Data Inputs

Life history.—Information on Gulf Sturgeon life history (particularly the location, timing, and characteristics of spawning habitats) has been collected for several Gulf Sturgeon populations (Marchant and Shutters 1996; Sulak and Clugston 1998; Fox et al. 2000). Some life history information such as age at maturity was based on previous Gulf Sturgeon studies (Huff 1975), while other information such as maximum age or growth rates was updated based on estimates derived from long-term capture-recapture studies (Pine and Martell 2009). Growth curves, age-length, and length-weight relationships were developed by Flowers et al. (2009) and Flowers (2008) following standard allometric relationships and von Bertalanffy growth equations. The parameter values and form of relationships used to represent life history traits are described in Table 1, equations (M.1–M.4) and (M.6).

TABLE 1.

Notation, definitions, and equations of the main parameters and relationships used in the stochastic stock-reduction assessment model.

We developed a prior for adult natural mortality based on life history characteristics including longevity (Hewitt and Hoenig 2005) and individual metabolic demand (von Bertalanffy k parameter: Jensen 1996). Based on these two approaches, we set a lognormal prior distribution on adult mortality that had a mean of 0.095 and an SE of 0.05 (Table 2, equation P.1). Natural survival depended on mean length at age (Table 1, equation M.3) similar to the pattern described in Lorenzen (2000).

Recruitment compensation.—The recruitment compensation ratio (κ;) describes the relative improvement in juvenile survival at low stock abundance compared with the “unfished” stock (Goodyear 1980). Higher κ; values imply that populations have relatively greater increases in juvenile survival at low population sizes relative to unexploited population sizes. In general, populations with higher κ; values are more resilient to exploitation than populations with low κ; values because they have a stronger compensatory response (Walters and Martell 2004). We constructed a weakly informative prior distribution for κ; following the approach in Martell et al. (2008) that used the management parameters of maximum sustained yield (MSY) and the exploitation rate needed to achieve this yield (Pine and Martell 2009). This approach provides probability density estimates for a range of κ; parameter values (Table 2, equation P.2). Estimated κ; for Gulf Sturgeon was 5 (a steepness of ∼0.56), similar to the estimated value for White Sturgeon A. transmontanus (Walters et al. 2006). This value is relatively low across species (Goodwin et al. 2006) but would be expected given sturgeon life history characteristics of long life and late sexual maturation (Pine et al. 2001). For comparison, Myers et al. (1999) meta-analysis for 246 stocks found a mean steepness of 0.78, though anadromous species, such as Atlantic Salmon Salmo salar and Pacific salmon Oncorhynchus spp., had steepness ranging from 0.46 to 0.65, similar to that used in this analysis.

TABLE 2.

Notation, definitions, and equations used in the objective function for the stochastic stock-reduction analysis.

Catch.—Catch statistics (Figure 2) were collected from the U.S. Bureau of Fisheries, the Report of the U.S. Commissioner of Fisheries from 1896 to 1936, and from the Florida State Board of Conservation from 1938 to 1985 (see Pine and Martell 2009). Recorded statistics were missing from 26 years during the 89 years of harvest. The largest data gap occurred from 1903 to 1917; catches were imputed for this time period assuming an exponential decay rate to match the patterns observed for Atlantic Sturgeon populations (Spear 2007). For shorter gaps of 2–4 years, we averaged the landings for the preceding and following years. Catches were assumed to have originated from the river closest to the county in which they were reported. Countyspecific records were available for 43 out of the 89 years; these were used to allocate harvest removal between the Suwannee and Apalachicola rivers. Linear interpolation was used to impute the proportional allocation for missing years. This backfilling of catches was checked by comparing predicted landings with reports by U.S. Bureau of Fisheries agents. Our interpolated catches were within the reported ranges (Flowers 2008). Uncertainty in the missing landings values can have an impact on the estimated scale parameters. We checked the sensitivity of these parameters by varying the imputed landings values by ±20%.

Abundance data.—Ongoing life history research and population assessment efforts include periodic tagging programs for Gulf Sturgeon populations throughout their range by academic, state, and federal cooperators for over 30 years. Abundance data from a number of mark-recapture studies are available for each of the seven critical habitats assessed (summarized in Appendix A in USFWS 2009).

River morphology.—We assessed seven critical habitat units for Gulf Sturgeon in nine rivers in the southeastern United States (Table 3). We compiled data on historic river discharge and anadromous length (which we defined as the distance available for passage of anadromous fishes below nonpassable barriers to the ocean) from USFWS recovery documents and habitat protection efforts (Table 3). River discharge was measured at the most downstream U.S. Geological Survey (USGS) gauging station on each river having at least 50 years of discharge data (Table 3). When a critical habitat unit was comprised of more than one river, anadromous river lengths were summed. The annual metric used to relate total juvenile production to river habitat was the product of mean annual discharge (cm/s) multiplied by total anadromous length (km). A variety of river metrics have been related to the production of juvenile salmonids such as, substrate type, velocity, and woody debris (Cramer and Ackerman 2009). However, watershed area and stream length can be stronger predictors of juvenile production for these anadromous species. Unfortunately, juvenile Gulf Sturgeon abundance is not measured (unlike many salmonid populations) making it difficult to characterize the relationship between specific river attributes and juvenile production. Our intention with the choice of anadromous length and mean annual discharge as metrics of juvenile production was to select metrics that were available for all rivers in our analysis and would capture finer scale attributes that may allow for more accurate prediction of juvenile production.

TABLE 3.

The USGS gauge number, geographic location, critical habitat length, and reduced habitat length due to obstructions used to develop the juvenile habitat metrics used in the stochastic stock-reduction analysis. River lengths include tributaries.

Access to potential spawning and rearing habitats is significantly impeded by dams (USFWS 1995, 2009) in the Bogue Chitto in the Pearl River watershed and the Apalachicola River. The fragmentation of rivers by dams is considered a major cause of diadromous fish declines across the Atlantic coast of the United States and a significant impediment for population recovery for many historically abundant species including Atlantic Sturgeon (Brown et al. 2013). We assessed how these barriers to spawning and rearing habitat may decrease the potential carrying capacity in each system. Our assessments can inform recovery criteria for these rivers, for example, the potential benefits from habitat restoration and from mitigation efforts through dam removal or innovative fish passage development.

For the stock-reduction analysis, annual discharge data were available from 1931 and 1941 to the present for the Suwannee and Apalachicola rivers, respectively. For dates prior to the period of record, flow discharge was imputed as the average of the first 5 years on record. The Jim Woodruff Dam on the Apalachicola River was completed in 1957; this reduction in available habitat was included in the stock-reduction analysis.

Stock-Reduction Analysis

We developed a Bayesian age-structured stochastic stock reduction analysis (sSRA) to simulate population dynamics from a historical reference point to the beginning of fishery exploitation. This model uses age-structured representations of growth, survival, and recruitment. The sSRA can differ from other age-structured, forward-projecting population models in that it is conditioned on catch; i.e., the number of fish removed from the population by fishing is treated as a known quantity and subtracted from the estimated total population size. Details of the sSRA approach are available in Walters et al. (2006) and the general framework is described below. All model equations are presented in Table 1 and components of the objective function are provided in Table 2. Numbers at age of Gulf Sturgeon were assumed to change over time following discrete time equations (Table 1, equation M.8) and individuals 50 years and older were modeled as a plus group. The age structure was initialized in 1897 and assumed that juvenile capacity had been near the capacity calculated for 1897 (Table 1, equations M.10 and M.11). Vulnerability at age (Table 1, equation M.5) was length dependent and modeled using a logistic function. The vulnerability schedule was used to represent individuals within the populations vulnerable to commercial nets and scientific sampling (referred to as vulnerable numbers) and allowed for direct comparison with mark-recapture population estimates that were obtained using similar gear. Parameter values describing this relationship were not estimated and are determined from examination of sizes captured in commercial landings and fishery-independent sampling (Huff 1975). Annual exploitation (harvest rate) on fully vulnerable individuals (Table 1, equation M.7) was calculated conditional on the observed catch.

We assumed a Beverton-Holt stock-recruitment relationship using the compensation ratio parameterization of the equation (Walters and Martell 2004) and linked juvenile capacity to available habitat area (Table 1, equation M.9). Incorporation of habitat area and change in available habitat area through time into the stock assessment model was done by linking the capacity parameter in the stock-recruitment relationship directly to habitat changes over time (H_y ; Table 1, equation M.14). In this formulation maximum age1 1 at high egg deposition rates is a function of habitat-scaling factor (γ) and the time-varying habitat metric (H_y in this assessment is mean annual discharge times anadromous length). Weak priors were placed on the habitat scaling factors (Table 2, equation P.3). Age-1 recruits are also dependent on relative spawning stock biomass (Table 1, equation M.12), and an estimate of the unfished relative spawning stock biomass per recruit (Table 1, equation M.13). The habitat-scaling factor γ is estimated within the sSRA framework for each river in the analyses. Although we have assumed that all density-dependent mortality is occurring during the first year, there is the possibility that it occurs at other life stages.

Parameter Estimation

We fit the sSRA to the Suwannee and Apalachicola rivers because these rivers have the longest history of removals via harvest and population monitoring efforts since the 1980s. Using equation (M.8) in Table 1 we calculated the number of Gulf Sturgeon in each age-class for every year that accounts for both natural survival and fishery removals with age-1 individuals entering the population modeled using the Beverton-Holt recruitment function described above. The leading parameters in this calculation are the compensation ratio (κ;) and adult natural mortality rate (M), which were shared between rivers. This assumption of a common M is not unrealistic given adult sturgeon are known to use specific locations in marine habitats in winter and are known to move between different river systems (Parauka et al. 2011; Rudd et al. 2014). In addition to the leading parameters, lognormal age-1 recruitment deviations and their associated variance were estimated for each river (Table 2, equation L.2; Table 1, equation M.9). Recruitment deviations can only be estimated for years with observations, but deviations were included for every year to incorporate recruitment variability in the posterior distribution of population numbers over time.

Estimates of leading parameters were obtained by fitting predicted population trajectories to observed mark-recapture estimates of vulnerable numbers assuming lognormal observation error with associated variances for each river (Table 1, equation L.1) in AD Model Builder (ADMB; Fournier et al. 2012). Of the total variability in the observed vulnerable numbers 40% was assumed to be the result of process variation (recruitment variation). The ADMB's Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm was used to map marginal posterior probability distributions of the leading parameters. Posterior distributions were assumed to have converged when the Gelman-Rubin scale reduction factor (Gelman et al. 1995) for each leading parameter was <1.1 (two chains each running for 10 million iterations of which the first 1 million iterations were discarded and the remainder thinned at a rate of 1,000).

Application to Other Rivers Included in Recovery Criteria

Currently seven critical habitat units are included in the Gulf Sturgeon recovery plan (USFWS 1995). Five of these units have limited historical information on landings, and current population trends in these systems are uncertain. This situation is typical for rare or listed species; the absence of this information precludes the use of traditional stock-assessment approaches to assess historic population carrying capacity and current stock status. However, we can utilize sSRA output, including estimates of M, κ;, the γ distributions in conjunction with anadromous length, and mean annual discharge from other systems to inform estimates of population size and carrying capacity. If we assume that the values for these rivers with sparse data are within the distribution of estimated parameters for the Apalachicola and Suwannee rivers (Figure 3), we can then estimate juvenile carrying capacity based on known riverspecific habitat metrics (mean annual discharge × anadromous length) for all river systems. Vulnerable adult population size given the estimated juvenile carrying capacity in each river can be estimated using equilibrium analysis (equilibrium solutions to equations M.8 and M.9 in Table 1). This estimation is done within a Monte Carlo framework where we randomly draw from the posterior distributions of k and M and a distribution for y. Capacity estimates for the Suwannee and Apalachicola rivers, then, are based on river-specific y distributions, while estimates for other rivers are based on a normal distribution with a mean and SD equal to the mean and SD of the combined posterior distributions calculation for the Suwannee and Apalachicola rivers. Posterior draws (n = 100,000) are combined with randomly selected mean annual discharge for each river over the last 20 years as well as the river's anadromous length to estimate juvenile carrying capacity. Juvenile carrying capacity was estimated with and without migration barriers in the Apalachicola and Pearl rivers. Age-1 capacity estimates were then used to estimate equilibrium vulnerable numbers (approximately ages 4+). These estimates were compared with the best available estimates of vulnerable populations from ongoing mark-recapture programs (USFWS 2009).

FIGURE 3.

Joint posterior densities (contour plots in the lower left boxes), marginal posterior densities (density plots in the boxes along the diagonal), and correlations (values in the boxes in the upper right) for the leading model parameters: compensation ratio (κ;), adult natural mortality (M), habitat scalar (γ) for the Suwanee (sw) and Apalachicola (ap) rivers. Joint posterior densities are demarked using the 5, 50, and 95% contour intervals. Gray lines on the marginal posterior distributions indicate prior distributions.

Stochastic Stock-Reduction Analysis: Model Fit to Time Series of Historical Landings, Habitat Changes, and Current Population Size

The inclusion of the habitat scaling metric 7 to account for changes in habitat availability, particularly within the Apalachicola River following completion of the Jim Woodruff Dam, allowed us to capture the different recovery trajectories of these populations (Figure 2) and helped us to develop an understanding of the population’s carrying capacity in each river under present habitat availability. For both the Suwannee and Apalachicola Gulf Sturgeon populations, historical removals caused a rapid decline in model populations beginning in the late 1800s. Within the Suwannee River, the Gulf Sturgeon population model biomass and vulnerable numbers declined during the early decades of the commercial fishery to below one-half of the unfished abundance of about 7,000 individuals, and peak exploitation rates of less than 30% occurred in 1900 (Figure 2). This model population slowly recovered in the first half of the 20th century (Figure 2) and then declined again as landings increased in the 1950s–1970s before the fishery closed in the early 1980s. The Apalachicola River Gulf Sturgeon population is estimated to have experienced a much larger decline in population vulnerable numbers of more than 90% from around 18,000 prior to 1900 to fewer than 100 individuals by the 1940s–1950s. Unlike the Suwannee River where landings continued throughout the 1960s and 1970s (Huff 1975), high removals during this time period did not occur in the Apalachicola River, allowing for limited population recovery. However, around the time of the completion of the Jim Woodruff Dam on the Apalachicola River in 1957 there was an increase in reported Gulf Sturgeon catch, which may have resulted in exploitation rates of nearly 100% of vulnerable individuals (Figure 2). Current estimates of vulnerable population size from our sSRA model explicitly included habitat changes, (e.g., completion of the Jim Woodruff Dam), which explain why our current abundance estimates for the Apalachicola River are extremely low compared with historical levels (Figure 2). These results also suggest that Gulf Sturgeon population recovery in the Apalachicola River much beyond these low levels is likely strongly curtailed by the reduction in habitat area following the completion of the Jim Woodruff Dam.

Parameter estimates.—Posterior probability distributions of κ;, M, and river-specific γ values are shown in Figure 3. There is a notable contraction in the posterior distribution of the κ; from the prior distribution and a decrease in the mode from 5 to 2.6, suggesting that recruitment compensation is weaker than that estimated using the approach in Martell et al. (2008). The posterior distribution for adult natural mortality rate contracts slightly with a slight increase in the mode. Posterior distributions for the habitat scalar 7 are well defined for the Suwannee and Apalachicola rivers. The habitat scalar for the Suwannee River was estimated to be greater than that for the Apalachicola River, suggesting that, per unit of habitat metric used, the Suwannee River has a greater capacity for juvenile production than the Apalachicola River. As anticipated, there was a strong positive correlation between natural mortality and 7, particularly for the Apalachicola River, with a correlation of 0.99 (Figure 3).

Habitat-based carrying capacity estimates.—We estimated the 90% credible interval for habitat-based carrying capacity for the Suwannee River to be about 2,359–9,555, which is similar to current estimates of population size suggesting that this population is approaching the preexploitation levels (Figure 2). Our Apalachicola River results suggest that the Apalachicola River before the dam would likely have supported an estimated 7,447–23,271 Gulf Sturgeon of age 4 and older, while postdam estimates of carrying capacity are approximately 1,923–6,066. Current abundance estimates in the Apalachicola River range from only a few hundred to a few thousand vulnerable individuals (Figure 2; Table 4). Carrying capacity estimates were sensitive to the imputed landings. A 20% change in the imputed values resulted in a 10% change in the Suwannee River capacity estimate and a 15% change in the Apalachicola River capacity estimate. Our results provide key information to resource managers in updating recovery targets for these populations that are currently not available, even with the uncertainty in the landing data and the associated sensitivity to the carrying capacity estimates.

We used the distribution of 7 values from the Apalachicola and Suwannee rivers to estimate population carrying capacity for the five other rivers considered as part of the Gulf Sturgeon recovery plan: Pearl, Pascagoula, Escambia, Yellow, and Choctawhatchee rivers (Table 4). Our results for these rivers demonstrate that carrying capacity is highly dependent on estimated available juvenile habitat and river discharge. Our 90% credible intervals of carrying capacity estimates for vulnerable numbers range from about 185–811 in the Yellow River to 4,022–18,077 in the Pascagoula River (Figure 4; Table 4). Much like the Apalachicola River, results for the Pearl River, where access to historic habitat is blocked by a sill on the Bogue Chitto River, suggest capacity estimates of 6,336– 28,856 without any migration barriers but only about 10% of this level (686–3,076) under current habitat availability.

Current status relative to capacity.—To assess their recovery potential we compared the ratio of current mark-recapture-based estimates of vulnerable population numbers to model-based capacity estimates of vulnerable Gulf Sturgeon abundance for each river (Table 4). We found that for the Yellow, Choctawhatchee, and Suwannee rivers, current population size is similar to the estimated posterior distribution for carrying capacity, while the Pascagoula, Apalachicola, Escambia, and Pearl rivers are likely <30% of their estimated carrying capacity (Figure 5). For the Apalachicola and Pearl rivers we calculated these ratios both in terms of their current available juvenile habitat with the existing impediments to migration (noted with “S” for short in Figure 5) as well as in the absence of migratory barriers (noted with “L” for long in Figure 5).

TABLE 4.

Median as well as the lower (5%) and upper (95%) limits of the 90% credible interval values for estimated vulnerable numbers of Gulf Sturgeon produced at juvenile production capacity for sturgeon rivers flowing into the eastern Gulf of Mexico. Carrying capacity estimates for the Pearl and Apalachicola rivers are shown with (S) and without (L) migration barriers. Recent estimates of vulnerable population size were taken from the 2009 Gulf Sturgeon 5-year review document.

FIGURE 4.

Estimated vulnerable population size in numbers of Gulf Sturgeon individuals at carrying capacity for sturgeon rivers flowing into the eastern Gulf of Mexico. Light dots represent a sample of 3,000 points from the posterior distributions. Horizontal dark grey lines represent the 90% credible interval. Horizontal black lines represent the 50% credible interval and closed black circle represents the median. Carrying capacity estimates for the Pearl and Apalachicola rivers are shown with (S for short) and without (L for long) migration barriers. Note that the x-axis has been log scaled for clarity.

Lessons for the Gulf Sturgeon Recovery Plan

Our results for Gulf Sturgeon suggest that population biomass for this species was severely reduced during a short, but intense, period of commercial harvest in the eastern Gulf of Mexico. After large-scale fishing was abandoned, a small fishery persisted, primarily on the Apalachicola and Suwannee rivers, until regulation closed all sturgeon fishing in the early 1980s. Gulf Sturgeon populations in the rivers that likely supported the largest fisheries (Apalachicola and Suwannee rivers) have demonstrated stable or increasing populations during the last 20 years (Zehfuss et al. 1999; Pine et al. 2001; Sulak and Randall 2002), but recent estimates of abundance may be uncertain (Pine and Martell 2009). Threats to Gulf Sturgeon populations and riverine and estuarine habitats are increasing from a wide variety of anthropogenic sources that include alterations to surface and subsurface waters (e.g., dams and water withdrawals: Seavey et al. 2011), expanding risks from increased oil and gas extraction activities (e.g.. Deepwater Horizon oil spill: USFWS 2010,  http://tinyurl.com/cvbcmpk), and in-river industrial accidents (e.g., recent Temple-Inland pulp mill spill in the Pearl River), all of which could impede or reverse population recovery.

A key basic need in many population recovery and fishery management plans is to determine measurable, objective, population target levels to answer the question of how many individuals are needed for long-term viability of a population or species (Tear et al. 2005; Sanderson 2006; Wilhere 2008). Our results provide guidelines in using historical data to estimate current potential carrying capacities for use as recovery reference points. As an example, currently the Suwannee River population of Gulf Sturgeon is likely at more than 80% of its estimated carrying capacity or very near carrying capacity. In contrast, the Gulf Sturgeon populations in the Apalachicola and Pearl rivers in which critical habitat for sturgeon is reduced primarily by the Jim Woodruff Dam are estimated to potentially support only 50% of the age-4-+ individuals that would be supported if all of the identified critical habitat were available. Thus, for both the Pearl and Apalachicola rivers, recovery targets near the historical abundances are likely dependent on whether access to historic spawning and rearing sites are available. The need to develop measurable, quantifiable goals for recovery criteria have long been recognized (NRC 1995); yet, for many populations this information is not available because of sparse data. For Gulf Sturgeon we have shown how key population parameters can be estimated for a portion of the range and then used to inform decisions for areas where data are sparse. In this way, critical decisions, such as whether to define recovery goals with or without habitat change, or the potential benefits to a species from management actions, such as dam removal, can be better informed and thus lead to more effective conservation actions and an increased likelihood of the species' recovery.