SOME STATISTICAL TECHNIQUES FOR ESTIMATING ABUNDANCE 



INDICES FROM TRAWL SURVEYS 



Michael Pennington 1 



ABSTRACT 



Methods are presented for estimating an index of relative abundance from trawl survey catch per tow 

 data. The estimated variance of the index takes into account the within survey variability in catch and 

 possible yearly changes in catchability. Applying the techniques to a series of surveys for yellowtail 

 flounder, Limanda ferruginea, off the northeast coast of the United States yields an abundance index 

 with a variance which is 40% lower than the variance of the original survey index for the current value 

 and 57% lower for values not near the ends of the survey series. 



The average number of fish caught per tow during 

 a trawl survey is often used as an index of a species's 

 relative abundance (Grosslein 1969; Clark 1979). 

 Catch per tow data are usually quite variable 

 because of the heterogeneous distribution of many 

 fish stocks (Byrne et al. 1981). A further source of 

 variability for survey indices of abundance is that 

 the catchability of a particular species with respect 

 to the survey trawl may change from year to year 

 (Byrne et al. 1981; Collie and Sissenwine 1983). As 

 a result, the observed time series of abundance in- 

 dices reflects changes in the population, within 

 survey sampling variability, and varying catchabil- 

 ity over time. 



This paper uses various statistical methods to con- 

 struct from the catch per tow data an index of abun- 

 dance which more closely tracks the population than 

 does the original (average catch per tow) series. 

 Specifically, since the distribution of catch per tow 

 data is often highly skewed and contains a propor- 

 tion of zeros, estimates of the mean catch per tow 

 for each survey are made based on the A-distribution 

 (Aitchison and Brown 1957). Next, time series tech- 

 niques are used to estimate the component of the 

 series generated by the actual changes in the 

 population. 



The methods are applied to data for yellowtail 

 flounder, Limanda ferruginea, from a series of 

 groundfish trawl surveys conducted off the north- 

 east coast of the United States as part of the 

 National Marine Fisheries Service's MARMAP pro- 

 gram. The resulting index of abundance is substan- 

 tially more precise than the original index. 



Northeast Fisheries Center Woods Hole Laboratory, National 

 Marine Fisheries Service, NOAA, Woods Hole, MA 02543. 



STATISTICAL METHODS 



Sources of Variability 



Let y t denote the observed average catch per tow 

 for the survey conducted in year t and z\ = E[y t ], 

 the expected value of y t . Since a species catchabil- 

 ity may change from year to year with respect to 

 the survey trawl, let z = E[z'\p] denote the expected 

 value of z given a population level p. Then 



y, = z t + e t . 



The error term, e t , can be expressed as 



e t = (Vt ~ z't) + (z't ~ Zt), 



where the first error component is due to the within 

 survey variability and the second is due to changes 

 in catchability. 



In order to construct an index of abundance, it is 

 necessary to assume a functional relationship be- 

 tween z t and p t . A reasonable assumption made in 

 practice (and in this paper) is that 



z t = ap t . 



If the relationship is not linear, then the unadjusted 

 catch per tow index will be a biased measure of 

 relative abundance. 



Estimating the Mean Catch per Tow 



The distribution of marine survey data often can 

 be described by what is called a A-distribution (Ait- 

 chison and Brown 1957). That is, the data contain 



Manuscript accepted October 1985. 

 FISHERY BULLETIN: VOL. 84, NO. 3, 1986. 



519 



