Bayesian hierarchical species distribution modeling of blue catfish, an invasive species in tidal rivers of Virginia

Blue Catfish, an invasive species introduced into tidal waters of Virginia from the 1970s to mid-1980s, have rapidly expanded into many major tributaries in the Chesapeake Bay watershed. The increased abundance of Blue Catfish threatens the biodiversity of aquatic ecosystems through direct predation effects or indirectly by competition for limited resources with native species. To gain ecological insights and to predict the distributions along environmental gradients, four Bayesian species distribution models, were applied to estimate the abundance changes of the Blue Catfish by examining the relative influence of environmental and temporal factors on Blue Catfish catches from annual surveys in tidal rivers of Virginia. The analyses were based on sampling data collected from low- and high-frequency electrofishing surveys. The Bayesian hierarchical model was selected as the final model based on the deviance information criterion (DIC) value and a consideration of the underlying data structure. In this study, the presence and relative abundance of Blue Catfish were influenced by salinity and temperature. The detected density of Blue Catfish decreases when salinity and temperature increase in general. Standardized relative abundance among years was highly variable but increased over time in the low-frequency electrofishing survey. However, in the high-frequency electrofishing survey, this trend was not apparent. We recommend continued monitoring in these and other tidal rivers to provide management strategies that control the spread and limit the ecological impacts of Blue Catfish on native species. Our analysis also provides a standardized framework for evaluating invasive Blue Catfish distribution and relative abundance across multiple rivers.

1 Introduction

The James, York, and Rappahannock rivers are major tributaries of Chesapeake Bay and represent a network of large, tidal river systems with steep gradients in salinity, temperature, and habitat structure (Kuo and Neilson, 1987). Each river shifts from freshwater upstream to oligohaline and mesohaline tidal zones downstream, with seasonal changes driven by freshwater flow, tidal forces, and climate ocean oscillation. These gradients create diverse environments that can both promote and limit the establishment and spread of non-native species.

Blue Catfish, Ictalurus furcatus, is a large-river fish, native to the major rivers of the Mississippi, Missouri, and Ohio River basins (Graham, 1999), which were intentionally introduced into Virginia rivers between the 1970s and mid-1980s to establish recreational fisheries. Initial stockings occurred in the James and Rappahannock rivers in 1974, and additional introductions took place within the York River watershed in 1984. Since introduction, Blue Catfish have rapidly spread into many tributaries of the Chesapeake Bay, supporting large recreational and commercial fisheries in Virginia and Maryland (Schloesser et al., 2011; Greenlee and Lim, 2011; NMFS, 2012). Blue Catfish in the Chesapeake Bay region have currently expanded into estuarine habitats (Fabrizio et al., 2018; Nepal and Fabrizio, 2019; Fabrizio et al., 2021). Due to rapid population expansion, Blue Catfish have produced some unintended ecological effects in the region. They compete with native species, such as the white catfish (Ameiurus catus), whose population has declined in abundance with the increase of Blue Catfish (Schloesser et al., 2011). As an omnivore-generalist feeder, Blue Catfish consume a variety of species, including vegetation, molluscs, and fishes, which threaten the biodiversity of aquatic ecosystems and may cause environmental degradation. Blue catfish are now considered an invasive species in the Chesapeake Bay region (Schloesser et al., 2011; Fabrizio et al., 2018).

Because the increased abundance of Blue Catfish might have a negative effect on native species, estimates of relative abundance, species distribution, and stock assessments are necessary to devise control strategies for Blue Catfish (Hilborn and Walters, 1992; Quinn and Deriso, 1999). One of the most common approaches to model species distributions is to use generalized linear models (GLMs) (Cheng and Gallinat, 2004; Maunder and Punt, 2004). GLMs provide a flexible framework for modeling a wide range of response variable distributions, such as non-normally distributed responses (e.g., relative abundance). Survey catches often include a large proportion of zero records, which results in a loss of information and bias if zero records are ignored (Maunder and Punt, 2004). One approach is to replace the zeros by adding a small number and then applying GLMs. However, the standardized relative abundance using this approach is sensitive to the value of the constant, especially when the proportion of zeros is high (Maunder and Punt, 2004). Alternatively, the delta approach can be used. The delta model consists of two components: one that estimates the probability of obtaining positive relative abundance with the binomial distribution and a second component that fits the positive relative abundance using the lognormal or gamma distribution in the GLM framework (Cooke and Lankester, 1996; Punt et al., 2000; Maunder and Punt, 2004; Ortiz and Arocha, 2004). The delta GLM approach has been widely used in standardizing relative abundance and estimating species distributions in fisheries research (Stefansson, 1996; Ye et al., 2001; Li et al., 2011; Yu et al., 2011).

Previous studies found that Blue Catfish distributions are influenced by both salinity and temperature (Lagler, 1961; Graham, 1999). Blue Catfish have a moderate salinity tolerance (Allen, 1969; Graham, 1999); in the Chesapeake Bay, Blue Catfish have been collected from higher-salinity waters with salinities of up to 21.8 psu (Fabrizio et al., 2018). Based on studies in their native range, Blue Catfish are believed to be the most migratory of the ictalurid catfishes, moving upstream in the spring and downstream in the fall in response to water temperature (Lagler, 1961; Pflieger, 1997).

The effects of environmental factors on Blue Catfish abundance may vary spatially. Blue catfish across Virginia tidal rivers exhibit varying growth patterns (Hilling et al., 2021), suggesting it is more appropriate to treat them as separate subpopulations. The subpopulations of Blue Catfish in different rivers are expected to respond similarly to environmental conditions. The Bayesian hierarchical method provides a desirable tool to address the similarity and possible differences in subpopulation reactions to environmental conditions by using a hierarchically structured approach with multilevel priors (Gelman et al., 2013; Jiao et al., 2009a; 2010; Harrison et al., 2018; Kettunen et al., 2023). Bayesian hierarchical models incorporating multilevel priors have been found to yield stable results even when sample sizes are small and demonstrated superior robustness than model with single-level priors (Andrews et al., 1993; Roberts and Rosenthal, 2001; Jiao et al., 2009; Bi et al., 2021).

In this study, we aimed to estimate the relative abundance from low-frequency and high-frequency electrofishing surveys from the Virginia Department of Wildlife Resources (VDWR, Orth et al., 2017). Specifically, we integrated the delta model with a Bayesian approach to examine the relative influence of environmental and temporal factors on Blue Catfish populations in the tidal rivers of Virginia. We employed two sets of Bayesian species distribution models, namely, the Bayesian hierarchical model, and Bayesian non-hierarchical model. The selection of models and variables was carried out using Deviance Information Criterion (DIC) values. We also investigated the trends of the Blue Catfish populations through the standardized relative abundance in these surveys with the selected model.

2 Materials and methods

2.1 Field sampling

The surveys conducted in the tidal rivers of Virginia include high-frequency electrofishing and low-frequency electrofishing surveys from 1995 to 2011 (Table 1). Low-frequency electrofishing is the most efficient approach for sampling Blue Catfish in reservoir and riverine environments and could provide a representative sample of Blue Catfish (Bodine and Shoup, 2010). High-frequency electrofishing is much more intensive than low-frequency electrofishing and is used to monitor the fish community to assess trends in the fish assemblage. These surveys, although not current, can be used to identify predictive environmental variables and population trends during the early spread of this introduced species.

Table 1

Table 1. Time period and river system sampled in high- and low-frequency electrofishing surveys.

Blue Catfish were sampled using low-frequency direct-current electrofishing (15 pulses/s) with a Smith-Root 9.0 GPP (generator powered pulsator) electrofishing unit mounted on a 5.5-m aluminum boat (Greenlee and Lim, 2011; Hilling et al., 2021; 2023). Voltage was generally set at 680V within a 60%-100% range, but 340V was used sparingly in higher salinity situations. Amperage generally ranged from 0.2 to 13 amps (Hilling et al., 2023). The surveys were conducted mostly during summer (July–August) when water temperatures were suitable for low-frequency electrofishing (>18C, Bodine and Shoup, 2010) (Figure 1). Additionally, high-frequency electrofishing (60–120 pulses/s, 340–680 V) surveys were conducted to monitor the Blue Catfish using a Smith-Root 7.5 or 9.0 GPP boat-mounted electrofishing unit during fall (September–November) (Greenlee and Lim, 2011; Hilling et al., 2021). Samples were mostly collected with the 9.0 GPP unit, while the 7.5 GPP was used occasionally. Electrofisher settings for the 9.0 GPP were adjusted based on conductivity: 680V with 100% range when conductivity was <500 μS/cm; 680V with 50%–60% range when conductivity was 500–1500 μS/cm; or 340V with 60%–80% range when conductivity was >1500 μS/cm. For the 7.5 GPP, a single setting was used: 1000V with 50%–100% range and an output of 5.6–11.7 amps (generally 9–10 amps, Hilling et al., 2023). These surveys were conducted at fixed sites in low salinity (generally <6 psu, but up to 11–12 ppt) regions of four Virginia tributaries in the Chesapeake Bay: James (rkm 79–150), Pamunkey (rkm 52–124), Mattaponi (rkm 52–99), and Rappahannock (rkm 67–151) rivers, as well as in several smaller tributaries. The effectiveness of the shocking unit declines when salinity is too high because higher conductivity allows electrical current to dissipate through the water column rather than through fish bodies, reducing the field strength experienced by fish and thus lowering catch efficiency (Beaumont et al., 2002; Bodine and Shoup, 2010; Bodine et al., 2013; Smith-Root, 2020). The observations from the Pamunkey and Mattaponi rivers were combined and referred to as observations from the York River because the confluence of the Mattaponi and Pamunkey rivers forms the York River. Thus, we considered six datasets: three collected by low-frequency electrofishing and three collected by high-frequency electrofishing. For each dataset, three continuous explanatory factors, salinity, temperature and conductivity, were considered. The number of samples per year ranged from 0 to 11 for James River, 1 to 25 for York River, and 2 to 17 for Rappahannock River in low-electrofishing surveys; the number of samples per year ranged from 2 to 54 for James River, 4 to 12 for York River, and 1 to 21 for Rappahannock River in high-electrofishing surveys (Table 1). The range of catches per samples from each river with each electrofishing survey are also presented in Table 1. Because the survey effort varies among trips, the survey catch per unit effort (CPUE) (i.e., relative abundance) was expressed as the number of fish caught per 10 min of electrofishing, which was further used to study the Blue Catfish distribution and standardized relative abundance indices. Because there was a large proportion of zero records in the survey CPUEs, each dataset was separated into two subsets according to the survey CPUEs. One contained the positive CPUEs and the other was a binary part of the data, which contained an indicator such that indicator = 1 represents Blue Catfish was observed and indicator = 0 represents there was no Blue Catfish observed.

Figure 1

Figure 1. Sites sampled by two fishery-independent surveys (HF = high-frequency electrofishing survey, LF = low-frequency electrofishing survey). In this study, observations for the Chickahominy River were included in the James River System.

The correlation between every two variables was first examined by calculating pairwise Pearson’s correlation coefficients. Because pairwise scatter plots of three continuous explanatory factors for positive CPUE and binary data from the six datasets were similar, we show the results for the positive CPUE for the James River in low-frequency electrofishing survey only (Figure 2). Most of the Pearson’s correlation coefficients among the river-specific factors were less than 0.5, indicating weak to moderate correlations. Not surprisingly, the correlation coefficients of conductivity and salinity for the low- and high-frequency electrofishing surveys were higher than 0.9 in all datasets, indicating conductivity and salinity had a strong positive linear relationship. The high correlation may cause multicollinearity problems in parameter estimation and interpretation. Conductivity was removed from the analysis to reduce multicollinearity because salinity is considered a common factor that influences Blue Catfish biology and distribution in tidal rivers in comparison with conductivity (Nepal and Fabrizio, 2019; 2020).

Figure 2

Figure 2. Pairwise scatter plots of positive relative abundance and standardized explanatory factors collected by the low-frequency electrofishing in the James River. Abbreviations are as follows: CPUE = positive relative abundance of Blue Catfish, Sal = salinity (psu), Temp = water temperature (C), Cond = conductivity.

To compare the relative importance of the explanatory factors, the remaining four continuous factors, salinity, and temperature, were standardized as shown in Equation 1:

$x_{i,j}=\frac{x_{obs,i,j}-{\overline{x}}_{obs,i}}{s_i}(1)$

where $x_{obs,i,j}$ is the jth observation of factor i, ${\overline{x}}_{obs,i}$ is the mean of factor i and $s_i$ is the standard deviation of factor i.

2.2 Bayesian delta models for species distribution analysis

Because of the high proportions of zero catches in the high-frequency electrofishing survey (50.4% in the James River, 23.3% in the York River, and 26.5% in the Rappahannock River), a delta model was used to analyze the standardized survey data. The probability distribution for data in the delta model is specified in Equation 2:

$B_{y,t,s}=\left\{\begin{array}{c}0{CPUE}_{y,t,s}=0\\ 1{CPUE}_{y,t,s}>0\end{array}\right.$

$P\left({CPUE}_{y,t,s}\right)=\left\{\begin{array}{l}\left(1-p_{y,t,s}\right){CPUE}_{y,t,s}=0\\ p_{y,t,s}\frac{1}{d_{y,t,s}{\sigma }_{t,s}\sqrt{2\pi }}\exp \left(-\frac{{\left(\log \left(d_{y,t,s}\right)-{\mu }_{y,t,s}\right)}^2}{2{\sigma }_{t,s}^2}\right){CPUE}_{y,t,s}>0\end{array}\right.(2)$

where t represents the river system (James: t = 1; York: t = 2; and Rappahannock: t = 3), s represents pulse rate (high: s = 1; low: s = 2) and y represents year. $B_{y,t,s}$ is the binary catch data where 0 indicates no catch and 1 indicates a positive catch. $d_{y,t,s}$ is the positive relative abundance of Blue Catfish in the survey s in the tth river in year y. The binary catch data (1: Blue Catfish present; 0: no Blue Catfish observed) were modeled as a Bernoulli random variable with a probability of positive catches, $p_{y,t,s}$. Histograms of the log-transformed positive relative abundance data showed approximate normal distributions (an example graph is shown in the Supplementary Figure S1) and thus the model assumes a lognormal distribution for positive relative abundance (i.e., positive CPUEs) with parameters ${\mu }_{y,t,s}$ and ${\sigma }_{t,s}$.

In this study, survey catchability may be different in low- and high-frequency electrofishing surveys; therefore we considered pulse rates and river systems as low levels in the hierarchical model, allowing regression coefficients to vary by survey and river and shrink toward shared hyperparameters. Parameters in the level of pulse rates and rivers were further governed by higher group level distributions. Salinity and water temperature were included as explanatory covariates in both the encounter (Bernoulli) component and the positive CPUE (lognormal) component of the model, allowing these environmental factors to influence both the probability of capture and the magnitude of catches conditional on availability. The Bayesian hierarchical linear model could be expressed as Equation 3:

$\mathit{log}\left(\frac{p_{y,t,s}}{1-p_{y,t,s}}\right)={\beta }_{1_{t,s}}^{\prime }{x}_{1_{t,s}}+{\beta }_{2_{t,s}}^{\prime }{x}_{2_{t,s}}+{\beta }_{y_{t,s}}^{\prime }$

${\mu }_{y,t,s}={\beta }_{1_{t,s}}{x}_{1_{t,s}}+{\beta }_{2_{t,s}}{x}_{2_{t,s}}+{\beta }_{y_{t,s}}$

${\beta }_{i_{t,s}}^{\prime }\sim N\left({\beta }_i^{\prime },{\sigma }_i^{\prime 2}\right)$

${\beta }_{i_{t,s}}\sim N\left({\beta }_i,{\sigma }_i^2\right)(3)$

The parameters with prime marks represent the effects on binary catch data and the parameters without prime marks represent the effects on positive relative abundance data. $x_i$ represents the explanatory factor i. Year is a categorical explanatory factor in this model and ${\beta }_{y_{t,s}}^{\prime }$ and ${\beta }_{y_{t,s}}$ represent the effects of the yth year from survey s in river t. The effects of explanatory factor i (i = 1, 2, y) from survey s in river t are expressed by ${\beta }_{i_{t,s}}^{\prime }$ and ${\beta }_{i_{t,s}}$. The coefficients, ${\beta }_{i_{t,s}}^{\prime }$ and ${\beta }_{i_{t,s}}$ (i = 1, 2, y), are assumed to be from the normal distributions with mean ${\beta }_i^{\prime }\text{\hspace{0.17em}and\hspace{0.17em}}{\beta }_i$ (hyperparameters). We did not include factor interaction terms (i.e., $x_i{x}_j,\text{where\hspace{0.17em}}i,j\in \left\{1,2,y\right\}\text{\hspace{0.17em}and\hspace{0.17em}}i\ne j$) in the above model since factor interaction terms often create additional multicollinearity problems (Maunder and Punt, 2004) and our preliminary study also shows the interaction terms resulted in higher multicollinearity. In addition, introducing the factor interactions increases the complexity of the model. To prevent overfitting and ensure convergence of our Bayesian model, we refrained from including interaction terms.

A Bayesian hierarchical quadratic model was then specified in Equation 4 to account for possible nonlinear relationships in the data that may not be adequately represented by a linear specification:

$\mathit{log}\left(\frac{p_{y,t,s}}{1-p_{y,t,s}}\right)={\beta }_{1_{t,s}}^{\prime }{x}_{1_{t,s}}+{\beta }_{2_{t,s}}^{\prime }{x}_{2_{t,s}}{+\beta }_{3_{t,s}}^{\prime }{x}_{1_{t,s}}^2+{\beta }_{4_{t,s}}^{\prime }{x}_{2_{t,s}}^2+{\beta }_{y_{t,s}}^{\prime }$

${\mu }_{y,t,s}={\beta }_{1_{t,s}}{x}_{1_{t,s}}+{\beta }_{2_{t,s}}{x}_{2_{t,s}}+{\beta }_{3_{t,s}}{x}_{1_{t,s}}^2+{\beta }_{4_{t,s}}{x}_{2_{t,s}}^2+{\beta }_{y_{t,s}}$

${\beta }_{i_{t,s}}^{\prime }\sim N\left({\beta }_i^{\prime },{\sigma }_i^{\prime 2}\right)$

${\beta }_{i_{t,s}}\sim N\left({\beta }_i,{\sigma }_i^2\right)(4)$

where the effects of explanatory factor i (i = 1, 2, 3, 4, y) from survey s in river t follow a normal distribution with “mean” effect across rivers and surveys, that is ${\beta }_{i_{t,s}}^{\prime }\sim N\left({\beta }_i^{\prime },{\sigma }_i^{\prime 2}\right)$ and ${\beta }_{i_{t,s}}\sim N\left({\beta }_i,{\sigma }_i^2\right)$.

For comparison, two non-hierarchical counterparts were also considered: a Bayesian linear model corresponding to the first model, and a Bayesian quadratic model corresponding to the second, where the effects of explanatory factors from different surveys and rivers were assumed to be independent and were assigned uniform prior distributions $U\left(-200,200\right)$.

The priors for ${\beta }_i^{\prime }$ and ${\beta }_i$ (i = 1, 2, 3, 4, y) are uniform distributions with lower bound −200 and upper bound 200. The priors for variance ${\sigma }_{t,s}^2$ (t = 1, 2, 3 and s = 1,2), ${\sigma }_i^{\prime 2}$ and ${\sigma }_i^2$ (i = 1, 2, 3, 4, y) are $U\left(0.0001,10000\right)$. These priors are very wide given the reality that all the continuous explanatory factors were standardized with mean 0 and variance 1. We also conducted a sensitivity analysis on these priors by doubling the upper bound and decreasing the lower bounds by 50% to examine the influence of the priors. It turned out that different priors had little influence on the results.

2.3 Model selection

For each of the four models, including the Bayesian hierarchical linear model, the Bayesian hierarchical quadratic model, the Bayesian linear model and the Bayesian quadratic model, we used a variable selection technique (backward elimination) informed by the deviance information criterion (DIC) to select the important explanatory factors of Blue Catfish relative abundance. Because year is a categorical factor and the Blue Catfish abundance in each survey has a visual fluctuation over the years, this factor was kept in the model and the variable selection method was implemented to select the important continuous factors. Models with lower DIC values were preferred. The starting model included all candidate explanatory factors; factors were excluded using a backward elimination approach such that the exclusion of the candidate explanatory factor resulted in a model with a lower DIC value. Thus, “redundant” factors were removed from the delta models. This process was repeated until no further improvement was possible. All analyses were implemented in R and WinBUGS (Spiegelhalter et al., 2004). To diagnose the convergence by Gelman-Rubin diagnostics (Gelman and Rubin, 1992; Spiegelhalter et al., 2004; Jiao et al., 2009b), three chains were generated with different initial values. The first 50,000 iterations were treated as a burn-in period and the other 50,000 iterations with a thinning of 50 were saved as draws in the Bayesian analysis to ensure the convergence of the Markov chains and address potential autocorrelation in the MCMC runs.

2.4 Posterior inference

Once the best model was selected, we drew posterior predictive samples and assessed the effect of each factor on the proportion of positive catches, positive relative abundance and CPUEs using Equation 5:

${\widehat{p}}_{i,t,s}={logit}^{-1}\left({\beta }_{i_{t,s}}^{\prime }\right)$

${\widehat{u}}_{i,t,s}=\mathit{exp}\left({\beta }_{i_{t,s}}\right)$

${\widehat{CPUE}}_{i,t,s}={\widehat{u}}_{i,t,s}\times {\widehat{p}}_{i,t,s}(5)$

where i represents the explanatory factor and i = 1, 2, 3, 4, y. ${\widehat{p}}_{i,t,s}$ is the predicted proportion of positive catches, and ${\widehat{u}}_{i,t,s}$ is the predicted positive relative abundance of Blue Catfish associated with factor i in the survey s in the tth river. For each of the continuous explanatory factors, salinity and temperature, because each continuous factor was standardized to have a mean of 0 (see Equation 1), we conducted the calculation by holding all other continuous factors at zero and maintaining the year at the reference level. Similarly, to evaluate the effect of the year on the responses, we kept all continuous factors at their mean value of 0. The predicted CPUEs, ${\widehat{CPUE}}_{i,t,s}$, for each river and survey were calculated as the product of ${\widehat{u}}_{i,t,s}$ and ${\widehat{p}}_{i,t,s}$.

3 Results

In all four models, namely, the Bayesian hierarchical linear model, Bayesian hierarchical quadratic model, Bayesian linear model and Bayesian quadratic model, the salinity and temperature were retained in the final models for both binary data and positive relative abundance data because the full models produced the lowest DIC values (Table 2). For the binary data, the Bayesian linear model yielded the lowest DIC (DIC = 436.546) value compared to the Bayesian hierarchical models and the Bayesian quadratic model, suggesting that the data lack hierarchical structure and that a linear relationship better describes the relationship than a quadratic one. For the positive relative abundance data, the Bayesian hierarchical quadratic model yielded the lowest DIC values at 3814.02. This suggests that the effects of explanatory factors from different rivers and surveys share identical parameters, indicating the data are hierarchically structured, and a quadratic relationship provides a better fit than a linear one. Figure 3 presents parameter medians and 95% credible intervals from hierarchical and non-hierarchical Bayesian linear models (binary data) and quadratic models (positive relative abundance data). Notably, the hierarchically structured model resulted in parameters estimates with narrower credible intervals compared to the non-hierarchical model.

Table 2

Table 2. Bayesian model selection results.

Figure 3

Figure 3. Parameter estimates with posterior medians and 95% credible intervals from hierarchical and non-hierarchical Bayesian linear models (binary data) and quadratic models (positive relative abundance data). t represents river system (James: t = 1; York: t = 2; and Rappahannock: t = 3), s represents pulse rate (high: s = 1; low: s = 2), i represents the ith explanatory factor (salinity: i = 1; temperature: i = 2; quadratic term for salinity: i = 3; quadratic term for temperature: i = 4). Parameter estimates from Bayesian hierarchical models are represented in black, while parameter estimates from Bayesian non-hierarchical models are denoted in red.

Figures 4-9 show the effects of each factor on the proportion of positive catches, positive relative abundance, and CPUEs. With regard to the river and pulse-level parameters, for the high-frequency electrofishing survey, the presence of Blue Catfish significantly declined with an increase in salinity in the James river (Figure 4; Table 3). Temperature had a positive impact on the presence of Blue Catfish in the Rappahannock rivers (Figure 6; Table 3). Together, this suggests that encounter rates of Blue Catfish in the high-frequency electrofishing survey are greater in habitats characterized by low salinity and warm temperatures. When Blue Catfish were present in the high-frequency electrofishing survey, salinity had a significant negative impact on Blue Catfish positive relative abundance in the James and Rappahannock rivers (Figures 4, 6; Table 3). In the low-frequency electrofishing survey, the positive CPUEs of Blue Catfish significantly decreased with an increase in salinity in the York River (Figure 8; Table 3).

Figure 4

Figure 4. The effects of salinity and temperature on the positive relative abundance, the probability of Blue Catfish presence and the CPUE for high-frequency electrofishing survey in the James River (solid line: median; dotted lines: 95% credible interval).

Figure 5

Figure 5. The effects of salinity and temperature on the positive relative abundance, the probability of Blue Catfish presence and the CPUE for high-frequency electrofishing survey in the York River (solid line: median; dotted lines: 95% credible interval).

Table 3

Table 3. The summary of marginal posterior distributions for parameters of interest in the selected models. t represents river system (James: t = 1; York: t = 2; and Rappahannock: t = 3), s represents pulse rate (high: s = 1; low: s = 2), i represents the ith explanatory factor (salinity: i = 1; temperature: i = 2; quadratic term for salinity: i = 3; quadratic term for temperature: i = 4).

Figure 6

Figure 6. The effects of salinity and temperature on the positive relative abundance, the probability of Blue Catfish presence and the CPUE for high-frequency electrofishing survey in the Rappahannock River (solid line: median; dotted lines: 95% credible interval).

Figure 7

Figure 7. The effects of salinity and temperature on the positive relative abundance, the probability of Blue Catfish presence and the CPUE for low-frequency electrofishing survey in the James River (solid line: median; dotted lines: 95% credible interval).

Figure 8

Figure 8. The effects of salinity and temperature on the positive relative abundance, the probability of Blue Catfish presence and the CPUE for low-frequency electrofishing survey in the York River (solid line: median; dotted lines: 95% credible interval).

Figure 9

Figure 9. The effects of salinity and temperature on the positive relative abundance, the probability of Blue Catfish presence and the CPUE for low-frequency electrofishing survey in the Rappahannock River (solid line: median; dotted lines: 95% credible interval).

The predicted CPUE shows the Blue Catfish abundance with the passage of time in each river by low-frequency and high-frequency surveys. In general, the abundance of Blue Catfish was low in the early years but began to increase after 2005 (Figure 10). In the high-frequency electrofishing survey, catch rates reached a peak in 2006 in the James River. However, the catch rates of 2007 and after were much lower than 2006, but were still gradually increasing compared with pre-2005 catch rates. There were only two survey records in 2006 and both got high CPUEs. Therefore, the probability of Blue Catfish presence was around 1, much higher than those in the years that followed. Though high CPUEs were observed after 2006, the predicted CPUEs were much lower than that in 2006 because of the low probability of Blue Catfish presence. In the low-frequency electrofishing survey, catch rates reached a peak in 2010 in the James River, 2011 in the York and Rappahannock rivers (Figure 10). The 95% credible intervals of the relative abundance are much wider in some years due to the small number of surveys conducted (e.g., two high-frequency electrofishing surveys in 2006). Thus, it is suggested that more surveys should be conducted every year to help reduce the estimation variability and improve the prediction precision.

Figure 10

Figure 10. Annual patterns in standardized relative abundance from the electrofishing surveys by VDWR. (A) High-frequency electrofishing survey in James River; (B) low-frequency electrofishing survey in James River; (C) high-frequency electrofishing survey in York River; (D) low-frequency electrofishing survey in York River; (E) high-frequency electrofishing survey in Rappahannock River; (F) low-frequency electrofishing survey in Rappahannock River. The bars display the 95% credible intervals.

4 Discussion

The model-based approach in estimating relative abundance has been found to be more robust or less influenced by the survey design than the design-based approach (Yu et al., 2012). Because both the low-frequency and high-frequency surveys were based on fixed stations along the rivers and the sampling effort varied among years (Hilling et al., 2021; 2023), the model-based approach we used provide opportunities to evaluate the trend of relative abundance of Blue Catfish, and how the Blue Catfish distribution and abundance vary under different environmental factors (Maunder et al., 2006).

The relative abundance of Blue Catfish decreased with increasing salinity and decreasing temperature in the surveys. These results align with previously studies on Blue Catfish (Lagler, 1961; Allen, 1969; Pflieger, 1997; Graham, 1999). The overall effects of salinity and temperature on CPUEs were similar to those on positive CPUEs in the electrofishing survey. In most survey conditions, the probability of Blue Catfish presence was around one and thus the overall effect of an environmental factor on CPUEs was similar to that on positive CPUEs.

The survey catches of Blue Catfish were likely affected by gear saturation, particularly during the low-frequency electrofishing survey, because Blue Catfish were very abundant in later survey years and in some survey areas, a large proportion of the catch was comprised of Blue Catfish. In this case, relative abundance may be affected by the number of fish already captured, resulting in an underestimation of the abundance of fish. Our analysis was conducted assuming no gear saturation; gear saturation is expected when sampling crews encounter more fish than can be netted (Schoenebeck et al., 2015). In practice, the saturation effect may have a strong effect on fitting parameters of any stock assessment model (Arreguín-Sánchez, 1996).

Salinity and temperature are expected to influence both Blue Catfish distribution and electrofishing efficiency. Blue Catfish have limited tolerance to elevated salinity, which may reduce true abundance in higher-salinity tidal habitats, while increasing conductivity and temperature can also reduce electrofishing effectiveness by altering electric field properties and fish behavior. Accordingly, the effects of salinity and temperature in our Bernoulli–lognormal delta model should be interpreted as composite effects reflecting both ecological processes and observation processes. Because sampling consisted of single-pass electrofishing and low- and high-frequency surveys were not conducted at the same locations, these two mechanisms cannot be fully disentangled. The resulting CPUE estimates therefore represent a covariate-standardized relative index of distribution and abundance rather than a direct estimate of true population density, although this approach substantially reduces environmentally driven bias relative to unstandardized CPUE. Disentangling environmental effects on abundance from those on catchability would require additional sampling structure, such as repeated passes, repeat visits within seasons, or paired low- and high-frequency electrofishing at the same sites to estimate capture efficiency directly. Future studies incorporating such calibration data would enable stronger mechanistic inference regarding salinity- and temperature-dependent habitat limitation versus sampling efficiency.

Based on the standardized annual relative abundance in the low-frequency electrofishing survey, Blue Catfish abundance increased in the James, York, and Rappahannock rivers. However, in the high-frequency electrofishing survey, this trend was not apparent. One possible explanation is that the survey period was of insufficient duration to detect a change, or that limited sampling during each year reduced the precision of the survey catch data. Because the standardized relative abundance of Blue Catfish in the high-frequency electrofishing survey peaked in the mid and late 2000s, a non-linear regression might be used to improve the description of the temporal patterns apparent in these data. On the other hand, high-frequency electrofishing targets to monitor the fish community and Blue Catfish is more sensitive to lower-frequency pulses than that are commonly used for other teleosts (5–30 versus 30–60 pulse/s; Cailteux and Strickland, 2009; Bodine et al., 2013), which might affect the catchability of the high-frequency electrofishing surveys and lead to no clear overall trend in species abundance.

Although high-frequency electrofishing is generally less efficient for sampling ictalurid catfishes than low-frequency electrofishing (Bodine et al., 2013), these surveys provide additional temporal coverage in years when low-frequency sampling was not conducted. Rather than excluding high-frequency data, we explicitly accounted for survey-river-specific differences in catchability by modeling electrofishing frequency and river within the hierarchical framework. This method allows data from both survey types to contribute to standardized indices and species distribution while accounting for differences in sampling efficiency.

The credible intervals of the population-level coefficient hyperparameters contained zeros, which may be due to the wide range of priors used in this analysis, and predictors centered at 0. We retained wide ranges on our priors because we lacked biological evidence to construct appropriate informative priors. A sensitivity analysis using wider priors yielded similar results, which indicated that our current priors are not informative. Moreover, increasing survey sample size conducted every year could help narrow the credible intervals of estimated parameters and improve prediction accuracy and precision.

In this study, the delta model directly considered the zero observations, without having to rely on ad hoc adjustments to the survey catch data. We considered the effects of spatial (rivers), and environmental (salinity, temperature) factors, and sampling types (pulse rate) on Blue Catfish abundance, and estimated the coefficients. The results demonstrate that while the Bayesian hierarchical approach improves estimation in the presence of small samples and hierarchical structure, simpler non-hierarchical models may provide a better fit when such structure is absent and the data does not support borrowing strength across rivers and surveys. In our case, the Bayesian non-hierarchical linear model provided the best fit for the binary data, indicating that the presence of Blue Catfish in the survey-river combinations behave more independently. In contrast, the Bayesian hierarchical quadratic model better captured the structure in the positive data, suggesting that modeling Blue Catfish positive abundance benefits from hierarchical pooling and borrowing strength across surveys. Through the standardization of survey relative abundance, our study provided abundance indices to inform population trends of this introduced species, which can be directly used in further population dynamics models and stock assessment for Blue Catfish. The surveys in these tidal rivers are necessary to monitor Blue Catfish population changes in the future and improve our understanding of the distribution and dynamics of this introduced species.

Data availability statement

The data analyzed in this study is subject to the following licenses/restrictions: The dataset used in this study is owned and maintained by Virginia Department of Wildlife Resources. Access may be restricted, and researchers should request permission directly from the data provider. Requests to access these datasets should be directed to https://dwr.virginia.gov/wildlife/information/blue-catfish/.

Ethics statement

Ethical approval was not required for the study involving animals in accordance with the local legislation and institutional requirements because as this study relied on data from fishery surveys conducted under state management programs, additional animal ethics approval was not required.

Author contributions

MT: Writing – original draft, Writing – review and editing, Formal Analysis, Methodology, Software. YJ: Writing – review and editing, Conceptualization, Methodology, Resources, Validation. DO: Conceptualization, Supervision, Writing – review and editing.

Funding

The author(s) declared that financial support was received for this work and/or its publication. We thank the Virginia Department of Wildlife Resources for funding this project and their efforts in collecting and sharing data. We also thank Robert S. Greenlee for his guidance and assistance during our Blue Catfish research.

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fenvs.2026.1716908/full#supplementary-material

References

Allen, K. O. (1969). Effects of salinity on growth and survival of channel catfish, Ictalurus punctatus. Proc. Southeast Assoc. Game Fish. Comm. 23, 319–331. Available online at: https://seafwa.org/sites/default/files/journal-articles/ALLEN-319.pdf

Google Scholar

Andrews, R. W., Berger, J. O., and Smith, M. H. (1993). Bayesian estimation of manufacturing effects in a fuel economy model. J. Appl. Econ. 8 (S1), S5–S18. doi:10.1002/jae.3950080503

CrossRef Full Text | Google Scholar

Arreguín-Sánchez, F. (1996). Catchability: a key parameter for fish stock assessment. Rev. Fish Biology Fisheries 6, 221–242. doi:10.1007/BF00182344

CrossRef Full Text | Google Scholar

Beaumont, W. R. C., Taylor, A. A. L., Lee, M. J., and Welton, J. S. (2002). Guidelines for electric fishing best practice. Almondsburry, Bristol: Environment Agency R&D Technical Report W2-054/TR, 197.

Google Scholar

Bi, R., Jiao, Y., Weaver, L. A., Greenlee, B., McClair, G., Kipp, K., et al. (2021). Environmental and anthropogenic influences on spatiotemporal dynamics of alosa in Chesapeake Bay tributaries. Ecosphere 12 (6), e03544. doi:10.1002/ecs2.3544

CrossRef Full Text | Google Scholar

Bodine, K. A., and Shoup, D. E. (2010). Capture efficiency of blue catfish electrofishing and the effects of temperature, habitat, and reservoir location on electrofishing-derived length structure indices and relative abundance. North Am. J. Fish. Manag. 30 (2), 613–621. doi:10.1577/m09-084.1

CrossRef Full Text | Google Scholar

Bodine, K. A., Shoup, D. E., Olive, J., Ford, Z. L., Krogman, R., and Stubbs, T. J. (2013). Catfish sampling techniques: where we are now and where we should go. Fisheries 38 (12), 529–546. doi:10.1080/03632415.2013.848343

CrossRef Full Text | Google Scholar

Cailteux, R. L., and Strickland, P. A. (2009). Evaluation of three low frequency electrofishing pulse rates for collecting catfish in two Florida rivers. Proc. Annu. Conf. Southeast. Assoc. Fish Wildl. Agencies 61, 29–34. Available online at: https://seafwa.org/sites/default/files/journal-articles/Cailteux-29-34.pdf

Google Scholar

Cheng, Y. W., and Gallinat, M. P. (2004). Statistical analysis of the relationship among environmental variables, inter-annual variability and smolt trap efficiency of salmonids in the tucannon river. Fish. Res. 70, 229–238. doi:10.1016/j.fishres.2004.08.005

CrossRef Full Text | Google Scholar

Cooke, J. G., and Lankester, K. (1996). Consideration of statistical models for catch-effort indices for use in tuning VPAs. ICCAT Col. Vol. Sci. Pap. 45, 125–131. Available online at: https://www.iccat.int/Documents/CVSP/CV045_1996/colvol45.html#

Google Scholar

Fabrizio, M. C., Tuckey, T. D., Latour, R. J., White, G. C., and Norris, A. J. (2018). Tidal habitats support large numbers of invasive blue catfish in a Chesapeake Bay subestuary. Estuaries Coasts 41 (3), 827–840. doi:10.1007/s12237-017-0307-1

CrossRef Full Text | Google Scholar

Fabrizio, M. C., Nepal, V., and Tuckey, T. D. (2021). Invasive blue catfish in the Chesapeake Bay region: a case study of competing management objectives. North Am. J. Fish. Manag. 41, S156–S166. doi:10.1002/nafm.10552

CrossRef Full Text | Google Scholar

Gelman, A., and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences (with discussion). Stat. Sci. 7 457–472. doi:10.1214/ss/1177011136

CrossRef Full Text | Google Scholar

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2013). Bayesian data analysis. 3rd ed.

Google Scholar

Graham, K. (1999). “A review of the biology and management of blue catfish,” in Catfish 2000: proceedings of the international ictalurid symposium. Am. Fish. Soc. Symp. Editors E. R. Irwin, W. A. Hubert, C. F. Rabeni, H. L. SchrammJr, and T. Coon 24, 37–49.

Google Scholar

Greenlee, R. S., and Lim, C. N. (2011). “Searching for equilibrium: population parameters and variable recruitment in introduced blue catfish populations in four Virginia tidal river systems,” in Conservation, ecology and management of catfish: the second international symposium. Symposium 77. Editors P. H. Michaletz, and V. H. Travnichek (Bethesda, Maryland: American Fisheries Society), 349–367.

Google Scholar

Harrison, X. A., Donaldson, L., Correa-Cano, M. E., Evans, J., Fisher, D. N., Goodwin, C. E., et al. (2018). A brief introduction to mixed effects modelling and multi-model inference in ecology. PeerJ 6, e4794. doi:10.7717/peerj.4794

PubMed Abstract | CrossRef Full Text | Google Scholar

Hilborn, R., and Walters, C. J. (1992). Quantitative fisheries stock assessment: choice, dynamics, and uncertainty. Springer.

Google Scholar

Hilling, C. D., Jiao, Y., Bunch, A. J., Greenlee, R. S., Schmitt, J. D., and Orth, D. J. (2021). Growth dynamics of invasive blue catfish in four subestuaries of the Chesapeake Bay, USA. North Am. J. Fish. Manag. 41, S167–S179. doi:10.1002/nafm.10506

CrossRef Full Text | Google Scholar

Hilling, C. D., Jiao, Y., Fabrizio, M. C., Angermeier, P. L., Bunch, A. J., and Orth, D. J. (2023). A size-based stock assessment model for invasive blue catfish in a Chesapeake Bay sub-estuary during 2001–2016. Fish. Manag. Ecol. 30 (1), 70–88. doi:10.1111/fme.12601

CrossRef Full Text | Google Scholar

Jiao, Y., Hayes, C., and Cortés, E. (2009a). Hierarchical bayesian approach for population dynamics modelling of fish complexes without species-specific data. ICES J. Mar. Sci. 66 (2), 367–377. doi:10.1093/icesjms/fsn162

CrossRef Full Text | Google Scholar

Jiao, Y., Reid, K., and Smith, E. (2009b). “Model selection uncertainty and Bayesian model averaging in fisheries recruitment modeling,” in The future of fisheries science. Editors R. J. Beamish, and B. J. Rothschild (Berlin: North America. Springer), 505–524.

Google Scholar

Jiao, Y., Rogers-Bennett, L., Taniguchi, I., Butler, J., and Crone, P. (2010). Incorporating temporal variation in the growth of red abalone (haliotis Rufescens) using hierarchical Bayesian growth models. Can. J. Fish. Aquat. Sci. 67, 730–742. doi:10.1139/f10-019

CrossRef Full Text | Google Scholar

Kettunen, J., Mehtätalo, L., Tuittila, E. S., Korrensalo, A., and Vanhatalo, J. (2023). Joint species distribution modeling with competition for space. Environmetrics e2830. doi:10.1002/env.2830

CrossRef Full Text | Google Scholar

Kuo, A. Y., and Neilson, B. J. (1987). Hypoxia and salinity in Virginia estuaries. Estuaries 10 (4), 277–283. doi:10.2307/1351884

CrossRef Full Text | Google Scholar

Lagler, K. F. (1961). Freshwater fishery biology. Dubuque, Iowa: William C. Brown Company.

Google Scholar

Li, Y., Jiao, Y., and Reid, K. (2011). Assessment of landed and non-landed by-catch of walleye, yellow perch and white perch from the commercial gillnet fisheries of Lake Erie, 1994–2007. J. Gt. Lakes. Res. 37 (2), 325–334. doi:10.1016/j.jglr.2011.02.007

CrossRef Full Text | Google Scholar

Maunder, M. N., and Punt, A. E. (2004). Standardizing catch and effort data: a review of recent approaches. Fish. Res. 70 (2), 141–159. doi:10.1016/j.fishres.2004.08.002

CrossRef Full Text | Google Scholar

Maunder, M. N., Sibert, J. R., Fonteneau, A., Hampton, J., Kleiber, P., and Harley, S. J. (2006). Interpreting catch per unit effort data to assess the status of individual stocks and communities. ICES J. Mar. Sci. J. Du Conseil 63, 1373–1385. doi:10.1016/j.icesjms.2006.05.008

CrossRef Full Text | Google Scholar

National Marine Fisheries Service (NMFS) (2012). NMFS landings query results. Available online at: http://www.st.nmfs.noaa.gov/pls/webpls/MF_ANNUAL_LANDINGS.RESULTS (Accessed May 07, 2013).

Google Scholar

Nepal, V., and Fabrizio, M. C. (2019). High salinity tolerance of invasive blue catfish suggests potential for further range expansion in the Chesapeake Bay region. PLoS One 14 (11), e0224770. doi:10.1371/journal.pone.0224770

PubMed Abstract | CrossRef Full Text | Google Scholar

Nepal, V., and Fabrizio, M. C. (2020). Sublethal effects of salinity and temperature on non-native blue catfish: implications for establishment in Atlantic slope drainages. PLoS One 15 (12), e0244392. doi:10.1371/journal.pone.0244392

PubMed Abstract | CrossRef Full Text | Google Scholar

Orth, D. J., Jiao, Y., Schmitt, J. D., Hilling, C. D., Emmel, J. A., and Fabrizio, M. C. (2017). Dynamics and role of non-native blue catfish Ictalurus furcatus in Virginia's tidal rivers. Henrico, Virginia. Available online at: https://repository.library.noaa.gov/view/noaa/44066/noaa_44066_DS1

Google Scholar

Ortiz, M., and Arocha, F. (2004). Alternative error distribution models for standardization of catch rates of non-target species from a pelagic longline fishery: billfish species in the Venezuelan tuna longline fishery. Fish. Res. 70, 275–294. doi:10.1016/j.fishres.2004.08.028

CrossRef Full Text | Google Scholar

Pflieger, W. L. (1997). The fishes of Missouri. Missouri department of conservation. Jefferson City.

Google Scholar

Punt, A. E., Walker, T. I., Taylor, B. L., and Pribac, F. (2000). Standardization of catch and effort data in a spatially-structured shark fishery. Fish. Res. 45, 129–145. doi:10.1016/s0165-7836(99)00106-x

CrossRef Full Text | Google Scholar

Quinn, T., and Deriso, R. B. (1999). Quantitative fish dynamics. Oxford, UK: Oxford University Press.

Google Scholar

Roberts, G. O., and Rosenthal, J. S. (2001). Infinite hierarchies and prior distributions. Bernoulli 7, 453–471. doi:10.2307/3318496

CrossRef Full Text | Google Scholar

Schloesser, R. W., Fabrizio, M. C., Latour, R. J., Garman, G. C., Greenlee, B., Groves, M., et al. (2011). “Ecological role of blue catfish in Chesapeake Bay communities and implications for management,” in Conservation, ecology, and management of worldwide catfish populations and habitats. Editors P. Michaletz, and V. Travnichek (Bethesda, MD: Am. Fish. Soc. Symp.), 369–382.

Google Scholar

Schoenebeck, C. W., Lundgren, S. A., and Koupal, K. D. (2015). Using electrofishing catch rates to estimate the density of largemouth bass. North Am. J. Fish. Manag. 35 (2), 331–336. doi:10.1080/02755947.2014.996686

CrossRef Full Text | Google Scholar

Smith-Root (2020). Things to consider when electrofishing. Available online at: https://www.smith-root.com/support/kb/things-to-consider-when-electrofishing.

Google Scholar

Spiegelhalter, D., Thomas, A., Best, N., and Lunn, D. (2004). WinBUGS user manual. Cambridge, UK: Mdeical Research Council Biostatistics Unit.

Google Scholar

Stefansson, G. (1996). Analysis of groundfish survey abundance data: combining the GLM and delta approaches. ICES J. Mar. Sci. 53, 577–581. doi:10.1006/jmsc.1996.0079

CrossRef Full Text | Google Scholar

Ye, Y., Al-Husaini, M., and Al-Baz, A. (2001). Use of generalized linear models to analyze catch rates having zero values: the Kuwait driftnet fishery. Fish. Res. 53, 151–168. doi:10.1016/s0165-7836(00)00287-3

CrossRef Full Text | Google Scholar

Yu, H., Jiao, Y., and Winter, A. (2011). Catch-rate standardization for yellow perch in Lake Erie: a comparison of the spatial generalized linear model and the generalized additive model. T. Am. Fish. Soc. 140, 905–918. doi:10.1080/00028487.2011.599258

CrossRef Full Text | Google Scholar

Yu, H., Jiao, Y., Su, Z., and Reid, K. (2012). Performance comparison of traditional sampling designs and adaptive sampling designs for fishery-independent surveys: a simulation study. Fish. Res. 113, 173–181. doi:10.1016/j.fishres.2011.10.009

CrossRef Full Text | Google Scholar