Plants and Population: is there time?
5-6 December 1998
Beckman Center of the National Academy of Sciences, UC Irvine
Limits to Crop Yield
Thomas R. Sinclair
USDA-ARS, Agronomy Department
University of Florida
Gainesville, FL 32611-0965
In recent years crop yield increases have slowed dramatically in both less-developed and developed countries worldwide (Alexandratos, 1995; Calderini and Slafer, 1998). This worrisome situation has resulted in a call for large increases in agricultural research. An essential feature of such research is improvement in the capture of input resources that are needed for growth of the plant and production of grain. These resources include (a) solar radiation to provide the energy for accumulation of plant dry weight, (b) water to allow CO2 uptake by leaves, and (c) nitrogen to form the essential proteins and nucleic acids of the plant. Importantly, quantitative functions can be derived to express the limitations of each of these input resources on maximum crop yield (Sinclair, 1997).
In this paper, functions are presented to illustrate the limits imposed by either solar radiation, water, or nitrogen on crop yields under field conditions. While each of the functions that are presented are based on optimistic assumptions, they do illustrate that there are real limits to increasing yields. Importantly, these yield limits have already been attained under experimental conditions. Identifying the limits on yields helps to define those situations with the greatest opportunity for yield increase and to focus efforts on those factors that are important in constraining current yields.
Virtually all the energy used by crop plants to grow is derived from sunlight, or more precisely, solar radiation. Therefore, the amount of solar radiation intercepted by crop leaves through a growing season sets the ultimate limit on yield. Since most crops are annuals that grow from seeds each year, leaves must develop to produce the large surface area required to intercept the solar radiation. To intercept 90% of the solar radiation, for example, the combined area of the crop leaves (one-side) must be four times the land area on which the crop is growing.
An important factor in crop yield increases has been new technology to achieve high total area of the leaves early in the growing season. For example, maize was traditionally sown in row widths greater than 1 m so that work-horses could readily pass down the rows. Mechanical cultivation removed this limitation and row widths have been decreased to 75 cm or less, which in itself resulted in more leaves and a more even distribution in leaf display across the field. Breeding of plant cultivars that withstood more crowded conditions also allowed more plants per unit area to be sown and further increased crop leaf area.
Plants have evolved an especially efficient system of photochemistry to use the absorbed solar radiation in the assimilation of CO2. As a result, the amount of CO2 assimilated per unit of light absorbed under low light levels in leaves is high (approximately 14 to 20 mole, i.e. quanta, light per mole assimilated CO2). Under high light levels, however, the CO2 supply inside the leaf is decreased and the efficiency in using the absorbed light energy is consequently decreased. Nevertheless, the CO2 assimilation capacity of the entire leaf canopy is still closely linked to the photosynthetic capacity of the individual leaves. As it turns out, when the photosynthetic production of all the leaves is summed, the amount of CO2 assimilated by the total crop canopy is nearly stable per unit of intercepted solar radiation (Sinclair and Muchow, 1999). This ratio, called radiation use efficiency (RUE), is measured over a period of time as the crop weight increase divided by the amount of solar radiation intercepted during that period.
Both theoretical analyses and experimental results have identified two major sources of variation in RUE among species (Sinclair and Muchow, 1999). One source of variation results because some plant species have evolved a preliminary CO2 concentrating pathway inside leaves using 4-carbon organic acids (C4) that allow somewhat greater CO2 assimilation rates than in other species. A second source of variation is the difference among crop species in the biochemical composition of the plant products. Those species that produce high energy components, i.e., lipids and proteins, have lower RUE than those that accumulate carbohydrates. Consequently, soybean, which has a high amount of lipid and protein and does not have the C4 pathway, has a maximum RUE of only about 1.1 g accumulated plant mass per megajoule (MJ) of intercepted solar radiation energy. Rice also does not have the C4 pathway but it produces a large fraction of carbohydrate, so its maximum RUE is greater at about 1.4 g MJS1. Maize produces high levels of carbohydrate and also has the C4 photosynthetic pathway, giving a maximum RUE of about 1.7 g MJS1.
From estimates of total intercepted solar radiation and RUE, it is possible to calculate the maximum crop weight that can be accumulated during a growing season. Grain yield can then be readily calculated using the ratio of crop grain weight to total accumulated crop weight. This ratio defines the harvest index (H) and indicates the fraction of the total plant weight that can be harvested as grain. The value of H for high-yielding varieties is nearly constant over a wide range of conditions for any particular crop variety. The stability of H was important in the Green Revolution because high-yielding varieties could be developed by increasing H so that more grain could be harvested even though the total weight of the crop was not increased. Before the Green Revolution, H of many crops was 0.3 or less, and now it has been increased to about 0.5 in many cases (Sinclair, 1998). Increasing crop yields by increasing H has been nearly fully exploited, however, because some plant weight must always be assigned to roots, stems, and leaves simply to grow the crop. It is estimated that high-yielding crops are unlikely to have H greater than about 0.6 (Austin, 1994).
It is possible to calculate the maximum grain yield (Y) of various crop species by multiplying H, maximum RUE for that species, and the summation of daily intercepted solar radiation (I) over the duration of the cropping season (d). That is,
Y = H * RUE * _ I . 
n = 0
Assuming maximum RUE as discussed previously and further progress in H leading to a value of 0.55 in high-yielding cultivars, maximum yields for soybean, rice, and maize can be calculated as a function of the total intercepted solar radiation during the cropping season. Realistic values of seasonal intercepted solar radiation for many cropping situations are likely to be about 1200 to 1400 MJ. At 1400 MJ of seasonal intercepted solar radiation, maximum crop dry-weight yields are calculated to be 13, 11, and 8 t haS1 for maize, rice, and soybean, respectively. These are high yields, to be sure, but not exceptionally large compared to experimental yields. That is, the genetics and physiology of current crop varieties have been shown to be fully adequate to achieve maximum yields possible in view of the energy input limitation imposed by intercepted solar radiation.
Water has been recognized for centuries as critical to crop production. Cropping in the ancient world was often organized simply to ensure water availability. The need for large amounts of water in crop production results from the fact that CO2, which is the basic input resource for photosynthesis, must diffuse from the atmosphere through small pores in leaf surfaces, called stomata, to the interior of the leaf. The opening of the stomata allows evaporated water to diffuse out of the leaf. Hence, there is a close physical relationship between the amount of CO2 that diffuses into leaves and the amount of water lost from leaves because both of these gases diffuse through the same stomatal opening. Considerable evidence shows a close correlation between the accumulation of plant weight (W) and the amount of water evaporated from leaves (i.e., transpiration, T) (Tanner and Sinclair, 1983). There are two variables that fully define the correlation between W and T: k, which is a species-dependent water-use constant, and atmospheric vapor pressure deficit (VPD), which defines the moisture content of the atmosphere.
W = T ( k / VPD 
The value of k is now known to be dependent on some of the same factors that influence RUE (Tanner and Sinclair, 1983). That is, k is high for those species with the C4 photosynthetic pathway and high carbohydrate plant material. Maximum values for k have been estimated both by theoretical derivation and experimental results. These maximum values of k for maize are about 11 pascal (Pa), for rice about 6 Pa, and for soybean about 5 Pa.
The value of VPD reflects the environment in which the crop is being grown with low values for humid regions and high values for more arid regions. One approach for decreasing the value of VPD is to grow the crop during the cooler months when VPD is low. Winter growth of some cereal crops is a good example of a shift of the cropping season so as to minimize VPD.
Since Y = H ( W, substitution using Equation  results in,
Y = H ( T ( k / VPD 
Equation  can be used directly to calculate maximum crop yields as a function of T. VPD was assumed to be approximately 2.0 kPa, which is representative of many temperate regions where crops are grown. Under many circumstances, no more than about 500 mm (mm3 of water per mm2 of land surface area) of water may be available for T. In this case, the estimates of maximum crop dry-weight yields based on water availability are 15 t haS1 for maize, 8 t haS1 for rice, and 7 t haS1 for soybean. Even with this high level of water availability for T, maximum yield levels for rice and soybean are less than calculated based on solar radiation.
In a number of areas of restricted rainfall, a crop may only have available sufficient water for a T of 200 mm or less. In the case of 200 mm of T, maximum crop yields are restricted to 6 t haS1 for maize, 3.5 t haS1 for rice, and 3 t haS1 for soybean. Also, it is assumed that this water is available uniformly through the growing season. Variable patterns of rainfall can result in yields well below these limits, even though the total amount of water received is unchanged.
It is important to remember that the above estimates of maximum yields are based only on the amount of water to be used in transpiration. The total water supplied to a field crop must be substantially greater than that used in transpiration because water is also consumed in surface runoff, deep percolation in the soil, and soil evaporation (Sinclair, 1999). Generally, no more than about 60% of the total water received on fields in rainfed cropping systems is available for transpiration. Since the fraction of water used in transpiration can be much lower than 60%, minimization of the other losses of rainfall may offer important opportunities for increasing crop yields. Soil surface mulches and the retention of crop residues on the soil both help to increase the fraction of rainfall that is available for transpiration.
In irrigated systems, water is lost in leakage and evaporation from irrigation canals, and during water application in the field as a result of evaporation and deep percolation in the soil. Increased efficiency in irrigation systems is an especially important method for increasing the total crop harvest per unit of available water. Consequently, in those environments dependent on irrigation the yield per land area may not necessarily be increased by improved irrigation efficiency but the total area that might be irrigated could be increased with better use of the water resource.
Rice is a special case in estimating the water limitation. For those rice crops grown in flooded paddies, continuously flooded conditions ensure that there is no water limitation. Nevertheless, Equation  indicates that large amounts of water must be supplied to paddies for high rice yields. For rice grown under nonirrigated conditions (i.e., upland rice), which accounts for a substantial fraction of the crop, the water limitation may be critical.
A crucial factor in past crop yield increases has been increased availability of manufactured nitrogen for fertilization of crop fields. Nitrogen is an essential component of proteins and nucleic acids and the responses of individual physiological processes in the plant to nitrogen have been well documented (Sinclair, 1990). However, no simple overall mechanistic relationship similar to those for solar radiation and water has been developed. Instead, a descriptive equation can be written to express the maximum grain yield that might be achieved for a given amount of seasonal nitrogen uptake by a crop (Nup). This equation is based on the nitrogen content of the harvested grain (GN) and the proportion of the total amount of nitrogen taken up by a crop that can be stored in the grain (HN).
Y = Nup ( HN / GN 
The value of GN has proven to be quite stable within a crop species and is about 0.016 g N gS1 for maize, about 0.013 g N gS1 for rice, and about 0.065 g N gS1 for soybean. While it is possible to shift GN somewhat within each species, this can be deleterious in the use of the grain because the nitrogen-containing proteins are frequently critical to the quality (i.e. cooking characteristics, taste, nutritional value) of the grain. Decreased GN, for example, may well require a reconsideration of the use of the grain for human food and/or animal feed.
The variable HN in Equation  is analogous to the H for weight distribution in the plant. Similar to H, there is a limit on HN because some nitrogen must be committed to compounds that cannot be eventually translocated to the grain. The maximal value of HN in a high-yielding cereal crop appears to be about 0.75.
In unfertilized situations, it is likely that no more than 20 kg N haS1 is available to a cereal crop. In the case of Nup equal to 20 kg N haS1, maximum grain dry-weight yields are estimated to be only 0.9 t haS1 for maize and 1.2 t haS1 for rice. Clearly, yield increases demand that nitrogen be made available to cereal crops in substantial quantities. Even so, it has proven difficult to grow cereal crops so that Nup is greater than about 250 kg haS1. Assuming Nup equal to 250 kg haS1 results in estimates for maximum grain dry-weight yield of about 12 t haS1 for maize and 14 t haS1 for rice. The nitrogen limitation is more important for maize than rice because of its slightly higher GN.
The above estimates were made based only on the total amount of nitrogen taken up by the crop. Calculation of yield response to the amount of nitrogen in the soil available to the crop is a much more complicated matter. The diminishing fraction of nitrogen uptake from the soil, and the consequent diminishing increase in crop yield with increasing amounts of applied nitrogen, does not allow yields to be increased by simply applying ever greater amounts of nitrogen. The diminishing return results because there can be substantial losses of nitrogen applied to soil, no matter whether the nitrogen is in organic or inorganic form. In a well-managed system, recovery by the crop of no more than about 70% of the applied nitrogen can be expected, but commonly less than half of the applied nitrogen is taken up by the crop. The fraction of recovery depends on the amount and form of the applied nitrogen, method of application, status and type of soil, weather, and plant growth pattern. Research into the various factors under localized conditions controlling the efficiency of nitrogen uptake by the crop may offer important opportunities for increasing crop yields.
Soybean is a legume and, therefore, can take advantage of a symbiotic relationship with specific bacteria to fix atmospheric nitrogen for use by the plant. While the nitrogen fixation process requires plant energy to fuel the fixation process, there is an economic advantage to the grower in that little or no nitrogen fertilizer needs to be applied to the crop. Still, the high value of GN for soybean results in a major yield limitation. Even when a soybean crop fixes 400 kg haS1 of nitrogen, maximum yield is calculated to be only 4.5 t haS1.
Crop yields are limited by input levels of the environmental resources of solar radiation, water, and nitrogen. Based solely on the maximum yields allowed by each of these resources, it is clear that crop yields cannot increase indefinitely. Indeed, maximum yields calculated above for each crop species have been obtained under experimental conditions (Sinclair and Bai, 1997; Muchow et al., 1990; Spaeth et al., 1987). Recognition of yield limits may help to alter the agenda in considering the challenge of meeting the food requirements in the 21st century.
Much of the current slowing of yield increases appears to be directly linked to water and nitrogen limitations. Approaches to raising yields to the solar radiation limit have not been a primary objective of growers in industrial countries for several reasons. Growers are subjected to a number of socioeconomic factors that directly influence their decisions about the level of water and nitrogen, for example, to be made available to the crop. Growers are interested in optimizing return on investment rather than maximizing yields. The costs of obtaining and applying water and nitrogen both have important diminishing returns with increasing application, therefore the more profitable yields may well be achieved at lower input levels. In addition, availability of water is restricted when competing demands, such as urban households and manufacturing plants, are given higher priority. Nitrogen applications in either organic or inorganic forms is regulated in some regions to restrict the levels of nitrogen reaching the ground water used for drinking and in runoff into streams and wetlands.
Nevertheless, there are many regions of the world where increased availability of water and/or nitrogen would allow substantial yield increases. The basic science of plant genetics and agronomic management are generally known for effective use by crops of added water and nitrogen. The challenge is to apply and adapt breeding and management technology for those areas where yields can be substantially increased. This also must be accompanied by relieving socioeconomic limitations on farmers currently achieving low or even modest yields. That is, infrastructure will need to be constructed to provide the water and nitrogen resources, credit to purchase and use resources has to be arranged, equipment and technology for application of these resources will have to be obtained by farmers, and markets for the farmers to profit from such yield increases will need to be developed.
This analysis does not lead to quick fixes for the current slowing of yield increases. No gene is suggested that might be inserted into crop plants to alleviate the yield limitations imposed by limited resource availability. Intensive, focused efforts are needed to develop technologies in regions of low yield so that crops and cropping systems can efficiently and effectively use solar radiation, water, and nitrogen resources.