Reposted for Steve Fleischman, [log in to unmask]
Patrick
I've seen this argument before, and in my opinion there is no problem here. The result you mention does not truly indicate that a bias exists. When fitting a Ricker curve, one is primarily interested in modeling the degree to which recruitment departs from a linear relationship where recruitment is proportional to number of spawners (return per spawner is constant). When recruitment falls off from this proportional relationship at high levels of spawners, compensation is in effect. The return per spawner declines as the number of spawners increase. A significant result in a Rickertype analysis correctly indicates that the (log) return per spawner declines with increasing S.
Therefore, by generating independent random values for R and S, one is not specifying the null hypothesis correctly. The true null hypothesis that one is interested in rejecting is the one specified above: R being a constant proportion of S. If one were to do the simulation in this manner, with the mean of R proportional to S, I would bet that only the expected alpha=5% of simulated datasets would result in significant slopes.
By the way, there are plenty of other things to worry about with spawnerrecruit models (e.g., the effect of measurement error). See Quinn and Deriso's new book on Quantitative Fish Dynamics for a good discussion.
Steve Fleischman Assistant Biometrician Sport Fish Division Alaska Department of Fish and Game [log in to unmask]
> Original Message > From: Scientific forum on fish and fisheries > Sent: Tuesday, March 31, 1998 10:06 AM > To: AllenB; [log in to unmask] > Subject: Bias in StockRecruit Models > > Dear FishSci: > > In the management of Pacific salmon stocks, the common method > for fitting > stockrecruitment data to a Ricker model is to use the > following equation: > > log(R/S) = a  (a/b)S, > > which is then treated as a linear regression, which provides > estimates of > stock productivity and carrying capacity. > > Apparently this treatment of the data will on average result in a > correlation coefficient substantially different than zero > (usually r about > .70), even when random numbers are used for R and S or an > existing set of > RS data is shuffled. Supposedly the correlation occurs because the > proportion (R/S) in the left side of the equation is also > dependent upon > the S term found on the right side, thus the high degree of > association > observed between the "x" and "y" variables is an artifact of > the analytical > approach (bias). > > My question to the list is this: is anyone aware of > literature exploring > the impacts, if any, of this type of bias on the commonly > used (Ricker, > BevertonHolt) stockrecruit models and the > populationdynamics parameters > that are derived from these models? > > Many thanks, > > Patrick Monk
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