**The title, authors, and abstract for this completion report are provided below.  For a copy of the completion report, please contact the GLFC via e-mail or via telephone at 734-662-3209**

Estimating the Relationship between Sea Lamprey-Induced Mortality on Lake Trout and Observed Marking Rates

Brian J. Irwin¹, Travis O. Brenden², Weihai Liu², and James R. Bence²

¹ Quantitative Fisheries Center, 153 Giltner Hall, Department of Fisheries

and Wildlife, Michigan State University, East Lansing, MI 48824

² 13 Natural Resources Building, Department of Fisheries and Wildlife,

Michigan State University, East Lansing, MI 48824

March 2009

ABSTRACT:

We modified existing stock-assessment models for lake trout to evaluate the relationship between sea lamprey-induced mortality and observed marking rates on lake trout in the upper Great Lakes. The overall objective of the project was to evaluate the ability to estimate the proportionality between sea lamprey-induced mortality and wounding marking rates used in lake trout assessment models. We considered models for the following assessment units: Lake Huron MH1, MH2, and MH3456; Lake Michigan MM123, MM4, MM5, and MM67; and Lake Superior MI5 and MI7. The primary method used to estimate the new scaling parameter was to estimate this parameter simultaneous to other assessment-model parameters, but we also considered an iterative approach to estimation where the scaling parameter was estimated separately from other model parameters. We considered models at the scale of individual assessment units (listed above), for each lake separately (combining across assessment units – “combined-by-lake” model variants), and by combining across lakes (“combinedacross-lake” model variants). The combined-by-lake approach was intended to take advantage of contrast in patterns in marking rates among areas. Prior to combining, individual models were adjusted to a consistent compiler format and given assessment-unit-specific naming conventions. Reflecting the high degree of model complexity and large number of included parameters, several attempted alternative models could not be fit either because of convergence issues or because standard errors for estimated parameters could not be calculated. For example, we were unable to estimate a lake-specific scaling parameter for Lake Superior. Such problems persisted despite our efforts to modify the models to reduce the number of parameters to be estimated. We were able to generate estimates of a scaling parameter for four model variants, spanning different levels of spatial aggregation. The point estimates of the scaling parameter for the combined-by-lake versions for both Lake Huron and Lake Michigan and for the combined-across-lake model variant were greater than 1, suggesting that model fit could be improved by increasing the mortality rate associated with a given level of observed marks from sea lamprey parasitism. We further estimated a weighting factor to allow the estimated scaling parameter to change monotonically over ages for one variant of the combined-by-lake model for Lake Huron. This weighting factor suggested that the influence of the scaling parameter was largest for the youngest ages of lake trout in Lake Huron, despite the marking data being essentially pre-adjusted to account for laboratory-based estimates of how size influences lethality of sea lamprey attacks.