Selection and the role of body size in migration
Binomial logistic regression following Janzen and Stern (1998) was used to investigate the potential role of body size mediating the success (or absolute fitness) of upstream migrating individuals. Specifically, the fate of individuals as alive vs. dead was coded binomially as a zero or one and used as the response variable in a generalize linear model. Fixed effects of measured body size (at weirs for the alive individuals and from surveys for the dead individuals) and a categorical effect of sex were included in the model with binomial error structure and a logit link function.
To quantify the magnitude of the estimated selection acting on length, I calculated the standardized selection differential following Kendall et al. (2009), using the equation
\(({\overset{\overline{}}{X}}_{\text{Alive}}-\)\({\overset{\overline{}}{X}}_{\text{Dead}})/\ \text{SD}_{Alive+Dead}\)
Where \({\overset{\overline{}}{X}}_{\text{Alive}}\) is the mean (mm) of fish measured at weirs on the spawning grounds and\({\overset{\overline{}}{X}}_{\text{Dead}}\) is the mean of (mm) of fish to have died en route , and \(\text{SD}_{Alive+Dead}\) is the pooled standard deviation of all length measurements (alive + dead). Standardized selection differentials measure total selection acting on traits though both direct and indirect agents. To quantify uncertainty in selection estimates, I conducted 10,000 randomization simulations through the following procedure. For each simulation, the pooled distribution of all lengths (alive + dead) was sampled with replacement 500 times and used to calculate means for alive and dad individuals that were then used to calculate a standardized selection differential. The observed standardized selection differential calculated from the field was compared to the simulated distribution of differentials to better understand the probability of the observed strength of selection occurring through chance alone. Strength of selection was compared to a recently compiled dataset by (Siepielski et al. 2017).