'The grain graph One'     shows the annual rate of increase of global grain yields (kilos of grain per hectare),  both as 5 year moving averages, and as the 32-year trend line since 1965. Although  5-year moving averages vary widely (individual years vary even more), the trend of yield increase is strongly downwards. The   rate of increase in population is almost linear on this scale.  Population and the yield trend cross in 1985. At that date the increase in grain yield becomes less than that of population,  so that per capita grain falls, as shown in the next Figure.
 
 
 

 Figure Two, 'Global per capita grain' shows  that 1985  is an important date - the point at which the rate of increase of grain yield became less than that of people, and  per capita grain started to fall. 1950 is the earliest date for which there is data.

 
Figure Four, 'The grain graph 3'  shows  what the experts forecast. The experts are all optimists.  The institutional position of all of them, particularly Alexandratos [1] with FAO and Mitchell with the World Bank  [3], would make a Malthusian position difficult. Dyson [2], of the London School of Economics is less constrained. However, having been supported by the Economic and Social Research Council, he would be under the same pressure as all social scientists. This is to provide the  answers that their paymasters would like to hear.

        In effect, what they are probably doing is to estimate what the world needs (their estimates are all very similar)  and then to  forecast that this is what it is going to get. How they  make their forecast is not always clear.  They  all forecast that the yield increase is going to be maintained at more than 1% to 2010 or 2025 - unjustifiable optimism. 
 

 

Figure Five, 'The grain graph 4' is in black and white without any lettering. This enables its general shape to be seen better.   The  psychological effect of a graph  with two obliquely intersecting lines  is  much  influenced by the proportions of its axes.  This figure  shows  it with  its  vertical axis shorter than its  horizontal one.  It does not look hopeful.  However look at what happens if  the axes are equal.
 

 
 
 
Figure Six, 'The grain graph 5'   has equal axes and makes the  prospects of feeding the world even more alarming.

                 How should one show a graph like this? We suggest that the most objective way of showing it, is to make its axes equal.

                 This also gives some indication of the shortfall and the scale of the starvation that this means - unless there is much greater sharing of global grain.

 
   
Figure Seven, What the experts expect is  for  yields to  follow Line A.  They expect them to suddenly  stabilize and level off at  an increase of 1.2-1.5%  annually, and  to remain at that level for the next 20 years - in spite of  the previous 30 year falling trend.

        In reality,  yields may already  have already fallen to less than 1%.  Since  yield increases vary so much,  and  are only  reliably  plotted as 5 year moving averages,  the last reliable figure to plot is that for 1993, even though FAO does have   data  up to 1997, the most recent ones being provisional.  If indeed   yields are already below 1%,  experts require the yield trend to follow Line B - to suddenly increase back to the 1% level and then to  remain stable at 1%. This requires that it makes two inflections, which would seem most unlikely.

First graph. We start with  a a graph showing what global per capita grain has been doing since 1950. It rose until 1985 and has been falling since.
 
 

Second graph.  Since agricultural land is approximately constant, increasing numbers of people can only be fed by increasing yields. Yields were increasing at  about 3% in the 1960s, but are now increasing at only about 1%.  The trend line is strongly downwards. In future it  seems  much more likely to follow the dotted line, than it is to follow what three experts think it  will do (for which read what it needs to do) which is to follow the horizontal lines C, D or E.
 
 
 
 
 
 

The third graph. This shows what population  what had population has done to date, together with what the  UN population division think it is going to do in future - the high variant, the medium variant and the low variant.   The population in the grey area has to be fed  in a situation of decreasing global per capita grain.  Thee are at lest two billion, and possibly even four billion  more people to be fed in a  situation of  of declining global  per capita grain. 
 
 
 

Tim Dyson's straight line    

                Lady M.  I understand you had a vigorous  exchange of views with Tim Dyson recently?

                MHK.  Indeed we did - 'benign uproar'!  See the BSPS  meeting. Tim bases his optimism on this graph.
 

Figure Nine, Tim Dyson's straight line.  Tim argues that global grain yields have been increasing linearly for  about the last 50 years since 1950, and that they are going to continue to do so for half as long again. That is for another 27 years to 2025.

                Lady M.  His thick  blue line  seems to be to be very hopeful indeed.

                MHK. The uninitiated might be forgiven for thinking so.  The pessimistic arguments  in the face of this graph are as follows.
 

                  1. Tim's straight line is a  segment of a sigmoid curve. Put a thin blue line between its ends and you will see that the thick blue line is gently curved.  This is particularly obvious if you look at a printout and put your eye close to the paper. It suggests  that  what we are seeing is  a segment of a sigmoid ('S'shaped) curve   which is ultimately going to level off and  fall.

                Lady M.  "Where  do you people think you are  in the sigma? How near the top are you?

                MHK. It is difficult to know.  I have a  suspicion that we may be  near the top.  Forget the last two years, and  consider only the trend of the previous ten. They are not reassuring.

                But there are other reasons for questioning Tim's straight line.

                2.  Ecology abhors straight lines.  A 75 year linear increase  from 1950 to 2025 is a very long straight line indeed for an ecological system such as global agriculture, which represents the interplay of so many variables.

 

                3. The dynamism of global agriculture is slowing.  Take the extreme case. Say the yield was 40 kg hectare, and it increased by 40 kg in a year.  It would increase 100% - an enormous  increase, and indicating enormous potential capacity for further increase.  Say the yield was 4000 kg or 4 tonnes, and it went up by 40 kg. This would be an increase of 1% - minute, suggesting that there was not much potential for further increase to come.  This is the approximately present situation.

                In effect,  the declining percentage increase in yield suggests that the agricultural system as a whole is 'running out of  steam' and that this will shortly be reflected in a falling  arithmetic  increase,  and  eventually   a declining one.

                Lady M.   But the thick blue line  in Figure 9 is rising, even if it is curved. Actually, it even suggests a rising rate of increase!  I still don't see why this  matches with the pessimism of  declining grain yields in Figure 4?
 
                Figure 9 says nothing about population. Before we can say anything about whether or not we are going to be fed, we have to consider  the rate of increase or both grain yields and people.   The most reliable way to compare them is to compare the percentage change in each. 
 

           4. Per capita grain has been falling since 1985. Even assuming that yields are going up linearly,  there came a point in 1985 when population started to grow faster than yields,  with the result that per capita grain has been falling ever since, and is still falling, as in Figure 2.    This is hardly grounds for optimism.

                'Dyson's straight line' - (actually  a curve)  is shown as  AB.  Segment CE of the percentage increase is not shown  on the earlier 'Grain Graphs'  because it was highly erratic  in the early 1960s,  as the result of Chairman Mao's great leap forward and the starvation that followed.  Nevertheless there was a substantial overall percentage increase in yield  from 1950 to 1965. It is only since 1965 that the percentage increase in grain yield has been falling.   The period  1965 to 1997 (strictly to 1993) is that covered by 'The Grain Graphs'. It is shown here as convex,  whereas  in reality it is erratic, and if modelled as the trend line,  is linear.

                Y is the present yield, 2.69 tonnes to the hectare.  Z is the  figure it has to reach  when the global population stabilizes. X  is the additional yield that is required to reach that level.

                If there was immediate replacement fertility (an instant 2.1 child world)  global population would increase from nearly 6 billion to to 9.5 million in 2150 - an increase of about  67%.   Z then needs to be at  least  4 tonnes to the hectare.  X needs to be   67% of Y. As shown here it is less than half.

                If population followed the medium variant, it would reach nearly 11 billion in  2150, Yields would have to increase  to 4.9 tonnes to the hectare.   X needs to be 80% of  Y.

                To the mathematical modellers. 1. What more can be learnt about the shape of the sigmoid curve, from data we already have? 2. Where can this model be improved?

Figure 11. Who eats what?  'The grain graphs'  assume that global per capita grain consumption is constant at about the present world average of 350 kg.  However, the grain yield increase necessary to feed a particular population depends on how much people eat. If people were to eat less, more people could  be fed. Consumption varies from 200 kg a year in India to 800 kg a year in the United States.

           Since farm animals waste a great many calories in converting grain into themselves, high per capital grain consumption is the result of a diet high in animal products. If the world were to eat a more photon-efficient diet  more people could be fed. It is one of the elements of a sustainable lifestyle.

               The reasons for the yield increases forecast by the experts are not always clear. Dyson (Table 4.6) assumes that the average 1981-1993 yield increase will continue to 2020. More recently he has assumed that the annual yield increase of 39 kg hectare between 1981 and 1997 will continue to 2025 [5].  Alexandratos (Table 2.1) gives a projection for global production in 2010, without the assumptions on which it is based. Mitchell and Incgo (page 137) expect consumption (for which read production) to grow 1.4% to 2010 - again without adequate explanation. All three appear to use the UN medium variant for population.

               Short term variations. The yield projections shown here are averages over 12-32 years. Since only about 15% of the world grain crop is stored from one year to another, short term deficiencies  caused by a run of bad harvests may be much more serious, even than the longer term trends, especially since harvests are becoming increasingly variable (Dyson page 87).

               Why grain? Grain provides about 60% of all food calories. Grain data are better than those for many other foods. Grain is also a useful proxy for other foods. [2]

 Water, may be  an even greater constraint on grain  production than  land.  500 litres of water are needed to produce a kilo loaf of bread. 500 to 1000 tonnes of water (cubic metres) are needed for a tonne of grain. This can be  2 or 3 times  more in badly managed agriculture.  Countries, especially dry ones, which import much grain (the Middle East) are in effect importing much of the water they need.

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500 litres of water for a loaf of bread

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               How original are these graphs? Although they may exist, I have not seen graphs which show percentage yield increases and percentage population increases matched in this way against projections of the necessary yield increases - if widespread starvation is to be avoided. Since these graphs succinctly summarize what we are going to eat (or not going to eat), they must rank as some of the world's most important - along with the graph of global temperature.
 
               Why be unduly worried when even the 5-year moving averages are so variable? It is the 32 year trend line of these averages that is so disturbing.
 

               The background to this study. In 1995 Tim Dyson wrote the standard work on global food [2] which is guardedly optimistic. Suspecting that Tim's optimism might be unfounded, I  (MK) read it with great care and wrote the paper described below [4] which included a simpler version of 'the grain graph'.  Tim was magnanimous enough to say that it was the ':...best paper that Charles Elliott and I had ever written..." (an opinion from which I, at least, dissent!). This is unfortunately (since its theme is not optimistic) a solid indication of the validity of our paper - and this part of the website. See also.
 

 Data sources and statistical methods. Data are from FAO's Faostat database, from the web, as of  september 1998, and giving provisional figures for 1996 and 1997. Yields have been calculated for all cereals with rice in unmilled form, using Excel and  SPSS.  Here are the data.  I shall be happy to send them by email on an Excel file.  I shall  be delighted if anyone  has further statistical ideas on the interpretation of the data for the four most recent years, shown here in red.  I am about to work on this myself.

1. Alexandratos Nikos, Ed. World Agriculture towards 2010. FAO

2. Dyson Tim. 'Population and food, global trends and future prospects' (London Routledge), Rome.

3. Mitchell Donald O, Ingco Merlina D, Duncan Ronald O. The World Food Outlook, Cambridge University Press. 1997.

4. King MH, Elliott, CM. 'Averting a world food shortage: tighten your belts for CAIRO II' BMJ (1996);313:995-997.

5. Dyson Tim.  World Food Prospects: Malthus Denied or Delayed. Handout to the Meeting of the British society for Population Studies September, 1998.