Jason Doll (QFC Post-Doctoral Research Associate) and Stephen Jacquemin (Wright State University) recently published an article in Fisheries describing the fundamentals of Bayesian modeling and inference for a fisheries management audience. The focus of the feature article attempts to answer three questions fisheries professionals might have about Bayesian inference; 1) What is Bayesian inference? 2) Why should I care about Bayesian inference? and 3) What can Bayesian inference do for me? In the article, readers are exposed to the law of inverse probability (i.e., Bayes’ Theorem), some of the advantages of Bayesian inference, and presented with two applied fisheries data analysis examples. The first example uses a Bayesian t-test to compare relative weight between two time periods. This example demonstrates how Bayesian inference results in a probabilistic outcome and how this type of analysis can answer the question; “What is the probability relative weight has reached my management benchmark?” Their second example fits a von Bertalanffy growth model with prior information. This example demonstrates how to transparently incorporate a data based informative prior probability distribution to improve our ability to make a conclusion about our own data.
The article can be found here. Computer code to accompany the analysis in the article can be found here. The citation for the article and abstract is below.
Doll, J.C., and S.J. Jacquemin. 2018. Introduction to Bayesian modeling and inference for fisheries scientists. Fisheries 43:152-161.
Bayesian inference is everywhere, from one of the most recent journal articles in Transactions of the American Fisheries Society to the decision making process you go through when you select a new fishing spot. Bayesian inference is the only statistical paradigm that synthesizes prior knowledge with newly collected data to facilitate a more informed decision – and it is being used at an increasing rate in almost every area of our profession. Thus, the goal of this article is to provide fisheries managers, educators, and students with a conceptual introduction to Bayesian inference. We do not assume the reader is familiar with Bayesian inference, however, we do assume the reader has completed an introductory biostatistics course. To this end, we review the conceptual foundation of Bayesian inference without the use of complex equations; present one example of using Bayesian inference to compare relative weight between two time periods; present one example of using prior information about von Bertalanffy growth parameters to improve parameter estimation; and finally, suggest readings that can help to develop the skills needed to use Bayesian inference in your own management or research program.
QFC Scientific Programmer/Research Scientist, Dr. Norine Dobiesz, and QFC Co-Director, Dr. Jim Bence, along with several colleagues recently published a paper in Journal of Great Lakes Research evaluating sea lamprey-associated mortality sources on a generalized lake sturgeon population in the Great Lakes. The lake sturgeon is a benthivore, valued for its historical role in the Great Lakes fish community, as a key element in the culture of native peoples, and for its unique prehistoric ancestry that attracts considerable public attention. Large Great Lake tributaries support critical sturgeon spawning but also provide spawning areas for invasive sea lamprey, fish parasites that seek out and frequently kill hosts in the open waters of the Great Lakes. Lake sturgeon populations experience two age-specific mortality sources that are influenced by the sea lamprey control program: lampricide exposure-induced mortality on age-0 fish and sea lamprey predation on sub-adults (ages 7-24). Jim and Norine’s research objective was to understand what mortality source had a greater effect on lake sturgeon abundance and its potential influence on restoration efforts.
For their research, an age-structured population model was used to show that although lampricide-induced mortality on age-0 lake sturgeon can limit attainable population abundance, sea lamprey predation on sub-adult lake sturgeon may have a greater influence. Because each lake sturgeon population experiences unique environmental conditions and sea lamprey predation pressure, they found that in some circumstances the absence of TFM toxicity could lead to a 5.7% increase in adult lake sturgeon populations. However, small increases in sea lamprey predation pressure could tip this balance leading to a 13% decrease in adult lake sturgeon abundance. A reduction or elimination of TFM toxicity on larval lake sturgeon, while maintaining TFM toxicity on larval sea lamprey, was the best approach to promote lake sturgeon restoration and minimize negative impacts on other fish community members. Until then, fisheries managers will need to balance the trade-off between lake sturgeon rehabilitation and allowing higher sea lamprey predation on the larger Great Lakes fish community.
The citation for the published article and the abstract are below. The paper can be viewed here.
Dobiesz, N.E., J.R. Bence, T. Sutton, M. Ebener, T.C. Pratt, L.M. O’Connor, and T.B. Steeves. 2018. Evaluation of sea lamprey-associated mortality sources on a generalized lake sturgeon population in the Great Lakes. Journal of Great Lakes Research 44:319-329.
Lake sturgeon populations in the Laurentian Great Lakes experience two age-specific mortality sources influenced by the sea lamprey Petromyzon marinus control program: lampricide (TFM) exposure-induced mortality on age-0 fish and sea lamprey predation on sub-adults (ages 7–24). We used a generic age-structured population model to show that although lampricide-induced mortality on age-0 lake sturgeon can limit attainable population abundance, sea lamprey predation on sub-adult lake sturgeon may have a greater influence. Under base conditions, adult lake sturgeon populations increased by 5.7% in the absence of TFM toxicity if there was no change in predation; whereas, a 13% increase in predation removed this effect, and a doubling of sea lamprey predation led to a 32% decrease in adult lake sturgeon. Our estimates of lake sturgeon abundance were highly dependent on the values of life history and mortality parameters, but the relative impacts of ceasing TFM treatment and increasing predation were robust given a status quo level of predation. The status quo predation was based on sea lamprey wounding on lake sturgeon, and improvements in this information would help better define tradeoffs between the mortality sources for specific systems. Reduction or elimination of TFM toxicity on larval lake sturgeon, while maintaining TFM toxicity on larval sea lamprey, can promote lake sturgeon restoration and minimize negative impacts on other fish community members.
Charlie Belinsky (QFC Distance Training Curriculum Specialist) recently completed a revamping of the online R course that the QFC has offered since 2008. A major focus of the course, now titled R Fundamentals for Research, is on teaching programming skills and practices. Additionally, the class is now project-based and students can use their own data for the project. A description of the course is provided below. To enroll in the course click here.
R Fundamentals for Research
The purpose of this class is to introduce students to the principles of and structures in programming using the R and RStudio software packages. R and RStudio are powerful and versatile data analysis packages that are freely available. The R community is extensive and is constantly developing new tools that rival and, in many cases, surpass commercial statistical software and graphing packages. This class is project-based and students are encouraged to use their own data for their project. While the class focus is on programming using R and RStudio, the programming skills taught are designed so that students can transfer their skills to other programming platforms, like AD Model Builder or C.
Travis Brenden (QFC Associate Director), along with Derek Ogle (Professor – Northland College) and Josh McCormick (Biometrician – Idaho Department of Fish and Game), co-authored a chapter on growth modeling in a recent book published by the American Fisheries Society entitled Age and Growth of Fishes: Principles and Techniques. Major sections of the chapter include data types and needs for growth modeling, a catalog of growth functions, fitting growth models through nonlinear regression, comparing growth models through significance testing or information criterion, Bayesian inference of growth models, and hierarchical growth models. Interspersed throughout the chapter are numerous box examples demonstrating actual applications of the concepts discussed in the chapter using real fish-growth data and the R statistical computing and graphing environment. The chapter should serve as a resource for graduate students and working professionals interested in both basic and advanced applications of fish growth modeling and statistical inference.
A full citation for the chapter is below. A copy of the chapter or book can be purchased here.
Ogle, D.H., T.O. Brenden, and J.L. McCormick. 2017. Growth estimation: growth models and statistical inference. Pages 265-359 in M. Quist and D. Isermann, editors. Age and growth of fishes: principles and techniques. American Fisheries Society, Bethesda, Maryland.
New QFC Publication – Feasibility of Using Vaccinated Hatchery Fish to Minimize Disease Spread in Wild Populations
Lori Ivan (QFC Post-Doctoral Research Associate) and Travis Brenden (QFC Associate Director), along with colleagues from the Michigan State University Aquatic Animal Health Laboratory, recently published a paper in Ecosphere exploring the feasibility of vaccinating and stocking hatchery-propagated fish as a means to protect a wild fish population against viral outbreak. They constructed a spatially explicit individual-based model patterned after the Lake Michigan Chinook salmon population. The modeled population was susceptible to disease outbreaks exhibiting characteristics similar to viral hemorrhagic septicemia genotype IVb. To prevent disease spread, it was assumed that hatchery fish could be vaccinated against the disease prior to their being stocked into the system with immunization conferring 100% life-time protection against the disease. At typical stocking levels, vaccination decreased the percent of the population infected with the disease by 23–74% per year depending on the factors evaluated. Complete disease eradication was only achieved if it was assumed previously infected individuals could not resume viral shedding. The use of vaccination programs in aquatic settings to date has largely been limited to aquaculture/hatchery facilities, although interest in expanding vaccination programs to include protecting wild populations is expanding. Lori’s and Travis’ research is the first to explore how protection might be expected from a vaccination program in an aquatic setting.
The citation for the published article and the abstract are below. The paper can be viewed here.
Ivan, L.N., T.O. Brenden, I.F. Standish, and M. Faisal. 2018. Individual-based model evaluation of using vaccinated hatchery fish to minimize disease spread in wild fish populations. Ecosphere 9:e02116.
Although vaccination programs are routinely used in terrestrial environments to protect wild and captive populations against infectious disease, their use in fish populations has been limited to aquaculture/hatchery facilities. A major challenge to enacting a vaccination program for wild fish populations is how to efficiently vaccinate large numbers of susceptible individuals. One possible solution to this dilemma would be vaccinating hatchery‐propagated fish prior to their being stocked into infected systems, although the effectiveness of such a program is uncertain. We constructed a spatially explicit individual‐based model to evaluate the effectiveness of vaccinating hatchery‐propagated fish to protect wild Lake Michigan Chinook salmon Oncorhynchus tshawytscha against a disease exhibiting characteristics similar to viral hemorrhagic septicemia genotype IVb. Simulations tracked growth, movement, mortality, maturation, wild reproduction, and disease transmission during a 25‐yr time period. Disease states consisted of vaccinated, susceptible, infected, shedding (i.e., infectious), and recovered. Factors that were examined included level of clustering among at‐large individuals, infection probability, relationship between viral exposure and mortality, number of stocked individuals, whether recovered individuals could resume viral shedding, and disease initialization status. At an annual stocking level of 2.4 million Chinook salmon, vaccination decreased the percent of the population infected by 23–74% per year depending on the factors evaluated. Doubling the stocking level of vaccinated individuals resulted in similar levels of protection. The largest decrease in percent infected occurred under a condition of low infection probability, high exposure mortality, and high degree of clustering. The protection stemming from vaccination was just slightly smaller under conditions of high infection and high exposure mortality. Complete disease eradication only occurred when recovered individuals could not resume viral shedding. Under such conditions, vaccination sometimes was not even necessary for disease eradication. Our modeling efforts showed that a vaccination program based on immunizing hatchery‐propagated individuals prior to stocking may help protect wild fish populations, although disease eradication may be difficult to achieve when recovered individuals can resume shedding viral particles.
On October 24, 2017, QFC co-Director, Dr. Mike Jones, testified before the Senate Commerce, Science, and Transportation Committee Oceans, Atmosphere, Fisheries, and Coast Guard Subcommitte on a hearing related to the re-authorization of the Magnuson-Stevens Fishery Conservation and Management Act, which is commonly referred to as the Magnuson-Stevens Act. This act is the primary law governing marine fisheries management in US federal waters and was enacted to promote optimal exploitation of coastal fisheries. The focus of the hearing was on the state of U.S. fisheries and the science that supports sustainable management. As part of his testimony, Mike discussed the importance of accounting for uncertainty in management decisions and how management strategy evaluation methods, which use computer simulation methods to evaluate how alternative fishery management strategies are likely to perform relative to pre-defined sets of management goal, account for uncertainty. Mike testified on two MSE-applications that he and other QFC staff have worked on in recent years, Great Lakes sea lamprey control and Lake Erie walleye and yellow perch management. A recording of Mike’s testimony can be viewed here.
Several QFC staff and student recently taught a revised version of the R graphing short course entitled “Unleashing the Power of R as a Graphing Tool.” The developers (Lisa Peterson, Yang Li, Sam Truesdell, Matt Vincent, and Charlie Belinsky) refined and restructured the short course into its current version using feedback from the participants of the original course taught in 2016. The short course provided an introduction to creating advanced and publishable graphics using the R base package. The instructors covered a variety of topics, including adding components to existing graphs (e.g., error bars), the use of color (e.g., creating a color ramp), multipanel plots, and creating graphics using spatial data, as well as tips on how to fulfill journal requirements. Information was conveyed through both lecture and “hands-on” sections where participants, using an R environment on their own computer, went through the code with the instructor. Participants also worked on exercises that gave them an opportunity to graph their own data. Twelve graduate students from the Michigan State University Department of Fisheries and Wildlife participated in the day-long course. The feedback on the course was very positive, with participants reporting an increase in their practical knowledge of R and the belief they would be able to apply the concepts that were taught to their own work in the future.
The Quantitative Fisheries Center (QFC) recently hosted a two day workshop (June 22-23) as part of a larger structured decision-making (SDM) exercise to address management of Grass Carp in Lake Erie. Grass Carp is an invasive herbivorous fish that at high densities can pose a threat to coastal wetlands and aquatic communities. Some Great Lakes states allow inland stocking of sterile Grass Carp (triploid), which have been sporadically captured in Lake Erie; however, increasing captures of reproductively viable Grass Carp (diploid), and documented reproduction and recruitment over the past several years have raised concerns about potential effects on Lake Erie aquatic and wildlife communities. The SDM exercise is being led by Drs. Kelly Robinson, Mike Jones, and Mark DuFour and is designed to bring fisheries managers and researchers together to cohesively develop a management strategy for Lake Erie Grass Carp. Twenty-nine individuals participated in the June workshop from ten different institutions and agencies: Michigan Department of Natural Resources, Ohio Department of Natural Resources, Ontario Ministry of Natural Resources and Forestry, U. S. Geological Survey, U. S. Fish and Wildlife Service, Department of Fisheries and Oceans Canada, University of Toledo, Michigan State University, University of Toronto, and the Great Lakes Fishery Commission. Because the Grass Carp threat to Lake Erie is new, there are many uncertainties about their potential effects on the Lake Erie ecosystem as well as the likelihood of success of different management options. During this workshop, the research and management group discussed these uncertainties and the QFC presented a Grass Carp population model to help evaluate our current knowledge and inform future management actions. A final workshop is tentatively scheduled for September 2017, where the QFC will present the results of our uncertainty analysis. These initial workshops, and SDM exercise as a whole, represent the first step in an adaptive management process, where we can refine our management strategies as we learn more about the Lake Erie Grass Carp population and the effectiveness of management options.
In February, Alex Jensen, QFC Master’s student advised by QFC Co-Director Dr. Mike Jones, successfully defended his MS thesis, entitled “Modeling the Impacts of Barrier Removal on Great Lakes Sea Lamprey”. Alex’s thesis research addressed two key uncertainties regarding barrier removals in the Great Lakes region: how much suitable sea lamprey habitat is available above barriers and what is the expected sea lamprey population response to barrier removal. To address these uncertainties, Alex developed and evaluated competing models to predict larval sea lamprey habitat availability upstream of Lake Michigan barriers using reach-scale landscape predictors. Alex then modified and used a sea lamprey management strategy evaluation (SLaMSE) model to evaluate the impacts of barrier removals on the response of the Lake Michigan sea lamprey population. Alex’s simulation modeling revealed a disproportionate, exponential response to increasing barrier removals, due in part to decreasing control effectiveness with a fixed lampricide treatment budget. The same model was used to inform the potential effects of different management actions associated with the possible removal of the Grand River’s Sixth Street Dam.
Alex will remain at the QFC through the spring finalizing edits to his thesis and preparing the chapters of his thesis for potential journal publication. In early summer, Alex will be moving to Oregon to pursue a PhD with Dr. Jim Peterson at Oregon State University. Congratulation Alex!
Travis Brenden (QFC Associate Director) recently co-authored 4 papers with colleagues from the Michigan State University Aquatic Animal Health Laboratory on viral hemorrhagic septicemia virus genotype IVb (VHSV-IVb) disease dynamics in the Great Lakes region and the potential of using vaccination to protect fish against outbreaks of the virus. VHSV-IVb is an emerging sublineage of VHSV with a wide host range that quickly spread throughout the Great Lakes watershed and caused multiple large fish die offs. In the first paper (Throckmorton et al. 2017), potential reservoirs of VHSV-IVb were examined in Budd Lake, a Michigan inland lake that is considered enzootic for the virus. VHSV-IVb was detected in multiple samples of amphipods both in 2011 and 2012, but was not detected in Notropis spp., Lepomis spp., mussels, leeches, or water samples, suggesting that amphipods might serve as a reservoir or vector for the virus. In the second paper (Millard et al. 2017), a DNA vaccine containing the glycoprotein gene of VHSV-IVb was developed and evaluated in its ability to protect muskellunge, which is a species that is highly susceptible to the virus, against infection. The relative percent survival of immunized muskellunge when challenged with the virus was 45%. In a follow-up paper (Standish et al. 2016a), relative percent survival of immunized muskellunge when challenged with VHSV-IVb increased to 100% when vaccinated individuals were given a booster dose and allowed a longer incubation period prior to the challenge. In the fourth paper (Standish et al. 2016b), a laboratory study was conducted to determine whether a herd immunity response, which is a necessary precursor for a vaccination program to be successful, could be elicited in fish. The study used a novel flow-through tank design in which different combinations of naïve and immunized muskellunge housed in tanks were exposed to VHSV-IVb via infected muskellunge housed in a tank supplying water to the other tanks. The mortality of naïve muskellunge on average was lower when co-occurring with immunized muskellunge than when naïve muskellunge were housed alone (36.5% when co-occurring with vaccinated muskellunge versus 80.2% when housed alone), indicating a possible protective effect based on cohabitation with vaccinated individuals. Travis and QFC Post-Doctoral Research Associate, Lori Ivan, have recently completed a modeling project using the information learned from the Standish et al. (2016b) study to determine the feasibility of vaccinating and stocking hatchery-propagated fish as a means to protect a wild fish population again viral outbreak. They hope to publish this research soon. Travis and Lori will be giving presentations on their modeling results at two upcoming meetings: American Fisheries Society Fish Health Section meeting and the International Association of Great Lakes Research annual conference.
Millard, E.V., S.E. LaPatra, T.O. Brenden, A.M. Bourke, S.D. Fitzgerald, and M. Faisal. 2017. DNA vaccination partially protects muskellunge against viral hemorrhagic septicemia virus (VHSV-IVb). Journal of Aquatic Animal Health 29:50-56. (see here)
Standish, I.F., E.V Millard, T.O. Brenden, and M. Faisal. 2016a. A DNA vaccine encoding the viral hemorrhagic septicemia virus genotype IVb glycoprotein confers protection in muskellunge (Esox masquinongy), rainbow trout (Oncorhynchus mykiss), brown trout (Salmo trutta), and lake trout (Salvelinus namaycush). Virology Journal 13:203; doi:10.1186/s12985-016-0662-8. (see here)
Standish, I.F., T.O. Brenden, and M. Faisal. 2016b. Does herd immunity exist in aquatic animals? International Journal of Molecular Sciences 17:1898; doi:10.3390/ijms17111898. (see here)
Throckmorton, E., T. Brenden, A. Peters, T. Newcomb, G. Whelan, and M. Faisal. 2017. Potential reservoirs and risk factors for VHSV IVb in an enzootic system: Budd Lake, Michigan, United States. Journal of Aquatic Animal Health 29:31-42. (see here)