Agriculture Reference
In-Depth Information
between crops or over longer distances. Generally, it is easiest to measure gradients
over short distances within crops, although gradients have been measured over km
distances, for example down river valleys (Gregory, 1968; Fitt
et al.
, 1987). It may
also be possible to observe gradients within crops from above using remote sensing
techniques, such as infra-red aerial photography (Lacey
et al.
, 1997) and optical
techniques from satellite or tractor-mounted platforms (West
et al.,
2003; see also
Chapter 2). Long distance transport of spores over 100s of kilometres is important in
the spread of some epidemics, such as black stem rust (caused by
Puccinia graminis
)
in North America; such spores can be sampled at heights of 1000 m with samplers on
aircraft (Gregory, 1973) but are generally dispersed by wind and deposited by rain in
relatively uniform clouds so that gradients are not observed.
When plotted on a linear scale, spore dispersal and disease gradients are generally
hollow curves, which are difficult to compare. Therefore, to compare gradients, the
empirical negative exponential (Equation 6.3) or inverse power law (Equation 6.4)
models are generally log-transformed to give the forms for disease (
Y
):
ln(
Y
)
=
ln(
Y
)
−
α
x
(6.16)
0
and
ln(
Y
)
=
ln(
A
)
−
β
ln(
x
)
(6.17)
When the models are fitted in these forms, linear regression can be used to estimate
parameters to describe and compare gradients. When disease gradients are fitted by
an exponential model they can also be expressed as a half-distance (McCartney and
Fitt, 1985; Fitt and McCartney, 1986). If disease incidence is expressed as the
proportion of individual plants affected, then a multiple infection transformation
must generally be used to account for multiple infections of the same plant by
different spores (Gregory, 1973):
NN
−
YN
/
=
(1
−
)
(6.18)
i
t
i
t
This allows calculation of the probable number of infections
Y
i
that occurred when
N
i
leaves are diseased out of a total of
N
t
plants or leaves. Although only one new
infection among 100 plants is required to increase the percentage of plants diseased
from 1 to 2%, 69 new infections are required to increase it from 98 to 99%. A
problem which arises in using these transformed models is that log-transformation
cannot be used if the value of
Y
or
C
is zero. This can be overcome by adding a
small quantity to each value (Gregory, 1968), which can distort the gradient, or by
more complex procedures, including non-linear transformations (Minogue, 1986).
Ideally, there should be sufficient measurements so that the gradient can be
truncated at a distance before zero values occur.
Field experiments to study horizontal or vertical spore dispersal or disease
gradients are difficult to design and to do. The experimenter has to contend with the
