Fish Tagging
Selection of the primary and secondary sampling periods for the robust design was guided by an understanding of movement patterns of blue catfish in their native range and the need to ensure secondary periods during which the population was closed. The primary samples of the robust design corresponded with sampling events in July–August 2012, 2013, and 2014 (Fig. 1); these time periods occurred at the putative conclusion of spawning and when migratory movements are expected to be minimal (Graham 1999). The long interval between successive primary periods (1 year) allowed additions and deletions to the population. In 2012, we tagged fish and monitored recaptures during a single secondary period. Within the 2013 primary period, we tagged and monitored (live) recaptures and (dead) recoveries during four closed sampling sessions (each of these secondary sessions corresponded to a 1-week period; Fig. 1). Fish from each of the four secondary samples were batch marked (the same tag placement was used for all fish in a given week), and intervals between and among the four successive secondary samples were sufficiently short to satisfy the closure assumption. After the completion of tagging in 2013, we monitored the commercial harvest for recoveries during an additional secondary sampling event (T5 in Fig. 1). In 2014, we did not tag fish, but we monitored the commercial harvest for recoveries during the single secondary period in that year. Thus, tagging and observation events in 2012 and 2014 occurred during a single secondary period, whereas in 2013, tagging and observation events occurred during multiple secondary periods.
We used coded-wire tags (CWTs; Northwest Marine Technology, Inc.) to mark blue catfish because CWTs generally have high retention rates, and automated tag applicators allowed efficient marking of large numbers of fish (Brennan et al. 2007; Hand et al. 2010; Simon and Doerner 2011; Lin et al. 2012; Ashton et al. 2014). To our knowledge, our use of CWTs in blue catfish represents the first application of these tags in this species and with relatively large (post-juvenile stage) fish. Taggers were either trained or experienced with operation of the automated tag applicator and achieved estimated retention rates of 0.82 to 1.00. All procedures followed an IACUC-approved protocol (The College of William & Mary IACUC-2012-02-24-7720-mcfabr).
Blue catfish were supplied by a fisher who captured fish with baited hoop nets (approximately 1 m in diameter) that were fished in a 12-km portion of the James River between the mouth of Upper Chippokes Creek and the mouth of the Chickahominy River (Fig. 2). The study area encompassed 3017 ha. Fish were transferred from the fisher to a net pen, which was lashed to the side of the research vessel. In 2012, we tagged and released 15,721 blue catfish with CWTs using automated CWT injectors (Mark IV tag injector; Northwest Marine Technology, Inc.); in 2013, we tagged and released 18,531 blue catfish (Table 1). Prior to tagging, fish were scanned with a handheld wand detector (Northwest Marine Technology, Inc.) to determine recapture status; fish lacking a CWT were tagged, scanned again to ensure tagging success, and released as the vessel drifted within the study area. On each day, about 50 fish were randomly selected from the net pen and measured prior to tagging; randomization was facilitated by the high turbidity such that fish within the net pen were not visible from the surface. In 2012, fish ranged in length between 214 and 464 mm fork length (FL; n = 899); in 2013, fish ranged between 247 and 466 mm FL (n = 799; Fig. 3). In both years, most of the tagged fish were > 250 mm FL; this size class was representative of the bulk of the blue catfish population in the James River subestuary (Fabrizio and Tuckey, unpubl. data). We used simple ANOVAs to test for annual differences in mean fish size (F statistics, least-square means) using an α level of 0.05.
Table 1 Summary of blue catfish tagging and inspection events by year in the James River subestuary, VA
To monitor environmental conditions in the sampling area, we measured temperature [°C], salinity [psu], and dissolved oxygen [mg/L] in surface and bottom waters on each sampling day. Additionally, we calculated monthly mean river discharge for the James River near Richmond, VA, using daily discharge data (USGS gauge 020375000) to compare freshwater flow during summer 2012 to 2014. As with fish length, we used simple ANOVAs to test for annual differences in mean environmental conditions (F statistics, α = 0.05).
All fish tagged in 2012 received a CWT in the right dorsal musculature; in 2013, we used multiple tag-placement locations, such that each location corresponded with a unique secondary sample (Table 2). A similar approach was used by Goulette and Lipsky (2016) to permit CWT tagging of fish and nonlethal determination of group (i.e., batch) membership. The nonlethal identification of the 2013 secondary sampling period allowed us to observe more than two encounter events per fish because upon recapture, the location of the tag could be used to discern tagging week.
Table 2 Tag location for blue catfish marked with coded wire tags (CWTs) and released in 2012 and 2013 in the James River subestuary, VA
In 2013, we recorded GPS coordinates to track the drift of the research vessel during release of tagged blue catfish in the James River; examination of drift patterns allowed us to assess the validity of the critical assumption of mixing of tagged and untagged fish. The location of drift releases varied with tide (and hence, week) but generally alternated between upriver and downriver reaches in any given week (Fig. 4). As such, released fish were well dispersed in the study area during the tagging period in 2013 and presumably well mixed with the population of untagged fish. Because the same drift-release approach was used in 2012, we believe that the mixing assumption was reasonable for both years.
Live Recaptures and Dead Recoveries
Recaptured fish were detected during tagging operations in 2012 and 2013 as noted above. Some fish that were tagged in 2012 were also recaptured in 2012 (n = 930 or 5.9% of the total tagged in 2012); these fish were euthanized and removed from the tagged population, and as such, were treated as “losses on capture” in the Barker Robust Design Model. Fish tagged and released in 2013 and subsequently encountered (either alive or dead) were assigned to a secondary sampling period based on the location of the CWT. Fish tagged and recaptured in 2013 were fin clipped prior to release such that the clip (upper caudal, lower caudal, or adipose) indicated the secondary period of recapture (Table 2). Thus, some fish had CWTs (in unique locations) as well as fin clips to indicate multiple recapture events.
In 2013 and 2014, we inspected the fisher’s catch to recover tagged fish using an R9500 tunnel detector (Northwest Marine Technology, Inc.); 10,797 fish were scanned on 11 days in 2013 and 41,925 fish were scanned on 29 days in 2014 (Table 1). Prior to using the tunnel detector in the field, we conducted experiments in a controlled laboratory setting to determine tag-detection error rates. The false-negative rate (i.e., failure to detect a tag) was zero, a result consistent with that reported by Vander Haegen et al. (2002). Our tag-detection experiments also indicated that false-positive detections may occur, but these instances were rare and were readily verified by scanning with a handheld wand detector. All positive detections identified by the tunnel detector were scanned with a handheld wand to determine tag location and permit assignment of fish to the appropriate primary (2012 or 2013 releases) and secondary period (2013 releases). Daily effort (net nights), total harvest (kg), the portion of the harvest that was inspected (kg), the size of harvested fish (estimated from a random subsample), the number of fish recovered with CWTs, and the tag placement from recoveries were recorded during each harvest inspection. The total number of harvested fish was estimated by converting the weight of daily catches to numbers of fish using a relationship developed from 34 collections of blue catfish from the James River subestuary and valid for samples between 217 and 1409 lb (Number of fish = 64.889 + 1.223*W, where W is in pounds; Fabrizio and Tuckey, unpubl. data). When feasible and the fisher permitted, the entire daily commercial catch was inspected in 2014 (we inspected 60.1% of the fish harvested by the fisher between 7 July and 22 August). In 2013, we inspected only a portion of the harvest (22.7% of fish harvested between 20 July and 25 August). During inspections, a subsample of the harvest was measured; harvested fish measured 152 to 463 mm FL (n = 525) in 2013 and 116 to 463 mm FL (n = 2850) in 2014.
In addition to monitoring recoveries from the commercial fishery, scientists conducting fishery-independent sampling programs in the James River scanned blue catfish for CWTs between July 2012 and December 2014 (Table 3). Electrofishing, gillnets, and bottom trawls were used during 441 sampling events to intercept 6149 blue catfish captured between mesohaline habitats at the mouth of the James River near Hampton, VA, and freshwater habitats near Richmond, VA (Fig. 2). Recoveries from areas up- or down-estuary from our study site provided information on movement and could be used to address the closure assumption during the closed portion of the experimental design.
Table 3 Effort expended by gear and number of blue catfish inspected for coded wire tags (CWTs) in auxiliary surveys in the James River subestuary, VA, in 2012–2014
The Barker Robust Design Model
We fitted several models to the encounter histories for blue catfish, using Barker’s modification of the robust design implemented in Program MARK (White and Burnham 1999). The model permits estimation of detection probabilities, tag recovery rates, population size, and annual survival rates. Three types of encounters are permissible in the Barker live-dead formulation: (1) mark and release of live fish that are subsequently recaptured live; (2) dead recoveries (from the harvest); and (3) resightings, that is, tagged fish that are captured by fishers and released alive. For our study, we informed the Barker model with the first two types of encounters because resightings were not applicable. The likelihood for the Barker Robust Design Model comprises three parts: (1) the closed-captures portion for estimating population size and detection probabilities, (2) the Cormack-Jolly-Seber (CJS) portion from live recaptures, and (3) the dead recovery portion from dead recoveries. The closed period occurred in 2013 (with multiple secondary occasions); thus, fish tagged in 2013 and recaptured in 2013 provided information on population size at the beginning of 2013. The 2012 releases and recaptures were used to estimate survival rates using the open-population CJS model estimators.
In this design, dead encounters (recoveries) are assumed to occur in the interval between primary sampling periods. The robust design assumption of closure during the secondary occasions is violated when fish are removed by harvesting (which occurred in 2013). However, because the estimated population size is the size on the first sampling occasion in 2013, these removals lead to individual heterogeneity in the detection probabilities but do not directly affect the estimate of population size. Fish removed (harvested) during the closed secondary occasions in 2013 had their probability of live capture set to zero in subsequent secondary occasions.
The closed-captures portion of the likelihood for the Barker Robust Design Model is joined to the CJS likelihood via the detection probabilities, p. That is, the CJS likelihood estimates the probability of a fish being detected one or more times during the secondary occasions within a primary occasion; this probability is denoted as p* in robust design models. The closed-captures initial detection probabilities relate to p* as
$$ {p}^{\ast }=1-\prod_t\left(1-{p}_t\right). $$
That is, the product of 1 − p
t.
values is the probability of never encountering a fish during the secondary occasions, so that one minus this product (p*) is the probability of encountering a fish one or more times during the primary occasion. Thus, the p
t
parameters in the closed-captures likelihood are also influenced by the CJS detection probabilities via p*. The CJS portion of the likelihood is joined to the dead recoveries portion of the likelihood via the annual survival rates, S.
Population size, N, is computed as a derived parameter based on the closed-captures portion of the likelihood, using the Huggins (1989, 1991) and Alho (1990) approaches. Effectively, the number of unique fish seen one or more times (commonly denoted as M
t + 1) is divided by the probability of being observed one or more times to estimate population size:
$$ \widehat{N}=\raisebox{1ex}{${M}_{t+1}$}\!\left/ \!\raisebox{-1ex}{$1-\prod_t\left(1-{p}_t\right)$}\right.. $$
The Huggins estimator was extended to include individual heterogeneity (White and Cooch 2017), so that now, the probability of capturing each individual is summed across the individuals captured. Because we did not have multiple secondary occasions during 2012 and 2014, population sizes could not be estimated for these primary sessions.
Confidence intervals for probabilities S, r, and p were computed with a logit transformation, where logit(θ) = log[θ/(1 − θ)] and θ = S, r, or p; here, S is the annual survival probability, r is the probability that a tag is recovered given that the fish has died, and p is the detection probability of untagged fish (see Table 4 for description of these parameters). Confidence intervals for S, r, and p were computed on the logit scale and then transformed back to the original scale.
Table 4 Parameters of the Barker Robust Design Model used to estimate population size, survival rates, detection probabilities, and tag recovery rates for blue catfish in the James River subestuary, VA, 2012–2014
Confidence intervals for N were computed assuming a lognormal distribution on the number of animals never captured (f
0), with \( \widehat{N}={\widehat{f}}_0+{M}_{t+1} \), where M
t + 1 is the number of animals captured at least once during the primary period. The following equations describe the procedure:
$$ {\displaystyle \begin{array}{c}\hfill {\widehat{f}}_0=\widehat{N}-{M}_{t+1}\hfill \\ {}\hfill \mathrm{LCI}={\widehat{f}}_0/C+{M}_{t+1},\hfill \\ {}\hfill \mathrm{UCI}={\widehat{f}}_0C+{M}_{t+1},\kern0.5em \mathrm{and}\hfill \\ {}\hfill C=\exp \left\{1.96\times \sqrt{{\mathrm{log}}_e\left[1+{\left(\frac{SE\left({\widehat{f}}_0\right)}{{\widehat{f}}_0}\right)}^2\right]}\right\}.\hfill \end{array}} $$
Models Considered
We allowed the S and r parameters of the Barker Robust Design to vary with year and the p parameters to vary with sampling occasion; however, some parameters were fixed because they could not be estimated from the data. In particular, detection probability p for the 2012 primary occasion was fixed to one because this parameter was not identifiable from the single secondary occasion; we note that fixing this parameter to one does not affect the CJS portion of the likelihood nor the dead recoveries portion of the likelihood because p for 2012 is not included in these parts of the likelihood. The p values (probability of detecting fish alive) for the 2014 primary session were fixed to zero; here, no live fish were captured in 2014, so the probability of detection (of live fish) in 2014 was actually zero. Fidelity, the probability of remaining in the study area, was fixed to one because with the exception of a single fish, no tagged fish were encountered outside of our study area (see the “Results” section). Recapture probabilities were assumed equal to initial capture probabilities in all cases.
Because live encounters did not occur in 2014, and because no releases occurred in 2014, the survival estimate for 2013 was confounded with the inestimable p* value for 2014 and the estimate of survival for 2014. Further, the survival rate for 2014 was confounded with the recovery rate, r, for 2014, and thus, only the product, S(1 − r), was estimable. Out of the possible three S and three r parameters, only four quantities are estimable because no newly tagged fish were released in 2014. Therefore, three models for S and r were considered with various constraints:
$$ {\displaystyle \begin{array}{l}\mathrm{S}.\mathrm{r}.\kern1.00em \\ {}\mathrm{S}.{\mathrm{r}}_{2012,2013=2014}\kern0.5em \mathrm{and}\kern1.00em \\ {}{\mathrm{S}}_{2012,2013=2014}\kern0.5em {\mathrm{r}}_{2012,2013=2014}.\kern1.00em \end{array}} $$
The notation “2012, 2013 = 2014” denotes that the parameter for the first year (2012) was estimated separately, and parameters for 2013 and 2014 were set equal. The motivation for fixing the last 2 years for S or r was that the harvest rates or the inspection of harvested fish were similar for 2013 and 2014, whereas these values were different for 2012, when no harvested fish were inspected.
We considered multiple models for detection probabilities p in 2013. The first model estimated a separate p for each secondary session—denoted p
secondary session
; the second model specified p as a constant across secondary sessions-denoted p
.. To account for individual heterogeneity in detection probabilities, an extension of the p
secondary session
model following White and Cooch (2017) was considered where a random effect was added to logit(p) on the logit scale for each individual, i.e.,
$$ {p}_i=\frac{1}{1+\exp \left(-\left[\mathrm{logit}\left(\overline{p}\right)+{z}_i\right]\right)}, $$
where z
i
is a normally distributed random variable with mean zero and standard deviation σp associated with fish i. The likelihood was integrated numerically over the normal distribution so that σp could be estimated. Another model for p included the effect of fishing effort, which was measured as net nights in each of the 2013 secondary occasions. Effort ranged from a high of 168 net nights in week 1 to 113 net nights in week 4. The use of effort as a covariate allowed time variation in p but was different from p
secondary session
. The individual random effects model was also considered with the effort models. Model selection was based on quasi-AIC (due to the adjustment for overdispersion, see below), which was corrected for small sample sizes.
Overdispersion and Model fit
The confounding of the S and r parameters precluded evaluation of model fit for the open-population portion of the model. However, due to individual heterogeneity in detection probabilities and the possible lack of independence among captures, extra-binomial variation may exist within the closed-captures portion. Although the logit normal model described above provided strong evidence of individual heterogeneity (see the “Results” section), we considered the possibility that additional extra-binomial variation may be present. Therefore, we used the median \( \widehat{c} \) procedure in MARK to assess the extent of overdispersion in the closed-captures portion of the likelihood (Cooch and White 2016). Here, we used the encounter histories for the 2013 live captures applied to the model that included individual random effects to estimate median \( \widehat{c} \). We generated three estimates of \( \widehat{c} \) (1.46, 1.48, and 1.50) and assessed the extra-binomial variation using Monte Carlo methods; logistic regression was used to estimate the median value. The mean and median value of \( \widehat{c} \) was 1.48 (standard error of the mean = 0.013). This estimate of \( \widehat{c} \) was applied to the full Barker Robust Design Model.