en>R.e.b.: /* A ring that is catenary but not universally catenary */ Expanding article

2013-08-07T20:10:40Z

A ring that is catenary but not universally catenary: Expanding article

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{{Infobox scientist
| name = Milner Baily Schaefer
| image = 
| image_size =
| alt =
| caption =
| birth_date = {{Birth date|1912|12|14}}
| birth_place = Cheyenne, Wyoming
| death_date = {{Death date and age|1970|07|26|1912|12|14}}
| death_place = San Diego
| residence =
| citizenship =
| nationality =
| fields =
| workplaces = [[Inter-American Tropical Tuna Commission]], [[Scripps Institution of Oceanography]]
| alma_mater = [[University of Washington]]
| doctoral_advisor =
| academic_advisors =
| doctoral_students =
| notable_students =
| known_for = The Schaefer model, [[fisheries science]], [[Bioeconomics (fisheries)|bioeconomics]]
| author_abbrev_bot =
| author_abbrev_zoo =
| influences =
| influenced =
| awards =
| signature = 
| signature_alt =
| footnotes =
| spouse = Isabella Long
}}

'''Milner Baily ("Benny") Schaefer''' was born in [[Cheyenne, Wyoming]], in 1912 and died at the age of 57 in [[San Diego, California]] in 1970.<ref name=biography>[http://scilib.ucsd.edu/sio/biogr/Schaefer_Biogr.pdf Milner Baily Schaefer Biography] Deborah Day. La Jolla, CA: UCSD Libraries, 1997</ref> He is notable for his work on the [[Population dynamics of fisheries|population dynamics]] of [[fisheries]].

Schaefer worked as a biologist at the Washington State Fisheries Department and from 1937-1942 as a scientist for the [[International Pacific Salmon Fisheries Commission]] in [[New Westminster, British Columbia|New Westminster]], [[British Columbia]], [[Canada]]. In 1946 he joined the [[United States Fish and Wildlife Service]] and held various posts at the Fishery Biology Headquarters at [[Stanford University]]. Later, he worked at the Pacific Oceanic Fisheries Investigations Laboratory in [[Honolulu, Hawaii]] and completed a doctorate in [[fisheries]] from the [[University of Washington]] in 1950. In 1951 Schaefer became Director of Investigations at the [[Inter-American Tropical Tuna Commission]] (IATTC). IATTC established its first headquarters at the [[Scripps Institution of Oceanography]].<ref name=biography/>

==Schaefer short-term catch equation==
During his period at the IATTC, Schaefer worked on the development of theories of [[Population dynamics of fisheries|fishery dynamics]] and published
<ref name=sch1954>{{Citation
| last = Schaefer
| first = Milner B.
| title = Some aspects of the dynamics of populations important to the management of commercial marine fisheries
| journal = Bulletin of the Inter-American Tropical Tuna Commission
| volume = 1
| issue = 2
| year = 1954
| pages = 27–56
| url = http://aquacomm.fcla.edu/3530/
| doi = 10.1007/BF02464432
| ed = reprinted in Bulletin of Mathematical Biology, Vol. 53, No. 1/2, pp. 253-279, 1991
}}</ref>
a fishery equilibrium model based on the [[Pierre François Verhulst|Verhulst]] [[Logistic function#In ecology: modeling population growth|population growth model]] and an assumption of a bi-linear catch equation, often referred to as the Schaefer short-term catch equation:

<math>H(E,X)=q E X\!</math>

where the variables are; ''H'', referring to catch (harvest) over a given period of time (e.g. a year); ''E'', the fishing effort over the given period; ''X'', the fish stock biomass at the beginning of the period (or the average biomass), and the parameter ''q'' represents the catchability of the stock. Assuming the catch to equal the net natural growth in the population over the same period (<math>\dot{X}=0</math>), the equilibrium catch is a function of the long term fishing effort ''E'':

<math>H(E)=q K E (1-\frac{qE}{r})</math>

''r'' and ''K'' being biological parameters representing intrinsic growth rate and natural equilibrium biomass respectively.

Schaefer published during the 1950s a range of papers of empirical studies based on the model,<ref>[http://scilib.ucsd.edu/sio/bibliogr/SchaeferBibliogr.pdf Milner Baily Schaefer Bibliography] Deborah Day. La Jolla, CA: UCSD Libraries, 1997</ref> the most famous perhaps being ''A study of the dynamics of the fishery for yellowfin tuna in the Eastern Tropical Pacific Ocean''.<ref>{{Citation
| last = Schaefer
| first = Milner B.
| title = A study of the dynamics of the fishery for yellowfin tuna in the Eastern Tropical Pacific Ocean
| journal = Bulletin of the Inter-American Tropical Tuna Commission
| volume = 2
| issue = 6
| year = 1957
| pages = 243–285
| url = http://aquacomm.fcla.edu/3531/}}</ref>
Other researchers also soon saw the potential of developing the model tools further.<ref>{{Citation
| title = Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty
| year = 1992
| isbn = 0-412-02271-0
| last1 = Hilborn | first1 = R.
| last2 = Walters | first2 = C. J.}}</ref>

==Gordon-Schaefer model==
Schaefer's seminal paper<ref name=sch1954/> further extends the biological model to account for dynamics of fishing pressure in an unregulated fishery, assuming that fishing effort increases until profit can no longer be made. Thus, the fishery reaches an equilibrium, referred to as the ''bionomic equilibrium'' by H. Scott Gordon in a paper published the same year as Schaefer's but focused on purely economics of fishing.<ref>{{Citation
| last = Gordon
| first = H. Scott
| title = The economic theory of a common-property resource: the fishery
| journal = Journal of Political Economy
| volume = 62
| year = 1954
| pages = 124–142
| doi=10.1086/257497}}</ref>
Apparently, Schaefer and Gordon did not know about each others work, and today their [[Bioeconomics (fisheries)|bioeconomic]] model is known as [[Gordon-Schaefer Model]]. It is a common to credit Schaefer only for the biological part of this model<ref name=Clark1990>{{Citation
| title = Mathematical Bioeconomics: The Optimal Management of Renewable Resources
| year = 1990
| author = Clark, Colin W.
| isbn = 0-471-50883-7}}</ref>
, but this is a mistake. Together, the work by Schaefer and Gordon set the basis for quantitative analyses of fisheries economics.

==References==
{{Reflist}}

{{Fisheries scientists}}
{{Fisheries and fishing}}

{{Authority control|VIAF=13415366}}

{{Persondata 
| NAME = Schaefer, Milner Baily
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American fisheries scientist
| DATE OF BIRTH = 1912
| PLACE OF BIRTH = Cheyenne, Wyoming
| DATE OF DEATH = 1970
| PLACE OF DEATH = San Diego
}}
{{DEFAULTSORT:Schaefer, Milner Baily}}
[[Category:1912 births]]
[[Category:1970 deaths]]
[[Category:American marine biologists]]
[[Category:Fisheries science]]

Catenary ring - Revision history

en>R.e.b.: /* A ring that is catenary but not universally catenary */ Expanding article