Schlick and de Mutsert: Growth of adult river herring that spawn in tributaries of the Potomac River 
65 
Table 5 
Parameter estimates from von Bertalanffy growth function for males, females, and sexes combined of ale- 
wife (Alosa pseudoharengus) and blueback herring (Alosa aestivalis ), with subsequent sums of squares 
(SSQ) from model fitting and sample size. The parameters are mean asymptotic length (L„), given in stan¬ 
dard length in centimeters, growth rate coefficient ( K ), and the time (or age) at which the average length 
was zero (t 0 ). 
Species 
Model 
Sex 
L„ 
(cm) 
K 
(per year) 
^0 
(per year) 
SSQ 
n 
Alewife 
von Bertalanffy 
Male 
233.8 
0.218 
-5.97 
30,131 
329 
Female 
250.9 
0.237 
-5.25 
34,579 
244 
Combined 
257.2 
0.179 
-6.04 
96,589 
573 
Blueback herring 
von Bertalanffy 
Male 
213.7 
0.387 
-3.27 
8,763 
162 
Female 
219.0 
0.837 
-0.75 
11,522 
123 
Combined 
220.3 
0.525 
-1.69 
34,956 
285 
examine the difference between sexes. All of 
the models converged, indicating that enough 
data was available for the models to success¬ 
fully run. 
The von Bertalanffy growth parameters dif¬ 
fered between alewife and blueback herring 
(P<0.0001). Alewife grew faster and obtained 
larger sizes than blueback herring (Table 5). 
A likelihood ratio test confirmed the difference 
between species was not due to coincidence 
(X 2 =39, df=3, P<0.0001); however, no single 
parameter was responsible for this difference. 
For alewife, parameters between sexes were 
statistically different when the von Bertalanffy 
growth function was used (P<0.0001). The 
models for both species show females growing 
faster than males and attaining larger values 
of (Table 5, Fig. 3A). The standardized re¬ 
siduals for the von Bertalanffy growth curve 
were randomly distributed, indicating that the 
model was a good fit (Fig. 3B). A likelihood ra¬ 
tio test confirmed that the difference between 
sexes was not due to coincidence (% 2 =229, df=3, 
P<0.0001); however, differences were not sig¬ 
nificant between individual parameters. 
For blueback herring, an analysis of residual 
sum of squares revealed that female blueback 
herring grew significantly larger and faster 
than males (PcO.OOOl; Table 5, Fig. 4A), and 
a likelihood ratio test confirmed the differenc¬ 
es were significant (% 2 =138, df=3, P<0.0001). 
Standardized residuals between the von Ber¬ 
talanffy growth function and observed values 
were random (Fig. 4B). Differences between 
sexes were based on the interactions between 
the parameters of L x and growth rate coeffi¬ 
cient ( K ) (x 2 =8, df=2, P=0.02) and interactions 
between and the time (or age) at which the 
average length was zero (t 0 ) (von Bertalanffy: 
200 210 220 230 
Predicted length (mm) 
Figure 3 
(A) Observed length at age for female (gray dots) and male 
(black plus signs) alewife (Alosa pseudoharengus ) captured 
in the Potomac River between 2007 and 2015, with predicted 
length at age from von Bertalanffy growth models (solid lines). 
(B) Standardized residuals versus fitted values for the von Ber¬ 
talanffy growth curves for female (gray dots) and male (black 
plus signs) alewife. 
