Patterns in oyster natural mortality in Chesapeake Bay, Maryland using a Bayesian model
Introduction
The eastern oyster Crassostrea virginica in Chesapeake Bay, Maryland (upper Chesapeake Bay) supported the largest oyster fishery in the world at its peak in the 1880s, as the Maryland catch was double the total catch of all countries besides the United States at this time (Kennedy and Breisch, 1983). While harvest has declined since the 1880s peak, upper Chesapeake Bay still supports an active commercial oyster fishery, open from October to March. The harvest during the 2014–2015 season was 388,658 Maryland bushels (1.78 × 107 L) in upper Chesapeake Bay, about 2% of historical peak harvest in Maryland (Tarnowski, 2016). Despite harvest declines, the eastern oyster remains economically important in Maryland; for example, the Maryland harvest in 2014–2015 ha d a dockside value of $17.1 million USD (Tarnowski, 2016). Oysters are ecologically important in part because they build reefs (also known as bars) that provide habitat for other organisms, including fish, clams, amphipods, and polychaetes (Rodney and Paynter, 2006), and because they are filter feeders that potentially exert top-down control on phytoplankton, sequestering nutrients and potentially reducing hypoxia in the Chesapeake Bay (Newell, 1988; Newell et al., 2007).
Natural mortality (i.e., all mortality due to non-fishing causes) is a key process in population dynamics. Stock assessment models typically require accurate estimates of natural mortality to accurately estimate abundance and fishery management reference points (Clark, 1999; Deroba and Schueller, 2013; Johnson et al., 2015). Despite this need, natural mortality is often difficult to estimate because natural mortality events are rarely observed. However, for many bivalves, indirect observation of natural mortality frequently occurs. Bivalves often leave behind articulated valves (i.e., shells connected by the hinge ligament) when they die, providing evidence that natural mortality has occurred, and thus allowing natural mortality to be estimated at much higher resolution than is possible for other organisms (e.g., Ford et al., 2006). The time scale at which natural mortality can be estimated depends in part on how long the articulated valves remain intact.
One method for estimating the annual natural mortality rate (i.e., the proportion of oysters that die each year) is the “box count method” (a “box” is a set of articulated valves from an oyster; Ford et al., 2006). The box count mortality rate is calculated by dividing the number of boxes in the sample by the sum of the number of boxes and live oysters in the same sample.
Estimates of natural mortality rates for the Maryland portion of Chesapeake Bay are obtained using the box count method with samples from 43 fixed sites, which are then averaged to obtain the “observed” mortality index (Tarnowski, 2017). While the box count method is a logical choice for these annual survey data because it is straightforward to calculate and has minimal data requirements (counts of live oysters and boxes from a single sample in a year is sufficient to calculate an estimate of natural mortality), it relies on strong assumptions to ensure unbiased estimates.
Violations of the assumptions of the box count method may lead to bias in the estimates of natural mortality obtained using the method. Some assumptions of the box count method include that 1) boxes do not persist in the environment for more than one year (i.e., after being on the bottom during the time of one survey, the box will have disarticulated by the time of the next year’s survey), 2) there is no net loss (or gain) of boxes between time of death and time of sampling within a year, and 3) live oysters and boxes are equally collected and retained by the survey gear (i.e., the relative collection efficiency of live oysters and boxes is equal). These assumptions may be violated for oysters in the Maryland portion of Chesapeake Bay. Studies on time to disarticulation of boxes suggest that most boxes remain intact for longer than one year, while some will break down more quickly (Christmas et al., 1997; Ford et al., 2006), which could violate the first two assumptions. Collection efficiency studies using dredge survey gear suggest that efficiency is lower for boxes than for live oysters (relative to divers; Powell et al., 2007; Marenghi et al., 2017), violating the third assumption. Collection efficiency is defined here as the number of live oysters or boxes that remain intact in a dredge sample relative to the number present per area swept (divers are assumed 100 % efficient). Collection efficiency may be lower for boxes than for live oysters because boxes are more likely to be broken apart by the dredge, although other causes may also contribute.
Despite their potential to result in biased estimates of natural mortality, the implications of using the box count method for a population that does not adequately meet its assumptions have not been investigated, nor have there been attempts to modify the method to correct for potential violations of the assumptions and to obtain estimates of uncertainty. Therefore, our objectives were threefold. First, we wanted to develop a new statistical method in a Bayesian framework for estimating natural mortality using observations of live oysters and boxes that incorporates corrections for the length of time boxes persist in the environment, accounts for unequal collection efficiencies between live oysters and boxes, and quantifies uncertainty. Then, we applied this approach to oysters in Maryland using the Maryland Department of Natural Resources (MDNR) fall dredge survey data to estimate natural mortality in 32 statistical catch reporting areas (referred to as “areas”; Fig. 1a). Finally, we investigated temporal and spatial patterns in natural mortality among all areas by using dynamic factor analysis, a dimension reducing tool, on the 32 time series of natural mortality as estimated from the Bayesian model. All analyses were completed in R version 3.5.1 (R Core Team, 2018). The code and data necessary to reproduce this analysis are available at https://github.com/doering-kat/M_Mod_Pub.
Section snippets
Data
We used data on counts of adult live oysters and adult-sized boxes per half Maryland bushel (Maryland bushel ≈ 46 L) of cultch (i.e., broken oyster shell and rock on an oyster bar) in individual dredge tows from the fall dredge survey to inform parameter estimation in the model. The survey is described in Vølstad et al. (2008) and in greater detail in annual reports from Maryland Department of Natural Resources (MDNR; e.g., Tarnowski, 2016). In short, the survey samples 66 fixed sites (i.e.,
Model convergence
The conditions specified for determining model convergence were met for the base model. The Gelman and Rubin potential scale reduction statistic was below 1.1 for all parameters, and there were no divergent samples in any of the posteriors. All effective sample sizes were above 1000, and most of the parameters (>95 %) had the maximum possible effective sample size of 6,000.
Bayesian natural mortality rate estimates
The average (over years) of median natural mortality from the model by area varied from 0.11 yr−1 to 0.33 yr−1 during
Discussion
We developed a statistical estimator for natural mortality in a Bayesian framework that used articulated valves with generalizable assumptions about relative collection efficiency of live organisms and articulated valves and about the disarticulation rate. In addition, our Bayesian model can be used with annual (as opposed to more frequent) survey data. Several estimators of natural mortality use counts of live bivalves and articulated valves (e.g., Dickie, 1955; Caddy, 1989; Ford et al., 2006;
CRediT authorship contribution statement
Kathryn L. Doering: Conceptualization, Methodology, Formal analysis, Writing - original draft. Michael J. Wilberg: Conceptualization, Methodology, Formal analysis, Writing - original draft. Dong Liang: Conceptualization, Methodology, Writing - review & editing. Mitchell Tarnowski: Investigation, Methodology, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We thank five anonymous reviewers and the associate editor for their helpful comments. We thank the Maryland Department of Natural Resources for collecting and providing the fall oyster dredge survey data and to the Maryland Oyster Stock Assessment Team for suggestions to improve the analyses. J. Baxter provided access to the datasets. L. Harris provided helpful comments on a previous version of the manuscript. Funding was provided by Chesapeake Biological Laboratory (CBL) Graduate Education
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