FISHERY BULLETIN: VOL. 87, NO. 3, 1989 



3 |- 



2 - 



0.05 



0.1 



0. 15 



CX 



m 



Figure 9. — The estimated mortality coefficient (6) is biased by errors in the assumed growth 

 coefficient for feeding larvae, a,„ = 0.48. The true mortaHty coefficient (|J) was 1.5. 



eter values and their variances. Nevertheless, 

 most ichthyoplankton sampling problems are 

 sufficiently similar so that the results derived for 

 anchovy provide a general idea of the sample size 

 required for adequate precision of larval mortal- 

 ity estimates. (When using the regressions 

 derived in this study to estimate sample size, 

 parameter values should be within the range 

 used in the simulation [1.0 ^ P < 3.0, 0.5 < D < 

 2.0]. Values outside these ranges could lead to 

 unreliable estimates of sample size.) The results 

 also provide an assessment of the effect of biased 

 growth rates on estimates of larval mortality 

 rate, which has general applicabihty to many 

 species. 



Caveats 



Application to Site-Intensive Studies 



Small-scale site-intensive studies may be con- 

 ducted to study underlying mechanisms of larval 

 mortality rate by measuring larval condition, 

 gi'owth, starvation rates, and mortality rate in 

 small segments of the habitat. Such studies have 

 greater problems with bias and precision than 

 the CalCOFI surveys where the entire spawning 

 habitat is sampled. As noted above, an import- 

 ant potential bias is the transport of larvae in or 

 out of the study area. Taggart and Leggett 

 (1987) noted that failure to account for advective 

 losses of larvae from a small bay resulted in a 



significant overestimate of mortality. 



Another problem arises from the choice of 

 study areas. Many specimens must be collected 

 over a short period to assess growth, starvation, 

 and other condition factors. If sites are selected 

 that contain larval densities that are high, rela- 

 tive to the average density for the entire habitat, 

 and patchy, the effect will be to increase the 

 variance, because the variance is often positively 

 correlated with the density of larvae (Smith and 

 Richardson 1977), and thereby reduce the power 

 to detect differences in mortality rate between 

 sites. The simulations were based on large 

 regions of anchovy habitat and therefore under- 

 estimate sample size required to detect mortal- 

 ity rate differences between small areas of high 

 larval abundance. 



Application to Other Species 



A key difference between larval anchovy and 

 most other species of larval fishes is that an- 

 chovy are very abundant. The simulation results 

 indicate that surprisingly few positive tows are 

 needed to detect relatively small differences in 

 mortality rates. In the regions considered in the 

 simulation, 50-60% of the tows were positive, 

 and the number of larvae caught per tow aver- 

 aged 125, with 88% < 10 mm in length. For a less 

 abundant species, the proportion of positive 

 tows and the average number caught per tow 

 would be much lower, and many more tows 



412 



