p. 1

8. 0 Reference s Page , H.M. , J.E . Dugan , D.S . Dugan , J . Richards , D . Hubbard , Effect s ofa n offshor e oi l platfor mo n th e distributio n an dabundanc e o f commerciall y importan t

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197 5 throug h Apri l 1976 . Repor t t o Washingto n Publi c Powe r Suppl y System . BatteUe-Northwest , Richland , Washington . 1976 . Page , T . L. , D . A . Neitze l an dR . H . Gray . Comparativ e fish impingemen t (a t tw o adjacen t

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estimatin g northe manchovy , Engrauli s mordax , spawnin g biomass . Fish . Bull. , U.S . 78:541-544 . 1980 . Parker , K.R . an dE . DeMartini . Adult-Equivalen t Loss . Technica l Repor t

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Fis h Game , Fis h Bull . 126 . 7 0 pp . 1964 . Phili p William s an dAssociates , Ltd . Elkho mSloug h Tida l Hydraulic s Erosio n Study . Prepare dfor : U.S . Arm y Corp s o f

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antennarius, yello w crab Cancer anthonyi, an d Kellet' s welk , Kelletii kelletii, i n th e vicinit y o f Littl e Coj o Bay , Sant aBarbar aCounty , California . Calif. Fis h Game . 73:88-98 . 1987 . Reilly , P.N . Dynamic s o f Dungenes s crab , Cance r magister , larva e of

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8. 0 Reference s Ricker , W.E . Computatio n an dInterpretatio n o f Biologica l Statistic s o f

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excentricus (Eschscholtz ) embryo s an dlarva e b y zoe aofth e re dcrab Cancer productus Randall . J . Exp . Mar . Biol . Ecol . 90:193-208 . 1985 . Saila , S.B. , E . Lorda , J.D . Miller , R.A . Sher , an dW.H . Howell . Equivalen t Adul t Losse s o f

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Seabroo k

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h Us e o f Fuzz y Logi c t o Represen t Parametri c Uncertainty . Nort h America n Journa l o f Fisher y Management . 17(4):811-825 . 1997 . Sa n Filippo , R . Diet , gastri c evacuatio n an destimate s o f dail y ratio n ofth e gra y smoothhound , mustelu s californicus . M.A . thesis , Sa n Jos e Stat e University , 7 0 pp . 1994 . Schiel , D.R. , an dB.C . Welden . Response s t o predator s o f culture dan dwil dre dabalone , Haliotis rufescens, i n laborator y experiments . Aquacultur e 60:173-188 . 1987 . Schlotterbeck , R.E. , an dD.W . Connally . Vertica l Stratificatio n o f Thre e Nearshor e Souther n Californi a Larva l Fishe s {Engraulis mordax, Genyonemus lineatus, and Seriphus politus). Fisher y Bulletin . 80(4):895-902 . 1982 . Schweigert , J.F . an dA.S . Hourston . Cohor t analysi s an dmortalit y rate s ofth e Barkle y Soun dherrin g stock . 1972-1979 . Can . Tech . Rep . Fish . Aquat . Sci . 960 . 3 7 pp . 1980 . Selby , R.S . Som e aspect s ofth e ecolog y an dbiolog y o f tw o Cancer

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Tow . J . Cons . perm . int . Explor . Me r 32(2):232-248 . 1968 . Smith , P.E . an dS.L . Richardson . Standar dTechnique s for Pelagi c Fis h Eg g an dLarv aSurveys . FA O Fisherie s Technica l Pape r 175: 1 -100 . 1977 . Somerton , D . A . A compute r techniqu e for

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sexua l maturit y i n crabs . Canadia n Joma l o f Fisherie s an dAquati c Sciences . 37:1480-1494 . 1980 . Starr , R.K. , A . Johnson , E.A . Laman , G.M . Cailliet . Fisher y Resource s ofth e Montere y Ba y Nationa l Marin e Sanctuary . Californi aSe aGran t Colleg e Technica l Repor t NO . T-042 , 10 2 pp . 1998 . Steele , M . A . Populatio n regulatio n b y post-settlemen t mortalit y in tw o temperat e ree f fishes. Oecologia . 112:64-74 . 1997 . Stephens , J . S. , Jr. , R . K . Johnson , G . S . Key , an dJ . E . McCosker . Th e comparativ e ecolog y o f thre e sympatri c specie s o f

Californi ablennie s ofth e genu s Hypsoblennius Gil l (Teleostomi , Blenniidae) . Ecol . Monogr . 40(2):213-233 . 1970 .

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### Stevenson , J.C . Distributio n an dsurviva l o f herrin g larva

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dD . Foumier . Environmenta l variatio n an

drecruitmen

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l Workgroup . 1999 . (SEW) . htt p ://www . iep.water.ca.gov/suisun_eco_workgroup/workplan/repor t Svetovidov , A.N . Faun aofth e U.S.S.R. , Fishes , Vol . 2 , No . 1 Clupeidae , originall y Publishedi n Russi a i n 1952 . 1963 . Taft, E.P. , Fish Protection Technologies: A Status Report. In : Powe r Impact s o n Aquati c Resource s Conference , Atlanta , GA , April 12-15 , 1999 . Sponsoredb y Electri c Powe

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e (EPRI) . 1999 . Talent , L.G . Foodhabit s ofth e gra y smoothhoundMustelus heniei, the shovelnos e guitarfis h Rhinobatis productus, an

dthe Ba t ra y Myliobatis californica i n ElkhomSlough , California . Calif . Fis h Game . 68:224-234 . 1982 . Tasto , R.N . Aspect s ofth e biolog y of Pacifi c stagho msculpin , Leptocottus armatus Girard , i n Anahei m Bay . I n the marine resource s o f

AnaheimBa

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dC.W . Hill , eds.) , p p 123-135 . Californi aDepartmen

t o f Fis h an dGam e Bulleti n 165 . 1975 . Tener aInc . Diabl o Canyon 316(b ) Sampling Pla n an dModelling Evaluation . Prepare dfo r Pacific Gas an dElectri c Company . Sa

n Francisco , CA . 1998 . Tenera , Inc . Fina

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l offis h collecte dfro

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r Consolidate dEdiso n Company ofNe w York , Inc. , New York . 1977 . Teylaud , A . R . Foo dhabit s ofth e goby , Ginsburgellus novemlinaetus andth e clingfish , Acros rubiginosis, associate dwit h echinoid s i

n the Virgin Islands . Caribb . J . Sci . 11:41-45 . 1971 . Thomas , D.H . an

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Humbol t Bay

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dP.E . Smith . Filtratio n Performance . I n Zooplankto n Sampling , D.J . Tranter , Editor , UNESC O Monograph s o

n Oceanographi c Methodolog y 2:27-56 . 1968 . E9-053. 9 8-1 0 MLP P 316(b ) Resource Assessmen t 4-28-200 0P. 4 8. 0 References Trask , T . A descriptio n o f laboratory-reare dlarva e o f C . productus an dcompariso n t o larva e ofC. magister. Crustacean a18:133-147.1970 . Trumbl e R.J. , an dR.D . Humphreys . Managemen t o f Pacifi c herrin g {Clupea harengus pallasi) i n th e easter n Pacifi c Ocean . Can . J . Fish . Aquat . Sci . 4 2 (Suppl . l):230-244 . 1985 . Turner , C.H. , E.E . Ebert , an dR.R . Given . Man-mad e ree f ecology . Calif

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fishery o f

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E9-053. 9 8-1 1 MLP P 316(b ) Resourc e Assessmen t 4-28-200 0P. 5 8. 0 Reference s 

### Zweifel , J.R . an

dP.E . Smith . Estimate s o f abundanc e an

dmortalit y o f larva l anchovie s (1951-1975) . Rapp . P.-v . Reun . Cons . Int . Explr . Mer . 178:248-259 . 1981 .

E9-053. 9 8-1 2 MLP P 316(b ) Resource Assessmen t 4-28-200 0Appendi x A —Estimatin g Tota l Annua l Entrainmen t 

# Appendi x A Estimatin g Tota l Annua l Entrainmen t A n estimat e o f

tota l annua l larva l entrainmen t a t a n intak e sourc e (i.e. , eithe r th e ne w combined

cycl e [CC ] unit s o r

Unit s 6 an d7 ) can b e expresse da s 

# *= I ;= 1 

### D; di 

## v..

*= 1 L /= ! •ijkl (Al ) wher e x iiki = measure ddensit y o f larva e in th e /t

h to w (/ = 1,2 ) withi n th e k\h cycl e (k

- 1 , ...,4 ) o n th e y't h da y (_ / = 1,... , D ( ) i n th e rth stratu m(i =l,...,L); Vjj k = tota l wate r

intak e durin g th e kth cycl e {k = ],.. .,4 ) fro mtheyt h da y [j= 1,... , £),- ) i n th e rth stratu m(

z = 1,... , L); D t = numbe r

o f samplin g day s i n th e rth stratu mo f whic h d

t ar e sample d(nominall y d t = 2). Here , atempora l stratu mwil l b e define da s a2

- o r 4-wee k perio d(i.e. , dependin g o n tim e o f year ) wher e in 2 day s ar e selecte dfor sampling . Equatio n (Al ) can als o b e expresse di n term s of avolume-adjuste d estimat e wher e L 

# v A

v, *- i y=lL * 4 1/ 2 t= i L ijkl

/= 1 (A2 )

an dwher e d, 4

j=\ k=\ D i4 j=\ *= i Nominally , d( wil l b e 2 day s fo r al l tempora l stratum . Th e varianc e o f E [i.e. , Equatio n (A2) ] can b e expresse da s 

## Var{E\E) = £

JL 

## yVu 

# <*, 2 

# i- 4

D. ij 

### d, £ ijA A 4 S 2 

# -4zz ^ A i y= l *= 1 (A3 ) wher e P. 6

E9-053. 9 A- 1 MLP P 316(b ) Resource Assessmen t 4-28-200 0P. 7 Appendi x A —Estimatin g Tota l Annua l Entrainmen t

—\ 2

_ _\ X ijkl ~ ^ijk ) 

# st = 

# '= ' *l>* / 

# K*- 1 

# ) Xyk ~ ijkl N, ijk Njj k = tota l numbe r

o f tow s possibl e durin g th e kth cycl e (k = 1 , ...,4 ) o f

they't h da y (y = 1,..., dj ) in th e rth (i = \,...,L) stratum ; an dwher e

—\ 2



## "(A-i ) ; Ejj= tota l entrainmen t

durin g they't

h day ( y = 1,... , Z), ) i

n th e rth stratu m(/

' = 1,... , L); A E,= 7 = 1 D. Varianc e (A3 ) i s base do n th e assumptio n tha t d( ar e arando msampl e fromZ) , day s in th e rth stratu m (/ = 1,... , L). Th e varianc e als o assume s th e 2 to w volume s ar e arando msampl e ofth e intak e wate r durin g th e hh cycl e (k

= 1 , ...,4 ) o f

they't h da y ( y = 1,... , dj). A n unbiase dvarianc e estimato r ca n b e expresse d(Appendi x A ) a s

Var(E\E) = %

an dwher e /= i

- ,2 _ 7 _ ViJ j </ , 4 V

2 ? 2 n £, , n *->£-> ijk^xijkl D-. "• QJXM

2 (A4 ) 

# Z(V^ ) Z 4 1=^ - an dfurthe r 

# * 2 = —

x ijU 2__{

X iJ^X ijk) 

### (2-1 )

E9-053. 9 A- 2 MLP P 316(b ) Resource Assessmen t 4-28-200 0P. 8

' 1 " Appendi x A —Estimatin g Tota l Annua l Entrainmen t

X ijk ~ 2 2_ , X ijkl /= ] 

### 2 The estimator

fo r tota l annua l entrainmen

t fo r the Mos s Landing Powe

r Plan t new combined-cycj e unit s (E T 

### ) ca n the n b e written a s hj T = t c c 

### wher e E cc 

### i s the estimat

e o f tota l annua l entrainmen

t a t the combined-cycl e units , base do n repeatedus e o f Equatio n (2) . The varianc e fo r th e estimator

o f tota l annua l powe r plant entrainment

ca n then b e written a s Var^E T 

### \E T 

### ^ = Var{^E

cc 

### \E cc 

### y (A5 ) 

### Estimate s o f

E T 

### will be usedi

n FH an dAEL calculation s t

o estimat e annua l effects o f

entrainmen

t o n fish stocks .

E9-053. 9 A- 3 MLP P 316(b ) Resourc e Assessmen t 4-28-200 0Appendi x B —Derivatio n o f th e Varianc e an d Estimate d Varianc e o f E 

# Appendi x B Derivatio n of th e Varianc e an d Estimate d Varianc e of E Variance of

E The varianc e o f

E ca n b e derivedby taking th

e varianc e i

n stage s b y first conditionin g o

n the choic e o f d { 

### days , the n takin g expectatio n ove

r al l selection s o f

d t 

### o f £ > day s within the tempora

l stratum . Var{E) = E

di

### [ Var^ ) + Var dj

### [E^)

= E, i (

/= i 

### V,, ^ 

# HlfEf S l ijkl K r i y> 2 *

• i=\ J 

### + Var, ( L(V



### ^ 

## v„. 

# Si 1 

# ! * = i z /= i 2 "f t c (/* / 

## - £ , f

T. \ ( = 1 

# Z ^ z z d, 4 y * 

### 1 - ^j* / v w y y= i *=

i 

### + ^ 0 L



# I i= l V yi )j=\ 

### (Bl ) 

# ^/ v V r f 

# .Ai ^ /•= i 

### KVU \ V Ni*) *ijkl

i 

### *>iPk-l •+ i'= l f „ \ 2 

## yVu d,



# = z /= i 

## v Ti

I J 

### rf. 2 

### 1- D {

i J % J A 4 

# -+fzz ^

^ i y= i *= i 

## 'i--*-\ . AT *vH



### wher e P. 9

E9-053. 9 B- 1 MLP P 316(b ) Resourc e Assessmen t 4-28-200 0P.1 0 Appendi x B —Derivatio n o f th e Varianc e an d Estimate d Varianc e o f E A

—\ 2 

# Zte-5 > c 2 __= | E 

# >~ (A- 0 ' A 

# Z* > ZW = I 

### A an dwher e A',- ;

—\ 2



### Z J (*//* / ^y * j

x ijU l=\ 

# K- 0 

# z* * {/ « 

### y - /= 1 Ny* / 

### an dfurthermor e 4 N iju 

### E(j

### = Z Z x 

### ijki = tota 

### ' entrainmen t fo r they't h da y (y = 1,... , D) in th e rth stratu m(/ ' = 1,... , L). k=\ 1=1 

### Th e finite populatio n correctio n [i.e. , V N 

### m) ] wil l b e nearl y on e i n al l case s an dca n b e ignored . 

# Estimate d Varianc e of E Th e varianc e fo r

E i s 

# ^(% ) 

# = Z 'SL Y

yVi) 

### ( d-^

v A y d-. A 4 1 — 

### N u \ U

k J x ijU i y= i *= i 

### (B2 )

Th e ter m D, 4 

### 1

- N., V ly 

### 'J

k 

### J 

## A y y j/ 2 n £->*—i 'J

k o M j=\ k=\ z 

### i n Equatio n (B2 ) ca n b e unbiasedl y estimate db y th e quantit y ( ~ ^ x ijkl

di 4 

# ZZ ^ y= i k=\ 

### 1

- Nijk) x iju (B3 )

E9-053. 9 B- 2 MLP P 316(b ) Resourc e Assessmen t 4-28-200 0Appendi x B —Derivatio n ofth e Varianc e an d Estimate d Varianc e o f E p.1 1

whe n 

### s] = M

x ijkl ^\ x ijkl

x ijk) (2-1 ) However , 

## £|



# 4 „ 

# K Instead , \k=\ l l=\ J takin g th e varianc e in stage s

Varfa) = E

di [var[E^,)] + ^Far^,) ]



## = £ , 4 y y ijk 

# Var\ ^f , X 'jkl

/= 1 + Van 

## Var\ 2 "Uk .k=\ 

### 2 

### Y I

_ l r X 'jkl 1=1 dt )_ V 1 4 V ijk K~ N »J x ijU Var



## d,[Ey]

Df 4 

# iz z

u i j=\ k=\ >jk 1 —



### N„ \ ijk

J "ijkl + S:

E„

Hence , (



### d-^ v A y E >J 

### = 

### d

; ( 

### d-^ 

### v A y E "

Di 

# ^i-^lzz

V 2 v ijk x ijk (B4 ) whic h ha s apositiv e bia s o f



### D ; 

### 1 - 

### d

{ 

## v l \D 4 '>'

* 

### V A y 

# zzj=\ k=\ 1 —

% ; *y * (B5 )

In rum , th e bia s (B5 ) can b e estimate db y th e quantit y

E9-053. 9 B- 3 MLP P 316(b ) Resource Assessmen t 4-28-200 0Appendi x B —Derivatio n o f th e Varianc e an d Estimate d Varianc e o f E P.1 2



# )-it$- ijk 

### 1 x ijk 

### (B6 ) A n estimator

o f VaryE £jca n the n b e expressedb

y takin g int

o accoun t Equations ' (B3-B6 ) a s

/= ! 

### y-n 

### \



### A y 

# 4 - ( d 

### V ' 4 

# '-fZZ V u i )j=\ k=\ 

## vi

ijk 

### 1 - — x ijk

( d { 4 <J

k 

# +zz y= i *= i 

### »

. N 

### «*J



# = z 1= 1 V >

•y / 

### 4 ( d.^ 

### v A y F. 2 rf,- 4 V * 5 £ . + 

# ^zz M y= l A=

l 

### 1 - 

### K, V '

y ykJ

E9-053. 9 B- 4 MLP P 316(b ) Resourc e Assessmen t 4-28-200 0P.1 3



# 1 I Appendi x C —Estimatin g Proportiona l Entrainmen t an d th e ETM Calculation s 

# Appendi x C Estimatin g Proportiona l Entrainmen t an d th e ETM

Calculation s The empirica

l transpor t mode l {ETM) attempt s t

o estimat e the tota l annua l mortalit y probabilit

y fo r larva e fro mpowe r plan t entrainment . The annua

l estimat e i s basedo

n periodi c daily probabilitie s of

entrainmen

t mortality . Th

e calculation s wil

l assum e al l larva e entraine ddie . The daily probabilit

y o f entrainmen

t ca n b e define

da s abundanc e of

entraine dlarvae; :

u 

### P= — '' abundanc e of

larva e i n sourc e population^

= probabilit

y o f entrainmen

t o n they't h da y ( y - 1,... , d

t

### ) ofth e rth tempora

l stratum(/

' = 1,... . L). I n turn , th e daily probabilit

y ca n b e estimate dan

dexpresse da s pT 

### P=-£

- M« - S . (Cl ) 

### wher e Ej: = estimate dabundanc e o f larvae entraine do

n they't h da y ( y = 1,. . .,d

f 

### ) ofth e rth stratum( / = \,...,L); IL = estimate dabundanc e o f larvae a t risk o f entrainmen

t fro mth e sourc e population s o n they't h da y ( y = 1,... , d

t

### ) ofth e /t h stratu m( / = 1,... , L). 

# Estimatin g Dail y Entrainmen t The estimat

e o f tota l daily entrainmen

t ( E { j

### ) a t the combined-cycl e unit s ca n b e written a s E' = ES C 

### (C2 ) -cc wher e Er 

### i s th e estimat

e o f daily entrainmen

t fo r th e combined-cycl e unit s intake . E9-053. 9 C- 1 MLP P 316(b ) Resource Assessmen t 4-28-200 0Appendi x C — Estimatin g Proportiona l Entrainmen t an d th e ET M Calculation s P.1 4



### A t an y one intak

e site , the estimat

e of entrainmen

t ca n b e expresse da s 4 V 2 

# VZf Z

*• 1=1 l ijkl k=\ 

### wit h associate dvarianc e Vt. whic h ca n b e estimate dby jk K N 'jk ) *= I

f 2 ^ 

# H^K) =

# z ^

k=\ ^ N Uk

J "ijkl 

### Typically , the finit

e populatio n correctio n [i.e. , large . V N 

### UkJ (C3 )

(C4 )

(C5 ) 

### ] ca n b e ignore dfo

r N iJk 

### i s exceedingly 

# Estimatin g Dail y Number s of Larva e a t Ris k Wit h the well-define dandagreed-upo n source s o f Montere y Ba y (MB) , Mos s Landin g Harbor (MLH) , an dElkhor n Slough (ES) , the daily abundanc e of larva e a t risk ca n b e estimate db y hj= V

MB 

### • D MB

### ,. + V

MLH 

### • D MLH 

### .. + V

ES 

### • D ESj 

### , ( C6 ) 

### wher e V denote s volume a

t Monterey Ba

y (MB) , Mos s Landing Harbor (MLH) , or

Elkhor n Slough (ES) , andD denote s a n estimat e o f averag e density . The varianc e o f Expressio n (C6 ) ca n b e written a s Var(R v 

### \R v 

### )=V

2 B 

### .Var(b MBi 

### . E^MBa + VMLH 

## V«r{b MW>

## . D MLHij J 

### + V 2 ES 

### -Var(b ESi 

### . 

### D ESi 

### ). (C7 ) 

### The individua

l variance s withi n Formul a(C7 ) describ e temporal-spatia l varianc e i

n densit y withi n asourc e populatio n durin g the da y of sampling . Within Mos s Landin g Harbor and Monterey Bay , fou

r samplin g station s hav e no w bee n propose d(TW

G meetin g Septembe

r 15 , 1999) . Wit

h Elkhor n Slough , 2 fixed-location site s wer e selecte dfo

r samplin g (i.e. , The Dairie s an dKirb y Park) . Ideally , tow sample s woul db e collecte dprobablisticall y throug h tim e and spac e durin g asamplin g da y a t apotentia l sourc e population . E9-053. 9 C- 2 MLP P 316(b ) Resourc e Assessmen t 4-28-200 0P.1 5 Appendi x C —

Estimatin g Proportiona l Entrainmen t an d th e ET M Calculation s 

# Varianc e fo r Dail y Estimat e o f PM t

# . The varianc e fo

r the daily estimat

e of PM, ca n b e expresse da s Var{PM\PM^±Var which by the Deltametho dca n b e approximate db y 

## {** E ^ 

### Var^PM^PM^-jL \2 

# 4 + 

# « (C8)

an dca n b e estimate db y

ra,(PM

v 

### \PM v 

### ) = (PMijflcvfijlEjj) 2 

### + CV^R^ wher e CVl

# WlVaiffi) 

# v ETM Calculations B y combinin g Equation s (Cl) , (C2) , an d(C6) , th e estimat

e o f dail y entrainment

mortalit y ca n b e written a s p - M,ij 

# E? 

# [y»a'k

MB U MLH

^MLHu T v E S •*«. ) 

### El IJ 

### R, (C9) I f th e specie s ha s asingl e spawnin g perio dpe r year , then th e estimat

e o f total annua

l mortalit y ca n b e expresse db y D-a



# PM=\-flfl{\-PM

iJ 

# Y iJ 1= 1 7= 1 

### (CIO ) wher e

E9-053. 9 C-3 MLP P 316(b ) Resource Assessmen t 4-28-200 0P.1 6 Appendi x C —Estimatin g Proportiona l Entrainmen t an d th e ET M Calculation s 

### D\. = numbe

r o f day s represente db y the jt h sampl e (j=\,...,d j 

### ) i n the it h tempora l stratum {i = l.-,L). Alternatively , i f

the specie s ha s multipl e overlappin g spawnings , the n a n estimat e o f tota l annua l entrainmen

t ca n b e base do

n th e formul a PM=\-tif^-^ijf (Cll ) i= l y'=l 

### wher e fy = estimate dannua

l fraction of

tota l larvae hatche ddurin g the survey perio d represente dby they't

h sampl e i n the /t h tempora l stratum . Formul a(C11 ) i s base don the tota l probabilit

y la w wher e P{A) = f

j

### P(A\B i 

### ).P{B i 

### ). 1= 1 

### I n the abov e example , th e event A i s larva l surviva l an deven t B i s hatchin g wit

h P[B) estimate dby fy.

E9-053. 9 C- 4 MLP P 316(b ) Resource Assessmen t 4-28-200 0Appendi x D — Delt a Metho d fo r Calculatin g Varianc e 

# Appendi x D Delt a Metho d fo rCalculatin g Varianc e

Variance forPE, Usin g the deltametho d(Seber , 1984) , varianc e o f PF , ca n b e effectivel

y approximate db y Var{PE i 

### )=Var I N >



### = Var{N

t

### ) 

## W + f.MJ + Var{f t

### ) < -N. ^ 

# U a + 

# /,) v + Var{A i 

### )\ -N, \ 2 

## 0 + /H V 

# ___(__i + 

# ______! + 

# ___(__ ) Nf d+y;-) 2 

## 4 2



### = PE?[CV(N

( 

### ) 2 

### + CT( 1 + /) 2 

### + CV(A,) 2 

### ]. P.1 7



### ca n b e estimate dfro

m Varianc e fo rS A 

### S_=- 

### F-R-S

E

### S L 

### where : F= averag e eg g mas s pe r femal e pe r

year ; R = reproductio n longevity , averag e numbe r of year s o f reproductio n fo

r afemale ; S E 

### = eg g surviva

l rate ; S L 

### = surviva

l o f larvae fro mhatchin g to tim

e of entrainment . The varianc e o f

S A 

### base don the deltametho di s the n estimate db y the approximat e formul a

E9-053. 9 D- 1 MLP P 316(b ) Resource Assessmen t 4-28-200 0Appendi x D —Delta Metho d fo r Calculatin g Varianc e 

### Var{S A 

### ) = S] Var{F) , VarjR) , Var{S E

### ) Var{S

L 

### ) /? ' 

## Si 

# si For the exampl e of

monkeyfac e eel , the varianc e o f S A 

### i s estimate da s Var{S A 

### ) = (0.0001388) : 

### (4,667) 2 

### (2.08) 2 

### (0.0373) 2 

### (0.0314 ) •+ •+ + • 

### (32,000) ' (11.75) 2 

### (0.4240) 2 

### (0.0904) 2



### = 0.000000003 5 or SE{S A 

### ) = 0.0000590 5 Variance fo

rAEL The estimato r

o f adult equivalent

los s i s

A A

ACtlu —'Hi-p

' O j 

### wit h exac t varianc e Var{ AEL) = Var{E T



### )-S 2 A 

### + Var{S

A 

### f • E 2 

### + Var{E T



### ) 2 

### • Var{S

A 

### ) . Usin g th e varianc e formul ain conjunctio n wit h th e monkeyfac e eel dat aresult s i n a n estimate d varianc e o f Var{AEL) = (197,677,101)2



### (0.0001388)2 

### +(0.00005905) 2

### (160,544,555) 2 

### +(192,677, 1 Ol) 2 

### (0.00005905 ) = 934,541,905. 8 o r SE{AEL) = 30,570 3 . Variance forFH The estimator

of hindcas t fecundit y los t i s

._ _7 * 

### FH = SE'S

L - FT 

### wher e

E9-053. 9 D- 2 MLP P 316(b ) Resource Assessmen t 4-28-200 0P.1 9 Appendi x D —Delt

a Metho d fo r Calculatin g Varianc e 

### E T 

### = estimate dtota

l entrainmen

t of larvae ; S E 

### - surviva

l probabilit

y fo r eggs ; S L 

### = surviva

l o f larva e fro mhatchin g t

o time of entrainment ; FT 

### = estimate daverag e tota

l lifetim e fecundit y = F • R. Using the Deltamethod , a

n approximat

e varianc e estimator

i s Var{FH) = FH' Var{E T



### ) , Var{S

E

### ) , Var{S

L 

### ) , VarjF) , VarjR) A ^ r^—

r1 T T rj— ~ r~z~z 

# st R' For the exampl e o f

monkeyfac e eel , the varianc e o f FH i s calculate dto b e Var{FH) = (11,140) (192,677,101) 2 

### (0.0373) 2 

### (0.0314) 2 

### (4,667) 2 

### (2.08 ) •+ + •

or (160,544,555) 2 

### (0.4240) 2 

### (0.0904) 2 

### (32,000) 2 

### (11.75) 2



### = 201,208,63 0 SE{FH) = 14,18 5

E9-053. 9 D- 3 MLP P 316(b ) Resource Assessmen t 4-28-200 0