96 
Fishery Bulletin 110(1) 
end of the spawning season in the area. Nevertheless, 
applying a correction such as weighting samples accord- 
ing to sampling time should be considered to improve 
the accuracy of future estimates of larval production. 
The CPFV index and day-of-year variables only partly 
explain the small or zero catches that have occurred 
frequently in the 2000s (cf. Fig. 4 and Fig. 6). For ex- 
ample, the mean estimated probability of capturing one 
or more larvae for samples in the core area was 0.04 
in 2008 (range <0.01 to 0.18). Although it was unlikely 
that larvae would be captured at any single station, the 
predicted probability of capturing no larvae at any of 
the sixty-six core stations in aggregate was less than 
0.001. The model-predicted odds were similar for other 
recent years when no larvae were captured. Given the 
extremely small odds that the zero catches would oc- 
cur by chance alone for several years, these results 
indicate a lack of model fit. One potential explanation 
is that stock sizes have recently declined more than 
the CPFV index has indicated. The most recent stock 
assessment (Crone et al., 2009) included an alternate 
model scenario, denoted AB, which included potential 
changes in gear selectivity and catchability of Pacific 
mackerel through time. This scenario indicated that Pa- 
cific mackerel abundance may have been very low from 
2004 through 2007. If the CPFV index did accurately 
reflect the trend in stock size, one or more unmeasured 
habitat variables may have had particularly strong 
effects on the distribution of Pacific mackerel in the 
2000s. Another potential explanation is that habitat 
conditions were even more favorable in Mexican wa- 
ters or other unsampled areas than in the SCB during 
this time; therefore most Pacific mackerel may have 
spawned elsewhere. 
The model could discriminate moderately between 
habitats where larvae would be present or absent, as 
indicated by an area under curve of 0.80. We note 
that a model with area under curve of 0.5 would have 
the same ability as random selection to make correct 
predictions. The model may be useful for stratifying 
sampling effort in future cruises if capturing Pacific 
mackerel is a priority. When the distribution of fish 
is very patchy, their presence may not be detected in 
net samples by chance alone, even in habitat where 
they occur nearby (Mangel and Smith, 1990). The zero 
catches of Pacific mackerel in the CalCOFI samples in 
recent years have created a particular problem because 
the population models used in stock assessment cannot 
easily incorporate zero estimates for the population 
during a year as a whole (because zeros would indicate 
extinction; Dorval et ah, 2007). A similar model to this 
one could be employed adaptively during a cruise by 
adding additional net tows in areas (and times) where 
environmental conditions indicate Pacific mackerel lar- 
vae are likely to occur. Such an approach would require 
that zooplankton displacement volumes be measured 
onboard and the geostrophic flow field calculated by 
using satellite-derived sea-surface height data during 
a cruise. Survey estimates could be post stratified into 
several categories of predicted habitat quality (e.g., 
high-quality versus low-quality habitat as defined by 
ranges of predicted capture probabilities) to improve 
estimates. 
Conclusions 
Presence of Pacific mackerel larvae could be predicted 
in the California Current as a function of zooplank- 
ton displacement volume, geostrophic flow, the interac- 
tion between latitude and day of year, the interaction 
between latitude and water temperature, and the CPFV 
index as a blocking variable. The model had area under 
a receiver-operating-characteristic curve of 0.80 but did 
not completely explain the zero catches that occurred fre- 
quently in the 2000s. Two types of spawners overlapped 
spatially within the survey area: those that exhibited 
peak spawning during April in the SCB at about 15.5°C 
and a smaller group that exhibited peak spawning in 
August near Punta Eugenia, Mexico, at 20°C or greater. 
The SCB generally had greater zooplankton than Mexi- 
can waters but less appropriate (lower) geostrophic flows. 
Mexican waters generally exhibited greater predicted 
habitat quality than the SCB in cold years. Predicted 
quality of the habitat in the SCB was greater in the 
1980s to 2008 than in the earlier years of the survey 
primarily because temperatures and geostrophic flows 
were more appropriate. However, stock size the previ- 
ous year had a larger effect on predictions than any 
environmental variable, indicating that larval Pacific 
mackerel did not fully occupy the suitable habitat during 
most years. 
Acknowledgments 
We thank P. Crone for providing CPFV index data and 
reviewing the manuscript, N. Lo, A. MacCall, and three 
anonymous reviewers for their thoughtful comments on 
the article, and the many people who have collected and 
processed data as part of the CalCOFI program for more 
than sixty years. 
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