Appendix A. Adjustment for diel variability of age-1 cod catches.
Young cod are known to vertically migrate on a diel base, which may pose a problem in our analysis of spatial survival. The diel migratory behaviour is particularly pronounced in individuals smaller than 15 cm in length, roughly corresponding to the age-1 stage (Hjellvik et al. 2001), and in deeper waters (Hjellvik et al. 2002). To overcome the potential problem of diel variability we corrected the age-1 bottom trawl catches by a factor (s(δ)) related to the sampling bias introduced by migratory behaviour of the age-1 cod. Specifically, let s be a smooth function describing the natural logarithm (plus 1) of age-1 cod catches (x) in relation to time of the day (δ). It is then possible to construct a nonparametric additive regression model (GAM) to reproduce the diel variability of bottom trawl catches:
The quantity kt defines the average catch of age-1 cod as a function of the year (t), and it also accounts for the variability introduced by the yearly changes of age-1 cod abundance (including the one introduced after the 1994 gear change). The term is a random error at the latitude φ and longitude λ, assumed to be normally distributed over the sampled grid. The term s(δ), defines the anomalies of the cod catches as a function of time of the day. It follows that the quantity:
used in the analysis of spatial survival, represents the age-1 cod catches corrected by the bias introduced by the diel variability. The "mgcv" library of R (Wood 2004) was used to implement the nonparametric regression in (1). The local time (δ) was derived from the Greenwich Mean Time (GMT) corrected for local longitude as reported in Hjellvik et al. (2002).
Results of the above analysis indicated that daytime catches of age-1 cod were on average higher than night-time catches (Fig. A1). The found relationship between cod catches and time of the day resembled the one reported in Hjellvik et al. (2001). The procedure applied in this study (Eq. A.2) successfully removed the diel trend of age-1 cod catches, as the new established age-1 metric did not contain a diel trend, nor did any of the subsequent models applied on age-0 cod spatial survival.
Hjellvik, V., O. R. Godø, and D. Tjøstheim. 2001. Modelling diurnal variation of marine populations. Biometrics 57:189–196.
Hjellvik, V., O. R. Godø, and D. Tjøstheim. 2002. Diurnal variation in bottom trawl catches: does it pay to adjust? Canadian Journal of Aquatic and Fisheries Sciences 59: 33–48.
Wood, S. N. 2004. Stable and efficient multiple smoothing parameter estimation for generalized additive models. Journal of the American Statistical Association 99: 637–686.
|FIG. A1. Anomalies in diel variability of log-transformed age-1 cod catches as predicted from a nonparametric model applied to the 1981–2005 surveys. Values above or below the dashed horizontal line respectively have a positive or a negative contribution on average cod catches. The shaded region indicates the 95% point-wise confidence interval.|