Appendix A. Estimation of pike abundances from catch data.
A detailed description of the pike abundance estimation procedure from catch data is available in des Clers et al. (1994). In these models, fishing mortality was assumed to be proportional to fishing effort, and during a nominal year, the population was taken to experience recruitment, harvest and natural mortality sequentially. A lognormal process error was assumed for catches, leading to the following equations:
(A.1) 

(A.2a) 

(A.2b) 
and from Eqs. A.1 and A.2:
(A.3) 
where t is for year, A is for age class, G is for sex (gender) and B is for basin; N is the population abundance, C is the catch (all in numbers of fish), R is the number of recruits to the age 3 age group and M the natural mortality rate. The fishing mortality rate is given by fishing effort e (in numbers of gillnets during the winter sampling season) multiplied by a vulnerability coefficient q and a vulnerability correction factor, v. This correction factor constitute an index of growth up to age 3 and was estimated as, where ma(3) is the moving average of length at age 3 over three years, and is the over all mean for length at age 3. All parameters were estimated using the maximum likelihood method.
LITERATURE CITED
des Clers, S., J. M. Fletcher, I. J. Winfield, G. P. Kirkwood, P. R. Cubby, and J. R. Beddington. 1994. Longterm changes in Windermere perch and pike populations at the basin level. IFE Report WI/T11050d5/4, Institute of Freshwater Ecology.