Agriculture Reference
In-Depth Information
the time-scales involved are long, processes at the metapopulation level are probably
as important in determining the genetic structure and size of pathogen populations as
process at the population level (Burdon and Thrall, 1999). For example, Damgaard
(1999) showed that variability in the spectrum of virulence alleles present in a
population can be maintained without assuming a cost of virulence, in distinction to
all models based in single well-mixed populations, but making it easy to understand
why it has often been hard to show any cost associated with virulence alleles.
APPENDIX 7A
It is assumed that dispersal obeys an inverse power-law with an exponent
n
, on
intermediate scales. On very long scales, typical of the distance travelled by wind in
a day or so, there is an exponential decline, with a scale parameter
l
. To simplify the
calculations, it is also supposed that the wind is equally likely to blow from any
direction; this assumption can be relaxed without changing the important
conclusions from the argument. The density of spores moving a distance
r
, from a
source with density
ρ
per unit area is then described by:
r
ρ
−
(
)
l
kr
,
θα
e
(7.2)
(
)
n
1 /a
Here
a
sets the short-distance scale of dispersal. It has units of distance and the
larger it is, the further spores travel. Now the density of spores arriving from within
a distance
r
0
can be compared with the density of spores arriving from outside that
distance. Each overall density can be obtained by the mathematical technique of
integrating over all possible directions and all possible distances less than or greater
than
r
0
. The result of this can be expressed analytically, but is very complex. The
numbers in the text are obtained by substituting
r
0
= 10;
a
= 1;
l
= 100 and
n
= 2 or
2.5; the qualitative results are very little affected by the value of
l
chosen, provided
it is much larger than
r
0
.
REFERENCES
Adams, P.B. and Fravel, D.R. (1990) Economical biological control of
Sclerotinia
lettuce drop by
Sporodesmium sclerotivorum
.
Phytopathology
,
80
, 1120-1124.
Anderson, R.M. and May, R.M. (1986) The invasion, persistence and spread of infectious diseases within
animal and plant communities.
Philosophical Transactions of the Royal Society, B
,
314
, 533-570.
Augspurger, C. (1983) Seed dispersal of the tropical tree
Platypodium elegans
and the escape of its
seedlings from fungal pathogens.
Journal of Ecology
,
71
, 759-771.
Aylor, D.E. (2003) An aerobiological framework for assessing cross-pollination in maize.
Agricultural
and Forest Meteorology
,
119
, 111-129.
Barrett, J.A. (1988) Frequency-dependent selection in plant fungal interactions.
Philosophical
Transactions of the Royal Society of London B
,
319
, 473-483.
Bateman, G.L., Dyer, P.S. and Manzhula, L. (1995) Development of apothecia of
Tapesia yallundae
in
contrasting populations selected by fungicides.
European Journal of Plant Pathology
,
101
, 695-699.
Bayles, R.A. (1991) Varietal resistance as a factor contributing to the increased importance of
Septoria
tritici
Rob. and Desm. in the UK wheat crop.
Plant Varieties and Seeds
,
4
, 177-183.
