A Framework for Exploring How Density Dependence Early in the Life History Can Affect Louisiana’s Brown Shrimp Fishery

Abstract

The dynamics underlying fisheries stock–recruitment relationships are often obscure, especially with relatively short-lived invertebrate species, such as the brown shrimp Farfantepenaeus aztecus. Nonetheless, disentangling these dynamics can help to reveal optimal management strategies for long-term sustainability. We developed a matrix model to link early shrimp life history with the fishable stock and nested the degree of density-dependent settler (i.e., juvenile) survival in a Beverton–Holt framework. Density dependence in the settler stage was assumed to have an inverse relationship with marsh habitat availability. Thus, we could determine the level of potential compensation in the settler stage and compare how changes in habitat versus fishing pressure could ultimately affect Louisiana’s brown shrimp population. A simplified Bayesian state-space (i.e., hierarchical) model provided a theoretical framework for estimating density dependence and exploring how substantial increases in catch or density-dependent settler survival affected long-term abundance in all stages. At the baseline degree of density-dependent settler survival, which was estimated from observed CPUE data, the brown shrimp population was largely resilient to even a twofold increase in catch. However, a 50% loss of habitat had deleterious effects on brown shrimp abundances in all stages. Results highlight the importance of protecting and restoring important nursery habitat to maintain and enhance resiliency of the brown shrimp fishery.

Received February 23, 2017; accepted July 12, 2017

The Louisiana fishery for brown shrimp Farfantepenaeus aztecus is one of the most productive and commercially valuable fisheries in the United States. Multiple state and federal agencies have invested substantial resources into understanding brown shrimp population dynamics and factors contributing to large fluctuations in yearly catch (Perret et al. 1993). Although there has been evidence of overfishing at various times (Caillouet et al. 2008), it has been problematic to differentiate variation due to fishing efforts from variation due to environmental or demographic stochasticity, and long-term trends suggest that the stock is relatively stable.

The considerable resilience of many exploited fish stocks is evidence in favor of density-dependent mechanisms during recruitment (Shepherd and Cushing 1980). As a compensatory mechanism, density-dependent recruitment allows populations to withstand fairly high levels of fishing mortality (Rose et al. 2001). Determining the relative importance of compensatory mechanisms in exploited populations is essential for evaluating the probable response to harvest (Fogerty et al. 1991). Populations with strong compensatory relationships may be more resilient to high levels of fishing, appearing stable regardless of fishing effort for extended periods of time. Short-lived, fast-growing species like the brown shrimp may have much weaker compensation and less-predictable population fluctuations (Goodwin et al. 2006). Rapid changes in environmental conditions and anthropogenic stressors could have confounding effects on the brown shrimp population. Environmental fluctuations could increase interannual stock variability by affecting the timing of recruitment (Ehrhardt and Legault 1999), masking potentially strong compensatory mechanisms. However, there could also be indirect effects caused by changes in the quantity or quality of available habitat. Habitat limitations could make density-dependent pressures at certain life stages more pronounced, weakening a population with a limited compensatory reserve (Rose et al. 2001). Given the marked decline in coastal Louisiana marshes (Couvillion et al. 2011), there is a fundamental need to understand the potential role of compensation during the juvenile period of the brown shrimp’s life history, which is most vulnerable to these changes.

Research has clearly demonstrated the relationship between environmental covariates and juvenile shrimp abundance and survival; shrimp growth rates are highly sensitive to water temperature, and smaller shrimp are subject to higher mortality rates (Minello et al. 1989; Haas et al. 2001, 2004; Roth et al. 2008; Adamack et al. 2012). Additional field and laboratory studies of brown shrimp and other penaeid species have also shown a positive association between early shrimp survival and the presence of cordgrass Spartina spp. and similar estuarine vegetation, as shrimp without this shelter experience much higher predation rates (Minello and Zimmerman 1983, 1992; Minello et al. 1989; Pérez-Castañeda and Defeo 2001; Minello and Rozas 2002). Aside from the availability of marsh habitat, numerous studies have demonstrated the relatively positive effects of warmer temperatures and intermediate salinities, whereas low dissolved oxygen, high turbidity, and other physical covariates can negatively influence brown shrimp growth, recruitment, and survival (Zein-Eldin and Renaud 1986; Perret et al. 1993; Rogers et al. 1993; Benfield and Downer 2001; Li and Clarke 2005; Re et al. 2005; O’Connor and Whitall 2007).

Despite enhanced understanding of drivers behind postlarval and juvenile brown shrimp abundance, it has been extremely challenging to capture the possible latent effects on subsequent life stages and to link those effects to long-term trends in population abundance. In fact, the Gulf of Mexico shrimp fishery as a whole has been managed with a primary focus on recruits (i.e., slightly smaller subadult shrimp, which are found closer inshore and are part of the fishable stock but are not yet reproducing) and adults (Perret et al. 1993; Caillouet et al. 2008; Huang and Smith 2011). Although the role of estuaries as nurseries for numerous nekton species, including brown shrimp, has been well documented, a nursery-role hypothesis explicitly linking nurseries to adult productivity is relatively recent (Beck et al. 2001). Beck et al. (2001) did not introduce a new concept but rather defined the assumption inherent in most of the literature to date—that juvenile nursery habitats contributed more individuals to the adult population than other habitats where juveniles might occur. It was not our aim to explicitly test the nursery-role hypothesis, but we do provide a framework for (1) testing how vulnerable the entire population may be to decreases in available nursery habitat, potentially limiting the carrying capacity in the settler stage; and (2) whether density dependence during this nursery-supported stage may afford some resiliency to the population, as decreased adult abundance or larval supply could be offset by increased survival of settlers. For that purpose, we used a Bayesian state-space model to explore how density dependence affecting early shrimp settler survival could indirectly influence abundance of the fishable stock.

We acknowledge that density dependence can also affect processes such as growth and reproduction, leading to compensatory responses, but we limited density-dependent effects to the settler survival parameter in our model. This was a reasonable constraint given that density effects on shrimp growth are strongly linked to survival (Minello et al. 1989) and given that there is limited evidence for density-dependent brown shrimp reproduction. We incorporated density-dependent settler survival and held other parameters constant to allow for greater model identifiability (i.e., underlying parameter values can be successfully ascertained). As has been demonstrated in stock assessments for other commercially important species, the Bayesian framework allows for a clear distinction between variability due to process (e.g., in our case, the simplified model of the brown shrimp’s life history) versus observations (i.e., imperfect data) and uses all available data to estimate parameters of interest (see Meyer and Millar 1999; Massiot-Granier et al. 2014; Archambault et al. 2016). We then evaluated how density dependence during the settler stage could affect subsequent recruit and adult abundances. We compared the long-term population trajectory for brown shrimp under two primary scenarios: (1) increasing density dependence in the settler stage, equivalent to decreasing carrying capacity; and (2) increasing fishing pressure.

METHODS

Life History Model

Brown shrimp population dynamics were represented in a simplified matrix model with three primary stages: settlers (S), recruits (R), and adults (A). See van de Kerk et al. (2016) for a full explanation of stage-class generalizations and underlying assumptions. Growth rates were derived from published field-based studies and were assumed constant within a class; the growth rate was estimated at 30 mm/month for settlers and 11.55 mm/month for recruits (Rose et al. 1975; Lassuy 1983). As in van de Kerk et al. (2016), growth rates were divided by published size ranges (Lassuy 1983) to calculate transition rates between life stages α_i (equation 1). Settler mortality (M_S) incorporated a constant baseline instantaneous mortality rate (0.6/month) multiplied by a size-dependent modifier accounting for shrimp length L (equation 2; see Minello et al. 1989, Haas et al. 2004):

(1)

(2)

During model simulation, we set L to the median of the settler size range (45 mm) yielding a constant rate of density-independent mortality. Maximum settler survival (a_S) was simply 1 – M_S. Settler survival (ν_S) was assumed to be density-dependent:

(3)

with S representing the number of settlers and b_S representing the degree of density dependence in settler survival (van de Kerk et al. 2016). Baseline adult survival (ν_A) excluding fishing effects was assumed constant and fixed between 0.65 and 0.80 (Nance et al. 1994). Given the general lack of information on subadult shrimp survival independent of fishing in open-water bays, we set baseline recruit survival (ν_R) equal to ν_A. Only recruits and adults are targeted in the brown shrimp fishery, so catch was subtracted directly from those stage-classes as an additional source of mortality. The number of settling larvae per adult (ρ), was initially fixed between 25 and 125. This parameter was also largely unknown, so we ran simulations with ρ equal to 25, 50, 75, 100, and 125; we then assessed the overall fit to the data by using Bayesian posterior checking methods (Gelman et al. 2014), as outlined in greater detail in the description of model computations. Peak recruitment of brown shrimp into saltmarshes has been reported to occur between February and April (Lassuy 1983). Therefore, our model simulations assumed that all settlement occurred as a single pulsed event in March, with ρ in all other months set to zero.

Multiple data sets were used to estimate model parameters. The Southeast Area Monitoring and Assessment Program provided estimates of CPUE based on fisheries-independent (i.e., obtained by research vessels using a stratified random sampling design) trawl surveys conducted inshore and offshore semiannually. In addition, National Oceanic and Atmospheric Administration (NOAA) Fisheries provided monthly fishery-dependent (i.e., obtained from fishing vessels) catch data from June 1984 to 2010. We converted the biomass estimates from the catch data into numbers of shrimp by using mean estimates of individual shrimp mass from the CPUE data. This allowed us to subtract catch directly from stage vectors during model simulations. Oscillations in CPUE data beyond June 2010 were highly variable and thus were not used to estimate parameters in our baseline model. During model fitting, recruit stage-class parameters were fit to inshore (state waters) CPUE data, whereas adult parameters were fit to offshore (federally managed waters) CPUE data. Catch data were incorporated directly into simulations, with inshore catch representing additional mortality to recruits and catches offshore denoting the same for adults. Because we limited our analysis to Louisiana brown shrimp, coinciding with stage-specific CPUE data from the state, we assumed that half of the reported NOAA catch consisted of Louisiana brown shrimp, which is supported by Perret et al. (1993).

Trawl data collected in marsh habitat by the Louisiana Department of Wildlife and Fisheries (LDWF) provided the CPUE data for the settler stage in our model. Additional parameters representing the catchability coefficients (q_i) for adults, recruits, and settlers were necessary to translate the model-predicted abundance into CPUE estimates that could be compared with the observed CPUE values. The CPUE for each stage-class (i.e., S, R, and A) at the tth (monthly) iteration was calculated as each catchability coefficient multiplied by the stage-i abundance (equation 4),

(4)

We used a Bayesian framework to estimate the degree of density-dependent settler survival, q_i, and stage-specific error terms arising from both our simplified life history model (process) and CPUE data (observations). We used broad prior distribution assumptions so that the various sources of data would inform posterior parameter estimates. The following sections describe first how the population model was translated into process equations within a Bayesian state-space model. Next, we detail the observation equations, joint likelihoods, and prior distributions assigned to estimated parameters.

Process equations

Similar to the notation used by Meyer and Millar (1999), we represent the number of settlers, recruits, and adults in each month as unobserved states,

(5)

where the left side of each equation represents the conditional probability of the number of shrimp in the respective stage given the number in the previous time step, the degree of density-dependent settler survival (b_S; for settlers and recruits only), and the variance associated with that stage. The stochastic state equations are assumed to have lognormal error structures, where u_i,t are independent and identically distributed and normal with a mean of 0 and a variance .

Observation equations

State-space models are also termed hierarchical models because information about the unknown states (process) is nested within the observation equations. In our case,

(6)

where CPUE estimates are now conditioned on the shrimp number in each stage (Stage) i in month t from the process equations, along with q_i and observation variance. Again, the stochastic observations are assumed to have lognormal error structures, where w_i,t are independent and identically distributed and normal with a mean of 0 and a variance . The joint posterior distribution of the estimated parameters for each stage thus becomes the product of the prior information and the likelihoods associated with equations (5) and (6),

(7)

Priors

We used reasonable assumptions for Bayesian fisheries stock assessment models (Punt and Hilborn 1997) and a combination of uninformed and weakly informed priors for estimating model parameters. Prior distributions for the initial number of shrimp in each stage were based on the catch data. For adults and recruits, we assumed a lognormal distribution with a mean log equal to 10 times the maximum observed catch. For settlers, we also specified a lognormal distribution but with a mean log equal to 100 times the maximum adult catch. Standard deviations at the initial states, accounting for process error in stage-predicted abundances, were estimated from a uniform prior between 0 and 10,000. Upper values up to three orders of magnitude higher and lower were also tested; however, parameter posteriors were more robust (i.e., more distinct distributions) with the selected parameters. For b_S and q_i parameters, we based our prior assumptions on the order of magnitude of the estimated means from above. For the b_S parameter, bounds of the specified uniform distribution translated to survival at the initial settler abundance between 0.212 and 0.537. The latter estimate reflected the lower bound, which would represent a very low degree of density dependence and settler survival near the asymptote at 0.545. Uniform distributions on the q_i, which were essentially scaling factors, would have translated to initial CPUE estimates of 1–153 shrimp for settlers and adults and 1–182 shrimp for recruits. Uniform priors were also assigned to error terms associated with the process models and observations. The coefficient of variation of stage-specific CPUE data informed the upper and lower bounds of observation parameter error distributions. Table 1 outlines all parameters and prior distributional assumptions for unobserved quantities.

TABLE 1. Summary of parameters in the brown shrimp state-space model (CV = coefficient of variation).

Parameter and symbol	Value^a/prior distribution
Fixed parameters
Maximum settler survival (aS)	0.545
Recruit survival (), excluding fishing	0.65‒0.8
Adult survival (), excluding fishing	0.65‒0.8
Postlarval settlement (ρ)	25‒100^b
Settler growth rate (γS), mm	30
Recruit growth rate (γR), mm	11.55
Settler transition rate (αS)	0.5
Recruit transition rate (αR)	0.178
Estimated parameters
Density dependence in settler survival (bS)
Settler catchability coefficient (qS)
Recruit catchability coefficient (qR)
Adult catchability coefficient (qA)
Settler process error ()
Recruit process error ()
Adult process error ()
Settler observation error ()	^c
Recruit observation error ()
Adult observation error ()

^a All values are reported on a monthly time scale.

^b Settlement values were fixed at increments of 25 within the specified range.

^c The CVs for the stage-specific CPUE data were used to specify weakly informative upper and lower bounds.

Simulated Scenarios

Fitted model parameters were used to evaluate the potential long-term effects of decreasing marsh carrying capacity (i.e., increasing b_S) versus increasing fishing pressure. After running the baseline model for 301 months coinciding with observed catch and CPUE data, we ran additional simulations changing b_S or catch but with all other parameters sampled from their identified posterior distributions (“descdist” function in the R package “fitdistrplus”: Delignette-Muller and Dutang 2015; R version 3.2.2: R Development Core Team 2015). We extended the state-process model for 20 years, with monthly recruit and adult catch set to mean values observed during the last 5 years of the data set and increasing b_S or catch by 25‒200%.

Additional simulations in which b_S was increased according to projected coastal land change in Louisiana (Couvillion et al. 2011) were also run for comparison. Reported coastwide land area data between 1985 and 2010 (Couvillion et al. 2011) were incorporated into a basic linear regression model to determine the rate of change since 1985. A modifier was then added to the brown shrimp process model, adjusting b_S based on the proportional yearly change. Within the Bayesian framework, future population states were simply treated as additional unobserved quantities to be estimated. We could then compare the projected median CPUE under baseline conditions with those estimated using a higher degree of density dependence or increased catch. For each stage, we plotted CPUE estimates corresponding to the month with highest observed CPUE observations (settlers in May; recruits in July; and adult shrimp in June) in the data. This allowed us to more clearly visualize trends without the population cycles.

Model Implementation

All model simulations were performed within R version 3.2.2 (R Development Core Team 2015) with an interface to JAGS software (https://sourceforge.net/projects/mcmc-jags/) to run Markov chain–Monte Carlo methods (“run.jags” function in R package “runjags”: Denwood 2016). Successful convergence was based on the Gelman–Rubin convergence diagnostic with a potential scale reduction factor (PSRF) less than 1.05 (Brooks and Gelman 1998). First, the model was run to compare parameter convergence under different combinations of ρ, ν_R, and ν_A. We ran three separate chains, allowed the model to adapt for 1,500 (combined adaptation and burn-in) iterations, and derived inferences using a sample size of 1,000 iterations. We did not perform thinning of the chains (Link and Eaton 2012), and the sample size was sufficient for parameter convergence (i.e., all PSRF values were close to 1.0). In addition to a visual comparison between median CPUE estimates and data, posterior checks—with a calculated chi-square statistic as the discrepancy measure—were performed to ensure that model-predicted CPUEs were consistent with stage-specific CPUE data over the time series (Kéry and Schaub 2012; Gelman et al. 2014). Bayesian P-values (posterior probabilities) were calculated to assess model fit. We selected the combination of fixed parameters yielding the greatest b_S parameter convergence and simultaneous fit to CPUE data for subsequent baseline simulations to estimate parameters that were most reflective of observed stock conditions. We ran four separate chains, monitoring only b_S, q_i, and error terms, with an adapting phase of 2,000 iterations, a burn-in of 3,000 iterations, and inferences based on 20,000 iterations. These settings were tested and deemed sufficient for model tuning and parameter convergence. Parameter identifiability was evaluated using the degree of overlap between prior and posterior distributions estimated in the baseline model (“overlap” function in the R package “birdring”: Korner-Nievergelt and Robinson 2014). As with initial model runs to identify appropriate fixed parameters, the CPUE values at each time point were monitored and stored for all future projections. The CPUE trajectories—using the median value from each CPUE estimate—under baseline conditions were then compared with scenarios in which b_S or catch was altered. Due to the larger computational requirements when storing the full vector of CPUE estimates, inferences were based on 100 iterations of three chains with 1,500 burn-in and adaptive iterations combined.

RESULTS

Baseline Model

There were 142, 83, and 28 fishery-independent CPUE observations for the settler, recruit, and adult stages, respectively, between June 1985 and June 2010. During model runs to select suitable values for fixed parameters, the greatest convergence and fit were achieved with adult and recruit survival fixed at 0.8 and a ρ value of 75 settlers per adult spawner (Figure 1). Median settler CPUE estimates in April were often an order of magnitude higher than observed settler CPUE data; however, other CPUE estimates, including those for recruits and adults, were largely within range of the data (Figure 1). All estimated parameters (b_S, q_i, , and, again with i = S, R, A) converged (PSRF < 1.005) during longer model runs (Table 2). Estimated error terms were all near the lower bound of the parameter space, with right-skewed gamma or normal distributions (Figure 1). There were slight positive correlations between the fitted b_S and (r = 0.43), q_A (r = 0.30), q_R (r = 0.22), or q_S (r = 0.16); and between q_A and q_R (r = 0.15) or q_S (r = 0.13); all other correlation coefficients were less than 0.10 and were considered inconsequential. A comparison between prior and posterior distributions signified that most parameters converged with posterior densities distinct from the uniform priors (Figure 2). Although simulations estimated a fairly normal distribution for b_S, the degree of overlap (0.5) between samples drawn from the prior and posterior of the parameter was slightly higher than the threshold (0.35) suggested in the literature (Garrett and Zeger 2000; Gimenez et al. 2009). The seemingly weak parameter convergence suggested by the density plots for adult catchability and observation error reflected the relatively sparse amount of CPUE data (i.e., only one June observation per year) collected for that stage-class (Figure 2). Using equation (3) and posterior median estimates of settler CPUE, b_S, and q_S, the ν_S value corresponding to model simulations ranged from 0.0893 to 0.545, with a mean of 0.498 (Figure 3). Not surprisingly, the highest values of ν_S corresponded to months with the lowest settler abundance.

TABLE 2. Parameter summary statistics (mean, median, and 95% confidence interval [CI]; symbols are defined in Table 1) from longer model runs (4 chains; 20,000 iterations) with the brown shrimp postlarval settlement parameter (ρ) fixed at 75 settlers per adult spawner and with adult and recruit survival (ν_A and ν_R) fixed at 0.8. The potential scale reduction factor (PSRF) is also noted as an indication of successful convergence.

Parameter	Mean	Median	95% CI (lower limit, upper limit)	PSRF
bS	2.42 × 10^–12a	2.47 × 10^–12	7.88 × 10^–13, 7.69 × 10^–12	1.0006
qS	8.05 × 10^–10	8.52 × 10^–10	5.38 × 10^–10, 1.00 × 10^–9	1.0005
qR	1.30 × 10^–9	1.22 × 10^–9	1.00 × 10^–9, 2.09 × 10^–9	1.0005
qA	2.31 × 10^–9	2.18 × 10^–9	1.00 × 10^–9, 5.86 × 10^–9	1.0004
	7.53	7.42	4.60, 12.83	1.0012
	2.89	2.88	2.72, 3.25	1.0004
	2.95	2.95	2.72, 3.44	1.0034
	5.35 × 10^1	5.25 × 10^1	5.04 × 10^1, 6.05 × 10^1	1.0002
	5.31 × 10^1	5.21 × 10^1	4.98 × 10^1, 6.05 × 10^1	1.0002
	1.10 × 10^1	1.05 × 10^1	9.40, 1.53 × 10^1	1.0002

^a All values were back-transformed from a log scale and are approximate.

FIGURE 1. Left panels represent scatterplots of the discrepancy measure (chi-square statistic) for replicated (model) versus actual (observed) brown shrimp CPUE data describing (A), (D) settlers; (B), (E) recruits; and (C), (F) adults. Upper and lower Bayesian P-values (i.e., the probability of obtaining a test statistic at least as extreme as the statistic computed from the actual data, under the null hypothesis of a correct model) are also presented. Right panels depict model (solid lines) versus actual (solid circles) CPUE estimates. Rows distinguish results between stage-classes.

FIGURE 2. Parameter priors (dashed lines) versus posterior density plots from Markov chain–Monte Carlo chains (colored lines; each reflecting 1 of 4 chains) for the degree of density-dependent brown shrimp settler survival (b_S), stage-specific catchability coefficients (q_i), and error terms associated with the process () and observation () components of the Bayesian state-space model (S = settlers; R = recruits; A = adults). Note that all parameters are presented on a log scale, and scales differ between panels.

FIGURE 3. Yearly brown shrimp settler survival (ν_S) corresponding to median posterior parameter estimates for settler CPUE, degree of density-dependent settler survival (b_S), and settler catchability (q_S). The solid line (black) indicates the median survival estimate calculated for each month; the horizontal dashed line (red) specifies the mean settler survival calculated over the full data range (all simulations).

Simulated Scenarios

In baseline simulations, there was an initial increase in projected adult CPUE, likely the result of mean monthly catch values that were lower than the actual catch in the last 2 years of the observed data. Estimated CPUE values at the model-predicted level of settler density dependence indicated that all stages were somewhat resilient to changes in catch, although potentially less so for adults in comparison with settlers and recruits (Figure 4D‒F). Again, there were no drastic changes in median settler or recruit CPUE values when b_S was increased by 25%. Although adult brown shrimp numbers were negatively affected by even this modest scenario of increased density dependence, there were deleterious effects on all stages when b_S was increased by 50% or more (Figure 4A‒C).

FIGURE 4 Median projected brown shrimp CPUE estimates 20 years beyond the data series for (A), (D) settlers; (B), (E) recruits; and (C), (F) adults. Plots compare stage-specific CPUE under baseline model conditions (solid black line) with models increasing the degree of density-dependent settler survival (b_S; red lines) or increasing mean monthly catch (blue lines) by 25, 50, or 200%. Note the difference in scale between rows.

A basic linear model using published data for the changes in coastwide Louisiana land area from 1985 to 2010 revealed a significant (P < 0.001, R² = 0.717) decline over that period. The estimated annual decrease in mean coastwide land area was approximately 55.4 km² (21.4 mi²) per year. This corresponded to a proportional yearly decrease of 0.3% since 1985. Stages were largely unaffected by a 25–50% increase in catch when b_S was adjusted to reflect projected changes in Louisiana coastal land area (Figure 5A‒C), whereas a 50% increase in b_S coupled with increased fishing pressure caused all CPUE estimates to decline (Figure 5D‒F). Plots (Figure 4C, F) suggested that adults were more sensitive to changes in density dependence and catch than were settlers or recruits, although CPUE projections were highly variable, and the graphs are most useful as an indication of trend and relative effects rather than absolute predictions about CPUE.

FIGURE 5. Median projected stage-specific brown shrimp CPUE estimates 20 years beyond the data series for (A), (D) settlers; (B), (E) recruits; and (C), (F) adults. Plots demonstrate the effects of increasing catch by 25, 50, or 200% when the degree of density-dependent settler survival (b_S) is modified according to a projected yearly decrease (0.3% per year) in Louisiana (LA) coastwide land area (panels A, B, and C) or when b_S is increased by 50% (panels D, E, and F). Projections under baseline conditions (solid bold line) and the baseline habitat-adjusted b_S (dotted bold line) are also depicted for comparison.

DISCUSSION

Utilizing a Bayesian state-space framework and long-term brown shrimp data from various sources, our model not only allowed us to integrate density dependence at the settler stage into a holistic population framework but also provided a basis for exploring the potential long-term effects of management scenarios targeting catch reduction versus habitat restoration. Increasing the degree of density-dependent settler survival—presumed to reflect reduced marsh habitat availability—affected adult and recruit populations substantially more than changes in catch of equal proportion. At least some of the recruitment variability in brown shrimp, as observed for other marine species (Houde 1987; Fogerty et al. 1991; Ehrhardt and Legault 1999; Myers 2001), could be due to the amount of available habitat and density dependence occurring early in the life history (Shepherd and Cushing 1980).

Rose et al. (2001) classified short-lived fisheries species with early maturation, relatively small body size, and somewhat variable interannual recruitment as opportunistic strategists with low to intermediate levels of compensation. As such, the population as a whole may be more vulnerable to significant reductions in settler habitat. Fishing not only could confound recruitment variability (Hsieh et al. 2006) but also could reduce an already depleted stock beyond levels of compensatory mortality. Without compensatory mechanisms acting to increase survival beyond the settler stage (Rose et al. 2001; Goodwin et al. 2006), there could be devastating consequences for the overall stock. Given these stakes, it is imperative that environmental and anthropogenic factors influencing carrying capacity be incorporated into assessments of fisheries stocks and productivity.

Our goal was to explicitly link dynamics in the settler stage to the rest of the brown shrimp’s life history. To date, numerous studies have used models to estimate shrimp abundance under varying habitat assumptions. One such study incorporating field data developed regression models to estimate juvenile shrimp abundance in Galveston Bay, and distance from the marsh edge was a major predictor (Minello et al. 2008). Roth et al. (2008) developed an individual-based model (IBM) to track brown shrimp growth and survival from postlarva to subadult stages under varying degrees of habitat fragmentation and marsh inundation, which were presumed to influence shrimp access to vegetated habitats. Those authors found that although the amount of edge habitat was an important predictor for shrimp growth and survival beyond the settler stage, the inundation regime was the most important determinant of shrimp productivity (Roth et al. 2008). Marsh inundation was also demonstrated to be a strong predictor of shrimp abundance in other studies using long-term data on coastal water levels, abundance estimates, and inshore shrimp catch (Childers et al. 1990; Minello et al. 2012). Another study simulated juvenile brown shrimp movement and growth by using an IBM that incorporated aerial photographs of marsh habitat and demonstrated that survival was highest in simulations with more edge habitat (Haas et al. 2004). All of these investigations have highlighted the importance of vegetation—and edge habitat specifically—for juvenile shrimp growth and survival (Minello et al. 2008; Roth et al. 2008; Haas et al. 2004).

Our more general framework demonstrates the importance of settler/juvenile habitat in contributing to resilient brown shrimp populations. Several difficulties have inhibited rigorous testing of the Beck et al. (2001) nursery-role hypothesis, including an inability to track individuals as they transition between juvenile and adult habitats, differences in sampling gear between stages, and poor sampling of the diverse range of habitats potentially inhabited by juveniles and adults (Gillanders et al. 2003). Thus, relatively few studies have investigated the link between juvenile shrimp abundance and subsequent patterns in recruitment and adult stock size (Haas et al. 2001; Baker et al. 2014; Leo et al. 2016). Haas et al. (2001) used Bayesian model averaging, stepwise multiple regression, and other statistical models to link adult brown shrimp abundance estimates to covariates that included the abundance of shrimp in other stages. While temperature and salinity were significant predictors, adult shrimp abundance was also sensitive to early juvenile abundance (Haas et al. 2001).

We did not include environmental covariates in our model but instead relied on long-term observations from multiple independent data sets to assess how density-dependent settler survival may have contributed to past trends and to project how changes in habitat could affect future stocks. This type of integrated approach has limitations and assumptions (e.g., see Maunder and Piner 2015) that warrant serious consideration before making any specific management recommendations based on, for example, projected stage-class abundances. The methods can help to answer questions related to broader trends and explore underlying mechanisms. When implemented in a Bayesian framework, as in our case, the underlying uncertainties are at least more transparent. For example, the moderate degree of correlation between the estimated degree of density-dependent settler survival and the settler process error reflected a relatively high degree of uncertainty in both parameters and insufficient data to parse out the variability. Additionally, we did not account for variations in stage-specific CPUE data that may have been driven by fluctuations in environmental factors outside the scope of our framework. Discrepancies in settler CPUE may have also been an artifact of our model’s single settlement pulse in March, which largely simplified the complexity of settler influx into coastal marshes. Baker et al. (2014) incorporated stage-specific vital rates into a population model for white shrimp Litopenaeus setiferus. Their results indicated that juvenile growth and survival might have a greater influence on population growth than fishing-related mortality, again highlighting the importance of incorporating more integrated population models into fisheries stock assessments. Although we took a slightly different approach with brown shrimp, our model does not include the level of detail typical of spatially explicit IBMs (Haas et al. 2004; Leo et al. 2016), and we did not make predictions about shrimp abundance in a particular marsh. Our more simplistic model structure with relatively few parameters facilitated an exploration of the hypothetical effects of density dependence early in the brown shrimp’s life history, with a specific interest in potential latent effects on the fishable stock.

We incorporated changes in marsh carrying capacity and fishing pressure into a theoretical model, clearly linking early life history to later fishable stocks, to make predictions related to the sustainable harvest of brown shrimp. We demonstrated a means for assessing the population-level responses to changes in catch versus marsh carrying capacity for brown shrimp populations in Louisiana. Our results highlight the potential for decreased marsh carrying capacity to not only affect settlers but also to significantly reduce adult and recruit abundances. Sufficient marsh and wetland habitats are indeed essential to the long-term viability of brown shrimp populations. When we consider that Louisiana has lost approximately 25% of its coastal wetland habitat since the 1930s (Couvillion et al. 2011), there is a clear need for models with the capability to assess the consequences for species that are reliant on those resources for all or part of their life history. Although the brown shrimp population seemed largely resilient to catch increases when we adjusted the degree of density dependence to reflect the rate of change in Louisiana coastal land area between 1985 and 2010 (Couvillion et al. 2011), the underlying assumption was that the rate of change would remain constant over the next 20 years. Given the ongoing interplay between sea level rise, land erosion, freshwater diversions, climate variability, and other factors (Couvillion et al. 2013; Nyman et al. 2013), models based on past change are largely conservative, and it will be difficult to predict exactly how brown shrimp populations will fare over the next several decades. It is therefore essential to include density-dependent processes when considering harvest and management goals in the context of a sustainable brown shrimp fishery.

Acknowledgments

We thank the LDWF, NOAA Fisheries, and Gulf States Marine Fisheries Commission for providing the data that were incorporated into our models. We also appreciate the thoughtful feedback provided by Edward Camp, Marisa Litz, and Andi Stephens during the revision process. This work was undertaken as part of an interdisciplinary research effort supported by the National Science Foundation (NSF)-sponsored Quantitative Spatial Ecology, Evolution, and Environment Integrative Graduate Education and Research Traineeship program at the University of Florida (NSF Grant DGE-0801544).