ML20148H482
| ML20148H482 | |
| Person / Time | |
|---|---|
| Site: | Indian Point  |
| Issue date: | 11/13/1980 |
| From: | Barnthouse L, Van Winkle W OAK RIDGE NATIONAL LABORATORY |
| To: | Reed P NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| References | |
| CON-FIN-B-0423, CON-FIN-B-423 NUDOCS 8011180729 | |
| Download: ML20148H482 (85) | |
Text
{{#Wiki_filter:....1. .. i i - l r INTERIM REPORT Accession No. Contractor's Report No. Contract Program or Project
Title:
Hudson' River White Perch i Subject. of this Document : Quarter 1v Progress Report Type of Document: Interim Contractor Report Author (s): Webster hn Winkle, Lawrence W. Barnthouse Date of Document: Responsible NRC Individual and NRC Office or Division: _ Phillip R. Reed, Environmental Effects Research Branch, Division of Safeguards, Fuel Cycle and Environmental Research , Office of Nuclear Regulatory Research
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This documnt was prepared primarily for preliminary or intemal use. It has not received full review and appmval. Since there inay be substantive changes, this document should not be considered final. ,
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. Prepared for U.S. Nuclear Regulatory Comission h $ '
Washington,,D.C. 20555 -[ r ' h NRC FIN No. B0423 ' B f THIS DOCUMENT CONTAINS NRC Research and Technice'! i h POOR QUAUTY PAGES , n
. Ass!s4ance neport.
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M'(- m' s. s e, ..-_ . l t QUARTERLY PROGRESS REPORT FOR PERIOD
' April 1 through June 30, 1980 l ENVIRONMENTAL SCIENCES DIVISION, 0AK RIDGE NATIONAL LABORATORY PROJECT-(189No.): B0423 - Hudson River White' Perch
-PERSON IN CHARGE: Webster Van Winkle PRINCIPAL SCIENTIST: Lawrence W. Barnthouse TECHNICAL OBJECTIVES: To complete the topical reports on estimating and evaluating collection rates and conditional mortality rates due to impingement of white perch at the Indian Point Nuclear Station cnd the other power plants on the Hudson River. To col';ct, compile, and analyze data on white perch entrainment losses and density-dependent growth. To review data and information on white perch ,
from other water bodies. To document in a second topical report the results of the new analyses and to make a determination whether the combined entrainment and impingement losses may have an adverse , impact on the Hudson River white perch population. STATUS OF SUBTASKS: Work on all subtasks is proceeding on schedule. MAJOR ACCOMPLISHMENTS: , A. Direct Impact of Impingemert on the Hudson Rive _r, White Perch Population Except for publication of results in the Final Report, all work on this subtask has now been completed. Our analysis showed that the ' impact on the Indian Point Nuclear Station on the Hudson River white perch population is greater than the combined impacts of.the Bowline, ; Lovett, Roseton, Danskamer, and Albany plants. Most of this impact ! occurs during the months of December through April. ! These results were presented at the Fifth National Workshop on Entrain- ! ment and Impingement, San Francisco, May 5-7, 1980. A manuscript will be published in the workshop proceedings. A copy of this manuscript , was attached to the Quarterly Report for the period January 1 through ; March 31, 1980. B. Analysie of White Perch Impingement Rates , The manustript entitled "An evalt.ation of impingement rate as an index of year-class strength" will not be pursued further. Van Winkle r discussed the current draft of the manuscript with R. Klauda of Texas : Instruments (TI) in May. In light of TI's most recent analyses in-cluding 197?.1979 data, .Klauda expressed serious reservations con- . cerning the assumption that year-class strength ,fon wh te pe ch is l NRC Resead ano lecW : [k,gsistance R0p0ft l
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. fixed by:early fall of' their first year.'. The' results of the addi- L; i
-tional analvses performed by.0RNL since publication of- ORNL/NUREG/
TM-361 will be included in.the Final Report foc.the white perch
' project, but.the results 'do not merit publicatica in the open litera- .&
ture.
.The manuscript entitled "An analysis of the-minimum detectable re-duction.in_ year-class strength.of.the Hudson River white perch popu-
<1ation based on impingement rate data" is still ~ being- revised Lfor review. .A; copy of the current draft is' attached. ,
' C .' Multispecies Effects lFour models have now been examined.using loop analysis:
1.,. A' 3-compartment food chain consisting of detritus, macroinver-tebrates, and white perch.
- 2. - A 4-compartment model in which another fish competes with white perch.
- 3. .A 4-compartment model in which another fish preys on white ;
-perch.
- 4. A 5-compartment model that includes both a competitor and a predator.
It appears from these analyses that the long-term effects of power pla d on the Hudson River white perch population may be strongly influenced by
. interactions between white perch and ~other species. Two particularly .
.inte esting implications are:
- 1. - Indirect impacts caused by'entrainment _of prey organisms (macroinvertebrates) can be more important that the direct effects of entrainment and impingement on white perch. ,
- 2. Adding a competitor ~to the basic three-compartment model markedly changes the response of the white perch population to power plant mortality, but adding a predator does not.
PUBLICATIONS, PRESENTATIONS, AND MEETINGS: Publications: Barnthouse, L. W., B. L. Kirk, K. D. Kumar, W. Van Winkle, and D. S. Vaughan. 1980.. Methods to Assess Impacts on Hudson River White Perch: Report.
-for the Period 0ctober 1, 1978 to September 30, 1979. NUREG/CR-1242, Oak Ridge National Laboratory, Oak Ridge, Tennessee, i Van Winkle, W.,; L. W.- Barnthouse, B. L. Kirk, and D. S. Vaughan. 1980. ~
- Evaluation of Impingement Losses of White Perch at the Indian Point
. Nuclear Station and Other Hudson River Power Plants. NUREG/CR-1100,
,0ak Ridge National Laboratory, Oak Ridge, Tennessee. _.
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l Presentations: Barnthouse,l.. W. The Direct Impact of Impingement on the' Hudson River White:P!rch Population. Presented at,:the Fi#th National Workshop , on Entrainment and Impingement, San Francisco, May.5-7, 1980. Meetings: L. W.'Barnthouse and W. Van Winkle represented EPA, Region II in two
. - meetings with representatives of the Hudson River utilities, the-State of New York, the Natural Resources Defense Council, and the Hudson River Fishermans' Association. The purpose of these meetings, held in Pearl River, New York, on April 22-24 and May 21-22, 1980, was to. discuss an out-of.-court settlement of the Hudson River Power Case. ORNL's participation was funded by EPA.
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l 1AN ANAlisis Ji ;nt i,. ;i;Jd DEiECTABLE REDUCTION IfLYEAR-CLASS 1 STRENGTH,OF TkC EUDSON RIVER WHITE PERCH POPULAT10N ,2 W; Van' Winkle, D. S. Vaughan, L. W. Barnthouse, and B. L. Kirk j Environmental Sciences Division . Oak Ridge National Laboratory Oak Ridge, Tennessee 37830 , v
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i Research sponsored by the- U.S. Nuclear Regulatory Ccomission, Office of Nuclear Regulatory Research, under Interagency Agreement DOE 40-550-75 with the U.S. Department of Energy, under contract W-7405-eng-26 with < Union Carbide Corporation. 1
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t l Rc t ., e t Van Winkle, W. , D. S. Vaughan, L. d. Barnthouse, and_ B. L. Kirk. 198_. An analysis ofL the minimum'detec table redection in year-class - strength-of the Hudson RiverLwhita perch population. J. Fish. . Res. Board Can. Relative abundance data for young-of-the-year. white perch in the
' Hudson River are anlayzed to address -two questions: (1) assuming a specified number of years of additional data, what is the minimum detectable fractional reduction in year-class strength which can be detected, and (2) assuming a specified fractional reduction in year-class strength, how many additional years of impingement data are required? Our results indicate that the variability in the baseline data is so cret that 10 more years of data are not adequate for detecting even substantial reductions in year-class strength and that more than 50 years of data would be required to detect an actual 50% reductica in year-class strength, given a Type II error of 50%. The generic applicability of the methodology for establishing bounds on reductions in fish stocks and number of additieral years of data required to detect such reductions is discussed.
1
sq. . 4 1 Ir.tr ' liiua ' I l Fisheries 1 managers and other d2:ision aakers frequently mast decide
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whether there .may be a reduction in' tne' size of. a fish ' stock or in the - _ strength iof year .' classes subsequentL tc the imposition' of: some- ne.( or
.i additional-impact on .the population. Although'it may not be possible !
to address the problem directly with the degree of certainty. desirable, it'is possible to estimate what reductions might be expected independently
. of. new or additional impacts using standard statistical techniques.if an historical time series of stock sizes or year-class strengths is available.
Then a paragrpah on.the Hudson River white ~ perch population. Why of.importance. What we have already done. We concluded, based on regression analyses of impingement rate of young-of-the-year whita perch on year, that.there has been no statistically significant change in year-class s:rength during the period 1972 through 1977. Given this situation we. can use impingement rates for 1972 through 1977 as baseline
' data to-provide a measure of " natural" variability in year-class strength.
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- (1) Based on a gi,en nurt.ber of years 'of additional impingement data, what is ' the minimum detectable. fractional reduction in' year-class strength 'of white perch in the' Hudson River which we can' hope to detectp(2)' Given that' we want to -be able to ,
detect a specified fractional reduction in year-cl' ass. strength ef--+:h+te-pena-4n- the ':etan Ri.= (e.g. .. say a 25 or'50% . reduction), how many additional years of impingement data are required? Obviously these two questions are related in that for the first question fractional reduction is the dependent variable and number of
;. w cwe 4. m.e ~C additional years of, data is# the independent variable, whereas for the second' question the two variables are reversed. However, the two questions merit separate answers because they represent different '
m a. m e.m a.,9 mp points :f vie On monitoring the Hudson River white perch population in
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years to come. ( f
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I-n--pmerc1,. to stud 9 the rcle. tie.nsh ip be.c..ar 1.he :n er n" sua. i 3ti ;si te,t ar.d tha siz.p . s ize., it is firc.t e:assacy to specify the null and. alternative hypote eses. Our null hypothesis is that there t s is no difference between the underlying means of. two samples,',i.e., Ho: ul " #2 (1) . where p1 is the t%4Hy mean inde:i of year-class strength for- . p r u a r- to I??8 young-of-the-year white perch in the Hudson River duMng--the-per.iod. , 1973 - thr=gh- 1977, and p is the e4e%mean inhf year-class 2 ' o.a ht -<.v . y ws . strength for the-peMef-seantimy1978 g The set of alternative hypotheses is:'that-the =dcrlyMg m=_# +he--seeond-samp-le-{q)--is- .
-1ess-tlian the-underlying- mean of.-thenf.irst sample-(pp):;=iver, H'
A M1>M2 - (2)- Inotherworks,H is one-tailed and includes those cases where there A is a. re-:icn in .the rirly' ; mean ir.dsa f year-class strength for m.L laa., ywr .s. p e s.'o r b 19 "? s. the perihd starting 1978, relative to that f.or the period 4974thr-ough-M7-7-:-
- If we assume an underlying normal distribution for each of the two
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samples, as well as a common underlying variance, then the appropriate test statistic for the difference between the two means is given by t= X1-X2 , (3) s p - 1
+1 l "1 "2 l l
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. - . ne ue s*=. ,
.se v s vu ...es-se n* s: * > > r:*u* f
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,, _ b .}* L _ _ _ __
a: ; , i4 3 .- UmL/i?Ji'.CGih551-where X7 Lanf */;. nrc- t'* samle eci.a , of the first and second s upl es , r..c;si:. t ' c'. , , ay ane c.3 are ti.a sacple sizes (i.e., number of ' years, since only one index of. year-class strength is obtained each year) of the first' and second samples, respectively; and s p is the pooled standard deviation such that s 2=("1-1)sf+(n2-1)sf p
(4) n1 + n2-2 _ ,,
where s2 and s 22 are the sample variances of the first and second samples, respectively. -This test statistic is distributed as a central-t'-distribution with (=-ny+n2 -2) degrees of freedom. The null hypothesis is rejected when the calculated t (or test statistic) is greater than the tabled value for tv,a (see Fig. Ohl). - @ on co.ck s.4 Thus, under the null hypothesisg (H : t!yh=0): o f m J ^ u-5 5.igs Pr { t >' vt ,a} " " , (5)
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where Pr' { } indicates the probability of occurrence for the event within the braces. But, under the set of alternative hypotheses
, (HA W 1 -g > 0), the difference is positive such that .
Pr { t > ty,3} = 1 B , (6) where S is the probability of accepting the null hypothesis when it is false. The porter of a statistical test (1-6) is the probability of correctly rejecting the null hypothesis. g.,q r t hr . c;y r,.,u.., , .. e ,se s the te-t sh tistic, t, is na 1 a.1ger d i; :. t : .: . 3- .-d is t 6 4 Nn. D.0 t . ~ : -: . A. ( ? '
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froi.r each of the tv:o terc.3 ,1ithir P.a brace , of rn (6), ha ob ta:n l X1-X2 X, '- X 2 i
, ' Pr { t . 3 ,
y , 7, g ,
+ s ,
'P p The ; difference on the left side' of the inequalf ty in E7 (7) is -
distributed under H A as a central t-distribution. Therefore, . the ., difference on the right side of the inequality in fS (7) can be set i
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equal to a central t, analogous to {gf (5), i.e.,- - X .X'2 ' 1 v,1, S =t via (8) t - . s E 1+1n '
"1 2 .
If the first sample has already been obtained, then n y and
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2 estimates of X 3 and's are available. Using sy as an estimate of s , th e" p 1 2
;(g) ty,1,,g = t y ., 1
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where the degrees of freedom are appropriately reduced to (Baker 1935) ] I a v = ni - l' , (10)~
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instead of j l
'> = n; + ng - 2 . (11) 1 l
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General discussions of the concepts of statistical pcwer of a significance test inn'.i minima:a cete:nble difference may be fcund'in l NcCaughran (1977), Sokal and Rchlf (1969, Section 7.8), and Iar (1975). i
,- 'In the present application the null and alternative hypotheses ara
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most usefully derir.sd in terms of a mean fractional reduction 'in w ) h &sv y aws - year-class' strength for the4er.ted-start 4ng.19784 relative to the mean
. ,s eCa r A, I A 7e , -
ye ar-c 1 as s - s t re ng th ,due ing =.th --p ecj odds 73--throu gh-1Wf'. Thus, we define the mean' of the second sample2(X ) as a-fraction (1-b) of the u mean of the'first sample (Xy ), i.e., . . X2 = (1-b) _X1 , (12) where b is the fractional reduction in year-class strength for the period starting 1978, with possible values ranging from 0.0 (i.e., no reduction and X2 = 1X ) to 1.0 (i.e., the white perch population is
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eliminated and X2 = 0.0). Note that because of the one-tailed form of the altenative hypothesis (i$. 2), we are not considering cases t
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with b less than zero (i.e., an increase in year-c1'a'ss strength for the period starting 1978 such that X2 > A1 )' The differenci: between the two sample means in E4 (9) clay now be 9
/ expressed as Y1 - Y2 " Y1 - (1-b)X1=bXI, (13) and Mi-(9) becomes .
t y,1.g = tv,a - b X /s1 1 g/l/n1 + 1/n2 (14) 5
!. , .,'3/U1 ' f/?2 .
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. -t n ._
- h.. 7 t f
- .. ::.;L ';C.MGl111%%: .
-4 where CV(= si/5) is the coeffi:ient of variation for'the sc ple of
, ; . m .::;, : y. ,
indices M "w -c s;. .+ . eng th f cr the- pericd 19/3-thecugh -197_7..
' Addressing the first question posed in the -introduction-to-th4s--
appendix requires that R@ (14) be solved for b, the fractional reduction in year-class strength for the period starting'1978. Since a - central t-distribution is synnetrical about 0.0, . t v,1'_ g = - _ t y, g ,_ and we get
+
b = [ty, g + ty, a] (CV) . (15) Then, for given values of c, S, n1 and CV, one can solve Eil. (15) for-a range of n2values to explore how b, the minimum detectable fractional reduction in the year-class strength of young-of-the-year thi's :sm in the Hudson River, varies as a function of the number of years (starting with 1978) for which indices of year-class strength are av ailable. Note in;Et$ (15) that as n2becomes very large, the minimum detectable fractional reduction approaches a lower bound, B,
/ given by t
B = [t y, g + t y, 3] (CV) .
'(16 ).
~
5ddressing the secon'd question posed'in the' introduction requires , that E(~. (14) b'e solved for n2 , the number of years (starting with ,
*. '; 72 ) r.3.- e i 3. !.d t - e "ni class strengt', are avail.Sle: i
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1 2 i- ( cv ) 2 L n, [f.',y ,, + 't'y + g[
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., -_7,,, ._--
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lThen;. for givan values of a, S,Eni. and CV,'one San so'tveit:5 (17 } fc,- a i a range of b values to' explore how.the number.of years of additional
. data (starting in 1978) varies as a function of tNe minin.ua fr7_ctional reduction in year-class strength that one judges should be derec. table. .
o .I b 4 6 A n 9 9 D D 1 9 e 7 r' 8.
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. Ap;11 :: tion .dh. (15) and (,17) requires that the coefficient of variation (CY) n specified. To ma'<e this analysis ~ of statistical power as relevant as possible to the two questioni posed in the introduction,to tVsgp nd% coefficients of variation asscciated ,
with beac% seine-Mdiccc-amt impingement-rate indices of year-class strength for the young-of-the-year white perch population in the Hudson River 'were examined.
} the4eua-n ;ne-indices fc,- the years-1972-through-1976'.are
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Ir i t&hted 4n-4pbie -C-1 oT---Appendix-G;- t.he ccaff-ic-ient-tif variatic,wis- 9 Q l ( T1W . ;. y {,dF,fMh erimping ema n t-rate--MMees.4+e re-ex am i n ed An-mo re--d e ta ib 7 Th e - coefficient 'of variation, number of years of data, mean, and standard
% h!,% kk. <h a.L. ( 19 ?o deviation for impingement rates presented in Appedi -A are given in ' Opp A
Table d-1 for cach of the twelve months for each of five Hudson River power plants. In addition, these statistics are tabulated by month for impingement rates averaged over the five plants and by plant for impingement rates averaged over the twelve months. The frequer.cy distribution of the 71 CV values from Table 0-1 is plotted in Fig. 52. Based on this frequency distribution, we selected 50% and 4 ' 100% for use in Ecis., (15) and (17). These two values for the - coefficient of variation bracket the median CV value of 78% and more than half of the frequency distribution, although both smaller and larger variations in impingement rate were net $ common. . Application of-4s: (15) and (17) also requires specification' of values for a and B, the type I and type II errors, respectively, and of '
.a , . m -,nb.v- 3f y.r - J < - " s u t r . M d,- ta .. . il :'.31 e rc.- tF e .
m.-- -
.., . .. ~ . ,_ . , s , n es .. :~. e . .v.- r - r , . . . . . . . . . - -
e.w , , x.. i.hRi.G : i':~ .& . . - 1r.. period prior to 1978. F or -tha.4imi-%d- nr.s itv.d tyel,"swi ncludad- i n;
. .: . i .. -.
-t'?i's c r e W /;< pe has select- .' only one vel.e of c. (a JJ 05) 3.;h ich' means that we are accepting a Y; risk of falsely rejecting the null -c hypothesis o' no reduction in par-class strength in favor of'the set of one-tatied alternative hypot?. eses that there is a reduction. For -
eacn of the two values of the coefficient of variation, we selected a .. range of values of 3 to illustrate the .importance of the concept of the power of a statistical. test. The value of ni is 5, corresponding to the period 1973 through 1977. . the K -- The answer to Jie-first question posed in the introduction tc tM-
^ 3.
rr:~W is illustrated in Fig. JT1-h For example (Fig.'GI 3 (b)), if the coefficient of variation is assu ed to be 50% and if impingement data are' collected for the next 10 years (1978.- 1987), then there is only a 10% chance that a reduction in year-clats abundance of 16% would be detected. The smallest fractional reduction that can be detected with s a probability of SC' or higher given ten additional years of data is 0.53, and the sm&llest that can be detected with a p'robabilkty of 75% , or higher is 0.79. For a coefficient of variation of 100%, the
, situation is far worse (Fig.'ID3(a)). In this case there is only a 25%
/ W ," t.k. 1 chance that a fractional reduction of 0.76 would be detected i:om/ 10 I l
more years of data, and there is essentially no level of impact short of extinction that could be detected with a probability of SOA or higher. , , The answer to' the second question posed in the introduction is
, illustrated in Fig. 54. For example, if the coefficient of' variation i.;i-: cn a i f i t i :; r.ex.c . .. , , :u;4 6 di. eced 3;. . o.:3..... e j ;
l - [ l i f } .
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- (1- S =i 0'.25) . or. t7 years . (1-S = 0.50) off additional ir.pinge,nsat cata (starting in 1973) would be reg'lired, again-depending on the risk we ,
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4 are willing to the of concluding that there.his been.no reduction .in '
. year-class strength Vnen :in fact there has 'been '(Fig.'tI4(b)).
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.h.is ap;ww.h are ra thw 4M-ing-- They findicate that-the 'Wter:P' vriability in the existing ' aseline time series of impingement rates cM-beach' Wine CM is so g ea$ that:' (1) y.'R 10 additional years of indices of year-class strength Js not-likely to j
provide a ~very poserful -data set for detecting even substantial, actual
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1 reduction', in year-class strength;A (2) M exeew.ive number of years df. If ? b 1[ greater than. the expec.ted lifetime of the power plants involvedD(ef ' ,' l r. l- additional data would be required to detect. an actual 50% reduction in l on2 1 the mean index of. year-class strength, even if n-cr. Lt.s= willing to accept { a Type II error. of 50%. 'In reality the situation is even worse, be'dse if there actually were a long-term reduction. in the size of the White perch population, it would not occur as a step. function but more likely as a gradual decline. l
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series 'of in.! ices of , rear. .:ic:n: s tr.Taf,th i:: pailu.c. .e . Lince 4..c:t.v. " .;
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year _ class strength of the Hudson River wLt4 white perch population are not unusually great compared to those for other fish ,pepulations, it seems likely _ r
' thesimilarly coberitig 'results will' be obtained for other species, even if the
. .tn.14.is-1 *-mbWrEMaM;p=.ioager.
' historical- time series already available is appreciacly' longer. For exa ple,- ', '
the ' coefficient of variation -for is-Thus,R our anal' y sis of the mar minimum detectable : eduction in years class strength of tha Hudson River white perch population highlights 4- . : U n i, aes
. sti ai 1 n.se. a~ generic proble: which is already well recogniced. F.e.< eve r, our methodology offers a generic tool for establishing bounds on ' #-"-
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- "' P. d e p c p M.dttr',a . r detectable reductions in fish stocks and t%=rm on the number of ms.dditional A
years of data required to be able to detect a specified reduction. . I a b S h e
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' The impingement p-Ae data analyn.: in this paper u6re cellected b9 Tey.r.s Instruments ' Incorporated (Indian Nint it .:iear Power Plant) 'and
' Lawler, Matusky.& Skelly' Engineers (Scwiine, Lovett, P,cseton', anc: Dan ske.:nner'
' power plants). 'The hoech e# s dirtweve--eA-1-cW+sta?-by Tr&s-kr,4nwerts-
@mpar.sted+ The data were made available 'te us through Central' Hudson
- Gas &' Electric Corporation, Consolidated Edison Company of New York, Inc.,
and. Orange and Rockland Utilities, Inc. as part of- the'll. 5.- Environment:.1 Protection Agency, Region .II, Adjudicatory Hearing in the matter'of National Pollutant Dischcrge Elimination System Permits (316(b)). The authors tha:G: for their critic .1 revie < of the =anuscript. a
/
-f
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-l-35--- - G.R i: ._;> r.u e, e ,;' .. . .. m. ,
'% , . , ,;. . 3. .
' h/ . Baker, G. li. 1935. The' p. cbability tnat the r.aa, o! a '.seccca,
- c. ' sample will_ differ:from the mean 'of' a first sample by less the a ~ !
~
certain multiple of the standard deviation of the'first sa::ple.' gAnn. Math. Statist.'6:[97201. ,
- 2. McCaughran,b D. A. - 1977.: Thefquality of inferences concerning the c.
. effects of ~ nuclear power plants on the environment Op [
J n . 229-242. , In ~ W. . Van Winkle {edh Prce. Conf. Asse:: sing the Effects of1
. t Power-Plant-Induced Mortality on Fish Populations. Pergamon-
~ ~ '
' Press,NewYorkgNY..
r m-i3. Sokal, . R. R., and F. J. Rohlf. 1969. Biometry, the Principles and" .
. , J )
Practice of S'tatistics in Biological Research.
~
W. H. Freeman and C/Co., San Francisco, pp. 776. -
- ~
l
. Zar, J. H. 1975. Statistical considerations in assessing biological effects of aquatic industrial effluer.ts, pp. 482-491.-
r m : 1 In R. J. Krisek ' and E. F. Mosonyl hds.hProc. Int. Seminar and' Exposition on Water Resources Instrumentation, Water Resources Instrumentation, Vol. 2, Data Acquisition and Analysis. Ann Arbor , f, Science Publishers, Inc., Ann Arbor, Michp . J l i 1 1 e 9
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.* . T-1. Coef ficient of variation, nucher of y' ears, mean (over years nd 3tandard deviation for impinge:nent-rate indices of ye: -law strength of the yoypite perch population in the liudson Ri rgtafrulated-fror values-preter.ted-irr.*gper.dirW
; yowg. Of-f k e- par- /
.gy ytn n nth Peellne Lovett Indian Point 2 Roseton Danskaanar .cVer N.ut 55 78 32 49 72 F.ea y 108 (5/557.99/307.!O) (5/12610.48/9895.51) (4/10.25/3.29) . (6/16.49/8.10) (5/2733J!J/i%9.85)
(5/553.55/597.29) 106 .130 124 103 127 l'e!,ru 3ry 118 (5/326.60/33G.49) (5/271.77/207.07) (5/18101.25/23567.42) (4/9.15/11.32) (6/7.51/7.72) (5/3791.10/r.323.15) 85 17 67 50 36 -- 71
- h. *:
. (5/332.90/285.31) (4/134.77/22.93) (5/4234.06/2832.53) (4/14.95/7.41) (6/29.27/25.06) (5/107931/751.51) 65 75 114 87 53
, c; - G 66 (5/!c;r .. /7115.1 )
(5/577.95/304.70) (5/315.74/206.41) (5/5022.79/4370.12) (4/149.61/171.29) .(6/303.10/2G4.77) . 51 101 120 68 -- 51 . in
. .s .i, (5/53.79/54.50) (4/1565.67/1874.96)
(4/233.52/157.64) (6/305.95/248.54) (5/390.10/340.S0) (5/75.62/40.95)
.: : 3 (~ -
- hoyoung-of-the-yearwhiteperchimpingedduringJune) 105 82 70 luly 137 64 40 (4/33.97/13.64)' (5/0.43/0,51) (6/8.10/6.G4) (5/9. 7);1. 5; '.
i (5/5.63/7.72) (5/5.19/3.33) 8 77 120 83 52 - 63
.h.st 105 i .
~
(5/3).01/41.01) (5/33.37/25.59) (4/406.27/487.97) (5/65.69/54.40) (6/78.66/41.23) (5/105.EG/M.17) e. 65 106 110 35 55
; 5. ;-:es.ber 119 (5/13.04/8.52) (5/239.19/252.49) (5/115.57/127.47); (6/110.57/39.50) (5/95.1U/t3.15)
(5/4.80/5.70) 115 42 83 33 23
*- s i ur 129 (5/71.93/82.44) -(5/111.47/463.76) (5/246.80/205.72) (6/412.95/158.10)' (5/371.31/O.F.5)
(5/17.94/23.150 28 94 78 C0 G
.- Ler 101 -
. (5/274.23/?76.19) (5/3a4.84/103.66) (5/2918.3?/2741.95) (5/286b4/224.78) (6/432.87/337.28) (5.*331.36/333.06) t 72 85 80 - 56 140
'ser 79 (5/767.15/606.78) (5/273.93/198.60) (5/7942.42/6776.79) (5/37.48/20.28)' (6/81.65/?.6.16) (5/1537.45/2113.55) 25 59 21 39 j ' ant
. 52
((/83.13/23.88) (6/153.18/60.00)
; .nnth (5/247.95/129.87) (4/172.79/43.64) (4/2942.56/2922.64).
The . -ntry Jn e'ach cell is the coefficient of variation. 'the bottom entries .in each . cell'are ~ (nwrlier of yeart s ic i i dev ':.i !.on ) . Tlle in: ann and standard deviationc have units of ntunber.....,m. of yoy white perch impitir;a Pr .411 '
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QUARTERLY PROGRESS REPORT FOR PERIOD _ . , , April 1 through June 30, 1980 i y ENVIRONMENTAL SCIENCES DIVISION 0AK RIDGE NATIONAL LABORATORY PRbJECT (189 No.): -80165 - Hudson River' Striped Bass
. PERSON IN u!ARGE: Webster Van Winkle .
PRINCIPAL SCIENTIST: Lawrence W. Barnthouse
>n! . ~ .
TECHNICAL' OBJECTIVES: To further develop.and apply computer simulation models and other methods of quantitative' analysis in assessing the effects of power plant entrainment and impingement on the striped ' bass population in 'the Hudson River. STATUS OF SUBTASKS: Work relating to the detectability and precision of estimates:of entrainment mortality is on schedule; a draft will
'be ready for review by September 30, 1980. Work has resumed on tha effects of stochastic variation on estimites of entrainment mortality .
(subtask f); a draft NUREG report wili je in review by September 30, lt 1980. Tm analysis of stock-recruitment relationships (subtask II) is proceeding on schedule; a draft NUREG report will be in review' by September 30, 1980.. The analysis of the relative contribution of the Hudson River striped bass stock to the Atlantic Ccastal population is behind schedule and will not be completed during l FY 1980 (explanation below). Due to the long lead-times associated with the review and publi- ; cation of NUREG reports, we are requesting permission to Jeliver : finished reports in FY 1981, under a no-cost extension. ; MAJOR ACCOMPLISHMENTS: i
- 1. Quantitative Methodologies for Estimating the probability of Entrainment Hortality r The. Introduction and Methods sections of a NUREG report entitled ;
"Detectability and Precision of Estimates of Entrainment Mortality i of Ichthyoplankton" have been completed. A complete draft will r be ready for_ review by September 30, 1980.
Work has resumed on the effects of stochastic variation on esti-mates of the. probability of entrainment mortality. Documentation of the computer code'has been the highest priority. Unless un-forseen complications arise, a draft NUREG report will be in re- '5 view by September 30, 1980.
, . . ~ -~
- . . w
)
II.. Stock-Recruitment' Analysis
-Effort has. Shifted from preparation of a manuscript to preparation ofcthe NUREG Report.from which we wili extract material for a-manu-
. script to' submit for open-literature ~ publication. Although the
'reportfis'not yet ready _ to be reviewed, a . copy of what is aviilable Eat'present irJenclosed. . The report will be entitled " Statistical Examination.of Stock-Recruitment. Relationships in Three Fish j Populations", i III. Relatise Contribution We are request'ing permission to postpone further statistical analysis and writing'until FY 1981 unde a .no-cost extension. l The. two researchers responsible ~ for this task, W. Van Winkle and K. D. Kumar, have other connitments that will make it extremely l difficult-:to meet a September 30, 1980-deadline'for a draft. '
- NUREG reportLand still maintain the _ quality of the work. Both were asked'to assume major administrative responsibilities within
~
the Environmental Sciences Division subsequent to the initi-ation of this subtask,LDr. Van Winkle as Head of the' Aquatic Ecology.Section:and Cr. Kumar-as Manager of the division's com-1puting facilities. PUBLICATIONS, PRESENTATIONS, AND MEETINGS Publications
'Barnthouse, L. W. , S. W. Christensen, B. L. Kirk, K. D. Kumar, W. Van Winkle, and O. S. Vaughan. -1980. Methods to Assess Impacts on Hudson River Striped Bass: Report for the period October 1, 1977 to~ September 30, 1979. NUREG/CR-1243, Oak Ridge National Labora-tory, Oak Ridge, Tennessee.
Presentations: None Meetinos: L. W. Barnthouse and W. Van Winkle represented EPA, Region II in two meetings with representatives of the Hudson River utili-ties, the State of New York, the Natural Resources Defense Council, and the Hudson River Fishermans' Associatior.. ' The purpose of these meetings, held in Pearl River, New (ork, on April 22-24 and May 21-22, 1980,. was to discuss an out-of-court settlement of the Hudson River Power Case. ORNL's participation was funded by EPA.
I is d .;4 - -
. . _ _ . , [ . [_ . ... _, ._ , ,, , _2j _ , ' . ,,,_ _, . _ , , _ , _ _ , , , , , _
.,) , 3 Contract No. W-71605-eng-26 4
. RFGRESSION ANALYSES OF STOCK-RECRUITMENT RELATI0mna.26 IN THREE
' FISH POPULATIONS 1
R. M. Yoshiyama, W. Van Winkle, B. L. Kirk, and D. E. Stevens ,
. ENVIRONMENTAL SCIENCE > DIVISION
']
P.iblication No7--
~
./
' ' Bay-Delta Fishery Project, California Depatt=ent of Fish and i
Game, Stockton, California. 1 1 l i l l l Prepared to the U.S. Nuclear Regulatory Cecnission Office of Nuclear Regulatory Research I Washington, D. C. 20555 Under Interagency Agreement DOE 160 -550-75 NRC Fin No. 30165 1 Mt"theS.s hO ltL1M$ Inf-% h *n Task: - .< ' Hudson River Str!. ped Bass Prepared by the OAK RIDGE NATIONAL LABORATORT Oak Ridge, Tennessee 37830- > uperated by UNION CARBIDE CORPORATION
; .For the DEPARTMENT OF ENEP.GY
ljp .. ..;__:-._-_..... .._.._._1....___...._.___., r,, . La Q7' 1 N J q; ; 1j . TABLE OF CORTENTS-Page
' ABSTRACT-
SUMMARY
LIST OF, TABLES LIST.OF FIGURES-l INTRODUCTION- .I I METHODS AND MATERIALS Statistical and Analytical Piteedures
- Basic stock-recruitment functions Measurement.of deviations Nonlinear-fit Comparison of models Analysi's for California Striped Bass Analysis f:r Atlantic Menhaden Analysis for Connecticut River American Shad RESULTS
. Striped Bass Atisntic Menhaden American Shad DISCUSSION AND CONCLUSI0?E .
LITERATURE CITED APPENDIX 1. California Striped Bass Data AFF2tDIX 2. Measures of deviations from predicted recruitment. APPENDIX 3 Outline cf regression analyses and su= mary of results. I- . _ . -
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' Abstract
.y II The statistical dependence of recruitment level upon stock size and ,
~
selected environmental factors vas'examineu for three fish stocks: California striped bass (Morone saxatilis), Atlantic menhaden (Brevoortia tyrannus), and' American shad (Alosa sapidissima). The analysis involved ((l)f simple and multiple linear regressious of recruitment' against stock . size and environmental' variables, (2) nonlinear regressions of recruitment
- against stock size using Ricker and Beverton-Holt stock-recruitment models, ;
and (3) nonlinear regressions using Ricker and Beverton-Holt models modified *
- to include environmental effects. The relative effectiveness of linear and nonlinear models 12 accounting for variation in recruitment level of the three fish stocks-vas evaluated, with effectiveness of regression models gau6ed 'by the magnitude. of residual mean square (MG) values. and by whether or not regression models collapsed to simpler forms (due to '
, parameter es-imates taking the value 0.0) after being fitted to data. ' No sinsic class of models (linear, .stmple stock-recruitment, modified , stock-recruitment)wasconsistentlysuperiortotheothersinexplaining variation in recruitment for all three fish stocks.. Linear models appeared more effective than nonlinear models for striped bass and Atlantic menhaden data-because linear models yielled lover E4S values and because fits of
.e- .
nonlinear models to data gave parameter estimates which included 0.0. In contrast, two modified stock-recruitment (nonlinear) models showed the best' fit to American shad data. The si=ple Ricker and Beverton Holt models , L y
'did'not satisfactorily describe recruitment trends for any of the three
' ~ fish stacks. < Although . detailed aspects of the results may be specific to the a .aly-i tical procedures and time-series of data utiliced, general features are j e e
pi?;., ;,. 4 J..
-t 1 ;
, _5 .; ; ,. 1..'. f
., n 7 still' evident. ; Striped bass: and ' Atlantic menhaden recruitment showed much -
. f w
stronger statistical relationships to environmental factors (particularly to water; transport variables for striped ba'ss) than to stock size, wheress
- stoch. size Japparently has been by: far the most important detezuinant.of
, Trecruitmenti variation in shad (in the Connecticut River). I I a b h I
'I I
i
% 1
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l ey y l
~_;....._.. . _ - . _ , . . -
f > l Summary-
. Regression analyses were performed on data for striped bass in 1 ,
California, Atlantic menhaden, and American shad in the Connecticut River. . k*e examined the statistical dependence of recruitment levels upon stock size y and environ:nentall factors by employing 11nere knd nonlinear regression models, with the primary goal of detemining which models most accurately described the data. The regression models we employed included simple (one predictor variable) 4
. linear. and multiple linear models, basic Ricker and Beverton-Holt relations, a linearized Beverton-Holt model, two foms cf the Ricker relation modified to include an environmental variable as a predictor variable, and one fom
- of' the Beverton-Holt relation modified to include an envircamental variable.
tesults of the analyses for each of the three fish stocks follov,. Striped Bass There ve-e 14 environnental (vater transport) variables which yielded statistically significant simple linea'. regressions for striped bass, but t. all were significantly cross-correlated and therefore were statistically redundant. The single best variable for predicting recruitment was percentage of water flow (through the Sacramento- San Joaquin Delta) diverted in May (PDM). Linear regression of recruit =ent against stock was nousignificant. Multiple linear regression using both stock and PDM as predictors was little better than linear regression using FPM alone in explaining reernitment variation. Simple stock-reciuitment (Ricker and Beverton-Holt) models included 0.0 as estimates for all parameters after they were fitted to data, and , the models therefore were not appropriate for describing the data. The i i t
p:,.; n x - .. ;
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l T modified stock-recruitment models (using PDM as the environmental variable) .
~
~
- also/ yielded parameter'. estimates of 0.0 (for at least two out of thfee 9 ; parameters),:land soithey were judged t'o'be' inappropriate.. I 1 ~
Linear.models therefore were superior to nonlinear forms in explaining ] i
'0 -variation'in striped bnsi recruitment.'
I l l Atlantic-'Menba?en
.. i
. Water temperatum was the only environmental variable which yielded l
' a significant linear regression for menhaden recruitment. Stock size j ,
showed no significant relationship with recruitment, and multiple regression' i
. using both . stock and temperature as predictors shaved little improvement i in fit to data over 11nsar regression using temperature alone.
{ Simple stock'-recruitment models included 0.0 for all parsmeter esti-
- mates, and the modified -stock-recruitment mode's (with water temperature i included as a predictor variable) each had two out of three parameter estimates which included 0.0. Thus, the nonlinear models were not valid. l r
. descriptions of the data.
1 A=erican Shad i ) , 5 Simple linear regressions showed that recruitment in American shad . [ l
.vas' not significantly related to any of the environmental variables examinedi. 4
! + l However, recruitment showed a highly significant (p < 0.001) statistical j dependence on stock size. . Multiple regression of recruitment against stock size 2d the most important (but statistically nousignificant) environ-mental variable (logarithm of river discharge rate) showed an imprevement in fit to data over linear regression of recruitment against atock alone. l c Both.the basic Ricker and 3everton-Holt models included G.0 as an i
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y m m g,,.. , , 1 l 1 - t. estimate for',one parameter after fits to data, which resulted'in sis $lia , A i fication to : linear;fom. They therefore were equivalent to simple linear f regression models. .One modified Ricker model (with logarithm of river L discharge rate.'as .a predictor variable) had two out of three parameters . f vith estimates .which included 0.0, and .it therefore was considered an < inappropriate . description' of the data. - However, the other modified Ricker model and' the modified BevertoncHolt model each had nonzero ! estimates . for all parameters after fitsito data, . and they also 'gave. lower res1Gual ' i mean square values than did linear regressions. Thus,'relatively complex' '{ nonlinear models were the most accurate ones for, explaining reemitment variation in American shad. j s , .!
). ,
It is concluded that neither linear c:r nonlinear models are consis- ' tently superior.in explaining recruitment variation for all three fish stocks. Which modeln are judged best (in tems of accuracy in describing ! the data) depends' upon the date and probably also upon the analytical 1 procedures employed. It seems, however, that general features such as the i ! strong dependence of striped bass and Atlantic menhaden recnitment upon ; a
.. envi*camental fautors and of American shad reemitment (in the Connecticut :
i River) on stock si::e would be apparent regardless of the details of the !
'I regression nodels and procedures empicyed. !! -)
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-e- l LIST OF TABLES .
.s.
Table i > 1.. Results from simple linear regressions of recruitment index t )~
~
(R) on independent, environmental' variables (E) for the striped bass population'in the Sacramento-San Joaquin Delta, California. s The fourteen most significant regressions are listed in decreasing order of r value.. ,.
- 2. Correlations among water. transport- parameters and stock size.
.Second entries are significance levels (p).
- 3. Results of linear and nonlinear regressions of striped bass recruitment on stock size and' an envir = ental variable. First value in each cell of the table is the residual meen ' square for the corresponding regression. Entries ia parentheses for each line n regression are the r2 value and the overall significance
. level for the regression (ns = nonsignificant). Values in parentheses (x/y) for each nonlinear regression are: x= ,
number of par =eters in the model for whdch 9/f, asymptotic ! I confidence intervals included 0.0; y = number of parameters , in the model.
- k. Results of. linear and nonlinear regressions of Atlantic mechtalen }
recruitment on stock index and an er J'numental variable. Models j f and fornat are- as in Table 3. ' 5 Results-of linear and nonlinear regressions of American shad ; l
. recruitment on stocic size and an environmental variable. Models and format are as;in Table 3 h
v ,.
- g. , . .y .
. . . . # ^
;'% - ; ,. ~ , y LIST!OF FIGURES-
$ Figure- - Page !
1 [4 i
- 2/. Plots of recruit' ment level .yersus stock size for striped bass.
'U Models fitted to data are (a) Ricker (equation (1) in text),
j .
- (b) Beverton-Holt (equation (2a) in text), and (e) linear i:
I regression. J g. Plots of recruitment level versus stock size for Atlantic menhaden. Models fitted to data are as in Figure 1. p.' Plots"ofrecruitmentlevelversusstocksizeforAmerican shad. Models fitted-to de ta are as in Figure .l.
'1. Linear regressions of recruitment level against the most s
important environmental variable for (a) striped bass (recruitment vs. percent water diversion in May), (b) Atlantic menhaden .(recruitment vs.' vater temperature), and (c) American
. shcd (recruitment vs. log (river discharge rate)).
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. l3
- e. . y 1 Introduction i
Explaining fluctuations in year-class strength of fish stocks is 1 an important and challenging problem in' fisheries science. Three approaches which have been employed to study variation in year-class strength of single species are (1) linear regression of year-class strength (pgh-recruitment), using various environ = ental factors _as independent variables (Marcy 1976), (2) fitting of a stock-dependent recruitment function to data, followed by regression on stock-independent factors to determine the importance of factors other than stock in affecting recruitment (Leggett 1977, Nelson et al.1977), and (3) fitting to data of a stock-recruitment model which directly incorporates environ:nental variables (Som:nani 1972, McFadden and Lawler 1977). In this paper, we enploy these three approaches to examine the roles of stock and envirmnental factors in determining levels of recruit-ment in t %_ fish populations: striped bass in California, Atlantic menhaden, and American shad in the Connecticut River. Specifically, we compare the effectiveness of linear regression models versus nonlinear models (based on classic stock-recruitment functions) in explaining year-class variation, and we assess the relative importance of stock and various environmental factors to this variation for each of the three
- i Stocks.
e D i l 5 7 d
e '; s. r; Methods and Materials-t ,
. Statistical and Analvtical Procedures f 1
Linear regressions were perfomed with recruitment. regressed against each of several*## # ** variables judged to be of potential,importance. The variable which was most effective in explaining variation in recruit-ment vas then combined with stock into a multivariate regression model- . The multivariate model was subsequently compared with the nonlinear re-gressions (below). . We judged effectiveness of linear models by the
- proportion of variation explained by regression (r ). ,
Examination of the more complicated, nonlinear regression models : invoked four steps: (1) stock-recruitment function (Ricker or Beverton- ; Holt) was fitted to the data. (2) Deviations of " observed" recruit- { ment values from predicted values were co=puted, followed by linear regress 1,ns of deviations against environ = ental variables. This second set of res-easions allowed us to identify the factors which best explained variation in recruitnerJ beyond that explained by stock. (3) D:rportant environmental variables identified in (2) were incorporated into a stock-recruitment function, and the modified function was fitted to the data. ! (h) The modified stock-recruitment models vere compared with the basic stock-recruitment foms and with the linear models in tems of their fit f to data. Details of each c' these.four steps follow. ! l i Basic Stock-Recruitment Functions P The basic stock-recruitment functions we utilized vere the Ricker (1973) ' equation + ,
'l !
3
,, em R(t,+T) = a,S(t,) exp -b_S(to)_ ,. . (1)
- add the 3everton-Holt -(lf)ST) equation R(t,+T)= ~
1 (2a)
- c+d,,/.S(t,)'
5
=,
e_S(t.) , (2b) ; 1 + f,S(t,)
$ak.a- !
where R() and S() denote recruitment and stock, respectively, g M -e p .
//, are constants, t. is some initial point in time, and T is a time increment. These equations are derived from the general form i
} -M N(t),
= (3) at ,
where N() is nu=ber of fish and M is a mortality function, by integration 4 (I) l. between the limits N(t) = F S(t o ) at time t = t, and 3(t) = R(t o+T) at time t = t o +T. F is the mean number of eggs spawned per fish. The Ricker form is obtained from the integration when M = g + gS(t ), and the 3everton-Holt fom is obtained when M = g + m 4 N(t), where the m 4 's are constants. Note that both mortality functions include a density- i (or stock-) independent ec=ponent (g, m 3
) *** * #*"" '#~(' ~}#
pendent component (g, m4) . parameter a_ . < astion (1) represents stock-independent components of the relation (Ricker 1958,. p. 264; Harris , r 1975)., while parameter b_ represents stock-dependent components. If b,,= 0, equation (1) reduces to a simple linear function with slope a, and intercept O. para =eter e, in equation (2b) . represents density-independent j components, while parameter f represents density-dependent co=ponents (3everton and Holt 1957, p. 48; Harris 1975). (7or a distinction between ; i ________mm_- _._ _________ _- __ _ _ . _
4 9 ' 4, . g m ,
-stock-dependence and: density-dependence,#see Harris'1975.) If _f,=-O,
. equation (2b)' reduces to c' simple linear function with slope e_ and 1. ter-cept' O. - Thus, the simple linear regressions we examine belov may be
- viewed as 'special cases of the Ricker and Beverton-Holt relations. - tieasurement of Deviations. Deviations of empirically derived (or observsd) recruitment values, a
' R, from predicted values, $t, were computed as 6, a R - R. We used A
values of R~ obtained from nonlinear re6ressions of the Ricker (1)-and Beverton-Holt (2a) relations and from linear regressions of the following lineariced form of the Beverton-Holt model: 1 b-
~
- = a+~ 3 3, b, constants. (h)
R S The Ricker relation could not be linearized to a satisfactory fom, and A so only its nonlinear fom was used to generate R values. Values of 6, were then regressed against etrrironmental variables to detemine if stock-independent va-iatien in recruitment could be attributed to environmental variation and, if this were so, to identify the environmental factors which contributed most to recruitment variation. A second possible measure of denations from predicted recruitment 4 eThet , is 6 w 2 R/R, temed the survival index and employed by eaa44er vorkers to study stock-independent sources of variation in recruita ut (Leggett 1977, Nelcon.et al. 1977). However, we did not employ 6 in our m1yses
'for reasons give? in Appendix 2.
4 Nonlinear Fit We selected the environmental variable which yielded the most' i k . _ _ , , . _ _ _ _
p y .. - + 5 , j
~ . effective regression (highest r ) for fj deviations, and that variable Lvas then incorporated into the stock-recruitment relations (1) and.(2).
To incorporate an environmental variable' (E), we redefined the moA,ality rate M in. equation (3) as a furetion of the environmental variable.
' For the Ricker fom, where M = g + g S(t,), ve set g = g + gE (environmental effect in the stock-independent term of M; gg 's constant)
. Lor m2
- b + h1 E (environmental effect in the stock-dependent tem of M; h_g's constant), which yielded upon integration R(t,+T) = a,g S(t,)exp[,ggE+a2 3( o (5)
R(t,+T) = g S(t o) exp S(t ) (a4 + a 2E) , (6) respectively, with constants af. For the 3everton-Holt fom, where M=m 3 '+ m4 N(t), ve set g = g + _gE (environnental effect in the density-independent tem of M;qk 's constant) or m4 = g + gE (environ- ! F tental effect in the density-dependent tem of M; g's constant) to obtain i R(t,+T)= "o S(t,) exp(-agg - e,y_gE) 1 + a g S(tg) 1 - exp( gyg0 -a_y_kE) y - (3, + _kyE) : i R( t +T) = g S(t,) , (g) j 1 + S(t o) (_a1 + aqE) respectively, with constants g and kg . We used the modified stock-recruitment relations (5), (6), and .
'(8) as nonlinear regressit n models for fitting to data. Relation (7), i containing five constants, tould not be reduced to a three-constant fom ,
. (as could the other three relations). Because of the increase in diffi- ,
culty of fitting ce slicated nonlinear models to data and, more importantly, of the ambiguity in interpretation of such fits, we did not include model , (7) in our analyses. t i
By .,p -
... 6 ;y n
- .- I
I
'camparison of Models The final' step of the analysis involved comparison of all models
)
against each other with respect to their effectiveness in explaining
'tde 9*udly ped h i variation in reczuitment. 3 Eelative effectiveness.d',,g4 l
i
, - r --i by,Chitresidual-mean-square (RMS) values, with lower . RMS indicating i better fits of the models to data. However, comparisons among linear j a
models were based on r values, with higher r value indicating a better 4 model. In addition to using RMS values, ve employed a second criterion j j for evaluating nonlinear models. If, after fitting models to data, ] the estimate 'of a constant (" parameter estimate") included the value l 0.0 in its 9% asymptotic confidence interval, the constant was considered j 7 not statistically significantly different fron 0.0. This meant that j
)
the corresponding nonlinear model probably could be simplified, If it could be si=plified to a linear fom, the nonlinear model was considered i inappropriate to the data, since it was then no better than si=ple linear ] l regressi:m. A nonlinear model was also considered inappropriate if it simplified to a nonsensical form (e.g., R = 0). All regression analyses vere perfomed by using the Statistica.1 Analysis System (SAS Institute Inc.1; 79). The procedure for fitting l the nonlinear mode] s to data used the Gauss-Newton method (Beck and Arnold 1977).
x s 3 J c-Analysis for California Striped BaJs
~
Annual values for recruitment and stock size (Appendix 1) vere computed using data from Stevens (1977 and unpubl. data) on the striped bass, Morone saxatilis, population of the Sacramento-San Joaquin Delta, , California. Recruitment {R() = number of fish 3 years old] vas computed from R(t) = N(t) - N(t-1) p(t-1) (9) ; whereN()isthenumberoffisha 3 years old, p(t-1) is the probability of survival of fish a 3 years old within the time interval t-1 to t,. and i values in parentheses denote time in years. Stock size S() = nu=ber of fish 2 5 years old was computed from
~ !
S(t) = N(t-2) p(t-2) p(t-1) (10) Since recruits are here defined as 3-yr olds (the earliest age at which fish =n te harvested), the stock-recruitment regression equations ve employed for striped bass express recruit =ent at time t as a function of stock size at time t-3 That is, although stock size in a given year detemines reproduction levels for that year, this effect is not mea-sured until three years later vhen recruitment for that year-class is estimated. Two environ = ental factors which appear to strongly affect the striped bass population in the Sacramento-San Joaquin Delta are (1) water flow out of the Delta into the San Francisco Bay system and (2) diversion , (pu= ping) of water out of the Delta to other parts of the state (Turner andChadwick1972,Chadwicketal.1977,Stevens1977). Such water t transport parsmeters are especially important because of their effect l l on the distribution of young in the months following the spawning period 1
\
l
4 l f i O ; 4
. i
'1
. . i in April-June (Turner and Chadwick 1972). We therefore used, as pre- ..'
t ' l
. dictor variables in the regressions, water transport parameters. for .
various periods from May to June. We considered logaritt::n of outflow and percentage of water diverted as well as absolute amounts.of outflow azzi diversion (data in Appendix 1) ~. . I l
.r s
1
+
i 1
?
i
)
l t f i a h I I i, 1 I
?
o I 5 .-
., n. ., ;
- 9 j Analysis for Atlantic Menhaden .
i Data..for Atlantic menhaden, Brevoortia tyrannus, on the United States Atlantic coast vere taken from Nelson et al. (1977; Tables 3, 6) . These data included total ntricer of . eggs produced (a measure of stock size) , ; and recruitment for each of 14 consecutive years. Relevant envizenmental
. parameters (data from Nelson et al.1977) included, for eanh year t, the sum of twelve monthly averages for zonal (westward) Ftemn transport' rate at each of four locations, the miniwns of the mean surface water '
temperature at the mouth of Delaware Bay, and the sum of monthly average ; discharge rates from the Susquehanna, Potomac, and James rivers in July-Septe=ber of p ar t-1. Discharge rates frc= these three rivers in July-September are directly related to Chesapeake Bay discharge in. the following October-December period when larvae begin entering the Bay in increasing numbers, and discharge rates in year t-1 thus affect larval 1 abundance in year t. Westward D: san transport (an onshore movenent of water) is important for survival of menhaden larvae because it carrie eggs and larvae from offshore spawning grou=ds (particularly in the southern part of the species' I i range)toestu.'inea nursery grounds. Temperature directly affects larval survival, with periods of extrene cold apparently resulting in heavy I kills of larvae overvintering in the estuaries. Combined discharge ; rates of the Susquehana, Potomac, and James rivers is also possibly i i an important indicator of larval survival beause of the substantial l, inflow from these rivers into Chesapeake Bay, which is a major nursery : i area for. Atlantic menhaden (Irel.on et al.1977). ; Recruits were defined as 1-year old fish. Since all enviroc= ental i variables are viewed as acting upon the larval state (Nelson et al. 1977), we regressed recruitment of a given year against values of envi- l
. I ron= ental variables (and stock) for the preceding year.
t
. p &, . .,
10 Analysis for Conneetteut River American Shad L ' Data for American shad, Alosa sapidissima, of the Connecticut River - l l vere taken from Leggett (1977; Table 1). The data (for each of 12 years) following included measures of stock, recruitment, and the Atuti environmental vari-
)
ablestmean water, temperature in June and mean river discharge rate in - June (the month of maximum spawning activity). Both temperature and ] l discharge rate appear to be important determinants of juvenile year- l l classstrength(Marcy1976). ; j Leggett defined recruits as newly sexually matured fish (Lyr old ! malesand5-yroldfemales). Since the two environmental factors chosen , eA Fed . for. study are viewed as operating on the juvenile stage, it vould seem 4 l I more desirable to perfom regressions usir4as the dependent variable;
=1uven11e year-class strength rather than class strength of the much older .
recruits (especially since different or additional environmental factors probably affect the survival of fish between the juvenile and rec 2 nit stages) . Unfortunately, data on juvenile year-class strength vere not available for all the 12 years in the period of interest. However, Leggett showed that a significant positive correlation existed betveen of rec,rceauhee ; his p-M+--at index and n juvenile year-class strength for the year in which the recruits were spawned, and so ve were able to use Leggett's recruitment index as the dependent variable in regressions against stock and environ = ental variables .(vith recruitment index for recruits spawned in year t matched with values for stock and environmental variables in yeart).
- c. .
e Results Striped Bass Values for recruitment of striped bass, computed via equation (9), vere negative for three years ( Appendix 1). Negative recruit:nen+: levels are biologically impossible, but we have nontheless utilized them for regression analyses in the absence of alternative esti=ates. Although individual negative values must be viewed as computational artifacts, they did not detract from the primary purpose of computing recruitment values, which was to statistically conpare alternative stock-recruitment relationships. We felt that using all egted values rather than se-lectively cha:ging or deleting aberrant values yielded regressions with the least bias, and no realism is necessarily lost as long as the re5:es-sion line* 3appear reasonable. Simple linear regressions of reemitment index on independent variables varied videly in effectiveneas, with r ranging fro = 0,05 (for % vater diversion in July) to 0.69 (% water diversion in May). of the 25 si=ple regressions perfomed, ik had statistically significant (p 5 0.05) nonzero slopes (Table 1). The results indicated that (1) recruitment was a log-arittsie function rather than a linear function of Delta outflow, (2) i recruitment was nore closely related to relative amounts of water di-verted out of the Delta (relat$ve to flov into the Delta) than to abso-lute amounts, (3) water transport parameters were = ore i=portant in May and June than in July, an1 (4) stock size was relatively unimportant to recruitrent levels (r = 0.08, p 5 0 33). As expected, water transport paraneters shoved strons enss-correlations (Table 2) . There were statistically significant (p < 0.01) positive correlations among relative diversion variables and among outflow varia-bles and significant negative correlations betvcen relative diversion e
~ ,u,. ,
12 ! variables and outflow variables. This latter observation indicates that , water diversions have an appreciable impact on water flow through the Delta. Correlations between stock size and all vater transport parameters vere statistically nonsignificant (Table 2), although stock size correla-tions vere positive with outflov and negative with. relative diversions. Because of the strong observed cross-correlations a=ong vater trans-port variables and the weak regression of recuitment on stock size, mul-tiple regressions involving two or more environnental variables or includ-ing stock size as a sec5nd independent variable would not provide a much more effective description of the data than did the simple reg es-sions. However, for the purpose of comparing linear with nom Nar regressions belov, we performed a =ultiple regression using stock size and percent water diversion in May as the two independent variables (% vater diversion in May was the environ = ental variable yielding the ' g syd j highest r ; Table 1). The multiple regression explained approxi=ately the sede proportion or variation in recruit:ent (r = 0 71) as did the the simple regression using percent diversion in May as the single inde-pendent variable (r = 0.69). Thus, these two models were equally effective, and they also were superior to various extents (i.e., had lover RMS values) to all other regression models in describing the striped bass data (Table 3). l Fits of the basic stock-recruitment relations (1) and (2a) to data (Ep2 h yielded roughly equivalent residual cean square (RMS) values (entries D and G in Table 3), and both models gave FlG values which were slightly 1cuer than the RMS value for the simple linear regression of recruitment against stock. However, the 95fo asymptotic confidence intervals (9/g ACI's) for constants a, b,, c, and d in equations (1) and (2a) all included 0.0, with the result that the models simplified to the. nonsensical forn l 1 l
E ".1 q. .
~
t 13 R' = 0 and indicating that the models were inappropriate for the data. A Linear regressions of 6, deviations (based on R values frcm the basic Ricker and both basic and lineariced Beverton-Holt relations) were perfomed against water transport variables. . Regressf.ons against , percent water' diverted in May most consistently yielded 'among the highest , r values,' and so this variable was chosen to represent the 'environmentd j factor (E) in the modified Ricker and Beverton-Holt functions (5), (6), and (8) . . The results of fitting functions (5), (6), and (8) to data (entries E, .R, and I in Table 3) indicated an improvement in explaining , variation in recruitment'(lower RMS values) over that 'shown ,by the ' basic Ricker and 3everton-Holt models (entries D, G in Table 3)- This result parallels the observation that multiple linear regression of re-cruitment against stock and an environ = ental variable was superior to
- r linear regression of recuitment against stock alone (entries C, B in l Table 3). However, the modified Ricker and 3everton-Holt models each yielded es+tes for at least two out of three parsmeters for vbich :
9% ACI's included 0.0, indicating that these three nonlinear models 1 could be si=plified and therefore probably were inappropriate for the dat a. l 4 i j I j' i ( l l 4
14 Atlantic Menhsden Simple linear regressions of recruitment against stock index or t log (stock) vere ineffective and statistically nonsignificant in explain-ing recruitment variation of Atlantic menhaden (r = 0.03 for stock, r = 0.08 for log (stock)) . But for comparison with nonlinear models below, we used linear models involving log (stock) rather than stock since log (stock) yielded the higher r value. Among all environmental variables (and their logarithms), only temperature (nontransformed) yielded a significant linear regression of 2 a Fy l recruitment against environment (r = 0 39, p < 0.013). Total discharge rate of major rivers into Chesapeake Bay, which was uncorrelated with temperature (r = 0.15, p < 0.590), had the next highest r value {= 0.23). All of the D:=an transport variables (or their logarith=s) ve-- either significantly correlated with temperature (p < 0.025) or had very low p4Un values of r (' r <0.07),andthereforethey3vould not contribute much =:re t' explaining variation in recruitment than vould be explained by temperature alone. None of the environmental variables shoved a sig-nificant correlation with stock. . We chose te=perature to represent the environ = ental factor in the multiple linear regression model. Multiple regression of recruitment against temperature and log (stock) yielded a significant overall fit o (r = 0.40, p < 0.0hh), although only the parameter corresponding to te=perature was significantly nonzero (T < 0.025) and the multiple re- , gression was little better than the linear regression on te=perature alone. Nonlinear regressions using the basic . stock-recruitment models (1) and (2a) were equally effective in explaining variation in recruitment, Wyv 3 l judged by their similar BMS values (Table 4). However, both models had l 9% ACI's which included 0.0 for both of their parameter estimates,
. c.. 4 ,: j 15 'I
, , l
' indicating that the medels were inappropriate for. describing the data. 3
; Linear regressions' of 6, deviations against environmental variables ;
showed that. temperature provided the best (and only significant) regres- . 4 . sions; for deviations- computed from Ricker and 3everton-Holt $1 values (r = 0 35, p < o.o2o and r2, 0 37, P < o.o20, respectively). . There were 4 . 5
.no significant' regressions for 6, deviations based on R values from- the -
linearized 3everton-Holt model. We stherefore used temperature as the en- ;
-vironmental factor in the modified stock-reczuitment relations (5), (6), .
and (8) . i The nonlinear models (5), (6), and (8) each had two of thzwe para . .j i meter estimates vith 95% ACI's which included 0.0, leading to simpli- .l fication of equation (6) to a linear fom and of equations (5) and (8) l to R = 0.- Thus, none. ef. the f'ive nonlinear models we considered provided a valid description of the menhaden data, even though three of them , showed better fits to data (lower RMS values) than were shown by the ' linear models. 1 l, l
+
I I l e L f e 8 r 1 . - ,,.,4 - . . . . . , ,, , ,e <,.~,,..,w.. ...,-#,,,. ,w.-,-,wy, ,r-. -
..rw.
t 16 American Shad Simple linear regressions showed that stock size was very important in explaining variation in recruitment levels of Anerican shad (r2= 0.65). No environmental variables were significantly correlated with stock, and none yielded significant linear regressions for recruitment. Although not statistically significant, the linear regression for the logarithm of river discharge rate (= log (discharge)) yielded the next ahytI highest r value (= 0.03), and so ve used log (discharge) together vith stock in the multiple lize ar regression. The multiple regression showed a noticeable improvement in the proportion of recruitment variation
~
vhich was explained (r = 0 76) over that which was explained by regres-sien on stock alone. Nonlinear regressions using the basic Ricker (1) and Beverton-Holt h (2a) relations produced about equal RG values (Table $),w"n which4 were s:mewhat lover than the value shown by linear regression on stock alone but higher =- the EG for the multiple linear regression model. H0v-ever, these two nonlinear models each yielded one parameter estimate with' 95% ACI including 0.0, and each model could be simplified to a linear fom. They therefore may be considered equivalent to the simple linear model for stock, in consonance with the similar RMS values observed for the three models (Table 5). A Linear regressions of f, deviations (for R values from the basic Ricker and both basic and linearized Beverton-Holt relations) shoved that regressions on log (discharge) consistently yi-ided the highest - (but not significant; p 2: 0.06) r values, and so ve used log (discharge) as the environ = ental factor in the modified stock-recruitment 'relatiens (5), (6), and (8).
f , .', Fitting of models (5), (6), and (8) to data fielded nonzero para . I meter estimates '(i.e., 9$ ACI's did not include 0.0) for all three parameters in models (6) and (8). Model (5) had two out of three para-meters with 9 % ACI about the estimated value which included 0.0, and the , model could be discounted as 'inappropriate. Thus, the modified Ricker relation (6) and the modified Beverton-Holt relation (8) were the only .
.c '
valid nonlinear models for the sbad data and, based on their relatively , lov RMS values (Table 5), they appeared superior to the linear regression i models as well. i I i i e t i i t l i 5 i l
?
i l i i l . i , i
. }
t f (: m . t
*. . .~ ~ .-- ......n.. ~ , - - . . ~ >- . ...
l . .
7 h.N , 6 wr
. . _ . - .b.__ . .: ....', '_...,_
' 7
' Discussion
;_.Results from regression analyses showed that neither linear nor I .(cW hth' ,
n3nlinear models were 4 superior' to the other in explaining variation in ,
., recruitment for all three fish stocks. Linear models ; appeared best for '
. striped bass in that they resulted in the lovest residual mean square (RMS)l values. Also, fits of nonlinear models to . striped bass. data generally yielded parameter estimates .which did not differ significantly .;
~
from zero, suggesting that the nonlinear models were 1nappropriate; - in soms cases l they could be simplified to a linear fom. As with the 't striped bass regressions, fits of all five nonlinear models to Atlantie ? i menhaden data generally yielded parameter estimates which did not diifer !
.significantly from zero, and the models were discounted as inappropriate. ,
. Therefore,' linear models again appeared superior for describing the data.
In (.ontrast, regressions for the American abad data showed that : i' two mom *ted (-*"=ar) stock-recruitment models (models 5 and 8) could. not be reduced to a simpler fom, and they furthemore yielded the best 2 h fits to the data. T ma,inonlinear models p.sroyided 4 valid descriptions i only for the American shad data, and for none of the three fish stocks ! did the basic Ricker (1) ani 3everton-Holt-Holt (2a) relations prove l to be satisfactory. j The relative importance of stock and enviromental factors to re-cruitment variation differed for the three fish populations. Stock appeared to be much less important for both striped bass and menhaden in . explaining recruit =ent levels, as shown by the ineffective - linear regressions on stock and by the poor fits to data (relatively high RMS values and zero parameter estimates) of the basic Ricker and
'3everton-Holt models. In- contrast, shad recruitment appeared closely
- - - _ _ . . - , , _ _ . . . . ~ , - - ; .+,
~ ~ , -
1 t H. ,; 19 ';
, s L :
- ~ , tied to stock levels, althoughJan environmental factor proved to be 4 l . s . .. l1*
-important. in improving the . fits'of both linear aad nonlinear models. _
f Detailed aspects of our results are specific to the data used in ;
-l f , the analyses, and it is possible that somewhat diff erent results vould ;
-)
l emergojfrom analyses of longer time series of data. For example, l 3 i if ' longer time series were available which showed larger ranges :
- i. , ;
. in stock site for- striped bass or Atlantic menhaden, then perhaps stoch .j vould emerge as a more important determinant of recruitment, and the .i
\
nonlinear stock-recruitment models might show a better fit to the data. However, this is-not to say. that general' features of the relation- t i ship between recruitment and its determinants cannot be recognized in our results. For example, environmental factors (vater transport variables) ) appear to be statistically so important to striped bass recruitment tbst l g . it seems unlikely that longer time series of data vould fail to show j a strong relationship between them. This conclusion seems especially l snce $ , valid water transport factors are known to directly influence ! i the survival a:d distribution of striped bass eggs and larvae (Chadvick l t et al. 1977). l As with striped bass, there was a significant statistical relation- i ship between an environmental factor (vater temperature) and recruitment ; for Atlantic menhaden. Although the relationship between temperature j and menhaden recruitment was weaker2(r = 0 39)' than the relationship j between percent water diversion in May and striped bass recruitment ; (r = 0.69), temperature still appeared important enough (statistically) that the relationship probably vould have been detected had we used data t covering a, longer time period. Indeed, there is good biological reason j i for the observed statistical relationship between temperature and menhaden j recruitment levels, for larval abundance in esturaries seems to be reduced during periods of extreme cold and laboratory studies have shown that j i r
' 20 larvae are sensitive to lov temperatures (Nelson et al.1977).
In contrast to striped bass and menhaden, American sbad showed a strong dependence of stock sice upon recruitment (r = 0.65), and data from over a longer time period probably also would indicate such a relationship. Apparently stock sice for shad, at least in the Holyoke-Turner Falls area of the Connecticut River, is at levels where fluctuations 8 It is tempting in stock are strongly reflected by variation 31n recruitment. to suggest that stock levels are low relative to the carrying capacity i of the environment and that stock sice could increase by a nontrivial umount ; before some envirotmental factor limits the population. This suggestion I is compatible with the fact that the shad spawning population has been 1 increasing in previously inaccessible segments of the Connecticut RiveI*. after installation of a fish lift at Holyoke Dam in 1955 (Leggett 1977). Another factor which limits the generality of our results is the choice of analytical procedures used in this study. Comparison of our results with those of earlier workers using the same data serves to illustrate .he dependence of our results upon the methods e= ployed. Leggett (1977) perfo xmed simple linear regressicas of 26 deviations (= R/R; R from the Ricker relat! ion) for shad on Connecticut River discharge rate and temperature, and he found that these two environmental factors accounted for -16% of the variation in the 62values. Leggett also perfoz=ed regressions on discharge rate alone, although he used a longer time serica of data, and he found that discharge rate accounted for no more than 3% of the variation in 62 values. The indication, therefore, is that ,
' temperature was the more important of the two environmental factors in explaining recruitment variation, aside from the variation explaine.d by l
stock. In contrast, our results shoved that log (discharge rate) accounted l for more of the variation in 6, (r = o.29 as compared t, r2 < o.02 for at I temperature a=* log (temperature)) and therefore was the more important
'L of the two environnental factors in explaining stock-independent varia-
-tion in recruitment.
Similarly, simple linear regressions of 6 deviations for menhaden on environnental factors were performed by Nelson et al. (1977), who found that the most important factorJ(ie., factors which gave the highest increasa 1. r in a stepuise multiple regression analysis) were several vater transport variables and discharge rates into Chesapeake Bay (Table 4inNelsonetal.1977). Our results based on regressions usin6 S g 2 deviations showed that temperature yielded the highest r value and the only statistically significant regression of stock-independent recruitment. Thus, choice of the definition for deviation of observed recruitment from predicted recruitment ( 4 or 6 ) affects the results, as may other , details of our analytical procedure, and interpretations must be te=pered accordingly. But a6ain, general conclusions may be drawn. For instance, i although e=-i c= ental factors shoved some effect on recruitment of shad (i.e., they improved the fit of both linear and nonlinear models), they . appeared to be substantially less important than stock size. This con-clusion was indicated by the failure of any environmental variable to pro-duce statistically significant regressions for fj deviations. Leggett l (19T() ;ag.4(y eencluded that envirocmental factors were i=portant determinants of shad recruitnent because k, deviations (his " density-independent variation in egg-to-adult survival") over the period 1935-1970 appeared r large and because environmental factors were shown by Marcy (1976) to i regulate juvenile year-class strength (which is highly correlated with t recruitnen+;) . Yet Leggett's regressions of fz deviations on environ = ental variables yielded even lover r values (:s 0.16) than did our best but nonsignificant regressions for 6, (r = o.29), and they therefore probably wre also nonsignificant. Leggett's results thus seem to parallel ours.
., q ? f %'} .,.-
j . 225 u
}
Asia final example, ~our ( $j) regressions showed that an environ-- j mental factor'(temperature) was 'significant in' explaining the variation . l t
.in ij:anhaden recruitment not explained by stock. Nelson.et al. (1977). .
. . likewise found environmental factors (albeit' different factors from the j one we found) to be important to reemitment after removing the influence !
.of- stock (1 e., 'by perforning regressions for 6 2) * '
It has been impluit in our analyses that the best regression ! I models were the most accurate ones (i.e.,themodelswhichmostclosely
' described the' data). Accuracy in estimating current abundance levels of fish stocks and predicting future levels of stocks, given information f t
on other (e.g., environment'al) variables, is certainly desirable and ; important, especially for valuable ecumercial fishes such as American stad j
. for j and Atlantic menhaden ands highly-regarded sport fishes such as. striped- l 3
bass. But there are criteria aside frca accuracy by. which the attractive- j t ness and . utility of modelsksometimes judged-- e.g., generality, f realism.(Levins 1966,) and simplicity. Thus, stock-recruitment relations l ( iRicherand3everton-Holtmodels) whi'ch attempt to portray in their ' structure the functional dependence of recruitment upon stock and other
.l t
factors may be more satisfactory than linear models because they are .; i more realistic, even though they may scmetimes be no more or even less l I accurate than linear models. On the other hand, linear models are mathe- l matically simple and therefore easy to use, and so linear models may be - viewed as superior to, even if sometimes less accurate than, non- ; 7knfere a i linear forms. fgfina1qualifyingstatement is that our conclusions f are, to some extent, specific not only to the data considered and analy- j h W f tical methocir employed, but also to, intent of, study--that being to obtain ; f the most accurate models. Readers who are more concerned with other l
- aspects of models may. arrive at different interpretations
- W owt (tis $3, l
* ' ' ' ~ , ,_ , _ ! '
- -f;+,
l
'(
f .. j I Table l'.- Res'ults from simple linear regressions of recruitment index
~
n .! (R) on independent, environnental variables (E) for the striped bass .;
. population in the Sacramento-San Joaquin Delta,-California. The i i
. fourteen most significant regressions arelisted in decreasing order j of r value."
Environmental' Variable (E) r Slope (=b)" pd l t I i
% diversion M 0.69' -2.84 (3) < 0.001 l
% diversion M-Jn 0.68 .30(3) < 0.E l ,
l
' log { outflow)M 0.67 1*39 (0) < 0.0dL . f lofoutflow)M-Jn, 0.64 *9 ) < 0.001' l
'% diversion Jn 0.63 -179(3) < o ,oo 1 !
% diversion M-Jn-J1 0.58 -2.43(3) 0.002 !
lofdutflow)M-Jn-J1 0 58 133(5) o,oog j logfoutflov)Jn 0.55 1.06 ($ O.002
% diversic: Jn-J1 0'.48 -2.03(3) 0.006 l outflow M 0.46 l'N 0.007 .
1 ( log { outflow)Jn-J1 0.43 0.011- : 2. outflow M-Jn 0 39 0 017 l outflow M-Jn-J1 0 35
## 0.0 25 I outflow Jn 0.28 1 93 0.053 f
1 i
^ Regression model is R = a + SE. ;
Key: M= Nay Jn = June J1 = July l Outflov = vater flow out of the Delta into the San Francisco Bay system. ! Diversion = vater diverted out of the Delta by local consumers ! and government pumping operations. -]
% diversion = heffective Delta inflow) - outflow /(effective Delta inflov' j 3
" Exponents to base 10 given in (); e.g., -2.84 (3) = -2.84 x 10 ,
d Probability of observing a slope 2 lb} if true slope = 0.0. p l p y r- p v '
J,f. .. l P Table 2. Correlations among wat er transport parameters " ~ and stock Second entries are significance levels (p) b site. .
$ Diversion. Log { outflow)
Ace Hay-June May June May-June Stock
.% Diversion May' O.92 0 97 -0 94 -0.85 -0 92 -0.18 4
- t
- V (0.53)
June 0 99 -0 94 -0 95 -0 95 -0.26 f T Y * (03'7). May-June -0 96 -0 93 -0 96 -0.23 W
- T (0.42) 0 95 0 99 0.16 l Logfoutflow) May t * (0.58) ,
June 0 98 0.12
* (0.68)- ,
0.14 May-June (0.63)
# Water transport parameters defined in Table 1, b Symbol (1) denotes significant nonzero correlation (p < 0.01) .
l t I
j' . s Table 3. Results of linear and nonlinear regressions of striped , bass recruitment on stock size and an environnental variable." First value. in each cell of the table is the residual mean square for the corresponding regression. Entries in parentheses for each linear regression are the r value and the overall' significance level fcr the regression (ns = nonsignificant)._ Values in parentheses (x/y) for . each nonlinear regression are: x = number of parameters in the model for which 9"$ asymptotic confidence intervals included 0.0; y = number of parameters in the model. Regression Model" . Source of Variation Environnent5 Stock Environnent + Stoch Linear (A) 136 x 109 (3)4.09 x 109 (o) 1.ho 'x 109 (o.69,pr-o.o) (o.o8,ns) (o.71, p < o. coa) Nonlinear Ricker (D)h.01 x 10 9 (E)179 x 109 (2/2) (3/3) J. (F) 154 ^x 109 (2/3) Beverton-Holt (G)390 x 10 9 (H) (2/2) ; (I)1.89'x109 (2/3) s
)
i l i
r, . 3 a. s-Table 3 cent. The environmental variable was percent of water flow diverted in May (Table 1). b Vaen the 9 % asymptotic confidence interval for a parameter included 0.0, it implied that the corresponding model could be simplified and r-still describe the data. Symbol (4.) denotes nonlinear models which did not simplify to a linear fem after fitting to data (No such cases j for striped bass). Entries (D), (G), _(E), (F), and (I) were based on regression 'models (1), (2a), (5), (6), and (8) in the text. The model for (E) included - i the environ:nental effect in the stock-independent tem of the mortality function M of equation (3), and models for (F) and (I) included the environmental effect in the stock- (density-) dependent tem. Regres-I sion model for (H) was intractable, and a fit to data was not perfo=ed. s b t I l l
*e
. f
> .,,. -t w
Table 4. Results ' of linear and nonlinear regressions of Atlantic -; a i menhaden recruitment on stock index and 'an enviror; mental variable. i Models and for=at are as 'in Table 3
' Regression Model Source of Variation Environment -Stock Environment + Stock 1 l Linear D (A) 4.657.x lo (B)701 x 10 '(C) 4 91 x lo (0 39, P< o.ol3) (o.08,ns) (o.2,pc.o4N Nonlirear l
Ricker. (D) 6.454'x lo (E) 1.16 ~x 10 (2/2) (2/3) I (F) 8 33 I lo (2/3) ! 18 (g) Beverten-Holt (c)6.88 x 1o (2/2) 1 i (I) 6.25 x 1o 7 (2/3) The environmental variable was the minimum of mean surface te=perature l at the mouth of Delaware Bay.- b Linear regressions were based on log (stock) in place of stock. ) 4 1 I i
, 1 i ..L
w=**** - i 4' e Table 5 Results of linear and nonlinear regressions of American - shad recruitment on stock size and an anviremental variable." Models and fomat are as in Table 3 Regression Model Source of Variation . Environment Stock Emriroment + Stock Linear (A)1496 x 109 (B) 5.4 x 10 9 (0) 4.13
- x 109 i (0.03,ns) (0 70, p< 0.001) (0 76, p< 0.001) l Nonlinear Ricker (D) 5 24, x 109 (D)309 x 10 9 (1/2) (2/3)
(F) 2 35 x 109 (6/3) * ; Beverten-E0lt (0)522 x 109 (H) . (1/2) ( I) 2 .11 x 109 , (0/3)* ! l a b ! The emrircumental variable was logarit6 of mean river discharge rate in June. P l I e
,h w v
4 ss,,
-e ,
E . .. - , Appendix 1. California striped bass data. Data for recruitment, stock, and relevant enviro : mental' variables , are given in Table Al for the striped bass population of the Sacramento-San Joaquin Delta, California.
.1, ,
W s L I. i l t 1
)
l i 1 1 a t I
u_ 3
. Table A1. Data .for the striped bass population in California. -
-x:
t>s LTA t>CILBo[Cf5f DnEA5eoso eF EFf E cTsu r D Ft I A I p ac Yt va n 3 nr > 1rvsma et Ruews atcg wg ,y7 ,p ,m y p pp.g % l'oN h18M gnJrx sam' ,f _ 4.m,4 ggp iM4 [4g da d - $15TE A4 (cf5Y ggp gd . 'y,,g g,,i,J (p p 14g ' hot dmIp-4 . s a
~
-' '\ We' I *" 'I 1953 139,160 0.319 1959 191,363 0.534 :. '
'3,756 1P,*70 0.601 *,ffg- /23,71 12,205 3,835 2,245 2,699 3,666 '16.426 11.100. .
1930 218 630 4,699 13,290 .11,1J7 1 ,775 322,250 0.622 ' 61,570 -8,500 3,655 1,85f 75 2,C62 4 C17 1931 2,974 3,815 4,260 20,679 14,500 ' ?'.E33 a 1962 207,460 0.592
- 0. 51 ._ /. 366,670 , {45900 18,180 10,320 2,f 3 5,0.,0 "- 2,791 3,563 53,940 i9,375
~
236,a40 52,989 19,060 4.228 21.CC3 19G3 1954 125,220 0.51}r # " 5,1905 1N','290 86 % 0 9.791 5,223 3.112 3,235 ^ - 3,798 - 4,650 '14.453 : 11,325 1 ,703; - 67,410 .32,365 .16,135 5,865 3,220 3,714 4,390 34,033 16,503 1 ,005! 19G5 127,610 0.655 0.623 l 5?,300 l'A,300 - 46,050 -9,836 2,435 3,150 3.332.- 3,101 4.613 9,6E5 1.,655 : 1956 247,9:0 . 1,935- 2,168- -2,732- ^75,593 14,433 . 61,69 27,203 0.647 -6,720 52.490 74,558 59,670 23,815 IM7 148,993 3,665 5,526 4,723 5,187 13,749- 11,451 12,623 ' t 1953 133,700 0.637 - 92,310 100,740 6 3736 3,590
-13,800 66.220. 64,335 46,175 13,015 3,205 2,504' 3 3382 ' 65,630- <3,3 *7 - 22,5;3 1969 115,7 3 0.647 -
13,555. 1970 125,470 0.515 . 50,560 83,830. 10,635 6,029 5,143 '4,016 5,025 5.252 114,721 12,C70 . 21,410 25,402 20,990 11,710 4.455 5.748 6,423 33,639 28,220 21,430 1971 06,020 0.695_ 33.5E3 15,033 5,131 2,a75 6,237 6,341 5,227 5,024 13,227 13, % 9 1972 203,130 6- 0.572 - 143,400r 44,910 ~* 30,200 .34,200,' 11.525 g 7 ,237 4,550 ~6,358 -7.345 7.577 17.653 15,763 15.535, 1973 -143,500 0.5S3 - . 1974- 213,420 0.683 125,810 , 1975 2G,510 0.537 -58,620 . . 1976 60,370 . 13,910 - Data in columns (2)-(1): 6 from Stevens (1977, Table 1) for 1958-1.72; unpublished data for 1973-1976. Symbol (f)denotesrevisedestimate.
Calculated using equation (9) in this paper.
! Calculated using equation (10) in this paper. l*NANftE8W'Uhld _ 4
/
Mean of the daily estimates from the California Department of Water l'esourses. C From California Department of Fish and Game (1976, pp III-16). - Values are means of daily watier diversion 1
- from the Delta by state and federal pumping stations.
E Effective Delta inflow =(total water inflow to the' Delta) - (inflow froma theSanJoaquinRiver). Inflow from the San Jea, quin River is considered totally diverted by' pumping stations, !i .
+ ,
- t
- I
- i
.---..._.m_ m _m. -___.,--. _ . . _ .. _+ - . . - ..c _~ , .- .. . e- 4- - . - ---s .- 2 - _ - - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
?
.i Appendix 2. }Jf eviations from predicted reentit=ent.
A ' l We employed standard residuals, f, = R-R, to represent deviations of observed recruitment (R) from predicted recruitment (R). positive values indicate greater than predicted recruitment and negative values indicate less than predicted reentitment, with 6, = 0.0 being the null value (i.e., no deviation from predicted recruitment). An alternative definition of deviations is the survival index, 6 =R/A (Leggett 1977, Nelson et al.1977), 1 vith null vaiue 6 =g 1.0 and where values of 6 2> 1.0 tndicate greater than predicted recruitment and values of 6t< 1.0 indicate less than predicted, recruitment. We used only 6, in our analyses, however, for the follwing tVo reasons. If we cnnsider R and $1 to be randem variables, then 8, and 6s are also randes variables. T M ng expected values, E(d)=E(R$)=E(R)-E(R)=0, f h3
-irea., E(6,, ) is egal to the null value. However,
= 1.0, E( k) = E(R/R) / E(R)
E($) ll 1.e., E(k,) does not equal the null value of 4, . Values of 6, vould deviate i from the null value, on the average, simply as a consequence of the definition of 8,. Thus, values of f j 1.0 do not necessarily reflect l a poor fit between data (R) and the function used to generate R, which I deterred us from employing $g in the analyses presented in the text. A second, e=pirical reason for preferring deviations 6, to 6 energed from preliminary regressions of striped bass data using both i 5, and bg. Simple linear regressions of d against environnental 3 variables yielded higher r values and more significant slopes (smaller p values) than did similar regressions of f . This was true for deviations j
+ i 1
l \ I l l
r .y ,.
*WW*D* 4
- e.
derived from both Ricker (Table A2) and Beverton-Holt recruitment functions. Thus, deviations defined by 6, yielded more effective regressions .than did deviations defined by 63 . Table A2. Regressions of deviations from predicted recruitment, k and 6, , against environmental variables for California striped bass data." g8 b g2b. 'l Environmental Variable (E) j r Slope (=b)* P d r Slope (=b) p t l Log (outflov) May 0.59 1.24 (5) 0.001 0.22 3 32 0.09 June 0.53 9 83 (4) 0.003 0.20 2.63 o.11 May-June 0.58 1.17 (5) 0.002 0.22 3 15 0.09 1
% diversion May 0.61 -2.53(3) 0.001 0.29 -T.61 (-2) 0.05 -
June 0.51 -1.53 (3) .0.004 0.17 -3 83 (-2) 0.14 I May-June 0.57' -1 99 (3) 0.002 0.22 -5.k (-2) 0.09 ! i I g i Regression model is {(or6)=a+SE. 2 { D 6,=R-R; 8=R/R. 2 Values in () are exponents to base 10; e.g.,1.24 (5) = 1.24 x 100 . [ t Probability of observing a slope 2: }b} if true slope = 0.0. l: I I h f I l i es **=. we e a e me+-- == een enemusmaam,
.P. .. /.
, /? , x ;
% I Appendix 3 Outline of Regressi$n Analyses and Su= mary of Results.
Outline of Analytical Procedure Re6ression analyses were performed for each of the fish stocks in the fol' loving sequence.
- 1. Simple linear regression of recruitment versus stock and environmental factors to identify the most important (statistically significant) predictor variables.
- 2. Multiple linear regrersion of recruitment versus stock and the most i=portant envirecmental variable ('s) identified in step.1.
- 3. Nonlinear regression (parameter estimation) of recruitment versus stock using basic Ricker and 3everton-Holt stock-recruitment relations, and s1=ple linear regression of rec:uitment (transformed) versus stock (transf :med) using a linearized 3everton-Holt relation. These regressions also provided predicted values for recuitment (R) which were used to compute deviations of observed recruitment values from predicted values (b, deviations in text and below).
- 4. Simple linear regressions of k deviations (from step 3) versus environ-mental variables. This step identified the environmental factor which was most closely related to variation in ree:uitment level after the 1 effect of stock upon recuitment had been accounted for.
- 5. Nonlinear regressions of recruitment versus stock and one envirocrental :
1 variable (frcm step h ) using Ricker and Bevercon-Holt relatt ons modi- l l fied to include an environmental variable . I l Results from steps (1), (2), (3), and (5) were used to compare the -l 1 l effectiveness of the regression models employed.
[ ij . i _ ,'. i , . . . : ; ..
. ' -. - . . - . . - ~ . -- . .c._ .- . . .
' {~ ~
1 1 s, l 98 .* . i List of ~ Abbreviations l All Stocks
't = recruitment level S = stock size E = exponent to base 10 Exp = exponent to base e Log'= logarithm to base 10 a,b,c,d,e, - parameters (coefficients)'of regression models.- ;
Striped Bass i Delta outflov = vater flow out of the Sacramento-San Joaquin Delta into the San Francisco Bay system.
-Diversim = vater diverted out of the Delta by 1cc al con?'=2rs and government punping operations.
Effective Delta inflov = (total water inflow to the Delta) - (inflov from the San Joaquin River). Percen- (%) diversion = ((effective Delta inflow) - Delta outflow)/ ! (effectiveDeltainflov). DM = diversion. in May DJN = diversion in June ! DJL = diversion in July l DMJN = diversion in May-June DJWJL = diversion. in June-July i DiUNJL . diversion in May-June-July ; PDM = % diversion in May _, l PDJN = ~ % diversion in June PDJL = % diversion in July __
/ .s' 't@'MN Nl, PDMJN = % diversion in May.-June ,
PDJNJL = % diversion in June-July ! PDMJNJL = % diversion in Ma -June-July ' h s _._____m_ _ - _ . _ _ _ . _ _ _ _ _ _ _ . _ .
- 7.. y .
F: e, OM = Delta outflow in May OJN - = Delta outflow in June. OJL = Delta outflow in July OMJN 1 Delta outflov in May-June OJNJL = Delta outflov in June-July OMJNJL = - Delta outflow in May-June-July OML = Log f Deha outnow in May 10 OJNL = Log 10 of Delta outflow in June OJLL = Log 10 f Delta ouflov in July OMJNL = Log 10 f Delta outflow in May-June OJN7LL = Log1 0 f Delta oufflow in June-July CMJNJLL = Log 10 f Delta outflow in May-June-July Atlantic Men'haden DG = sum of monthly average discharge rates from the Su:squeha--a, Potomac, and James rivers in July-September of the yegygng EK1- = sum of mont$$y[$$$al (vestward) Ecnan transport rates in Ja""a 7-March of the year-class year at lat. 35'N 1ong. 75 W. 3 EE2 = s.:= of monthly averaSe zonal (vestvard) Ecnan transport rates in January-March of theyear-class year at lat. 33*N, long. 78*W. EK3 = sum of monthly average zonal (westward) Ekman transport rates in November-December of the year prior to the year class and January-February of the year-class year at lat. 39'N, long. 72*W. EK4 = sus of monthly average zonal (vestvard) Ek=an transport rates > in November-December of the year prior to the year class and January-February of the year-class year to lat. 39' N,1.VI. 75 W. T? = minimum of mean surface water te=perature at the mouth of : i Delaware Bay in the year-class year. American Shad DG = mean discharge rate of the Connecticut River in June. TP = mean water temperature in June. 1
. i. , ,
/* ~
Regression Su:znary .. __ .____. ._ .. _..._ _ _. . _ . ___ .. _ _ _ _ _ _ _ _ _
\ ._. - ._ . . . _ . . _ . _ . . . _ - - . . _ . _ . . . _ _ .
_____._____._I. Residual 2 . Remarks
'Model .
i Mean- - r . P > lFl Square (linearmodels) (linear
- -mode 1s)
. . - . . _ . ,(RMS)
.. _____.... Striped Eass. .. .-.__ ._ ____ _ _ _. _ _ _.. _ _ .- - _ - - _ _ .--__
. f.__ A*_ _a _t E S _. __ W.O.D_.AS__ M.#C 0 341- Modd5_1-L6..n.re._.51%e_
J. A a.__.d J 6 . 0M 2'39.5 _E *L (0,M) o,.o p_o l[ntat_tegrf EIon_rW4ed5. - J. A. s a _4 h. 03 LAla_E.9 /o AS). c 053 4 A* a +b_03L_ _._3.d ?_5._G8 (Q00 . O ,A S_S _ - 6 _R - a *6_0MUN t.9Lx_.Ea. _ _LO.:0)_ c.e l a. L R.
- cc+.__k.:_ c.3ML __.3AU E9 (0A0 0.0.81
- 7. g. . q + b_. o.g.g at_,_ _g S SA_.E 9
. . Co.8J) e,o25 _.
8
&*_oLibl.eML __.. _L_4 8_d. E 9 40,00/
. . . _ (0.4.7) _ ..__3. _..Fn_ 4 +_.b ou t.
._ . A.e o. r E9...._. _(.o. 55)___ . __ o. coa . __ _ _ _ _ _ . . _ _
( 10. __ RL.ALb:.oc Lu - n. ft:_ M_b osNL 3.M x 19._ _ lo>vi).. .__ ._o.l.40 l.. /.t .x_ El Co,6$. _ 4.o oo;
.. It.. _ R.= 0. + . b * 'U . _ _. _1.S N x E T /0 4&)_ o. o l L _ _. ._ _ _ . _ _ _ _ _ . _ _ _ _ . _ _ _
- 13. 9.=__qt.brom,m:nL l,21x_30f __(0.fS._) _. c. eor .,
ee l *f. 8 '_' _Qt.b *.D Pt ___ 3 44 r_ Et. _ (01s). e.J 31 . . . .
.. . _. .. .. ._. 11 __ J.? ot t_ b .Due ..-- _._. . _J M.d Ei . _. . (O. II) . ___. _ _o. g.4 6 __ -_. . _ _ _ _ _
_ I6... R = At b . Dn 4 A0x Ei . (0.c5) _. O. Vro . . _ _ _ . _ _ __ __ __ . . _ _ . .
. . ro . . _ R.t o.+ b -DMs N M 4.xE.9.._ (0.JO_.___.o.159. . _ _ . . . . _ _ _ _ _ _ _ _ . . _ _ . _ _ _ .
. _ . . . 11___. R
- At b D393L 47 4 E3 __ _. (0 01) . . . c. 3 40 . . _ . _ ._. _ . _ . _ _ . . ,
_. . H. .R. t c4 +b . 2 MWJ L ___.3.S9 x. Ect. . (0 l A) . o. Al L -___ ____ _
. _ _ _ . . Ao.. . _ R 'L CLt b ?? M _ _._ l. 5 6 x.F C L_ _.(o.69) _._ 3 e. e o 1_ _ _ _ . _ _ _ _ _ _ . - - - -
]
. . . . . _ A l... .. . S. ' OL + h TD 'N _. _ L 6'5 LE.1_. . .Co.6 3).___ _4 c. e o L __..__ __ .__ _ ___ _. _ _ -
. . . . ._ . 2A. .. R.'. 9.i b f D J L_ _ 3J6 r E.'} _. M 11).. ._ ~ 0. L3 E ._.._ . ... . _ . _ _ _ l 1
. .M_ .. D 0 K..E9 br. d .. . 4. 0.0l .____ . . . .
_ . M. . _ M clth _. TONG.L _.A.3M_E9..(OMS)
. . c. o 0 6 _ __ __ _ _ _ . ._ . _ _ . _
(_. . . _. As . . ..V_.A+ b 3.D n*Ln.D. ._J. dor 3.1 . (L51) .o.ecx__.._- __...__ . - . . . . _ . _
.tL it. _ a.+.b .l.eg (s) 4'.# . M 1o. 06_ _ o. fs L. .__ _____ _._ _ -. __ . . _ _ . .
- ___ -.- _ ---_-______-.__ . _.__-___ j
3 S
'2 Model ___ _.__ .PMS . ,_ _. _.. . J. ._ __ _ p >_ lF j _. _ . Remarks . . . . , _ _ .
_ _ . . . . - . _ . . _ . . - 1 _.tt. A= _as_.b.5.t_c J D 6 idoe.EL __Co.oll_ o oo L_ _ .__ ModelsM:AB .w multiple
._. ._. AS. . _8.=__ o.a_bS 3(.0 t.e .en M _L 414.E 3 (o.701.,._.o. col
_. _ [0)ee.0,._qdon _ m od'el5..
.21.__R=_g. S. _Eg (-b 5)_ 3.o l x. El _. _ _ . _ hsil.bAc2so4sI 30,,_8,, :. a5 ____3to.xp b ic. B e o t d o n _1 h o_ E I+ b 5 JL h'8 A d/S + b l.0.03 2:-R (0,o$ Q.910 lmfattyd_.2tevt/ ton-Molt clo
. . _ JA._&:.cu.s.Eq_(_b.fD6._c0)_l_9.13._M
.. PocL14M__kiMet..no3*l JLth
.._ 'estonesa.fsLisa *
._ . . _ _ . . _ _ _ . _ . _ Sb ck-iWg.endco.t__tsco
. . . _ 331= e.S_Eq[ bit _c/S!fDB) WM9 __ ___ ._._ Modifdd._Rwe.c.m 4(L_wM _
. . . _ , _ . _ _ . _ _ _ _ . _ _ . _ . _ . . __ _.__ __.ewWnntA14_eMd in . . . _ _
( . _ dl 3
- .._Mocr. .attuaeret_:tser- _ _ . .
_ _ __. . __ ._3s. . _f.=. _ 2 . M_M _ . __ Ao&6W hetten:%lt_rtodeL
. _ . . .Ab. C ~. . _N4 . _ . _ __. _= with..enven mada.LeMecidn _
_ . _ . _ _ _ den @ _degenden6_ftm. .- __ 35 6, .= . ot s _b .cH-.. _ . ... M02E9 . @fD 0 01b _ -.. . Modsts 35~9b are Single _ ~ . 3L. by A t_.b Ow___.-._ A 4U 2 8 - (0 33h o.0 3% - . Ntv ys&dns--_6g . .
. . . 37._ 6, = 4 + b 0MN 4 f 9 3 Ei. _ . (0 3C._ e.o 1.o _ ___._ . devdit' erd _ _ln Mode 35 . ..'35'.'33 _
_ _ . 3 6. __i h = ._os +. b2. o mm'JL. ._. . A M x E.9_ _ . Co . 30. . o.o;yt .__... _ _. ce tx56_.on. k .3ake.s_. ppm, . _ _ 6... 6, i_A t b t oM k _ _..l4 3 xE 1 _ .__.(0 59 L. o.oc) .._____ 'dc 6asic. E Mer.nodel_ . . .
._% _ k = 4. _.b *_o M L 1.f8 x E3_ .__(o.531 0. 0 0 3._. - ____ _. - -
__.E. , h = . E_t b... o M W L . l.65.x Ecl._.._(G IFl___o. coo _.
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Model. RMS r' p >. l Fl Remarks __...._..._...._p __ ._,_
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r1 y . v Model RMS r p>lF, Remarks . . . .J13 b,.*_-.Cetb :lkl- . . 0 05.e EJ3 30 005)_ ...._.. O. 8l7. . .. __.Q.d Ma;tum5 . in Ee 4*IJ . ,_ . . . _ H . 6 J ._ A t b E K L _ _ _ . - 6./16318 _.I0.00 _ .._ 0.300. l'A3.-D4.Atr. _botd cm.$ _ . _ : _l AS- b 4_8t.t.b *..EK3_.- --. . _ . _. . . 00 0_^ E18_10 0 %) .__ . .._o.5 94. .. va kea efrom T.ht._liarijel. J Ah .;be* ._ott b E84 _. . _ _6.81.E.11S_.40.0.9) . 0 137. 3werton _kMinodt.L N441 09_ (023?1 __o.ots _ . _.J1L__h_ _ av b I R ._ _ L21 di '._ at b. D6 sm x 09 (o.11 c. tat @ b,* _ A tb _le (A rJ,) . 7.09x E:11 I 92000__ __0.411 . . . __.13 k &_b_LapEG) sa3x E11 /oJO o.13 0 (3L.___d.2 __f loix Ei2 (0.09h a.356 Ath % lsF3) 90 _k : D.bdeg. LEK 4) 6.0J r .c r9 lo.ji) e,103 R1 k* 4.tb.z_1.03CTO . f.$.tt218 fodf) 0:11 1 _ __.6J31.E !8_._C0J3) 0,1M .. _ . ._A_ M 8._ _M b. .14gID 6) { American Sh_a_d ... ls S. _. .R, .n oa h :_S __. 5 44' M f0 651 n,oot Ma.dels fSS-MO._Gr% s kgC .. . 134._. __R*__A+ b iT E _. l.53xmp_ la.oi)_. o. Dig Idea.c_regec>sien._rse.dels. 13 9. _ A? _R+ b :_DG. . - .._lJ4_.x Elp__GO 00 i)__. - 0. '!!5 _ ___ ._. .. 138. .. . R.* At b . le g (5) _ _ _ ._ . ._. 3 05319 (0. 6 0 ___ _ . 0.003 __ ._. . _ . _ _ _ _ _ _ . . _ . _ . . .___. . 131. _ _ R :.9.+b - Q(7P) . _. ._.. __L53 x en..(o.oi) _ o.94S __.__ __ .. _. . ._ . l't 0. . . R. 4.r b l o;6G) .. l.50x Ei0. (o.o3) _ . 0.600 _. . . . . _ _ _ . . . . l . . ..t%_. . b_ . A+ b. S 1. c.D G._ . .. __. _.d:3"> E3._.fo.?4) . . __.o. cot _ _.dodt h _.l'tl.-JiT.Ar.!._.nulf@ .. .Jft.__R!.e b S.4._C l#$CM)___ _88 e 39_ (0.00_.. ... 04 0 R..___ .J dee . Mrc65en _ Mod Sl5 _p3, _R,s a+. b.S i .t'.7P ._ ._ .._.5,1?r. M _ lo.6S') . ._.O.o09 .._ 1 _ .. .. . . . JM _..ks+_b.S y & Log.OC. J.'33x Eci10 6s')_ o.00't - . - a a. a m ab.s>.._ _s.u a, __ sam.~w. _ A D,- a. 5 _._, ._. _ _g. p.g i n __ _ __ . _ . . _hio .keeten.__%it node) _1+ b 5 ._. - _. _ _ - .. _._ _ _ . - . _ - _ _ . . _ . . _ - - . . . . h w &em.m.. .+4_4 .r b, ; ... - E _.. . n v .i _. _ M i G. . _. .. ._ ____ _ M .. 2 .. ._P_,d Fl -Remarks t . .. -_..... . .. _ _ ___ _ _ _ _ . _ . _ _ . . . _ _ _ . . . . ._ - . _ _ . 180. %. . xf t_ b _. . 2ao ... co.w) . . e.co t _ ..___.knedgea _5 eserw-%h - .. . . . _ - . _ _ . . . . . .__ _ _ _ _ _ _ _ . _ . _ . _ - - oo del .. ist _. P.
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Njiftid_.Esec_.redeLiech _. digttof. Pit ftk CMt l'M diV t'adt%LM "defM. i ft b e.$._ Q.l_bd2_e.S_g(msa _ __ _ _ __. Adp M4r_mh.LM . _ _ 4.s.sn9 - . _ _ . e a r,a m afalt M ec4 A ___ shteF.de.paded b _ , _. iso. L a5 s.itrE9 ._ _ _. ModiM4_hte_ tar-%2e mejeJ_ D b'S + c.* %lDGM _ dwam&t ak.O. _ _ . . _ _ . . . _ _ _ _ . . . 4u_5H 3 dytod en.t_lerfs;__ __... ( __ _ 15k._h,i_ Afb.T.P 62._ _c$, =__a. .t b f.DG__ . __ __. GdB A.11__lo.og __. . CtJ3L___ 3.98tE_'l_lo.M) ._ - . _o. las_. Models_151-16L. ate _sibrle _. hhee_.tysMens,_.6rdeht6n is3 _6,*A.e Ly.-S). _ .__ .S.16 x E3. (0.00 _. _. .o.?oL__ . _ in.modth_1st-lSqJttf.__bue,d. en . __.. 15 4 6, " Clt b *l.og CD M 3.90s E_'Lio.3ol. _. . o.oks "R._ 9 f ac._f.ren_ the _htsiz . _ _ _ _ _ _ _ _ . . . M k e._nated .. ; I SS. b,=.x1b.TP _ ___. _.. _ S.l4 x .E9 .(0.0 0 0.03 _.. bs .ded.%s sh na k (s 1 s s - ss . . . Isb. by.s A t b D 6.. ._ ... _ __ _.. _.3.9 51 E9 lo.M) 0.10 5 . . _ An.. based _o it $._.t<hes._h tn . 157 . . b, = Ath f.c GTf) . __ .-_ F83.xE.1l.0.04..- .0 613 . _lke. hetsti_3evtttsfLGald r is8 . b,.Eatb . log (D&) _. . 3bh.E3f.o.M).. 0 069_. _ - . _ ~. J 5 t. . 57 c._Rt b .TP_. 6.lD El.. (0 ot) . ._ . 0 ?4t.. ..__.6._ d.e v(q.6.045_lnEodc.ls_tS.T. ... A 6' . 160 . 6pt.A+b iDG_ _ ..__S.3? x E9. (013) _.. 0 M/ IM afe._lg. sod _on_Ltdue5 . l 6l, . 6, _Q1b :_%CTP) ... ._.__. 4.11x g() (0 00 _ o,?S3 % ._t%._lineq63t,d . . . _l G t. . 6, . 4+b % CDG) .._. _.6%.f.'L(041) _ __ 0.130- - 3tuerten-9/0 ft.14cdt L ___. .. f%- -.w .p g . p . - 4 l . . ... .' S..ign_if_ic. a.n.ce_.l.e.v. e.l. , of_'o. ver.all.. regres sion. .. .. :.. . .2 . . - . _ . .. . - - - - - - . t The linearized Beverton-Holt model gave very small PM3 values because - the criterion variable (1/R) for this model had verf anall values for .g.h'bM 'cannot be dampaFed'iFith~5tlief liio'dels g g,- , 1 --by-using-RMS-values -because- the- other-m,dels -had a-different criterion ON1y. comparisons.vith_other 11near models.,. using-r 2 ._- vaH able (R) val'es; u are valid. L I' 4 .k 5 e .I e M em. e 4 e I l i s f .e i n..- ' l . . . . _ . - . . . . -- .- - - - ..~ - . -- - - -- . - . -- --- 1
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