96
Herbivores and Algae: Food Utilization, Growth and Reproduction .•.
preted as a purging of weak individuals, leaving a reduced population with
higher survival probability. This kind of survivorship is usually well
described by a convex or "bathtub" -shaped (Lawless 1982) force of mortality q(x) (see Appendix A4 for details). The simplest possible force of
mortality with this convexity property can be written as
11 = 110 (1- xl x'y ,
(4.27)
with 110 being the instantaneous mortality rate (dati) at age x = 0, and x' the age
at which 11 = O. The corresponding survival function is given by substituting Eq.
(4.27) into Eq. (A4.5) and solving the integral in the exponent:
lex) = exp(-i 110 x' Q - (1 - xl X
l
)3»
(4.28)
When Eq. (4.28) is fitted to the survival curves shown in Fig. 4.14, the
parameters of Eq. (4.27) are estimated as 110 = 0.0226 ± 0.0060 dati and
x' = 12.6 ± 1.2 days. In other words, approximately 2% of the neonates die per
day, while mortality is practically zero at an age around 12 days; 50% of the
population die before reaching an age of35.9 days (the median survival time).
The deviations from the average survival function within each cohort did
not seem to vary systematically among experimenters or treatment levels.
Fig. 4.14 shows that much of the variability among individual survival
curves is within the expected range for the small initial cohort sizes (mostly
20 individuals) used in these experiments. Although more than 5% of the
survival scores in Fig. 4.14 fall outside the binomial 95% confidence limits,
the presence of additional within-treatment variance as shown in Appendix
A4 indicates that these confidence limits are not sufficiently robust to reject
the hypothesis that all the survival curves in Fig. 4.14 are members of the
same population.
Daphnia Survival in Food-Limited Transfer Culture. In experimental setups
with continuous food supply, such as Taylor (1985), the total number of
animals that can be handled in a single run is much lower than what is possible in transfer culture designs. This is probably the reason why apparently all
published survival curves for Daphnia have been measured in transfer culture experiments (e.g., Ingle et al. 1937; Frank et al. 1957; Goulden et al. 1982;
Porter et al. 1983; Lynch 1989). This means that all data on Daphnia survival
under limiting food conditions might suffer from the same limitations as
discussed in Section 4.4 (cf. Tillmann and Lampert 1984; DeMott 1989).
Survival curves for Daphnia populations raised at low food levels generally show increased juvenile mortality in addition to reduced longevity
(Frank et al. 1957; Goulden et al. 1982; Lynch and Ennis 1983; Porter et al.
1983; Lynch 1989). Juvenile mortality has been proposed to result from a
lower resistance to withstand starvation than in adults, but this cannot be
the full explanation as juveniles in transfer-culture experiments receive a
much higher per capita food supply than adults (cf. Section 4.4).
Herbivores and Algae: Food Utilization, Growth and Reproduction .•.
preted as a purging of weak individuals, leaving a reduced population with
higher survival probability. This kind of survivorship is usually well
described by a convex or "bathtub" -shaped (Lawless 1982) force of mortality q(x) (see Appendix A4 for details). The simplest possible force of
mortality with this convexity property can be written as
11 = 110 (1- xl x'y ,
(4.27)
with 110 being the instantaneous mortality rate (dati) at age x = 0, and x' the age
at which 11 = O. The corresponding survival function is given by substituting Eq.
(4.27) into Eq. (A4.5) and solving the integral in the exponent:
lex) = exp(-i 110 x' Q - (1 - xl X
l
)3»
(4.28)
When Eq. (4.28) is fitted to the survival curves shown in Fig. 4.14, the
parameters of Eq. (4.27) are estimated as 110 = 0.0226 ± 0.0060 dati and
x' = 12.6 ± 1.2 days. In other words, approximately 2% of the neonates die per
day, while mortality is practically zero at an age around 12 days; 50% of the
population die before reaching an age of35.9 days (the median survival time).
The deviations from the average survival function within each cohort did
not seem to vary systematically among experimenters or treatment levels.
Fig. 4.14 shows that much of the variability among individual survival
curves is within the expected range for the small initial cohort sizes (mostly
20 individuals) used in these experiments. Although more than 5% of the
survival scores in Fig. 4.14 fall outside the binomial 95% confidence limits,
the presence of additional within-treatment variance as shown in Appendix
A4 indicates that these confidence limits are not sufficiently robust to reject
the hypothesis that all the survival curves in Fig. 4.14 are members of the
same population.
Daphnia Survival in Food-Limited Transfer Culture. In experimental setups
with continuous food supply, such as Taylor (1985), the total number of
animals that can be handled in a single run is much lower than what is possible in transfer culture designs. This is probably the reason why apparently all
published survival curves for Daphnia have been measured in transfer culture experiments (e.g., Ingle et al. 1937; Frank et al. 1957; Goulden et al. 1982;
Porter et al. 1983; Lynch 1989). This means that all data on Daphnia survival
under limiting food conditions might suffer from the same limitations as
discussed in Section 4.4 (cf. Tillmann and Lampert 1984; DeMott 1989).
Survival curves for Daphnia populations raised at low food levels generally show increased juvenile mortality in addition to reduced longevity
(Frank et al. 1957; Goulden et al. 1982; Lynch and Ennis 1983; Porter et al.
1983; Lynch 1989). Juvenile mortality has been proposed to result from a
lower resistance to withstand starvation than in adults, but this cannot be
the full explanation as juveniles in transfer-culture experiments receive a
much higher per capita food supply than adults (cf. Section 4.4).