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Subject: Re: depensatory exploitation
From: Patrick Cordue <[log in to unmask]>
Reply-To:Scientific forum on fish and fisheries <[log in to unmask]>
Date:Sun, 30 Jul 2006 10:19:16 +1200
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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

On Sunday 30 July 2006 08:16, you wrote:
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> Thanks for the comment and suggestion, Trevor.
>
> As I'm sure you know, the normal assumption in
> most fisheries is that exploitation rate or
> fishing mortality rate is constant as a function
> of abundance. Hence, in fisheries management we
> attempt to find that rate (F or u) which produces
> a sustainably fished stock, for example by
> maximizing yield or protecting a fraction of the
> spawning stock using target or limit biological
> reference points. In this case the form of the
> function relating exploitation rate to abundance
> is linear (= constant), and is analogous to a
> predator's Type I functional response. Constant
> exploitation rates as a function of abundance may
> not be that uncommon, as exemplified by the following recent paper:
>
> David B. Eggleston, Eric G. Johnson, G. Todd
> Kellison and David A. Nadeau. 2003. Intense
> removal and non-saturating functional responses
> by recreational divers on spiny lobster Panulirus
> argus. Mar. Ecol. Prog. Ser. 257: 197207.
>
> When the response is non-linear, it is not
> necessarily depensatory, particularly at low to
> moderate population levels. The actual form
> depends on a combination of fisher behavior and
> the behavior and response of the species, similar
> to what we see in predator-prey dynamics. The two
> major non-linear forms of the response are a Type
> II functional response (= depensatory) in which
> exploitation rate or proportional mortality
> increases as abundance declines. The other
> function is a Type III functional response (=
> compensatory) whereby proportional
> mortality/exploitation rate decreases as
> abundance declines from moderate to low abundance levels.
>
> A compensatory response is commonly observed when
> a prey or fishery species becomes more and more
> spread out as abundance declines, which makes it
> more difficult both logistically and
> economically, to catch a sufficient number of
> prey to make the fishing worthwhile. A
> depensatory response might be expected when the
> prey remain aggregated even at low abundance,
> such as in schooling fish, such that it is still
> worthwhile to fish the schools until every last
> one has been caught. Whether one would expect a
> compensatory, depensatory or constant
> exploitation or fishing mortality rate is thus
> not a straightforward problem with a simple
> answer. For many, if not most, vertebrate
> predators, the response is usually Type III
> (compensatory), so that we might expect the
> response of fishers to be compensatory if comparable mechanisms are in
> effect.
>
> You are correct that there is likely to be a fair
> amount of information in stock assessments on
> fishing mortality rates and exploitation rates
> along with stock abundance/biomass, but I am not
> aware of many attempts to characterize the form
> of the function quantitatively (other than in
> theoretical treatments), particularly with direct
> population estimates of exploitation rate and
> abundance, as opposed to modeled estimates of
> exploitation or fishing mortality rates. I am now
> thinking that it would be useful to conduct a
> comprehensive review of this issue across various
> fisheries, and will be requesting suggestions as
> to where I can most readily acquire this information.
>
> I should also note that Lobo Orensanz, Gordon
> Kruse and Tito de Morais kindly provided some
> initial leads on this issue, in particular the
> following publication that I am currently using
> to extract some of the published information:
>
> Orensanz, J.M., Armstrong, J., Armstrong, D.A.
> and Hilborn, R. 1998. Crustacean resources are
> vulnerable to serial depletion- The multifaceted
> decline of shrimp and crab fisheries in the
> greater Gulf of Alaska. Reviews in Fish Biology and Fisheries 8: 117-176.
>
> Regards,
> Rom
>
> At 06:36 PM 7/28/2006, Trevor J. Kenchington wrote:
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> >If you reply to this message, it will go to all FISH-SCI members.
> >
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> >Rom Lipcius wrote:
> >>Yes, exploitation rate or fishing mortality rate increases at
> >>decreased stock/population levels, for instance when fishers
> >>attempt to catch the same number of animals annually, irrespective
> >>of stock size.
> >>
> >>>>I am investigating depensatory exploitation of the Chesapeake Bay
> >>>>blue crab population, and have been searching for published
> >>>>examples of depensatory exploitation, particularly in marine
> >>>>invertebrates. I have found some examples for fish, but none yet
> >>>>for marine invertebrates. Does anyone know of any published
> >>>>examples of depensatory exploitation in marine (or estuarine)
> >>>>invertebrates?
> >
> >Thus defined, I would expect some degree of "depensatory
> >exploitation" to be a normal feature of all fisheries (though, as
> >ever, there will be specific exceptions), at least across some ranges
> >of biomass and subject to masking by other  factors (e.g. a collapse
> >in market prices as biomass declines).
> >
> >Most stock assessments that document time series of biomass and
> >fishing mortality should provide examples.
> >
> >
> >Trevor Kenchington
>
> 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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-- 
----------
Patrick Cordue
Director
Innovative Solutions Ltd
www.isl-solutions.co.nz

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