Agriculture, Ecosystems and Environment 80 2000 71–85
On crop production and the balance of available resources
Ramun M. Kho
∗
International Centre for Research in Agroforestry, P.O. Box 30677, Nairobi, Kenya Received 11 March 1999; received in revised form 22 November 1999; accepted 23 January 2000
Abstract
One of the main insights achieved in the early days of agricultural science is that each environment has a specific balance of resources, which is available to the crop. This balance determines crop production, the effect of resource addition and the effect
of agronomic operations. However, attempts to quantify this balance are scarce. It is normally taken into account indirectly by a general description of soil, climate, topography, land use history, etc. This paper advocates quantifying this balance by
quantification of the degree of limitation of resources. A coefficient between zero and one is developed which implements this idea. The paper shows that under a moderate assumption, the sum of the limitation coefficients of all resources equals
one. This makes the deduction possible of non-limiting resources. The original binary concept of limitation can be regarded as a special case of this coefficient. The paper shows that crop response to addition of a resource can be viewed as the product
of: the limitation coefficient, the use efficiency, and the amount of the dose. General crop production principles as the law of diminishing returns and the law of the optimum can be interpreted easily this way. Methods to estimate experimentally
the limitation coefficients are discussed. The methods are illustrated by estimating the degree of limitation of nitrogen and phosphorus in southwest Niger. These two elements account for more than 70 of the total limitation of carbon dioxide,
radiation, water, and all nutrients, which is in agreement with other scientists in this region who indicate these two elements as the ‘principal’ limiting factors. © 2000 Elsevier Science B.V. All rights reserved.
Keywords: Agriculture; Concepts; Agroecosystem characterisation; Production ecology; Methods; Resource limitation
1. Introduction
Until the Second World War, much agronomic research was directed towards the search for laws
governing the relation between input of resources and crop yields De Wit, 1994.
Almost one century ago, Blackman 1905 formu- lated the ‘law of limiting factors’ which states that
crop production shows only a response in a propor-
∗
Present address: Agrotechnological Research Institute ATO, P.O. Box 17, 6700 AA Wageningen, The Netherlands. Tel.:
+ 31-317-475311; fax: +31-317-475347..
E-mail address: r.m.khoato.wag-ur.nl R.M. Kho
tional relation to modifications in the availability of only one, the limiting, factor. If another factor be-
comes limiting, this imposes a plateau on the response curve where a modification of the first factor does not
affect crop production any longer Fig. 1. Half a cen- tury earlier Von Liebig 1855 had already found this
concept in slightly different terms as the ‘law of the minimum’. The validity of the concept is confirmed by
many experiments in the sense that the response curve shows diminishing returns and arrives at a plateau as
the availability of a resource increases all other fac- tors constant. Rabinowitch 1951 shows that the un-
derlying kinetic view must be that plant growth is a sequence of processes, whereby the process on which
0167-880900 – see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 8 8 0 9 0 0 0 0 1 3 5 - 3
72 R.M. Kho Agriculture, Ecosystems and Environment 80 2000 71–85
Fig. 1. Response curves according to Blackman 1905 with high and low levels of a second resource.
the limiting factor acts determines the overall flow rate. This slowest process creates so a ‘bottleneck’ for the
overall process. Originally, the concept is qualitative binary: a factor is limiting or not, and in each specific
environment there can be only one limiting factor.
However, in most environments the crop responds to increased availability of several factors. Liebscher
1895 formulated the ‘law of the optimum’, which states that plants use more efficiently the production
factor which is in minimum supply, the closer other production factors are to their optimum. In other
words, the initial slope of the response curve increases, if the availabilities of the other limiting resources
increase see Fig. 2. De Wit 1992 has shown that the law of the optimum is confirmed by numerous ex-
Fig. 2. Response curves according to Liebscher 1895 with high and low levels of a second resource.
periments in the past century. The underlying kinetic view is that plant growth is not a sequence of pro-
cesses whereby each process is determined by only one factor. It is a sequence of processes whereby each
process is determined by two or more factors which can also influence other processes and the plateau
Rabinowitch, 1951. Crop production is still deter- mined by the slowest process, but the crop does not
respond to a modification in the availability of only one, but of several factors. In such circumstances, it
may be better to think and speak in terms of multiple limiting factors, each with its own degree of limita-
tion, instead of limitation as a binary variable. This is widely recognised as appears from the use of terms as
‘major limitations’ Sanchez, 1995 or ‘principal lim- iting factor’ Shetty et al., 1995. Use of these terms
implies the existence of ‘minor limitations’ and ‘sec- ondary limiting factors’. The original binary concept
of limiting factors has been evolved into a quantitative concept in which the more a factor is in short supply,
the bigger its influence on crop production.
One of the main lessons learned from the early days of agricultural science is that each environment
has a specific balance of resources that is available to the crop. This balance determines crop production,
the effect of resource addition and the effect of agro- nomic operations. However, attempts to quantify this
balance are scarce. Jones and Lynn 1994 proposed a ‘relative resource limitation’ see Section 2.2. Nijland
and Schouls 1997 discuss the concept of ’ecological subspaces’ for interpretation of the Michaelis–Menten
growth model see Section 2.4. The balance of available resources is normally taken into account
indirectly by a general description of soil, climate, to- pography, land use history, etc. This makes it difficult
to extrapolate and to be aware of the limited scope of experiments and the resulting recommendations.
After the Second World War, agricultural science highlighted increasingly the physical, chemical and
biological processes that govern the growth of crops De Wit, 1994. The new paradigm studied the growth
rate in, e.g. g dm m
− 2
per day as a function of re- source capture e.g. MJ m
− 2
for light, mm for water, and g m
− 2
for nutrients. Seasonal biomass produc- tion g m
− 2
can than be found by integration. For example, if the resource is light, the total biomass
accumulated over a growing season W can be found by Azam-Ali et al., 1994:
R.M. Kho Agriculture, Ecosystems and Environment 80 2000 71–85 73
W = ε
s
Z fS
δt where f is the fraction of incident radiation intercepted
by the crop canopy, S is the daily incident radiation
MJ m
− 2
, and ε
s
is the conversion efficiency of solar radiation e.g. in g dm MJ
− 1
. If the resource is water, seasonal biomass produc-
tion W can be expressed as Ong et al., 1996: W = ε
w
X E
t
where P
E
t
is the cumulative transpiration mm H
2
O and where ε
w
is the conversion efficiency of water g dm mm
− 1
H
2
O transpired. The representation of light capture by an integral and of water capture by
a sum is only a matter of convention. In both cases the process runs in continuous time integral but is
usually calculated in discrete steps sum. The con- version efficiencies are mostly considered species spe-
cific and conservative, which explains why they are kept outside the integral. Concerning water, instead of
the conversion efficiency itself, its product with sat- uration vapour pressure deficit is also considered the
species specific constant Cooper et al., 1987. Mon- teith 1994 describes the principles of resource cap-
ture by crop stands. The last decades, many research efforts have been devoted to the measurement and
modelling of resource captures and to the estimation of conversion efficiencies see Hanks and Ritchie, 1991;
Monteith et al., 1994.
In line with De Wit 1992, 1994, this paper contin- ues with the old paradigm of before the Second World
War. It aims to quantify the balance of available re- sources in the environment, make it measurable, and
explore some relationships with the old and the con- temporary paradigm.
2. Quantifying the balance of available resources
