Kupchik and Shaw: Age, growth, and recruitment of larval and early juvenile Micropogomas undulatus 
23 
into the distance measurements for location of the 
sinusoidal peaks and, therefore, of the position and 
width of the respective rings along the radius used for 
reading (Fig. 2D). 
Ten otoliths were selected at random to be analyzed 
by using the traditional paired-reader method. These 
results were then used to compare them against 2 new, 
independently run FFT-generated ring counts. The 
same number of rings were observed for all 10 otoliths 
through the independently run FFT method, and only 
1 otolith had a difference of 1 ring between the FFT 
method and the paired-reader method. 
Otolith aging and larval hatching dates 
Larval age, estimated as days after hatching (dah), 
was determined from the increment counts for each 
otolith radius with the methods previously described. 
Daily formation of increments has been validated and 
deposition has been confirmed to have a positive rela- 
tionship to growth of larval Atlantic croaker (Searcy, 
2005). Moreover, daily increment formation has been 
confirmed and validated for other species in the fam- 
ily Sciaenidae that live in similar environments, such 
as red drum ( Sciaenops ocellatus\ Wilson et al., 1987) 
and spot ( Leiostomus xanthurus; Warlen and Chester, 
1985). For the purposes of our analysis, we, therefore, 
assumed that increment deposition occurs daily. Fol- 
lowing the methods used by Cowan (1988) and on the 
basis of laboratory work (Arnold 3 ), we applied a 4-d 
lag for first increment formation after hatching for 
larvae of Atlantic croaker, (Warlen and Chester, 1985). 
This application resulted in a calculation of total age 
by adding 4 to the otolith count. Estimated ages were 
calculated for specimens for which otolith radii were 
measured. Ages were estimated for all other larvae and 
early juveniles not selected for dissection by using age- 
length keys and the FSA package for R software, vers. 
2.13.0 (R Development Core Team, 2011). The hatching 
date was determined by subtracting the age (dah) from 
the date of collection. 
Growth and timing of estuarine ingress 
A linear model was run to allow direct comparison of 
our results with those of previous studies where a lin- 
ear model was used. Larval growth of Atlantic croaker 
is slowest near the hatching date, increases thereafter, 
and slows again as larvae settle and begin further or- 
gan and sensory development; therefore, a derivative 
of the Gompertz model was selected as the nonlinear 
model for our study because it highlights this specific 
pattern of growth (Gompertz, 1825). Somatic growth of 
larval Atlantic croaker was modeled with only the di- 
rectly analyzed otolith data by using a Laird-Gompertz 
growth model (Laird et al., 1965; Zweifel and Lasker, 
3 Arnold, C. R. 1983. Univ. of Texas Mariculture Project 
1982-1983, 36 p. Marine Science Institute, Univ. Texas, Port 
Aransas, TX. 
1976; Lozano et al., 2012). This model had a set inter- 
cept of L nu n=1.5 mm in notochord length (NL) to ac- 
curately represent the hatching length (dah=0; Warlen, 
1980; Cowan, 1988; Barbieri et al., 1994a, 1994b). We 
used the following equation for the Laird-Gompertz 
growth model: 
where L t = 
L 
null = 
a - 
k = 
the SL, measured in millimeters, at an age 
(dah); 
the SL at hatching for Atlantic croaker; 
the rate of exponential decay; and 
a dimensionless parameter so that ka rep- 
resents the instantaneous growth rate at 
hatching. 
Hindcasting was used to estimate growth rates with 
the Laird-Gompertz growth model (Lozano et al., 2012) 
for ages of larvae that were not sampled, because lar- 
vae were located offshore at these early ages, 
Instantaneous growth rates (i.e., the rate of growth 
at a particular time in dah) were estimated with the 
maximum growth rates calculated both from the equa- 
tion for the first derivative of the Laird-Gompertz mod- 
el and from the mean growth rates calculated on 10-d 
intervals. We used the following equation to determine 
the first derivative of the Laird-Gompertz model: 
G m = L Dull e ka - e ~ at) *(kae- at \ (2) 
where Gpj = the instantaneous daily growth rate by 
means of the first derivative of the 
Laird-Gompertz model. 
Mean growth rates for the 10-d interval were calcu- 
lated with the following equation: 
G f - = '- Lt2 ~ - t - 1 ] , where t2 > tl (3) 
10 A t 
and where = the average growth rate for that 10-d 
interval; 
L t i = the modeled SL at an initial time ; and 
L t 2 = the modeled SL at time . 
Instantaneous growth rates then were determined 
from the natural log of the lengths in the mean growth 
equation described above. 
The estuarine recruitment date for larvae was de- 
termined from the difference in the width of the daily 
increments and variation in distance of the ring from 
the otolith core. The recruitment date for the pretrans- 
formation larvae (<10 mm) was determined as the day 
after hatching at which there was an increase in the 
ring width and an increase in the distance between 2 
adjacent rings. Movement by the larvae into the estu- 
ary, where there is lower salinity, increased nutrient 
loads, and higher primary production, has been shown 
to cause a rapid increase in growth for larvae and 
young-of-the-year juveniles (Hoss et al., 1988; Moser 
and Gerry, 1989). 
A multivariate analysis of variance (MANOVA) 
was performed to test for differences in length and 
