SAMPLE SIZES AND CONFIDENCE INTERVALS FOR
WILDLIFE POPULATION RATIOS
RAYMOND L. CZAPLEWSKI,1 WyomingGame and Fish Department, Cheyenne, WY 82002
DOUGLAS M. CROWE, WyomingGame and Fish Department, Cheyenne, WY 82002
LYMAN L. MCDONALD, Departments of Statisticsand Zoology, Universityof Wyoming,Laramie,
WY 82071
One ofthemostcommontypesofdata used are not available untilthe data are at least
in applied wildlifemanagementis the popu- partiallycollected.The computationsneceslationratio.These data are used to gauge re- saryfordetermination
of whetheror not an
productivesuccessand the effectof selective adequate sample size has been obtainedare
harvesting
of wildlife.
rathertediousand do not lend themselvesto
A commonproblemfacingwildlifeman- quick reviewwhilein thefield.
how manyanimalsneed
agersis determining
A secondapproach,whichis the subjectof
to be classifiedin orderto obtainan accept- thisdiscussion,considersthe individualaniable estimateof these populationratios. A mal as a unit.This procedureavoids mostof
closelyrelatedquestionis the determination theabove-mentioned
problems.However,the
of confidenceintervalsaroundthe ratiosob- user mustbe willingto meet the following
tained.
requirements
whichare listedin orderof imGiven a populationof animalsthereare 2 portance:
generalsamplingstrategies
forcollectingdata
1. The populationis clearlydefined.
to estimatepopulationratios.One approach
2. The individualanimalsare sampled in a
assumesthatthe area occupiedby the popurandomand unbiasedmanner.This is diflationcan be divided into quadrats (plotsficultto accomplishin applied manageperhapsbelt transects)and the quadratsare
the problemcan onlybe addressed
ment;
randomly
sampledwithina givenhabitattype,
in thispaperas applicationwill
superficially
i.e.,thequadratis thesamplingunit.A survey
vary
with
and habitat.Essentially
species
(census)of theanimalsis made on each of the
therequirement
is
thateach animalin the
sampled quadratsand the numbersof (e.g.)
population
has
an
and independent
equal
fawnsand does are recorded.In thiscase, the
chanceofbeing"sampled."Extremeeffort
populationratiois estimatedas usualwhileits
shouldbe made in designof the studyto
precisionis obtainedaccordingto "classical
meet this condition.If the sampling is
finiterandomsample theory,"see forexambiased,
e.g., for"too many" does in estiple, Cochran(1977). Samplesize formulasexmation
of
a buck: doe ratio,thennaiveapist for the necessarynumberof quadratsto
of
plication
themethodology
presentedwill
survey.However,in practice,sucha designis
not
matters.
help
The
final
ratios
are still
oftenimpracticalwhenfacedwiththereality
biased!
of time,budgetary,and planningconstraints.
Also,the samplesize formulasdepend on es- 3. An upper limiton the populationsize is
available,e.g.,themanagermustbe willing
timatesof the sample varianceswhichoften
to estimatethat thereare no more than
N = 5,000 bucksand does in a population.
1 Present address: USDA Forest Service, Rocky
Fortunately,
sample size formulasare not
Mountain Forest and Range ExperimentStation,240
West ProspectRoad, Fort Collins,CO 80526.
sensitiveto errorsin thisvalue. Also,if the
121
122
Wildl. Soc. Bull. 11(2) 1983
(a ? b):100
estimatedupper limitis set too high,then
the indicatedsample size is conservative (e.g.,[70 ? 8
fawns]/100does).
(i.e., largerthannecessary)forthe desired
precisionand confidence.The upper limit 1. Example for calculating adequate sample
is forthepartofthepopulationunderconsizes and confidence intervals.
sideration.For example,if a buck: doe raA wildlifemanagerneedsan Augustfawn:
tio is desired,thenan upper limiton the
antelopeherd.The
totalnumberof bucksand does is required doe ratiofora pronghorn
(total population minus the number of necessarynumberof does and fawnsto be
classifiedmustbe determined.There are apfawns).
5,000 animalsin thisherdand it
4. In as faras possible,thesampleconsistsof proximately
distinctanimals,i.e., the samplingis con- is feltthatat least3,600 are does and fawns.
N equals 3,600in thefollowing.
It
Thisis more Therefore,
ducted"withoutreplacement."
thattherewill be about
efficient
than allowinganimalsto be "re- is also hypothesized
sampled"and shouldbe a goal ofthestudy 80 fawns/100does. This will put thevalue of
design.If the studyis conductedso thata "a" at 80. The desiredprecisionof the estiof theanimalscould matedratiois b = ?8 fawns/100does. Using
proportion
significant
be classifiedmorethanonce,thentheoret- Table 1, underthecolumnheaded 80:100,we
as one could find ?8.0:100 in the fifthrow which correicallythepopulationis infinite
continuesampling"withreplacement"in- spondstocurvenumber5 in Fig. 1. UsingN =
The figures
and tablesin thispa- 3,600 in Fig. 1 and curvenumber5, the redefinitely.
per can be used when animalsare resam- quiredsamplesize is about825. That is,a few
to morethan800 does and fawnsshouldbe claspled by takingtheresultscorresponding
the largestpopulationsizes reported(i.e., sifiedto insure(with90% confidence)thatthe
N = 12,000 is essentiallyinfinitewith re- fawn:doe ratio will have precisionof ?8
fawns/100does.
spectto theformulas).
In a similarmanner,Table 1 and Fig. 1 can
of the procedureto be deJustification
be used in reverseto obtainan approximate
scribedis containedin the appendix where
confidenceintervalon the estimatedratio.In
formulasare derivedthatwill providemore
the above example,supposethe sample size
withinthetaexactanswersthaninterpolation
actuallyobtainedis n = 1,200 and the comblesand curvespresented.As a generalguideputed ratiois 70 fawns/100does. The point
line,all resultsare developedat the90% con- n =
1,200 and N = 3,600 is close to curve
fidencelevel(see theappendixforotherlevels
number6. EnteringTable 1 withtheratio70:
of confidence).
100 and curve(row) 6, the precisionis ?5.7:
100. In conclusion,
thefawn:doe ratiois withESTIMATING SAMPLE SIZE AND
in (70 ? 5.7 fawns)/100does withapproxiCONFIDENCE INTERVALS
mately90% confidence.
Populationratiosare oftenexpressedin the
formof young/100femalesor males/100fe2. Example for adequate sample sizes with
males. This expressionof a ratiowill be demore than 2 classes.
notedas "a: 100." A ratioof70 fawns/100
does
wouldtherefore
be expressedas 70:100,where
Continuingexample 1, supposethe buck:
a = 70. Usingthisnotationforexpressing
pop- doe ratiois also of interest.
Withthehypothulationratios,the end pointsof the 90% con- esized ratioof 80 fawns/100does we expect
fidenceintervalare denotedby:
1,600 fawns,2,000 does, and 1,400 bucksin
WILDLIFE
I
3,000
000000000
000000000
co co _ co O CD t
0 CO
+
+1+1+1+1
+1 +1 --l+1 _1
+1
_ OC
_
.
_CO
O
OC
ill
+- +- 7l 11-l
RATIOS * Czaplewski et al.
POPULATION
1
l
2,500
1
COO
+-l +l
2,000
t
,T
00
0 0 t0
00 co 0 C 00
0c0 00 0t C6
50,500
6
+l +l +l +l +l +l
--+
1,000
X
a)
-a
>)
-
4
.
O
..
_
..
..
..
..
x
LooO
--+
.. .. ..
I'l co co
500
+l +l + +l +l+
0
._
+1
~~~+1
Ca
N
a)
-+1
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000000000
-z
-
C
CI cc o-
..
.
..
.
..
..
..
Ct!
Lo
..
..
..
co cq CtI
. g
aO0
0)
c?
~~~~+I+I
+l +l+
+
+l +l ++l +I
+l +I
+l+1+I
~+l
~~~+1
ut
k
o CQ
000000000c
Co C
0)~~~~~~~
4.^
En
t
_
+1 +1 +1 +1 +1+1 +1 +
C, L 0000000
_
C0
CZ
+l +l +l +l +l +l +l +l
~~~+l
ct
o
C)
c
Lt
0
0
'_
6
X
es
m=5
Q)
X
o~~~~~
4000
6000
POPULATION
SIZE
8000
K3300
12,000
C
o
.~~~~o _________i~6dcC,
Q.
O3
o
o
C)t
00
2000
Fig. 1. Samplesize (n) as a function
of population
size (N) of 2 age or sex classesand a givenlevelof
precision
indicatedin Table 1 (90%confidence).
C)
=
5
+1 +
~~+1
C)
123
CS: 00 CIO CO C
't
C, _
_
~~~+1
+1 +1 +1 +1 +1 +1 +1 +1
~~+l+l
o Lo +l
o Go om
o. +l+l+l
ooo +lI+l+l
the populationof 5,000 animals.Also,about
367 fawnsand 458 does shouldbe in thesample of 825. The hypothesized
buck: doe ratio
is 1,400:2,000or 70 bucks/100does and suppose the desiredprecisionis ?8 bucks/100
does. Usingthecolumnheaded 70:100 in Table 1, ?8.0:100 is foundtocorrespond
tocurve
number4 on Fig. 1. Also N = 1,400+ 2,000
= 3,400 in thiscase. From Fig. 1, about 690
bucks and does should be sampled,and we
expectto obtainabout284 bucksand 406 does
given the hypothesizedratio 70 bucks/100
does.
Taking the largerof the 2 values for the
does (e.g., 458 does in example 1) the adequate size forthecombinedsampleis:
n = 367 fawns+ 284 bucks+ 458 does
= 1,109animals.
About 1,100 totalanimalsfromthe populationof 5,000 shouldbe sampled.
MINIMUM AND MAXIMUM SAMPLE SIZES
a)
=
Fig. 2 containsa simplified
versionofTable
1 and Fig. 1. It is intendedthatFig. 2 be used
Wildi. Soc. Bull. 11(2) 1983
124
PRESPONDING
TO CURVE
20
be selected.The samplesize would be larger
in bothcases.
POPULATION RATIO
100
A
?4: 100
8
?3:100
C
?2: 100
40
50
:1:00
?67100
70
7 91
?4:100
?5:100
43:100
0100
100
i00
?7:
100
5:100
?00
13:100
t1I:
1X
4. Example for calculating maximumrecommended sample size.
? 7:100
2POO~~~~~~~~~~~SZ
We desireto estimatethe postseasonbull:
cow ratio of an elk herd. We estimateapproximately
5,000 bulls and cows are in the
herd.
UsingcurveC fromFig. 1, a realisticmaximumsample size is approximately
1,625. If
1,625bullsand cowsare classified
and thebull:
So.
cow ratioapproximates
20:100,thenthe90%
confidenceintervalfromthe top of Fig. 2
wouldbe (20 ? 2):100. "Tighter"confidence
Fig. 2. Recommended
samplesize (n) as a function intervalsrequire larger sample sizes. Howof populationsize (N) of 2 age or sex classesand a
givenlevelofprecision
indicatedin theinserted
table ever,increasingthe sample size above 1,625
willnotyieldmeaningful
in the
(90% confidence).
improvements
precision.To see this,the sample size 1,625
to curve7 in Table 1. Increasing
corresponds
by fieldpersonnelas a generalguidelinefor the sample size to 2,750 (curve9) yields(20
minimumsamplesize,maximumsamplesize, ? 1.1):100. The workloadmustbe approxiand the correspondingprecisionassociated matelydoubledin orderto improvethe prewitha givencombinationof samplesize and cisionto ?1.1 bulls/100cows.
theestimatedratioat approximately
90% confidence.
.DOC~~~~~~~~~~~~
1,5001
1,000
'
v
_
500an EZ-
0
2000
4000
6000
8000
10,000
12,000
POPULATION SIZE
SAMPLING "WITH REPLACEMENT"
Ifeveryanimalhasan equal chanceofbeing
classified(reclassified)on each samplingoccasion,thentheoretically
thepopulationis inIt is desiredto estimatethepreseasonfawn:
finite(N = oo). Figures1 and 2 extendonly
doe ratioin a mule deer herd. Currentestito N = 12,000. However,the curvesare almatessuggestapproximately
3,000 does and
mostflatin thisregionand N = 12,000 can
fawnsare presentin the population.
safely be used in place of N = x0 in all but
Usingcurve A fromFig. 2, the minimum
themostprecisestudiescorresponding
tocurve
numberof does and fawnswhichwe recom9 in Fig. 1. In this extremecase (curve 9),
mendforthesampleis about530. If thefinal
samplesizes in the neighborhood
of 4,000 to
fawn:doe ratio is approximately70 fawns/
are necessaryto obtaintheprecisionin5,000
100 does,theapproximate90% confidenceindicatedin thebottomrowof Table 1.
tervalis ?9:100, i.e., (70 ? 9 fawns)/100does
(see the tablereproducedon Fig. 2).
5. Example for calculating recommended
Assumingthe samplingprocedureis ransample size when sampling with replacedom and unbiased,thereis a 90% chancethat
ment.
the truefawn:doe ratioof the herd lies between61 fawns/100does and 79 fawns/100 In a "quick and dirty"census,severaldifdoes. If one desiresa smallerconfidencein- ferentindividualsare to cruisea networkof
terval,thencurveB or C fromFig. 2 should roads over severalweeksand classify(or re3. Example for calculating minimumrecommended sample size.
WILDLIFE POPULATION RATIOS * Czaplewski et al.
125
classify)
everyantelopetheysee. Assuming
that
thiscan be done in a randomand unbiased
manner,how manydoes and fawnsshouldbe
classified(reclassified)in orderto achieve a
precisionof ?8.0 fawns/100does? Also assume thatundersimilarconditionsthispopulationhas had a fawn:doe ratioof about80:
100. Using Table 1, curve 5 is selectedand
fromFig. 1 a sample size of n = 1,000 doe
to N = 12,000.
and fawnantelopecorresponds
Because curve5 is almostflatin thisregion,a
sample of about n = 1,000 is adequate fora
doeseventhough
precisionof ?8.0 fawns/100
From Fig. 2,
animals are being reclassified.
our minimumrecommendedsample size is
about n = 600 and the maximum recommendedsamplesize is about2,000.
As in the otherexamples,the processcan
be reversedto obtainapproximate90% confidenceintervals,i.e., use N = 12,000 in the
figures.
assumea maximumof N = 2,000 males and
femalesand a desiredprecisionof ?2 males/
100 females.Becausethenecessary
samplesize
decreasesas the hypothesized
ratiodecreases
(see Example6), thecolumnheaded 10:100in
Table 1 is recommendedand will give a conservative
answer.Usingcurve4 and N = 2,000
in Fig. 1, a samplesize of 600 is largerthan
necessaryfor precisionof ?2.0:100 if the
"true"ratiois 5:100 (90% confidence).
We recommendthatthe left-handcolumn
headed (10:100) in Table 1 be used for all
hypothesized
ratiosbelow 10:100.
Afterdata are collectedand a computed
ratiobelow 10:100 is obtained,say 8:100, the
precisionindicatedin the firstcolumnof Table 1 is conservative.
For example,withn =
1,000animalssampledout of N = 2,000total,
n = 1,000is abouthalf-waybetweencurves6
and 7 in Fig. 1. Usingthefirstcolumnof Table 1 (10:100)theprecision
is betterthan? 1.3:
100.
The
confidence
interval
(8 ? 1.3 males)/
SPECIAL CASES
100 femalescan be reportedwith>90% con6. Exampleto be usedforincreasesin thehy- fidence.
pothesizedratio.
Considerthe fawn:doe samplingproblem 8. Exampleto be usedforhypothesized
ratios
in Example 1, except that the hypothesized
above 100:100.
ratiois 100 fawns/100does.UsingthelastcolIf a ratioof 125 fawns/100does has been
umn of Table 1 we mustdrop to row 6 to
obtained (for the given herd under similar
achieve a precisionof ?8.0 fawns/100does.
conditions
in previousyears),we are againout
Hence in Fig. 1 we mustmove up to curve6
of therangeof Table 1. We recommendthat
and therequiredsamplesize corresponding
to
the manager use the last column (100:100)
N = 3,600 is approximately
n = 1,125.
when planningforsample sizes in thiscase.
The sample size mustincreasefromabout
Theoretically,
theroleofdoesand fawnscould
800 to about 1,100 in order to achieve the
be reversedto obtain80 does/100fawnsand
same precision(?8:100). This is a generalrethecolumnheaded 80:100 used to determine
sult.As the hypothesized
ratioincreased(left
sizes. However,most managerswill
sample
to rightin Table 1) the usermustdropdown
express
the
ratioas fawns:doe and the larger
in the table in orderto achievea fixedprecisizes
sample
suggestedby thelastcolumnare
sionand henceup in Fig. 1 to a largersample
recommended.
As an alternative,
themoreexsize.
act formulasin theappendixcan be used. We
125 fawns/100doesand suppose
hypothesized
7. Exampleto be usedforhypothesized
ratios
N = 2,000 is an upperbound on the number
below10:100.
of does and fawnspresent.For precisionof
Considera sample problemwherethe hy- ?8:100 and usingthecolumnheaded 100:100,
pothesizedratioofmales/females
is 5:100.Also curve 6 in Fig. 1 is suggested.This yieldsa
126
Wildl.Soc. Bull. 11(2) 1983
recommendedsamplesize of about900. Suppose the data are collectedwithn = 900 and
a ratioof 110 fawns/100does is computed.As
a trickto obtaina confidenceinterval,express
110 fawns/100does as 91 does/100fawns.Usbetween80:100
ing row 6 and interpolating
and 100:100,theprecisionis about ?7.3 does/
100 fawns (90% confidence)-or (91 ? 7.3
does)/100fawnswhichyields83.7 does/100
fawnsto98.3 does/100fawns.Theselastratios
convertback to 102 fawns/100does to 119
fawns/100does (90% confidence).The precisionis almost(110 ? 8 fawns)/100does.
CONCLUDINGREMARKS
Table 1 and Fig. 1 are presentedto allow
thesamplesize
whenestimating
interpolation
necessaryfora statedprecisionand hypothesizedratio(90% confidence).
Also,theycan be
used to allow interpolationwhen obtaining
approximate90% confidenceintervalsfor a
computedpopulationratio.
Figure2 containsour recommendation
for
minimumand maximumsamplesizesand the
levelofprecision.It is intended
corresponding
thatFig. 2 be used by fieldpersonnelduring
data collection.
Hypothesized
ratiosmustbe availableto use
the tablesand figures.Such valuesmay come
froma preliminarysample, prior data collected in the same area undersimilarcondiconsiderations
tions,theoretical
(e.g.,theratio
of male fawnsto femalefawnsmightbe assumedto be 100:100 forplanningpurposes),
themanager'sintuition,
etc.Clearlywithmore
precise input information,
adequate sample
size is estimatedwithmoreprecision.
The estimatedsamplesizesare notsensitive
to errorsin theestimatedpopulationsize. The
curvesin Figs. 1 and 2 are relativelyflatfor
populationsexceeding500 animals.
The requirementfor a random and unbiasedsamplingprocedureis difficult
to meet.
This is especiallytruewhen membersof the
classesoccupydifferent
segmentsof the hab-
itator whenmembersof 1 classare morevisible thanmembersof the otherdue to plumage, feedinghabits,tendencyto runin herds,
etc. It will testthe manager'sknowledgeto
overcomesuchproblemsand insureunbiased
data collectiontechniques.A secondproblem,
whichis not quite so serious,is thathidden
correlations
may be introducedintothe data
whenclusters(herds,all animalson a quadrat,
will not
etc.) are classified.These correlations
causebiasedratiosbutthestatedprecisionmay
be incorrect(too high or too low). No good
guidelinesexistin the literatureforthe solutionof thisproblem(in as faras the authors
are aware). If the precisionis betterthanthe
value claimed by the theorybehindthispaper, thenthe manageris conservative
and is
usinga samplesize largerthannecessary.In
the othercase, his sample size is not large
enough. We recommendthe methodology
presentedin this paper as a very general
guidelineforadequate samplesize whenever
the manageris confidentthat his sampling
procedureis unbiased.For studieswherethe
exactprecisionof theratiosmustbe known,a
professional
statistician,
knowledgeablein finitesamplingtheory,shouldbe consulted.A
variationof quadratsamplingor clustersamplingwill likelybe recommended.
SUMMARY
Adequate sample sizes are given for the
numberofanimalstobe classified
in a random
and unbiasedstudyforestimationof populationage and sex ratios.The desiredlevel of
precisionand confidence
can be specified.Advantagesof thisprocedureare: (1) the data
and precisionare summarizedin standard
forms(e.g., 40 ? 3 males/100females),(2)
the tablesand curvesare easy to use in the
field,(3) minimumand maximumsamplesizes
can be recommended,
and (4) the tablesand
curvescan be used in reverseto obtainapproximateconfidenceintervalson the estimatedpopulationratio.
WILDLIFE POPULATION RATIOS * Czaplewski et al.
Acknowledgement.-Thispaper was originally developed as PlanningReport6-A by
the PlanningSectionof the WyomingGame
and Fish Department,Cheyenne,WY 82002.
Now
Z
1-
(1 (1
A2
COCHRAN, W.
G. 1977. SamplingTechniques,3rd
ed. JohnWiley& Sons,New York.413pp.
Received26 July1982.
Accepted25 September
1982.
lOO(P - c)
=
(l 1P)
and
LITERATURE CITED
looP
-A
2
+
C(l
lOO(P + c)
(1
lO0c
p)2
-
(6)
-
P)
lOOP
(P+C)
-
(P -C)
lO~c
loom
P)2
1-
127
C(l
(l-P)
-
P)'
(7
For an approximatesymmetricprobabilityinterval on a:100, i.e., (A + B):100, take
=
APPENDIX
lO
loom
(8)
of N animalswhereP
population
Considera finite
valuebetween(A - A,) and (A2- A)
inthefirst
ofthepopulation an intermediate
category
is theproportion
in thesecondcate- inequations(6) and (7). Solvingequation(8) forc and
and Q = 1 - P is theproportion
ofanimalssampledwithout substituting
into(3) together
with(4), we obtain
gory.Let n be thenumber
and za, be the"2-tailed"valuefromthe
replacement
zZa2AN
For nP 2 5.0 and nQ - 5.0
normaldistribution.
.N
(9)
value
to10:100,theminimum
corresponding
(roughly
B2100(N
-1)
probability
in Table 1), a 100(1 a)%
inconsidered
tervalon p is givenby
(100 + A)2
Givenequation(9), therelationships
in Table 1 and
Figs.1 and2 weredevelopedbya computer
program.
Also,givena hypothetical
valueforA:100,thedecategory siredprecision?B, thepopulation
inthefirst
proportion
wherep is theobserved
size N and thede(Cochran1977:51).To have precisionof ?c forthis siredlevelofconfidence,
1 - a, (i.e.,za) theadequate
we can solve
interval
samplesizecan be computedby(9).
Finally,afterthedata are observedand A is estimatedbya, equation(8) can be written
in theform
(2)
c,
PQ\n(N-1)
p
+Z"
P(N-n)
n(N -l)
(1)
b
forn
Za(a
+ lOG0)
10
a(N -n)
n(N - 1)
0
Nz2PQ
to obtainan approximatesymmetric
100(1- a)%
confidence
interval
on a:100.
If the samplingis conducted"withreplacement"
to the formof thenequation can be
can be transformed
The proportions
usedwithN = oc.Dividing
(9)
ratios(a:100,[A ? B]:100,etc.)bythefor- thenumerator
population
anddenominator
by N, itis easytosee
mulas
thatequation(9) willconverge
to
looP
A
zaA(100 + A)2
100 + A'
(1-P)'
(11)
100B
100
loop
(4) Similarly,equation (10) convergesto
100+ A'
(Ic2(N - 1) + z2pQ
(3)
Giventhe probability
p ? c, the resulting
interval,
ona:100wouldbe from
interval
A1:100toA2:100where
100(P - c)
A
+ 100) V10
a/n.
9. Example for the use of equation (9).
1 - (P - c)
1-0(P + c)
b -zj(a
(5)
Supposethehypothesized
buck:doe ratiofora postseasonmuledeerherdclassification
is 30 bucks/100
128
Wildl.Soc. Bull. 11(2) 1983
does.We estimate
aboutN = 2,000bucksand doesin
the herd.For 95% confidence,
zo5= 1.96 and from
(9) theadequatesamplesizeforprecision
of?B ?3
bucks/100
doesis
n=
(
(1.96)2(30)(2,000)
[?3]2100[1,999] + (1.96)230
[100+ 30]2
230,496
[106.46 + 115.25]
=
1,040bucksand does.
10. Example for the use of equation (10).
Thereare 109 bucksand 402 does observedin an
unbiased,randomizedpreseasonantelopeclassifica-
tion.The herdratiois 109:402or27.1bucks/100
does.
Therefore,
a = 27.1, n = 109+ 402 = 511,and we estimatethataboutN = 2,000bucksanddoesareinthe
preseason
herd.If90%confidence
isdesired,
zl = 1.645
and fromequation(10)
1.645(27.1 + 100)
10
27.1(2,000 - 511)
511(1,999)
= 20.9(0.1988)
= 4.2.
Therefore,
thereis (approximately)
a 90%chancethat
thetrueherdratiofallsin theinterval
(27.1 ? 4.2 bucks)/100
does.
COYOTE PREDATION AVERSION WITH LITHIUM CHLORIDE:
MANAGEMENT IMPLICATIONS AND COMMENTS
RICHARD J. BURNS, U.S. Fish and Wildlife Service, Predator Ecology and Behavior Project,
Utah State University,UMC 52, Logan, UT 84322
Conditionedtaste aversionhas been proposed as a methodto detercoyotes(Canis latrans) frompreyingon sheep. The method
involvesplacing muttonbaits laced with a
strongemetic,lithiumchloride(LiCl), on the
range. Coyotessupposedlyfindand eat the
baits,becomeill,and subsequently
avoidsheep
because theyassociatethesheepwithsickness
et al. 1974,1976,Ellinset al. 1977).
(Gustavson
Attempts
also have been made to controlcoyote predationon turkeys(Meleagrisgallopavo) usingLiCl-laced turkeycarcasses(Ellins
and Catalano 1980).
Someinvestigations
priorto 1978castdoubt
on theeffectiveness
of usingLiCl baitsto deter coyotesfromkilling(predationaversion)
and,in a summary
paper,Griffiths
et al. (1978)
concludedthatno judgmentcouldyetbe made
regardingthevalueofLiCl in preventing
coyote predation.In thispaper I synthesizethe
literature
on thesubjectsince1978,discussthe
mostprobablemanagementimplication(assumingLiCl producedpredationaversionin
coyotes),
and pointout somepresentinformationneeds.
In defending
an earlierpublication,
Conoveret al. (1979) maintained
thatmoreresearchwasneededonpredation
aversion
with
LiCl, whereasGustavson
(1979)feltthatthe
existing
studiesdemonstrated
the successof
themethod.Cornelland Cornely(1979)believedthatLiCl fedtocoyotes
in a variety
of
foodsdiscouraged
potentially
dangerous
coyotesfromsoliciting
foodat a campground.
Burns(1980b)demonstrated
thatLiCl's salt
flavor
interfered
withtheability
ofcoyotes
to
formaversions
tobaitsandpreykilling.
Burns
and Connolly(1980) thenproduceda measurableblack-tailed
jack rabbit(Lepus californicus)
baitaversion
withlowdosesofLiCl
thatappearednotto provideflavorcues to
coyotes.
The baitaversion,
however,
wasnot
transferred
topredation
aversion;
coyotes
continuedto killjackrabbits.
Ellinsand Martin
(1981)laterfoundthatcoyotescoulddetect
LiCl and avoidbaitsat concentrations
below