urn problem. Unfortunately this may give very unreasonable estimates
and is too erratic for practical use. He also presented a modification
of the unbiased estimator which, though not unbiased, always gives
reasonable results. The modified estimator, which was deemed suitable
1 Submitted for publication June 1962.
(253 )
254 CALIFORNIA FISH AND GAME
for estimating the number of persons purchasing special angling lic en s e s
during 1961, is
s' = — ^7 7T~ x 2 if s' > laX
A
k' =
n(n—\)
j^i
UXi if s' < Li Xi
i— 1 i— I
where N is the number of special licenses in the population, n is the
number of licenses sampled and Xi is the number of persons in the sample
who purchased i licenses. To estimate the ratio of license purchasers to
A A
licenses, p' = k'/N was used.
Raj (1961) derived an unbiased estimator for the variance of
x 2 [N(N— l)]/[n(n— 1)] under the assumption that n,<2 for all j. We
have used his formula,
a f N(N-l) -| 2 r n(n-l) (JV— 2) (JV-3) -|
V ^ = Ln(n-l) * 2 J L 1 N(N-1) (n-2) (n-3) J
, N(N-1) r (N-2) (N-3) 1
+ n(n-l) 2 L(n-2) (n-3) J
as an approximation to the variance of s'. The approximation will be close
if very few persons purchased more than two special licenses. It should
also be noted that the mean square error of k ' is less than MSE(s ') . Sim-
A A
ilarly, the variance of s'/N was approximated by V(s')/N 2 and MSE(p )
< MSE(s'/N).
ESTIMATES FOR 1961
Of 142,597 special angling licenses sold during 1961, 134,936 license
stubs were available for sampling. A sample of 7,500 including seven
illegible stubs was randomly selected. Examination of the sample revealed
52 pairs purchased by the same persons and one quadruplicate. Thus,
JV = 134,936, n = 7,493, Xi = 7,385, x 2 = 52 and x 4 = 1. Computing the
components of k', we obtain 2 x { = 7,438 and s' = 118,070. Then, be-
cause s' > S x if the estimated number of persons purchasing 134,936
special licenses in 1961 is k' = s' = 118,070. The estimated ratio of license
purchasers to licenses is p' = .875. With respect to the bias oMhese
estimates, it can be shown that for the iV and n of this problem, k' and
p' tend to yield underestimates. Further, if the number of persons pur-
chasing three or more licenses is small, the bias will be negligible relative
to the estimate.
A A
The approximate standard errors of k' and p' are 2,305 and .017
respectively.
ESTIMATING LICENSE BUYERS 255
SUMMARY
An estimated 118,070 persons purchased 134,936 special California
angling licenses during 1961. The corresponding ratio of license pur-
chasers to licenses is 0.875. Approximate standard errors of the number
of purchasers and the ratio are 2,305 and .017, respectively. Estimates
were obtained from a random sample of 7,493 license stubs using a
method involving examining the sample for persons purchasing more
than one license.
REFERENCES
Goodman, Leo A.
1949. On the estimation of the number of classes in a population. Ann. Math.
Stat., vol. 20, no. 4, pp. 572-579.
Mosteller, Frederick
1949. Questions and answers. Amer. Stat., vol. 3, no. 3, pp. 12-13.
Raj, Des
1961. On matching lists by samples. Amer. Stat. Assoc, Jour., vol. 56, no. 293,
pp. 151-155.
POTENTIAL PROFITS IN THE CALIFORNIA
SALMON FISHERY 1
DONALD H. FRY, JR.
Marine Resources Branch
California Department of Fish and Game
INTRODUCTION
More and more water and power projects are being built in Cali-
fornia. Many of these will put dams in the paths of migrating fish,
flood out their spawning areas and divert their spawning streams. In
such instances, the Department of Fish and Game is legally required
to order the construction agency to take appropriate steps to mini-
mize damage to fish life by installing fishways, fish screens or fish
hatcheries. Other state and federal statutes require the Department
to report on and recommend other protective or compensating measures,
including water releases to maintain fish life, and suggest changes
in the project's design and operation to maintain and enhance these
resources.
The Department is not required to demonstrate the cash value of
these fish in order to take steps to save them. Neither is the U.S. Coast
Guard required to demonstrate that a sailor on a sinking ship is worth
what it will cost to rescue him. In either instance, the victim's death
would be apt to occur before the matter could be settled. This does
not mean the Department can ignore the species or numbers of fish
involved. Often, extensive studies must be carried out in order to
determine how best to provide for fish runs, but such studies are based
primarily on biology and engineering rather than on economics.
Sometimes when studying a project it becomes evident that not only
can runs be maintained but by spending a bit more money they can
be increased. At this point, economics become of primary importance.
Government agencies are required to regard fish production as one of
the beneficial uses of water. If, in a state or federal project, an addi-
tional expenditure would increase the run above its former (pre-
project) level and the extra fish produced would more than offset
the cost of producing them, there is an excellent chance that money
to increase the run will be forthcoming. Conversely, if the cost of
providing extra fish exceeds their value, the project will usually supply
finances to maintain the run at its natural level — but no more.
Once the cost of producing extra fish is known, the problem can be
settled by determining the value of each fish. Unfortunately there are
all too many ways to calculate this, and the answers are ridiculously
far apart. For commercially-caught salmon, values from zero to well
1 An evaluation of the fishery based on a method suggested by Dr. James Crutchfield,
Associate Professor of Economics, University of Washington, Seattle. Submitted
for publication May 1962.
(256)
POTENTIAL SALMON PROFITS 257
above the retail cost-per-pound have been seriously suggested. In this
paper, I will present a method of evaluating commercial salmon ; sport-
caught fish pose altogether different problems and will not be dis-
cussed.
Quite logically, men who evaluate water projects want to be able
to appraise the fisheries involved by methods comparable to those
used on other parts of the project. Most values assigned to water, for
example, are based on the increased profits that will be realized. A plot
of land will ordinarily produce more if irrigated than if dry-farmed,
but the costs of farming will be greater. Profits due to irrigating are
calculated by deducting the extra expenses from the extra money
gained from the larger (or different) crop. Commercial fisheries' values,
on the other hand, have usually been expressed by the Department of
Fish and Game as the total received for the fish at dockside, or some-
times at the wholesale level, with no deductions for the cost of catch-
ing them. On occasion this has led to the fisheries receiving little con-
sideration because no one had calculated the profits involved. Some
economists have insisted that, according to economic standards some-
times used in business, many fisheries (including salmon) have no value
because the fishermen could have made as much or more at almost any
other job — the fishermen were, in effect, running a small business,
paying themselves a bare minimum wage for long hours of hard work
and, on the average, making no money whatever on their investment.
Some American traditions and laws tend to reduce a fisherman's
cash profit (above day wages) to the vanishing point. Truly efficient
fishing gear is outlawed in the interests of conservation or to spread
employment among as many people as possible. In California, for
example, commercial fishermen may take salmon only by trolling — a
grossly inefficient method made a trifle less so by a large investment
in mechanized gear and electronic fishing aids. There is no limitation
on the number of men who may enter this business. If too many do
enter it, catches of individual fishermen fall off and the least efficient
or most easily discouraged individuals drop out. If the dictates of
conservation demand it, the State may hasten the process by shorten-
ing the season. Limiting the number of boats and thus letting each
make a fair living would be one approach — but our society has not
chosen to use it. We do use this approach in some businesses such as
radio and television stations, liquor stores, and power plants. It is
often against the profits of a power-plant monopoly that fisheries'
profits are compared.
A farmer is allowed to own or lease land and manage it as efficiently
as he is able. His crop is not open to harvest by anyone who comes
along. A fisherman has no such protection even though his investment
in boat and gear may exceed the cost of a farm. He must share the
harvest with everyone who. enters the fishery and is often compelled
by law to operate very inefficiently.
Obviously, if the net economic yield concept is to be used to com-
pare such differently managed businesses as power generation, farming
and commercial fishing, it must be modified. For commercial fishing
this could be done by calculating the profits a fishery would realize if
it operated as a virtual monopoly, if it used the most efficient gear and
258 CALIFORNIA FISH AND GAME
if the eatcli were adjusted to that which the resource could continuously
produce under best management practices. For the salmon fishery of
California's Central Valley, such profits can be calculated without
wandering too far into fields of conjecture.
A HYPOTHETICAL SALMON FISHERY
I will describe a fishery which has been proven efficient. I am not
proposing that such a fishery be created; it is only used as a method to
calculate the potential net benefits of the resource — nothing else is
implied.
Assume that all commercial trolling was stopped and all commercial
catches were made where they could be taken most efficiently. The
Sacramento-San Joaquin Delta would be an excellent area — the fish
are still in prime condition (they are mature and have reached their
maximum growth). A fishery would get maximum production out of
Sacramento-San Joaquin fish. It would not harvest fish from other
California rivers, but there is no reason why similar but smaller
fisheries could not be established in other streams.
Salmon in inland waters could be caught by many methods. Some
of these are proven ones, having been used either in California or other
parts of the world. Even electrical fishing could be considered in a
study to determine the cheapest way to harvest fish ; however, I have
chosen proven methods for this model in order to be on firmer ground
when calculating costs. Some which might be used are :
Salmon traps similar to those recently used in Alaska were once
used in California but were not particularly effective in this State
and were gradually being abandoned when the Legislature outlawed
them.
A dam with a fishway. This would have to be constructed upstream
from the levee system controlling the lower river. Fish taken this far
upstream would be approaching spawning condition and their desir-
ability would be greatly reduced. Furthermore, capital investment
would be very high, particularly because several streams would have
to be dammed.
Fishwheels have not been proven on the Sacramento. In any event,
suitable sites are so far upstream that fish quality would have deterio-
rated badly.
Beach seines once met with moderate success but would never harvest
the entire crop. There are not enough suitable seining sites in the Delta
or in the lower Sacramento River.
Gill nets were the only gear which proved successful for many
decades in the inland waters of the Central Valley. Legislation reduced
their effectiveness through the years, and gill-net fishermen had to be
content with salmon that had escaped the expanding troll fishery.
Finally, in 1957 salmon gill-netting was outlawed completely. A small
gill-net fleet could be very effective if it operated to take the maximum
sustainable yield for the lowest reasonable cost.
In the last decades of the fishery, many gill-netters operated from
Carquinez Strait to Pittsburg — an area with much open water which
gave the fish a chance to scatter. Carquinez Strait is narrow but it is
deep, has violent tides and such heavy boat traffic that the ship channel
POTENTIAL SALMON PROFITS 259
must be kept free of nets. In the strait and other downstream areas,
the boats had first chance at migrating fish but they were fishing in
the large end of the funnel. Farther upstream in the Sacramento River,
from Collinsville to Rio Vista and corresponding places on the San
Joaquin, the boats were at the small end of the funnel but were catching
only those fish that had escaped trollers and downstream gill-netters.
To make sure they did not catch too many salmon, gill-netters were
required to stop fishing on weekends. 2 The season closed September 26 —
at the peak of the fall migration — and did not open till November 15,
by which time the run was down to a dribble. There was another closed
season in early summer, but not nearly as many fish were moving at
that time. All these restrictive measures (closed seasons, closed areas,
etc.) were imposed largely because there were too many boats.
Assume that instead of a large fleet scattered over a wide area, a
small fleet fished in the small end of the funnel. Assume that instead
of having two lengthy closed seasons, the fleet was kept small enough
to permit the necessary escapement. This could be done by restricting
the number of boats fishing when salmon were relatively scarce. The
weekend closure could be lengthened when more escapement was needed
and eliminated in times of excessive abundance. Assume also that this
fleet was manned exclusively by competent fishermen. Such a fleet could
harvest the Sacramento-San Joaquin at a very low cost.
WHAT WOULD BE THE SIZE OF THE HARVEST?
Obviously if there were no troll fishery, many more salmon would
enter the Delta. Tagging and marking experiments have demonstrated
that landings of salmon produced in the Sacramento-San Joaquin River
system exceed the total salmon from all sources which are landed in
California. In other words, tonnages of Central Valley salmon taken
by trollers off Oregon, "Washington, and Canada exceed all California
catches of salmon from rivers outside the valley. Extensive additional
analysis and possibly some additional marking experiments will be
needed to demonstrate the amount of this excess, so for this study
total state salmon landings will be used as a measure of how many
pounds could be taken in the Delta if there were no troll fishery. This
is a minimum figure, not only for the reason given above but because
trollers keep many 5-pound salmon that two years later would weigh
20. In some years, the average weights of gill-netted salmon were almost
twice those of troll-caught fish. Furthermore, many still-smaller fish
are unintentionally killed in the course of being hooked, unhooked, and
returned to the water.
Average salmon landings over the 10 years 1952-1961 were 7,895,000
pounds, which will be used as the average catch of our hypothetical
gill-net fleet operating in the Delta.
How would the catch be distributed through the year? To determine
this, the monthly gill-net catch of each of the last 10 complete years
of the fishery (1947 through 1956) was expressed as a percent of that
year's total catch and then averaged (column 1, Table 1). During this
period, there were closed seasons during all of July and October, half
•Weekly closed periods are useful to permit escapement and should probably be re-
tained even with a much smaller fleet.
260
CALIFORNIA FTSII AND GAME
TABLE 1
Theoretical Catch of a Gill Net Fishery Operating All Year
Col. 1
Col. 2
Col. 3
Col. 4
Average
percent of
yearly catch
1946-1955
Column 1
expanded
for closed
periods
Calculated
average
percent of
yearly catch
Catcli per
month
calculated
from Col. 3
.69
2.15
1.88
3.15
5.62
1.05
7.10
76.53
.77
1.06
.09
2.15
1.88
3.15
5.02
2.101
0.052
10.00'
88.304
54.035
1.54«
1.06
.39
1.21
1.06
1.78
3.17
1.18
3.41
5.64
49.85
30.84
.87
.60
31,000
96,000
84,000
141,000
250,000
93,000
209,000
445,000
September,
October
November
3,935,000
2,435,000
69,000
47,000
100.00
177.17
100.00
7,895,000
1 June — Col. 1 doubled (15 days closed).
2 July — Interpolated between June and August (after expanding Avg.).
8 Aug. — x 31/22 (9 days closed).
* Sept. — x 30/26 (4 days closed)
5 Oct. — Used ratio of Sept. to Oct. catches taken by Fish and Game employees in
tagging traps operated in the lower Sacramento River 1953-1956.
6 Nov. — Doubled (15 days closed).
of June and November, the first nine days of August and the last four
days of September. To make a somewhat better estimate of the probable
catch of a gill-net fleet operating throughout the year, the June and
November catches were doubled, the August catch wa.s multiplied by
31/22 and the September catch by 30/26. The July catch is an interpo-
lation between those of June and August since trap catches made by
Fish and Game personnel in the lower Sacramento River indicated the
run was gradually picking up over this period. The October catch was
estimated by averaging our September and October trap catches for
four years and using the ratio of the average September to the average
October catch (column 2). 3 Since this yielded 177.17 percent, it was
reduced to 100 percent by multiplying each month's catch by 100/177.17
(column 3). Finally, the last column contains the theoretical monthly
poundages that would be landed, assuming a total catch of 7,895,000
pounds. These figures will be used even though the total catch probably
could be greater because only full-grown fish would be harvested.
HOW MANY BOATS WOULD BE REQUIRED?
The Sacramento-San Joaquin gill-net fleet increased from about 100
boats in 1872 to about 750 in 100!) and then gradually declined to about
150 in the mid-30 's. In 1946, each of 242 boats landed 1,000 pounds or
* See Hallock, Fry, and LaFaunce (1957). The traps were fished through September
and October in each of four years, but were operated from June through August
in only one year.
POTENTIAL SALMON PROFITS 261
more for the season. 4 The 1909 fleet, presumably oar or sail powered,
covered a much larger area than was legally fishable in later decades,
but still overcrowded the fishing grounds. The 242 boats fishing in 1946
were covering a wider area than would be necessary for a smaller fleet
— and they too were overcrowded. This fleet was gasoline powered but,
with possibly one or two exceptions, nets were pulled by hand. Our
hypothetical fleet would have power-driven net rollers and one man
could handle a boat except during the height of the fall season. How
many such boats, placed in the most strategic areas, would be required
to take about 8,000,000 pounds per year?
In 1946, the gill-net catch was 6,463,000 pounds — the highest year
in which we have records of catches of individual boats. The September
catch in 1946 was 3,674,000 pounds, although the season ended Sep-
tember 26. Had fishing continued through September 30, the catch
would almost certainly have exceeded 4,250,000 pounds — more than we
would expect from our hypothetical fleet in an average September.
The 1946 fleet had 219 boats fishing in September. There were too
many of them; they got in each other's way. Boats and nets drift with
the tide, and on the better drifts boats lined up and had to await a
turn. Each boat caught some fish, alarmed others, and made fishing
worse for the boat behind it. Half as many boats fishing the same
drifts would have had a much better average-catch-per-boat. A quarter
as many boats fishing only the best drifts would have had still better
catches.
The 59 poorest boats took only 283,000 pounds (Table 2). The re-
maining 160 boats took over 3,390,000 pounds and had they fished at
the same rate through September 30 would have taken over 3,900,000
pounds.
Without a troll fishery, salmon in an average year would be more
abundant than in 1946 — catch-per-boat would be greater and a smaller
fleet would suffice. "We do not want our small fleet to take as high a
proportion of the fish as the old fleet did — we want enough fish to get
past the nets to eliminate all need for lengthy closed seasons.
TABLE 2
Sacramento-San Joaquin River Fishery, September 1946
Salmon Boat Catches
Catches in Number
thousands of
of pounds boats
Under 5,000 30
5,000- 9,999 29
10,000-14,999 30
15,000-19,999 46
20,000-24.999 39
25,000-29,999 29
30,000-34,999 12
35,000-39,999 2
40,000-44,999 1
45,000-49,999 1
219
4 From Fry (1949), and unpublished records of the Department of Fish and Game.
262 CALIFORNIA FISH AND GAME
The 1946 fleet pulled its nets by hand. Power rollers will bring a net
in faster and with less effort and more time can be spent actually catch-
ing fish.
The 1946 fleet used linen nets — linen is relatively inefficient, especi-
ally in the daytime. When nylon nets were tried in the Delta they took
many more fish than linen. 5 Monofilament nets were developed after all
net fishing had been outlawed in the Delta. They have been used in
other areas and took from two to more than three times as many fish
as nylon nets with which they were competing. 6 Monofilament nets have
been outlawed in Washington and British Columbia — they are too ef-
fective.
The 3,900,000 pounds that the 160 "high" boats in 1946 would have
taken had they been allowed to fish through September 30 were about
what our hypothetical fleet would be expected to take in September.
Without their 59 inefficient competitors, a somewhat smaller fleet could
have done the job. Probably fewer than 40 boats would be required to
take 3,900,000 pounds if they were using power pullers and fishing in
the best places with nets capable of catching several times as many fish,
and with salmon at a higher level of abundance. To allow for higher
catches in above-average years, I am proposing a hypothetical fleet of
50 boats. These 50 boats would probably be able to take so much fish
that weekend closures would be needed in most years to permit adequate
escapement. The lengths of these closures could be varied to suit the
sizes of the runs.
Thus far I have stressed the fishery as it could be expected to exist
in September, since that is the peak month and the one in which, his-
torically, the largest catches were always made. In recent decades,
October was always closed. Our hypothetical fishery could expect to
make excellent catches in October. Based upon experimental fishing by
department employees near the mouth of the Feather River, October
catches would average about 62 percent as much as those made in Sep-
tember.
The limiting factor during September and October would not only
be the catching capacity of the nets — it would include the fishermen's
endurance. During the rest of the year neither of these problems would
be serious and fewer boats could do the job. Ten boats would probably
be sufficient to harvest the catch during 6 of the 12 months (Table 3).
It might be necessary legally to limit the number of boats by law which
could fish during months other than September and October, but eco-
nomics probably would do a fairly good job of regulation. In the past
only a small part of the fleet was fishing during poorer months.
8 The most comprehensive comparison of nylon and linen gill-net catches I found was
that by Davis and Posey (1959). They compare catches made with several mesh
sizes and three twine sizes of cotton, two of linen, and five of nylon that could
be directly compared with the cotton and linen. Gill nets and trammel nets were
among the gear tested. (A trammel net is a highly modified form of gill net —
both gill and trammel nets were used in the Delta salmon fishery.) The number
of net days of fishing ran into the thousands. Comparing the most effective twine
size of nylon with the most effective linen twine size for each mesh size, the
weight of fish taken by nylon trammel nets averaged about 2.5 times that taken
by linen trammel nets, and nylon gill-net catches averaged about 3.5 times those
of linen gill nets. (Cotton ran third.) Monofilament was not Included in their