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(B + 100) (A - A) j^.jj^^j_

(300+ 100) (80-25) „ ,, ,, ^ , , ^.

= 0.44, or 44 percent of population

( 80 + 100) (300 - 25) , .„ ,

killed

The above example demonstrates the formulas to be mathematically
exact. However, practical application depends upon sampling to determine
representative sex ratios in the population before and after the hunting
season and in the hunting season kill.

Application of this method to determine percentage killed by hunting
will be easiest when both sexes are legally taken. With this condition,
adequate sampling of the hunter's bag would determine the sex ratio of
the total bag taken. Unless there is cause for believing otherwise, the
sex ratio in the bag could be assumed to be representative of the ratio
of the total kill.

In some instances males only may be taken legally, particularly with
deer and pheasants. However, a realistic appraisal of the total hunting
kill must recognize that some females undoubtedly are killed when males
only are legal game.

Thus, the formulas presented generally are applicable when hunting
regulations permit the taking of males only. However, it is more difficult
to obtain the sex ratio of the kill under such conditions. If cock pheasants
only are legal game, fluoroscopic examination to determine percentages
of each sex carrying shot after the hunting season may provide the best
indication of comparative hunting kill by sexes. In some instances, bag
checks together with field searches for unrecovered dead might be used
to determine the sex ratio of the total hunting kill.

^^^2 CALIFOKXIA IISII AND C.AMi;

Example 2. Use With Age Ratio Data

An cxainplo showing application of the basic formulas to compute
poj)ulation losses from age ratio information is given below. The example
deals witli determining percentage's of winter kill in a deer herd by use

Numbers of deer Age ratios

Alive before winter 50 100 150 50

Winter deaths 30 20 50 150

Alive after winter 20 80 100 25

From data in the above table giving total population numbers and
winter losses, it is evident that 60 percent of the fawns, 20 percent of the
adult deer, and 33 percent of the total population died during the winter.
To demonstrate use of the formulas for such conditions, these percentages
of winter loss will be calculated using only the age ratios given in the last
column of the above table.

In this example, adult deer are the base population and fawns the ratio
population. Ratio values for svmbols in the basic foi'mulas are:
B = oO
K = 150
.4 = 25

Applications of formulas to calculate fractions or percentages of loss are:

B — A

K — A

50 — 25

loO — 2r>

2. —F^TT^ r^ = decimal fraction of fawns dead.

B{K - A)

— ' \',^ K^ = 0.60, or 60 percent of fawns dead.

oO (loO — 2o)

/ r. -, ^r. — 7T^ -TT = decimal fraction of total population dead.

{B + 100) (A —A)

(150 + 100) ( 50 - 25) ^ ^^ ^„ ^ n , , ,

50+100 150 -25 = f-f Z I " ""

For such use it would be desirable, where practicable, to make herd
composition counts to obtain age ratios in the herd when it entered and
when it left the winter range, or at times shortly before and after the
period of winter loss. Sample carcass counts would give the age ratios
in the winter kill.

Variations for Practical Use

riame managers working infrecjuently with such procedures may have
difficulty in rememl^ering or looking up various fcrmulas which enable
the desired information to be calculated. Such individuals frequently

CALCULATING THE KILL 313

prefer to attempt to remember as few formulas as possible, and may prefer
a S5''stem such as follows.

All percentages of kill may be calculated by use of the simplest basic
formula :

B — A

= decimal fraction of base population killed.

K - A

Also, modif\nng the syml)ols in the formula may help the worker to
keep in mind the tj'pe of ratio used, which is the base population, and
what the results will be.

Using a system of this typo, the percentage of kill calculated in Example
1, by use of sex ratios, could be determined as follows:

B 9 — A9
1- T^ ^ r^:^ = decimal fraction of hens killed.

K9 - A9

QQ 25

0.20, or 20 percent of hens killed.

300 - 25

The sex s3'mbols indicate that hens are the l)ase population, the ratios
used are cxi)resscd as males per female or per 100 females, and the result
is the decimal fraction of hens Idlled.

2. Then, ., ^ ". ^ = decimal fraction of cocks killed.

The symbols show that males are the base population, the ratios are
expressed as females per male or per 100 males, and the result is the
decimal fraction of males killed. Recalculating ratios in Example 1 on
the basis of females i)cr 100 males and substituting in the above formula:

—~ 7jr^ = 0.75, or 75 percent of cocks killed.

oo — 4U0

The negative quantity that would result from the particular ratio
values presented above is changed to positive by the standard algebraic

procedure of multiplying b}^ — — ,

3. With the percentage kill for each sex determined, the percentage
of the total population killed maj^ be calculated by applying the sex ratio
to obtain a weighted average kill. In Example 1, sex ratios before the
season showed the population to consist of 44 percent cocks and 56
percent hens.

0.44 cocks X 0.75 cock loss = 0.33 of total population killed due to

cock kill only.
. 56 hens X . 20 hen loss = 0.11 of total population killed due to
hen kill only.

Total, or weighted average = 0.44, or 44 percent of total population
kiUed.

Some users may prefer to add X 100 to the formulas so that the product
is a percentage figure instead of a decimal fraction. Others may prefer

314 CALIFORNIA FISH AND GAMK

to koo]) the formulas as simple as possible and shift the decimal point
two places to eonvert the decimal fraction to a percentage hgure, as in
the examples gi\('ii hcic

Use for Calculating Populations

Wiien the total kill is known, the foninilas pi'eseiitcd may also be used
to calculate populations. The fraction of kill dividcxl into the numljers
killed, w'hen both figures can be determined, gives the population number.

Use of this method is illustrated as follows, with figures from Example
1 above:

7^ 9 _ ^4 9

= decimal fraction of hens killed.

K9 -A9

- = 0.20 of hens killed.

300 - 25

20 hens killed
0.20 of hens killed

= 100 hens in population.

Other sex or age groups of the population, and the total population,
may be calculated in a similar manner by use of the formulas, or by
applying population ratios to the first population segment computed.

Because the formula used is simple and comparatively easy to remem-
ber, some workers may prefer this method to the use of more detailed
formulas which give the population figure directly.

Use of Other Formulas

The usual use of Kelker's (op. cit.) and similar fornuilas is to calculate
population numbers from sex or age ratios in the population and the
total kill. One of the main limitations in such use of the formulas is that
total kill figures must be obtained — usually a difficult or impossible
task — to produce accurate population figures.

Another application of formulas of this type, which evidently has not
been pointed out previously, is their use to calculate percentage of kill
when the kill data are incomplete but a representative sample of the
kill has been obtained. This ai)plication is illustrated by use of one of
Kelker's formulas, as follows:

Symbols :

hh = ratio of males per female before hunting season.

ba — ratio of males per female after hunting season.

A'jd = kill of females.

Kb = kill of males.

-~ 5 = number of females before hunting season.

ba — h

CALCULATING THE KILL 315

Substituting the total kill and sex ratios of Example 1 above in Kelker's
formula :

= 100 hens before season, actual population.

0.25 - 0.80
20 hens killed
100 total hens

0.20, or 20 percent of hens killed.

Assume that instead of the total kill of 60 cocks and 20 hens, only
a sample of 20 birds of the total kill could be checked. If this sample was
representative of the total kill, it would consist of 15 cocks and 5 hens.

Using these kill values in Kelker's formula :

(0.25 X 5) - 15

0.25 - 0.80

5 hens checked
25 hens total

25 hens before season, sample population.

= 0.20, or 20 percent of hens killed.

Use of the sample kill figures gave the same percentage of kill as did
total kill data.

Because the kill figures used were less than the total kill, the population
figure obtained was low. However, in this and similar formulas, the
population figures obtained are directly proportional to the kill figures
used.

Thus, if the sex ratio of the kill figures remains the same, formulas
of this type will yield the same fraction, or percentage of kill, by dividing
the population figure produced into the kill figure used, regardless of the
numbers of kill used. Therefore, percentage of kill may be determined
by use of sample kill data in such formulas.

SUMMARY

New and simplified formulas are presented for calculating percentage
of kill from sex or age ratios in a population before and after a kill and
in the kill. Total kill figures are not needed to calculate percentage of
kill, but population numbers may be calculated by use of the formulas
if the total kill is known.

Application of Kelker's formulas to calculate percentage of kill from
sample kill data, without knowing the total kill, is shown.

Either type of formula may be used to calculate percentage of kill
with ratio data, or population numbers with ratio data and total kill.
However, the new formulas presented are simpler and believed to be
easier to use and remember.

:!l(i CALIKdliMA IISII AM) CAME

REFERENCES
Allen, Durward L.

1942. A pheasant invt'iitoi-v method based upon kill i-coords and sex ratios.
Seventh No. Amer. Wihll. Conf., Trans., p. 329-383.

Dasmann. Raymond F.

1952. Methods for estimating deer popnlations from kill data. Calif. Fish and
Game, vol. 38, no. 2, p. 225-233.
Kelker, George H.

1940. Estimatins deer jiopulations by a differential hunting los.s in the sexes.
Utah Acad. Sci.. Arts and Let., Proc, vol. 17, p. 65-69.

1943. Sex ratio equations and formulas for determining wildlife popnlations.
Utah Acad. Sci., Arts and Let., Proc, vol. 20, p. 189-198.

Lauckhart, J. Burton

1950. Determining the big-game population from the kill. Fifteenth No. Amer.
Wild!. Conf., Trans., p. 644-<i50.
Petrides, Geoi-ge A.

1949. Viewpoints on the analysis of open season sex and age ratios. Fourteenth

No. Amer. Wildl. Conf., Trans., p. 391-410.
1954. Estimating the percentage kill in ringnecked pheasants and other game
species. Jour. Wildl. Mangt., vol. 18, no. 3, p. 294-297.
Riordan, Laurence E.

1948. The sexing of deer and elk by airplane in Colorado. Thirteenth No. Amer.
Wildl. Conf., Trans., p. 409-430.

Robinette, W. L.

1949. AVinter mortality among mule deer in the Fishlake National Forest, Utah.
U. S. Fish and Wildl. Serv.. Spec. Sci. liept. 65, 15 p.

NOTE

SECOND RECORD OF THE GREEN STURGEON IN
SOUTHERN CALIFORNIA^

On April 27, li)57, a green sturgeon, Acipenser medirostris Ayres,
774 millimeters in total length and weighing 3 pounds 14 ounces was
speared in 18 feet of water by Billy J. Walker, just north of Point
Vicente, Los Angeles County, California. It was discovered swimming
over a sandy bottom between small rocky reefs. The small cove in which
it was taken is known locally as "Old Man's Cove".

The fish had nine shields in the dorsal row, 29 shields in the right
lateral row, and 28 shields in the left lateral row. Both lateroventral
rows had nine shields. The dorsal fin ray count varied from 40 to 42,
depending ui)on whether or not the small anterior bony elements were
counted. Similarly, the anal fin ray count varied from 28 to 29. The
pattern was typical of that recorded for the green sturgeon, as was the
placement of the four sub-rostral barbels.

The green sturgeon has previously been reported south of Monterey
on one occasion (Roedel, 1941). In this instance a 7:j-pound specimen
was taken between Huntington Beach and Newport Beach in a bait
net set in 10 fathoms of water.

The specimen reported here has been deposited in the fish collection.
Department of Zoology, University of California, Los Angeles.

REFERENCE
Roedel, P. M.

1!)41. A sturgeon in southern California waters. Calif. Fish and Game vol. 27,
no. 3, p. 191.

— Kenneth S. Norris, Marineland of the Pacific,
Marineland, California, May, 1957.

''■ Contribution No. 4, Marineland of the Pacific Biological Laboratory.

( 317 j

Chapter

I.

Part 1

. Tl

Part 2

. Ai

Chapter

II.

Chapter

111.

Chapter

IV.

Chapter

V.

('hapter

VI.

Chapter

VII.

Chapter VIII.

Chapter

IX.

Chapter

X.

REVIEWS

The Physiology of Fishes. Volume I: Metabolism

Edited by Margaret E. Brown; Academic Press Inc., New York, 1957; xiv + 447

p., 84 figs., 1 plate. \$12.
With the sight of this book, like that of an overdue paycheck, one instinctively
exclaims, "I thought it would never get here". But here it is, the most detailed book
on this subject so far published in English and probably in any language.

Although scientific investigation into the physiology of fishes has lagged behind
that of other vertebrates and insects, a considerable wealth of information — scat-
tered through periodicals published all over the world — has accumulated over the
years. This volume and its companion. Volume II — Behavior (soon to be published),
consist of reviews of the present state of knowledge on the various phases of fish
physiology.

The impressive array of authorities and their subjects must be seen to be ap-
preciated :

Respiration
The Aqua tic Respiration of Fish by F. E. J. Fry
Air Breathing by G. S. Carter

The Cardiovascular System by J. C. iMott

The Alimentary Canal and Difjestion by E. J. W. Barrington

E.Tcretion and Osmoregulation by Virginia Safford Black

The Skin and Scales by John Van Oosten

Endocrine Organs by William S. Hoar

The Gonads and Reproduction by William S. Hoar

Early Development and Hatching by Sydney Smith

Experimental Studies on Grotvth by M. E. Brown

The Biocheniical Composition of Fish by R. M. Love

Each chapter is a bulging sourcebook of technical information, containing, in
addition, an extensive list of references of worldwide coverage. Only one. Chapter
V, tenders a skimpy and wholly inade(iuate set of references. A fine subject and
author index merits attention and praise, as do the clear and concise figures and
tables.

This book performs an immeasurable service to the advancement of fisheries con-
servation, a field just now achieving the recognition it deserves as an important
contrilmtor to national well-being. Successes in this field ultimately depend on inti-
mate knowledge of the behavior and reactions of each species under varying condi-
tions. To this end, a considerable store of data on fish life histories has accumulated
but concomitant studies on fish physiology, necessarj- for complete understanding
of fisheries problems, have not kept pace. This volume compiles much of what is
known on the physiology of fishes and, at the same time, indicates gaps in knowl-
edge and possible fruitful lines for further research. Here is a new starting point
for many fisheries biologists, offering many avenues of approach to complex prob-
lems. — Ahno J. Cordone, California Department of Fish and Game.

Trouf Fishing and Trout Flies

By Jim Quick ; The Countryman Press, Woodstock, Vermont, 10.j7 ; 2-52 p. illus.
\$5.

This is a thoroughgoing manual on the art of trout fishing with artificials.
Methods and gear are covered in detail. .Tim Quick knows his trout flies and how
to use them. He wisely stresses the principles behind successful fly fishing, so in-
terested duft'ers should be able to improve their "luck" by digesting and applying
his ideas. Good fishermen will enjoy comparing notes with an expert.

( .".10 )

:?2() OAT.IFORXIA FISH AND GAME

TIh' Imok is rcadaltlo, after you wado throujili four rather peculiar introductions.
It is nicely i)ut up, and fjenerously illustrated Avitli ink drawings by the author.
Tliere are fuur color plates of flies, plus three of pliotograplis of flies and the mate-
rials used to ni.ike them. There is ample good reference material on gear and angling
methods, jilong with tables of data on the characteristics of lines, leaders, and flies.

The brief section on trout life history and management gives the impression of an
afterthought tossed in l)ecause works like this arc supposed to have one.

The chapters on flies and liy-tying arc particularly good.

There is a brief chapter on the much-ueglected subject of sportsmen's ethics, to
supplement the pleasant overtone of good sportsmanship that runs through the book.
— Alcr Calhoun. Calif onii'i Drixirtiiieiif of Fish and Game.

The Galatbea Deep Sea Expedition

By Anton F. Bruun et al. (translated from the Danish by Reginald Spink) ;
The Macmillan Company. New York, 1957 ; 2!)G p.. illus., 1 map. \$S.

During the years 1950, 1951, and 1952 the Danish research vessel Galathea
carried out a highly successful investigation of many of the known abyssal depths
of world seas. A number of the scientists who participated in the expedition de-
scribe, in this volume, the particular phases in which they played a major role.
These various accounts are presented in such a smooth flowing, easy-to-read style
and are so interesting that, with the turning of each successive page, it becomes
increasingly difficult to set the book aside unfinished.

After the reader is acquainted with the multitude of details attendant with
planning a trip such as this, he is given an insight into the pitfalls and minor
disappointments which invariably crop up and cause unforeseen delays in starting
on time. There follow brief accounts on the ship and her complement, the objects
of the expedition, and research techniques and methods u^ed in studying the depths
of the ocean.

Considerable specific, as well as general, information is presented on many of
the biological discoveries of the expedition. Data are given on people, fish, birds,
snakes, invertebrates, bacteria, and plants encountered in the course of the trip,
and several little-known, seldom-visited localities where stopovers w^ere made are
interestingly described.

The index, a map showing the route of the expedition, and numerous, well-chosen
black-and-white illustrations add immeasurably to the value of the book. — John E.
Fitch, California Department of Fish and Game.

Sea Treasure

By Kathleen Yerger Johnstone ; Houghton MitHiu Co., Boston, 1957 ; xiv + 242
p., illustrated by Rudolph Freund and Rene Martin. \$4.

The keynote of this volume is procedure — procedure in finding, cleaning, labeling,
nected with shell collecting as a hobby. In addition, a considerable amount of basic
general information on sea shells and the animals that make them has been included.

Several chapters deal with the multitude of uses to which man has put shells
throughout the ages. It is pointed out how- the travel and trade routes of ancient
man have been determined from the kinds and numbers of sea shells left in Indian
burial mounds, encampment areas, and kitchen middens. All of this information is
extremely interesting and has been presented in an easy-to-read style.

The color illustrations are superb and the black-and-white drawings ai-e exactingly
portrayed. Most of the illustrations are of east coast shells but this should not
deter from the value of the book to a west coaster. — John E. Fitch, California De-
partment of Fish and Game.

How/ts, Owls and Wildlife

By John J. Craighead and Frank C. Craighead, Jr. ; The Stackpole Company,
Harrisburg, Pennsylvania, and Wildlife Management Institute, Washington,
D. C, 1956 ; xx + 443 p., illus. \$7.50.

This book is an ambitious w^ork that covers a study of raptor predation in two
study areas. The main one was Superior Township in Michigan. This area consists
primarily of dairy farms and grassland. Eleven percent of it is made up of wood
lots. The second study area was a semiwilderness one at Moose, Wyoming.

REVIEWS 321

For two years, year-round population densities, activities, movements, mortality,
and productivity of the raptor and major prey populations were determined in the
Superior Township area. Similar data were gathered during the spring and sum-
mer in the area at Moose, Wyoming.

The authors believe the major contributions of the book to be :

1. A quantitative analysis of the mechanics and functions of raptor predation.

2. A comprehensive study of raptor movements, ranges, territoriality, and inter-
specific and intraspecific behavior as related to collective raptor populations.

8. Quantitative proof of the efficacy of raptor predation as a natural biological
control or regulator, and clarification of the relationship of this phenomenon
to other environment;il forces that regulate the population levels of vertebrates.

4. A study of collective populations presenting a new approach to a further un-
derstanding of the forces or processes which regulate the densities of animal
populations.

This book goes into great detail regarding the methods used ; this will be of
great value to research workers who wish to make a critical evaluation of the
work, or who wish to conduct similar investigations. However, this detail does

The information presented in this book is excellent and makes possible a much
Itetter understanding of avian predation and how it functions in relation to prey
popul.-itions. This book adds much specific detail on how raptors act as a natural
control on prey populations and how the prey population levels in turn tend to
limit the raptor population.

It is too bad the authors did not make use of some of the excellent work by David
Lack in 1954. However, since the latest cited reference was dated 1953, perhaps
the nninuscript was completed prior to the publication of Lack's work.

In any case, this book makes a valuable contriliution toward a better knowledge
of a poorly understood group of animals, and their effects on game and nongame
animals. — Wallace G. Macgregor, California Department of Fish and Game.

Animal Navigafion

By J. 1). Carthy; Charles Scribner's Sons, New York, 19.".(>: 151 p., illus. \$.3.95.

This book is in no sense a textbook. The subject of animal navigation is reviewed,
with many theories discussed at great or lesser length. But to this reviewer, at least,
few questions were answered, and he was left with many more questions and doubts
concerning the validity of some current navigation concepts than he bad before
beginning the book. This, of cour.se. is as it should be, for this most fascinating
aspect of animal behavior is yet in its struggling infancy and offers a boundless
opportunity to speculate.

The scope and interest in this book nuiy perhaps be best expressed through a
consideration of chapter headings and some quotes and reviews from each.

Chapter I is entitled Animals and Men, and here the author sets the stage by
equating animals with men in their reasons for moving to new lands.

Navigation seems to imply guidance to a goal. Many animals, particularly the
smaller invertebrates, wander on, encountering the right places by chance, but the
probability of finding the most favorable is increased by their inborn reactions to
certain kinds of stimuli.

Chapter II, headed i^cent Trails, develops among other things the concept of
A. Forel, who considers that ants sense not only "smell", but the shape of a smell I
The idea of an "odor arrow" assisting in the direction of ants is developed here also.

Chapter III is entitled Home Is the Hunter and discusses the methods by which
hunting insects such as wasps find their Avay back to the nest. Several methods
apparently are used, including memorization of landmarks from ground level and
flying back ; memorization from an aerial viewpoint and walking back ; and climbing
plants, looking around for landmarks, and then continuing on the ground to the nest.

The Xectarseekers. Chapter IV, discusses the work of Lubbock and Von Frisch

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