Dealing with interactions between area and year Mark Maunder IATTC

Clear example: school shark in southern Australia

Ambiguous example: EPO BET longline CPUE

Method to deal with interactions between area and year Explicitly ignore the interaction Average the year effects for each area Treat the interaction as a random effect Model separate populations

Explicitly ignore the interaction Avoids considering the problem May lead to bias if substantial interactions Large data sets may result in significant interactions even if year effects are similar Vignaux, M., Catch per unit effort (CPUE) analysis of west coast South Island Cook Strait spawning hoki fisheries, 1987–93. NZ Fisheries Association Research Document No. 94/11.

Average the year effects for each area Difficult to define the area weighting Use habitat area for the weighting factor Different trends in different areas may require different management actions Punt et al. (2000) weighed the year×area interactions by the physical area between 20 and 80m depth of each area in the analysis when standardizing catch and effort data for gummy shark (Mustelus antarcticus) off southern Australia. Punt, A.E., Pribac, F.,Walker, T.I., Taylor, B.L., Prince, J.D., Stock assessment of school shark Galeorhinus galeus based on a spatially-explicit population dynamics model. Mar. Freshw. Res. 51, 205–220.

Treat the interaction as a random effect If a year×area interaction is assumed to have arisen because of the random changes in the distribution of the population Does not deal with differences in trends Chang, S.-K., Analysis of Taiwanese white marlin catch data and standardization of catch rates. ICCAT Col. Vol. Sci. Pap. 55, 453–466. Miyabe, N., Takeuchi, Y., Standardized bluefin CPUE from the Japanese longline fishery in the Atlantic including those for mixing studies. ICCAT Col. Vol. Sci. Pap. 55, 1190–1207.

Model separate populations Spatial structure in the population dynamics Do you have to model movement? Punt et al. (2000) used a spatially structured model for gummy shark (Mustelus antarcticus) off southern Australia. Punt, A.E., Pribac, F.,Walker, T.I., Taylor, B.L., Prince, J.D., Stock assessment of school shark Galeorhinus galeus based on a spatially-explicit population dynamics model. Mar. Freshw. Res. 51, 205–220.

Missing strata Methods require that year × area interaction factors are available for all combinations Algorithms for specifying the missing year×area interactions. Use information for the year × area combinations with data to interpolate (and perhaps extrapolate) to the remaining combinations. Unfortunately, the resulting index of abundance (and hence the results of any subsequent stock assessment) may be highly sensitive to the algorithm chosen for interpolation and extrapolation (Campbell, 2004; Butterworth et al., 2003). Campbell, R., CPUE standardisation and the construction of indices of stock abundance in a spatially varying fishery using general linear models. Fish. Res. 70, 209–227. Butterworth, D.S., Ianelli, J.N., Hilborn, R., 2003.Astatistical model for stock assessment of southern bluefin tuna with temporal changes in selectivity. Afr. J. Mar. Sci. 25, 331–361.

Sharing information in GLM Separate GLM for each area vs interaction terms Allows for sharing other parameters e.g. month effect

Sharing information in population dynamics model Sharing information about q between populations provide information on relative abundance Requires that the indices of abundance are calculated appropriately The sub-areas are often different sizes and contain different densities of fish. The index should represent the relative abundance in each sub-area. Include all areas in single GLM and sum area effects to get weighting factors

EPO BET longline CPUE

Area effect

Model fit – no interaction

Residuals

EPO BET Explicitly ignore the interaction –The difference may be important for management Average the year effects for each area –Don’t know what the relative abundance is among areas Treat the interaction as a random effect –The year-area interaction is not random Model separate populations –Best way to proceed (see presentation later in workshop)