<scp>Estimating</scp> the effects of smolt size and migration timing on salmon marine survival using a multivariate mixed‐effect model

Abstract When the conditions encountered by a migratory species are highly variable, the timing of migration and migrant condition are critical to survival. Spring/summer‐run Chinook salmon in the Snake River of the Northwestern United States are listed as threatened under the US Endangered Species Act because of decades of poor adult returns; juvenile smolt‐to‐adult survival is often 0.5% or less. Juveniles pass through eight dams en route to the ocean, and despite changes to the hydropower system, there has been little recent improvement in survival. We analysed the effect of migration date, fish length and their interaction on the survival to adulthood of 409,747 wild juvenile Chinook salmon as they migrated through a large, dynamic riverine ecosystem and through the ocean, measured over 20 years. Parametric 2D smoothers are often used to quantify unexplained heterogeneity across space; however, these same statistical models can be applied to 2D datasets to uncover patterns of covariance of two biological processes important to management actions. We employ Gaussian Markov random fields (GMRF) and a 2D smoother to estimates of fish survival to identify the nature of variation in survival with respect to length and date. We found significant effects of fish length, migration date and the date‐by‐length interaction on resulting riverine and marine survival. Unlike the gradual shifts in survival in relation to length and timing that marginal estimates demonstrate, we show that within year, changes in survival with length and timing are often more abrupt than previously thought. Synthesis and applications : Inter‐annually, we identified distinct combinations of fish length and migration timing leading to elevated smolt‐to‐adult survival. Often these ‘hotspots’ are compressed into fish sizes greater than 100 mm and passage timings of only a week or two, demonstrating that even modest shifts in body size and migration timing can have a significant effect on survival. Further research can concentrate on these distinct annual periods to identify sources of mortality that have previously been elusive.