Abstract. — Index-based assess- 

 ments, in which research survey 

 indices serve as the primary source 

 of abundance information, are used 

 for many commercially harvested 

 stocks in the Northeast region. 

 Such assessments generally pro- 

 vide advice only on trends in the 

 relative size of the stock, lack a bio- 

 logical reference point or level, and 

 lack a decision framework for 

 drawing statistical inferences 

 about the state of the resource. We 

 present a stochastic simulation 

 technique for inferring population 

 status relative to an index-based 

 reference point. We applied an in- 

 tegrated moving average model to 

 trawl data on Atlantic wolffish, 

 Anarhichas lupus, to derive fitted 

 indices and propose using the lower 

 quartile (25th percentile) of the fit- 

 ted indices as a reference point. 

 From bootstrapping techniques 

 applied to model residual errors we 

 empirically characterized the vari- 

 ance and shape of the parent dis- 

 tributions of both a fitted abun- 

 dance index at any point in time 

 and the lower quartile. Treating 

 these distributions as jointly con- 

 tinuous random variates, we gen- 

 erated the cumulative density func- 

 tion for the condition Priindex < 

 lower quartile). Thus, for any value 

 of the lower quartile, we can deter- 

 mine the probability that the fit- 

 ted index at any point in time lies 

 below that value of the biological 

 reference point. An examination of 

 the joint cumulative probability 

 satisfying this condition is impor- 

 tant because it allows us to ascer- 

 tain quantitatively the likelihood of 

 correctly deciding whether such a 

 stock is below a prescribed thresh- 

 old level. 



Providing quantitative management 

 advice from stock abundance indices 

 based on research surveys 



Thomas E. Helser 



Northeast Fisheries Science Center 

 National Marine Fisheries Service. NOAA 

 166 Water Street, Woods Hole. MA 02543 



Daniel B. Hayes 



Northeast Fisheries Science Center 

 National Marine Fisheries Service, NOAA 

 166 Water Street, Woods Hole, MA 02543 



Present address: Department of Fisheries and Wildlife 



1 3 Natural Resources Building 



Michigan State University, East Lansing, Ml 48824 



Manuscript accepted 31 October 1994. 

 Fishery Bulletin 93:290-298 (1995). 



Standardized multispecies bottom 

 trawl surveys conducted annually 

 in the spring and autumn by the 

 Northeast Fisheries Science Center 

 (NEFSC, 1993) have been integral 

 to the scientific advice for manag- 

 ers of the northwest Atlantic fish- 

 ery resources. Not only do the sur- 

 veys provide an efficient means of 

 collecting biological and ecological 

 information on a suite of finfish and 

 invertebrates in the Northwest At- 

 lantic, but they also provide the 

 principal means of monitoring 

 changes in population abundance. 

 The trawl surveys use a stratified 

 random sampling design in which 

 stations are allocated to strata 

 roughly in proportion to stratum 

 area and are randomly assigned to 

 specific locations within strata. 

 Generally, the stratified mean num- 

 ber or weight per tow is used as an 

 index of relative abundance (Gross- 

 lein, 1969; Clark, 1979). Such indi- 

 ces of abundance can be quite vari- 

 able because of heterogenous spa- 

 tial distributions (Byrne et al., 

 1981), year to year changes in 

 catchability (Byrne et al., 1981; Col- 

 lie and Sissenwine, 1983), and natu- 

 ral changes in population abun- 

 dance. As such, the observed time 



series of abundance indices reflects 

 two sources of random variation: 1) 

 measurement error arising from 

 within and between year survey 

 sampling variability; and 2) true or 

 "process" error arising from actual 

 changes in population abundance. 

 Measurement error in the survey 

 estimates can be filtered from pro- 

 cess variability by using auto- 

 regressive-integrated-moving-aver- 

 age (ARIMA) models (Box and 

 Jenkins, 1976). However, the esti- 

 mation of the parameters of a full 

 ARIMA model for fisheries research 

 surveys is often problematic be- 

 cause of the relative shortness of the 

 time series (Pennington, 1985). 

 Pennington ( 1985) described an ap- 

 proach based on an a priori specifi- 

 cation of an integrated moving av- 

 erage model in which change in 

 population size follows a simple ran- 

 dom walk. Pennington (1986) and 

 Fogarty et al. (1986) have applied 

 this approach to a number of north- 

 west Atlantic species or stocks, such 

 as yellowtail flounder, Pleuronectes 

 ferrugineus. This approach has be- 

 come the standard method for de- 

 riving "fitted" abundance indices 

 used in the Northeast region 

 (NEFSC, 1993). 



290 



