We conducted a study to assess the efficacy of using a parentage-based tagging survival model (PBT N-mixture model) to evaluate two sources of mortality for juvenile Chinook salmon (

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Funding for this research was provided by the U.S. Army Corps of Engineers. Staff from Oregon State University provided information from recent studies on copepods in Willamette Basin reservoirs that was useful in this study, and we thank Dr. James Peterson, Travis Neal, and Dr. Christina Murphy for their insights. Data are not currently available from funding organization, the U.S. Army Corps of Engineers. Contact the U.S. Army Corps of Engineers for further information.

Estimates of survival for specific life-stages of Pacific salmon (

The U.S. Army Corps of Engineers (USACE) operates the Willamette Project (Project) in western Oregon, which includes 13 dams and reservoirs, approximately 68 kilometers of revetments, and several fish hatcheries. The primary purpose of the Project is flood risk management, but it is also operated to provide hydroelectricity, irrigation water, navigation, instream flows for wildlife, and recreation. The Project was determined to jeopardize Upper Willamette spring Chinook salmon and winter steelhead (

The U.S. Geological Survey (USGS) developed a study design to estimate survival of juvenile Chinook salmon in Lookout Point Reservoir, located on the Middle Fork Willamette River, and completed 2 years of research and survival estimation in 2017 and 2018 (

In response to the uncertainty about trends in survival in Lookout Point, we conducted additional analyses to determine if the PBT N-mixture model could separately estimate mortality because of predation from that of copepod infection. This study was conducted in two parts. In the first part, we reevaluated field data to determine whether separate effects of copepod infection and predation could be discerned with PBT N-mixture model. In the second part, we designed and implemented a simulation study to evaluate the ability of PBT N-mixture model to discern a trend with multiple years of data.

Monthly survival estimates for subyearling Chinook salmon (

Figure 1. Boxplots showing monthly survival estimates for subyearling Chinook salmon in Lookout Point Reservoir during April (0)–October (6) 2017 and 2018

Proportion of juvenile Chinook salmon (

Figure 2. Graph showing proportion of juvenile Chinook salmon infected with the copepod

Field data from Lookout Point Reservoir collected in 2018 were reanalyzed to determine whether mortality could be statistically attributed to two different sources. These data are described in detail in

We hypothesized that the two sources of mortality should have countervailing effects. That is, absent any effect of copepod infection, monthly survival probability should increase over time because of decreased predation as juvenile Chinook salmon grew to larger sizes. Survival estimates from the 2017 field study supported this hypothesis as

We used the PBT N-mixture model previously described in

_{ik}

The likelihood of the data _{jk}_{jk}

_{j}

This model assumes the following:

The number of individuals with each PBT mark at the time of release is assumed known without error.

Reservoir survival and capture probabilities are equal among PBT marks. These assumptions should be fulfilled if PBT marks are well mixed in the reservoir such that the distribution of PBT marks is similar among sampling locations.

Fish remain in the reservoir and are available for capture, and no mortality occurs over the

The capture probability parameter,

_{g}_{,0} is the intercept (capture probability of gear type

_{g}_{,1} is offshore offset of capture probability for gear type

_{p}_{,}_{k}

For survival, we fit three models to the data. The first model corresponded to a “predation-only” model which assumed that monthly survival increased or decreased at a fixed rate over time. Here, time is treated as surrogate for fish growing larger and changing behavior to better evade predators. The second model corresponded to “copepod-only” model which assumed that monthly survival depended only on the proportion of captured fish with visible copepod infection. The third model included both effects and is represented as:

_{0} is the intercept (survival for the first month after release with assumed copepod infection rate of zero),

_{1} is change in survival due to time (predation),

_{2} is change in survival due to copepod infection,

_{k}

_{k}

We used standard normal prior distributions for all slope and intercept parameters. Models were compared based on the whether 90 percent credible intervals (CI) for parameter estimates of the covariate effects contained only positive or negative values. If the CI contained both positive and negative values, then we concluded no effect of the covariate could be discerned. We also estimated and compared the six period-specific survival estimates for the three models: (1) mid-April to mid-May (_{1}), (2) mid-May to mid-June (_{2}), (3) mid-June to mid-July (_{3}), (4) mid-July to mid-August (_{4}), (5) mid-August to mid-September (_{5}), and (6) mid-September to mid-October (_{6}).

We conducted a simulation study to assess the potential for a study design to separately attribute mortality to predation and copepod infection. There were two major motivating factors to the design of this simulation study. First, we designed the study to use an assessment for copepod infection based on a subsample of captured fish. Second, we designed the study to be conducted over the course of multiple field seasons with interannual variation in copepod infection rates. In the simulation study we varied the subsampling rate, the number of years and the degree of interannual variation.

We simulated a subsampling scheme out of concern that using adult copepod presence as a measure of infection rates may not be an accurate measure of copepod infection dynamics. Emerging evidence suggests that the presence of adult copepods may be a lagging indicator of copepod infection rates. For example,

To better evaluate the feasibility of identifying two competing sources of mortality, we structured our simulation study to mimic a field effort conducted over the course of 2 or more years. A major challenge to estimating covariate relations in observational studies is the phenomenon of multicollinearity, defined as a correlation between two or more predictor variables. Data from the 2018 field study demonstrated such collinearity between copepod infection and time as adult copepod prevalence increased monotonically over the course of the study. The consequence of multicollinearity is that a statistical model will produce unreliable estimates of the coefficients for correlated variables. Overall predictions from a model under multicollinearity will tend to be accurate (in this case, time-interval specific survival estimates), but estimates for separate covariate effects (that is, time and copepod infection) may not be. For example, estimates for the coefficients will tend to have large standard errors. The only remedy for multicollinearity is to design a study in such a way that the correlation between two variables can be broken. In observational studies, where it is usually not possible to experimentally manipulate covariates, one way to break this collinearity is to collect data over a broad range of conditions such that the correlation between variables is lessened. In the case of the PBT N-mixture model for Lookout Point this means sampling over 2 or more years.

The extent to which copepod prevalence varies from year to year in Lookout Point is unknown. There is only limited evidence to suggest that the relation between copepods and time may differ in different years. Data on adult copepod prevalence were not collected by

Given the unknowns of copepod infection dynamics, we structured our simulation to evaluate multiple scenarios of interannual variation in copepod infection rates. We generated three families of copepod infection curves with respect to time: “Low,” “Moderate,” and “High.” These curves were drawn from the Richard distribution (

Simulation of copepod prevalence curves for a hypothetical population of juvenile Chinook salmon (

Figure 3. Graphs showing simulation of copepod prevalence curves for a hypothetical population of juvenile Chinook salmon for three different year-types over five sampling occasions

We produced a series of simulated datasets with common characteristics varying only the number of years in the study, the type of copepod infection curves in each year, and the number of fish subsampled during each sampling occasion. For simplicity, all fish in the simulation were released as a single group at the start of the simulated study. The common characteristics included the number of distinct PBT family groups

Example survival curves used in the simulation model, (

Figure 4. Graphs showing example survival curve used in the simulation model, (

Each simulated dataset was constructed by iteratively stepping through the data generating process implied by the PBT N-mixture model. The simulations began with a release of

Each simulated dataset was analyzed using a modified version of the PBT N-mixture model described above. The model was modified to apply to multiple years by looping over likelihoods for all years. Capture probability was also simplified because we ignored the complexities of multiple gear-types and off-shore/on-shore effects for the purposes of simulation. The final modifications accounted for uncertainty in the true copepod infection prevalence because of the subsampling effect and related survival to the latent true infection prevalence. That is for each timestep, we assumed

The results of the simulation study must be interpreted with caution because it makes several assumptions which may not hold in the field. Among these, we assumed that the survival effects would be constant from year to year, which is unlikely to be the case in nature. We also assumed that there was no interaction between time (a surrogate of fish size) and copepod infection which may not hold in nature. Examples of interactions between the two covariates include the following: (1) if larger fish are more likely to die from copepod infection than smaller fish (given equal infection rates); or (2) if larger fish are more likely to be infected but equally likely to die from infection. The true field implementation is also likely to be more complicated than the relatively simple simulation model obtained here; in particular, capture probability was set to be a constant. If it is necessary to account for additional parameters (for example, capture probabilities from different gear types) this may reduce the ability of the model to detect an effect. There is no empirical evidence for the effect of copepod infection prevalence as defined here (that is, infection damage prior to the appearance of adult copepods) and an effect of lesser magnitude is less likely to be detected. Finally, it is unclear whether such a subsampling approach is feasible in a field study; that is, we do not know if gill tissue recovered in the field will be of sufficient quality for histopathological examination.

Re-analysis of the 2018 Lookout Point data was unable to identify separate effects of both time and copepod adult prevalence on survival. Whereas both the “predation only” and “copepod only” models detected a negative effect of the respective covariate, the model with both covariates estimated a negative effect for time that was larger than the effect of the “predation only” model and a positive effect with high uncertainty for the copepod model (

Graphs showing (

Figure 5. Graphs showing (

The multiyear data simulation suggests that identifying a signal of the two countervailing covariates will be challenging. Of 96 simulated datasets, only 6 had both 90 percent posterior intervals which contained the true values and did not overlap zero. That is, these simulations had neither Type S nor Type M error. Two of these occurred in simulations of 2-year studies (36 total simulations,

Parameter estimates and 90-percent posterior uncertainty intervals for the coefficients of survival in the simulated 2-year PBT N-mixture model. B0 is the intercept, B1 is the slope of time, and B2 is the slope of the copepod effect. The red dashed line is the true parameter value, and the blue dotted line for the slope terms is zero. For B1, if the posterior interval is entirely above the blue-dotted line and overlaps the red-dashed line then the model was able to successfully detect that effect for that replication of the model. For B2, the interval should be below the blue-dotted line and overlapping the red-dashed.

Figure 6. Graphs showing parameter estimate and 90-percent posterior uncertainty intervals for the coefficients of survival in the simulated 2-year PBT N-mixture model

Parameter estimates and 90-percent posterior uncertainty intervals for the coefficients of survival in the simulated 3-year PBT N-mixture model. B0 is the intercept, B1 is the slope of time, and B2 is the slope of the copepod effect. The red dashed line is the true parameter value, and the blue dotted line for the slope terms is zero. For B1, if the posterior interval is entirely above the blue-dotted line and overlaps the red-dashed line then the model was able to successfully detect that effect for that replication of the model. For B2, the interval should be below the blue-dotted line and overlapping the red-dashed.

Figure 7. Graphs showing parameter estimate and 90-percent posterior uncertainty intervals for the coefficients of survival in the simulated 3-year PBT N-mixture model

Identifying relations between environmental conditions and ecological processes from observational studies is a challenging endeavor. Environmental conditions often covary (for example temperature and river flow) and ecological process (for example, survival of fish species) are often only imperfectly observed and must be estimated using models paired to rigorous field study designs. Results from this study showed that several limitations exist which prevent the PBT N-mixture model from estimating mortality separately for predation- and copepod-related covariates in Lookout Point Reservoir. These include limitations in recapture probabilities, correlation between covariates of interest, the anticipated duration of a future multi-year field study (2 or 3 years), and critical uncertainties about methods to assess copepod infection and the effect of copepod infection on juvenile salmon survival. Whereas the PBT N-mixture has proven useful for estimating survival and trends in survival when other methods fail, it is important to acknowledge these limitations.

Recapture probabilities during field studies in 2017 and 2018 were very low, ranging from 0.00074 to 0.01303 (

Correlation between two or more predictor variables (multicollinearity) greatly complicates the ability for any statistical model to obtain reliable estimates of the independent contribution of each predictor to the observed outcome. In the case of copepod infection and predation, both are expected to change monotonically over the course of a field season, which leads to multicollinearity. Absent the ability to experimentally manipulate these two covariates in the field, the only way to realistically reduce the influence of multicollinearity is to collect data over multiple field seasons in the hope that the relation between copepod infection and predation differs between years. We developed the simulation for this study to include 2-year and 3-year scenarios based on the assumption that funding entities would be unwilling to commit to expensive, multi-year studies that extended beyond 3 years. Simulation results showed that four of the six simulated datasets without Type S or Type M errors occurred during the 3-year study period, which illustrate the value of additional years in contributing to modeling success. However, the only successful simulations of multiyear studies occurred when years were drawn from different copepod curve-families. Thus, the ability of a multiyear study to discriminate an effect is likely to be reliant on substantial interannual variation over the course of the study. For example, studies that pair wet, cold years with one or more hot, dry years are more likely to produce different relations between time and copepod infection than a study that included years with similar climatic conditions. The potential value of these additions to the data could be considered along with financial costs associated with additional years of study and the likelihood of conducting a study over a set of years with sufficient interannual variation.

Finally, whereas recent studies have provided new insights into the effects of copepods on the performance and survival of juvenile Chinook salmon, critical uncertainties remain. Several recent studies have assessed copepod effects on juvenile Chinook salmon in field (

For more information about the research in this report, contact

Director, Western Fisheries Research Center

U.S. Geological Survey

6505 NE 65th Street

Seattle, Washington 98115-5016

Manuscript approved on September 30, 2022

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