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A ceiling on what smart farmers can raise on a plot


A course of changing yields illustrated by Figure 7.2.1 rather than a yardstick of events customarily begins an analysis of agricultural progress and how it may continue. I now follow that custom. Figure 7.2.1 depicts the rising yield per plot of three crops in the United States. Although the figure shows the outcome for only three crops and one nation, global data confirm that yields of many crops and nations followed a similar course during the twentieth century.

During the 1970s and 1980s, population rose 1.7% per year. Nevertheless, farmers improved the average per capita diet of both calories and protein about 0.5%/yr. To improve the per capita diet, farmers did expand arable and permanent crops 0.2%/yr. Nevertheless, in global terms and annually, farmers fed 1.7% more people 0.5% more energy and protein while shrinking the amount of land farmed per person by fully 1.5%gif

Pessimists and optimists see different clues in the rise of yields since 1940. Pessimists search for hints that the rise will level off. Pessimists will worry whether national averages can approach yields on experimental or prize-winning plots. They will reason that yields far above primitive ones mean more effort must go into maintenance (Plucknett and Smith, 1986[PS86]) and see that averages have recently fallen farther below the trend than during 1940-1970.

Optimists will see clues that humanity will continue to sidestep the Malthusian apocalypse while sparing more land for Nature. Optimists will trust that new techniques can raise the ceiling on yields and that a relay race of maintenance research and application can steady the annual averages.

Optimists and pessimists can agree on some things. About maintaining higher and higher yields, both would agree with a philosopher:

For certainly progress in civilization has not only meant increase in the scope and intricacy of problems to be dealt with, but it entails instability. For in multiplying wants, instruments and possibilities, it increases the variety of forces which enter into relations with one another and which have to be intelligently directed .... Since all objective achievement only complicates the situation, the victory of a final stability can be secured only by renunciation of desire. Since every satisfaction of desire increases force, and this in turn creates new desires, withdrawal into an inner passionless state, indifference to ad ion and attainment, is the sole road to possession of the eternal, stable and final reality (Dewey, 1922[Dew22]).

Neither optimists nor pessimists would be surprised that much, perhaps most, research must be devoted to maintaining the gain in yield already attained.gif

Both would agree that using the record from 1940 to today to foresee the next half century is only an extrapolation. They would agree that only unremitting work by scientists, sensible incentives, and smart farmers will sustain the rising trend. And the optimists would admit to the pessimists that nothing goes up forever. Everyone agrees that rising yields eventually must strike such a limit as the supply of solar energy or water.

The simplest summary of N rising at a proportional rate r toward a limit K is the logistic equationgif
The proportional rate r raising N exponentially can be called the Malthusian parameter. It seems most fitting for a population multiplying in proportion to its numbers, N. If technology makes more technology easier to find and also encourages farmers to adopt it, a proportional rate r also can be conceived for the rising yields after 1940.

But for yields, where is the limit K? Because only equivocal hints of a limit can be seen in such graphs as Figure 7.2.1, searching for a limit by fiddling and fitting the logistic equation still will end with an equivocal estimate of K. Instead, I shall substitute concrete measurements for the limit in the logistic equation and see how it fits such courses as Figure 7.2.1.

In the preceding section, I examined physical limits like sun for photosynthesis and water for turgor. Solar energy plus measurements of photosynthesis in the laboratory set limits of 45 t/ha of biomass at 400 and of 30 t/ha at 500 latitude. These would correspond to about 22 and 15 t/ha grain. Because several species of plant actually grew as fast as 200 kg/ha/day, the limit of 22 t/ha at 500 North seemed a reasonable upper limit for the accumulation of biomass  during a season. Or at least deWit and Alberda concluded so one-quarter century ago.

The winner of a contest with a productive crop also can set the limit, at least for the time being. Maize, with its efficient C4 photosynthesis, is surely a productive crop. In 1992, the National (U.S.) Corn Growers Association competition enrolled 2,470 entries from 44 states. To qualify for the contest, farmers had to enter a minimum of 4 ha of maize and to keep the accurate production and harvest records required by rules. The winning, irrigated field in Pasco, Washington (tex2html_wrap_inline2417 North and sunny climate) grew fully 21 t grain/ha! Other yields above 18 t/ha prove that the 21 was not a fluke (Figure 7.3.1) (National Corn Growers Association, 1993[Ass93b]).

figure7.3.1 Figure 7.3.1. The three highest yields of maize in irrigation and tillage classes of the National (U.S.) Corn Growers Association competition in 1992. Although the excess is less than in regional averages, irrigated exceed rain-fed yields even among the winners among 2,470 entries from 44 states (National Corn Growers Association, 1993). [Ass93b] 

Twenty-one tons stands incredibly near deWit's limit of 22. Of course, one-quarter century of breeding of a C4 plant and enrichment of the air with tex2html_wrap_inline2319 since deWit's calculation plus irrigation and 1992 husbandry lie behind the 21 t. In the mid-nineteenth century, a farmer reasonably might have speculated that the limit on maize yield was greater than 5 t/ha, which was then about three times the national average. Near the end of the twentieth century we reasonably could speculate that the limit exceeds 21 t/ha, which is three times our present national average. Because 21 t/ha actually has been produced, however, I shall take K to be 21 in the logistic equation.

figure7.3.2 Figure 7.3.2 The logistic rise of the national average of maize yields toward a maximum of 21 t/ha (National Corn Growers Association, 1993; U.S. Department of Agriculture, various years).[Ass93b][USDa] 

I compare in Figure 7.3.2 the rise of the national average yield of maize since 1940 with a logistic rise of 3.6%/yr toward the limit of 21 t/ha. I extended the time to the middle of the twenty-first century, more or less when population will reach ten billion. Comparison of the national averages with the logistic curve is reassuring. Although the averages have varied--as during the 1988 drought, they generally follow the curve. And, of course, they have a long way to go before striking the limit of the yield on the 4 ha that won the 1992 contest.

Section 6.1 concluded that sun, warm days, and land to stand on will not soon limit food supply. The present section can conclude that the ceiling on what a smart farmer can raise per plot stands well above present averages because real crops and husbandry existing today have yielded fully 21 t/ha.

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Next: Smart farmers get more Up: Can Smarter Farming Spare Previous: Smart farmers raise yields

Yasuko Kitajima
Thu Jun 19 16:20:56 PDT 1997