Survival Curves and Mortality Rates
with the expectation and variance of N(x) being
E(N(x»="oI(x) and
Var(N(x»=no1(x)(1-I(x».
241
(A4.11)
(A4.12)
It is seen from Eq. (A4.12) that the variance in the observed survival curve
N(x), will be maximal at the median survival time, that is, when l(x) = Y2. It is
also seen from Eqs. (A4.11), (A4.12) that N(x)ln o is an unbiased estimator of
true survival function l(x), and that it is consistent (the variance of decreases
to zero as no ~ (0). A 1 - a confidence interval for the number of survivors at
age x will be given by numbers n' and n" satisfying
n=n'
LPr{N(x) = n}= a/2 and
(A4.13)
n=O
n=n"
LPr{N(x)=n}= l-a/2·
(A4.14)
nzO
Due to the amount of work involved in a typical life-table experiment,
most Daphnia survival studies have followed only a single cohort per
treatment, with a relatively small initial cohort size (20-40 individuals). A
notable exception is the work of Frank et al. (1957), who used initial
cohorts of up 800 Daphnia pulex individuals, with up to eight replicates
within each treatment (see Section 4.4 for more details on their
experimental design). Frank et al. (1957) reported the standard deviation of
the observed survival curve for each treatment, which can be compared to
the predicted standard deviation from the binomial model Eq. (A4.12):
SI(x) =In: l(x)(l-l(x».
(A4.15)
As Frank et al. (1957) used a constant culture volume of 25 ml, the initial
cohort size no in their experiments will be directly proportional to animal
density in each treatment (1-32 mr
1
).
Figure A4.1 shows that the standard deviation of the survival curve has a
general resemblance to the concave relationship predicted by Eq. (A4.15),
although the actual variability among replicated survival experiments is,
for most treatments, much higher than would be expected from the
binomial model. This means that the binomial confidence limits Eqs.
(A4.13), (A4.14) should be regarded as very optimistic, and that other
sources of variance can contribute strongly to the total variability among
replicated survival experiments, even within the same laboratory.
with the expectation and variance of N(x) being
E(N(x»="oI(x) and
Var(N(x»=no1(x)(1-I(x».
241
(A4.11)
(A4.12)
It is seen from Eq. (A4.12) that the variance in the observed survival curve
N(x), will be maximal at the median survival time, that is, when l(x) = Y2. It is
also seen from Eqs. (A4.11), (A4.12) that N(x)ln o is an unbiased estimator of
true survival function l(x), and that it is consistent (the variance of decreases
to zero as no ~ (0). A 1 - a confidence interval for the number of survivors at
age x will be given by numbers n' and n" satisfying
n=n'
LPr{N(x) = n}= a/2 and
(A4.13)
n=O
n=n"
LPr{N(x)=n}= l-a/2·
(A4.14)
nzO
Due to the amount of work involved in a typical life-table experiment,
most Daphnia survival studies have followed only a single cohort per
treatment, with a relatively small initial cohort size (20-40 individuals). A
notable exception is the work of Frank et al. (1957), who used initial
cohorts of up 800 Daphnia pulex individuals, with up to eight replicates
within each treatment (see Section 4.4 for more details on their
experimental design). Frank et al. (1957) reported the standard deviation of
the observed survival curve for each treatment, which can be compared to
the predicted standard deviation from the binomial model Eq. (A4.12):
SI(x) =In: l(x)(l-l(x».
(A4.15)
As Frank et al. (1957) used a constant culture volume of 25 ml, the initial
cohort size no in their experiments will be directly proportional to animal
density in each treatment (1-32 mr
1
).
Figure A4.1 shows that the standard deviation of the survival curve has a
general resemblance to the concave relationship predicted by Eq. (A4.15),
although the actual variability among replicated survival experiments is,
for most treatments, much higher than would be expected from the
binomial model. This means that the binomial confidence limits Eqs.
(A4.13), (A4.14) should be regarded as very optimistic, and that other
sources of variance can contribute strongly to the total variability among
replicated survival experiments, even within the same laboratory.