Loading...
HomeMy WebLinkAboutSUS10044-j .- F,.sh ...trr Biology (1981 )11,361-·368 A desk study oftbe relationship between temperature and hatching time for the eggs of fivespecies of salmonid fishes D.T.CRISP Freshwater Biological Associaton,Teesdale Unit,England SUMMARY.Information on temperature (1"C)and time from fertilization ' to 50%hatch (D d ays)fo r five species of salmonid fishes has been used to assess several mathematical models relating D and T.No single equation gave the best fit to all five data se ts.The power law with temperature correction (a),log"D =log,oa +b log"(T -a)and the quadratic , Iog,oD =log "a+bT+b,T'(where a,b ,b ,and a a re constants),each ac- counted for over 97 %o f the variance of D and were good fits to the observed data points for all five s pecies .There was little difference between the predictions obtained from these two equations within t he range of observed temperatures .Therefore ,th e simpler power-law model is preferred. However. t here were s ubstantial within-species differences between val ues of D predicted from ex trapolations o fth e two model s from 2 or 3°e d own to O"C.When more data for low temperatures become a vailable it will be possible to make a more o bjective choice of model. Introduction Knowledge of the relationship between wat er temperature and hatching time for the eggs o f sa lmonid fishes would be ofconsiderable value in hatchery management.in the management o f field research projects concemed with th is part of the life history.and in giving insight into differences in the time of oviposition in different salmonid populations.The literature contains relatively few data on these relat ionships for sabnonids.Most of the publ ished in fo nnation is on North American species. Humpesch Ik Elliott (1980)briefly review models used to describe the relationship between hatching and temperature (7)for poikilothenns and conclude tha t the general Correspondence:D .T .C mp,Freshwater BiG- Jogjcal Associalion .Tecsdale Un it ,c/o Northumbrian WalCr Authority,lArtinJlon Tree tmenr Planr, Laning ton.Barnard Caslle.Co .D urham,E ngland . equation for a hyperbola and power law . D=a(T-a)'where Q .b and a are constants.if frequently an adequate empirical model.Several basic models were described by Hayes (1949)with special reference to salmonid fishes and a number of variants of these a nd other basic fonns are possible. However ,apan from a comprehensive analysis o f data for the chinook salmon [On<orh yndaus ISha"'Ytscha (Walbaum)} by Alderdice Ik Velsen (1978),there has been lillie attempt to evaluate the models b y comparing them with the a vailable data. In the present paper pub &Jlcd data for five sa lmonid species are considered in tennsofthree basic models and several variants thereof. Materials A s ummary of the so urces and nature of the data is -pv en in Table I.Embody (1934)gave results , t 0046-5070/81/08OlHl361 502 .00 ©1981 Blackwell Scientific Publicat ions d 362 D .T.Crisp TABLE I .A ,"umma ryoflhe VlUrcnand naturc oflhc five data sehU10Cd m the'.na l ~.An refer 10 lpJIfO.imate:ly comtanl temperatures .,.K the number of dal .pa irs Temperature .....("C}• Brown trout f S4Jlmo tr1dtfI L .) Brook lIout (SoIwli"",ftN1lUulliJ MildliD ) Rainbow t rout (S4lmo pint,.".Richan:bon) Chi nook sa lmon (Onrorlt yncluu uJutwybCha (WalblIum l) Atlantic salmon (SaImo Milu L.) Embody (1934) Embody (1934) Embody (1934) AIdcnfia:"V.....(1978) Pcle ....."01.(1977).Gun.... (19l9).Cond (l9l9) 1.89-11.24 29 1.64-14 .110 19 J.23-I5 .~2J 1.1\0-18 .10 'l7 2.«1-12.00 10 Mod.11 A pow er-law relationsh ip in two forms (la and Ib).Th e basic linear form is A p lot of D against T is a patabola ,i .e ., D =.1"A better fit can etten be obtained if a temperature correction factor (a)is incorporated (.'0"Mcl.aren,1963)in the basic:equation to give (Ia) (lb) log D ~b log T+log. log D -b log (T-a)+log. Throughout the followioS aa:oun..the in- dependent variabl.(tempetature .."C)is T.the dependent variable is D (-da)'l from fertilization toSO%hateh)or I /O (-tate of development).a is a temperature correction in -cand a.b and b. are constants.Throughout the tellt and bibles the .quatiom for Modeb I and 2 and the ir variants are given in their linear form unless the contrary is dearly indicated ;log refen to common logarithms with base 10,lln'refers to natural logarithm.(bale e). In the more specialized ....where b =-1.0 in the basic:equation. (Ia).the eurve isa hyperbola a nd a thennal su ms approach .in which hatch ing requires a constant number of degrce-days above a threshold temperature.is applicable (EUioll.1978).Th.applO",ial.linear fonn is then:(1/9 (Ie) for four saImonid species but his infonnation on lak.troul [$aMlinus namaycusn (Wafbawn)) eoesered of only seven dala pail>and was excluded from lhe present analysis.The bulk 0/ Embody'•.....tIS were obtained by lbal author tWnS .peeially design«!flowing-water lanks to givc constant temperatures.A few of his results were obtained from outside sources.He fined exponenlial eurves (see Model 2 below) to his result'and found that for some species two or more intersecting curves had to be fined to COY.:r the observed temperature range AId.rdice &.V.ken (1978)based their analysis on a large collection of data from a vari.ty of published and unpublished sources . They examined information on several On- corhynchw species b It concluded that adequate data for analysis Wf :re available only for the chinook salm on .They examined a variety of models and assumed a single unbroken relationship between temperature and incubation time over the whole range of observed temperatures.The present anal ysis concentrates mainly on their data for constant temperatures. Published infonnation on the relatiomhipl between hatching and temperature for the Atlantic Wmon appears 10 be sparse and scattered.Catrick (1979 )stared that British laImon .88'kept at 4"C gave SO%halcb in lIS days ,whibt Gunnel (1979)gave SO%ba teh lima for Norwegian material at 8 .10 and 12"C. Petersoe ,Spinney &.Sreedharan (1977) exam ined temperature relatiomhips of Canadian Atlantic salmon eggo .From the ir publish<d figuteS a nd tab...i. is pmSI'bIe to obtain six data pai..for COll$l2tlt temperatum;. The Atlantic Wmon hal been included in the analysis on th e basis of thole few resaIIS .ehiefly for the ..ke of conplete ness . .'I '.,·.·.,:. .•I' '.Ir.! !:i ;.., •0 o · j! "• Eggs 0/fiy~salmonids 363 The theoretical development threshold temperature is -alb and the required thermal sumabove this temperature is lib . int ersection was detennined by an iterative process,The results of fining two intersecting lines are not given in the tables but references to them a re made in the text . Mod,/2 An exponential relationship in linear form :Results was used by Bottrell (1975)for ,''''egg;of Oadoc:craand Copepoda .The semi-logarithmic version (d.,Model 2): Polynomial expressions which arc extensi ons of Models I and 2.The simple quadratic (d.• Modella): IogD =loga+blog T +b,(1og T)'(3a) All of the equations la.b,2 and 3b are I reasonably good fitto the data.in that allof them account for 94%or more of the variance of D in its regression on T~for each species (Table 2).10 eqn 1a all of the values of b were significantly different from -1.0,at the 95%confidence level . so eqn lc is inappropriate for these data sets and has not been used. The two best -fitting e quations for all species are lb and 3b which account for over91o/c of the variance of D for each species.For all species except the brook trout the best fit is given by eqn 3b but the fi t for th is model is only marginally better than that given by eqns 2 and Ib for brown tr out o r cqn lb for the-other species (Table 3). If eqes la and 2 are fitted as two intersecting lines. then cqn la for brook trout and cqn 2 for rainbow trout give rather smaller values of the sum of squares of differences between observed and predicted values than does the quadratic expression (1131.3 and 70.5,respectively]but the improvement is small and,for this reason . the complication of using two calculated regressions has been avoided . Mean values of D predicted from eqns lb and 3b are shown in Table 4 .For each species the predictions cover the range of observed temperatures.together with extrapolated values down to OOC .For brown trout .the two sets of predictions differ by less than 0 .5 days throughout the observed temperature range and they differ by only 2 .1 days when extrapolated to <re.For the remaining species the two sets of predictions differ by 2 .S days or less over most of the observed temperature range,though dis- crepancies of up to 4 days occur at the upper end of the temperature range for brook trout and chinook salmon.However ~for all species except the brown trout there are discrepancies of up to 29 days between the predicted values of 0 at O"C . For reasons which willbe diSCU5SCd more fully below,eqn Ib has been preferred and the raw data points and calculated regressions are shown in Fig. I;to assist calculation.the subtotals from (3b) (2) log D =log a+bT+b,T' was used by Colby '"Brooke (1m)for egg;of lake hening and by Sarvala (1979) for t he egg;o f Copepoda.Equation 3b has been examined in the present paper. Equations la ~b~2 and 3b were fined to the data points for each sabnonid species and goodness- of·fit was assessed by inspection of plotted data points and calculated regression lines and by comparison of values of the coefficient of detennination (r)and the sums of squares of differences between observed and predicted values of D.The latter was the most sensitive method of ass:ment. Values of the temperature correction (a)for eqn lb were estimated to the nearest O.5OC by an iterative process.Changes of :OS'C :'l the value of e had negligible effect on the calculated reBJCSSions. Where plots of data points (after appropriate transformation)for Models la and 2 suggested that a single straight line was an inadequate representation of the relationsh ip.then two straight lines were fined and their point of Ib D =bT+ln a Mod,13 I 1, • ,, 3M D.T.Crisp TARLE 2 .C a lcu lated valuc'fur comlanls.a .log II (or In II for eq n 2 ).h :lntl hi in eq ns la .lb.2 a nd 3b ;"is the n umber of d ata pairs.,2is Ihe rocffic;ienl of detrrmi nalion Equation Species •,.1og.'95%CL h95%CL aorb, I.B rown tr out 2'l 0 .941 2.4\lOY .0 .0538 -0 .8385'0.0778 I .Brook t rout 39 0 .948 2.4812 '0.052.-0 .82Sh O.0646 I.R ainbow trout 2J 0.978 2.6638.0.0733 -1.1 623'0.0765 I.Chinook salmon 57 0 .975 2.6310'0.0399 -O.92J I .O.()lQ) I.At lantic sa lmon 10 0 .97.2.5925 %0.0996 -0 .9070.0.116 1 Ib Brown !rout 2'l 0 .992 28 .8392 %0 .9206 -13.9306%0.4769 -11I.0 Ib Brook t ro u t 39 0.989 19.6 7651:0.6224 -9 .5948%0 .33 18 -65.0 Ib Rainbow trout 2J 0 .982 4 .0313 :t0.1496 - 2.0961%0.1268 -6.0 a Ib Chinook salmon 57 0 .992 3 .9166%0.0.521 -1.8120.0.003 -6 .0 Ib Atla nt ic sa lmon 10 0 .996 5 .1908 '0.1561 -2.6562:t 0.1235 -11.0 2 Brown trout 2'l 0 .992 5.3J07 '0.OJ35 -0.1613'0.00S6 2 Brook t rout 39 0 .987 5 .2 106 .0.0415 -0.1315 ::t O.OO5O 2 R ainbow troul 2J 0.960 4.Q02J '0.12J7 -O.l 384:!:O.OI2$ 2 Ch inook sa lmon 57 0.956 5.2'>5 1'0 .0786 -0.1236.0.0071 2 Atlantic salmon 10 0.994 5 .3526'0.0768 -O.14n:!:O.0093 3b Brown tro ut 29 0.092 2 .3236 -0.07J6 0.00028 3h B rook tr out 39 0.991 2.3147 -0 .0757 0.00116 3h Rainhow trout 2J O.Q76 L I·ns -C.II 2J 0.00278 b l 3h Ch inook salmon 57 0 .996 2.4769 -0.1002 0.00248 3h Atlantic salmon 10 0 .998 2.3921 -O.08n 0.00166 T ABLE 3 .Sums of squares o f d ifferences betwe en observed a nd predicted values of D fo r t be fourmain model equations considered in this paper Model I. Ib 2 3b Species B rown t rout 3953.0 939.8 8-19 .1 8-12 .6 Br ook troet l1llSl.7 1416.8 1469 .9 1533 .2 R ainbow tr out 412.0 102.0 416.4 89.6 Chi nook sa lmon 10834.6 388.3 5611).3 162 .7 Atla ntic sa lmon nS .3 66.9 127 .7 58.6 b th e r egression are give n i n th e Appendix.Ifdai ly values of IOO/D.based on daily mean tem- peratures t a ken from t he d ay o f ferti lization . a re s u mmed.the n t he total will reach 100 on t he p redict ed d ay o f SOCk hatch . Additlon.1 sourees ol ••riation The literature refers to a number of possible causes o f variation in incubation ti me .addi tiona l t o m ean incubation temperature .In several instancestheauthors givesomeindication of the a mou nt o f va r iatio n a rising .The following fo ur major causes have be en identified . Variation in hatching time (DJ MlW nn qgJ from asingle individual H atching w ithi n ba tches m ay co ver 3-4 d ays in h igh temperatures a nd 15-20 da ys in low tern- EKJ:_f "I fH'r s"lmm,ids 36S TABL E 01 .Mean valun o f 0 cakulareJ from c-q'"IbandJh.Valu(,!i besed o n (u,apolalion,below lhe obse rved te mperature range arc markrd • Brown lroul T("C)Ib Chinook u lrnon A llanlic u,lmon o I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 3 212.8 •210.7 179.0 •177.9 ISO .9 ISO .5 127.4 m.4 107.9 108 .1 91.5 91.7 77.7 78.0 66.1 66.4 56.4 56.6 48.2 48.3 41.3 41.3 35 .4 35.3 Brook troul Rainbo",'trout Ib 3 Ib 3 191.4 206.4 251.3 •222.6 165 .3 173 .8 181.9 173 .0 143 .1 147 .2 137 .5 •136.2 12·1.1 12:'i .J 1Il7 ."108 .5 107.9 107.3 AA .I 87 .7 94.0 92.3 m .l 71.7 ll20 79.8 58."59.4 71.7 69.4 49.7 49.8 62.8 60.7 42.6 42.8 55 .2 53.4 36.8 36.5 48.5 47.2 32.2 31.8 42.7 "1.9 28.3 28.1 37 .7 37.4 25.1 25.1 33 .3 33.6 22.4 22.8 29.5 30.4 20.1 20.9 26.1 27.6 18.2 19 .4 Ib 320.7 • 2"2.S • 190.4 1 ~3 .S 127.1 106 .9 91.3 79.0 69.0 60.9 54.2 48.6 43.8 39.7 36.2 33.1 30.4 28.1 26 0 3 2'19 .8 239 .4 193.4 I ~.O 130 .6 109 .1 92.3 78.9 68.2 59.7 52.8 47.3 4 2 .8 39.2 36.3 34.0 32.3 30.9 30 0 Ib 3 265.9 246.7 211 .0 202.3 Im.6 167 .2 140 .1 1J9.3 11M 116 .9 98.3 98.9 83.7 84.3 71.9 72.4 62.3 62.6 50 54.6 47.7 48.0 42.2 42.5 37.5 37.9 Q 0 ,'"0'0 ,o "0 ,'""~ ! "Sl 300-CI\OInooII wttnOll•I 4I1o""c \0'_ ~zoo-\..'..,• 000-.,-'....'....,--........-----. 0 I I I I I 0 ,'""0 ,00 200-8_'"""e.ooll traul -R(ltf'bow troul KJO-~..-..,~-.,,.........~,,-.... ~..-.........-......--j T T ,I I r T~o lut••T r'tl FlG .1.Observed datapoints fo r fivesalmontd species e nd Modcllb regression lines plotted on arithmet icscalts. peratu res.This represe nts ~10 %of theobse rved mean fo r rainbow trou t over the5.7-17 .6°C range .(Embody,1934). between eggs from diffe rent strains o f the same s pecies it ca n be ~4 .3%o f th e mean (Embody . 1934 ). VQriaJio n in D ~tn eggs fr om differenl f·mtdn.£/lu IS01 temperature fluctuation In females of the same s t rain .variatio n in hatching time can be :!:2.3%o f the mean and 24 Fo r chinook sa lmon tggs be low 6-7"C . deve lopmental ve locity seems slower at cons tant I I "·. !!·n·.,·"•:I :i i."·. •iI: :~ JM D .T.C,iJp th an at ambient t empera tures (Aktcrc.l icc &: Ve lsen ,1978). Changa of temperature C'fNffiC;~"'within 1M ob served rQn g~o/trmIW ,alurn Gray (\928)suggested t haI c mbryooK: development a nd hat c hing is a com plel o f different p rocesses .all o f which may have different temperature rela t ionship!'.The fitting of a single line or ev en two o r mor e lines is, t herefo re .an oversimplificat ion .In p articular . Gray d istinguished two major processes ,namely embryonic developmen t and ha tching .He s tated that the latte r h ad a much higher tem perature coefficient t han the former a nd th a t the [',\0"0 processes a rc .10 so me extent ,inde pendent.This probably exp lains th e o bse rvatio n by E mbody (1934)t hat fo r la ke trout eggs t he incuba tion t ime was reduced (below the ex pected va lue )for o ne b al ch o f eggs wh ich was allowed to develop .u nt il wcll-eyed an d then p lunged ir.hl water 8"C Thus ,vari atio n in incubation t:mc o f at lea ~10%o f the mean can occu r wit hin a ..reeies a nd furth e r variation rna)'be ca used 1'1)'the liner de tail o f temperature fluctuatio n d uring incu - b ation .Th erefore .the calc ula ted regres - s io ns in th is p aper ca nno t give more th a n an a p ~~~tim_~!t o f incubatio n t ime . Discu$5ion G ray's (19"...8)co mments (!iC C abo ve}on t he complexity of the de velo pment a nd ha tching p rocess im p ly t ha t tbe fitting o f t wo o r mo re inte rsecting lines to a ny given da ta set may be b iological!)rea son able .I n [\'0 instances , namely eqn l a (or br ook tr ou t a nd eq n 2 for ra inbow tro ut .th e use o f two in tersecting lines gives th e best fit but th e su ms o f squ ares of observed min us expected values a re o nly mar- ginally 1es.s th a n t he va lues o btained hy use o f eqns Ib o r 3b a nd th is d iffe rence i!'t oo srnall to justify th e more complex p roc edure . Th e two be st equatio ns (or general ap plication to all o f th e fin species co nsidered a rc the pow er -law relat ionsh ip (wit h te mpera ture correcti on ) [e qn Ib) a nd th e q uadrat ic e x- pr e s.l;io!1 rel ating log D a nd T(eqn ;1'1).Th e latt e r gives marginall y t he be tter fi t ror Iour o f the speces b ut it is more com plex to a.lculale and ib t heo ret ical a pplicatio n to biological proccssn can be qu estioned (Hum pc:sch 8<E1l ion .1980). The pr cdictiom givcn by the5c two equations a re similar o r ide n tical ove r most of the observed temperature range for each spccin (Table 4)so th at eqn Ib m ight be preferred as the more s imple o ne fo r practical usc. Ex trapolation o f (J"C gives more substantiAlI d iffere nces (sev eral weeks for some species) between Ill<,p rcdK:liom given by lbe two e quatio ns ,Ald erdice 8<Velscn (\978)noled t~ sca rcity of data po ints below a1>out3.6'C for th<i ch in ook sa lmon .A s imilar paucity of data at ttwi lower end of the temperature range is apparen ~ for the o ther four species (Tabl e t ,Fig .I).The acquisition o f more data at these lower tcmpera..\ t ures would permit a more meaningful choice of m odel e quation .Despite this p roblem a nd t he fact tha t e xtrapolation beyond the range of I observed data po ints is sratist ically unsound, some e xtrarolatien into the o-TC range may be necessary in or der to obtain a 'best available . estima te'.beca use in many of the areu where salm onid fishes s pawn ,wa ter tempera tures may be be low J"C fo r a su bsta ntial p roport ion of the incubat ion pe riod .In these circu mstances most o f th e de velopme nt will occur du ring the higher I temper atures o f autumn and spring.Rel ative to \ th ese ,wint er tem peratures in the range o-J-c will give low values of IOO/D and errors in pr ediction of th ese will make only a sm,." .diffe re nce t u predicted hat ching dal es.It is important to note th at pan of the cxtrapolation down to O"{:may be rendered redundant by the lower th ermal d eath po int.though the value of t his is un known wit h a ny precision for any o fthe I species considered. A lderd ice 8<vetse n (\978)e xam ined cbt a for chi nook sa lmon e ggs at bo rh cons tan t a nd ambient te mperat ures and stat ed tha t below \ 6-7'C deve lopme ntal vclocity see ms 'lower at c o ns ta nt t han a t ambien t tempera tures .Separate I model I b regressions for cons ta n t and a mbient I temperatures .calcula ted from Alderd ice &./ Velsen 's da ta .do predict mo re rap id de velop-f men t at amb ient th a n at cons tant tem pe ratur es.f For e xa mple.D -106.9 (97 .5-117 .2)cb y.at constant 5°C and D -98.3 (9 1.0-106.2)da ys al ambient temperatures avenging SOC .Sim ilarly, for J"C.D =\5 3.8 (140 .1-\68.9)d ays a t co nstant and 146.1 (135 .1-\58 .0)cb)"l al embi ent tem - pcratures. t _ p Alderdice D.F.&Vel srn F.P .J .(197H)Relation between temperature and incu hc t ion t ime (or e w (Man UJCriplacupl~J I flJul )'I980J £ggsof fi"" sa!monids 367 of Chinook sal mon (O ff€O rlry"cluu tslurw)"ndt.,. JOUTnGI o f IN FUMrln R'JtYlrcli 804Irdo f CillIDdd . 35,69-75. Bottrell H H.(191')The relatioMhip between temperature and du ration o f ea dc:\lClopment in so me epiphytic:a.docera a nd Copepoda from the R ivrr "Thamc'.R ~a din g.with a d i!ocu,~ion o r temper ature funct ions.fHcolugitJ (& ,/i" ,••1.63- 84. Carrick T.R.(1919) The effed of acid water on the hatching of salmonid elP.Jou'N1lol F"uIr Biology . 14.1M-172. Colby P .I ."emote L .T .(1m)Effects of temperature on embryonic development o f Lake Herring (C~ffu.J QnMii}.JounuJ of ,II, FuMrinRaNrcli /JoQ,doluIIl2M.lO.799-810. Ell iott J .M.(1978)Effect of temperature on the halchin,of cgp of Eplwm,rt'l14 igffiltJ (Poda) (Ephcmeroptera:Ephcmerellidac).F,nJi:fto'tU" Biof~.'.51-l8 . E mbody.a .c.(1934)Relation of temperature to the incubation pcriexh o f eIP o f four specin of trout . Trrlfuoetions of ,h,A m"icQff FIJIr,rirt Soci ny.64. 281 -292. Gray J .(1928)The growth o f lBh:III.The effects o f temperature o n the de vetopmcnt of esgs of S4lmo lario .British l oumu l 01 up'rimmJaJ Biology.6. IIlH24. G unnes K.(1919 )Su rvival and de velopment o f Allanite salmon eras a nd fry a l th ree diffc fC'nt temperatures .A qWJOJ,.,J".16.211 -218. Ha)'CS F .R .(1949)"The grow th.general chemistry ,and temperature re taticns o f salmonid cggs .QWIf1,rly R~'itw ol Biolo KY .24.28 1-Xll. Humpcsch U.H .&;EIHo tt J .M.(1980)Effect o f temperature on the hat ching time:o f eggs o f three Rlli,lIrog,ntJ s pp .(F.phcmcroptera)from Austrian st reams and an En glish stream a nd river .Jou,tull of Animal Ecolog)'.49.643-661 . Mclaren I.A .(1963)Effect s o f temperature on growth of zooplank ton a nd the adaptive value of vcnicaJ migration .}ou,tuII 01 UrI F"iSMrin RnltJr€1r Boo,d of CQMJa.2O .68S-721. Peterson R .H.• Sp inney H .C.E .&c.Srcedharan A. (1977)Developmenl of Allantic:sal mon (SDImo tiJIDr}eIP and alevim under va ried temperemre ~gimcl.J oumm nl ,lr,F"ulr,rin Rnnucll Bod,d of CalUJdD .Joe.3 1-43 . Sa rval.J .(191'9 )Effcct o f temperature on the duration of eg.naupliW'and copepoditc development o f some freshw ater bentbjc Copepoda.Frnlrtt'tJl"Biology.9 .SIS-S34.The author is indebted to Mn S .Robson for her assistance with the calculations and to Mn D . Jones who typed the manuscript. 1 .le predicted values at ambient temperatures generally rail within the 95 %oonfidcna: envelope of the predicted values at constant temperatures and an appreciable proportion of the d ifference between values predicted from the regressions for co nsta nt and a mbient tcm - pcnturcs can be accounted for in term s of the properties of the constant-temperature regres- sian alone. For example.the constant-temperature regression (Table 2) can be used 10 show that chinook salmon eggs will have 50%balCh in 106.9 (97 .S-1I7.2)days al rons'anl SOC or in 104.0 days when a mean temperature o f see is achieved by means of alternate daY'a'2.5 and 7SC.This difference 0'2 .9 days is equivalent 10 33%of the difference between the means for predictions for S·C from the two separate regressions. More data on hatching times at low water temperatures are needed (or salmonid fishes .If these could be obtained and used in conjunction with dctcnninations of 'lower t he nnal death point 'or some morc biologically me aningful assessment of the relationship between \ temperature and mortality rate,then a more objective choice of model equation could be made.However.in the present s tate of ,knowledge.the power-law relationship.with temperature correction is a good fit to the \ observed points and is a relatively simple model. Humpesch &Elliott (1980)point cut that the power law appears to be an adequate one for egg development in a wide range of aquatic -Dimals. They also state that it can be used only as an - empirical model and th is is also true for the:other models examined in the present paper. - i I :r )... .-... ::~,'~...r I (, .,..t i• 368 D. T.Crisp APPENDIX .Infonnalioo required for calcul ~rion o f confidence bmirs for n lun of D ~M:tcd from equation Ib Brown trout Brooktrout Rainbow trout ChinooK salmon A tlantic salmon U SS.97li074 72.4:12121 27.052710 68.222792 12.61l1OOO 1:<'Ill8.OS'.346 134.S51lOOS 32.003942 82.470286 IS.98S07S I I S6.SSSSOO 72.4Ool4OO 36.016S00 99 .S84400 18.3'JOOOO ~r 111.623291 136.829112 S7.223<6S 176 .682217 34.252103 Ul lOll .lJ692.ol;134.224672 41.976626 117 .7143S48 23.00893 a -Sl.O -6S.0 -6.0 -6 .0 -11.0 •29 39 23 S7 10