78 
Fishery Bulletin 1 15(1) 
shrimp population in each salinity zone on each sample 
date, we combined length-frequency distributions from 
all 4 habitat types in each zone from each sample date. 
Finally, we converted the combined length-frequency 
distribution in each salinity zone on each sample date 
into a relative frequency distribution and apportioned 
the total number of shrimp collected in each zone on 
each sample date to fit this distribution. These weight- 
ed length-frequency distributions were used in subse- 
quent analyses of mortality and growth. 
Daily instantaneous mortality rates (Z) were es- 
timated in each salinity zone by using a horizontal 
catch-curve analysis (Vetter, 1988). We assumed Z 
was equal to the daily instantaneous natural mortal- 
ity rate (M) because there was no fishery for juvenile 
white shrimp in our study area, and we removed only 
a very small fraction of the total population during our 
sampling. We combined and converted length-frequency 
data from multiple sampling trips within each salin- 
ity zone to age-frequency data by assuming a growth 
rate of 1 mm TL/d, a reasonable assumption for juve- 
nile penaeid shrimps in general (Dali et ah, 1990) and 
white shrimp specifically (Rozas and Minello, 2011). 
Using the age-frequency data, we calculated mortal- 
ity with the following 2 methods: 1) a linear regres- 
sion of the ln(density+0.1) against age, where the slope 
is an estimate of mortality (Ricker, 1975) and 2) the 
Chapman-Robson estimator (Chapman and Robson, 
1960) with the standard error corrected for overdisper- 
sion (Smith et ah, 2012). We started the catch curve 
with the regression method at the age of highest abun- 
dance and included all ages up to but not including the 
first age at which time there were <1 individual (Smith 
et ah, 2012). For the Chapman-Robson estimator, we 
included all ages greater than the age of peak abun- 
dance. We compared mortality rates between catch- 
curve methods and among salinity zones by first taking 
the difference between 2 estimates and then construct- 
ing a 95% confidence interval (CD for the difference. 
We considered results significantly different when the 
95% Cl of the difference between 2 estimates did not 
include zero (Schenker and Gentleman, 2001). 
Growth 
We calculated growth rates by following individual co- 
horts and using the mean size of a cohort on 2 consecu- 
tive sample dates to estimate a mean growth rate be- 
tween sample dates. Individual cohorts of shrimp were 
identified from each of the length-frequency distribu- 
tions on different sample dates in each salinity zone 
by using the mixdist package, vers. 0.5-4 (Macdonald 
and Du, 2012) in R, vers. 3.1.0 (R Core Team, 2014), 
and the mean growth rate for a cohort between sample 
dates was calculated as 
p _ /^t+i ~ Mt 
'-^absolute , . > 
n+1 ~ h 
where /J.^ = the mean carapace length at time t; and 
/^t + 1 = the mean carapace length at time ^ + 1. 
Before calculating growth, carapace length was con- 
verted to total length by using the formula TL = CL 
X 4.944 (Baker and Minello, 2010). This conversion 
makes it easier to compare our growth rates with pub- 
lished values. Mean growth rates among salinity zones 
were compared as described above for mortality rates. 
For each sample date in each salinity zone, we at- 
tempted to model cohorts by using normal, lognormal, 
or gamma distributions based on previous observations 
of length-frequency distributions of penaeid shrimp as 
they immigrated into estuaries (Baxter and Renfro, 
1967). We used Akaike’s information criterion adjusted 
for small sample size (AICc), AAICc values (the differ- 
ence in AICc values between a given model and the 
model with the lowest AICc value), and values (AIC 
weights, which can be interpreted as an estimate of the 
probability that a given model is the best among all 
models considered, given the data) to compare and se- 
lect the best model or models that described the shape 
and the mean size and standard deviation of the mean 
of shrimp cohorts (Burnham and Anderson, 2002). 
Secondary production 
Secondary production that occurred in each salinity 
zone over the 84-d sampling period was estimated in 
kilograms per hectare with the size-frequency meth- 
od (Garman and Waters, 1983) because we were not 
able to track cohorts over all sample dates. The size- 
frequency method uses the mean number and weight 
of individuals in each size class over time to estimate 
the biomass lost as individuals move through the size- 
frequency distribution. We used shrimp up to 60 mm 
TL to estimate secondary production because shrimp 
larger than this size begin to emigrate from estuaries 
into the Gulf of Mexico (Pullen and Trent, 1969). We 
used the length-to-weight conversion given in Minello 
et al. (2008) to estimate mean shrimp weights and as- 
sumed this relationship was similar for all 3 salinity 
zones. We also estimated total biomass, measured in 
kilograms per hectare, within each salinity zone for the 
84-d sampling period as the sum of the mean biomass 
of all size classes over all sample dates. 
One of the most influential parameters affecting 
production estimates with the use of the size-frequency 
method is the cohort production interval (CPI) (Benke, 
1979; Garman and Waters, 1983). The size-frequency 
method was originally developed to estimate produc- 
tion for insects whose larvae develop in aquatic habi- 
tats and produce only one generation per year. This 
original method was modified by including the CPI 
into the calculation to account for species that have 
multiple generations per year. Benke (1979) originally 
defined the CPI in terms of the amount of time taken 
to complete larval development (i.e., the aquatic stages 
when growth and production occur). Garman and Wa- 
ters (1983) defined the CPI for fish as the average max- 
imum age obtained by individuals in the population. 
In our study, the age of a shrimp depended on its 
length because we estimated age from length; there- 
