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Subject: Re: depensatory exploitation
From: Rom Lipcius <[log in to unmask]>
Reply-To:Scientific forum on fish and fisheries <[log in to unmask]>
Date:Sun, 30 Jul 2006 11:28:03 -0400
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Patrick,

The functional response of predators can be viewed in two ways, 
mechanistically and empirically. The mechanistic explanation deals 
with the factors that determine the "functional" response of 
predators to its prey and which therefore determine the form of the 
function. I believe that this is what you refer to when discussing 
the "functional" response. The other way to look at it is purely 
empirical whereby one simply attempts to determine the form of the 
function, whether linear or non-linear. From the empirical functional 
response of a predator guild, which includes other elements such as 
aggregation, one can determine the total proportional mortality of a 
particular prey species. The proportional mortality is analogous to 
exploitation rate in fisheries, and its form has major consequences 
for the likelihood that a fished population will persist, be driven 
to collapse, or recover.

It is the latter, empirical, approach that I have taken with regard 
to depensatory exploitation, and which is what Dick has explained. 
So, in the empirical situation, the exploitation rate is merely 
calculated by the Catch (in numbers) during the fishing year divided 
by the initial population size (N) of fishable individuals at the 
start of the fishing year, resulting in the standard calculation of 
exploitation rate as u = C/N. Once this has been done for several 
years, the form of the empirical function can be determined.

In the Chesapeake Bay blue crab case, Dick is correct that effort and 
catch controls have not regulated fishing effort effectively. The 
form of the exploitation rate function for the blue crab in 
Chesapeake Bay is a negative exponential curve, which indicates that 
exploitation rate is substantially higher (twofold) when the 
population is at low abundance than when it is at high abundance. 
This is what may be preventing the population from recovering in the 
Bay. If you are interested, the following paper describes the Bay 
blue crab population status, and our recent stock assessment 
indicates that the population has not recovered:

Lipcius, R.N. and W.T. Stockhausen.  2002.  Concurrent decline of the 
spawning stock, recruitment, larval abundance, and size of the blue 
crab Callinectes sapidus in Chesapeake Bay.  Marine Ecology Progress 
Series 226: 45-61.

If you wish additional information on the functional response, the 
following paper has reasonable explanations of the predator and guild 
functional responses:

Seitz, R.D., R.N. Lipcius, A.H. Hines and D.B. 
Eggleston.  2001.  Density-dependent predation, habitat variation, 
and the persistence of marine bivalve prey.  Ecology 82: 2435-2451.

Rom

At 02:42 AM 7/30/2006, Patrick Cordue wrote:
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>If you reply to this message, it will go to all FISH-SCI members.
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>
>Hi Dick,
>
>My comments apply to any fishery. Because there is a 1-many RELATIONSHIP
>between abundance and fishing mortality (or exploitation rate) then, by
>definition, fishing mortality is not a FUNCTION of abundance ALONE. Therefore
>to define "depensatory exploitation" in terms of the shape of the function
>cannot be generally applicable - because, in general, no such FUNCTION exists.
>
>I agree with you entirely, that understanding how fishermen respond to
>changes in abundance is critical (for a number of applications).
>
>Regards
>Patrick
>
>On Sunday 30 July 2006 15:32, you wrote:
> > ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>
> >
> > If you reply to this message, it will go to all FISH-SCI members.
> >
> > ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>
> >
> > Patrick,
> >
> > You assumed a managed fishery.  There are no effective controls on either
> > fishery inputs or outputs in the U.S. fishery for American lobster, for
> > example.  The same may be true for the Chesapeake blue crab fishery that
> > prompted Rom's inquiry.  In those cases, knowledge of the functional
> > response of the fisherman to changes in abundance of the target species is
> > critical.  In southern New England we are now moving into a regulatory
> > framework that will have the theoretical ability to control lobster trap
> > numbers.  The functional response of the fishermen will be a big factor in
> > the effectiveness of the effort control program.
> >
> > Dick Allen
> > Fisheries Dept. Graduate School
> > Univ. of Rhode Island
> > (401) 874-7153
> > [log in to unmask]
> >
> > -----Original Message-----
> > From: Scientific forum on fish and fisheries
> > [mailto:[log in to unmask]]On Behalf Of Patrick Cordue
> > Sent: Saturday, July 29, 2006 6:19 PM
> > To: [log in to unmask]
> > Subject: Re: depensatory exploitation
> >
> > ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>
> >
> > If you reply to this message, it will go to all FISH-SCI members.
> >
> > ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>
> >
> > Hi Rom,
> >
> > It was good to get the long definition, as the short definition was a bit
> > unclear. However, there appears to be a conceptual problem. You talk of
> > functional responses and fishing mortality as a function of abundance. In
> > some deterministic systems this will be true, but, in general, fishing
> > mortality is not a function of abundance (there is no 1-1, or many-1
> > relationship).  Consider a managed fishery. In year y1 biomass is B and the
> > catch is C1, in year y2 biomass is also B, but the TAC (for example) is set
> > at a different level (for whatever reason) and the catch is C2. There is a
> > 1-many relationship (not a function, not a functional repsonse).
> >
> > Regards
> > Patrick Cordue
> >
> > ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>
> >
> >        To leave the Fish-Sci list, Send blank message to:
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> >       Need help? Contact  [log in to unmask]
> >
> > ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>
>
>--
>----------
>Patrick Cordue
>Director
>Innovative Solutions Ltd
>www.isl-solutions.co.nz
>
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Romuald N. Lipcius, Ph.D.
2006 Aldo Leopold Leadership Fellow
&
Professor of Marine Science
Virginia Institute of Marine Science, The College of William and Mary
1208 Greate Road, Gloucester Point, VA 23062 USA
804-684-7330, [log in to unmask]
http://www.vims.edu/fish/faculty/lipcius_rn.html  

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