Implemented by: Flemming Nielsen (FACT/Banana hill) (2009)

Main findings: Forecast of annual Jatropha dry seed yield for twenty years based on the best knowledge currently available. See table and figure at the bottom of this page for details.

Objective

As part of the development of a business plan for the Bilibiza Biofuel Centre (BBC) it is important to have yield fore cast for Jatropha. The first part of this document will assess the

• Expected yield over the next 10 years of Jatropha planted in the project area with the current plantings of 250,000 plants kept constant

• Expected yield over the next 10 years with and annual expansion of the area planted with Jatropha of 25ha. Currently the equivalent of 250 ha has been planted.

Next the maximum Jatropha production per household will be assessed under the assumption that farmers continue to prioritise production of food for own consumption and only use surplus labour on Jatropha.

Next the geographical distribution of Jatropha production will be assessed using different scenarios:

• The Jatropha plantings remain constant

• Jatropha cultivation is expanded with 25ha per year

• Jatropha cultivation is expanded at each locality to the maximum.

10 Year Yield Prediction with Constant Area

Multiple Regression

An attempt was made to create a regression equation for yield.

Date for Jatropha yield based in relation to age and rainfall data was extracted from Figure 2 in Achten et al 2008.

Illustration 1: From Achten et al 2008: "Fig.2–Dry seed yield in relation to average annual rainfall (mm) and age of the JCL crop. The plotted points represent a mix of provenances, site conditions and plantage or average annual rainfall. Sources:[9,11,13,52,53,56] and personal communication: Kumar, 2005 and Buisman, 2005."

The article is available in pdf format and the data is not in table form but only in two graphs in Figure 2. To extract the numeric values from the graphs a screen dump was saved as a bmp file.

The Enguage Digitizer was used to obtain numeric values from the screen dump. Comparison of values extracted from the two graphs showed a difference of max ±2%. The imprecision is likely caused by the limited screen resolution.

Matching of data from the two graphs was done manually in OpenOffice Calc and the data was saved in ASCII file named 2009-09_Yield_data.txt:

age yield rain locality
NA 1318.1 219.22 NA
NA 502.57 219.41 NA
NA 3013.24 1018.11 NA
NA 2652.07 1018.2 NA
NA 637.2 1108.73 NA
NA 3492.21 1196.72 NA
NA 2166.03 1468.62 NA
1 811.22 1468.94 NA
1.24 1750.98 219.12 NA
1.99 357.46 1018.74 NA
2.5 1180.85 609.05 NA
2.5 333.65 609.25 NA
3 1748.94 448.49 NA
3.02 66.13 1369.68 ”Paraguay”
4.01 668.46 1369.68 ”Paraguay”
5.02 957.43 1369.68 ”Paraguay”
6.01 1965.94 1369.68 ”Paraguay”
7.01 2951.24 1369.68 ”Paraguay”
8.01 3959.75 1369.68 ”Paraguay”
9.01 3946.99 1369.68 ”Paraguay”
1.99 2330.38 1197.77 ”Nicaragua”
3 2781.81 1197.77 ”Nicaragua”
3.99 3476.99 1197.77 ”Nicaragua”
4.99 4984.53 1197.77 ”Nicaragua”

Further analysis was done in R. To import the data file:

Jatropha <- read.table("2009-09_Yield_data.txt", header=TRUE)

Misc. commands for data exploration:

hist(Jatropha$age)
hist(Jatropha$yield)
hist(Jatropha$rain)
levels(Jatropha$locality)
plot(Jatropha$age, Jatropha$yield)
plot(Jatropha$rain, Jatropha$yield)

A linear multiple regression model is fitted:

mreg <- lm(yield ~ age + rain, data = Jatropha)

Different sub-sets of the data was used but no sensible regression equation could be obtained. There are several reasons for this. First of all some of the data from areas with very low rainfall (< 600 mm) have high yields. Since Jatropha usually does not yield when the rainfall is below 600 mm those data must be from areas where Jatropha relies on water from other source, be it irrigation or high ground water tables.

Other data is problematic too. In the graph on yield by rainfall the peak yield has been used for Nicaragua and Paraguay. Other data from high rainfall area are very low but the age of the plants is not known.

Excluding all outliers leaves us with mainly the two most complete datasets namely the Nicaragua and the Paraguay data series. The rainfall is higher in Paraguay than in Nicaragua but the yield is lower. A regression equation based on these data alone will therefore predict higher yield with decreasing rainfall, i.e. grossly over-estimate the yield for the Bilibiza area.

The multiple regression method is therefore not appropriate with the current data set.

Generalised Logistic (Richard's) Curve

The longest data serie from Paraguay shows the S-curve shape that is characteristic for many yield curves. It can often be described with the generalised logistic curve, also called Richard's curve:

Where Y is the yield and T is the year. The five parameters are:

A, the lower asymptote;

C, the upper asymptote, i.e. the maximum yield

M, the time of maximum growth;

B, the growth rate;

T, near which asymptote maximum growth occurs.

The Paraguay data series was entered in a spreadsheet and visual curve fitting was done resulting in the following values:

A	0
C	3947
M	6,9
B	4
T	7

The model values are compared with the Parauay data set in Illustration 2.

Illustration 2: Richards'curve fitted to imperical Jatropha yield data from Paraguay

The average yield in the project area is estimated to be peak around 800 kg/ha. This may appear low considering the data in Illustration 1. However, poor management including poor pruning practise makes it unlikely that higher yields will be achieved.

Using the above mentioned parameters for the Richards' curve but with maximum yield set to 800 kg result in the following yield figures.

Currently the equivalent of 250 ha have been planted. Below the total harvest from the project area is forecast for two scenarios:

• The area with Jatropha is kept constant at the current level of 250 ha;

• Farmers expand the area under Jatropha with 25 ha every year.

The two scenarios result in the following harvest forecast.

year	Harvest from 250 ha	Harvest from 250 ha + 25 ha expansion/year
	t	t	ha
1	5	6	275
2	9	11	300
3	16	19	325
4	29	35	350
5	51	62	375
6	91	111	400
7	156	192	425
8	198	253	450
9	200	275	475
10	200	295	500
11	200	315	525
12	200	335	550
13	200	355	575
14	200	375	600
15	200	395	625
16	200	415	650
17	200	435	675
18	200	455	700
19	200	475	725
20	200	495	750

Table 1: Harvest forecast for the project area under two scenarios