210 
Fishery Bulletin 115(2) 
day) is expected to be fastest soon after first feeding, 
to decrease thereafter, and a large decrease or growth 
stanza is associated with an ontogenetic shift in feed¬ 
ing from selective particulate feeding to omnivorous fil¬ 
ter feeding (Deegan, 1990; Lozano et al., 2012) in com¬ 
bination perhaps with transgressing the coastal bound¬ 
ary layer. To represent this shift in feeding strategy 
between the larval and juvenile stages, a derivative 
of the Gompertz model (Gompertz, 1825) was chosen 
because it highlights this specific pattern of growth. 
Larval somatic growth of Gulf menhaden was modeled 
by applying only the directly analyzed otolith data to 
a 2-cycle Laird-Gompertz growth model (Laird et al., 
1965; Zweifel and Lasker, 1976; Raynie, 1991), and fit¬ 
ting the model with the use of R software. The 2-cycle 
Laird-Gompertz growth model is represented by the 
following equation: 
A = -^-null^ “ ^ 
= MIN it,t*),and (D 
Ag = MAXit — 
where = 
•t-null = 
7 = 
where A = 
a = 
t* = 
6 = 
where B = 
P = 
the SL (in millimeters) at age (dah); 
SL at hatching for Gulf menhaden; and 
A 
a 
the age specific instantaneous growth rate 
at spawning; 
the rate of exponential decay in growth rate 
before t*; 
the time at which there is a shift between 
somatic growth stages; 
B 
0 
the age specific instantaneous growth rate 
immediately after the stage shift at ^ = t*; 
and 
the exponential decay in growth in B. 
The length at hatching was estimated but was based 
on literature. To increase model speed, length at hatch¬ 
ing was constrained between 1 and 4 mm on the ba¬ 
sis of the literature reporting between 2 and 4 mm 
(Hettler, 1981; Warlen, 1988; Powell, 1994; Raynie and 
Shaw, 1994). Similarly, t* was estimated with a lower 
bound constraint of 20 dah, and an upper bound con¬ 
straint of 45 dah (Suttkus, 1956; Hettler, 1981; Raynie, 
1991). Hind-casting to estimate growth rates for larvae 
at ages not sampled, owing to larvae being offshore at 
these early ages, can be accomplished by using this 
2-cycle Laird-Gompertz growth model (Lozano et al., 
2012). The 2-cycle Laird-Gompertz model was applied 
to the pooled otolith data, and to each of the 2 sample 
years. Comparison between the yearly and pooled mod¬ 
els was conducted with an F-test in R software. 
The Laird parameterization of the Gompertz growth 
model was applied to both the pre-ontogenetic trans¬ 
formation period and the postontogenetic transforma¬ 
tion period for groupings based on SL from the distri¬ 
bution of SLs of larvae whose otoliths were examined 
and based on the estimated transformation age from 
previous literature (Raynie, 1991). The Laird-Gompertz 
model was fitted by using R software and took the fol¬ 
lowing form: 
ka- 
( 2 ) 
where Lj 
■^'null 
a 
k 
the SL (in millimeters) at age t (days); 
SL at hatching for Gulf menhaden; 
the rate of exponential decay; and 
a dimensionless parameter so that ka rep¬ 
resents the instantaneous growth rate at 
hatching. 
Hind-casting can also be used to estimate growth rates 
for larvae at ages not sampled with this model struc¬ 
ture (Lozano et al., 2012). 
Changes in the magnitude of growth rate were mea¬ 
sured by using differences in the width of the daily 
increments and variation in ring distance from the oto¬ 
lith core. Changes in otolith ring width and distance 
from the core are expected to occur after the ontoge¬ 
netic shift in feeding strategy. Ring width was mea¬ 
sured with the method described by Kupchik and Shaw 
(2016), and mean ring distance from the core and mean 
ring width were calculated for both the sampling pe¬ 
riod from October 2006 to March 2007 and the period 
from September 2007 to March 2008. 
Results 
Hydrology 
Water temperatures based on sampling depth yielded 
no statistical differences—a result that is consistent 
with a seasonally, vertically well-mixed tidal pass. 
Water temperatures (mean: 20.5°C) generally had low 
variability during any sampling effort. However, from 
late November 2006 to early February 2007, recorded 
temperatures were colder and fluctuations were great¬ 
er than those during other sampling efforts. In par¬ 
ticular, the January 2007 sampling had a maximum 
difference of 10.2°C during the 72-h sampling period. 
Water temperatures were warmer during September 
and October, cooled from November through February, 
and then began to warm again in March and April. 
During November 2006, there was a large decrease in 
water temperature, and median water temperatures for 
each sampling effort remained below 15°C until early 
February 2007. In November 2007, there was also a 
decrease in water temperature; however, median water 
temperatures remained higher than 17°C for all subse¬ 
quent sampling efforts. 
Seasonality of larval Gulf menhaden collections 
There were 2846 Gulf menhaden larvae collected in 
Bayou Tarellan during the sampling efforts from Octo¬ 
ber 2006 to April 2008; 2158 larvae were collected dur¬ 
ing year 1, October 2006 to March 2007, and 688 larvae 
were collected during year 2, September 2007 to March 
