Agriculture Reference
In-Depth Information
may not only not be independent but will have population dynamics very different
from a larger, effectively closed, system treated in the same way. For example, spore
transport by wind may be best modelled by an inverse power-law. One way to
understand this is to visualise spores travelling in wind, dying or settling out only
slowly, so that their trajectories spread out in proportion to distance. In this case the
chance of a spore passing through a point would decrease inversely to distance. In
practice, of course, many other factors reduce long-distance transport, but more
realistic models of turbulent atmospheric dispersal do predict a power-law
relationship between distance and probability of a spore reaching a given place. The
relationship has been observed for both pollen and spores (Aylor, 2003; Fitt
et al.
,
1987) and has been used in several models (Minogue, 1989; Paradis
et al.
, 2002; Xu
and Madden, 2004).
The consequences of such a relationship can be quite surprising. If spores
disperse approximately according to an inverse square law at intermediate scales
(for example, falling to 1/41 m from the source, 1/92 m from the source and so on)
and an experiment were conducted in a large uniform crop area, then a disc-shaped
plot 10 m across would receive the overwhelming majority of its spores from
outside (see Appendix 7A). Even with dispersal according to an inverse 2.5 power,
such a plot would receive almost equal contributions from inside and outside. In
practice, most spores do not escape a canopy to take part in long-distance air
movements, so the position is slightly less extreme than this; but plots of the order of
100 m
2
should not be assumed to be independent units.
For example, Bierman
et al.
(2002) reported experiments on fungicide resistance
selection of the eyespot pathogens,
Oculimacula
spp. They found that in the absence
of selection by carbendazim, (1) the frequency of resistance to the fungicide in plots
starting with a high frequency declined with time but that (2) the frequency
stabilised at an intermediate level. This indicates either frequency-dependent
selection for the trait - in other words, the resistance is valuable to an individual
possessing it, even in the absence of fungicide - or that immigration from treated
plots is common enough to counterbalance selection against the resistance. It would
not be easy to distinguish the two hypotheses by field observations unless the
experiment was designed with the problem in mind and the populations were
carefully genetically marked (see also Chapter 3).
A slightly different example is provided by a study of the likely effect of a
certification scheme for leek (
Allium porri
) seedlings carried out by de Jong (1996).
This estimated the equilibrium fraction of fields infected, assuming that fields might
be infected by airborne spores, or by planting infected seedlings. De Jong then
calculated how the proportion of infected fields depended on the proportion planted
with infected leeks. Certification could only be effective if the likelihood of
infection by airborne spores was low; if leek cultivation became too intensive, so
that fields were very close together, this was not possible.
A further point is that such calculations refer to averages. Because small packets
of air may be caught up in very large-scale movements, stochastic effects may be
very large, with many spores landing a long way from their source but relatively
close together. This will make the local dynamics subject to large chance
fluctuations.
