90 
Fishery Bulletin 110(1) 
Table 1 
Summary data determined with the logistic generalized additive model to predict presence of Pacific mackerel ( Scomber 
japonicus) larvae. The model was based on 10,278 samples collected from 1951-2008 that had complete physical data for predic- 
tor variables. Smooth terms were natural splines with three knots, except for the temperature xlatitude and day -of-y ear xlatitude 
interactions, which were tensor product interactions of natural splines with five knots for temperature or day of year and latitude. 
Note that predictor variables were scaled from 0 to 1 before modeling (Wood, 2006). 
Parametric coefficients 
Estimate 
Standard error 
z 
P 
Intercept 
-4.278 
0.183 
-23.34 
<0.01 
Commercial-passenger-fishing-vessel index 
0.010 
0.001 
9.46 
<0.01 
Estimated degrees 
Reference degrees 
of freedom 
of freedom 
Smoothing terms 
c 2 
P 
X 
P 
Log zooplankton volume 
1.883 
1.987 
19.55 
<0.01 
Index of geostrophic flow 
1.919 
1.994 
172.96 
<0.01 
Temperature xlatitude 
15.585 
17.355 
172.96 
<0.01 
Day of year xlatitude 
12.116 
13.456 
67.90 
<0.01 
dicated that there was essentially no support for the 
model without interactions (Burnham and Anderson, 
2001). The final logistic model indicated that presence 
of Pacific mackerel larvae could be predicted on the 
basis of zooplankton displacement volume, geostrophic 
flow, the CPFV index, the interaction between latitude 
and day of year, and the interaction between latitude 
and water temperature (Table 1). Mixed-layer depth was 
dropped from the model because the “select” procedure 
( i . e . , “shrinkage”) indicated it was not a useful predic- 
tor. The model exhibited acceptable discrimination, as 
indicated by the area of a receiver-operating character- 
istic curve (i.e., where probability of concordance ranges 
from 0 to 1) of 0.80. 
Partial effects of model predictors (i.e., the effect of a 
predictor at the median value of other variables in the 
model; Fig. 3) indicated that Pacific mackerel larvae 
were most likely to be captured when the stock size was 
large the previous year, as reflected by the CPFV index. 
Partial effects for the log of zooplankton displacement 
(peak 5.75 log[ml/1000m 3 ]) and geostrophic flow (peak 
5.0xl0“ 6 ) were unimodal. The effect for geostrophic flow 
was skewed so that the greatest predicted probability 
of capture occurred at greater geostrophic flows. The 
interaction surface between temperature and latitude 
exhibited a peak at 15.5°C that was centered between 
30° and 35°N latitude in the SCB, and a secondary peak 
at temperatures greater than about 22°C where only 
Pacific mackerel in Mexican waters were captured (Fig. 
3D). The interaction surface between latitude and day 
exhibited the largest peaks in April in the SCB and in 
August for latitudes less than about 27°N (Fig. 3E) but 
was more uniform throughout the range of latitudes 
sampled than was temperature. 
A larger proportion of the predicted high-quality 
habitat occurred in Mexican waters, particularly near 
Punta Eugenia, than in the core area during most years 
when both areas were sampled (Fig. 4). The greatest 
predicted probabilities of capturing larvae occurred 
in the early 1980s, particularly in 1981, when large 
catches actually occurred. The most important predictor 
influencing these values was stock size, as indicated by 
the CPFV (Fig. 5), although the zooplankton and tem- 
perature predictors also indicated conditions were good 
for Pacific mackerel larvae in the SCB during the early 
1980s. Model predictions followed the general trend in 
observed catches (Fig. 5, F and G) but did not coincide 
with the many zero catches that occurred in the 2000s 
(Fig. 2). The model indicated that mean likelihood of 
capturing larvae in the core area was only slightly less 
in the 2000s than in the 1990s. 
The most consistent differences between the core 
area and Mexican waters were that the core area had 
more appropriate (greater) zooplankton displacement 
volumes but less appropriate (slower) geostrophic flows 
than Mexican waters (Fig. 5, B and C). The northern 
portion of Mexican waters sampled (north of CalCOFI 
line 95) generally had greater zooplankton displacement 
volumes but less appropriate geostrophic flows than the 
southern portion near Punta Eugenia. 
All of the sampled areas exhibited greatest predicted 
probabilities of larval capture when their mean tem- 
peratures were near the 15.5°C temperature peak (Fig. 
5, A, G, and H). For example, the area near Punta Eu- 
genia exhibited greater probabilities of capture than the 
core area during the early 1950s. Mean temperatures 
were in the range of 15-16. 5°C in southern Mexican wa- 
ters at this time but cooler than 14°C in the core area. 
In contrast, the southern portion of the sampled area 
in Mexico was predicted to be relatively poor habitat for 
Pacific mackerel larvae in 1959 and 1965, despite the 
relatively high mean water temperatures (>19°C) that 
approached the second, warmer predicted temperature 
peak in the model. This outcome was due to the effect of 
