BIOS 3010: Ecology
Laboratory 3: Life Tables
The winter moth, Operophtera brumata
Varley et al. (1973)
In today’s lab we will be using data collected on winter moths,
Operophtera brumata, by George Gradwell and George Varley in Wytham Woods
near Oxford in England. This is a classical example of how life tables can be
used to describe and understand population fluctuations over time. We will
imagine that we are pest managers acting for a local government and must
implement a strategy to control winter moths according to the evidence found in
our life tables. The biology of this system is very like that of the gypsy moth,
Lymantria dispar, here in Michigan and the north eastern United States.
From life tables for winter moths, we can identify the main causes of
population change from year to year. Density dependent mortality serves to
regulate the population density and keeps it within limits.
BIOS 3010: Ecology, Dr. S. Malcolm
Laboratory 3
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Density dependence:
“A change in the influence of an
environmental factor (a density dependent factor) that affects population
growth as population density changes, tending to retard population growth
(by increasing mortality or decreasing fecundity) as density increases or to
enhance population growth (by decreasing mortality or increasing
fecundity) as density decreases” (Lincoln et al. 1992).
Density dependent mortality may either act directly, as in food
limitation, or indirectly, through behavioral responses of parasites and predators
to their own and to their host’s population densities.
The winter moth is an easy insect to study because it is very abundant
and has an annual life-cycle with each stage concentrated at different times of
the year. The same could be said for animals with restricted breeding seasons
(e.g., partridge, owls, grouse, fish). Because the winter moth has an annual lifecycle, our life table is called a cohort life table. A cohort life table considers a
group of individuals that are born within the same short interval of time and
follows each individual until death.
Life Table Variables
ax
lx
dx
qx
kx
Fx
mx
Ro
Tc
r
the total number of individuals observed in the population at each stage (a0
individuals in the initial stage, a1 individuals in the following one, etc.)
the proportion of the original cohort surviving to the start of each stage (age
specific survivorship)
the proportion of the original cohort dying during each stage (difference
between lx and lx+1) {can be summed}
the average probability of an individual dying in that stage (age-specific
mortality) {cannot be summed}
“killing-power”, reflects the intensity of mortality and is equivalent to: log10ax
- log10ax+1 {can be summed} Also, these values are standardized and can
be used to compare separate studies.
the total number of offspring produced at that stage
individual fecundity or birth rate, i.e., the mean number of eggs produced
per surviving individual
net reproductive rate, in an annual species it is the overall extent by which
the population has increased (Ro>1) or decreased (Ro<1) over that time, =
∑Fx/a0, also = ∑lxmx
the cohort generation time, = ∑xlxmx/∑lx mx
the intrinsic rate of natural increase, = lnRo/Tc, the change in population
size per individual per unit time. Populations increase in size for r > 0 and
decrease for r < 0.
BIOS 3010: Ecology, Dr. S. Malcolm
Laboratory 3
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Life History of Winter Moths
Larvae of the winter moth are able to feed on a wide range of trees and
shrubs, but they are especially abundant on oaks (Quercus robur), which they
sometimes defoliate. Winter moth adults emerge from the soil under the oak
trees in November and December. At dusk, the flightless females walk to the
trees and climb up them.
Varley et al. (1973)
The winged males rest by day and fly actively at dusk or during the
night and congregate on the lower part of tree trunks. Here they mate with
females (Fig. 7.1 from Varley et al., 1973) which continue to climb the trees to lay
eggs in crevices in bark and lichen high above the ground. When the oak buds
begin to open in early April, the eggs hatch and the first stage caterpillars feed on
the expanding buds, where they do great damage to the tiny leaves. By the latter
half of May, feeding is completed and the caterpillars spin down from the trees on
silk threads, burrow into the soil, spin cocoons and pupate. They will reappear
again in November. Larvae of the winter moths were parasitized by a tachinid fly
(Cyzenis) and by a Microsporidian protozoan. Larvae are also prey for numerous
BIOS 3010: Ecology, Dr. S. Malcolm
Laboratory 3
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bird species. Pupae are attacked by wasps (Cratichneumon) and some soil
insects and predators such as mice and shrews. Adults also have birds as their
predators.
Experimental Method
1.
2.
3.
4.
5.
6.
7.
8.
9.
Five oak trees were sampled.
One quarter of the females climbing each of the five trees were caught in
traps like small lobster-pots made of fabric supported with wire. Two traps
were placed on opposite sides of each tree, and each trap was arranged to
obstruct 1/8 of the perimeter of the tree. The total catch of females
multiplied by four and divided by the total canopy area of the five trees (282
m2) gave the estimate of females.
The numbers of adults per m2 was twice this amount because we knew
there were equal numbers of males to females in the pupae stage.
Females were dissected for counts of the eggs they carried (avg. 150
eggs).
From this count, we could estimate the number of eggs per tree.
Larvae were trapped by placing trays filled with water under the trees and
counting the number trapped.
The larvae were examined for external parasites and dissected for internal
parasites. From these figures, we could assume the survival of the larvae.
Pupae were trapped while they were emerging from the soil using two trays
(each 0.5 m2) on the ground.
Data were compiled and placed into our life table.
Procedure
1. Calculate the remaining values on the winter moth life table using a Microsoft
Excel spreadsheet.
2. Draw Graphs (using Excel) of:
(A) the k-values versus time or stages,
(B) survivorships (lx) versus time or stages, and
(C) mortalities (qx) versus time or stages.
3. Determine at which stage the population of winter moths experiences the
most pressure and determine which factors contribute.
4. Graph a survivorship curve for the winter moths (as in Begon et al. figure
4.12, plot ax against stage.
5. List management strategies for the winter moth without pesticides and
minimal disturbance.
BIOS 3010: Ecology, Dr. S. Malcolm
Laboratory 3
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Table 1.
A cohort life table for the winter moth, Operophtera brumata.
explained above.
STAGE
ax
Females from previous 4.39
year
Egg stage 658
Log10ax
lx
dx
kx
-------
Fx
mx
lx m x
-------
Larval stages:
Full grown larvae 96.4
Larvae alive after fly attack 90.2
Larvae alive after other
parasites
Larvae alive after
Microsporidian
Pupal stages:
Pupae alive after predator
attack
Pupae alive after wasp
attack
Adult female moths
qx
The columns are
k1 =
k2=
87.6
k3 =
83.0
k4 =
k5 =
28.4
15.0
k6 =
7.5
------
Ro = _______
∑ lx m x
r = __________
Reference:
Varley, G.C., G.R. Gradwell & M.P. Hassell. 1973. Insect Population Ecology. An analytical
approach. Blackwell Scientific Publications, Oxford. 212 pages.
BIOS 3010: Ecology, Dr. S. Malcolm
Laboratory 3
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