Fisheries Research 27 ( 1996) 179-201

Bio-economic modelling of a fishery under individual transferable quota management: A case study of the fishery for blacklip abalone Hdiotis rubra in the Western Zone of Victoria (Australia)

M.J. Sanders a, K.H.H. Beinssen b a 32 Moubruy Street, Albert Purk, Vie. 3206, Australia

b PO Box 847, Portland, Vie. 3305, Australia

Accepted I6 November 1995

Abstract

The present management of the abalone fishery in the Western Zone of Victoria (Australia) includes a total allowable catch (TAC) of 280 t (live weight) divided equally amongst 14 divers, whose entitlements to engage in the fishery are able to be traded. Five of the divers have gained their entitlements through purchase, while the others are from the original group whose entitle- ments were obtained without cost. Management also includes a legal minimum length of 120 mm maximum shell length.

This analysis examines the likely long-term effect from changing the TAC, number of divers and minimum size on the stock, fishery rents and the sharing of rents. The outputs include estimates of yield, catch rates, mean individual weights, exploited density, population fecundity, and fishery rents. The latter are sub-divided in order to examine the sharing between the divers, State and Federal governments, and the entities financing the purchase of licence entitlements. The validity of the outputs is examined by comparing estimates with independent observations of the stock and the fishery.

Keyluorrls: Abalone; Bio-economics; Fecundity; Growth; Individual transferable quotas; Management; Mortal- ity; Selection

1. Introduction

Australia has the world’s most productive abalone fishery, based on Huliotis rubru.

Exploitation occurs in the southern states of New South Wales, Tasmania, Victoria and

016.5-7836/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved.

SSDlO165-7836(95)00466-I

180 MJ. Sanders, K.H.H. Beimsen/ Fisheries Research 27 (1996) 179-201

South Australia. The fisheries are managed by each State independently. In Victoria there is a further sub-division into three zones, again with each being separately managed. This paper concerns the fishery in the Western Zone, which occurs along about 90 nautical miles of coastline between 140”59’E and 142”4O’E. Within this zone the exploitation of abalone is almost entirely by commercial divers.

Abalone are prosobranch molluscs which inhabit rocky reefs adjacent to the coast. They are collected by the divers working individually from fast 5-8 m boats crewed by a deckhand. The boats are normally anchored while the divers swim over the seabed in water up to 25 m in depth. Each boat is equipped with a compressor, supplying air to the diver through an lOO-m-long hose. The individual abalone are prised from the rocks and placed into bags, which typically carry about 100 kg. At the end of each dive, the diver is pulled back to the boat by the deckhand and the bag with its contents is winched on board.

The fishery was started in the Western Zone in about 1967, and the number of divers increased rapidly to over 30. In 1968, the Victorian government introduced a regime to stabilise the fishing effort. No new entrants to the fishery were allowed, and the annual licence fee charged to the existing operators was greatly increased. The latter led to some divers leaving the fishery. A minimum length of 120 mm maximum shell length was also legislated. Over the next 16 years the fishery progressed with minor adjust- ments to management, and the number of divers stabilised at 16.

In 1984 the divers were given the right to sell their licence entitlements, with the immediate effect that the entitlements acquired a realisable monetary value. In addition, each new entrant was required to purchase two existing entitlements, with one of them being retired. The objective was to achieve a reduction in the fishing effort. During the next 4 years, four entitlements were sold, with the effect that the number of divers reduced to 14.

Further major changes to management were introduced in April 1988, following requests from the industry to follow the lead of other Australian States in moving from input to output control. An annual total allowable catch (TAC) of 280 t was set for the zone, equally divided between the 14 divers, so that each received a quota of 20 t. This represented an estimated 20% reduction from the catches of the immediately preceding years, and reflected continuing concern that stocks were being over-exploited. At the same time the right to trade in entitlements was changed to allow selling on the basis of ‘one for one’, subject to a $10000 transfer fee. Although there is provision for annual adjustment of the TAC, it has remained at 280 t to the present.

There was general support for these changes because they allowed direct control over the magnitude of the annual catches, and could be expected to encourage economic efficiency within the industry (from the divers focusing more on cost-saving ways to increase profit; see Hannesson, 1993; Sanders, 1993). The divers gained two additional benefits: an immediate and large increase in the value of the licence entitlements (from being able to sell on a ‘one for one’ basis), and the ability, under civil law provisions, to lease entitlements (after payment of the $100.00 transfer fee), and hence to retain ownership without the need to continue diving.

The determination of annual licence fees was also altered in April 1988, with the new fees being based on a legislated formula which provides for the annual collection by the

MJ. Sanders. K.H.H. Beinssen/Fisheries Research 27 (1996) 179-201 181

State government of approximately 7% of the landed value of the catch. A system by which the divers record their catches, fishing efforts and fishing locations on daily dockets was introduced at the same time, to facilitate the administration of the quota system. This is now also used as the source of the official fishery statistics. The original minimum size of 120 mm has also been retained to the present.

This paper sets out to demonstrate a bio-economic model of the fishery in the Western Zone using catch, fishing effort and length-frequency data made available by the fisheries administration, and other information from the literature. In particular, the authors have sought to examine the application of ITQ management in both a biological and economic context, giving attention to stock conservation, economic performance, and the sharing of the fishery benefits. As presented here, the findings provide a useful example of the essential interplay between biologists and economists in the management of fisheries.

2. A bio-economic model of the fishery

The model was developed as a spreadsheet (Tables 1 and 21, with the biological component being a modification of the approach of Thompson and Bell (1934). The sources for the inputs are identified in the next section. The outputs from the biological component include the annual catch weight (yield), catch rate, mean individual weight, exploited density, and population fecundity. The annual recruitment was estimated internally as being when the estimated catch weight from inputting the observed fishing mortafity is equal to the observed catch weight. It was assumed to be constant, and hence the estimates of yields, etc. are equilibrium values.

In the economic component, there is a sub-division of gross revenue into fishery costs and rent. The former is defined as including all the normal costs, a return to the divers labour, and that part of the annual licence fees paid to the State government to meet the costs of research and management. Normal costs were taken as the sum of the labour costs (after subtracting the crew’s income taxes>, variable costs, fixed costs and the medicare levy. The fishery rent includes the balance of the licence fees, the income tax paid to the Federal government, the principle and interest paid to lenders by those divers who have purchased their licence entitlements, and the ‘surplus’ cash return to the divers. This conforms closely with the definition “Rent is the amount that could be charged by an owner of a fish stock for using it,. . _” given by Hannesson (1993).

In order to determine the payments for principle and interest, it was necessary within the model to make a prior estimation of the value of the licence entitlements. This was determined by iteration as being when the estimated after-tax return to a licence purchaser is equal to the input value for the divers’ return to labour (i.e. when the purchasers receive no ‘surplus’ cash return from rent). After determining the value of the entitlements, the payments for principle and interest were estimated as averages for the period of the loan term. It was assumed that all the money required to purchase the entitlements was borrowed.

Tab

le I

B

iolo

gica

l pa

rt o

f th

e bi

o-ec

onom

ic m

odel

Age

cla

ss

ReC

r.

(yea

r)

ogiv

e,

tI

t2

0’

0.0

0.41

7 1.

0 2.

0 3.

0 4.

0 5.

0 6.

0 7.

0 7.

36

8.0

9.0

10.0

11

.0

12.0

13

.0

14.0

15

.0

16.0

17

.0

0.41

7 1.

0 2.

0 3.

0 4.

0 5.

0 6.

0 7.

0 7.

36

8.0

9.0

10.0

11

.0

12.0

13.0

14.0

15.0

16.0

17.0

50.0

0.00

0.00

0.

00

0.00

0.00

0.

25

0.52

0.91

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

Sele

ct.

Fish

N

at.

Star

t M

ean

Cat

ch

Mea

n le

ngth

M

ean

ind.

C

atch

Se

x.

Pop.

og

ive,

m

art.

mar

t. PO

P.

POP.

N

o.,

(mm

) w

t. (g

>.

wei

ght

mat

. fe

cund

ity,

coef

., co

ef.,

No.

, N

o.,

0).

ogiv

e,

2

s F

’ M

;,

M’

N,

N’

c:,

L1

L2

w ’

G

H’

E’

k 3 96

0800

26

6 26

3 0.

0 14

.1

0.1

0.00

0.

00

0 n

0.00

0.

00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

1.00

1.00

1.00

I.00

1.00

1.00

1.00

1.00

1.00

I .O

O

I .O

O

0.00

0.

00

0.00

0.

00

0.00

0.

00

0.00

0.

00

0.00

0.26

0.

40

0.40

0.

40

0.40

0.

40

0.40

0.

40

0.40

0.

40

0.40

3.49

9

0.68

0

0.62

6

0.43

4

0.35

5

0.31

2

0.28

5

0.26

6

0.09

2

0.16

0

0.24

2

0.23

3

0.22

7

0.22

1

0.21

6

0.21

3

0.20

9

0.20

6

0.20

3

6.10

0

2903

0

1470

7

7864

5096

3573

2615

1967

1507

1375

907

477

253

135

73

39

21

12

6 3

2106

3

1093

1

6380

4289

3069

2275

1727

1440

1125

669

354

188

101

54

29

16

9 5 0 T

otal

0 0 0 0 0 0 0 0 0 288

268

141

75

40

22

12

6 3 2 2 860

14.1

31

.6

31.6

56

.2

56.2

75

.4

75.4

90

.3

90.3

10

1.9

101.

9 11

0.9

110.

9 11

7.9

117.

9 12

0.0

120.

0 12

3.4

123.

4 12

7.6

127.

6 13

0.9

130.

9 13

3.5

133.

5 13

5.5

135.

5 13

7.0

137.

0 13

8.3

138.

3 13

9.2

139.

2 13

9.9

139.

9 14

0.5

140.

5 14

2.5

2.2

14.6

46.6

91.7

142.

4

110.

9

239.

8

269.

5

288.

5

316.

3

345.

7

369.

7

389.

2

404.

9

417.

3

427.

2

435.

0

441.

1

453.

3

0.00

0.

00

0.00

0.

00

0.00

0.

00

0.00

0.

00

83.0

5

84.6

8

48.9

0

27.8

5

15.7

0

8.80

4.90

2.72

1.51

0.84

1.07

0.00

0.

00

0.00

0.

00

0.00

1 .

oo

1.00

I.00

I .oo

1.

00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

;I 0 i?

3

0 2

0 1 \

526

9 i;.

654

722

2 1 P 56

8 z

366

Q

226

5

136

Y

2 80

s

46

E

280.

02

26

: 14

8

2

4 3375

Inpu

ts

Ass

umed

F (

annu

al)

Rec

ruit

no.

at s

ettle

men

t A

sym

ptot

ic l

engt

h C

urva

ture

coe

ffic

ient

A

ge a

t zer

o le

ngth

W

eigh

t at

len

gth

cons

tant

s (w

in

g, I

in

cm)

Nat

ural

mor

talit

y co

effi

cien

t at

set

tlem

ent

Nat

ural

mor

talit

y at

age

con

stan

ts i

n re

cipr

ocal

equ

atio

n In

divi

dual

fec

undi

ty a

t le

ngth

con

stan

ts

([ i

n m

m)

Rec

ruitm

ent

ogiv

e Se

lect

ion

ogiv

e Se

xual

mat

urity

ogi

ve

Are

a of

fis

hing

gro

und

Sear

ched

are

a pe

r di

ver

hour

F=

0.40

0 R

= 9

60.8

mill

ion

La

= 1

42.5

mm

K

= 0

.251

yea

r- ’

t,

= 0

.0 y

ear

a=

1.6O

E-0

4 b=

3 h4

, = 8

.40

year

- ’

d =

0.1

63

6’ =

0.6

68

d’ =

4.7

5E-

I3

b” =

5.9

3978

0’

on

spre

adsh

eet

S on

spr

eads

heet

H

’ on

spr

eads

heet

A

= 7

.647

km

’ s=

11

96m

’

Han

dlin

g tim

e pe

r ab

alon

e A

vera

ge e

ffor

t pe

r di

ver

per

day

Ave

rage

eff

ort

per

dive

r pe

r ye

ar

outp

uts

Cat

ch n

umbe

r C

atch

wei

ght

Mea

n in

divi

dual

wei

ght

in c

atch

E

xplo

ited

area

M

ean

expl

oite

d de

nsity

E

xplo

ited

stoc

k nu

mbe

r E

xplo

ited

biom

ass

Popu

latio

n fe

cund

ity

Fish

ing

effo

rt

Mea

n ca

tch

rate

N

umbe

r of

div

ers

Cat

ch p

er d

iver

h=5.

l se

t d

= 5

hr.

e

= 5

3.94

7 da

ys

C,,

= 8

6OO

CO

C

, =

280

.0 t

w=

325g

r

= 3

059

km2

D =

0.2

8 no

. m

m2

N=

2151

000

B=

7OO

t E

= 3

375

billi

on

X =

377

6 di

ver

hour

s C

,/X=

74kg

h-’

D,

=

14.0

div

ers

Q =

20.

0 t

Equ

atio

ns

F=(1

, -r

,)O

’SF

iv:

=(r

, -

r,)M

,

M’

=(t

, -

r,X

u’

+ b

’/((t

, +

t,)

/LN

(t2/

t,)))

N

, =

N,e

xp(

- (F

’ +

M’))

N

’ =

(N,

- N

,)/(

F’

+ M

’) C

:, =

F’N

’

L, =

Lot

I -e

xpf-

K

tf -

lo

)))

w’=

(l/(

L,-

L

,)X

a/(h

+I~

XL

~+‘~

-L~~

+‘~

~ D

=C

,/r

c;

= c

;. w

’ N

=C

,/F

E’

=

H’N

,(u”

L,

A b

”)/2

B

=N

w

c,

=

SC

;, E

=

%E

’)

c,

=

-zcc

;j x=

(F~

/~)+

(C,h

/360

0)

w=

c,/c

, D

, =

X

/(k)

r

= F

A

Q=G

v/‘D

v

Tab

le

2

Eco

nom

ic

part

of

th

e bi

o-ec

onom

ic

mod

el

Inpu

ts

Ave

rage

pr

oduc

t pr

ice

Var

iabl

e co

sts

per

kg.

Var

iabl

e co

sts

per

divi

ng

hour

Cre

w

cost

s pe

r di

ver

Fixe

d co

sts

per

dive

r M

edic

are

levy

(%

of

taxa

ble

inco

me)

Lic

ence

fe

e (%

of

catc

h va

lue)

Man

agem

ent

and

rese

arch

le

vy (

% o

f ca

tch

valu

e)

Bor

row

ers’

in

tere

st

rate

Bor

row

ers’

te

rm

Aft

er-t

ax

inco

me

to d

iver

fo

r la

bour

Num

ber

of l

icen

ce

purc

hase

rs

Div

ers’

ta

xatio

n ra

te a

t $5

0000

Div

ers’

ta

xatio

n ra

te a

t >

$500

00

Cre

ws’

ta

xatio

n ra

te a

t $3

OC

OO

P=

25$k

g_’

u=o.

oo$k

g-’

v=24

5$h-

’

q=31

2OO

$yea

r-’

f =

28 1

60 $

yea

r-

’

m =

1.

4%

n=7%

r

= 3.

5%

x=

13%

t = 2

5 ye

ars

z =

3000

0

I! =

5 d

iver

s

t, =

28%

t2 =

47%

tj =

21%

Val

ue

of l

icen

ce

entit

lem

ent

Inte

rest

on

lic

ence

pu

rcha

se

Inte

rest

pa

ymen

t, al

l pu

rcha

sers

Pr

inci

pal

on l

icen

ce

purc

hase

Prin

cipl

e pa

ymen

t, al

l pu

rcha

sers

Tax

able

in

com

e fo

r pu

rcha

ser

Tax

able

in

com

e fo

r no

n-pu

rcha

ser

Tax

fo

r a

purc

hase

r

Tax

fo

r a

non-

purc

hase

r

Tax

fo

r al

l di

vers

Tax

for

all

crew

Med

icar

e co

st

to p

urch

aser

M

edic

are

cost

to

non

-pur

chas

er

Med

icar

e co

st

to a

ll di

vers

Aft

er

tax

inco

me

for

purc

hase

r

L,

= 20

28

In =

196

I, =

978

P,

=81

P, =

406

x,

=

197

X,

= 39

2

Tp

= 8

3

T,= 1

75

r,=19

90

T, = 8

8

I$=

3

M,=5

M,= 6

3 A

,=30

Out

puts

(i

n th

ousa

nd

dolla

rs)

Gro

ss

reve

nue

Gro

ss

reve

nue

per

dive

r

Fixe

d co

sts

Var

iabl

e co

sts

Lic

ence

fe

es r

even

ue

Cre

w

cost

s

G,=

7000

G,

/D,

= 50

0

c,

= 39

4

C,

= 18

5

L,=

490

L,

= 4

37

Aft

er

tax

inco

me

for

non-

purc

hase

r

Aft

er

tax

inco

me

to a

ll di

vers

Tot

al

fish

ery

cost

s

Ren

t sh

are

to t

axat

ion

Ren

t sh

are

to l

icen

ce

fees

Ren

t sh

are

to d

iver

s (c

ash)

Ren

t to

fis

hery

A,,

= 2

12

A,

= 2

058

Fc =

16

56

R,

= 2

078

R,

= 2

45

R,

= 1

638

R,

= 5

344

G;=

C,P

X

,=(G

,-

L,-

L

a-C

,-C

,)/D

, -

I,

L,

= G

,n/lc

fl

X,=

(G,-

L

,-

L,-

C,-

C,)

/D,

L,

= D

v9

Tp=

(500

00r,

/IO

O)+

((X

p-50

000)

1*/1

00)

Cr

= kf

r”

=(50

000r

,/IO

O)+

((X

,-50

000~

t,/l0

0~

c,

= U

C,

+(&

Y/d

)

I,=

-P

MT

(x/lO

O,t,

L,)

- L

,/t

I, =

q,

Pp=

L

,/I

P,

= U

Pp

T,=

UT

,+(D

,-U

)T,

T, =

D,3

0000

r,/1

00

M,

= X

,m/l

00

M,

= X

,m/l

GO

M,

= I

/M,

+((

D,,

- U

)M,)

PM

T

is t

he E

xcel

fu

nctio

n fo

r es

timat

ing

the

annu

al

re-p

aym

ent

(pri

ncip

le

and

inte

rest

) on

a

borr

owed

am

ount

.

A,=

X,-

T,-

P,-

M,

A,=

X,-

T,-

M,

A,

= C

IA,

+(D

, -

L’)

A,

F,=

(L-T

,)+

Cf+

C,+

M,

+(G

,r/l

CO

)+

D,

z

R,=

T,+

T,

R,

= L

, -

Grr

/lOO

R,=

A

,-

D,z

R,

= I

, f

P,

+ R

, +

R,

+ R

,

186 M.J. Sanders, K.H.H. Beinssen / Fisheries Research 27 (1996) 179-201

3. Deciding the inputs to the model

3.1. Growth

Growth is assumed to conform to the von Bertalanffy equation. The values used for the asymptotic length CL,) and curvature coefficient (K) are the means of those given in Table 3 from the literature. The constants (a and b) in the power-curve relationship between weight and length used in the model were taken from McShane (1990).

3.2. Natural mortalities

The natural mortality rate from immediate post-settlement to 5 months of age was treated separately from the mortalities applying for the remainder of life. According to McShane (1991), the post-settlement mortality CM,> is density-dependent. The value based on this work was taken from Shepherd and Breen (1991). With respect to the later periods of life, the mortality rates decrease substantially with age. The values from various sources given in Shepherd and Breen (199 1) were used to determine the constants (a’ and b’) in the relationship between mortality and age as shown in Table 4.

3.3. Areas of productive reef

McShane et al. (1986) provide estimates based on black and white aerial photographs and the information gained through interviews with the divers. Some of these estimates

Table 3 Growth parameter values from the literature

L, (mm) K (year-‘) 4 Method Authors

160 0.22

175 0.12

11.5-141 0.35-0.24

143 0.32

139 0.34

144 0.41

133 0.27

117 0.29

121 0.35

152 0.37

132 0.17

140 0.20

121 0.15

166 0.15

140 0.29

15s 0.47

127-146 0.13-0.17

142.5 0.275

1.751

1 S65

1.816

1.818

1.930

1.679

1.599

1.710

1.932

1.469 1 s91

1.345

1.616

1.755

2.053

1.708

Tagg% Harrison and Grant (1971)

+kg% Tagging, length frequencies

Hamer ( 1980)

Shepherd and Heam (1983)

Taggiw McShane et al. (1988)

‘Mghz McShane (1990)

Tagging, length frequencies

Taggmg Ageing

Prince et al. (1988a); Prince et al. ( 1988b)

Prince (1989)

Nash et al. (1994)

Means

Also included in this table arc the correspondmg estimates for the growth performance coefficient 4 =

log ,a( K) + 210g ,,(La) where L, is in cm (from Pauly and Munro, 1984).

MJ. Sanders, K.H.H. Beinssen/Fisheries Research 27 (1996) 179-201 187

Table 4

Estimation of natural mortality with age

M (annual) 1, (years)

0.5 0.9

1.9

2.0

2.0

2.0

6.0

6.0

6.0

r2 (years) l/At Reference

0.91

0.70

0.81

0.42

0.36

0.21

0.22

0.19

0.20

1.5 I .099

1.1 1.003

2.1 0.500

4.0 0.347

5.0 0.305

6.0 0.275

16.0 0.098

16.0 0.098

16.0 0.098

Day and Leorke ( 1986)

Prince et al. (1988a)

Day and Leorke ( 1986)

Shepherd and Breen (1991)

Shepherd and Bmen ( I99 1)

Shepherd and Breen ( I99 1)

Nash (1991)

Nash (1991)

Beinssen and Powell (1979)

Results: The output from a regression analysis of M against l/At is as follows:

Item Coefficient Lower 95% Upper 95% Regression statistics

Intercept 0.1631 - 0.008 1 0.3343 R = 0.8886

Slope 0.6675 0.35% 0.9754 R2 = 0.78%

Relationship: M = a + b/At where M is the natural mortality coefficient at mean age Ar [ = (t, - r,)/LN(r, /t,)] and a and b are constants (from Caddy, 1991).

Inputs: The values for M, t, and fz are from a selection of authors referenced in Shepherd and Breen (1991).

Conclusion: The estimates for the constants are a = 0. I63 arid b = 0.668

have recently been refined, using more detailed colour photographs, again with the assistance of the divers. The areas are given in Table 5. They do not include reef which is not exploited because of low abalone densities. Some other locations which are known to have worthwhile concentrations are also exchtded, because they are too deep to be exploited with current diving technology. In the event that these stocks become exploited in the future, it will be necessary to undertake new estimations of the reef area. While not contributing to the landings, the abalone at these locations are thought to contribute to egg production and recruitment on the currently exploited reefs.

3.4. Fishing mortalities

Two data sets were available for the direct estimation of fishing mortalities. The analysis in respect to the first, described in Table 6, utilised the catch and effort statistics

Table 5

Areas of productive reef

Location

Portland West

Portland East

Port Fairy Western Zone

Reef area (km21 Reef area (km21

determined in 1986 determined in 1995

I .303 1.154

3.842 3.970

2.523 (2.523) 7.668 7.647

188

Table 6

MJ. Sanders, K.H.H. Beinssen / Fisheries Research 27 (1996) 179-201

Estimation of fishing mortalities from catches and efforts

1988/89 1989/90 1990/91 1991/92 1992/93 1993/94

Portland West

Catch weight (t)

Effort (h)

CPUE (kg h - ’ ) Average individual weight(g)

Reef area (km* )

Estimated F

Portland East

Catch weight (t)

Effort (h)

CPUE (kg h- ’ ) Average individual weight (g>

Reef area (mZ>

Estimated F

Port Fairy

Catch weight(t)

Effort(h)

CPUE&gh-‘I

Average individual weight (g)

Reef area cm* I

Estimated F

Western Zone

Catch weight(t)

Effort(h)

CPUE (kg h-‘1

Average individual weight(g)

Reef area (km*)

Estimated F

65.5 69.7 68.9 55.7 66.1 51.1 765 762 835 695 910 649 85.6 91.4 82.5 80.1 72.6 78.7 329 339 332 336 328 322 1.154 1.154 1.154 1.154 1.154 1.154 0.50 0.49 0.56 0.48 0.65 0.44

125.0 130.7 124.8 120.6 85.8 109.2 1693 1579 1615 1623 1243 1589 73.8 82.8 77.3 74.3 69.0 68.7 342 341 345 317 313 316 3.970 3.970 3.970 3.970 3.970 3.970 0.35 0.31 0.33 0.33 0.26 0.33

89.5 79.6 86.3 103.7 128.1 119.7 1319 1137 1178 1439 1879 1908 67.9 70.1 73.3 72.1 68.2 62.7 355 330 320 327 328 333 2.523 2.523 2.523 2.523 2.523 2.523 0.46 0.38 0.38 0.47 0.63 0.66

280 280 280 280 280 280 3777 3478 3628 3757 4032 4146 74.1 80.5 77.2 74.5 69.4 61.5 347 340 334 329 323 324 7.647 7.647 7.647 7.647 7.647 7.647 0.41 0.36 0.38 0.40 0.44 0.46

Relationship: F =(X -(C, / w)h /36OO)s/ A where F is the fishing mortality coefficient, X is the fishing

effort, C, is the catch weight, w is the mean individual weight, s is the area of seabed searched per diver

hour, h is the handling time per abalone, and A is the productive area of the reefs.

Inputs and results: The catches and efforts are from data submitted to the Fisheries Research Institute by the

commercial divers. The mean individual weights were estimated from the length-frequencies of abalone

collected during research surveys. The values s = 1196 m* and h = 5.1 s are from Beinssen (19791, and the

areas for the reefs are from Table 5.

Conclusion: The contemporary fishing mortality for the Western Zone is about F = 0.45 and has averaged

about F = 0.4 since 1988.

reported by the divers along with the reef areas. Underlying the relationship used in this analysis was the assumption that the abalone are distributed randomly over the produc- tive reefs, and/or that the fishing efforts were applied randomly. In practice, the divers tend to target the high-density patches. This causes the area covered by the divers per unit time to be less than if they had fished randomly (because of the increased handling time), and hence to under-estimation of F. In the event that the divers over-stated their fishing effort, as suggested to the authors by some, the effect would be to over-estimate F.

MJ. Sanders, K.H.H. Beinssen/Fisheries Research 27 (1996) 179-201 189

Table 7 Estimation of fishing mortalities from densities

Portland (East and West) Catch weight (t)

Average individual weight (g)

Reef area (km2 )

Exploited density (no./30 rn’)

Estimated F

1991/92 I992/93 1993/94

176.3 151.9 160.3

323 320 318

5.124 5.124 5.124

12.7 10.7 7.9

0.25 0.26 0.37

Port Fairy

Catch weight (t)

Average individual weight (g)

Reef area (km* )

Exploited density (no./30 m*)

Estimated F

103.7 128.1 119.7

327 328 333

2.523 2.523 2.523

10.2 9.3 11.1

0.37 0.50 0.39

Western Zone

Catch weight(t)

Average individual weight (g)

Reef area (km* )

Exploited density (no./30 m*)

Estimated F

280 280 280

329 323 324

7.647 7.647 7.647

11.7 10.1 9.2

0.29 0.34 0.37

Relationship: F = C, /dwA where C, is the catch weight, d is the exploited density, w is the mean

individual weight and A is the productive area of the reefs.

Inputs and results: The catch weights are from monthly returns submitted by the divers. The mean individual

weights were estimated from the length frequencies of abalone collected during the research surveys. The

productive reef areas are from Table 5. The densities (for legal-sized individuals only) are from Gorfme and

Forbes ( 1994).

Conclusion: The contemporary fishing mortality for the Western Zone is about F = 0.35.

The second analysis utilised the abalone densities given in Gorfine and Forbes (19941, which derived from transect surveys by research divers of the Fisheries Research Institute. The surveys were undertaken at the same 13- 18 sites in about February of each year. At each site there were up to nine transects, from each of which the visible abalone were removed over an area of 30 m2. While some of the inputs, including the

area of productive reef, are the same as for the first method, there was no requirement to input fishing effort reported by the divers. The estimates for the fishing mortalities from this analysis are shown in Table 7.

3.5. Total mortalities

The available data were the length-frequency distributions from samples taken during the above-mentioned diving surveys by staff of the Fisheries Research Institute, along with the values chosen for the von Bertalanffy growth parameters. The surveys were conducted in about February at up to 18 sites within the Western Zone, from 1989 to the present. In undertaking the estimations, use was made of the length-converted catch curve analysis routine in the FISAT suite of programmes by Gayanilo et al. (1994). The results are shown in Table 8. Subtracting the natural mortality rates (for the

190

Table 8

M.J. Sanders, K.H.H. Beimsen/Fisheries Research 27 (1996) 179-201

Estimation of total mortalities from length frequencies

L, K Estimates for 2

1989 1990 1991 1992 1993 1994

Portland West 140 0.260 0.61 0.53 0.58 0.55 0.63 0.61 142.5 0.251 0.68 0.59 0.64 0.61 0.70 0.68 145 0.243 0.74 0.63 0.69 0.66 0.76 0.74

Portland East 140 0.260 0.49 0.48 0.47 0.73 0.72 0.78 142.5 0.25 1 0.53 0.52 0.51 0.83 0.82 0.89 145 0.243 0.57 0.56 0.55 0.91 0.91 0.99

Port Fairy 140 0.260 0.52 0.71 0.56 0.56 0.5 1 142.5 0.25 1 0.56 0.80 0.61 0.62 0.56 145 0.243 0.60 0.88 0.67 0.67 0.60

Western Zone 140 0.260 0.53 0.49 0.56 0.59 0.63 0.62 142.5 0.251 0.58 0.54 0.62 0.65 0.71 0.69 145 0.243 0.62 0.57 0.67 0.71 0.77 0.75

Relationship: The total mortality coefficient (Z> was determined by regression analysis using the relationship W(Cj /Arj) = a + btj where Cj is the number of individuals in length-class j, At is the time needed to grow through length-class j, t is the age (or relative age) corresponding to the mid-length of class j, and b with the sign changed is an estimate of Z (see Pauly, 1984). The von Bertalanffy growth parameters L, and K were used to estimate Ar and t for each length-interval. Inputs: The available data were the length-frequencies from diving surveys undertaken annually by staff of the Fisheries Research Institute. A range of L, and K values were used, based on a mean growth performance coefficient of 4 = 1.708 from Table 3. The regressions were undertaken using the frequencies for the eight length-intervals from 120 mm to 134 mm, and as such the estimates for Z are averages for approximately 4 years prior to the collection of the length-frequency data. Conclusion: The total mortality is presently about Z = 0.65 and since 1988 has averaged about Z = 0.6.

adult abalone) from these total mortalities provided mortalities.

3.6. Sexual maturity ogiue and population fecundity

additional estimates for the fishing

Very few data are available in the literature from which to determine the sexual maturity ogive. McShane (1990) provides general observations about the length at first maturity for a variety of sites, from which 100 mm was chosen as the length when 50% of the females of that length are mature. In the absence of suitable data, it was necessary to assume that the onset of maturity was ‘knife-edged’, even though it is known to be a more gradual process.

The constants (d’ and b”) in the power-curve relationship between individual fecundity and length are from McShane (1990). The individual fecundities for the mature female component within each age-class were summed to obtain estimates for the population fecundities. No individual fecundities were allowed to exceed 2.5 million eggs. Whether the estimates of population fecundity mirror the number of eggs released

MJ. Sanders, K.H.H. Beinssen/Fisheries Research 21(1996) 179-201 191

Table 9

Estimation of recruitment ogives

length class (mm) Recruitment (probability) ogives

Portland West Portland East

90-92 0.205 0.227

92-94 0.239 0.271

94-96 0.265 0.311

96-98 0.296 0.368

98-100 0.308 0.394

loo- 102 0.371 0.444

102-104 0.444 0.523

104- 106 0.508 0.620

106-108 0.575 0.700

108-110 0.641 0.766

110-112 0.767 0.865

112-114 0.881 0.956

114-116 0.946 0.999

116-118 0.988 1.000

1 IS-120 0.988 1.000

120-122 1.000 l.GQ3

122-124 1.000 1.cOO

Port Fairy Western Zone

0.130 0.188

0.157 0.223

0.178 0.252

0.199 0.288

0.229 0.31 I 0.289 0.368

0.368 0.445

0.437 0.521

0.539 0.604

0.606 0.670

0.729 0.785

0.835 0.890

0.937 0.967

0.988 1.000

0.988 1 .oOO

0.998 1 .oco 1.000 1.000

Relationship: The probability of capture within each length-class is the ratio of the number actually caught to

the number expected to be caught. The number expected to be caught (preceding full exploitation) was

determined by backward projection using the relationship LN(Cj/Arj) = a + brj (see Pauly, 1984). The

constants a and b were obtained as output from the estimation of Z shown in Table 8. The von Bertalanffy

growth parameters L, and K were used to estimate Ar and t for each length-interval.

Inputs: The data used were the length-frequencies from the diving surveys, along with the values for the

growth parameters of La = 142.5 and K = 0.251.

Conclusion: The ogives for the three sub-areas were found not to bc significantly different, and adequately

represented by the ogive determined from the combined frequencies.

the population fecundities. No individual fecundities were allowed to exceed 2.5 million eggs. Whether the estimates of population fecundity mirror the number of eggs released into the sea each year is unknown. It is possible that not all the eggs are extruded. It is also possible that new eggs may develop after the principal spawning period (spring) for release during a subsequent secondary spawning period. Further research will be required to clarify these matters.

3.7. Recruitment ogive

Probabilities of capture according to length were estimated using the outputs from the previously mentioned length-converted catch curve analysis (for estimating total mortali- ties). This was again assisted by use of the relevant routine in the FEAT suite of programmes. As the research divers were instructed to gather all the abalone they encountered, the ogive provides a useful representation of the change in the availability of abalone with size. In deciding the inputs to the model, which require the probabilities to be grouped according to age, simple means were taken of the probabilities over the relevant size-ranges from the ogive for the zone shown in Table 9.

192 M.J. Sanders, K.H.H. Beinssen / Fisheries Research 27 (19961179-201

Table 10 Monthlv DroduCt DriCes

Month

April May June July August September October November December January February March

Product prices ($ kg- ’ 1

1988/89 1989/90 1990/91 1991/92 1992/93 1993/94 1994/95

14.4 14.4 18.0 18.0 16.0 31.5 34.0 14.4 14.4 18.0 18.0 18.7 38.5 33.0 14.4 14.4 18.0 18.0 18.7 40.0 33.0 14.4 14.4 18.0 18.0 18.7 45.0 33.0 14.4 14.4 18.0 18.0 20.0 47.0 33.0 14.4 15.0 18.0 15.5 20.0 49.0 34.0 14.4 16.0 18.0 15.5 20.0 47.0 35.0 14.4 18.0 18.0 15.5 26.0 47.0 31.0 14.4 18.0 18.0 15.5 26.0 45.0 31.0 14.4 18.0 18.0 15.5 26.0 42.0 27.0 14.4 18.0 18.0 16.0 27.5 39.0 25.0 14.4 18.0 18.0 16.0 27.5 36.0 n.a.

Table 11 Annual costs scenario for a standard fishing unit

Category Type

Fixed costs Depreciation

Item costs ($1

Boat, trailer and accessories ($30000 @ 20%) 6000 -

Fixed costs sub-total Labour costs

Labour costs sub-total Variable costs

Variable costs sub-total

Insurance and registration

Administration

Miscellaneous

Salary on-costs

Fuel

Maintenance

Miscellaneous

Outboardsx 2 ($22000 @ 25%) Vehicle: 4WD ($30000 @ 22.5%) Diving compressor, etc. ($2400 @ 25%) Mobile phone ($600 @ 30%) Boat, trailer and accessories insurance Vehicle insurance Vehicle registration Boat registration and survey Travel, telephone and postal charges Accountant’s fees Bank charges Abalone Divers’ Association dues

Deckhand X 1 Workcover and supervision ($3OOOfl@ 4%)

Boat fuel Vehicle fuel Boat, trailer and accessories maintenance Vehicle maintenance Repair and replacement of diving equipment

5500 6750 600 180 1500 450 360 120 5000 1200 300 200 28160

30000 1200 31200

7000 2000 2000 1500 1500 14000

M.J. Sanders, K.H.H. Beinssen / Fisheries Research 27 (1996) 179-201 193

3.8. Product price and costs

Average monthly product prices for recent years are given in Table 10. A selection of these prices were used in the model. As prices are believed to be independent of supply (from Australian sources), no attempt was made to include a price-supply relationship within the model. Hypothetical costs determined by the authors for a standard fishing unit are given in Table 11. The capital items have been substantially depreciated, as is the case in the fishery. These costs do not include the annual licence fee, which is determined as 7% of the annual value of the catch. At present about 50% of the revenues from annual licence fees is used by the State government for research and management of the fishery. In the application of the model, it is assumed that the future costs for research and management (paid out of the revenues from licensing) will remain at 3.5% of the catch value.

4. Effect on biological performance of changing the fishing mortality

The biological output from the assessment, as shown in Table 12, generally supports the contention that the contemporary exploitation level is already substantial. The present yield of 280 t (from F = 0.4) is only about 20% less than at a fishing mortality of F = 1.5. In order to increase the yield to this higher amount, the fishing effort would need to be increased by nearly three times. The maximum sustainable yield does not occur within the range of mortalities considered.

Table 12

Biological performance at equilibrium with change in fishing mortality

Fishing Annual Annual Average Mean Average Population

mortality fishing effort catch catch rate individual exploited density fecundity

coefficient (diver hours) weight(t) (kg h- ‘) weight (g) (no. m _ a> (billion)

0.0 0 0 152 372 0.8 1 6654

0.1 1229 147 120 353 0.54 5179

0.2 217.5 216 99 341 0.41 4302

0.3 3006 255 85 332 0.33 3747

0.4 3776 280 74 325 0.28 3375 0.5 4512 297 66 320 0.24 3114

0.6 5224 310 59 316 0.21 2922

0.7 5922 320 54 313 0.19 2776

0.8 6608 327 49 310 0.17 2662

0.9 7286 333 46 308 0.16 2570

1 .o 7958 338 42 306 0.14 2494

I.1 8626 342 40 304 0.13 2431

1.2 9289 346 37 303 0.12 2378

I .3 9949 349 35 302 0.12 2332

1.4 10607 351 33 301 0.11 2293

1.5 11263 354 31 300 0.10 2258

194

Table 13

MJ. Sanders, K.H.H. Beinssen/ Fisheries Research 27 (19%) 179-201

Biological performance at equilibrium with change in minimum length and TAC

Minimum length (mm) Total allowable catch (t)

240 260 280 300 320

Fishing mortality coefficient

95

100

105

110

115

120

Fishing effort (diver hours)

95

100

105

110

115

120

Mean catch rate (kg h- I ) 95

100

105

110

115

120

Mean individual weight (g)

95

100

105

110

115

120

0.147 0.171 0.199 0.234 0.276

0.151 0.176 0.205 0.241 0.286

0.157 0.183 0.214 0.253 0.301 0.172 0.202 0.238 0.283 0.342

0.196 0.235 0.284 0.349 0.437

0.256 0.317 0.400 0.519 0.705

2192 2470 2782 3139 3559

2185 2465 2780 3142 3570

2187 247 1 2793 3166 3611

2232 2534 2882 3293 3796

2320 2678 3105 3634 4320

2650 3140 3776 4649 5956

109 105 101 96 90 110 105 101 95 90 110 105 100 95 89

108 103 97 91 84

103 97 90 83 74

91 83 74 65 54

272 268 263 258 253

279 275 271 266 260

287 283 279 274 269

300 2% 292 287 282 318 313 308 303 297

336 331 325 320 313

Average exploited density (no. m-*)

95 0.79

100 0.75

105 0.70

110 0.61

115 0.51

120 0.37

Population fecundity (billion)

95 3774

100 3794

105 3810

110 3848

115 3926

120 3962

0.74 0.70 0.65 0.60 0.70 0.66 0.61 0.56

0.66 0.61 0.57 0.52

0.57 0.53 0.48 0.43

0.46 0.42 0.37 0.32

0.32 0.28 0.24 0.19

3501 3220 293 1 2634

3522 3243 2957 2662 3539 3261 2976 2682 3579 3303 3019 2728 3641 3349 3050 2745 3673 3375 3073 2770

MJ. Sanders. K.H.H. Beinsscn/Fisheries Research 27 (1996) 179-201 195

The estimate for the population fecundity at the present exploitation level is about 50% of that in the unfished population. The ratio between this population fecundity and the estimated number of recruits of zero age is 3512:l (i.e. 3 375000:961). With the present minimum length, it seems that the population fecundity cannot fall below about 1902 billion (i.e. 526 + 654 + 722; see Table l), even if the fishing mortalities become extreme. The likely effect of adopting different legal minimum lengths is dealt with in the next section.

5. Effect on biological performance of changing the minimum size and TAC

The model allowed investigation of the likely effect of changing the minimum length. The procedure in respect to each minimum length required adjusting the partitioning of the age-class containing the chosen length as well as the values in the associated parts of the columns containing the recruitment, selection and maturity ogives, and the estimates of population fecundity. The model also allowed investigation of different TACs. After adjusting the model for the particular minimum length, this involved determining through simulation the fishing mortality which resulted in the chosen yield.

Results for combinations of minimum length and TAC are given in Table 13. These show that successive reduction of the minimum size has the effect of requiring less fishing mortality to achieve the chosen yield. In association, the required fishing efforts are reduced, and the catch rates are increased (despite the reduction in the average individual weights). At minimum lengths below 100 mm these latter trends are reversed, as the consequence of the substantially reduced availability of small abalone (indicated by the recruitment ogive).

The population fecundity was found to decline only marginally even from a substan- tial reduction in the minimum size. This occurs because even though the abalone become available to capture at younger ages as the result of reduction in the minimum size, there is some compensation through the effect of lowering the fishing mortality over all exploited age-classes. The consequence of this is that the stock in equilibrium contains more of the older (more fecund) individuals than it would otherwise do.

6. Effect on fishery rent of changing the number of divers and TAC

The procedure for investigating the effect of having different combinations of diver number and TAC involved two simulation exercises. The first was to determine the input value for the fishing mortality which produces the chosen yield, and the second was to determine the input for the average number of diving days per diver per year which produces the chosen number of divers. In all cases the average daily effort per diver was kept at 5 h.

The results given in Table 14 show that the rent could be increased by increasing the TAC. The potential gain from increasing the TAC to 320 t, while keeping the present number of divers, is about 15%. This would require an increase in fishing effort of about

196 MJ. Sanders, K.H.H. Beinssen / Fisheries Research 27 (1996) 179-201

Table 14

Fishery rent at equilibrium with change in the number of divers and TAC

No. of divers Fishery rent (thousand dollars) a with TAC (t) in parentheses b

240 260 280 300 320

Product price $35 kg-’

6 7421 (88)

10 7072 (53)

14 6735 (38)

18 6401 (29)

Product price $30 kg- ’ 6 6272 (88)

10 5926 (53)

14 5589 (38)

18 5256 (29)

Product price $25 kg- ’ 6 5 122 (88)

10 4779 (53)

14 4444 (38) 18 4112 (29)

Product price $20 kg- ’ 6 3972 (88)

10 3632 (53)

14 3298 (38)

18 2967 (29)

Product price $15 kg-’

6 2823 (88)

10 2485 (53)

14 2153 (38)

18 1822 (29)

8068 ( 105) 8708 ( 126)

7717 (63) 8356 (76)

7379 (44) 8017 (54)

7045 (35) 7683 (42)

6822 ( 105)

6475 (63)

6138 (44)

5805 (35)

7367 (126)

7018 (76)

6681 (54)

6347 (42)

5577 (105)

5233 (63)

4897 (44)

4565 (35)

6026 (126)

5680 (76)

5344 (54)

5011 (42)

4332 (105)

3991 (63)

3656 (44)

3325 (35)

4684 (126)

4342 (76)

4008 (54)

3676 (42)

3086 (105)

2748 (63)

2416 (44)

2084 (35)

3343 (126)

3004 (76)

2671 (54)

2340 (42)

9336 (154)

8982 (93)

8643 (66)

8308 (52)

7899 (154)

7549 (93)

7211 (66)

6877 (52)

6462 (154)

6115 (93)

5779 (66)

5446 (52)

5025 (154)

4682 (93)

4347 (66)

4015 (52)

3588 (154)

3249 (93)

2915 (66)

2584 (52)

9943 ( 199)

9587 ( 120)

9247 (85)

8912 (66)

8410 (199)

8058 (120)

7720 (85)

7386 (66)

6877 (199)

6530 (120)

6193 (85)

5859 (66)

5344 (199)

5061 (120)

4665 (85)

4333 (66)

3811 (199)

3472 (120)

3 128 (85)

2807 (66)

a These estimates relate to a minimum length of 120 mm, an after-tax income to diver’s labour of $30000, and

there being five purchasers of licence entitlements. (The effect from using a different number of purchasers is

small, as can be seen with reference to Table IS.)

b The values in parentheses are the estimated average numbers of fishing days per diver per year after

assuming rive diving hours per diver per day.

35%. The extent by which the fishing effort can be increased is constrained, however, by the number of possible working days in the year. The general view is that rough sea conditions and other commitments would prevent divers working more than about 100 days per year.

The risk associated with any substantial increase in the TAC would be the possible associated reduction in annual recruitment to the stock. Lower recruitment might occur as a consequence of reduced population fecundity. The latter reduces to about 40% of the unfished (virgin) level for a TAC of 320 t.

M.J. Sanders, K.H.H. Beinssen/Fisheries Research 27 (1996) 179-201 197

The potential to increase the rent through a reduction in the number of divers is similarly constrained by the number of available working days in the year. A decrease in the number of divers to ten, while keeping the TAC at the present level, would generate approximately $300000 of additional rent. This is modest, bearing in mind the possibil- ity of a substantial short-term cost of implementation (e.g. to buy licence entitlements out of the fishery) which was not included in the analysis.

Although the results are not shown, there is only a very small amount of additional rent to be gained from reducing the minimum length. As previously indicated, the main benefit would be a reduction in the number of days the divers need to work in order to attain their quota. A reduction in the minimum size to 100 mm, while maintaining the present TAC and number of divers, would increase the rent by less than 1% while allowing the divers to obtain their quota from 26% fewer fishing days. The reason that the increase in rent is so small is the relatively low daily operating costs in this fishery.

7. Effect on the sharing of rent with changes in licence fees and number of purchasers

This section examines the sharing of the rent between the divers, the lenders of money (to purchase licence entitlements) and the community (represented by the State and Federal governments). In particular, consideration is given to the effect of increasing the annual licence fees, and by the inevitable movement over time for all the entitle- ments to be purchased. A selection of results are shown in Table 15.

As might be expected, the long-term effect of increasing the annual licence fee is a reduction in the share to all the other entities. The short-term consequence is obviously different. Apart from the increase in revenues to the State government, the immediate effect would be on the share to taxation and the cash share to the divers. As the divers are in the highest tax bracket, an increase in licence fee by a given amount would result in 47% of that amount being lost from taxation, and 53% being lost from the cash share to the divers.

A revealing outcome from the analysis concerns the rent share to the payment of interest. In the absence of the right to trade licence entitlements, the rent share to interest is obviously zero. At the other extreme, when all the entitlements have been purchased (and following the attainment of equilibrium), the payment of interest could take as much as 50% of the total fishery rent.

The rent share to the divers has two parts, the cash component and the accumulation of principle. As the percentage of divers who are purchasers of licence entitlements increases, the cash component to the divers becomes less and the accumulation of principle becomes higher. When both are considered together, the divers’ share may ultimately decline to about 20% of the rent. This is less than half the divers’ share in the event of there being no purchasers, and reflects the large disparity between the performance of the purchasers and the original divers (who gained their entitlements without cost).

There is a similar effect in respect to the share to the State and Federal governments from licence fees and taxation. At present, with only five of the 14 divers being

198

Table 15

MJ. Sanders, K.H.H. Beinssen/ Fisheries Research 27 (1996) 179-201

Rent-sharing at equilibrium with change in licence fee and percentage of purchasers

Licence fee percentage (%I Percentage of divers with purchased licences (o/o)

0 20 40 60 80 100

Rent share to licence fee revenue (thousand dollars)

5

I

10

15

20

Rent share to divers in cash (thousand dollars)

5

I

10

15

20

Rent share to taxation (thousand dollars)

5

I

10

1.5

20

Rent share to payment of interest (thousand dollars)

5

7

10

15

20

Rent share to payment of principle (thousand dollars)

5

I

IO

15

20

Total fishery rent (thousand dollars)

5

I

10 15

20

105 105 105 105 105 105

245 245 245 245 245 245

455 455 455 455 455 455

805 805 805 805 805 805

1155 1155 1155 1155 1155 1155

2620 20% 1512 1048 524

2.548 2038 1529 1019 510

2440 1952 1464 916 488

2259 1801 1355 904 452

2018 1663 1241 831 416

2603

2538

2439

2214

2110

2339 2280

2192

2046

2074

2023

1946

1818

1690

1809 1166

1700

1590

1545

1508

1453

1362

1210

1280

1251

1207

1134

0 563 1126 1689 2252 2815

0 547 1095 1642 2190 2731

0 524 1048 1513 2097 2621

0 485 971 1456 1942 2427

0 447 893 1340 1186 2233

0 234 461 701 934 1168

0 227 454 681 908 1136

0 211 435 6.52 810 1087 0 201 403 604 805 1001 0 185 311 556 141 926

5329 5337 5344 5352 5331 5338 5346 5354

5334 5341 5348 5356 5338 5345 5352 5359 5343 5350 5356 5362

5360

5361

5363

5368

5368

5369

5310

5312 5375

These estimates relate to a product price of $25 kg-‘, a quota of 280 t, 14 divers, a minimum length of 120

mm, and an annual after-tax income to diver’s labour of $30006.

purchasers, the combined revenues to the two governments is about 40% of the rent. In the event that all the licence entitlements are purchased, this share of the rent may reduce to about 30%, with all of the lost revenues being in respect to taxation.

M.J. Sanders, K.H.H. Beinssen / Fisheries Research 27 (1996) 179-201 199

Table 16

Observed virgin catch rates

Virgin catch rate (kg h- ’ )

Diver 1 204

Diver 2 140

Diver 3 136

Diver 4 173

Diver 5 187

8. Some verification of the model outputs

Several opportunities exist for comparing secondary outputs from the model with the available observations. The virgin catch rate (i.e. C,/X when F = 0) is estimated from the model to be 152 kg h - ’ . In the absence of reliable catch and effort statistics for the period, the authors chose to interview the original divers about their mean catch rates when the fishery first commenced. The responses of five divers, after conversion from the old units of meat weight in pounds to whole weight in kilograms, are shown in Table 16. Only in the case of one diver was the observed virgin catch rate claimed to be substantially different from that obtained from the model. The mean virgin catch rate for the other four divers is 159 kg h-‘.

Settlement density is another secondary output which can be compared with observed values. McShane (1990) gives mean densities from 6.2 to 157 m-*, with an overall mean of 45.5 m-* for newly settled larvae (shell lengths mostly between 0.5 and 2 mm> at seven sites within the Western Zone in January 1989. The means for three sites from unpublished data for subsequent years range from 0.4 to 56 m-‘, with an overall mean of 21 m- * (H.K. Gorfine, personal communication, 1995). The estimate of density from the model, determined by dividing the number of recruits at zero age by the productive area of reef, is 126 m-*. This can be expected to be higher than the observed densities. In the case of the latter, an unknown number of mortalities would have occurred between settlement and the measurement of density. There is also the possibility of individuals spawning after the dates when the observations were made. Bearing these factors in mind, the extent of agreement is good.

With respect to the output from the economic component of the model, it is possible to compare the estimates for the value of licence entitlements with observed prices. While there have been no recent sales, a licence was offered for sale at the end of 1994 for $2.8 million. The average product price during the previous 6 months was $33 kg-‘. Inputting this into the model gives an estimate for the value of an entitlement of $2.9 million. With respect to actual sales, there have been three since quota management was introduced. The associated prices were $1 million (October 1988), $1.32 million (January 1992) and $1.35 million (June 1992). Using the mean product price for the 6 months prior to these dates gives estimated values of $0.9 million, $1 .O million and $1 .O million, respectively. This extent of agreement is quite good bearing in mind that the costs used in the model are for the present day.

200 MJ. Sanders, K.H.H. Beinssen / Fisheries Research 27 (1996) 179-201

9. Concluding comments

The findings from the analyses reported here provide no compelling reason for change to the TAC or number of divers. The potential gain from a reduction in the minimum length is to decrease the fishing effort required to attain the TAC. While this would be worth achieving, there are possible ecological costs not considered within the analysis. A decline in the density of abalone (from lowering the minimum size) might lead to unfavourable changes in the relative abundance of other organisms. This could occur, for example, if grazing (by abalone) was necessary to avoid increased colonisa- tion of the rocks by non-food organisms. There is also the possibility of unfavourable changes in the balance of competitors and predators. Trials would need to be undertaken to investigate these possibilities.

Concerning the sharing of the rent generated by the fishery, it was an inevitable consequence of the decision in 1984 to allow licence entitlements to be saleable, that an increasing share of the rent would go to meeting the interest charges of the lenders. In association, as the proportion of purchasers increases, a decreasing share of the rent will be available to the divers and to the State and Federal governments. Whether these outcomes are to be avoided or reduced are matters to be decided by the industry and governments, presumably to be followed by negotiation if necessary.

During the history of the fishery, product price has had a major impact on the magnitude of the fishery rent. Its determinants are largely independent of the fishery and outside the control of management, since virtually all the product is exported, mostly to Asian markets (particularly Japan). While demand is expected to remain strong into the foreseeable future, prices will nevertheless continue to be influenced by movements in exchange rate parities between Australia and the importing countries. Insuring against unfavourable movements in exchange rates is already being practiced by the local buyers of abalone.

As applied here, the findings from the model relate to steady-state conditions. In the case of the biological component, the time to move from one equilibrium to another (as from a change in management) could take from 5 to 10 years. This takes account of the longevity of the abalone and its relatively slow growth rate. The time to attain equilibrium in respect of the economic component is much greater, something in the order of 25 years; the time for one generation of divers to be replaced by another.

In the event that the model were to be made dynamic, it would be desirable to include the discounting of future rents to account for the notion that these will be less valuable than rents accruing in the present. This would be important in deciding the strategy to be adopted in moving from one management regime to another. As no change to manage- ment (that would result in a change to the rents) has been proposed, it was judged unnecessary to include discounting within the model. If it did become necessary to examine the short-term consequences of a change in management, the model could readily be made dynamic by constructing a number of interlinked spreadsheets depicting consecutive years.

With respect to any future application of the model, a useful refinement would be to apply the biological component to each reef (or grouping of like reefs) separately. This would provide greater recognition of the differences in growth, recruitment and mortal-

M.J. Sanders, K.H.H. Beinssen/Fisheries Research 27 (1996) 179-201 201

ity rates that are believed to exist between abalone sub-populations. The catch and effort statistics are already being reported by the divers on a reef by reef basis. Additional tagging and other research work would be necessary, however, to obtain reef by reef estimates for the growth and mortality parameters. A very useful complement would be a scheme for sampling the commercial catches to obtain additional length-frequency data.

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