Geoscience Reference
In-Depth Information
factor analysis applies to population systems for which data exist on survival or
mortality of specific ages or life stages in a population over a series of consecu-
tive generations. The first methods developed were graphic ones. Varley and
Gradwell (1960) advocated plotting mortalities in each life stage expressed as
k
-values along with total generational mortality (
K
=
X
t
-
X
t
+2
; figure 6.5)
against generation number (time). They included changes in fecundity as a
k
-value so total
K
represents total generational change in density (
K
= -
R
) and
is the sum of
n
sequential, stage-specific
k
-values (
K
=
k
1
+k
s
+ . .
k
n
). The key
factor was the one whose fluctuations most closely matched those of total
K
.
For example, figure 6.5 shows key factor analysis of a 10-year study of par-
tridge populations in England (Blank et al. 1967). Mortality (or loss of fecun-
dity) in this population was attributed to eight sequential causes. Of these,
mortality of chicks (
k
4
) was the one whose fluctuations clearly matched of that
of total generational change (
K
).
For some species such graphic analyses might not yield a definitive answer.
Podoler and Rogers (1975) advocated calculating regression lines of each
k
-
value against total
K
. The key factor was the one with the largest positive slope.
They applied this technique to a number of data sets, including the English
partridge data in figure 6.5. Chick mortality (
k
4
) had the steepest slope, thus
confirming the conclusion of the earlier graphic analyses (figure 6.5; Blank et
al. 1967). Podoler and Rogers (1975) recognized that one could not test for
the significance of the slope in the usual way because the axes in the regression
were not independent. Manly (1977) offered a more definitive analytic
approach based on partitioning the variance of
R
into its additive components
and constructing a variance-covariance matrix of all the
k
-values or causes of
mortality. The key factor was the mortality or life stage with the largest vari-
ance component and was not always the same as that obtained with the earlier
graphic methods (Manly 1977). Manly applied his technique to the partridge
data given earlier and concluded that
k
7
(losses in late winter due to natural
causes) was the key factor. Whereas
k
4
accounted for much of the variation in
early season mortality, most of it was compensatory to the earlier mortality and
thus not the main cause of population change (Manly 1977).
Key factor analysis was originally designed for univoltine insects that repro-
duced during a short-lived adult stage and survival data were confined to
preadult stages (Morris 1959; Varley and Gradwell 1960). Problems arise
when this technique is applied to organisms, including most vertebrates, for
which reproduction extends over a substantial fraction of the typical life. Sur-
vival during the oldest age classes weighs equally with younger age classes in
