Kendall and Picquelle' Egg and larval distributions of Theragra chalcogramma 



151 



Appendix 1 



The mean density for each cruise or stratum was estimated by the Sette-Ahlstrom method: 



i A,  N, 



N 



(Richardson 1981) 



where N = mean number per 10 m-, 



A, = area represented by station i (in units of 10 m-), 

 A'', = number per 10 m'-^ in sample i, 



i\ 

 A = '^ A, = total area of survey or strata (in units of 10 m-), and 



n = the number oi A,?,m A. 



Total abundance was estimated by N = A  N, 



where N = total number in survey or strata. 



The areas A, are polygons as described in Richardson (1981). The variance of A/^ was estimated using methods 

 from probability sampling theory (Jessen 1978). The A,s may be different sizes, and one sampling unit (the water 

 below 10 m- of surface area) is sampled in each A,. Thus, the probability that a particular sampling unit is in- 

 cluded in the survey depends on which A, the sampling unit occurs. 



1 

 P., = 



" ~ A,-n 



where P,j = probability that sampling unit j in A, is selected in the survey. 

 This leads to the same estimate of iV as given in Richardson (1981): 



1 



A^, = 



y N, 



A  n i P, 



(Jessen 1978, eq. 8.15) 



1 



A  n 

 I A,  N, 



5! A^,  A,  n 



The estimate of the variance of mean density is 



Var A^ 



A'^  n  (n -1) 



P, n i P, 



(Jessen 1978, eq. 8.17) 



A-  ri  («--l) 



A^, • A 



,■ n - -- • i iV, • A, • 



n 



A-  (n-1) 



N,  A, - ^  N 

 n 



