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Fishery Bulletin 93(2), 1995 



tercepts. These predicted y-axis intercepts had small 

 standard deviations (SD) ranging from 1.3 h to 1.5 

 h, so this source of error in age estimation was con- 

 sidered negligible. The absolute values of the inter- 

 cepts were then added to the cumulative times of all 

 the observations to estimate the absolute ages for 

 each observed stage for each temperature (Fig. 2). 

 The model was then reestimated by using these ab- 

 solute ages (the fitted lines in Fig. 2). The regression 

 model predicted egg age as an exponential function 

 of temperature and a linear function of stage: 



age = 8.803 e -° 158(em P x stage ( 1) 



The fit had r 2 of 0.96. 



The justification for assuming that egg age was a 

 linear function of stage was as follows. The mean 

 duration of the stages given by New (1966) at 20°C 

 for killifish were 1.0 ±0.35 (1 SD) h for stages <10, 

 4.1 ±1.14 h for stages 11 and 21, and 9.0 ±1.15 h for 

 stages 22 and 25. Thus, stage durations were simi- 

 lar within each of these stage groups and differed 

 between the groups by the ratios 1.0: 4.1: 9.0. Evi- 

 dently, these ratios also applied to orange roughy 

 development, judging by the linear appearance of the 

 orange roughy age-at-stage data for each tempera- 

 ture (Fig. 2) when the x-axis (stage) was scaled by 

 these ratios for stages 1 to 10, 11 to 21, and 22 to 25, 

 respectively. Thus, to use Equation 1 to estimate age 

 from stage, the input value for stage had to be scaled 

 by these ratios (e.g., the appropriate input value for 

 stage 13 would be (H)(1) + (2M4.1) = 19.2). Orange 

 roughy egg stages from 26 to 30 deviated from that 

 of New (1966) and were not of a consistent length. 

 Therefore, scaling of these stages was not done and 

 ages for stages >26 were not modeled. 



The justification for assuming that egg age was 

 an exponential function of temperature was that the 

 egg development period for 140 species of pelagic, 

 spherical marine fish eggs was well predicted as an 

 exponential function of temperature and egg size by 

 Pauly and Pullin (1988). 



Egg ascent and descent rates 



To estimate egg ascent and descent rates, a gradu- 

 ated, perspex cylinder (7x100 cm) was suspended 

 from the ceiling of a shipboard laboratory; its bot- 

 tom was open in a bucket of seawater and the cylin- 

 der was filled with surface seawater (35.00 ppt sa- 

 linity; see below for the temperatures used). Orange 

 roughy eggs of various stages were introduced at the 

 bottom of the cylinder and, following an initial as- 

 cent of 10 cm (to allow the eggs to reach terminal 

 velocity), subsequent ascent was timed over four to 



seven 10-cm intervals. Older eggs sank; therefore 

 these were introduced to the top of the cylinder and 

 descent rates were measured by following an initial 

 descent of 10 cm. Means and standard deviations of 

 these rates were estimated from estimators for a two- 

 stage sampling design, weighted for unequal 

 subsample sizes (Eq. 5 in Picquelle and Stauffer 

 [1985]). 



The water temperature within the cylinder for the 

 experiments on younger eggs (unfertilized, newly 

 fertilized, cell division, and morula-early blastula 

 eggs: stages 0-11 in Fig. 3) was between 6 and 7 de- 

 grees and characteristic of the water column at the 

 depth of the spawners. Since these eggs were very 

 positively buoyant, it was clear (see Results section) 

 that the older of these stages occurred shallower in 

 the water column, so it was necessary to predict how 

 fast they would ascend under the temperature-sa- 

 linity conditions at shallower depths. This was done 

 by using a combination of experimental observation and 

 theory in the following way. 



First, it was observed that unfertilized and stage- 

 1 eggs ascended the experimental cylinder at a mean 

 rate of 275 m-day" 1 at 6°C and 35.00 ppt (Fig. 3). 

 This ascent rate was used to predict the density of 

 these eggs by using the theoretical relationships in 

 Robertson (1981), the seawater density, and seawa- 

 ter viscosity (Sverdrup et al., 1964) in the cylinder. 

 The predicted density was 1.02488 g-cm -3 . To test this 

 theoretical density against experimental determina- 

 tions, the density of unfertilized and stage-1 eggs was 

 measured by diluting the seawater medium (35.00 

 ppt, 10°C) of the eggs with distilled water until the 

 eggs became neutrally buoyant and by calculating 

 the density of the seawater (1.02425 gem 3 ). The 

 theoretical and experimental densities can be com- 

 pared if the former value (determined at 6°C) is ad- 

 justed to 10°C by using the coefficient of thermal 

 expansion of seawater to account for the decrease in 

 density of the eggs with increase in temperature 

 (taken to be equal in seawater and fish eggs: Coombs 

 et al., 1985). The coefficient of thermal expansion was 

 interpolated from Table 3.1 in Neumann and Pierson 

 (1966) at 35.00 ppt and 8.0°C and atmospheric pres- 

 sure and was 151- 10~ 6 per 1°C change in tempera- 

 ture. The resulting theoretical density was 1.02428, 

 virtually the same density as determined experimen- 

 tally. This strongly suggests that the theoretically 

 determined density was realistic and that the theory 

 could be used to adapt experimental ascent rates 

 determined at particular temperatures and salinity 

 to various conditions in the oceanic water column. 



Accordingly, Robertson's (1981) theoretical rela- 

 tionships were used to calculate the density of stage 

 1-11 eggs from their experimentally determined 



