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<br />G' 't'11 a nSll 0VU lI11U. u, ': "<"P F' 46 it will be seen tnat ~e '1'
<br />n. d referrll1!! to l~ure, th 'eraCTe hne
<br />Posterior (hameter, an '.' \:ith t.he absC'issa 300 at e a\ <',.0' '. '.
<br />l' .t 170 does n.ot rcnnode \ 1 1 . .ale is hr"er tlmn a\ era",e .,.
<br />ore 1I1a e. 't 1 (ther won s. tIP Sl .' ~ fi ar was.
<br />but lies]] unils ahoY(' I. 1~' ] " ,,'de at the end of the rst ye,.,
<br />f. '1]11'S len"lh of fish. ThE' SlZf of t U,., Sl, "'I'II'~]]\' lar!!e for the length ~f .~
<br />01 ..,. . t 'ClS pro1'01. l' ".' 1 . It""
<br />ao units and at that lmj(> I, "< s,'ah' sizl:' to the ('111'\"1' we J1l11st rc( ute ~~
<br />the fislJ. If we wnnt to appl:, till. . .~
<br />
<br />Fork Lengfh -Inches : ~
<br />9.0 11.0 13.0 150 170 19.0
<br />50 7.0
<br />
<br />
<br />zoo 300 400
<br />
<br />Standard Length - Millimeters b
<br />. and fish length for squa'\lV1\S
<br />Regressi~~ ~~~l~~mtc scale
<br />
<br />
<br />
<br />i i t
<br />
<br />. :
<br />
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<br />. .-- . --
<br />..---= = c::':'__ .~._c
<br />.~- :~~--~~- --~~-:-
<br />
<br />
<br />CIl
<br />-
<br />'c
<br />::> 20
<br />
<br />CD
<br />....
<br />'JJ
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<br />'j l !. i! ,i I: 1
<br />, :
<br />
<br />II i
<br />
<br />c:
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<br />
<br />Q)
<br />o
<br />u
<br />(f)
<br />
<br />': '.:.:.1= =~O::_
<br />
<br />~...--------.
<br />
<br />2..-,-.-
<br />
<br />, .
<br />. ,
<br />
<br />i
<br />, ,
<br />
<br />,
<br />I: .
<br />
<br />I . I
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<br />I ~ ;
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<br />
<br />II.
<br />
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<br />
<br />I '
<br />
<br />I I
<br />
<br />i'
<br />! ~ I I
<br />
<br />I"
<br />100
<br />
<br />FlGURE 47.
<br />
<br />
<br />. ;f~
<br />it
<br />~.
<br />
<br />
<br />;l.-h
<br />
<br />'f
<br />i
<br />{~
<br />-~~.
<br />I
<br />
<br />I: '
<br />\ II
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<br />
<br />500
<br />
<br />,'H. I...VJ...II..\..~ ..I.....JJ~Ul \JJ, l.IJt" JJ:,u a.t lJJt' Ulue 0:" ;ornlCill0n 01 tne tirst annulus.
<br />To aeC'omplish the transformation wit]JOnt ea!C:\J]ation the curve of
<br />Fi~ure .Hi hCls been dr:nm m1 a ]og-llrit ]nnie s('n]e in Figure .E. The effe(~t
<br />01' the logari1lunic scale is to g-iye equal proportional value ill units for
<br />"'!,1iI1 (listance ou the ordinates. l'sing- the c1nta of t]le lH'eyiollS illustra-
<br />lillJl ill Figure .J7, the ordinale J7f1lies J.;) nlln. ahow the awrage line at
<br />1 Ill' il],seissa 300. To ta]c-u]ate tl1f' ]eng-th nt thf' ell(l of the first year it is
<br />",,)y IIPcessilry to find the point oJl the an'I'i1;.!f' tlll'\"t' whieh is 1.5 mm,
<br />.Iirl'l'11.'- bel 0\\' the ordinate 30. This \Wllllc1 giw Cl leng-th at the ell(l of
<br />Iii., til'st yt'i1r for this fisll of 5f; mill, ?llellslll'(,Ill{'lI1s of this kiJlll can be
<br />.1"111' wry Ijlli(.k]y with dividers. The c/fed of the lo~arithllli(' seille is
<br />'',,,,,In'lIt if it is ll01('(1 that] .5Illm. aboye tIll' aY(,l'<Jg-e elll'ye at abs('issCl :{()()
<br />ill.liriltps all illtrease ill s('Clle size of H llllits. wJlilp al abscissa 58 it ilHli-
<br />,'att'~ illl illerease ill seale size of 2,5 units.
<br />.\pp]ying this tn)e of c-orrec:tion as.Sllmes that a seale that is ]ar~e
<br />at olle tilJle in the life of lhe fish is largt' at all times.
<br />To test this in the squClwfish, 21 s('ales 'rere taken from tlH' al'ea below
<br />Iii" tlol'sal of a four.."ear-o]d fish. EReh stale was mea';lln'c1 f(l!' the size at
<br />tll" ditf"ereJlt year mark" and for total sizt'o T]w (lata are slJO\\'n g-raphically
<br />1111 iI logarithmic- sc-ale in Fi~ure 48. This g-rClph demonstrates that., with
<br />. minor eXteptiolls, a scale which is small at the end of the first year is
<br />proportionally small throng-hout the fonr years.
<br />'1'0 test this method of cah.u]ation two collections of fish wei'e usell.
<br />'I'll(' fil'st collec-tion c-onsisted of 69 fish from Coyote Creek, near 1\Iadrone
<br />HI.jtl~e. Taken l\larch 7, 1927. These fish were'all completing their first
<br />.\('111'. ..:\8 has been shown prt'\'iously the :,'ear mark is formed during
<br />!\)al'cl!. The second collection consisted of fiij fish taken in the same plaee
<br />Fdll'llal'." 20, 1928. These fish were all eomp]eting tlleir second ~'ear,
<br />wllil'll would make them of the same year class as the fish of the first
<br />(..,JJ('ction. '
<br />Using- Figure 47 the lengths of this seeondlot at one year of age were
<br />,.ali-ulr.tec1. Two curves showing- the leng-th freql1ency of the two groups
<br />111 om. .'-ear of age are g-iyen in Fig-ure 49. The measures of central ten-
<br />dt'llt.it.s of the two groups are as follows:
<br />.lIp""
<br />';rulIp] ---------------____________ :)6.22
<br />Group 2 ----___uhhn_____ _____n 51.47
<br />
<br />.\1 etT;,m
<br />
<br />:1Iode
<br />flO.O
<br />50.0
<br />
<br />~3 .2fi
<br />(;2.12
<br />
<br />'n,. mean of group 1 is high beeause of a number of fish which were large
<br />j"" tJleir Clg-e. In fact, six of them 'were larger than any in a collection of
<br />7f; fis!, of the same year class, t<lken in the same place June 13, 1927, two
<br />IlIollths after group 1 was taken.
<br />Tn spite of the close corre$pondence of the medians it is still possible
<br />that tIle ealeu]ated lengths are too low. However, the difference is not
<br />hll':,!{' enough to affed greatly the yalue of the calculations.
<br />Using this method the lengths at preyious years were calculated for
<br />1111 fish oyer 1 veal' of a!!e from Coyote Cr{'ck and from the Sacramento-
<br />l-iillJ Joaquin at Pittsburg. '
<br />
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