquisition Lüttge, 1997, or in leaves
with persistent photosynthetic activity Field, 1988, Fig. 2. Such a steering of the photosynthetic capac-
ity by way of adaptive N distribution in plants may be seen as a series of a Type-2 pattern of input–output
relations, although with variable a- and c-coefficients. The model is subject to the rule that input–output ef-
ficiency often depends on the investments in capacity to perform. It should still be noted that the physiolog-
ical mechanism as described is not the only strategy for plants or plant parts to maximize their competitive
ability or biomass accumulation. Thus, the described pattern is not unique.
3.2. Nitrogen use efficiency in Dutch dairy farms van der Meer 1982 studied nitrogen balances of
Dutch dairy farms with intensive and extensive man- agement. He found the efficiency of N utilization on
the extensive farm to be much better than on the in- tensive ones, with apparent recoveries of 34 and 16,
236 D. Zoebl Agriculture, Ecosystems and Environment 79 2000 233–244
Fig. 2. Correlation between photosynthetic capacity and nitrogen levels in leaves of Piper hispidum and Piper auritum. The persistent leaves of P. hispidum appear to invest more heavily in N-content per unit area than leaves of P. auritum, shedding its leaves more easily. Original
data from Field 1988, with added drawn lines range in which measurements were obtained and extended dashed lines extrapolations by Lüttge; individual observations are deleted.
respectively Table 1. de Wit 1992 adapted other, similar figures from van der Meer on the gradual in-
tensification of dairying in the Netherlands Fig. 3, but reached an opposite conclusion. He argued that
the efficiency of N use did not decrease over time, in spite of the dramatic increase of N inputs during
those years. The paradox may easily be explained by
Table 1 Nitrogen balances kg Nhayear of dairy farms in 1975–1976 in the Netherlands with intensive and extensive management van der Meer,
1982 Intensive
Extensive Nitrogen input
: Fertiliser
383 –
Biological fixation –
65 Purchased feeds 5389 kg DM
127 870 kg DM
24 Precipitation
23 23
Total 533
112 Nitrogen output
: Milk 13511 kgha per year
72 5867 kghayear
31 Liveweight 468 kgha per year
12 250 kghayear
7 Total
84 38
Nitrogen not accounted for 449
74 N-outputinput ratio
a
84533=0.16 38112=0.34
a
The N-outputinput ratio is additional.
the response curve Type-1. Fig. 3 shows that N use efficiency has not decreased from 1965 to 1985. The
marginal increases from N inputs in the form of fer- tilizer and concentrates were as high in the 1980s as
they were in the 1960s, in spite of substantially higher inputs. The high efficiency as cited by van der Meer
on the extensive farm is shadow rather than substance.
D. Zoebl Agriculture, Ecosystems and Environment 79 2000 233–244 237
Fig. 3. Input–output relations of nitrogen in Dutch dairying from 1965 to 1985. The apparent output per unit input seems to de-
crease at increasing input rates when the contribution of soil-N is not deducted, but the marginal responses to external inputs are
constant adapted from van der Meer, in de Wit, 1992.
In low input systems, a larger part of the output arises from N supply from precipitation, biological N fixa-
tion, N mineralisation or other natural processes with no monetary expenditures involved. The marginal in-
creases remain constant, however, all along the time trajectory. Thus, the large differences quoted by van
der Meer between extensive and intensive, or in inten- sifying management systems, are mainly illusory.
A further analysis of the remarkable constancy of the marginal increases focuses on the changing ratio
of fertilizer-Nconcentrate-N during the time span. In the beginning, total N input contained relatively
more fertilizer, at the end more concentrates per ha, partly via a higher dairypasture density van der
Meer, 1982. Thus, diminishing returns as occurring in N-fertilizer dressings at increasing rates could have
been more or less counterbalanced by the increased gain in efficiency from a greater input in the form of
concentrates, because the N use efficiency of balanced feeds is higher than that of the two-step conversion of
fertilizer-N to grass to milk.
3.3. Water use efficiency in alfalfa Another interesting case of input–output relations
subject to a variable interpretation of field figures is an experiment on irrigated alfalfa in Oakes, North
Dakota, by Bauder and Bauer 1978. When compar- ing the field water use of this crop at four irrigation
rates, Huibers and Stroosnijder 1992 state that it could easily be concluded that the efficiency increases
with increasing rates: apparently, less water is needed per kg of forage at the higher rates. However, again,
this is only seemingly so. In this case, input–output relation Type-2 applies. The ca intercept Fig. 4 rep-
resents mainly non-productive water soil evaporation, unavailable soil water and other losses to the crop.
This amount appears to be constant, irrespective of the treatments Huibers and Stroosnijder, 1992. Beyond
this intercept, the marginal water use efficiency ap- pears to be constant over the trajectory of treatments.
As in the section on Dutch dairying, it seems ap- propriate to further analyse and speculate on Huibers’
and Stroosnijder’s interpretation. The linear extrapo- lation and the 100 mm intercept Fig. 4 may be seen
to express the authors’ assumption on the crop wa- ter use efficiency, as is also, and more explicitly, pro-
nounced by Richards 1991 in his hypothetical linear water use functions. An S-type response curve, how-
ever, is more likely to occur, as is sketched in the alternative dashed lines of Fig. 4. At the lowest use
levels, responses increase; at supra-optimal rates, they gradually decrease Fig. 4. Because of lack of field
data in the specific trajectories, this cannot be proved, but it is likely because of inefficient water use through
relatively high evaporation losses at the lowest water use levels. However, even if confirmed by field trials
in trajectories without practical relevance, this does not invalidate the simple, linear response curve as pro-
posed by Huibers and Stroosnijder. Obviously, these authors had the crop water use component of the pro-
duction function in mind, not the overall field response to irrigation and seasonal rain combined.
3.4. The critical point Q: unrealistic but important Small amounts of water, nutrients and crop protec-
tion agents have been cited as not being effective un- til a certain critical level has been reached de Wit,
1977. The initial rates of investments in physical or economic terms can be expressed by point Q on a
Function-2 type of input–output relation Fig. 1. It shows the inputs needed before any yield or other
useful output is obtained. This point Q is a virtual
238 D. Zoebl Agriculture, Ecosystems and Environment 79 2000 233–244
Fig. 4. Yield responses of alfalfa to irrigation treatment in N. Dakota. Drawn straight line: response as envisioned by Huibers and Stroosnijder. Dashed curved lines: alternative response as suggested by M. Smith. Water use efficiency appears to increase when the evaporation and
other water losses the intercepts are not deducted. Marginal responses in both cases are, however, constant in the trajectory of treatments.
value, because no farmer will ever consider applying inputs to a level at which he cannot harvest something,
as was already long ago expressed by the husbandry economist Aereboe 1923. Even scientific trials with
input levels where outputs would be about zero are uncommon, with the annotation that this applies more
to field crops than to livestock, where preservation at maintenance costs might make sense. Under the con-
ditions of the above cited alfalfa trial, the water use for zero return appears to be 100 mm per crop season in
Huibers’ and Stroosnijder’s linear response function.
Even if virtual, this point Q has practical mean- ing. In analogy with zootechnical calculus for feed
conversion van Es, 1972, it could be maintained that the ‘maintenance’ application consists of the
non-productive water because of evaporation, dissipa- tion and unavailable sorption that may occur before
water is taken up and transpired by the crop as part of the production process. In the animal feed analogy, the
maintenance feed cannot be simply measured. Some authors even state that a distinction in maintenance
and productive feed is completely artificial van Es, 1972. Whether for convenience or otherwise, where
quantification of this maintenance feed is aimed at, it has to be approximated by extrapolation of the per-
formances of animals with varying production levels towards the zero production level van Es, 1972.
As is the case in animal physiology, the portman- teau term evapo-transpiration from crop physiology
clearly indicates that evaporation and transpiration cannot easily be separated. Nevertheless, knowledge
and best estimates of the virtual amount of water for evaporation and other losses to the crop is important
for technical and economical evaluation of irrigation and dry farming systems.
3.5. Decreasing and increasing returns The concept of decreasing returns in agricultural
production has intrigued agriculturists since the phe- nomenon was first expressed by Turgot in the 18th
century. Arthur 1990 maintains that, in industry, the
D. Zoebl Agriculture, Ecosystems and Environment 79 2000 233–244 239
principle of increasing returns applies as often as that of decreasing returns. In branches of industry where
large initial investments have to be made, such as in the airplane and software industry, marginal costs per
unit produce may fall dramatically as outputs or mar- ket shares increase. This applies the more so, where
so called lock-in processes or pioneer advantages occur Arthur, 1990, as is also noted by software
manufacturer Bill Gates 1995. Consequently, the producer’s margins improve: increasing returns of
input–output function-2
I
apply where costs are cal- culated as combined fixed and variable expenditures
Fig. 5, the accentuated form is chosen for these com- mercial input–output relations where no soils or other
such natural resources are involved.
Modern agriculture is increasingly an industrial pro- cess, with a decreasing share of natural resource ex-
ploitation; hence, the concept of increasing returns also applies to agriculture. de Wit 1979 found in-
creasing returns even in practices carried out by hand labour such as in land amelioration or irrigation. So,
also in non-industrial, low-input production systems, increasing returns to labour inputs may apply at in-
creasing yield levels, where yield is plotted against the combined efforts of reclamation and seasonal field
operations. De Wit’s statement seems to contradict
Fig. 5. Input–output relations at varying shares of fixed inputs. At increasing outputs, increasing returns to combined fixed and vari-
able inputs applies. The effect is gradually reduced at decreasing fixed inputs. Where fixed inputs are zero, constant returns to vari-
able inputs applies Function-3. For an explanation of Function-2
I
and the one in-between, see Section 3.5.
Arthur’s insight that agriculture is for the most part subject to diminishing returns. The paradox can be re-
solved by focusing on the pattern of the single func- tions of the production complex.
Fig. 5 also shows function Type-3, the response curve where fixed costs are zero. In this function, re-
turns to variable inputs are constant. An example is the wage of a farmhand with increasing input of work-
days. Finally, the figure reveals that gain in output at increasing labour inputs is almost constant where
fixed investments are very small or negligible, such as in weeding a crop by hoe by the farmer or his family
members.
4. Some tentative conclusions
