Agriculture Reference
In-Depth Information
over one or a few pathogen generations. Similarly, a potato crop stops producing
new leaves a few months before harvest, while the life cycle of
P. infestans
can be
completed in a week or so. So, once the crop has stopped producing new leaves, it is
possible to ask how the potato blight epidemic develops for the remainder of the
season in an approximately
fixed
host population; after harvest, it is possible to ask
how the population in the tubers changes during the off-season, without considering
changes in the tuber population.
Many very interesting processes require the simultaneous study of host and
pathogen populations because both are changing at comparable rates. In the example
of
P. infestans
, it is not possible to study the transfer of fungus from a pre-
dominantly tuber-borne population in the off-season to a predominantly foliar
population in the growing season without considering how both populations are
changing. Similarly, a fungus like
Sclerotinia sclerotiorum
infects annual crops like
oilseed rape and sunflower once a year, so the generation times of host and pathogen
are similar and neither population can be considered fixed.
7.4 CHANGES IN POPULATIONS
Changes in population size may come from birth, death, immigration or emigration
(Begon
et al.
, 1996). Changes in the stage-structure of a population may arise in the
same way: individuals may progress from one stage to the next (for example,
cleistothecia
immature mycelia) or may enter the stage from a previous one in the
life-cycle (for example, immature mycelium
→
sporulating mycelium). Immigration
and emigration will usually only occur at certain stages.
If a population is described by specifying the number of individuals in each of a
series of stages, matrices can be used to model the population and the ways in which
it will change (Caswell, 2000). Such models describe the change of the population in
jumps, specifying the numbers and structure at one time and then attempting to
specify how these will have changed at a definite time, one time-step, later. The
time-step appropriate depends on the biology of the organism and the time-scale of
interest; for some pathogens, changes from hour to hour may be appropriate, for
others, changes from year to year may be useful to study.
The data describing the population can be set out in a vector or list of numbers in
each stage. The changes to this list from one time-period to the next can be set out in
a matrix or table showing two things: the proportion of each stage which will have
advanced to the next stage (for example, from latent infection to sporulating
infection, or from sporulation to over-seasoning stage), and the number of new-born
individuals. The number of new-borns will be proportional, among other things, to
the total number of propagules produced by all the infectious stages of the pathogen.
Emigration will usually be implicit in such a representation, causing a reduction in
the number of births, since a live pathogen individual is usually associated with a
plant host that cannot move far.
Immigration can be included by adding to each stage in the population vector the
number of individuals in the stage that immigrate in one time-step. Often, it is useful
to consider a large area of host, so that almost all new infections come from parent
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