Not to be cited without permission of the author(s1

New Zealand Fisheries Assessment Research Document 88/4

A generalised bioeconomic simulation model for fish population dynamics

P.M. Mace and I.J. Doonan

MAFFish Fisheries Research Centre P 0 Box 297 Wellington

December 1988

MAFFish, N.Z. Ministry of Agriculture and Fisheries

This series documents the scientific basis for stock assessments and fisheries management advice in New Zealand. It addresses the issues of the day in the current legislative context and in the time frames required. The documents it contains are not intended as definitive statements on the subjects addressed but rather as progress reports on ongoing investigations.

New Zealand F i s h e r y Assessment - - R e s e a r c h Document 8814

A genera l ised bioeconomic s imula t ion model f o r f i s h populat ion dynamics

P. M. Mace and I. J. Doonan

F i s h e r i e s Research Centre MAFFish

P.O. Box 297 Wel l ington

I n t r o d u c t i o n . -

~ i m u l a ~ t i o n models a r e u s e f u l b f o r : investigating-th-e- dynamic-behaviour .

of-complex systems./The model presentkd here 7 s reasonably s i m p l e , y e t =.

f l e x i b l e . I t has been developed g radua l l y over t h e pas t two years i n response t o t h e needs f o r sumnarising e x i s t i n g b i o l o g i c a l and economic data, per forming stock assessments w i t h sparse data and/or l a r g e u n c e r t a i n t y i n parameter est imates, and eva lua t i ng t h e l i k e l y b i o l o g i c a l and economic consequences o f a l t e r n a t i v e management act ions.

We f i r s t o u t l i n e the purposes o f the model and i t s general features. Th is i s f o l l owed by t h e focus o f the paper: a d e t a i l e d d e s c r i p t i o n o f the equat ions and opt ions used i n t h e model. The d e s c r i p t i o n i s developed w i t h re ference t o a f l o w cha r t showing the sequence o f c a l c u l a t i o n s (F igure I ) , and a t a b l e t h a t l i s t s and descr ibes t h e parameters t h a t can be spec i f i ed , and the v a r i a b l e s t h a t can be tabu la ted o r graphed (Table 1). A l t e r n a t i v e models t h a t represent s l i g h t v a r i a t i o n s 3 f t h e ~ a j a mode; a re then presented. L i m i t a t i o n s o f t h e models a re discussed b r i e f l y . Three appendices con ta in supplementary in fo rmat ion : how t o run t h e model(s) on the Pyramid 98xe a t F i she r ies Research Centre (Appendix I ) ; an annotated demonstrat ion example (Appendix 11); and an annotated l i b r a r y o f se ts o f comnands t h a t can be used t o manipulate the model (Appendix 111).

Purposes o f t h e Model

The o v e r a l l o b j e c t i v e s o f the model a re to :

( i ) Synthesise e x i s t i n g b i o l o g i c a l and economic da ta ( i i ) Ca lcu la te est imates o f optimum y i e l d ( i i i ) I n v e s t i g a t e t h e e f f e c t s o f unce r ta in t y i n parameter est imates ( i v ) I n v e s t i g a t e t h e e f f e c t s o f v a r i a b i l i t y i n s tock product ion ( v ) Determine the l i k e l y consequences o f a l t e r n a t i v e management

s t ra teg ies , f rom b o t h b i o l o g i c a l a n t ezsnc:~:ic perspect ives ( v i I d e n t i f y p r i o r i t y areas f o r f u t u r e research.

General Features o f the Model

The model i s a d i s c r e t e time, dynamic pool (age-st ructured) s imu la t i on model w r i t t e n i n FORTRAN 77. I t i s l i n k e d w i t h SIMCON, a SIMula t ion CONtrol language ( o r i g i n a l source: R. H i lborn , J. Stander and W. Webb, I n s t i t u t e o f Animal Resource Ecology, U n i v e r s i t y o f B r i t i s h Columbia, Vancouver, Canada) t h a t handles a l l input , ou tpu t and i n t e r v e n t i o n needs. The reader i s r e f e r r e d t o t h e SIMCON u s e r ' s guides (Mace 1988, Beals 1981) housed a t F i she r ies Research Centre. Greta Po in t , Wel l ing ton f o r i n s t r u c t i o n s on the use o f SIMCON. Although the model cannot be run w i t h o u t SIMCON, i t i s o n l y necessary t o l e a r n about t en SIMCON comnands t o per fo rm a l l necessary funct ions.

Parameters can be s e t i n t e r a c t i v e l y , o r s to red i n a spec ia l f i l e . A l t e r n a t i v e se ts o f parameters can be s to red i n named MACROs (a MACRO i s a s e t o f SIMCON comnands) and c a l l e d i n t e r a c t i v e l y by name when required. MACROs may a l s o be created i n t e r a c t i v e l y o r s to red i n the spec ia l f i l e . Simple SIMCON comnands can be used t o s e t parameter values (SET comnand), d i s p l a y the cu r ren t va lue o f a v a r i a b l e o r parameter (DI comnand), change the value o f a v a r i a b l e a t a s p e c i f i e d

- - -

t ime (AT=time comand), per form a s p e c i f i e d number o f i t e c a t i o n i o f the. model (SIM, GO and CONTINUE comnands), t a b u l a t e t h e values o f v a r i a b l e s . over s imulated t ime (PR comand), graph t h e values o f v a r i a b l e s over s imulated t ime (VIEW, GRAPH and PLOT comnands), compute bas i c s t a t i s t i c s (minimum, maximum, mean, standard dev ia t ion , standard e r r o r ) f o r s p e c i f i e d va r iab les over s imulated t ime (STATS, ONSTAT comnands), and r e s t o r e any prev ious model s t a t e (TIME comnand).

Simulat ions begin w i t h v i r g i n r e c r u i t e d biomass and a s t a b l e (equ i l i b r i um) age d i s t r i b u t i o n . V i r g i n biomass can be back-calculated us ing recent biomass, t h e catch h i s t o r y and demographic parameters. The parameters used t o c a l c u l a t e v i r g i n biomass, na tu ra l m o r t a l i t y , age o f recru i tment , age o f m a t u r i t y and growth can e i t h e r be s p e c i f i e d e x p l i c i t l y o r drawn from p r o b a b i l i t y d i s t r i b u t i o n s . Mean l e n g t h o f any subset o f the popu la t i on can be ca l cu la ted f o r a t p ~ c i f i a d aga o r l e n ~ t h i n t e r v a l . There are f o u r s tock-recru i tment r e l a t i o n s h i p s t o choose from. Recruitment can be e i t h e r d e t e r m i n i s t i c o r s tochast ic . There are f o u r op t ions f o r represent ing f i s h i n g : zero, o r s t r a t e g i e s based on s p e c i f i e d f i s h i n g m o r t a l i t y , s p e c i f i e d catch, o r s p e c i f i e d escapement. The economic submodel a l lows separate s p e c i f i c a t i o n o f f ob p r i c e , f i x e d costs, v a r i a b l e harves t ing costs and v a r i a b l e processing costs. There a r e f o u r op t ions f o r represent ing harves t ing costs. A d iscount r a t e can be app l i ed t o c a l c u l a t e ne t present value.

The b i o l o g i c a l submodel can be run w i t h o u t the economic submodel, b u t the economic submodel cannot be run on i t s own.

The maximum number o f i t e r a t i o n s f o r a s i n g l e run i s about 1000. The model i s s u f f i c i e n t l y small and f a s t t h a t r e s u l t s can be viewed i n t e r a c t i v e l y .

Model Desc r ip t i on

The model i s based on mid-season est imates o f biomass. For example, i t i s assumed t h a t the beginning o f season number o f f i s h o f age 1 (i.e. recru i tment t o the popu la t ion) i s produced by t h e spawning biomass present a t mid-season i n the prev ious year. Thus t o achieve accurate r e s u l t s mid-season should correspond approximately t o t h e mid-point o f the spawning season, f i s h i n g m o r t a l i t y should be spread more o r l ess evenly e i t h e r s ide o f spawning and the von B e r t a l a n f f y growth curve should be c a l i b r a t e d (by a l t e r i n g t o ) so t h a t the f i r s t b i r t h d a y (age = 1) o f the f i s h i s approximately h a l f a year a f t e r spawning.

Table 1 l i s t s and descr ibes the parameters and v a r i a b l e s used i n t h e model. I n general, the user w i l l want t o s e t parameter values, and t a b u l a t e o r graph v a r i a b l e values. F igure 1 sumar i ses the sequence o f ca l cu la t i ons . The numbers used below correspond t o those i n t h e f igure . FORTRAN names a r e g iven i n brackets i n upper case l e t t e r s . Refer t o Table 1 f o r f u r t h e r d e t a i l s on t h e i r usage.

1. .Seeding the random number generator (ISEED)

The random number generator i s reseeded i n the same way (whether i t i s needed o r no t ) each t ime the model i s res tar ted . Th is means t h a t the same random number sequence w i l l be generated f o r consecut ive runs

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(prov ided the re i s no change i n the number o f c a l l s t o the random number generator) and r e s u l t s from d i f f e r e n t runs w i l l be d i r e c t l y comparable.

2. Demographic parameters

V i r g i n biomass (VIRBIO), n a t u r a l m o r t a l i t y (M), age o f rec ru i tmen t (AR), age o f m a t u r i t y (AM) and growth (K, LINF, TO) can be de f i ned by t h e i r expected values o r drawn from p r o b a b i l i t y d i s t r i b u t i o n s . Separate random number i n d i c a t o r s a r e s e t t o " o f f " o r "on" r e s p e c t i v e l y depending on which o p t i o n i s required. The parameters a r e ca l cu la ted a t t h e beginning o f a run and remain f i x e d throughout a s imulat ion. They cannot be changed unless t h e model i s res tar ted .

a) V i r g i n biomass (VIRBIO)

I f t h e random number i n d i c a t o r (IRANDBIO) i s 0, v i r g i n biomass i s s e t equal t o a user s p e c i f i e d constant (VIRBIOM).

I f the random number i n d i c a t o r (IRANDBIO) i s 1, v i r g i n biomass i s de f i ned as fo l lows. Mean biomass E i s drawn f rom a un i fo rm d i s t r i b u t i o n such t h a t

- B = un i fo rm (EL, EH) F

w i t h

where - B i s the mean o f the d i s t r i b u t i o n o f means (VIRBIOM) - BL i s the smal les t m u l t i p l i e r o f F (VIRBIOL) - BH i s the l a r g e s t m u l t i p l i e r o f (VIRBIOH)

V i r g i n biomass i s then drawn from a normal d i s t r i b u t i o n w i t h mean E, standard d e v i a t i o n o (VIRSD), lower bound L (VIRMIN) and upper bound H (VIRMAX). Note t h a t v i r g i n biomass i s assumed t o be t h e mid-season r e c r u i t e d biomass.

(b) Instantaneous na tu ra l m o r t a l i t y r a t e (M)

I f t h e random number i n d i c a t o r (IRANDM) i s 0, n a t u r a l m o r t a l i t y i s s e t equal t o a user s p e c i f i e d constant (MMEAN).

I f t h e random number i n d i c a t o r (IRANDM) i s 1, na tu ra l m o r t a l i t y i s drawn from a un i fo rm d i s t r i b u t i o n w i t h lower bound L (MMIN) and upper bound H (MMAX).

( c ) Age o f recru i tment (AR) and age o f m a t u r i t y (AM).

I f t h e Fando f iumber . ind icator (IRANDA) i s 0,Bges o f recru i tment and m a t u r i t y a r e s e t equal t o user -spec i f ied constants (ARMEAN and AMMEAN respect ive1 y ) .

I f t h e random number i n d i c a t o r (IRANDA) i s 1, ages o f recru i tment and m a t u r i t y a r e drawn from un i fo rm d i s t r i b u t i o n s w i t h lower bound L-0.5 (ARMIN - 0.5 o r AMMIN - 0.5) and upper bound H + 0.5 (ARMAX + 0.5 o r AMMAX + 0.5). They a r e then rounded t o the nearest in teger . (Example: i f ARMIN = 4 and ARMAX = 6 the re w i l l be an equal p r o b a b i l i t y t h a t AR = 4. 5 o r 6).

(d) Growth parameters (K, LINF and TO)

I f t h e random number i n d i c a t o r (IRANDG) i s 0, growth parameters a r e s e t equal t o u s e r - s p x i f i e d constants (KMEAN, LINFMEAN and TO respec t i ve l y ) .

I f t h e random number i n d i c a t o r (IRANDG) i s 1, growth parameters a r e de f i ned as fo l lows. The Brody growth c o e f f i c i e n t (K) i s drawn from a normal d i s t r i b u t i o n w i t h mean K (KMEAN), standard d e v i a t i o n a ( t h e square r o o t o f CORRKK), lower bound L (KMIN) and upper bound H (KMAX). The maximum average length L, i s then drawn from a normal d i s t r i b u t i o n w i t h mean

PL + - OLK (K - PK) 'JKK

and standard d e v i a t i o n

where

PL i s t h e mean value o f L, (LINFMEAN)

K i s t h e Brody growth c o e f f i c i e n t chosen i n t h e prev ious step (K)

PK i s t h e mean value o f the Brody growth c o e f f i c i e n t (KMEAN)

OLK i s the covariance o f L, and K (CORRLK)

OKK i s t h e var iance o f K (CORRKK)

'OLL i s t h e var iance o f L, (CORRLL)

Th is procedure r e f l e c t s the (negat ive) sampling c o r r e l a t i o n between L, and K i n the von B e r t a l a n f f y growth equation.

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(TO) i s unchanged - f rom the user -spec i f ied value.

3. Mean weights a t age (W)

Mean weights a t age a r e ca l cu la ted from the von B e r t a l a n f f y growth equat ion

combined w i t h t h e length-weight r e l a t i o n s h i p

where

L t

L,

K

t o

W t

a

b

i s t h e mean mid-season l e n g t h (cm) a t age t - ( L i )

i s t h e maximum average mid-season l e n g t h (LINF)

i s the Brody growth c o e f f i c i e n t (K)

i s the x - i n t e r c e p t (TO)

i s the mean mid-season weight (kg) a t age t (Wi)

i s the constant o f t h e l e n g t h weight r e l a t i o n s h i p , f o r l eng th i n cm and weight i n gm (A)

i s the power c o e f f i c i e n t o f t h e length-weight r e l a t i o n s h i p (B)

The maximum average weight i n kg, W, (WINF), i s c a l c u l a t e d from t h e equat ion

W, = a L, / 1000

( L i ) and W t (Wi) a re a r b i t r a r i l y s e t t o zero f o r a l l ages l e s s than (TO).

V i r g i n recru i tment (RVIRG) and the s t a b l e age d i s t r i b u t i o n

V i r g i n recru i tment i s the i n i t i a l beginning o f season numbers a t age I t s computation i s based on the r e c r u i t e d mid-season v i r g i n biomass

... tonnes (VIRBIO) and t h e assumption o f a s t a b l e age d i s t r i b u t i o n . V i r g i n biomass can be expressed as

S i m i l a r i l y t o t a l mid-season v i r g i n biomass ( a l l ages combined) i s g iven by

max

The assumption o f a s t a b l e age d i s t r i b u t i o n imp l i es t h a t

where

Bv i s r e c r u i t e d mid-season v i r g i n biomass (VIRBIO)

B t i s t o t a l mid-season v i r g i n biomass (TOTBIO)

N i i s the mid-season number o f f i s h o f age i

W i i s the mid-season weight ( i n tonnes) o f a f i s h o f age i

a r i s the age o f recru i tment t o t h e f i s h e r y (AR)

max i s the maximumage used i n t h e model (MAXAGE)

M i s na tu ra l m o r t a l i t y (M)

Comb i n g equat ions (1) and (3) g i ves

-M(i - a r ) Bv = Nar Z e i =ar

W i

Combining equat ions (2) and (3) g ives

I t a l s o f o l l o w s from equation (3) t h a t

-.

D i v i d i n g equat ion (5) by equat ion ( 4 ) , s u b G i t & i n g f o r Nar-from equat ion (6 ) , cancel 1 i n g and rearranging g i ves

Th is equat ion cons i s t s o n l y o f known parameters. The mid-season number o f f i s h a t age 1, N1, can thus be c a l c u l a t e d f rom equat ion (5) us ing t h e value o f B t c a l c u l a t e d from equat ion ( 7 ) . Assuming t h a t n a t u r a l m o r t a l i t y i s spread evenly throughout the year , t h e beginning o f season number o f f i s h a t age 1 (RVIRG) i s t he re fo re g iven by

The beginning o f season v i r g i n s t a b l e age d i s t r i b u t i o n i s ca l cu la ted from equat ion (3) w i t h the v i r g i n recru i tment l e v e l (RVIRG) s u b s t i t u t e d f o r N1. Note t h a t N i represents mid-season numbers i n equat ions (1) - (6) i n c l u s i v e d u r i n g t h e computation o f v i r g i n recruitment;. Bu t s ince the model s t a r t s a t the beginning o f the season, the N i a r e replaced by beginning o f season numbers once the v i r g i n s t a b l e age d i s t r i b u t i o n has been ca lcu la ted .

5. V i r g i n spawning biomass (VIRSPAWN)

I n the modci i t 4 5 assumed t h a t the beginning o f season number o f f i s h o f age 1 (i.e. recru i tment t o the popu la t ion) i s produced by the spawning biomass present a t mid-season i n the prev ious year. The mid-season v i r g i n spawning biomass (VIRSPAWN) i s c a l c u l a t e d as

max Z Ni W i e -MI2

where

N i i s t h e beginning o f season v i r g i n numbers a t age i ca lcu la ted from a s t a b l e age d i s t r i b u t i o n

W i i s the h e i g h t o f a f i s h o f age i i n tonnes

M i s t h e instantaneous r a t e o f n a t u r a l m o r t a l i t y (M)

am i s t h e age o f m a t u r i t y (AM)

max i s the maximum age used i n the model (MAXAGE).

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NOTE:.; Steps 1 t o 5 above are use 'dto i n i t i a l i s e t h e model. The v a r i a b l e s and parameters'calculat&d i n these steps remain f i x e d throughout a s imulat ion. They cannot be changed unless t h e model i s res ta r ted .

6. Beginning o f season r e c r u i t e d biomass (BEGBIO)

Beginning o f season r e c r u i t e d biomass (BEGBIO) i s c a l c u l a t e d as

max z Ni W i i =ar

N i i s the beginning o f season numbers a t age i

W i i s the mean (mid-season) weight o f a f i s h o f age i (tonnes)

a r i s the age o f recru i tment t o the f i s h e r y (AR)

max i s the maximum age used i n the model (MAXAGE)

7. Annual removals (REMOVALS), catch (CATCH) and f i s h i n g m o r t a l i t y (F)

A user -spec i f ied f i s h i n g i n d i c a t o r (IFISH) i s used t o choose amongst f o u r op t ions f o r represent ing f i s h i n g .

I f t h e f i s h i n g - i n d i c a t a r (IFISH) i s 0, t he re i s no f i s h i n g and removals (REMOVALS), catch (CATCH) and f i s h i n g m o r t a l i t y (F) a r e s e t equal t o zero.

I f t h e f i s h i n g i n d i c a t o r (IFISH) i s 1, f i s h i n g i s represented by a f i s h i n g m o r t a l i t y l eve l . A user -spec i f ied f i s h i n g m o r t a l i t y (FCON) i s used t o c a l c u l a t e an i n i t i a l est imate o f annual removals (REMOVALS) from the ca tch equation:

max F C = z (1 - e-(F+M)) NI WI

where

C i s annual removals i n tonnes (REMOVALS)

F i s the instantaneous r a t e o f f i s h i n g m o r t a l i t y (F)

M i s the instantaneous r a t e o f na tu ra l m o r t a l i t y (M)

Ni i s the beginning o f season numbers a t age

. -~

W i i s z t h e m i a n (mid-seasan) weight.-if..a f i s n of age'i (tonnes)

a r i s the age o f recru i tment t o the f i s h e r y (AR)

max i s t h e maximum age used i n t h e model (MAXAGE)

I n t h i s o p t i o n F i n equat ion (8) i s s e t equal t o t h e user s p e c i f i e d f i s h i n g m o r t a l i t y (FCON). I f a user -spec i f ied parameter represent ing t h e d i f f e r e n c e between t r u e removals and repor ted catch, expressed as a f r a c t i o n o f repor ted ca tch (WASTE) i s 0, then removals (REMOVALS) and repor ted ca tch (CATCH) a r e bo th s e t equal t o C i n equat ion (8). Otherwise repo r ted ca tch (CATCH) i s s e t equal t o C i n equat ion (8), and removals (REMOVALS) a r e c a l c u l a t e d by multiply in^ reporked ca tch iC.4TCiij by ( 1 + WASTE). I f t h e r e s u l t i n g removals (REMOVALS) a r e g r e a t e r than the beginning o f season r e c r u i t e d biomass (BEGBIO), then removals (REMOVALS) a r e s e t equal t o t h e beginning o f season r e c r u i t e d biomass (BEGBIO) and repo r ted ca tch (CATCH) i s recomputed by d i v i d i n g removals (REMOVALS) by (1 + WASTE). A new value o f f i s h i n g m o r t a l i t y (F) i s then c a l c u l a t e d i t e r a t i v e l y from equat ion (8) w i t h C s e t equal t o t h e new est imate o f removals (REMOVALS).

I f t h e f i s h i n g i n d i c a t o r (IFISH) i s 2, f i s h i n g i s represented by a catch l eve l . Reported ca tch (CATCH) i s s e t equal t o a use r -spec i f i ed value (CCON). I f a use r -spec i f i ed parameter represent ing t h e d i f f e r e n c e between t r u e removals and repor ted catch (WASTE) i s 0, then removals (REMOVALS) a r e s e t equal t o repor ted ca tch (CATCH). Otherwise removals (REMOVALS) a r e c a l c u l a t e d by m u l t i p l y i n g repor ted catch (CATCH) by ( 1 + WASTE). I f t h e r e s u l t i n g removals (REMOVALS) a r e g rea te r than the beginning o f season r e c r u i t e d biomass (BEGBIO), then removals (REMOVALS) a r e s e t equal t o the beginning o f season r e c r u i t e d biomass (BEGBIO) and repor ted ca tch (CATCH) i s recomputed by d i v i d i n g removals (REMOVALS) by (1 + WASTE). F i s h i n g m o r t a l i t y (F) i s ca l cu la ted i t e r a t i v e l y from equat ion (8) w i t h C s e t equal t o removals (REMOVALS).

I f t h e f i s h i n g i n d i c a t o r (IFISH) i s 3, f i s h i n g i s represented by a biomass (escapement) l eve l . Removals (REMOVALS) a r e c a l c u l a t e d as the d i f f e r e n c e between the beginning o f season r e c r u i t e d biomass (BEGBIO) and a use r -spec i f i ed t a r g e t biomass o r escapement (BIOCON). I f the d i f f e r e n c e i s negat ive, removals (REMOVALS) a r e se t equal t o zero. Reported ca tch (CATCH) i s c a l c u l a t e d by d i v i d i n g removals (REMOVALS) by (1 + WASTE), where WASTE i s a use r -spec i f i ed parameter represent ing t h e d i f f e r e n c e between t r u e removals and repor ted catch ( i t may be zero). F i sh ing m o r t a l i t y (F) i s c a l c u l a t e d i t e r a t i v e l y from equat ion (8) w i t h C s e t equal t o removals (REMOVALS).

8. Mid-season numbers, r e c r u i t e d biomass (MIDBIO), t o t a l &iomass (TOTBIO), biomass by age classes (BIOAGEi), t h e r e l a t i o n s h i p between c u r r e n t mid-season r e c r u i t e d biomass and v i r g i n mid-season r e c r u i t e d biomass (PBIO), and mean leng th o f f i s h (XLEN, XLENSD).

Mid-season numbers a t age a r e ca l cu la ted by m u l t i p l y i n g beginning o f season numbers by

Th is assumes t h a t f i s h i n g m o r t a l i t y (F) and na tu ra l m o r t a l i t y (M) a r e spread evenly on e i t h e r s ide o f t h e mid-season.

Mid-season biomass by age classes (BIOAGEi) i s c a l c u l a t e d as

Mid-season r e c r u i t e d biomass (MIDBIO) i s g iven by

max z B i

i = a r

Mid-season t o t a l biomass (TOTBIO) i s g iven by

max 1 B i

i = l

where

B i i s t h e mid-season biomass o f f i s h o f age i (BIOAGEi)

N i i s the mid-season numbers a t age

W i i s the mean (mid-season) weight o f a f i s h o f age i ( t o m e s )

a r i s t h e age o f recru i tment t o t h e f i s h e r y (AR)

max i s the maximum age used i n the model (MAXAGE).

The r e l a t i o n s h i p between cu r ren t mid-season r e c r u i t e d biomass (MIDBIO) and v i r g i n mid-season r e c r u i t e d biomass (VIRBIO) i s g iven by d i v i d i n g the former by the l a t t e r (PBIO).

Mean l e n g t h o f f i i h (XLEN) i s g iven by-

max 1 - Z Ni L j

i=min

w i t h standard d e v i a t i o n (XLENSD)

where

N i i s t h e mid-season numbers a t age i

L i i s t h e average mid-season l eng th f o r f i s h o f age i (cm)

min i s t h e minimum leng th (ILENL) o r age (IAGEL) used i n t h e c a l c u l a t i o n s

max i s t h e maximum l e n g t h (ILENH) o r age (IAGEH) used i n t h e c a l c u l a t i o n s

n i s the number o f f i s h i n t h e se lec ted p o r t i o n o f the popu la t i on =ax

( = Ni i =mi n

9. Mid-season mature biomass (MATWT)

Mid-season mature biomass (spawning stock biomass) i s ca l cu la ted as

max Z N i W i i =am

where

Ni i s the mid-season numbers a t age

W j i s t h e mean (mid-season) weight o f a f i s h o f age i (tonnes)

am i s the age o f m a t u r i t y (AM)

ma2 i s the-maximumage "sed i n t h e model ( ~ G E ) ;

10. Recruitment t o the popu la t ion (R)

I n t h e model recru i tment t o the popu la t ion i s de f i ned as the beginning o f season numbers a t age 1 (R) t h a t were produced by the spawning biomass present a t mid-season i n t h e prev ious yea r (MATWT).

A user -spec i f ied recru i tment op t i on i n d i c a t o r (ROPT) i s used t o s e l e c t one o f f o u r s tock-recru i tment re la t i onsh ips . Recruitment (R) may a l s o be d e t e r m i n i s t i c o r s tochast ic .

I f t h e recru i tment op t i on i n d i c a t o r (ROPT) i s 0, t he re i s no recru i tment (R=O) .

I f the recru i tment op t i on i n d i c a t o r (ROPT) i s 1, next y e a r ' s mean recru i tment i s s e t a t the v i r g i n recru i tment l e v e l (RVIRG).

I f the recru i tment op t i on i n d i c a t o r (ROPT) i s 2, nex t y e a r ' s mean recru i tment i s ca l cu la ted from a knife-edge r e l a t i o n s h i p (F igure 2a). I f mid-season mature biomass (MATWT) i s g rea te r than o r equal t o 20% o f the v i r g i n spawning biomass (VIRSPAWN), next yea r ' s mean recru i tment i s s e t a t the v i r g i n recru i tment l e v e l (RVIRG). Below t h i s threshold, next y e a r ' s mean recru i tment i s ca l cu la ted as

where

R v i s the v i r g i n recru i tment l e v e l ( R V I R G )

BvS i s the v i r g i n spawning biomass (VIRSPAWN)

Bs i s the cu r ren t spawning biomass (MATWT)

I f the recru i tment op t i on i n d i c a t o r (ROPT) i s 3, next y e a r ' s mean recru i tment i s ca l cu la ted from a Beverton-Holt s tock-recru i tment r e l a t i o n s h i p (F igure 2b). Next y e a r ' s mean recru i tment i s g i ven by

where

Bs i s the cu r ren t spawning biomass (MATWT)

a. B a r e parameters.

The parameters's and 8 are ca l cu la ted by s p e c i f y i n g a re fe rence p o i n t (VIRSPAWN, RVIRG) and t h e steepness, A (STEEP);of t h e re la t i onsh ip . Steepness i s de f ined as the f r a c t i o n o f the v i r g i n rec ru i tmen t (RVIRG) t h a t i s a t t a i n e d when c u r r e n t spawning biomass (MATWT) i s 20% o f v i r g i n spawning biomass (VIRSPAWN). Th is f r a c t i o n must be l e s s than 1.

Thus

Rv = Bv s

a + 8 Bvs

so t h a t

and 8 = A - 0.2 0.8 A R v

where a l l symbols a r e as de f ined imned ia te ly above.

The choice between d e t e r m i n i s t i c and s t o c h a s t i c rec ru i tmen t i s determined by t h e use r -spec i f i ed value o f a random number i n d i c a t o r (IRANDR).

I f t h e random number i n d i c a t o r (IRANDR) i s 0 , rec ru i tmen t (R) i s s e t equal t o next y e a r ' s mean value, as ca l cu la ted above.

I f t h e random number i n d i c a t o r (IRANDR) i s 1, rec ru i tmen t (R) i s drawn f rom a lognormal d i s t r i b u t i o n w i t h mean

l o g (R,) - 0.5 a2

where

Rm i s next y e a r ' s mean recru i tment c a l c u l a t e d from one o f the l a t t e r th ree s tock- recru i tment r e l a t i o n s h i p s above

o i s t h e use r -spec i f i ed standard d e v i a t i o n o f t h e l oga r i t hm o f recru i tment (RSD).

I t i s a l s o necessary t o s p e c i f i y lower a-nd upper bounds on rec ru i tmen t i n numbers (RUIN and RMAX respectively).. S ince logar i thms o f t h e bounds a r e used i n t he lognormal d i s t r i b u t i o n t h e bounds must be g r e a t e r than o r equal t o one.

(NOTE: Beddington and Cooke (1983) compiled a t a b l e o f var iances o f l o g rec ru i tmen t f o r a v a r i e t y o f f i s h species ( t h e i r Table 2). A sumnary o f t h e i r r e s u l t s suggests t h a t o = 0.4 represents low rec ru i tmen t v a r i a b i l i t y , o = 0.7 represents moderate rec ru i tmen t v a r i a b i l i t y and o = 1.0 represents medium-high recru i tment v a r i a b i l i t y ) .

11. End o f season numbers and r e c r u i t e d biomass (ENDBIO)

End o f season numbers a t age a re ca l cu la ted by mu l t i p l - y i ng mi:-season numbers by

Th is assumes t h a t f i s h i n g m o r t a l i t y (F) and n a t u r a l m o r t a l i t y (M) a re spread evenly on e i t h e r s i de o f t he mid-season.

End o f season r e c r u i t e d biomass (ENDBIO) i s c a l c u l a t e d as

max 2: Ni W i i =ar

where

N i

W i

a r

max

s t he end o f season numbers a t age

s t he mean (mid-season) weight o f a f i s h o f age (tonnes)

s t he age o f recru i tment t o t he f i s h e r y (AR)

s t h e maximum age used i n t he model (MAXAGE).

Note t h a t use o f mid-season weights throughout t he model means t h a t growth f rom mid-season t o end o f season i s n o t taken i n t o account.

12. Moving age c lasses up

.Numbers a t age a r e moved up one year c l a s s a t t he end o f each i t e r a t i o n . Old f i s h a r e cumulated i n the l a s t age c l a s s (MAXAGE); i.e. t he l a s t age c l a s s represents a p l u s group. New r e c r u i t s (R) a r e moved i n t o N1.

- .~ - - -

Note t h a t i f numbers_ a t age- (Ni ) a re tabu la ted a f t e r a s imu la t i on they w i l l represent t h e numbers-present a t t h i s stage o f the c a l c u l a t i o n s (equ iva len t t o the numbers present a t t h e beginning o f the nex t season) because the a r r a y N i s updated throughout the season.

13. Ca lcu la te a d i scoun t i ng f a c t o r

A use r -spec i f i ed d i scoun t i ng i n d i c a t o r (IDISC) determines the year a t which d i scoun t i ng begins.

I f t h e d i scoun t i ng i n d i c a t o r (IDISC) i s 0, the d iscount ing f a c t o r (DISC) and d iscounted revenues (DISREV) a r e no t ca lcu lated.

I f t h e d i scoun t i ng i n d i c a t o r (IDISC) i s 1, t h e d i scoun t i ng f a c t o r (DISC) i s c a l c u l a t e d as

where

6 i s the instantaneous d iscount r a t e (0)

t i s t h e number o f i t e r a t i o n s f o r which the d iscount ing i n d i c a t o r (IDISC) has been assigned a va.lue o f 1.

Annual f i s h i n g revenue (ANREV) i s then discounted by t h i s f a c t o r (DISC) and cumulated over t ime t o produce net present va lue (DISREV).

(EXAMPLE: A s i m u l a t i o n i s run over t h e pe r iod 1970 t o 2000 w i t h the d i scoun t i ng i n d i c a t o r (IDISC) s e t t o zero p r i o r t o 1983 and one i n t h a t year and the rea f te r . Discounted revenue (DISREV) w i l l then represent the n e t present va lue i n 1988 d o l l a r s ) .

14. Costs o f f i s h i n g (COST, UCOST)

A use r -spec i f i ed cos t i n d i c a t o r (ICOST) i s used t o s e l e c t one o f f o u r op t ions f o r represent ing harves t ing costs.

I f t h e cos t i n d i c a t o r (ICOST) i s 0, t h e t o t a l cos t o f harves t ing (COST) i s zero.

I f the cos t i n d i c a t o r (ICOST) i s 1, t h e t o t a l cos t o f harves t ing (COST) i s t h e product o f removals (REMOVALS) and a use r -spec i f i ed constant cos t per tonne (COSTCC).

I f the cos t i n d i c a t o r (ICOST) i s 2, the t o t a l cos t o f harves t ing (COST) i s r e l a t e d t o f i s h i n g m o r t a l i t y (F) by a use r -spec i f i ed p r o p o r t i o n a l i t y constant (COSTC). Th is o p t i o n i s based on t h e f o l l o w i n g assumptions

where

C i s annual removals i n tonnes (REMOVALS)

B i s mid-season r e c r u i t e d biomass (MIOBIO)

q i s a c a t c h a b i l i t y c o e f f i c i e n t

f i s f i s h i n g e f f o r t (e.g. boat-days)

F i s t h e instantaneous f i s h i n g m o r t a l i t y r a t e (F)

c i s t h e t o t a l cos t o f harves t ing (COST)

Thus t o t a l cos t o f harves t ing (COST) i s t h e product o f f i s h i n g m o r t a l i t y (F) and a constant (COSTC) which i s ca l cu la ted from the r a t i o c l F f o r some rep resen ta t i ve combination o f c and F. The assumptions a r e v a l i d o n l y i f t h e r e l a t i o n s h i p between removals and e f f o r t i s l i n e a r and f i s h i n g m o r t a l i t y (F) does n o t exceed about 0.3.

I f t h e cos t i n d i c a t o r (ICOST) i s 3, the u n i t cos t o f harves t ing each tonne (UCOST) i s i nve rse l y r e l a t e d t o biomass (F igure 3). The u n i t cos t o f harves t ing i s g iven by the hyperbola

where

c i s t h e cu r ren t cos t per tonne (UCOST)

B i s the mid-season r e c r u i t e d biomass (MIOBIO)

a,b a r e parameters

The parameters a and b are ca l cu la ted by spec i f y i ng a reference p o i n t (REFB. REFC) on the hyperbola, spec i f y i ng a parameter, A (COSTP), r e l a t e d t o the steepness o f t h e hyperbola, and assuming t h a t b ( t he l i m i t o f c as B tends t o i n f i n i t y ) i s approximately equal t o the u n i t harves t ing cos ts a t v i r g i n biomass (VIRBIO, COSTBO). The reference p o i n t (REFB, REFC) might, f o r example, be the c u r r e n t mid-season r e c r u i t e d biomass and the cu r ren t u n i t cos t ( 8 ) o f ca tch ing each tonne. Steepness i s de f i ned by the r a t i o o f the u n i t cos t o f f i s h i n g when biomass (MIDBIO) i s 20% o f the v i r g i n l e v e l (VIRBIO) t o t h e u n i t cos t a t v i r g i n biomass (COSTBO). This r a t i o must be g rea te r than 1. Thus

R B

so t h a t

CBV = RC

and a = 0.2 Bv (A - 1) CBV

where

BV i s t he r e c r u i t e d mid-season v i r g i n biomass (VIRBIO)

CBV i s t h e c o s t o f ca tch ing each tonne when biomass i s a t BV (COSTBO)

RC i s a re fe rence cos t pe r tonne (REFC) corresponding t o a reference biomass (REFB)

RB i s a re fe rence biomass (REFB) corresponding t o a re fe rence cos t pe r tonne (REFC)

A i s t h e r a t i o o f cos t pe r tonne a t 20% o f BV t o t he c o s t pe r tonnz a t BV (COSTP).

I n a l l cases t h e u n i t cos t pe r tonne (UCOST) i s equal t o t he t o t a l cos t (COST) d i v i d e d by t h e removals (REMOVALS).

15. Other economic parameters (PRICE, PCOST, FIXCOST)

A l l o t h e r economic parameters a r e i n p u t as use r - spec i f i ed constants. These comprise f o b p r i c e pe r tonne (PRICE), p rocess ing cos ts pe r tonne (PCOST) and f i x e d annual cos ts (FIXCOST).

16. Annual f i s h i n g revenue (ANREV) and d iscounted revenues (DISREV)

Annual revenue ($) i s ca l cu la ted as

(P - cp - c) C - Cf

- - .where

-

P i s t h e f o b p r i c e per tonne (PRICE)

cp i s t he processing cos ts per tonne (PCOST)

c i s t h e c u r r e n t cos t o f harves t ing each tonne (UCOST)

C i s t he c u r r e n t removals i n tonnes (REMOVALS)

c f i s t he f i x e d annual cos ts (FIXCOST)

Note t h a t use o f removals (REMOVALS) r a t h e r than repo r ted ca tch (CATCH) means t h a t i t i s assumed-that r imova ls a r e equ i va len t t o t r u e land ings (i.e. t he above equat ion o n l y takes account o f m is repo r t i ng , n o t losses o r d iscards a t sea).

Discounted revenue (DISREV) o r n e t present va lue i s c a l c u l a t e d as

where

t i s t he number o f years f o r which t h e d i scoun t i ng i n d i c a t o r (IDISC) has been a c t i v a t e d

end i s t he l a s t year o f t he s imu la t i on

6 i s t he instantaneous d iscount r a t e (D)

and the o the r parameters a re as de f ined imned ia te ly above.

Cont ro l i s now re tu rned t o t he b i o l o g i c a l submodel and a new i t e r a t i o n begins.

A1 t e r n a t i v e models

Two a l t e r n a t i v e vers ions o f t he model have been created. They a re i d e n t i c a l t o t he model descr ibed above (main v a r i a t i o n ) i n every respect except t he fo l l ow ing .

V a r i a t i o n 1.

Th i s model i s focussed on beginning o f season biomass, n o t mid-season. I n p a r t i c u l a r v i r g i n r e c r u i t e d biomass i s assumed t o be a beginning o f season est imate and so i s no t d i v i d e d by e-MIZ t o back-ca lcu la te from mid-season t o beginning o f season. S i m i l a r i l y recru i tment t o t he popu la t i on i s based on beginning o f season mature biomass. Thus recru i tment i s lagged by a f u l l year, r a t h e r than h a l f a

~ ~

yearp(i.e. beginning o f season numbeis a t age 1 a& der ived from We-: spawning biomass present a t the beginning o f the prev ious season); Cost o f f i s h i n g are, however, s t i l l based on the r e c r u i t e d biomass present a t mid-season.

Thus, t h e c a l c u l a t i o n s i n F igure 1 a r e changed so t h a t t h e phrase "beginning o f season" i s s u b s t i t u t e d f o r "mid-season" i n steps 5 and 9, and the sequence o f c a l c u l a t i o n s i s changed so t h a t steps 9 and 10 preceed steps 7 and 8. The c a l c u l a t i o n s performed a t s tep 8 (see t e x t ) a re a l l moved back t o s tep 6. A l l parameters and va r iab les i n Table 1 r e t a i n t h e same name and most r e t a i n the same meaning. The parameters and v a r i a b l e s t h a t s l i g h t l y a l t e r t h e i r meanings are:

VIRBIOM, VIRBIOL, VIRBIOH, VIRMIN, VIRMAX, V I R S J , 'iIRBIO, VIRSPAWN, TOTBIO, MATWT, PBIO, XLEN, XLENSD, BIOAGEi

These a r e a l l now based on beginning o f season numbers and weights, no t mid-season.

V a r i a t i o n 2.

The second v a r i a n t o f t h e model inc ludes a l l t h e changes made f o r v a r i a t i o n 1, a long w i t h a number o f ref inements t h a t a l l o w the user more f l e x i b i l i t y i n s p e c i f y i n g i n i t i a l cond i t i ons (biomass and age d i s t r i b u t i o n ) , and t h e shapes o f t h e stock-recru i tment and cos t o f f i s h i n g f u n c t i o n s (equat ions 9, 10 and 11).

A l l re fe rence t o v i r g i n biomass i s deleted. The user i n p u t s t h e i n i t i a l numbers o f f i s h a t age (N i ) f o r a l l ages i n t h e popu la t ion , i n c l u d i n g age 1 ( t h e number o f f i s h t h a t would have r e s u l t e d f rom t h e prev ious y e a r ' s spawniag);--A new v a r i a b l e (FIRSTBIO) i s used t o s t o r e the i n i t i a l r e c r u i t e d biomass.

Equat ion (9) i s replaced by

r a constant (RCON) i f spawning biomass (MATWT) i s above a

Rm = s p e c i f i e d th resho ld (CUTOFF)

MATWT i f i t i s below the th resho ld

where

Rm i s mean beginning o f season recru i tment a t age 1, t h e constant (RCON) i s expressed i n terms o f numbers a t age 1, and the th resho ld (CUTOFF) i s expressed i n terms o f spawning biomass.

The constant (RCON) i s a l s o used t o s p e c i f y t h e recru i tment l e v e l under the constant recru i tment o p t i o n (ROPT = 1).

Equation (10) remains unchanged, bu t t h e parameters, a and 8 (ALPHA and BETA), must be s p e c i f i e d d i r e c t l y . The steepness parameter (STEEP) used p r e v i o u s l y i s deleted.

- - . -

Equat ion (11) remains unchanged,'but the-parameters, a and b (ACOST and BCOST), must be s p e c i f i e d d i r e c t l y . The steepness parameter (COSTP) and t h e re fe rence p o i n t s (REFB, REFC AND COSTBO) used p r e v i o u s l y a r e deleted.

Thus, t h e parameters and va r i ab les om i t t ed from Table 1 are:

IRANOBIO, VIRBIOM, VIRBIOL, VIRBIOH, VIRMIN, V I R M I N , VIRSD, STEEP, COSTP, REFC, REFB, VIRBIO, VIRSPAWN, R V I R G ,

The parameters added are:

FORTRAN TYPE name

RCON R

CUTOFF R

ALPHA. BETA R

ACOST. BCOST R

DESCRIPTION AN0 USAGE

A constant l e v e l of beginning o f season recru i tment t o t h e popu la t i on (numbers a t age 1). Only needs t o be s p e c i f i e d i f ROPT = 1 o r 2. The spawning s tock biomass i n tonnes (MATWT) below which rec ru i tmen t s t a r t s t o decl ine. Only needs t o be s p e c i f i e d i f ROPT = 2. Parameters o f t he Beverton-Holt s tock recru i tment r e l a t i o n s h i p (equat ion 10). Only need t o be s p e c i f i e d i f ROPT = 3. Parameters o f t he cos t o f f i s h i n a f u n c t i o n (equdt ion 11). Only need t o be i p e c i f i e d i f ICOST = 3.

The o n l y new v a r i a b l e added i s FIRSTBIO, t h e i n i t i a l beginning o f season r e c r u i t e d biomass.

The advantage o f t h i s model i s t h a t i t a l l ows fo rward p r o j e c t i o n s o f popu la t ions w i t h known c u r r e n t age d i s t r i b u t i o n b u t unknown v i r g i n cond i t ion .

L i m i t a t i o n s o f t he models

The l i m i t a t i o n s o f t he models a r e t h a t a) they a r e t o o complex, and b) they a r e t o o simple.

Because t h e models a r e age s t ruc tu red , t hey r e q u i r e many i n p u t parameters. Parameter est imates may be imprecise when the re i s l i t t l e known about a species. However, the models a r e s u f f i c i e n t l y f l e x i b l e and . fas t t h a t ex tens ive s e n s i t i v i t y a n a l y s i s can be conducted f o r numerous combinat ions o f f e a s i b l e parameter est imates.

Several p o t e n t i a l l y complex r e l a t i o n s h i p s a r e t r e a t e d as constant. Th is a p p l i e s p a r t i c u l a r l y t o t he economic submodel, where da ta f o r New

Zealand f i s h e r i e s a r e most lack ing. B u t t h e FORTRAN source code has been s e t up i n such a way t h a t i t can be r e a d i l y mod i f i ed by a competent computer p r o g r a m e r and customised t o i n d i v i d u a l needs.

Probably t h e most important ref inement t h a t cou ld be made t o the models i s t o i nc lude r e s t r i c t i o n s on f i s h i n g e f f o r t . A t present i f the t a r g e t ca tch f o r a constant catch s t ra tegy exceeds t h e s tock s ize, then i t i s poss ib le t o f i s h o u t t h e e n t i r e r e c r u i t e d biomass i n a s i n g l e year. (Note t h a t t h i s does no t necessa r i l y lead t o e x t i n c t i o n imned ia te ly because the un rec ru i t ed year c lasses have y e t t o e n t e r t h e f i s h e r y ) . Th is anomaly does n o t occur f o r f i s h i n g s t r a t e g i e s based on f i s h i n g m o r t a l i t y o r escapement.

Other poss ib le ref inements i nc lude a breakdown o f t h e model i n t o stasanal components w i t h seasonal f i s h growth and seasonal f i s h i n g pa t te rns ; a d d i t i o n o f s p a t i a l components; and mode l l ing o f between o r w i t h i n popu la t i on v a r i a b i l i t y i n growth, m o r t a l i t y and reproduct ion.

Table 1. Parameters and v a r i a b l e s used i n t h e s imu la t io r imode l . The v a r i a b l e type i s s p e c i f i e d as e i t h e r I ( i n t e g e r ) o r R ( rea l ) .

l a ) Parameters - -

Parameters a r e constants t h a t can be se t o r d i sp layed ( t abu la ted and graphed) by t h e user, e i t h e r i n t e r a c t i v e l y o r i n a MACRO l i b r a r y . + i n d i c a t e s t h e parameters t h a t can be changed p a r t way through a s i m u l a t i o n by use o f an "AT t ime SET va r = va lue" comnand. * i n d i c a t e s those parameters t h a t t he user must, o r should, s e t a t t he beginning o f t h e s imulat ion.

FORTRAN TYPE DESCRIPTION AND USAGE name

+ ISEED

INIT

IRANDBIO

I RANDM

I RANDA

IRANDG

IRANDR

MAXAGE

* VIRBIOM

VIRBIOL

VIRBIOH

VIRMIN

I n d i c a t o r f o r seeding the random number generator ; 0 = OFF. 1 = ON. D e f a u l t i s 1 on f i r s t i t e r a t i o n , 0 t he rea f te r . I n d i c a t o r f o r i n i t i a l i s i n g the model; 0 = OFF, 1 = ON. D e f a u l t i s 1 on f i r s t i t e r a t i o n , D the rea f te r . Random number i n d i c a t o r f o r v i r g i n biomass; 0 = OFF. 1 = ON. De fau l t = 0. Random number i n d i c a t o r f o r na tu ra l m o r t a l i t y ; 0 = OFF, 1 = ON. D e f a u l t = 0. Random number i n d i c a t o r f o r ages o f recru i tment and m a t u r i t y ; 0 = OFF, 1 = ON. D e f a u l t = 0. Random number i n d i c a t o r f o r growth parameters; 0 = OFF, 1 = ON. D e f a u l t = 0. Random number i n d i c a t o r f o r recru i tment ; 0 = OFF, 1 = ON. D e f a u l t = 0. Maximum age considered i n t he model. D e f a u l t = 70; must no t be g rea te r than 70. Mean va lue o f r e c r u i t e d mid-season v i r g i n biomass (tonnes). Must be s p e c i f i e d by t h e user. Lower bound on mean r e c r u i t e d mid-season v i r g i n biomass (tonnes) expressed as a m u l t i p l i e r o f t he mean. Only needs t o be s p e c i f i e d i f IRANOBIO = 1. Upper bound on mean r e c r u i t e d mid-season v i r g i n biomass (tonnes) expressed as a m u l t i p l i e r o f the mean. Only needs t o be s p e c i f i e d i f IRANDBIO = 1. Minimum l e v e l o f r e c r u i t e d mid-season v i r g i n biomass (tonnes). Only needs t o be s p e c i f i e d i f IRANDBIO = 1.

Table 1.- cont 'd .

- ~ ~

-

FORTRAN == TYPE name . .

V I RMAX R

V I R S D R

* MMEAN R

MMIN R

MMAX R

* ARMEAN I

ARL R

ARH R

* AMMEAN I

AML R

AMH R

* KMEAN R

KMIN R

KMAX R

* LINFMEAN R

LMIN

LMAX

Maximum l e v e l o f r e c r u i t e d mid-season v i r g i n biomass (tonnes). Only needs t o be s p e c i f i e d i f IRANDBIO = 1. Standard d e v i a t i o n o f r e c r u i t e d mid-season v i r g i n biomass (tonnes). Only needs t o be s p e c i f i e d i f IRANDBIO = 1. Mean value o f instantaneous n a t u r a l m o r t a l i t y ra te . Must be s p e c i f i e d b y t h e user. Minimum l e v e l o f instantaneous n a t u r a l m o r t a l i t y rate. Only needs t o be s p e c i f i e d i f IRANDM = 1. Maximum l e v e l o f instantaneous natura' l m o r t a l i t y ra te . Only needs t o be s p e c i f i e d i f IRANDM = 1. Mean age o f rec ru i tmen t t o t he f i s h e r y (years). Must be s p e c i f i e d by t h e user. Lower bound on age o f rec ru i tmen t t o t h e f i s h e r y (yeqrs). Only needs t o be s p e c i f i e d i f IRANDA = 1. Upper bound on age o f rec ru i tmen t t o t he f i s h e r y (years). Only needs t o be s p e c i f i e d i f IRANDA = 1. Mean age o f m a t u r i t y (years). Must be s p e c i f i e d by t h e user. Lower bound on age o f m a t u r i t y (years). Only needs t o be s p e c i f i e d i f IRANDA = 1. Upper bound on age o f m a t u r i t y (years). Only needs t o be s p e c i f i e d i f IRANDA = 1. Mean va lue o f Brody growth c o e f f i c i e n t i n von B e r t a l a n f f y equation. Must be s p e c i f i e d by the user. Lower bound on Brody growth c o e f f i c i e n t . Only needs t o be s p e c i f i e d i f IRANDG = 1. Upper bound on Brody growth c o e f f i c i e n t . Only needs t o be s p e c i f i e d i f IRANDG = 1. Mean va lue o f L, (cm) i n von B e r t a l a n f f y equation. Must be s p e c i f i e d by the user. Lower bound on L, (cm). Only needs t o be s p e c i f i e d i f IRANDG = 1. Upper bound on L, (cm). Only needs t o be s p e c i f i e d i f IRANDG = 1.

Table 1. c o n t ' d

FORTRAN - name

CORRLK

CORRKK

CORRLL

* TO

+ ILENAGE

+ ILENL

+ ILENH

+ IAGEL

+ IAGEH

+* ROPT

TYPE

R

R

R

R

R

R

I

Covariance o f L, and K. Only needs t o be s p e c i f i e d i f IRANDG = 1. Variance o f K. Only needs t o be s p e c i f i e d i f IRANDG = 1. Variance o f L,. Only needs t o be s p e c i f i e d i f IRANDG = 1. X- in te rcept o f von B e r t a l a n f f y equat ion (years). Must be s p e c i f i e d by the user. Constant o f length-weight r e l a t i o n s h i p ( l eag th i n cm, weight i n gm). Must be s p e c i f i e d by the user. Power c o e f f i c i e n t o f length-weight re la t i onsh ip . Must be s p e c i f i e d by the user. I n d i c a t o r f o r c a l c u l a t i o n o f mean and standard d e v i a t i o n o f the length o f a s p e c i f i e d p o r t i o n o f the populat ion:

0 = no c a l c u l a t i o n s 1 = s e l e c t by l eng th 2 = s e l e c t by age

De fau l t = 0. Lower l i m i t o f l eng th (cm) t o use i n the c a l c u l a t i o n o f mean length. Only needs t o be s p e c i f i e d i f ILENAGE = 1. Upper l i m i t o f l eng th (cm) t o k e i n t h e c a l c u l a t i o n o f mean length. Only needs t o be s p e c i f i e d i f ILENAGE = 1. Lower l i m i t o f age (years) t o use i n t h e c a l c u l a t i o n o f mean length. Only needs t o be s p e c i f i e d i f ILENAGE = 2. Upper l i m i t o f age (years) t o use i n the c a l c u l a t i o n o f mean length. Only needs t o be s p e c i f i e d i f ILENAGE = 2. Recruitment o ~ t i o n chosen bv user:

zero' recru i tment - recru i tment constant a t the e q u i l i b r i u m l e v e l requ i red t o ma in ta in the v i r g i n biomass. Knife-edge recru i tment : recru i tment constant a t the e q u i l i b r i u m l e v e l requ i red t o ma in ta in the v i r g i n biomass, as long as

Table 1. c o n t ' d

FORTRAN name

+ STEEP

+ RMIN

+ RMAX

+ RSD

+* IFISH

+ FCON

+ CCON

+ BIOCON

+ WASTE

TYPE

t h e spawning biomass i s g rea te r than o r equal t o 20% o f the v i r g i n spawning biomass; recru i tment d e c l i n i n g

3 = a Beverton-Holt s tock recru i tment r e l a t i o n s h i p .

D e f a u l t = 1, b u t t h e user w i l l o f t e n want t o ove r r i de t h i s de fau l t . Steepness o f the Bever ton-hol t s tock recru i tment re la t i onsh ip . STEEP i s the f r a c t i o n o f the v i r g i n recru i tment t h a t w i l l be a t t a i n e d when t h e spawning stock f a l l s t o 20% o f i t s v i r g i n size. Must be l ess than 1. Only needs t o be s p e c i f i e d i f ROPT = 3. Minimum amount o f rec ru i tmen t t o t h e popu la t i on a t age 1 (numbers). Must be g rea te r than o r equal t o 1. Only needs to. be s p e c i f i e d i f IRANDR = 1. Maximum amount o f recru i tment t o the popu la t i on a t age 1 (numbers). Only needs t o be s p e c i f i e d i f IRANDR = 1. Ssandxd d e v i a t i o n o f l o g ( recru i tment a t age 1) (numbers). Only needs t o be s p e c i f i e d i f IRANOR = 1. F i sh ing o p t i o n chosen by user:

0 = no f i s h i n a 1 = constant h s h i n g m o r t a l i t y

I FCON) .~ - 2 = c o n s t i n t catch (CCON) 3 = constant biomass (BIOCON)

De fau l t = 0, b u t the user w i l l o f t e n want t o o v e r r i d e t h i s de fau l t . Instantaneous f i s h i n g m o r t a l i t y rate. Only needs t o be s p e c i f i e d when IFISH = 1. Catch (tonnes). Only needs t o be s p e c i f i e d when IFISH = 2. Target r e c r u i t e d biomass l e v e l (tonnes). Only needs t o be s p e c i f i e d when IFISH = 3. D i f f e rence between t r u e removals and repor ted catch, expressed as a f r a c t i o n o f repor ted catch.

� able 1. c o n t ' d

FORTRAN TYPE name

+ IECON I

+ IDISC I

+* PRICE

+* PCOST

+* FIXCOST

+* ICOST

+ COSTCC

+ COSTC

+ COSTP

+ REFC

Removals = repo r ted ca tch x (1 + WASTE). D e f a u l t = 0. I n d i c a t o r f o r c a l c u l a t i o n o f economic va r i ab les ; 0 = OFF, 1 = ON. D e f a u l t = 1. I n d i c a t o r f o r comnencement o f d iscount ing ; 0 = OFF. 1 = ON. D e f a u l t = 0. Only needs t o be s p e c i f i e d i f IECON = 1. Instantaneous d i scoun t rate. D e f a u l t = 0.1. Only needs t o be- s p e c i f i e d i f IECON = l . Fob p r i c e i n $/tonne. Only needs t o be s p e c i f i e d i f IECON = 1. Cost o f processing f i s h i n $/tonne. Only needs t o be s p e c i f i e d i f IECON = 1. F ixed cos ts i n $ / f i s h i n g year. Only needs t o be s p e c i f i e d i f IECON = 1. Cost o f f i s h i n g o p t i o n chosen by user:

0 = zero c o s t 1 = constant cos t pe r tonne 2 = t o t a l cos t p r o p o r t i o n a l t o

f i s h i n g m o r t a l i t y (F) 3 = cos t pe r tonne i n v e r s e l y

r e l a t e d t o s tock s i z e D e f a u l t = 0, b u t t he user w i l l o f t e n want t o o v e r r i d e t h i s defaul t . Only needs t o be s p e c i f i e d i f IECON = 1.

Cur ren t cos t o f ca t ch ing f i s h i n $/tonne. .Only needs t o be s p e c i f i e d i f IECON = 1 and ICOST = 1. The r a t i o between t o t a l cos ts o f f i s h i n g ($/year) and f i s h i n g m o r t a l i t y (F). Only needs t o be s p e c i f i e d i f IECON = 1 and ICOST = 2. A m u l t i p l i e r t h a t s p e c i f i e s t he increase i n c o s t ($/ tonne) a t 20% o f r e c r u i t e d v i r g i n biomass compared w i t h 100% o f r e c r u i t e d v i r g i n biomass. Must be g r e a t e r than 1. Only needs t o be s p e c i f i e d i f IECON = 1 and ICOST = 3. A re fe rence c o s t ($/ tonne) t h a t corresponds t o REFB and determines

Table 1. c o n t ' d

FORTRAN name

TYPE DESCRIPTION AND USAGE

+ REFB

the parameters o f t h e cost-biomass re la t i onsh ip . Only needs t o be s p e c i f i e d i f IECON = 1 and ICOST = 3. A reference biomass (tonnes) t h a t corresponds t o REFC and determines the parameters o f the cost-biomass re la t i onsh ip . Only needs t o be s p e c i f i e d i f IECON = 1 and ICOST = 3.

j b ) Var iables

Var iab les can be d isp layed, tabu la ted and graphed, b u t cannot be s e t by the user (i.e. they a r e ca l cu la ted w i t h i n t h e model).

VIRBIO R

VIRSPAWN R

BEGBIO

MIDBIO

TOTBIO

MATWT

ENDBIO

Recru i ted mid-season v i r g i n biomass (tonnes). The parameters VIRBIOM (VIRBIOL, VIRBIOH, VIRMIN, VIRMAX, VIRSD) a r e used i n i t s computation. Mid-season v i r g i n spawning biomass (tonnes). The v a r i a b l e s VIRBIO, R V I R G and AM a r e used i n i t s - . - - . . . . . .

computation. ( I f AM = AR then VIRSPAWN = VIRBIO). Beginning o f season r e c r u i t e d biomass (tonnes). The v a r i a b l e s Ni, W i and AR a r e used i n i t s computation. Mid-season r e c r u i t e d biomass (tonnes). The v a r i a b l e s Ni , W i and AR a r e used i n i t s computation. Mid-season t o t a l biomass (tonnes) (a1 1 ages i nc luded) . The v a r i a b l e s N j and W i a re used i n i t s computation. Mid-season spawning biomass (tonnes). The v a r i a b l e s N i , W i and AM are used i n i t s computation. End o f season r e c r u i t e d biomass (tonnes). The v a r i a b l e s Ni , W i and AR a r e used i n i t s computation. MIDBIO as a f r a c t i o n o f VIRBIO. Instantaneous n a t u r a l m o r t a l i t y rate. The parameters MMEAN (MMIN, MMAX) a r e used i n i t s computation. Age o f recru i tment t o the f i s h e r y (years). The parameters ARMEAN (ARL, ARH) a r e used i n i t s computation. Age o f m a t u r i t y (years). The

Ì able 1. c o n t ' d

FORTRAN TYPE: name^

LINF R

WINF R

XLEN

XLENSD

R V I R G

DESCRIPTION AND '%AGE -

parameters AMMEAN (AML, AMH) a r e used i n i t s computation. Brody growth c o e f f i c i e n t . The parameters KMEAN (KMIN, KMAX, CORRKK) a r e used i n i t s computation. Maximum average f i s h length (cm). The parameters LINFMEAN (LMIN, LMAX, CORRLK, CORRKK, CORRLL) are used i n i t s computation. Maximum average f i c b weight (kg). The v a r i a b l e LINF and the parameters A and B a r e used i n i t s computation. Mean leng th (cm) o f f i s h over a s p e c i f i e d range o f lengths o r ages. The parameters ILENAGE (ILENL, ILENH, IAGEL. IAGEH) a r e used i n i t s computation. Standard d e v i a t i o n (cm) o f f i s h l eng th over a s p e c i f i e d range o f lengths o r ages. The parameters ILENAGE (ILENL, ILENH, IAGEL, IAGEH) a r e used i n i t s computation. Beginning o f season recru i tment a t age 1 (numbers). The parameters ROPT (RMIN, RMAX. RSD) a r e used i n i t s computation. E q u i l i b r i u m beginning o f season v i r g i n recru i tment a t age 1 (numbers) requ i red t o main ta in t h e v i r g i n biomass. End o f season number o f f i s h o f age i ( i = 1, MAXAGE). Length (cm) o f f i s h o f age i ( i = 1, MAXAGE). The parameters and va r iab les K, LINF and TO a r e used i n i t s computation. Weight (kg) o f f i s h o f age i ( i = 1, MAXAGE). The parameters and va r iab les L j , A and B a r e used i n i t s computation. Mid-season biomass (tonnes) o f f i s h o f age i (i = 1, MAXAGE). The va r iab les N j and W j a r e used i n i t s computation. Instantaneous r a t e o f f i s h i n g m o r t a l i t y . The parameters IFISH (FCON, CCON, BIOCON, WASTE) and the va r iab les N i , W i , CATCH and REMOVALS a r e used i n i t s

Table 1. c o n t ' d

FORTRAN name

REMOVALS

CATCH

ANREV

DISREV

DISC

COST

UCOST

COSTBO

TYPE-

R

R

DESCRIPTION AND USAGE

computation. Biomass (tonnes) removed by f i s h i n g . The parameters IFISH (FCON, CCON, BIOCON, WASTE) and t h e va r iab les N i , W i , CATCH and F a r e used i n i t s computation. Biomass (tonnes) repor ted by f i she rs . The parameters IFISH (FCON, CCON, BIOCON, WASTE) and t h e v a r i a b l e s Ni . W i , REMOVALS and F a r e used i n i t s computation. Annual (non-discounted) revenue from f i s h i n g i n $. The parameters PRICE, PCOST, FIXCOST, ICOST (COSTCC, COSTC, COSTP, REFC, REFB) and t h e v a r i a b l e s REMOVALS (MIDBIO) a r e used i n i t s computation. Cumulative annual revenue f rom f i s h i n g i n $ d iscounted over time. The parameters IDISC and D and t h e va r iab les ANREV and DISC a r e used i n i t s computation. Cumulative d i scoun t i ng fac to r . The parameters IDISC and D a r e used i n i t s computation. To ta l cos t o f ca tch ing t h e c u r r e n t REMOVALS ($). The parameters ICOST (CXTCC, COSTC, COSTP, REFC, REFB) and t h e v a r i a b l e s REMOVALS (MIDBIO) a r e used i n i t s computation. U n i t cos t o f ca tch ing ($/tonne). The va r iab les COST and REMOVALS a r e used i n i t s computation. Cost o f ca tch ing one tonne o f f i s h (9) a t v i r g i n biomass l eve l s . Computed o n l y i f ICOST = 3. The parameters COSTP, REFC and REFB and the va r iab les MIDBIO and REMOVALS are used i n i t s computation.

Seed t h e random number generator &

Choose parameters f o r v i r g i n r e c r u i t e d biomass, na tu ra l m o r t a l i t y , age of rec ru i tmen t t o the f i she ry , age o f m a t u r i t y , growth

&

Ca lcu la te mean weights a t age &

Ca lcu la te v i r g i n recru i tment (numbers a t age 1) and the associated s t a b l e age d i s t r i b u t i o n

&

Ca lcu la te the mid-season v i r g i n spawning biomass

Ca lcu la te beginning o f season r e c r u i t e d biomass &

Ca lcu la te annual removals, annual catch and f i s h i n g m o r t a l i t y us ing one o f f o u r op t ions

4

Calcu la te mid-season t o t a l biomass

9. Ca lcu la te mid-season mature 13. biomass

4

10. Ca lcu la te recru i tment (numbers 14. a t age 1) as d e t e r m i n i s t i c o r s tochas t i c w i t h one o f f o u r op t ions f o r the stock recru i tment r e l a t i o n s h i p . . 15.

4

11. Ca lcu la te end o f season numbers and r e c r u i t e d biomass

& 16.

4- 12. Move age classes up one

and add recru i tment

numbers, r e c r u i t e d and

Ca lcu la te a d iscount ing f a c t o r

&

Ca lcu la te cos ts o f f i s h i n g us ing one o f f o u r op t ions

+ Choose parameters f o r f ob p r i c e , processing costs and f i x e d cos ts

&

Ca lcu la te annual f i s h i n g revenue and d iscounted revenues

F igure 1. Sequence o f c a l c u l a t i o n s i n t h e s imu la t i on model

Numbers

ut age I

Figure 2. Two o~tional stock-recruitment relationships used in the model. a) Knife-edge recruitment, b) Beverton- Holt stock-rec$itment relationship. Symbols are defined in the text (equations 9 and 10).

Figure 3. Optional relationship between cost of harvesting and biomass. Symbols are defined in the text.

APPENDIX I. HOW TO RUN THE MODELS ON-THE- PYRAMID 98xe

The models and cssoc ia ted f i l e s are conta ined i n the d i r e c t o r y

Users may copy t h e requ i red f i l e s from here t o t h e i r own d i r e c t o r i e s .

The d i r e c t o r y i n which the model w i l l be run must conta in t h e f o l l o w i n g

f i l e s :

System f i l e s : simcon makef i 1 e SUPCOM.

Model f i l e s : usermodel .f usermodelc. usermodel 8.

The names o f the f i l e s must be e x a c t l y as g iven above except t h a t

the term "usermodel" i s replaced by the name o f the des i red model. The

model names are:

bioecon:

bbioecon:

Main v a r i a t i o n (based on mid-season est imates o f biomass; i n i t i a l i s e d w i t h v i r g i n biomass and a s t a b l e age d i s t r i b u t i o n )

V a r i a t i o n 1 (based on beginning o f season est imates o f biomass; i n i t i a l i s e d w i t h v i r g i n biomass and a s t a b l e age d i s t r i b u t i o n )

ubioecon: V a r i a t i o n 2 (based on beginning o f season est imates o f biomass; i n i t i a l i s e d w i t h user -spec i f i e d numbers a t age).

The system f i l e , simcon, l i n k s the o the r f i l e s together and executes

the model. I t c a l l s makef i le , which s p e c i f i e s the l o c a t i o n o f the

compiled SIMCON l i b r a r y , uses t h e FORTRAN compiler, f77, t 3 compile the

usermodel i f i t i s n o t up t o date, and l i n k s t h e two together i n t o an

executable f i l e c a l l e d usermodel.runnab1e. The f i l e SUPCOM. conta ins

the system comnon b lock (system parameters).

With the poss ib le e i c z p t i o n o f makeg le , the system f i l e < should -

never need t o be changed. M o d i f i c a t i o n o f make f i l e w i l l be necessary i f

e i t h e r t h e pathname t o t h e SIMCON l i b r a r i e s changes, o r t h e user wishes

t o change t h e f l a g s used t o compile the usermodel (see SIMCON u s e r ' s

guide, Mace 1988).

The model f i l e s c o n s i s t o f t h e model name fo l l owed by the extensions

. f (FORTRAN source code), C. ( r e f e r r e d t o as the COMMON f i l e , con ta in ing

the user COMMON b lock ) and B. ( r e f e r r e d t o as the s e t f i l e , con ta in ing a

s e t o f comnands used t o i n i t i a l i s e the model and an o p t i o n a l l i b r a r y o f

SIMCON macros). I n general the novice user should n o t e d i t the f i l e s

usermode1.f and usermodelc.. An experienced FORTRAN p rog ramer should

be consul ted i f changes t o t h e s t r u c t u r e o f the models a r e required.

However, a l l users w i l l probably want t o customise the usermodelB.

f i l e s t o t h e i r own needs. Th is requ i res o n l y rudimentary knowledge o f

an e d i t o r and t h e s t r u c t u r e o f SIMCON comnands (see SIMCON u s e r ' s

guides: Mace 1988, Beals 1981).

A l l usermodelB. f i l e s conta in b r i e f desc r ip t i ons o f the parameters

o f t h e models, i n i t i a l i s a t i o n s f o r some parameters and a l i b r a r y o f

MACROs (se ts o f SIMCON comnands) w i t h d e s c r i p t i v e names. The model

bioecon conta ins an ex tens ive l i b r a r y o f (27) MACROs. An annotated

l i s t o f these MACROs, s p e c i f y i n g t h e i r s t r u c t u r e and purpose, i s g i ven

i n Appendix 111. The models bbioecon and ubioecon conta in abbrev ia ted

MACRO l i b r a r i e s w i t h examples o f v a l i d formats t h a t can be used t o

cons t ruc t i n d i v i d u a l i s e d MACROs.

None o f t h e MACROs a r e requ i red t o run the models. MACROs a r e used

o n l y i f they a r e c a l l e d by name from w i t h i n SIMCON. The models can be

~- .~ - ~ -- . -

parameterised'interactively - -- us ing SIMCONcomni71ds w i t h o u t t h e use o f - . . -

MACROS. MACROs can a l s o be de f i ned and c a l l e d i n t e r a c t i v e l y . The

advantage o f s t o r i n g MACROs i n a usermodelB. f i l e i s t h a t they do no t

need t o be recreated each t ime t h e model i s run. The MACROs c u r r e n t l y

s to red i n usermodelB. f i l e s a re prov ided f o r convenience, and as

examples on which t o base i n d i v i d u a l i s e d MACROs. Since t h e r e i s a l i m i t

on the number o f MACROs t h a t can be stored, the user may wish t o d e l e t e

thcse no t required.

Creat ion o f a customised ve rs ion o f the usermodelB. f i l e i s a l l t h a t

i s requ i red p r i o r t o running a model. A session i s begun by i ssu ing the

comnand:

simcon usermodel

where usermodel i s the name o f the model t o be run. For example, i f t h e

main v a r i a t i o n o f the model. i s being used, the appropr ia te comnand i s :

simcon bioecon

I f a f i l e c a l l e d usermodel.runnable does n o t a l ready e x i s t i t w i l l

be created by compi l ing usermode1.f and l i n k i n g i t t o t h e SIMCON

1 i b ra ry . I f i t does e x i s t , the message 'usermodel .runnable i s up t o

da te ' w i l l be issued. SIMCON w i l l then p r i n t ou t about e i g h t l i n e s o f

i r r e l e v a n t and p a r t i a l l y erroneous i n fo rma t ion (see Appendix 11). Due

t o a system problem the SIMCON l i b r a r i e s cannot be e d i t e d and recompiled

t o erase these statements. They should be ignored. (Other spurious

messages are a l s o h i g h l i g h t e d i n the example i n Appendix 11).

4

- ~ -

SIM~ON then^ performs a n h b e r o f i n i t i a l i s a t i o n s and re tu rns w i t h -

t h e prompt

when i t i s ready t o accept comnands. The user must then press t h e CAPS

LOCK key s ince SIMCON w i l l o n l y accept upper case comnands. Use o f

lower case w i l l r e s u l t i n an UNKNOWN COMMAND message.

A t the end o f a session type

Q

t o q u i t and e x i t SIMCON.

I t should be noted t h a t when a new SIMCON session begins, a l l

parameters a r e a u t o m a t i c a l l y g iven a value o f zero. The zeros a r e then

over r idden by any SET comnands contained i n the f i r s t p a r t o f t h e

usermodelB. f i l e (i.e. SET comnands t h a t a r e no t p a r t o f a MACRO). When

a MACRO i s c a l l e d a l l SET comnands t h e r e i n ove r r i de prev ious SET

comnands. S i m i l a r i l y any SET comnand entered i n t e r a c t i v e l y d u r i n g a

SIMCON session ove r r i des a prev ious SET comnand. This sequent ia l

o v e r r i d i n g does not , however, app ly t o "AT t ime SET" comnands. A l l AT

comnands t h a t have been s p e c i f i e d remain i n e f f e c t u n t i l the comnand "AT

CLEAR" i s given. Use the comnand "AT LIST" t o o b t a i n a l i s t o f a c t i v e

AT comnands.

An annoted demonstrat ion run f o r the model bioecon i s conta ined i n

Appendix 11. I n t h i s example a MACRO c a l l e d DEMO i s c rea ted and run

i n t e r a c t i v e l y . An i d e n t i c a l MACRO has been s tored i n the f i l e

bioeconB.. I t i s suggested t h a t new users repeat t h i s demonstrat ion by

c a l l i n g DEMO w i t h t h e i r own values for v i r g i n biomass and catch. F o r

example, issue the comnand

CALL DEMO 300000 20000

where

CALL i s an op t i ona l p a r t o f the comnand

t h e f i r s t number i s the v i r g i n biomass i n tonnes

t h e second number i s the ca tch i n tonnes f r o m 1989 onwards

Users should r e f e r t o t h e SIMCON use r ' s guides (Mace 1988, Beals

1981) f o r f u r t h e r i n fo rma t ion about SIMCON comnands and conventions, and

methods f o r ob ta in ing hardcopy output and graphics.

A P P E N D I X 11. ANNOTATED DEMONSTRATION E X P N P L E

SIMCON CDC VERSION 2 . 7 . 1 - CONVERTED TO RUN UNDER UAXlVMS V 3 . 7 - t h e n c o n v e r t e d t o unzx. so r e m e m b e r t o use UPPER c a r e

See 1-1 Doom- I F YOU HAVE ANY PROBLEMS - SEE P a m e l a Mace on UUCP n z f i s h - F . R D. e x t 807 - .

ext S S v y New c o m a n d s : MINMAX V A R N A M ( n i n r m a x ) t o s p e c i f y m i n & ma. f o r "VARNAM" - doesn% wok

p l u s t h e command HELP w i l l l i s t c u r r e n t v a l i d c o m m a n d s - eko indudcr ;nv&d co--4s

BATCH,COMMON,ULOG. a n d U F I L E o p e n e d f o r u s e r m o d e l

o p e n m s ma. 10000 - S p u r i o ( r ~ rucs q , t o qu i t . HELP f a r m o r e i ? f o . . . %=

MACRO DEFAULTS h a s been c a l l e d : a l l p a r a m s g i v e n d e f a u l t v a l u e s . . . MACRO DUMMYRAND h a s b e e n c a l l e d . . . . .MACRO Durr IYECDN h a 5 b e e n c a l l e d

? S E T ARMEAN=5 ?SET AMMEAN=S ?SET HnEAN=. 2 ?SET LINFMEAN='5Q. ?SET TO=O. ?SET A=. I ? S E T B=3. ?SET ROPT-3 ?SET STEEP=. 9 5 ?SET P R I C E = l 0 0 0 . ?SET PCOST=200. ?SET ICOST=3. ?SET COSTP=I . 5 ?SET REFB=50000 . ?SET REFC=500. ?SET FIXCOST=O. ?SET I D I S C = O ?AT 1987 SET I D I S C = l ?SET D=. 1 ?SET I F I S H = 2 ?SET UASTE=O. ?SET CCON=O. ?AT 1 9 8 0 S E T CCON=5000. :AT 1 9 8 1 S E T CCON=10000 '?AT 1 9 8 2 SET CCON=lOOOU ?AT 1 9 8 3 SET CCON=10000 ?AT 1 9 8 4 SET CCON=20000 ?AT 1 9 8 5 S E T CCON=2@000 ? A T I986 SET CCON=20000 ?AT 1 9 8 7 SET CCON=20000 ?END - a n d of

ENTER COMMAND 3

? ? ? ? ?MACRO DEMO V C

- - , ENTER MACRO TEXT a f k r P ~ s S ' " ~

?..MACRO DEMO has b e e n c a l l e d ? . . Y o u may now i s s u e S IM. D I a n d PR commands . ? . . I f y o u w a n t t o d o a n o t h e r run: C A L L RESTART; t h e n C A L L DEMO; Cull i f 6,- +&,re). ? . . t h e n y o u may issue y o u r dun SET c o m m a n d s t o o v e r r i d e DEMO'S ? . . p a r a m e t e r v a l v e s ; t h e n i s s u e S IM. D l and PR c o m m a n d s ?SET VIRBIOM=V ~ h ~ r ~ d e r s &/-ir. fwo w i l l b e ?AT 1988 S E T CCON=C p<;-+ed 0°C 6 '&= S U U ~ ?SET MMEAN=. 2 i& m m e o ;a cd led .

Y o u may nou issue SIM. D l and,PR commands. I f you w a n t t o do a n o t h e r run: CALL RESTARTi t h e n CALL DEUO, t h e n you may issue your own SET commands t o overr ide DEMO'. parameter values; t h e n i s s u e SIn. 01 and PR commands

&a n ~ ~ ~ l o IOISC ANREV D~SREV. COST - tobulote ST-u lded v * f u c * o f nore v ~ ~ ; ~ ~ ' ~ ~ over11: nymar 101 - ' P v ' ' ~ " ~ --a=-sLSC ucomio99s: i n d e x 1 irec+102) 0 -spu-;-=-' -*sr%ic

I TIME M I D D I O IOISC ANREV DISREV UCOST 0 . 0000OE+O0 ..00000E?QQ ... OODQE+S ,OOO.OOE+OO .00000E+00

1980 . 30000E+06 . 00000E+OO .00000E+00 .00000E+00 .00000E+00 1981 .29749E+O6 . 00000E+00 .22799E+07 .00000E+00 344. 01 1982 .29040E+06 . 00000E+00 .45522E+07 .00000E+00 344. 78 1985 .28173E+06 .00000E+00 .45422E+07 .00000E+00 345. 78 1984 . 27401E+06 .00000E+00 .45329E+07 .00000E+00 346. 71 1985 .26208E+06 .00000E+00 .90346E+07 .00000E+00 348. 27 1986 . 24701E+06 .00000E+00 .89909E+07 .00000E+00 350. 45 1987 .23362E+06 .00000E+00 .89474E+07 .00000E+00 352. 63 1988 .22185E+O6 1.0000 .89048E+07 .89048E+07 354. 76 1989 . 20629E+06 1. 0000 . 13262E+B '. 20904E+08 357.95 1990 . 188ObE+O6 1.0000 . 13129E+OB . 31654E+08 362. 35 1991 .17179E+Ob 1.0000 . 12988E+08 . 41276E+08 367.07 1992 ; 15734E+06 I . 0000 . 12837E+08 . 49881E+O8 372.09 1993 . 14450E+06 1.0000 . 12679E+08 . 57571E+08 377.38 1994 . 13309E+Oh 1.0000 . 12512E+08 .64437E+08 382. 94 1995 . 12287E+06 1. 0000 . 12336E+08 . 70563E+08 388. e0 1996 . 1 1369~106 i. 0000 . 12151E+O8 . 76023E+08 394.96. 1997 . 10536E+06 1.0000 . 11956E+O.E . 80884E+OB 401. 48 1998 97769. I. 0000 . 11748E+08 .85206E+08 408.39 1999 90785. I . 0000 . 11527E+08 .89043E+08 41 5. 77 2000 84311. 1.0000 . 11289E+OB .92443E+08 423. 70

. ? -

?RESTART -. C ~ ~ I & S T R e ~ (&- b;Oeuo-6.:) p e p d o - f& fe-rurn, Kr- -drP - .. wit^ diffouR pa,a-&rs

3 MACRO RESTART has been called: reinitialiser model - All AT commands cleared. TIME 0 recalled. random number generator reseeded. 'all random number indicators turned off. equilibrium recruitment and stable age d i ~ t r i b u t i o n recsluloted, discount rate indicator turned o f f . default maximum number o f iterations reset to LOO.

If this is the first run of t h e session, an error message "NO SIMULATION RECORD FOUND FOR TIME 0" will appear - Ignore it.

? ? Z,

joOM)O 50000 - C O I I D L ~ O ui* a d;f&n+ c ~ k h ieud

MACRO DEMO has been called You may now ~ r s v e SIM. 01 and PR commands. If you want to do another run: CALL RESTART' then CALL DEMO; then you may issue your own SET commands to override DEMO'S parameter values; then issue Sill. 01 and PR commands

? , ,

? 9

? ?SET W&TE=.~ -change f f i r ~ I u e of % ,parocefe5 WASTE ?Dl PRICE - Dirpl- Cur.ent volu.% of Pt2IC.E ?Dl PRICE PRICE = 1000.000

? ?SET pRlCE=20oO -cLa-ge CLL~-4 V-I-L 4 PRICE ?

701 PRlCE - D;+lg nw cue-,+ u a l u r cf P ~ I c E PRICE = 2000.000

?

.? ? ?s:n 1980 2o00 - I.-;fiato a n u ~ ; - - l a ) i h C

?PR BEGBIO MIoBIo REMOVALS CATCH F R -7bbulate S;mulated voLue~ of ~ o r ; ~ b l e s of i d e r e s t over11: nqmar 101 -.3@.';~u5 messsge ~comia994: index( irec+102) 0 - S P U ~ ~ O C L . -5-sc

1 TIME BEGBIO MIOBIO REMOVALS CATCH F R 0 .00000E+00 .00000E+00 .00000E+00 .30000E+00 .00000E+00 .00000E+00

1980 . 33155E+O6 . 30000E+O6 .00000E+00 .00000E+00 .00000E+00 . 19819E+O8 1981 . 33155E+O6 . 29674E+O6 6500.0 5000. 0 . 21859E-01 . 19816E+08 1982 . 32499E+O6 .28751E+06 13000. 10000.0 . 45103E-01 . 19808E+08 1983 .31254E+O6 .27624E+06 13000. 10000.0 . 46941E-01 . 19797E+08 1984 .30144E+06 .26619E+06 13000. 10000.0 .48712E-01 . 19786E+08 1985 . 291 66E+06 . 25062E+O6 26000. 20000. 0. 10335 . 19768E+08 1986 .26999E+06 .23098E+06 26000. 20000. 0.11211 . 19741E+08 1987 .25071E+O6 . 21350E+06 26000. 20000. 0. 12126 . 19714E+08 1988 . 23369E+O6 . 19808E+O6 26000. 20000. 0: 13066 . 19686E+08 1989 .'2I875E+06 . 16254E+06 65000. 50000. 0.39409 . 19601E+08 1990 . 16583E+06 . 1 1344E+06 65000. 50000. 0. 55946 . 19399E+OE 1991 . 11755E+06 67191. 65000. 50000. 0. 91873 . 18955E+08 1992 73206. 16209. 65000. 50000. 2.8155 . 16108E+08 1993 32311. 196. 99 32311. 24855. 10.000 .94264E+06 1994 27808. 169. 54 27808. 21391. 10.000 . 81662E+o6 P o n d s con+ 1995 27522. 167. 79 27522. 21171. 10.000 1996 26B92. 153. 95 26892. 20686. 10.000

eoe55E+06 be ~ , . ~ h ; ~ . - d . 7907bE+Ob 1997 22853. 139. 33 22853. 17579. 10.000 . 67600E+06 1998 1338. 4 8. 1600 1338. 4 1029.5 10.000 40886. 1999 1158.6 7.0635 1158.6 891. 20 10.000 35402. 2000 1147. 1 6.9936 1147. 1 882.39 10.000 35052. 1

.1 . ?- ? ?PR MIDBfD .. . IOISC .ANREV DISREV UCOST - *b.i!dc- ~ i - ~ ! a J c d bolues .of - 0 -*i-b!er - a " e r i i . n u m a , . -10~1 - Spur:-ur ~ l c y e . - -. - -

ucomia??a index I i r i c 7 1 0 2 ) 0 - spu-(04 -rao.ac i TIME UTDBIO IDISC

- -- ANREV- - -DISREV . UCOST

0 .00000E+00 .00000E+00 .00000E+00 .00000E+00 . 00000E+00- 1980 . 30000E+O6 .00000E+00 .00000E+00 . 00000E+00 .000WE+00 1981 . 29674E+06 .00000E+00 .94634E+07 .0000CE+oO 344. 09 1982 . 28751E+O6 .00000E+00 . 18914E+08 .00000E+00 345. 11 1985 . 27624E+06 .00000E+00 . 18896E+O8 .000OOE+00 346. 44 1982 . 26619E+Ob . OOOWE+00 . 18880E*OB . OWOOE+M) 347.72 1985 . L'S062E+O~6 . 00000E+W .37702E+08 .00000E+00 349.91 1986 . 23098E+O6 .000WE+00 .37620E+OQ .00000E+00 353.09 1987 .21350E+06 .00000E+00 .37533E+OE . MX)OM+oO 356.41 1988 . 19808E+06 1.0000 .37444~+08 .37444~+08 359.83

1989 . 1&254E+O6 1. 0000 .92938E+08 . 12154E+09 370. 18 1990 . 11344E+O6 1. OOCU .913166+08 . 1963M+09 395. 14 1991 67191. 1.0000 .87618E+08 .26121E+O9 452.03 1992 16209. I. 0000 . 59092E+08 .30082E+09 890. 89 1993 196. 99 1.0000 -. 14896E+10 -. 60269E+09 47904. 1994 lh9. 54 1.0000 -. 14963E+10 -. 14239E+10 55609. 1995 167. 79 1.0000 -. 14968E+10 -. 21672E+iO 56184. 1996 163. 95 %. 0000 -. 14977E+lO -. 28401E+10 57494. 0 - Z C 1997 139. 33 I. 0000 -. 15037E+lO -. 34515E+l0 67599. 1998 8. 1600 :. 0000 -. 15357E*10 -. 40165E+lO . 11492E+07 lp99 7. 0635 I. 0000 -. 15360E+lO -; 45277E+lO . 13276E+07. 2000 6. 9936 1. 0000 -. 15360E+10 -. 49904E+10 . 13408E+07

? ? 7 3

?VIEW n I o D ic REMOVALS - P M o h ef ~rc'oblss on 1;- plotlac 0 ~ ~ ~ 1 . 1 : nqmai 101 - dpun'ouc .-=SSOL~C ucomio??-i inder( irec+lOZ> 0 -rpu-;out - . S C y Q

. . 1

VARIAGLE I S NIOBIO MAX = Mar;-,, U& 0.f ind;v;duslb VaRIAnLF : I s REMovALs ~ p x = 2 by s r ~ c c d

+ X : . - ~ . ~ X X I X + x X X x x X X X X + X X X X X x X X X + X X x x x x x x x + x x x x x x x x x + x x x ~ x x x x x + nrr

/ : r*rDnto 2 : R t ~ o u a ~ s * z both

TIME J,

STOP: SllliON HALTED frc5: -D - q u i t scrip* s c r i p t done on Ued Ju l 13 00:35:33 1988

XPPENDIX -11-1. ANMBTATED LI~STING OF THE COPTPUTER FILE b i o e c o n B . .INELUDING ~ C R O LIB'RARIES

u e l c o m e to the generalised bioeconomic fish population dynamics ..simulation model constructed by Pamela Mace and Ian Doonan.

1 t i s a aood idea to CALL D E F W L T S at the start (only) of a

-- INITIALISATION AND DEFAULT VALVES FOR RANDOH NUMBER INDICATORS 3 $? c ~ - ~ * D L + ~ * z @o-c- h e . - ype-r 3.-0-4 ~ 3 s ~ ~ ~ ~ YE: 1:4ir=i - - t i 1. calculate. virgic.. rec. & eq. nos. st age (-(re--d PS LD* .~NNTS)

if 0. docsnti i. e. proceeds from current valuer (default is 1 at timc 0; 0 thereafter)

ISEED=I --if 1, seeds the random no . generator if 0, doernti i. e. p ~ o c e e d s from current point (default is 1 i t time Oi 0 thereafter)

~ t e : to re-run with vir. bio. & same rand. no. r e g u e n c e : use TIME 0;SIM 1 100 (or CALL RESTART)

tn rr-run with vir. bio. & cantinuina rand. no.

to re-run with current bio. & continuing rand. no seouence. use SIM 101 200 - - .-- ~ ~~~

-:?AND. is the random number indicator for virgin biomass, . .~ natural mortality. ages of recruitment and maturity.

growth parameters and recruitment . ~. it' 1, generates params from prob. distr.

if 0. doernt .. 1 .. . r IRANDQIO=O - - Random no. indicator for virgin biomass .,. .. :.=, !RANDM=O -- Random no. indicator for nat. mort. .. ... : IRANDA=O -- Random no. indicator for age rec. & maturity .. .. ;:., IRANDG=O -- Random no. indicator for growth ( K & LINF) z:::T IRANDR=o -- Random no. indicator for recruitment . ~. --BIOLOGICAL PARAMETERS : t : Mean valves (expected values, MUST be given in appropriate . .. MACROS. The variables associated with random number

lndicatars (orefaced below bu five dasher) ~ ~ - - -- are set to default (nonsensei values in MACRO ~ - DUMMYRAND. Any S E T command will overrid. the defaults. :Xi P!AXACE=70 --maximum age considered in the model (must not be ~. ~. greater than 70)

- ~ 3 i o m a s s - V I R B I O M --mean value o f virgin biomass -.--- VIRQIOL --lower limit of mean value a r multiplier of mean

VIRBIOH --upper limit of mean value as multiplier o f mean -. .-- VIRMIN --lower bound on biomass

VIRMAX --upper bound on biomass . VIRSD --standard dkviation of biomass

-rIdtural mortality - I I M E A N --me+" value of natural mortality .. MMIN --lower bound . ---- MMAX --upper bound --Aorr af recruitment and matvritu - - - - - ~ ~ M E A N --mean value of age O F recruitment

ARL --lower bound ARH --upper bound

--:.*~EAN --mean value of age of maturity .. . . . .. - AML --lower bound

A m - - u p p e r bound - - :rn,. ,eh . . . - . . . - - i f l E ~ N - -mean value of Brodq q ~ a w t h caeff o f vonkert equation .~ KMIN --lrwer bound . KflAX --upper bound

.. . ; .:NFMEAN --mean value o * maximum length in vonOert equation

---LMIN --!.?we? bound ~ L ~ A X --upper oauna . CORRLU --covariance LINF and.K

CORRKK --variance L . --- CORRLL --variance LINF

- : o --1-intercept.of yonOSrt equation

--Length-wPight pazmsterr' -**eight=arl*+b where Geight i r ~ i n grams

--B --power constant of lcsgth-weightrelationship --Pa$ulation length SET ILENAGE-0 --indicator for length calculations -- O=no calculationr -- . 1=select by length

. -- 2=select by age -----1LENL - --lower limit of length ----- ILENH --upper limit of length ----- IAGEL --lower Limit oP age ----- IAGEH --upper limit of age --Recruitment SET ROPT=1 - - 0 gives zero. I gives constant. 2 gives knife-edge, -- 3 gives neverton-Holt --STEEP -- Steepness af the Beverton-Holt relationship: -- Rec = (STEEP*RVIRG) when MATUT = .2rVIRSPAUN ----- RMIN '--minimum rscruitment.in numbers ----- RMAX --maximum recruitnent in numbers ----- RSD --standard dev. of log(rec1 -- --FISHING PARAMETERS -- SET IFISH=O --fishing indicator: -- O=no fishing IFCON. CCON & BIOCON ignoredl -- l=constant F (CCDN L BIOCON ignored) -- -.. --canstant catch (FCON I. BIOCON ignored) -- 3=constant biomass LFCON & CCDN ignored) -+CON --fishing mortality (used when ifish=l) --CCON --catch in tonne5 fused when ifish=Z) --BIDCON ---b~omais in tonne5 cured when ifish=3) SET UASTE=O. --prop.nf catch not landed or reported -- --ECONOMIC PARAETERS -- SET IECON=I --if 0, e c o n variabler not calc -- i f 1 . theg are -- MACRO OUMMYECON has dummy (nonsense) valuer far -- e ~ o n o m i i parameters. which can be overridden -- b y any SET command SET IDISC=O --if I, applies discount rate to revenue -- i f 0. aoesnt SET D - . I --aiscount rate for profits --PRICE --fob price per tonne in ) -+COST --cost of procrssing per tonne (<I SET ICOST=O --which cost function to use: -- 0 = zero cart -- I = constant cost -- 2 = cost prop to F -- 3 = cost inversely related t o stock sixe --COSTCC --current cost of catching per tonne --COSTC --iust-of-catching constant for cost prop to F --COST? --iasc=COSTPICOSTBo when MIDQIO-.2 VIRBIO --REFC --reference cost ~orrssponding to REFB --REFB ' --reference biomass corresponding to REFC --FIXCOST --fixed costs in I per fishing year . .

-1his i s +he e n d of +he non- M A C R O port of b ~ o e ~ o - 5 .

Do nod use an &NP d a i e - e r i f here .

f ) / l commands contained in +he above part of +he

f i l e w;l/ be e x e c u t e d i m n e d ; o + e f y d e n 4-c

model ds loaded.

The ievnolnder of %e file conds;qs 0 /;bra<, of

H A C e O a fkf ore e x e c u t e d only i f +hey are c a l l e d .

MACRO DEFAULTS

~ . . MACRO D E F ~ L T S has been- c8: led: - a l l . params given d e f a u l t v a l u e r - --THESE ARE ALL THE PAR&MS.THAT;MUST.BE RESET FOR THE - --DETE~M~NISTIC VERSION O F ?YE MODELS- I F - Y O U UANT TO -

---OVERRIDE THEE SET RNYMAX=IOl SET IRANDBIO=O- SET !RANoM=O- S E T I R A N D A q e S€T IRANDG=O-

:SET IRANDRzO S E T MAXfiGE=70 SET V I R B I O M = 1 0 0 0 0 0 . SET MMEAN=. 2 SET ARMEAN=5 SET AMMEAN=5 -SET HMEAN=. 2 SET .L INFMEAN=40. SET TO=O. S E T A=. 1

7 h i ~ H A c e o c&o pmu;des m i h + of

& p a k t need -to k s d

in rus*n;sed NAc&Oz

SET FCON=. 2 SET CCON=O SET B I O C G N = 5 0 0 0 0

MACRO DUMMYRANG . . . . . . . MACRO DUMMYRAND has b e e n c a l l e d --UPPER AND LOWER L I M I T S AND STANDARD D E V I A T I O N S FOR --RANDOM PIUMBER GENERATION SET V I R D I O L = . 4 S E T V I R B I O H = l . 6 SET V I R n I N = 5 0 0 0 . S E T V IRMAX=1000000 . SET V I R S D = 5 0 0 0 0 . SET PIPIIN=. I S E T MMi.X=. 3 S E T ARL=? ~. - be u s e d u -1csS bio-ors, noiucd -,-fay, SET A R H = ~ Oges of r c c s u , . 4 w - t a-d -Q&c;d S E T AML=4 y, "' S E T IMH=S avo-* ?-<a-ekrs are to .Le dr-- S E T KMlN=. 0 1 S E T KMAX=. 97 SET L M l N = l O . S E T LM,~,*=100. d E T CORRLK-. 0 1 5 SET CORR#.K-. 3 0 0 1 5 SET SORRLL=1. 6

SET RMAX=I. E l 2 SET RSD=l . END -- --

MACRO OUMMYECON . . . MACRO DUMMYECON has been c a l l e d

S E T I E C O N S I SET I G I S C - 0

-

SET R E F B = 5 0 0 0 0 S E T REFC=500 SET FIXCOST=O END --

MACRO RESTART - . . .

. . ,~~cRo RESTART " a s b e i n c a l l i d : - r e i n i t i a l i ; c s ~ ~ m o d e l - - ---

..i.ll AT c o m m a n d s ~ c l e a r e d , T I M E ~ O r e c a l l e d , r a n d o m n u m b e r g e n e r a t o r

. , - ~ 6 s e ~ d e d ~ a l l . r a n d o m n u m b e r i n d i c a t o r s t u r n e d o f f , e q u i l i b y i u m . : r e c r u ~ T m e n t a n d s t a b l e a l e d i s t r i b u t i o n r e c a l u l a t r d . d i s c a u n t

~ . . . . . . . . - r a t e ~ n d l c a t o r t u r n e d o f * . d e f a u l t m a z i m u m ~ u m b e r of ' l t e r a t i o n i -

- - . r e s e t tp-100. -- . . - . . If t h i s i s t h e f i r s t Y G n qf t h e s e s s i o r b an err--message r-.

"NO S I M U L A T I O N RECORD FOUND FOR T I M E 0" w i l l adpear - . . -~ - I g n o r e i t . . ' -

AT CLEAR T I M E 6 SET XNYMAX=IOl ~ - -

SET I S E E D = I - Sef TSs?€D'O b C ~ O O E C a . SET IRANDBIO=O --bifi&on of SET IRANDM=O doxo;l.aphic f a r r n n e ~ ~ r ~ SET IRANDA=O SET IRANDC=O SET IRANDR=O SET N ( A L L ) = O SFT I N I T = , - - . . . . . . . SET I D I S C = O END

MACRO V I R G I N VTRY --HELPS DETERMINE BACK-CALCULATED V I R G I N BIOMASS

.MACRO V I R G I N h a s b e e n c a l l e d w l t h fiAc@o vl R C J N fa " ~ ; f a f e f +w;d SET VIROIOM=VTRY DI VIRBIOM and ervoc c4&?&on of flce . . . vi-3;- b.'orrc.r~ &at w ; l l . . N o t e t h a t y o u m u s t c a l l nESTART a n d a t l e a s t one MACRO . . c o n t a i n i n g a l l n e c + s s a r y b i o l o g i c a l p a r a m e t e r s b e f o r e p & r e a know, b i o - ~ r s

I d at ao-e l ~ f e r dofe

MaCRO MBY CTfiY --HELPS DETERMINE MSY FOR CONSTANT CATCH P O L I C Y ..MACRO MSY h a s b e e n c a l l e d w i t h SET CCON=CTRY D l CCON . . . MACRO H S Y dcifofer f r d . . n o t c : TIME o r e c z ~ ~ e d a t b e g e a c h b u t not at end. and e-or cdCILa9fion of fk

T i m e h o r i z o n = 5 0 0 years. Maxi-u- mns+a?-t . CP&& . . RESTART - /k f Cur \ be SUS- SET #NuMAx=501 - ;ficrcoscs &e 011-able nu, rbe / SET UASTE=O. af i f c m f f n n s , a i n c r wnsCP.rC SET I F I s H = 2 cn&k po/#u.e& tpke o lor3 SET CCON=CTRY fi-e i o con& e srn I 500 - %is corn-od y3need -lo b e cha- e d . . . dcp-d- or, -%e +;- -.,;+r urrd8 O I BEG010 M I D 0 1 0 F REMOVALS S T OEGOlO MIOOIO F REnOVALS . . . 0 IOMASS AFTER

G I P O I D

END -- -- MACRO REPEATMSY

MACRO FMSY FT&Y . . , --HELPS DETERMINE MSY FOR CONSTANT CATCH POLICY- . . MACRO FMSY .has been-called with SET FCON=FTRY . ~

D I FCON I - -

. . . and ewor cd&&or. of

..note: TIME 0 r e c a l l e d at b e g o f each run, but not at end. . 3he w s r i . - ~ - cons+e.-.t,

. . T i m e h o r i z o n = 5 0 0 years.

. . . RESTART SET eNYMAX=501 - ; - ~ r ( - -ke allowable nurnber SET UASTEPO. of i&rof;ons SET I F I S H = I SET FCON=FTRY s ~ n l 5 0 0 - 6 L O - - C L - ~ need + b e cLam3ed

depe-di- - 6 +-c -.,;is & 'BEGBID M I D B I O F REMOVALS S T BECBIO M I O B l O F REMOVALS . . . . . B l O M A S S AFTER 5 0 0 YEARS A S % O F Bo: DI P a l o

-- MACRO REPEATFMSY CALL FMSY F T R Y ~ CALL FMSY FTRY2 CALL FMSY FTRY3 C A L L FMSY FTRY4 CALL FMSY FTRY5 END

MACRO RESULT . . . PR a E c a I o n i D a 1 o R E n o v A L s ANREV DISREV UCOST . . . . . . END -- -- MACRO RESBID

. . . END -- -- MACRO R E s a m E c . . . PR M I D B I D REMOVALS CATCH F ANREV D I S R E V . . . . . END -- --

UACRO CHATHArl . . . .uACRO CHATHAU h a s b e e n c a l l e 4 : b a s i c ORH 5 e ~ t

~~ S E T Y I R B I O U = 5 0 0 0 0 0 . . ~

. SET-HUEAN=. i- : . SET ARMEAN=6 - - -

S E T AM~EAN=~- SET WEAN=. 26 . . SET LINFMEAN=41. 2 SET TO=. 6 5 SET A=. 0963 SET W2.68 SET I F I S H = 2 SET CCON=O. --SET PRICE=3288 : SET PRICE=2567 . --price ha4 decreased SET PCOST=432.

SET COSTCC=1517. SET COSTC=180000000. SET COSTP=l. 5 SET REFB=968OO. SET REFC=1050. SET CIXCOST=O. A T 1979 SET CCON=llQOO. AT 1980 SET CCON=31100. AT 1981 SET CCON=28200. AT 1982 SET CCON=32605. AT 1983 SET. CCON=32535. AT 1 9 8 4 SET CCON=29340. AT 1 9 8 5 SET CCON=23420 AT 1986 SET CCON=34000. --AT 1 9 8 7 SET I D I S C = ? END -- --

llACRO C H i L RACKS CCHL b a r b e e n c a l l e d b a s x c OR14 params set

SET V IRBIOU=117000 . SET WEAN=. 10 SET ARUEAN=5 SET AUMEAN=5 SET HrlEAN=. 2 1 5 SET LINFr lEAN=39. 18 SET TO=2. 1 7 SET A=. 0963 SET 8=2. 6Q SET 1FlSH=2 SET CCON=O. SET P R I C E 4 2 8 8 . SET PCOST=432. SET I C O S T = ~ SET COSTCC=1517. SET COSTC=l80000000 . SET COSTP=l. 5 SET REFB=3263. SET PEFC=718. SET FIXCOST=O. AT 1981 SET CCON-4072. > AT 1982 SET CCON=11947.

f i r a - d g r values CC~ALLG-W f'l&od

o r u y cyhJ used - 198e

6.. hey A s s e s r ~ o + rnee f - - -y

SET E ~ A N = . ~ ~ G SET ARMEAN=b SET aMnEAN=6 S E T KMEAN-0. 26 S E T C!NF:IEAN=41.2 SET TO:iS.. 6 5 SET ! += 0963 SET 8=2. 68 S E T I F I S H = Z SET CCON=O. S E T P R I C E = 3 2 8 8 . SET PC@ST=432

AT !96 ; SET CCCN=3510. AT :T,F?.I ' l i T CCON=7200. A T iie.: 5zr c c o N = a 1 5 1 . . - . CCON=5939. A . - - AT !?El. SET CCON=9042. --+; 15.5: SET I D I S C = 1 - E N 3 -- --

,,f . ....<.A I L L . . . . . r . :.::: I . ; i 2 ~ has b e e n called: basic ORH params s e t S F T ,,.: .. ......., . ..c . . . .- .8679. S E T :::.!i.:. = 2 SET +<:.,:;:,=& SET C;!:?E;.,X=& SET Y,Y!:;.>::: 26 SET L i ?!'lL.<Pd=31 2 SET TC.. 5 5

s ~ i . v i ~ o r o n = i o 5 i 2 . SET nnEfiN=. 1 SET ARME*N=5 SET AHllEAN=6 SET *MEAN=. 26 SET .L INFnEAN=41;1 SET TO=. 6 5 -- ZLT A". 05.63 SET 6=2. 68 SET SFISH=2 SET CCON=O. SET PRICE=25b7. SET PCOST=432. SET ICOST=3 SET COSTCC=718. SET COSTC=15000000. SET COSTP-I. 5 SET REFB=32b3. SET REFC=718. SET FIXCOST=O. AT 1 9 8 2 SET CCON=253. AT 1983 SET CCON-353. AT 1 9 8 4 SET CCON=Z?87. AT 1985 SET CCON=22e5. J --AT 1985 SET CCON=2532. --AT 1 9 8 7 SET I D I S C = l END

--

UaiRU U C S l . . n A C R O U C S t has 5ern c a l l e d : b a s i c iiUH params s e t SET V IR l? iCM=10000 SET MMEAN=. 1 4 SET dRMEAN=t SET inllEAlr=; SET KMEAN=O. 26 SET LINFMEAN=41. 2 SET T0=0. 6 5 SET A=. 0 9 6 3 SET B=2. 6 8 SET I F I S H = 2 SET CCON=O. SET PR ICE=3288 . SET PCOST=432. SET ICOST=3 SET COSTCC=222?. SET COSTC=10000000. SET CCSTP-I . 5 SET REFB=3263. SET REFC=718. SET FIXCOST=O. A T 1983 SET CCON=2.

AT I?e4 SET CC.0N=282. WQS+ COOS+ SOUS& Island cafcL hisfor A T 1 9 8 5 SET CCON=1763. A T 1986 SET CCON=l691.

Y --AT 1 9 8 7 SET I D I S C = I END -- --

HACRO-HAKE MACRO HAKE: has. b e e n called: b a i i - c HAK . . -

SET v I R U 10n+0000. .. SET nnEAN=. 2 . . SET ARMEAN=lO SET AnnEAN=10 . SET KMEAN=. 1 8 SET LINFMEANS87. 1 SET TO=. 026 SET A=. 0 0 4 3 8 SET 8 = 3 . 0 6 7 S E T I F f S H = 2 SET CCON=O. SET PR.lCE=2567. S E T PCOST=432. S E T ICOST=3 SET COSTCC=500. SET COSTC=10000000. SET COSTP=I. 5 SET REFQ=3263. SET REFC=718. A T 1 9 7 5 SET CCON=71. AT 1976 S E T CCON=5005. A T 1 9 7 7 SET CCON=17806. AT 1 9 7 0 SET CCON=4?8. AT 1 9 7 9 SET CCON=4039. H4KE cU('h i T 1980. SET CCON=2000. AT I981 SET CCON=2776. A T 1982 SET CCON=1924. A T 1 9 8 3 SET CCON=1156. AT 1 9 8 4 SET CCON=667. AT 1 9 8 5 SET CCON=ld31 . 1 -- -- MACRO CHCTBB C I C 2 C 3 C 3 C 5 C b C 7 C 8 C 9 C l O RESTART L(I\CCOI &START -..d C U A W A r l CHATHAt! f roll,zd . . . SET V I R O I O m = i l SET REFB=?b8OO. SET REFC=1050 . S E T FIXCOST=O. SET PCOST=320. AT 1 9 7 9 SET N ( 1 1 = 0 . AT 1 9 7 9 SET N ( 2 ) = 0 . AT 1 9 8 0 SET N i l ) = o . AT 1 9 8 1 SET N ( l ) = 0 . aT 1 9 7 9 SET ROPT=CS

AT 1 9 8 2 SET ROPT-C3 AT :?a4 SET ROPT=C4 AT 1 9 0 6 SET ROPT=C5 SET MAST€=. 3 --AT 1 9 8 7 SET UASTE=Cb AT 1 9 8 8 SET UkSTE=C6 AT 1 9 8 7 SET O=C7 AT 1 9 8 7 SET I F I S H = C O AT 1 9 8 8 SET I F I S H = C I AT 1 9 8 7 SET CCON=ClO. SET FCOi-I=. 1 8 SET STEEP=O 9 5 --srn 1 9 7 7 zooo --PR n I o B x o CATCH F ANREV EISREVUCOS~ --Pf3 M I O Q l O CATCH F R P B i O . . .- END -- --

MACRO C H A L Q ~ C H I &I2 CH3 C H 4 C H 5 C H 6 C H 7 C H 8 CH9 C H l O

nAceos REsTFIeT +-d CHAL ' . ' C e l l e d

. . . SET V I R B l O n = C H l SET STEEP=O. 9 5 SET ROP.1-CH2 AT 1988 SET ROPT=CH~ AT 1 9 8 7 SET, CCONECH4 AT 1988 SET CCON=CH5 AT 1989 SET CCON=CH6 SET WASTE-CH7 AT 1989 SET UASTE=CHB AT 1989 SET IFSSH=CH9 A T 1989 SET FCON=CH10 S I M 1981 2000 PR M I D Q I O CATCH F R P B I O . . . END -- --

7iACRO N A I R A 8 8 W 1 U U 2 U U 3 UU4 UU5 UUb NU7 UUB UU9 U U l O RESTART] M4cs?oc Qfs-me~ o-d W A I R 6 U A I R A <a 11-d . . . A M&CRO So s;-ulo-fe L ~ A I U ~ R O P ~ SET V IRBIOM=UUl AT 1 9 8 7 SET CCUN=UU2 om-g" c y k 3 ,o~"~uta++h‘"" dynor, i d i SET ROPT=UU3 AT 1986 SET CCON=UU4 -& V a d O ~ i /&s 04 v ; c g r n SET STEEP=O 9 5 biomass a-d d c h ouerru,S, AT 1988 SET ROPT=UU5 SET UASTE=UUe d;[&-Z-f mmbioclfs'onr 0 f

ss.03 AT 1988 SET UASTE=UU7 sbck - W C U ; + - - ~ ~ d a ; ~ ; o , s ~ h r AT 1988 SET I F I S H = U U B AT 1988 SET CCON=UW~ and ~ ~ f l d u ~ l t ccfch or AT 1988 SET FCON=UUIO f;.s- ~ r o r t o l i + a+ro+o i e s . s in 1981 2000 9 PR r l I D B I O CATCH F R P B l O

-- MACRO U C S I 8 8 U L U 2 U 3 U 4 US U 6 U 7 U8 U9 U l O

&Ace- i?+SlWe~ and w C S Z c-llrd

i? 1988 S E T UASTE=U7 AT 1988 SET. IF;SH=U~ AT 1 9 8 8 SET CCON=U9 AT 1 9 8 8 S E T FCON=UIO S I N 1983 2000 PR MIDI310 CATCH F R P G I O . . . END -- --

PIACRO DEMO V C . .MACRO OEM0 har b e e n c a l l e d . . Y O U may n o w issue S l m . D I and PR c o m m a n d s . . . If y o u w a n t t o d o a n o t h e r r u n : C A L L RESTART; t h e n C A L L DEMO; . . t h e " y o u kau isrue your o w n SET c o m m a n d s t o override DEMO'S . . p a ~ i m e l e ~ v a l u e s ; t h e n l s ~ u e SIM. D l a n d PR c o n l m a n d s SET U I R Q l O n = U AT 1988 S E T CCON=C SET MMEAN=. 2 SET ARMEAN=5 SET AMMEAN=5 A demonsfroh.oc. N A C P 0 + the SET KMEAN=. 2 SET C INFMEANs50 . f i o ~ i a u s e r (see Appeodir T). S E T tO=O. SET A=. I SET B=3. SET ROPT=3 S E T STEEP=. 95 SET P R I C E = 1 0 0 0 . SET PCOST=200. S E T ICOST=3 SET COSTP=t . 5 S E T REFB=50000 . S E T REFC=500. SET FIXCOST=O. S E T I D I S C = O A T 1 9 8 7 SET I J I S C = l S E T D=. 1

SET CCON=O A T 1980 SET CCON=5000. AT 1981 SET CCON=10000. AT 1982 SET CCON=lO000 AT 1983 S E T CCON=IOOOO - - - . . - - - AT 1 9 8 4 SET CCON=20000 A T 1 9 8 5 S E T CCON=~OOOO. A T 1986 S E T CCON=20000. AT 1 9 8 7 SET CCON=20000. END --