Agriculture Reference
In-Depth Information
It is useful to begin by considering a very simple setting in which there is
negligible immigration and the host population does not change over the time to be
considered. In this setting, a pathogen population may change in two ways. First,
numbers overall may grow or decline. Second, the stage-distribution may alter. This
in turn involves two types of change: the relative balance between active infectious
phases of the pathogen, as when pathogen individuals advance from a latent to a
sporulating relationship with their host, and alternate or resting stages that may
increase or disappear as when over-seasoning or sexual stages develop. For
example, consider an apple orchard in which there is a population of
Venturia
inaequalis
(cause of apple
scab). At the start of the host-growing season, the
population is small and exists as perithecia and inactive mycelium on twigs. Then as
the season develops, these stages decline and disappear, while an asexual population
increases. At the end of the season, the asexual population generates over-wintering
forms once again (see also Chapter 18).
It is useful to imagine a thought experiment in which a single young pathogen
individual is placed in an otherwise healthy plant population. In the case of the
example in the previous paragraph, this would be a newly infected apple leaf. Each
subsequent unit infected by this initial one is immediately removed and replaced by
a new healthy one, until no new infections are produced. The total count of new
units infected is known as
R
0
. Real variants of this experiment involve complications
but can be done: for example, van den Bosch (1988) measured
R
0
for
Puccinia
striiformis
(cause of yellow
rust) growing on wheat in the Netherlands, between the
start of stem extension and flowering, as 55 ± 16; for
Peronospora farinosa
(downy
mildew) on spinach (
Spinacia oleracea
) in the Netherlands in the autumn the figure
was 3 ± 2. It is obvious but important that a disease cannot increase in a crop unless
R
0
is greater than 1: the 'threshold theorem'. This quantity is therefore of central
importance in managing invasions of new disease, in predicting ranges, or in
eliminating disease (Anderson and May, 1986; Gilligan, 2002).
An individual will not be infectious until some time after it has infected a host.
This interval is the latent period (Butt and Royle, 1980). Then typically,
infectiousness (for example, spore production) will increase before declining as the
pathogen ages or runs out of food. The exact timing of the different phases will vary
from individual to individual and will depend on the environment. However, it is
helpful to do some thought experiments to see what would happen over some time,
if such outside factors stayed the same.
To begin with, useful results can be derived by assuming that diseased hosts
remain uncommon, so that the proportion of propagules which infect does not
change. In this case, the conclusions important for pathology are as follows
(Caswell, 2000). First, as time passes, the proportions of the pathogen population
lying in each age class gradually stop changing. Second, these proportions are the
same regardless of the initial age structure of the population. Third, the total
population grows by a constant factor each day. Since the age structure is constant,
the number of pathogen individuals at any given stage also grows exponentially
at the same rate as the whole population. Because the age structure does not depend
on the initial composition of the population, this exponential growth rate is
