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B t = B e- lM - G)t + R (D

where B is initial biomass at time of reproduction,

t is interval between reproductions,

B, is biomass at time t (the following reproduction),

M is instantaneous coefficient of natural mortality,

G is instantaneous coefficient of somatic growth,
and R is a pulse recruitment, determined by previous reproductions.

If we consider the effects of continuous fishing, we have

B t = B e- ,F + M - G " + R (2)

where F is the instantaneous coefficient of fishing mortality. Equilibrium fishing
intensity (F.) is that value of F which results in a constant population size
(B, = B ), and we can write
B = Boe -iF. + M-G„ + R (3)

The corresponding equilibrium yield (Y e ) is

Y e = B (F e /(F e + M - C)) (1 - e -i* + *- G >») (4)

Potential population growth (AB pot ) is the increase in population size which
would occur if there were no fishery, and is equal to B, — B in equation (1 ).
However, B is also given by equation (3), so ABpot is calculated by (1 ) minus
(3), and recruitment terms cancel:
ABpo, = B e" ,M - G,t + R - (B.e- < Fe + M - G >* + R)
= B (e ~ (M - G " - e -if + M-Gj.) (5)

The above equation allows us to compare potential population growth undei


conditions of no fishing (5) with equilibrium yield (4). This comparison is best
expressed as a ratio (8) which is a function of F, M — G and t:

5 = vB^/Y. =[B (e- ,M - G "- e ~ (F . + M - G " )]/[B„(F./ (F. +M -C) )

= r (Fe + m-C) e- ,M - G,, (1 -e -'•')] /[F. (1 - e^'**- 01 ')] (6)

Example values of 8 are given in Table 1. The quantity 8 may be thought of
as a biological discount factor. When equilibrium yield is not harvested, the
population will grow, but by an amount less than the yield which is foregone.

The values in Table 1 indicate that the quantity ( M-C ) t is much more influen-
tial than Ft in determining the value of 8. Therefore, a single value of 8 may be
sufficient for most modeling purposes, and 8 can be treated as a constant for all
likely values of F. Since the above calculation is for continuous fishing, seasonal
fisheries will give different values of 8. For fisheries occurring just before repro-
duction, 8 will be near 1 , and for fisheries occurring just after reproduction 8 will
be smaller than the values in Table 1.

Table 1. Example Values of 8.


(M - G)t _0J 1.0

0.0 100 1.00

0.1 0.95 0.94

0.2 0.90 0.89

0.3 0.86 0.84

0.4 0.81 0.79

0.6 0.73 0.70

0.8 0.65 0.61

1.0 0.58 0.54

1.5 0.43 0.38

Consideration of 8 is particularly important in catch-transition methods of
estimating the parameters of production models such as in the generalized
production model of Pella and Tomlinson (1969). Continuous reproduction is
a basic assumption in production models, but they are very often empirically
applied to fisheries wherein reproduction is distinctly seasonal. Under continu-
ous reproduction, the relationship

AB = Y e - Y (7)

where Y is actual harvest, is appropriate. However, when reproduction is discon-
tinuous, the relationship

AB = 8 (Y. - Y) (8)

should be used. Equation (7) is therefore a special case of equation (8), wherein
t = and 8 = 1. Since production modeling is often applied when biological
information is minimal, a reasonable guess for the quantities (M — G) and t
should be sufficient, and will certainly be an improvement over use of equation
( 7 ) . Estimates of the catchability coefficient and the asymptotic maximum popu-
lation size which are obtained from the catch-transition approach are often
considered to be unreliable (Pella and Tomlinson 1969) and this modification
should improve accuracy.

Again, the discount factor may be an important consideration in rehabilitating
depleted resources. This factor may be a contributory cause of the apparently
slow recovery of the Peruvian anchoveta fishery, where 8 = 0.6 is a likely value.

NOTES 2 27

Conversely, when the potential rate of growth of a population is known, and
equilibrium yield is to be estimated, maximum sustainable yield will be greater
than maximum population growth rate by 8"'. Such is the case in the northern
anchovy fishery in California, where S - ' = 1.54.

In the case of marine mammals, the appropriate time interval (t) would not
be the gestation period, since mortality would result in the loss of offspring as
well as the parent. Rather, t would be the interval between the time when the
offspring would survive the death of the mother and the time when the mother
would next become pregnant. Since this is a relatively short time, and M — G is
relatively small, the discount rate for marine mammals may approach 1.0.


Pella, J. )., and P. K. Tomlinson. 1969. A generalized stock production model. Inter-Am. Trop. Tuna Comm.,
Bull., 13: 419^496.

— Alec D. MacCall, California Department of Fish and Game, Operations Re-
search Branch, c/o SWFC, Box 271, Lajolla, CA 92038. Accepted for publica-
tion March 1978.


On March 9, 1976, while scuba diving near the west end of Santa Catalina
Island, Los Angeles County, California, I observed a display of agonistic behavior
between two treefish, Sebastes serriceps (Jordan and Gilbert). I came upon the
treefish at a depth of about 7 m (23 ft) in front of a rocky cave approximately
0.5 m (20 inches) high by 1 m (39 inches) wide, and several meters deep. A
25-cm (10-inch) fish, subsequently identified as the defender of the cave, had
the head of a 20-cm (8-inch) treefish to about mid-orbit in its mouth. The two
fish slowly moved back and forth in front of the cave for several minutes while
interlocked in this manner.

After the two separated, the larger treefish went into the cave and the intruder
swam several meters away. When the intruder returned to the cave entrance,
he was approached by the larger fish with erect dorsal fin and a widely gaping
mouth. The intruder responded by erecting its dorsal fin and opening its mouth.
Both fish, facing one another, then made a series of short darts in an attempt
to grasp the other's jaw. When one fish did grasp the other's jaw, the attacked
fish would bite down on the attacker's snout. In this manner, the two fish again
moved back and forth.

During one dart, the attacker missed the lower jaw and its head went com-
pletely into the other fish's mouth. On another dart, one fish bit only one side
of the lower jaw and the two hovered at right angles for a short period.

The defender did not initiate agonistic behavior until the intruder approached
the cave entrance. At no time during any of the described encounters was
contact sufficient to cause visible damage to either fish.

This grasping behavior, which might inhibit respiratory efficiency, terminated
when the fish with the other's head in its mouth released its grip. This release
might be stimulated by reduced blood oxygen levels.

On February 20, 1970, a similar observation was made at the Los Angeles
County Fish and Game Commission's Redondo Canyon Artificial Reef by John
Duffy and Robert Hardy (Calif. Dept. Fish and Game, pers. commun.). They


observed and photographed what they presumed to be one sequence in the
mating behavior of the treefish. Two animals oriented head-to-head, grasped
each others lips, held on for several minutes at a time, and occasionally shook
each other violently. Unfortunately, the photographs they took are not of suffi-
cient quality to be published.

Little information has been published on aspects of treefish life history and
behavior. Phillips (1957) and Miller and Lea (1972) gave systematic accounts
of the treefish and described the adult color as yellow to olive with five or six
black bars along the body. Feder, Turner, and Limbaugh (1974) reported that
treefish are aggressive, territorial, and take shelter in rocky crevices.

The behavior exhibited by the treefish on both occasions was not observed
to completion, nor was either pair of fish collected; thus it cannot be determined
if the behavior was territorial or reproductive. In contrast to their normal adult
coloration, the treefish I observed were dark green overall; the black bars were
indistinct. However, photographs of the treefish observed at Redondo Canyon
show the usual adult coloration.

Leon Hallacher ( U.C. Berkeley, pers. commun. ) has observed displays similar
to those of the treefish in the gopher rockfish, Sebastes carnatus, including the
facing and grasping behavior. He considers such behavior rare, having observed
it only once in 7 years of diving. Kim McCleneghan and James Houk (Calif. Dept.
Fish and Game, pers. commun.) observed similar behavior in the kelp rockfish,
S. atrovirens.

Comparable displays, manifested by two individuals facing each other with
mouths agape and dorsal and pectoral fins erect, have been observed in several
Californian fishes, including sheephead, Pimelometopon pulchrum (T. J. Muell-
er, Univ. So. Calif, pers. commun.) and the blackeye goby, Coryphopterus
nicholsii (Wiley 1973). I have seen such displays in the blue banded goby,
Lythrypnus da///. Physical contact accompanying such activities has been only
a nip, which caused no apparent damage, and not prolonged grasping bouts as
in these treefish.

I wish to express my gratitude to John Duffy and Robert Hardy for allowing
me the use of their data and photographs. I also thank John Fitch and Leon
Hallacher for reading the manuscript and their valuable suggestions. These
observations were made during work performed under Dingell-Johnson project
F-27-D, Sportfish-Kelp Habitat Study.


Feder, Howard M, Charles H. Turner, and Conrad Limbaugh. 1974. Observations on fishes associated with kelp
beds in southern California. Calif. Dept. Fish and Came, Fish Bull., (160): 1-144.

Miller, Daniel )., and Robert N. Lea. 1972. Guide to Coastal Marine Fishes of California. Calif. Dept. Fish and Came,
Fish Bull., (157): 1-235.

Phillips, Julius B. 1957. A review of the rockfishes of California (family Scorpaenidae) . Calif. Dept. Fish and Came,
Fish Bull., (104): 1-158.

Wiley, James W. 1973. Life history of the western North American goby, Coryphopterus nicholsii (Bean). San
Diego Soc. Nat. Hist., Trans., 17(14): 187-208.

— Peter L. Haaker, Calif. Dept. Fish and Game, Marine Resources Region, 350
Golden Shore, Long Beach, California 90802. Accepted for publication March

Reviews 229


Bright Rivers

by Nick Lyons; J. B. Lippincott Co., Philadelphia and New York, 1977; 166p. $8.95.

Bright Rivers is an autobiography. It is a reflection on, and recitation of the successes and failures
of Nick Lyons as a fisherman. He uses the qualities developed in his profession of English professor
to enliven this work in a "literary" style. None of us could write so lucidly about fish lost and found.

However, Lyons has a tendency to dwell a little too long and often on his fishing skills, or lack
of skills. I think Nick Lyons is a better fisherman than he lets on. Close personal contact with the
better fishermen of the United States as he has, must sooner or later rub off. One consolation is that
our exposure to his troubles reduces the sting of our own.

The book is divided into two parts. The first deals primarily with eastern fishing, focusing especially
on a summer vacation spent in the Catskills. The second deals with fishing trips to the west, especially
to Montana. He really gets turned on by Montana — it must be heaven to him. It is in this section
that his writing seems to be more alive. The western reader may identify better with this section.
He may also be thankful there are more waters to fish and larger fish to be found in this part of the
country. Apparently 1 0-inch fish are a prize in many heavily fished waters where Lyons usually fishes.
I hope the author fully develops his skills as a fisherman. When he does, his literary training,
combined with angling skill, should coalesce to really produce fine quality angling works. — Ed Littrell

The Fresh and Salt Water Fishes of the World

by Edward C. Migdalski and George S. Fichter; Alfred A. Knopf, Inc. N.Y., 1976. 316 pp., illustrated in
color. $25.00.

This beautifully illustrated book represents another attempt to present to the general reader an
up-to-date review of the world's fish families. The very readable text leads off with a short discussion
of classification, fossil fishes, fish morphology, anatomy, physiology, age and growth, and migrations.
The discussion of the families highlights size, description, and life histories of some of the more well
known as well as rare species. Full color illustrations of over 500 species were produced by Norman
Weaver and are truly spectacular.

Unfortunately, I found the text to contain many errors or omissions. For example, the record size
of the white shark, Carcharodon carcharias, is reported to be 36.5 ft. However, a recent paper
indicates that this record is invalid; the statement that most chinook salmon, Oncorhynchus tshawyt-
scha, are caught as they move upstream to spawn, completely ignores the large ocean catches by
sport and commercial fishermen. The statement that the pink salmon, O. gorbuscha, "occurs in
greater abundances further south than do other species", I assume is a typographical error. Appar-
ently the authors did not refer to Miller and Lea's Fish Bulletin 157 as there are several mistakes in
geographical ranges, size records, and names of California fish.

On the positive side, some of the species descriptions I found to be very informative as well as
entertaining, in particular, the narrative on the carp, Cyprinus carpio.

Despite the faults in the text, I feel that the excellent color illustrations will make this book very
attractive to professionals and non-professionals who never tire of looking at fish. — Daniel W.

Inland Fishes of California

by Peter B. Moyle; Univ. of Calif. Press, Berkeley, Los Angeles, London, 1976; 405 pp; illustrated $20.00.
Inland Fishes of California is a much needed and valuable reference book for the student, biologist,
amateur naturalist, or interested angler. Unfortunately, there are errors throughout the text, which
undoubtedly will be corrected in subsequent editions. Meanwhile, Dr. Moyle has indicated that any
purchaser may get a three-page list of errors and additions to Inland Fishes of California by writing

Dr. Peter B. Moyle

Department of Wildlife and Fisheries Biology

University of California, Davis 95616
A significant difference exists in the quality of the drawings and there is a general lack of
illustrations of adult fish. In fact, some of the illustrations resemble juvenile specimens recently
removed from bottles of formalin or alcohol. When asked why his illustrations were predominately
of juvenile specimens, the author replied that it was partly a matter of availability and partly because
of his intention to illustrate sizes which might be encountered most often by students using the usual
collecting techniques (traps and seines).

I did not test the keys, however they seemed quit* simple and probably would be easy to use.


Although I share the author's feelings about the loss or deterioration of populations of native
(particularly non-game) species, his preoccupation with this sentiment reduces the objectivity of
his presentation. He tends to portray an aura of helplessness and resignation. When discussing the
Sacramento-San )oaquin Delta in his chapter entitled "Ecology", he says "Today it hardly seems
worthwhile even to devote much time to the interactions among the introduced species since if any
stable associations have been established they are likely to be soon upset as the waters of this zone
continue to change, and as other new species become established in them." One could argue that
in view of gross changes which are occurring, it should be desirable to predict the effect of such
changes and to consider the desirability of modifying them.

His strong identification with native species tends to make his "Ecology" chapter more of a
description of what the system was, or might have been, rather than the ecology of what now exists.
Introduced species seem to be regarded as "noise" to the theoretical system.

In his discussion of the ecology of Clear Lake, he gives a somewhat detailed description of the
ecological relationships of the native species which previously inhabited the lake. Although, as he
points out, "at least 13 species are now established and only 4 of the native species are still
maintaining large populations", he dismisses recent ecological relationships by saying "too little is
known about their ecology to make reasonable speculations about their interactions", and that the
species composition is still changing. No one can deny that much change has taken place recently,
but on the other hand, many ecological studies also have been made recently in Clear Lake. One
wonders if the ability to speculate is more constrained in the face of recent "hard", but conflicting
data. Certainly, the dynamics of change, itself, is an important facet of ecology, which is glossed-over

His descriptions of change consistently carry value judgments. In general, changes brought about
by man's influence are labeled "bad", while changes which took place without man's influence are
considered "good".

Knowing the author, one is aware that this is precisely the message that he is intending to convey.
While I appreciate his sentiments, empathize with him in these feelings, and recognize his right to
express them, I feel that a more objective treatment of these subjects would have improved the text

In summary, however, this is an outstanding book and should be included on the bookshelf of
any ecologist, student, or angler interested in California's inland fishes or fisheries. — John Radovich

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Online LibraryCalifornia. Dept. of Fish and GameCalifornia fish and game (Volume 64, no. 3) → online text (page 10 of 10)