110
N. WALOFF
where P o := the total number entering the stage, S = the fraction of
population that survives per unit time and a = the duration of the
stage (Richards, 1059; Richards, Waloff and Sprredbery, 1960; Richards
and Waloff, 1061).
The number of eggs (Po) was calculated from the formula y = b,s
+ b$ + c, where t = temperature and x = the mean age of the population (Waloff and Riohards, 1958). The calculated oviposition rate
multiplied by the number of females in the field gave the number of
eggs per week. The sum total of these weekly figures for the season gave
the va!ue of (Po).
The duration of the egg stage (and of all larval stages), i.e. (a), was
determined experimentally and fitted to Davidson's formula (1944),
where (a) is equal to 100 (1 + e b - - ' * ) K ; t being the temperature in "C.
The calculated values of the constants K, b, c, can be found in Waloff
and Richards (1958).
When the values of (Po) and (a) are estimated and (N) is obtained from
the samples the equation can be solved for (8). The percentage mortality
is 100 (1 - Sa) and this may be used to calculate the number surviving
the egg stage and those recruited into the first larval instar. Ideally, the
calculations can then be repeated for the first and the subsequent instars, in fact, frequently several instars had to be treated together.
The life tables compiled from the nnalysed data are given in Table XI
which shows that by far the greatest percentage of mortality was incurred by the immature Rtages on broom and that the total mortality
was high, ranging between 97.04 and 99.5970 of the original recruits
(eggs) eaeh year. Table XI1 summarises these percentages and gives
their annual deviations from those necessary for stability; the latter
are of course based on the average fecundity in each year. With the
exception of 1957, the differences in the two sets of mortalities gave
reasonable predictions of the trends in the population of Phyto&ecta.
3. The magnitude a d th causes of the population changes
The approximate maximum numbers of the spring adults were known
for 12 years (1948-59) and in that period the adult population fluctuated
between 33 500 and 1000, i.e. by a factor of 33.5. During the period of
the detailed study the population remained at a steady level for the
first three years and then rapidly declined. The fecundity of the females
also remained steady (between 71 and 78 eggs per female) in the first
three years and then declined to 58 in 1957 and to 33 in 1958. At all
times it wm vefy low compared with the potential fecundity of these
beetles (Waloff and Richards, 1958; Donia, 1958). From 4 to 10% of
the eggs collected in the field were sterile, but the degree of viability
was not related to fecundity.
N. WALOFF
where P o := the total number entering the stage, S = the fraction of
population that survives per unit time and a = the duration of the
stage (Richards, 1059; Richards, Waloff and Sprredbery, 1960; Richards
and Waloff, 1061).
The number of eggs (Po) was calculated from the formula y = b,s
+ b$ + c, where t = temperature and x = the mean age of the population (Waloff and Riohards, 1958). The calculated oviposition rate
multiplied by the number of females in the field gave the number of
eggs per week. The sum total of these weekly figures for the season gave
the va!ue of (Po).
The duration of the egg stage (and of all larval stages), i.e. (a), was
determined experimentally and fitted to Davidson's formula (1944),
where (a) is equal to 100 (1 + e b - - ' * ) K ; t being the temperature in "C.
The calculated values of the constants K, b, c, can be found in Waloff
and Richards (1958).
When the values of (Po) and (a) are estimated and (N) is obtained from
the samples the equation can be solved for (8). The percentage mortality
is 100 (1 - Sa) and this may be used to calculate the number surviving
the egg stage and those recruited into the first larval instar. Ideally, the
calculations can then be repeated for the first and the subsequent instars, in fact, frequently several instars had to be treated together.
The life tables compiled from the nnalysed data are given in Table XI
which shows that by far the greatest percentage of mortality was incurred by the immature Rtages on broom and that the total mortality
was high, ranging between 97.04 and 99.5970 of the original recruits
(eggs) eaeh year. Table XI1 summarises these percentages and gives
their annual deviations from those necessary for stability; the latter
are of course based on the average fecundity in each year. With the
exception of 1957, the differences in the two sets of mortalities gave
reasonable predictions of the trends in the population of Phyto&ecta.
3. The magnitude a d th causes of the population changes
The approximate maximum numbers of the spring adults were known
for 12 years (1948-59) and in that period the adult population fluctuated
between 33 500 and 1000, i.e. by a factor of 33.5. During the period of
the detailed study the population remained at a steady level for the
first three years and then rapidly declined. The fecundity of the females
also remained steady (between 71 and 78 eggs per female) in the first
three years and then declined to 58 in 1957 and to 33 in 1958. At all
times it wm vefy low compared with the potential fecundity of these
beetles (Waloff and Richards, 1958; Donia, 1958). From 4 to 10% of
the eggs collected in the field were sterile, but the degree of viability
was not related to fecundity.