A.J.J. Van Rompaey et al. Agriculture, Ecosystems and Environment 83 2001 83–94 89
where A
i
is the ith class of variable A e.g. the class ‘10–15’ of slope and B
i
is the ith class of variable A
e.g. the class ‘sand’ of texture. This means that the probability of ‘an event’ in our case the set-aside
of a field given conditions A
i
and B
i
is equal to the probability of the event under condition A
i
times the probability of the event under condition B
i
divided by the overall probability of the event. For example, the
transition probability of a field for which slope and texture are known can be calculated as
P fallow|slope class : ‘ 15’ ∩ texture
class : ‘sand’ =
P fallow|slope class : ‘ 15’
∗ P
fallow|texture class : ‘sand’ P
fallow 3
For n factors in this case field characteristics the theorem can be extended.
P fallow|A
i
∩ B
i
∩ · · · N
i
= P
fallow|A
i
∗ P fallow|B
i
∗ · · · P fallow|N
i
P fallow
n− 1
4 In this case the average probability for fallow
Pfallow is known since this is the minimum set-aside percentage of the EU-CAP see Table 1.
Using Eq. 4 the spatial pattern of transition prob- ability was calculated for a range of set-aside per-
centages. An example of such a transition probability map for a minimum set-aside percentage of 10 is
shown in Fig. 5. It is important to point out that the transition probabilities calculated using the procedure
described above are independent of the distribution of observations in the sample used to derive the tran-
sition probabilities. As the estimated single factor transition probabilities are the outcome of discrete
events fallow or non-fallow their accuracy can be assessed using the theory of binomial distributions.
The standard deviation of the sample mean, being the estimated single factor transition probability calcu-
lated from the observed relative frequencies, can then be estimated as follows for samples having more than
20 observations Conover, 1971
σ = r
p × 1 − p
n 5
where n is the number of observations, and p is the relative frequency of transitions observed. Thus, the
reliability of the transition probability is dependent only on the number of observations in each class as
well as the number of transitions observed. Based on these final transition probabilities, stochastic simula-
tions of possible set-aside patterns in the study area. This was done for different EU-CAP scenarios. The
study area was divided in square blocks of 5 km×5 km since these spatial units correspond more or less with
spatial distribution of the fields of one farmer and is therefore the level at which set-aside simulations have
to be carried out. For each of these blocks set-aside volumes of 5, 10, 20 and 25 were simulated.
A simulation was carried out as follows. A field of arable land in a 5 km×5 km block was selected
at random. Next a random number between 0 and 1 was chosen. This number was then compared with
the transition probability of the selected field. If the random number was less than the transition probability
then the field was accepted for set-aside; if not the field was left in production. This procedure was re-iterated
until the desired simulated percentage of set-aside land was reached. This way of field selection implies that
fields with a higher transition probability have a higher probability of being selected for set-aside.
As mentioned in the introduction fallow fields have to be protected with selected fallow crops and can thus
be considered as land units with no erosion. Therefore, new soil erosion risk maps were compiled for the dif-
ferent EU-CAP set-aside scenarios with soil erosion rates of 0 Mg ha
− 1
per year on the spots correspond- ing with a simulated fallow field.
3. Results and discussion
3.1. Slope of the fields The results of the t-test are listed in Table 4. The
variances of the two populations were not signifi- cantly different. The calculated T-value of 5.53 with
972 degrees of freedom on the other hand has only a probability of 0.0001, which means that the mean
slope of the fallow fields was significantly higher than the mean slope of the non-fallow fields.
The results of the statistical analysis showed that the slope gradient plays a significant role when
90 A.J.J. Van Rompaey et al. Agriculture, Ecosystems and Environment 83 2001 83–94
Fig. 5. Land use transition probabilities from cropland to fallow land set-aside percentage=10.
farmers make decision about set-aside. However, only 2 out of the 31 farmers that were questioned explicitly
mentioned the slope gradient as a decision criterion Table 3 This is a problem that already has been
Table 4 Slope distribution of fallow and non-fallow fields
Category I+ Category II
a
Category III
a
No. of observations 252
722 Mean slope gradient
5.84 4.67
S.D. of slope gradients 3.02
2.86 F
-value 1.12
P F
0.26 T
-value 5.53
P T
0.0001
a
Category I: fallow at the moment of the inquiry; Category II: no fallow at the moment of the inquiry but possibly next year
and Category III: no fallow and non-considerable in the future.
recognised by many researchers in psychology and related social sciences Austin et al., 1998a,b; Hengs-
dijk, 1998; Van Ittersum, 1998. In this particular case, farmers probably do not see slope gradient as a sep-
arate and isolated field property but incorporate it in the more general field property ‘good or poor quality’.
3.2. Soil texture The χ
2
-test Table 5 showed that fields with a sandy loam or a clay texture are more likely to be
taken out of production. Fields with a loamy texture on the other hand are more likely to be kept in produc-
tion. The analysis pointed out that the null-hypothesis ‘set-aside fields have the same distribution over dif-
ferent soil texture types as the total distribution’ can be rejected with a probability of 98.4. This means
that the soil texture class is a significant factor for the prediction of the spatial pattern of set-aside fields.
A.J.J. Van Rompaey et al. Agriculture, Ecosystems and Environment 83 2001 83–94 91
Table 5 Expected versus observed distribution of fallow fields over soil
texture classes Soil texture
class Expected
frequency Observed
frequency Loam
188 168
Sandy loam 31
43 Clay
8 13
Sand 25
28 Total
252 252
χ
2
10.2 Degrees of freedom
3 P
χ
2
0.016
3.3. Soil drainage type The null-hypothesis ‘set-aside fields have the
same distribution over different soil drainage types’ was tested by means of a χ
2
-test. The results are listed in Table 6. The analysis confirmed that the
null-hypothesis can be rejected. Thus, wet fields are much more likely to be taken out of production than
fields with good soil drainage.
3.4. Impact of set-aside on the soil erosion risk The former statistical analysis shows that slope
gradient, soil texture and soil drainage do have a significant influence on the choices made by farm-
ers. Apparently steep fields with a sandy or clay soil
Table 7 Transition probabilities for field characteristics
Total Non-fallow
Fallow Transition probability
a
S.D.
b
Slope class 5
670 536
134 0.20
0.01 5–10
49 33
16 0.32
0.07 10–15
32 21
11 0.34
0.08 15
23 10
13 0.56
0.10 Texture class
Loam 726
558 168
0.23 0.02
Sandy loam 121
78 43
0.35 0.04
Sand 31
18 13
0.42 0.09
Clay 96
68 28
0.29 0.05
Drainage class Dry
796 617
179 0.22
0.01 Temperature wet
147 95
52 0.35
0.04 Temperature dry
31 10
21 0.68
0.08
a
Single factor transition probability.
b
Calculated using Eq. 5. Table 6
Expected versus observed distribution of fallow fields over soil drainage classes
Soil drainage class Expected
frequency Observed
frequency Good drainage
206 179
Moderate drainage 38
52 Poor drainage
8 21
Total 252
252 χ
2
29.8 Degrees of freedom
2 P
χ
2
0.0000003
and a bad drainage have a higher chance to be taken out of production as a consequence of the EU-CAP
policy than fields with a low slope gradient, a loamy texture and a good drainage. These three field criteria
were, therefore, taken into account for the simulation of set-aside patterns. Eqs. 2 and 4 were used to
calculated the transition probabilities Table 7. The standard deviations on these transition probabilities
were calculated using Eq. 5. By means of the sim- ulation procedure, described in Section 2.3, set-aside
patterns for a range of set-aside percentages were generated. A combination of these set-aside patterns
with the soil erosion map allowed to calculate for each fallow percentage: 1 the average soil erosion
rate in Mg ha
− 1
per year on the remaining fields and 2 the total amount of soil erosion in the study area.
The results are listed in Table 8. The results of the
92 A.J.J. Van Rompaey et al. Agriculture, Ecosystems and Environment 83 2001 83–94
Table 8 Decrease in soil erosion risk as a consequence of set-aside
Minimum set- aside
Average erosion rate fallow fields
a
Mg ha
− 1
per year Average soil erosion rate remaining
arable fields Mg ha
− 1
per year Total amount of soil erosion in
the study area
b
Mg per year –
– 408 000
5 33.1
9.6 367 400
10 25.6
9.1 328 900
15 22.2
8.6 296 200
20 20.3
8.2 265 200
a
The listed erosion rates are theoretical. Since these fields are protected the real erosion rate is reduced to 0 Mg ha
− 1
per year.
b
The total surface area is 850 km
2
.
simulation show that there is lowering of the average soil erosion rate of the remaining arable fields when
set-aside is introduced. This is due to the fact that farmers tend to take out of production the steepest
fields. The preference for fields with sand and clay soils, on the other hand, has a negative effect on the
average erosion risk of the remaining fields since these texture are slightly less erodible than the loamy soils.
In Fig. 6 the ‘theoretical average erosion rate’ of fallow fields i.e. the erosion rate of the fallow
fields if they were not protected with fallow crops is plotted against the fallow percentage. It appears that
the theoretical average erosion rate of the fields that are taken out of production is much higher than the
Fig. 6. Average soil erosion rate on non-fallow fields. The erosion rates were calculated with the USLE. The set-aside patterns were simulated.
average erosion rate of the remaining arable fields. The theoretical average erosion rate of the fields that
are taken out of production is dependent on the fallow percentage. Fig. 6 shows that an increase of the fal-
low percentage leads to a degressive lowering of the theoretical average erosion rate of the fallow fields:
if more fields are taken out of production the num- ber of steep fields remaining in production decreases
reducing the probability that they are selected. The corresponding trend, though much more weakly, can
be found in the lowering of the average erosion rate of the remaining fields: the erosion risk drops but
the decrease is not perfectly linear. Since the theo- retical average erosion rate of the fields taken out of
A.J.J. Van Rompaey et al. Agriculture, Ecosystems and Environment 83 2001 83–94 93
Fig. 7. Reduction of the total soil erosion in the study area. The erosion rates were calculated with the USLE. The set-aside patterns
were simulated.
production is lower for higher set-aside percent- ages, the decrease of the average erosion rate of the
non-fallow fields is dropping as well. Combining the decreasing erosion rate on the
remaining arable fields with the linear decrease of the area arable land results in an faster than linear
decrease of the erosion rate with increasing set-aside percentages as is illustrated in Fig. 7. The observed
trend can be described with a power function of the form
D = aS
b
6 where D is the decrease in soil erosion in the study
area, S the set-aside percentage, and a and b are the regression coefficients.
4. Conclusions
