Dear Fellow FISH-SCI'rs ... I'm posting this response to
Patrick Monk's original query for a colleague who doesn't
subscribe to FISH-SCI ... so responses should be directed
to Steve Fleischman (see address below) or to the list.

Thanks-Allen Bingham ([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 Ricker-type 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 spawner-recruit 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 Stock-Recruit Models
>
>
> Dear Fish-Sci:
>
> In the management of Pacific salmon stocks, the common method
> for fitting
> stock-recruitment 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
> R-S 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,
> Beverton-Holt) stock-recruit models and the
> population-dynamics parameters
> that are derived from these models?
>
> Many thanks,
>
> Patrick Monk

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