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The main objective of discard sampling programmes is to estimate annual total discards of fish species whose stocks are routinely assessed from catch data. The Scottish discard programme is based on a stratified random design, and a ratio estimator is used to estimate total discards independently in each stratum. Total discards are then estimated by summing across strata. However, the small number of trips that can be sampled by scientific observers from fisheries institutes creates problems with this estimator. Here, a simulated population of fishing trips is used to investigate alternative estimators of total discards for the main fish species (haddock Melanogrammus aeglefinus, whiting - Merlangius merlangus, and cod - Gadus morhua) targeted by Scottish demersal vessels in the North Sea and the West of Scotland. The results show that when the sample size in each stratum is very small, the current methodology - independent ratio estimation in each stratum - can be very biased and imprecise. However, an alternative ratio estimator that relies on a collapsed stratification has negligible bias and greater precision. We use this alternative estimator to estimate total annual discards of haddock, whiting, and cod in the North Sea and West of Scotland from 1988 to 1993

Fish discarded from Scottish demersal vessels: Estimators of total discards and annual estimates for targeted gadoids