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POPULATION

DYNAMICS OF THE PRIBILOF ISLANDS

NORTH PACIFIC FUR SEAL (CALLORHINUS

URSINUS)

by ANDREW W. TRITES . B.Sc, McGill

University,

Montreal,

1980.

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department o f Z o o l o g y ) We a c c e p t

t h i s t h e s i s as c o n f o r m i n g required standard

to the

THE UNIVERSITY OF BRITISH COLUMBIA November 1984 ©

Andrew W.

Trites,•1984

In p r e s e n t i n g requirements

this thesis f o r an

of

British

it

freely available

agree t h a t for

that

Library

s h a l l make

for reference

and

study.

I

f o r extensive copying of

h i s or

be

her

copying or

f i n a n c i a l gain

shall

g r a n t e d by

publication

not

be

Date

DE-6

(3/81)

of

further this

Columbia

thesis

head o f

this

my

It is thesis

a l l o w e d w i t h o u t my

"Zoology

The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3

the

representatives.

permission.

Department o f

University

the

s c h o l a r l y p u r p o s e s may

understood

the

the

I agree that

permission by

f u l f i l m e n t of

advanced degree a t

Columbia,

department or for

in partial

written

ABSTRACT

A of

conceptual

the

model i s p r o p o s e d

Pribilof

Islands

(Callorhinus ursinus). regulated set

by

most the

Population in

the

rates

animals.

of

proposed

features.

the

decline

pup

e s t i m a t e s and

1980.

responsible Paul two

equally

true

of

of

to

independent

1950s.

The

the

Pribilof the

be of

the

The key herd

continued maintained

current

by

the

adult

decline

by

changes

of to

young shape

seal to

period

life

1950

male

to

female

rates

production

were

on

Saint

the

last

survival

was

male s u r v i v a l , appear

to

be

major d r i v i n g v a r i a b l e of

the

fur

i s the

not

a

explain

commercial

in adult

does

limits

space.

b u l l s counted during if

are

reconstructing

survival

i n pup

factor that

accounts

s u r v i v a l of

population by

fur

i s able

that

entanglement,

females.

and

regard,

appears

the

basic

population

juvenile

for

i s used

analysis

show

accounted

t o the

dispersal

males over

lower number of

be

and

seal

fur seals

breeding

model

observed d e c l i n e

to debris

system

decline this

due

Islands

c o u n t s of a d u l t

The

during

and

incorporates

results

that

primarily regulated

simulation

Pribilof

f o r the

d e c a d e s can

possibly

that

a s e r i e s of poor

Island.

higher

seal

the

and

food

dynamics

fur

levels close

conceptual

The

Simulation

harvesting

of

a p p e a r s t o be

formulation

of

suggested

at p o p u l a t i o n

the

Pacific

s u r v i v a l , reproduction,

The

mathematical history

is

availabilities growth

describes

North

It

strongly

that

decline

exogenous

management p r a c t i c e s .

f o r the

overall

juveniles.

In

t h r o u g h the

1980s

factors

that

Model r e s u l t s

are are

considered

reliable

i f simulation

survival)

contain

little

analysing

the

simulation is a revised fur

seals.

future

sensitivity

parameters procedure The

research.

parameters

error. of

A

model

(particularly

detailed output

procedure f o r

to

i s described

i n an a d j o i n i n g

for estimating

the s u r v i v a l

thesis

concludes

with

adult

errors

in

appendix

as

of

juvenile

recommendations f o r

TABLE OF

CONTENTS

ABSTRACT

. . i i

L I S T OF TABLES

vi

L I S T OF FIGURES

v i i

ACKNOWLEDGEMENTS CHAPTER

1

x

INTRODUCTION

. 1

CHAPTER 2

BIOLOGY OF THE NORTHERN FUR SEAL

.5

CHAPTER

3

THE FUR SEAL DATA BASE

.8

CHAPTER

4

A FUR SEAL CONCEPTUAL MODEL

4.1

Limiting

4.2

Population

4.3

C o n c e p t u a l Model

4.4

Discussion

CHAPTER

5

.11

Resources

12

Regulation

16 .........

23 27

A FUR SEAL MATHEMATICAL

MODEL

29

5.1

Methods

29

5.2

Model

31

5.3

Results

34

5.4

Discussion

40

CHAPTER

6

SENSITIVITY ANALYSIS OF A

FUR

MODEL

SEAL

POPULATION 46

6.1

Relative

Sensitivities

47

6.2

Analytic

Model V a l i d a t i o n

52

6.2.1

Independence and l i n e a r i t y

6.2.2

Model v a l i d a t i o n

CHAPTER 7

CONCLUSIONS

52 ...54 61

V

REFERENCES

CITED

66

APPENDIX A

FUR SEAL COMPUTER SIMULATION

APPENDIX B

ESTIMATING THE SURVIVAL OF JUVENILES

B.1

Details

of

the

Methods

of

PROGRAM

Estimating

:..

74 86

Juvenile

Survival B.2

Evaluation

91 o f t h e Methods

of

Estimating

Juvenile

Survival

96

B.3

R e v i s e d Methods of E s t i m a t i n g

Juvenile

B. 4

Revised E s t i m a t e s of J u v e n i l e

Survival

APPENDIX C

Survival

MODEL VALIDATION BY SENSITIVITY ANALYSIS Sensitivities

...104 106 115

C. 1

Relative

115

C.2

N u m e r i c a l Model V a l i d a t i o n

116

C.3

A n a l y t i c a l Model V a l i d a t i o n

117

C.3.1

D e t e r m i n i n g Dt

117

C.3.2

D i s t r i b u t i o n o f Dt

120

C.3.3

Validation

122

L I S T OF TABLES

Table on Table

5-1. Pup e s t i m a t e s and c o u n t s Saint

Paul

Paul

bulls

Island

5-2. E s t i m a t e s

Saint

o f harem and i d l e

30

of male j u v e n i l e

Island

used

fur seal

survival for

t o s i m u l a t e pups born

and b u l l s

counted. Table

35

5-3. T h r e e measures o f f i t used

three

simulated

observed Table

numbers

pup

o f pups born

best

on S a i n t

6-1. The r e l a t i v e s e n s i t i v i t i e s

b o r n ) t o 1% e r r o r s Table

productions

A-1.

Island

Number

from

to determine

which o f

reproduced Paul

the

Island

of model o u t p u t

39 (pups

i n input parameters of females

killed

55

by age on S a i n t

Paul

1956 t o 1968

80

. Table to

81

A-2. Number of f e m a l e s

killed

pelagically

from

1958

1974

82 83 .84

Table

A-3.

Island Table by Table

Number

from

of

males

killed

by age on S a i n t

1950 t o 1979.

85

B-1. T o t a l pup e s t i m a t e s and age s p e c i f i c year B^2.

Paul

c l a s s on S a i n t Counts

of

Paul

male

kill

Island

harem and i d l e

87 b u l l s on S a i n t

Paul

Island Table

B-3. C a l c u l a t e d

88 male

juvenile

fur

seal

survival

on

vii

Saint . Paul estimates

Island.

have been

assuming a c o n s t a n t Table the

B-4.

simulation

for

B-5.

Chapman and

reduced

to

birth

survival

a t age

of

model

juvenile

Revised

Saint Paul

developed

to

to

Polacheck

age

two

by

0.80

89

r a t e s used

i n the

test

Lander

the

survival

estimates Island

Smith &

t h r e e of

Some h y p o t h e t i c a l e x p l o i t a t i o n

estimator Table

The

of

juvenile

98 fur seal

survival 114

viii

L I S T OF FIGURES

Figure

4-1.

T r a j e c t o r i e s showing p o p u l a t i o n

hypothetical

home r o o k e r y

and n e i g h b o r i n g

g r o w t h of t h e rookery

over

t ime

.25

Figure

5-1.

Male

juvenile

survival

from b i r t h

t o age 2

years Figure

36

5-2. E s t i m a t e d

Saint Figure

simulated

pup

production

for

Island

5-3.

Paul Figure

Paul

and

38

Observed

and

simulated

bull

c o u n t s on S a i n t

Island

41

6-1. S e n s i t i v i t y

i n model Figure

input

6-2.

percent

birth

Dt

to percent

changes

rates

A comparison changes

deviance

of model o u t p u t

in

o f model o u t p u t

9

at times

...48

input

s e n s i t i v i t i e s to

parameters

measured

by

1954, 1959, 1964, 1969, 1974, and

1979. Figure born Figure

51 6-3. U n c e r t a i n t y i f input 6-4.

Figure

6-5.

B-1.

survival Lander

output

as m e a s u r e d by pups

e r r o r s o f 1 t o 5%

uncertainty

expressed

57 as

a

of v a r i a t i o n Contribution

uncertainty Figure

parameters c o n t a i n

Model

coefficient

i n model o u t p u t

i n output

58 of

input

expressed

error

rate

hypothetical

estimator

errors to

as a p e r c e n t a g e

Relative of

in

parameter

predicting

the

populations

59 juvenile using the ...100

Figure

B-2.

survival

Predictions rates

of

for

the

juvenile

hypothetical

Upper and

subadult

survival

Figure

B-4.

lower e s t i m a t e s rates

Upper and pup

B-5.

assuming

f o r the

juvenile

hypothetical

and

populations

B-6.

Upper the

and

year

class strength. The

mean

bounds

the

survival first

estimates

year

of

life 108

survival

annual

that changing

the

over

the

and

survival

juvenile

lower

80%

B-7.

103

Upper and

that

with

101

o v e r time

assuming

Figure

of

lower

survival

remains constant

Figure

the

the L a n d e r e s t i m a t o r

assuming

Figure

using

..

B-3.

using

subadult

populations

Lander e s t i m a t o r Figure

and

juvenile

lower

of

subadult

males

juvenile survival

annual s u r v i v a l bull

survival

of

subadult

counts are

estimates i s 80%.

.109

estimates males

representative

is of 110

of

the

described

Lander estimates

upper

and

i n f i g u r e B-6

lower are

juvenile contrasted 112

X

ACKNOWLEDGEMENTS

I am g r a t e f u l assistance

throughout

particularly ideas.

to Peter Larkin

helpful

Thanks

comments

various

must

the N a t i o n a l M a r i n e sharing Moira are

Justin

to

He

suggestions

which e n s u r e d

on

improving

C h a r l e s Fowler

and

Hahn

completion ending

extending

a n d Anne York o f

population

i n p r e p a r i n g the f i g u r e s .

t o a c k n o w l e d g e t h e never

been

and e x p r e s s i o n of

Mammal L a b o r a t o r y were e s p e c i a l l y

Helen

has

t o Andreas F i s c h l i n , J i m

i d e a s and i n f o r m a t i o n on f u r s e a l

extended

s u p p o r t and

Cooke, Mike B i g g , and Bob L a n d e r f o r

of t h e work.

Greaven a s s i s t e d

details

study.

my t h o u g h t s

a l s o be e x t e n d e d

and

sections

of t h i s

in clarifying

S p a i n , Jay Hestbeck, their

the course

f o r h i s continued

helpful in dynamics.

Special

thanks

f o r t a k i n g c a r e o f t h e numerous of t h i s work. support

Finally

I

wish

of my w i f e a n d f a m i l y .

1

CHAPTER

Various for

managing

Pacific

the

fur

have l a r g e l y to

themes

change

Company

excluding females

with

how

to

Beginning

increase

imposing

considered

kill

been

decimated

by

model of

the

commercial al.,

apparent reduced

the

herds

by

i n 1837,

by

94).

Protecting

population

growth,

harvested.

herd

model

Soon

was

t h a t had

at

fur seal

successfully

used

after

that

1931:

s y s t e m was

but

used

p e l a g i c s e a l i n g (Andrews

kill)

1940s

230).

the

g r o w t h t r e n d of

Evidence

was

l a c k of p r o d u c t i v i t y of r a t e s of

Chapman conceptual

reproduction

(Chapman,

supply

around

1961) the

questioned model.

the

by time

Such a until

population

began t o a p p r o a c h some k i n d o f c e i l i n g

1954).

survival food

the

later,

American

1950s.

During

et

the

1946:

c o u l d be

North

perceived

Russian

of

same c o n c e p t u a l

S t a t e s managers t o r e b u i l d

simple the

and

were

the

c l o s u r e s and

to

centuries

Islands

numbers

(Martin,

two

Management d e c i s i o n s

size

critical

the

past

Pribilof

i n 1799

the

hunting

from the

p u r c h a s e of A l a s k a

United

the

population

polygamous m a l e s were e x c e s s the

of

the

(Callorhinus ursinus).

time.

females was

have been u s e d over

depended on

experimentally

INTRODUCTION

population

seal

tried

1

presented the

fur seal

suggesting herd

was

(Kenyon e t a l . , 1954)

arising

Pribilof managing

from c o m p e t i t i o n Islands. with

Such t h o u g h t s were

the

At

and for a

the

(and

(Kenyon that

the

due

to

juvenile limited

same

time

male-only-harvest

independently

translated

2

into

mathematical

to produce achieved and

the

herd

continued

dependent

was

male

regulatory

(NPFSC,

The

after

decline

vital

i s no the

rates

there

no

reproducing

to

its

density

management

emphasis

maximum

sustainable

density

of

of

continued

supposed

dependent

t o do

so

been

harvestable

predicted

was

and

explanation

population

levels to

have

changes

suggests

of

genetic of heavy

for

(Anonymous,

harvest

survival

because

d e c l i n e might be

size

not

p r o g r a m and

short

Its failure

the

sources

has

recruitment

reduction

herd

sustained

evidence males

yield

that,

in the

reevaluation.

the or

and

far

through

rates.

parasites,

significant herd

Lowering

Pribilof

pregnancy

herd

satisfactory

i n d i c a t i o n that

is

1956

in a d d i t i o n

with

the

sustainable

falling

model needs

of

disease,

the

productivity

There

model

achieving

production

during

1981).

conceptual

no

maximum

i t s completion,

population

to

between

be

1962).

declined

increased

new

(1961)

p r o d u c t i v i t y could

a result,

concepts switched

A n n u a l pup

(Chapman,

As

Chapman

270,000 f e m a l e s

The

growth

projected

attained. males

r e d u c e d by

(1961) and

greater

population.

kill.

from r e g u l a t i n g h e r d yield

Nagasaki

r e s u l t s i n d i c a t i n g that

from a s m a l l e r

1963

the

models by

of

1983).

males

of pups on changes

the

has

land. in

the

harvest

selection.

metal

contaminants

of

mortality.

due

to a high

It i s speculated incidence

of

seals

continued There

is

altered Similarly size

of

Predation, are that

not the

becoming

3

entangled

in

resolved.

Other

rejected

are

rookeries,

The major

possibilities

emigration

seal

food

Islands. that

have

the

f o r the

population

prey has

species

been

such

of

in

and

must

the

case

be c o n c l u d e d

Pribilof

Haar,

1980).

season

that

population

growth r a t e s , (Fowler, being

of

can

is still

no e x p l a n a t i o n

the

Likely

fur

c a n be c l e a r l y

seal

abundant

35

common

base o f t h e s e a l

seals

and

commercial

(Salveson

and A l t o n ,

the

which

eaten

of

unresolved. for

and

and weight a t

numbers

the

demonstrated.

of

increases the by

fur

However, t h e a v a i l a b i l i t y a t times

with

1977)

t o other

pollock,

be

of

by l a c t a t i n g

1982a).

of

the food

fur

on

about t h e

inconsistent

et a l . ,

a r e r e d u c e d by f i s h i n g

j u v e n i l e s that

breeding

is

i n d i c a t e a d i e t of over

t o s e a l s o f d i f f e r e n t age c l a s s e s than

and h e r r i n g ,

of d i f f e r e n t s i z e s the

overfishing

(Gentry

1981) , o r t h a t

and

gear.

trips

well

been

examined

feeding

years

I t appears that

adults

number o f p o l l o c k

adult

not

human d i s t u r b a n c e

fur seals are switching

fish

that

cannibalistic

(Swartzman

signs

Kajimura

select

view

of

i n recent

that

increased.

pollock

t h e 1960s

(stomach samples

species,

fisheries 1976)

are

has

been

areas,

this

length

since

have

in fishing

resources,

increased

explanations

that

this

be due t o c o m m e r c i a l

s u r v i v a l of pups on l a n d ,

birth

however,

other

However,

f e m a l e has d e c r e a s e d

prey

to

h e r d d e c l i n e might

observations

that

debris;

and i n c i d e n t a l t a k e

fur

Pribilof

fishing

the

seals

of f i s h

year

other

In g e n e r a l i t decline

of

the

4

The seal

major

numbers

information related

of The

on

life

bull

counts

altered

offer

this

changed history

study

as

of

pup

they

and

population

results

model.

the

the

parameters analysis.

for past

f u t u r e management and

The

and

herd

impact are

Model

conclusions

1950

to

upon h e r d

results

model

observations 1980. dynamics

investigated

d y n a m i c s and

research.

b i o l o g y of

A mathematical

period

fur

available

f u r s e a l s and

the

over

of p r e d i c t i o n s and

explanations

have.

to reconstruct h i s t o r i c a l

estimates

sensitivity

i s t h e a n a l y s i s of why

of n o r t h e r n

i s reviewed,

proposed

and

reliability

techniques

of

in a revised conceptual

subsequently

of

for

have

pinnipeds

summarized is

focus

are

suggest

using

shown

to

directions

5

CHAPTER 2

The

northern

opportunistic, thirds

of

remaining

In

BIOLOGY OF THE NORTHERN FUR SEAL

fur

its life

one t h i r d

the case

a r e spent

barren

and

by

volcanic

tall,

territory

harem

territory half

Weighing

by

battle,

Successful

and d e a t h

losers will hauling

in

tend

grounds.

as they c r o s s to l i v e

occurs

black large

select

in

of S a i n t

grass

an a v e r a g e

and w a i t

covered

basalt l i e males

haul

o f 600 pounds and

secure

a

f o r the a r r i v a l of

females.

their

The

harem

defending

Two

land.

body w e i g h t

between

1981) and a r e c l a s s i f i e d

bulls.

during the breeding

unsuccessfull injury

double

(Lander,

idle

upon

of

May when t h e f i r s t

w i t h one o r more f e m a l e s

years.

positions

or

mammal.

T h e s e two t i n y

t h e mature b u l l s

A d u l t males t y p i c a l l y

either

gregarious,

a l l breeding

eruptions

t h e much s m a l l e r 90 t o 120 pound

a g e s of 7 and 8 y e a r s

pelagic

breeding

herd

(20%).

the rookery.

standing 7 feet

reproductive

polygamous,

between t h e B e r i n g Sea i s l a n d s

from November u n t i l onto

with

of the P r i b i l o f

produced

themselves

a

i n a p e l a g i c existence while the

i s occupied

(80%) and S a i n t George

islands

is

c a r n i v o r o u s , and m i g r a t o r y

r o o k e r i e s and i s d i v i d e d Paul

seal

harem

season.

will

o f one

and

not l e a v e

a a

their

bulls,

that

are

or h o l d i n g a t e r r i t o r y ,

often

risk

imaginary

on t h e f r i n g e s

Idle

as b e i n g

masters maintain

f o r an a v e r a g e masters

the

harem b o u n d a r i e s . of the rookery

Such

o r on t h e

6

From

June

until

decreasing

order

are u s u a l l y

less

hauling It

of age than

and

kill

interfering years)

with

are

not

whereabouts

As

the

t h e mature f e m a l e s

of d e c r e a s i n g age prospective harems.

contact

The

o c c u r s w i t h i n two hours again

process

is believed

of

giving

impregnated

Without

to

including

gestation

period

summer

the is

about

six

i n t h e B e r i n g Sea

storing

fat

r e s e r v e s f o r the

of

the

no

care

mating

from

the

olds

to

are

months.

in order

greeted

l a n d and

The

social

1981)

which

the

Within

female

newborn

remainder the

5,000 k i l o m e t e r m i g r a t i o n

bulls

by

the

trampled

Throughout

is

pup.

implantation,

weaning

to a v o i d being

their

i n c l u d e them i n

n o u r i s h her

delayed

(0-2

birth."-*-.

are

(NPFSC,

i s spent

fasting

without

harem c a p t i v i t y .

t h e harem m a s t e r s .

season

The

juveniles

12 pound pup,

t o f e e d and of

on

birth

female's

time

receive

July",'- t h e y

of h a u l i n g out

period

t o group t o g e t h e r

made.

g r o u n d s nor

that are anxious

female's

Pups t e n d

4 year

following their

to a s i n g l e

free

are

;

weeks o f " t h e

and

rookery.

The

hauling

stimulate

birth

t o e n t e r the

(S^Sijryea r s arid o l d e r ) a r r i v e

masters

which

seperate

animals.

d u r i n g June and

harem

in

f u r s e a l s makes i t p o s s i b l e t o

the

known d u r i n g the

out

in

t h e v a l u a b l e 3 and

on

haul

immature b u l l s ,

that k i l l i n g s

breeding

found

These

inability

immature

primarily

males

o l d , band t o g e t h e r

t h i s c l a s s of a n i m a l s of

young

size.

eight years

selected congregation

their

and

g r o u n d s b e c a u s e of t h e i r

i s from

drive

mid-August

the

of

pup

the and

south.

to death the

become t h i n n e r as

and

course their

7

stored

f a t r e s e r v e s are used

Soon a f t e r structure southward

breeding

quickly

breaks

Their

confirmed

by

herds

The

extent

travel

migrate

along

t i m e s and

young

by

oldest

of more

return

bulls

nonpregnant

with older

f e m a l e s , and

seals

indicated

to breed

leading

f e m a l e s , and

summarized

males

finally

by

surveys

i n the way,

of

(1899) 1958

females

to

but

that no

in

the

and a

occur

at The

consists Bering

Sea and

California.

i n o r d e r of age

f o l l o w e d by p r e g n a n t

immatures by d e c r e a s i n g

few

western

o f young m a l e s

towards

to

1974

Z e u s l e r (1936). geography

by

and

American

Peak d e n s i t i e s

wintering

spring

from

coast,

to

solitary

t h e B e r i n g Sea

It i s believed

by

harem

America

Townsend

concentrations

older

the

from

America.

respect

southern

North

intermingling

the A s i a t i c

North

of

is

understood.

along

the r i g i d

Many s e a l s b e g i n t h e i r

range

of

areas as

distribution

followed

first

i s not w e l l

predominately

The

as

seals

different age

i n August

t h e more r e c e n t p e l a g i c

1980b).

Pribilof herds

down.

migratory

southern C a l i f o r n i a

Asian

i s completed

m i g r a t i o n a l o n g t h e west c o a s t

November.

(Lander

up.

age.

with

the

females,

8

CHAPTER 3

The nature

p u r p o s e of of

the

information in

fur

by

killed

i n t o age

has

was

if

briefly

of t h e

the

available Laboratory

been p u b l i s h e d

on

rookery

to

(Lander

not

been

1972

and

Kill

are.

kill

of

rookery

age

(determined

females

has

from

C. C o u n t s of A d u l t M a l e s ,

used

1956

no

Islands After

For and

the

seals

extrapolate

entire

hunting

a

numbers

l e n g t h s of t h e to

are

1956

to break the

the

lost.

1918-83

restrictions

for

total

land

on and

Pribilofs.

1956-68. been

teeth)

For

recorded f o r both

1911-83.

c o n t a i n i n g one

older with

kill.

available

of F e m a l e s ,

the

George

male

no males have been h a r v e s t e d

s i n c e d i s c o v e r y of t h e

territory

of

numbers of

c o u l d have been u s e d

Since

Estimates

The

Saint

l e n g t h of s e a s o n

harvesting

(7 y e a r s and

1918-83.

and

Prior

i t had

B. Commercial

(defend

Most

recently

developed

r e c o r d e d and

S a i n t George. kill

and

classes.

restrictions

by

describe

a t the M a r i n e Mammal

Paul

was

a r e w e l l documented.

pelagic

file

to

base.

of M a l e s ,

date,

process

killed,

period

is

data

and

Saint

year,

aging

ages

seal

Kill

on

tooth

harvested

SEAL DATA BASE

It contains:

killed

available

FUR

chapter

Washington

A. Commercial seals

this

i s on computer

Seattle,

1980a,b).

THE

day

i n numbers

of per

Islands.

Counts

of harem

males

and

idle

males

have been made e v e r y

year

or more f e m a l e s )

territory)

each

9

with on

few

e x c e p t i o n s s i n c e 1911

both

Islands.

and

are

recorded

B e c a u s e harem b u l l s

f o r each

rookery

are c o n s p i c i o u s , the

data

is considered accurate.

D. from

Approximation

July

to

have been

and

counts No

46 p e r i o d of of

data

rapid

different

Island

all

10,

live

and

Beginning

1922) fixed

of M o r t a l i t y

counted

recently,

i n subsamples

d u r i n g the

herd

i n mid

tagged

1925-

stabilization.

to l a t e

August

after

occurred.

Data

yard

from Newborn F u r S e a l s .

study

respectively.

areas

study

on

Saint

1967

Paul

for periods

A u t o p s i e s were p e r f o r m e d

to determine

of pups b e f o r e g o i n g year

most

ratios

f o l l o w e d s i n c e 1964,1966, and

a two

rookery

partially

and

apparent

have been t a k e n has

each

r a t e s (1923-40),

1947-68),

i n c r e a s e and

8 years

i n 1976

and

pups were c o l l e c t e d

dead pups i n t h e s e a r e a s

the c o n d i t i o n

On

t h e p e r i o d 1912-83, newborn pups

(1941,

2,000 s q u a r e

have been 8,

on

land m o r t a l i t y

E. C o l l e c t i o n

1912-83.

made of marked/unmarked

dead pup

most of the

Three

over

assumed t o i n c r e a s e a t

(1968-83).

Counts

Numbers,

(1912-16,

recaptured in harvest

sheared

of

August

completely

(1917-21), and

mid

of Pup

t o sea was

the cause f o r the

conducted

of d e a t h first

on

Saint

on and

time. George

Island.

F. F u r During

Seals Entangled

in Fishing

D e b r i s and

the p e r i o d 1967-83 r e c o r d s were kept

Other

Materials.

of d e b r i s e n t a n g l e d

10

fur

s e a l s among

those

driven

from

the

hauling

grounds

for

harvest ing.

G. P e l a g i c selected Bering

Data,

1958-74.

Each

a r e a s of t h e m i g r a t o r y Sea

regions. numbers

were

Records seen,

surveyed.

of t h o s e c o l l e c t e d ,

s e a l s was

The

were made o f t i m e

prevailing

l e n g t h and w e i g h t ,

range

year from

area

environmental

pregnancy

rates,

period.

split

looking

conditions,

months, to

into for

the seven

seals,

age and sex

reproductive

and f o o d s p e c i e s consumed.

taken d u r i n g the study

2-4

California

was

spent

for

A total

condition, of

13,845

11

CHAPTER 4

The

a i m of t h i s

that w i l l

and

dynamics

from

and. from

pinnipeds.

the

of

The

fur

seal

proposed

general

theory

populations

fur. s e a l

principles

studies

upon c o n c e p t s

a general

of

is

1978).

limited

of b i r t h ,

the p r o c e s s e s

The c e n t r a l by p h y s i c a l death,

is

conceptual population

o f f u r s e a l s and o t h e r

of r e s o u r c e

l i m i t a t i o n and

of numbers, t h a t a r e common t o a l l p o p u l a t i o n

(see T a m a r i n ,

processes

level

population

It is built

regulation

i s t o put forward

maintained.

i s developed

growth

chapter

e x p l a i n how t h e

determined model

A FUR SEAL CONCEPTUAL MODEL

models

supposition i s that population c o n d i t i o n s and r e g u l a t e d by t h e

immigration,

and

emigration;

where

t h a t r e g u l a t e growth a r e f u n c t i o n s o f t h e l i m i t i n g

resources.

The the s i z e

chapter

of n o r t h e r n

discussing respect between

begins

the

fur

shortages.

concepts

comprehensive c o n c e p t u a l and

the v a l i d i t y

seal

the resources

populations.

It

that

limit

proceeds

mechanisms t h a t r e g u l a t e p o p u l a t i o n g r o w t h

to resource the

by i d e n t i f y i n g

of

Note t h a t a d i s t i n c t i o n limitation

model o f f u r s e a l

and

is

regulation.

biology

is

of t h e model a s s u m p t i o n s a r e d i s c u s s e d .

by with made A

proposed

12

4_.J_

Food limits

and

on

northern

generally the

size

fur to

a shortage than

food

limited

(Watson and

t h e most

populations

of b r e e d i n g

two

1983)

or

during

the

by

migration Ocean.

of

important

(Lack,

Food

factor

1954,

while other

is

limiting

1966).

space i s c o n s i d e r e d

season

of n o r t h e r n

land

But

in

t o be

populations

more

appear

simultaneously

the

resource

fur s e a l s congregate

food

fur seal

5000

circumstances

Instead,

and

fur seal

i n the

completes a

competition

in for

should

B e r i n g Sea

and

needed

I base t h i s

kilometers

shortages

populations

resources

t o p r o d u c e young.

t h a t each year

such

implausible. the

shortages

c o v e r i n g as much as In

abundance.

to set

1970).

breeding

the o b s e r v a t i o n

thought

more f a c t o r s a c t i n g

I b e l i e v e t h e maximum s i z e i s determined

conditions

population

be

(Duffy,

by

Moss,

physical

seal

of most a n i m a l

important be

are

considered

some c a s e s

to

space

L i m i t i n g Resources

be

the

upon

solitary Pacific

resources

is

apparent

as

upon t h e

breeding

grounds.

Fur

seals,

like

all

pinnipeds, are

need t o r e t u r n t o l a n d t o p r o d u c e young. sites is

t h a t meet two

the

suitability

protection

of

from

water

the

important of

the p u p s . and

the

They

criteria

(Payne,

breeding

site

Rookeries protect

p e l a g i c mammals t h a t

pups

must

be

choose 1977).

breeding The

first

for reproduction easily

from s t o r m

and

accessible

mortality.

The

13

s e c o n d c o n d i t i o n i s the a v a i l a b i l i t y females

to

produce

conditions

appear

and

along

in

depth

and

Kajimura,

Perez both

milk

for

t o be

and

upwelling 1982;

Bigg,

limited presence

either

of

restricts

Thus,

the

breeding

canyons,

feeding

seamounts,

abrupt

changes

bottom w a t e r "

al,

1984;

lactating

Optimum

where t h e r e a r e

Kajimura,

fur seals.

by

pups.

of n u t r i e n t r i c h

conditions apparently

of n o r t h e r n

their

see a l s o L l o y d e t

1980;

f o o d needed by

"near sea v a l l e y s ,

the c o n t i n e n t a l s h e l f and

of

1980;

Payne,

(Lander

David,

1977).

the geographic

1984;

Satisfying distribution

some f u r s e a l p o p u l a t i o n s

level sites,

of or

marine

may

productivity

perhaps

by

both

be

or

the

factors

simultaneously.

Historical

records

that

the a v a i l a b i l i t i e s

can

set

seal

limits

to

apparently (Payne,

i s an

been

breeding South not

seals

breeding The

Africa

alternative

found and

on

to

This

fur

in

South

is

have seal

limited

by

several small

the

colonize

c o l o n i e s have grown r a p i d l y

(David, early the

is

a l l of

the

been

occupied

(Arctocephalus

the

amount

islands

p a r t of mainland to

of

total

the

coast

of

population

The

island

to

suitable

this century beaches.

pusilus

believed

o f f the

The

fur

Georgia

because never

1984).

compared

space

example, t h e A n t a r c t i c

breeding

sites

confirm

breeding

example of a p o p u l a t i o n

Namibia

increase u n t i l began

Cape

populations

territorial

For

limited.

historically

space

f o o d and

gazella)

food

suitable 1977).

pusilus) have

be

of

abundance.

(Arctocephalus

believed

did

on

from some f u r s e a l

when

the

mainland colonies

14

(Butterworth unlimited and

breeding

The

a l , 1984),

breeding

upon which

its

er

space

factor

Pribilof

potential

difficult

space.

i s most

recorded

Townsend

Reexamination

At Bering

present,

and

its

limiting

In

mean

Elliot

T h i s makes i t limit

(1884),

provide

growth.

distribution when

carrying

1980) and

s p a c e on t h e P r i b i l o f

T h i s does n o t

depending

that

Islands

food

and

useful

the

information

space.

plenty

of

(personal

space

were

capacity.

i s an a p p a r e n t abundance o f f o o d

Sea (Swartzman and Haar,

breeding

and

o f f o o d and b r e e d i n g

there

food

i s b e l i e v e d t o be

could

apparent

s t u d i e s may

about p o s s i b l e s h o r t a g e s

both

growth

1982).

that

abundance

(1899)

near

of t h e s e

population

and K a j i m u r a ,

population

was

i t seems t h a t

i s f a r below what

the resources

of

due t o t h e p r e s e n c e o f

limiting.

(Lander

Observations

population

fur seal

population

to identify

by

In g e n e r a l ,

restrict

size

apparently

i n the

available

observation).

are

not

presently

the p o p u l a t i o n .

terms

of

food,

the c r i t i c a l

factors are a c c e s s i b i l i t y

( A n d r e w a r t h and B i r c h , 1954) and q u a l i t y

(White,

abundance.

An abundant B e r i n g

base

does

population

growth

are

unable

Nino

year,

resource.

During

dissappeared California.

from

if the

the most

around

Sea f o o d

fur

seals

recent San

Many f e m a l e n o r t h e r n

El

Miguel fur

1978); n o t o n l y not

ensure

t o use t h e seal

food

I s l a n d o f f the c o a s t of seals

from

this

island

15

failed food

to

s u c h as prey

personal

lactating weaned

for

Pribilof

It

that

the

choose

total

their

Females, where

males a r e the

to

suckled

also same

fidelity

of

females

are

spot

northern

neighboring

seems

confirmed

left

portions

day

(Lander,

successfully eventually

of

the

1980a

available

to

presently

recently

limiting

number

restricts

I t seems

in

upon

of

the

the

young

impact

exploited pgs.

95,

the

Adult return site

a r e a s where m a l e s

arid

increase Such

in

speculation

the

increasing given

limiting

density

females that

empty t i l l

i n any

physical

1953).

1980).

harvesting

The

location

frequently

empty.

157).

seals

This

will

rookeries

fur seals by

of

fur

of

experience'.

Wilke,

and

s e a l s means t h a t

remain

growth

that

(Gentry,

successful

capacity

approximate

sites

a f t e r year

the

'past

(Kenyon and

to breeding

the

constrained

of

be

the

of

variability

'local' carrying

based

pups

year

reproducing

set a

birth

a r e a s might by

be

pups

phenomenon,

i n a c c e s s i b l e to

restricting

sites

fur

their

productivity

The

may

r o o k e r y and

reproductively

while

could

population.

as

faithful

food

sufficient

reproduce.

to a given

breeding

and

fur seals.'

summer but

f o r space t o

island

find

Oceanographic

that

by

to

nourish

distribution the

the

f o r example, g i v e

they

properly

Thus f o o d

survive

is possible

of

the

example,

population

is specific

were u n a b l e

to

to

females d u r i n g

seals

part

alter

pups i n f a l l .

entire

that

milk'

available

means,

others

communication).

E l N i n o , can

species

supply

to

and

t o p r o d u c e enough

(DeLong,

fur

reproduce

area

has

present

numbers will

f a c t o r s such

of be as

16

p r e s e n c e of c l i f f s , and

so on.

rookeries

In

this

could

unlimited

the

way,

sites

the

availabilities

availability

Pacific

and B e r i n g

the t o t a l

secondary

is

of

variable

a

factor

Regulated

food. these

or

p r e s e n c e of

i s l i m i t e d by The

factor food

factor

number o f unlike

the

i n the North

limiting

limited

certain

requires

the s i z e

space

Pribilof

is

a

rookeries

growing.

Population

populations

availabilities

resources;

mechanisms

growth

that

and t h a t

that could prevent

variable

and

environment

constant

I suspect

population

Population

Regulat ion

r e g u l a r l y tend

of

food,

to

rates.

prevent

shelter,

1970;

Other

a

living

by c h a n g e s Many

that

Ricklefs,

Some

regulate

and

regulatory

from e x c e e d i n g populations

from c l i m a t e , d i s e a s e ,

populations

space,

in reproductive,

different

population

resources.

by m o r t a l i t y i n d u c e d

competition.

(Murdoch,

but a r e m a i n t a i n e d

dispersal

exist

towards a d e n s i t y

d e n s i t i e s a r e d e t e r m i n e d by t h e l i m i t e d and

s e t by e n v i r o n m e n t a l

regulated

colonies

the

resources.

Sea i s t h e u l t i m a t e

1973).

survival,

seal

two

be s u s t a i n e d by t h e e n v i r o n m e n t

limits

some in

Population

of food.

_4.2_

other

of

even

fur

relatively

Pribilof

from t e m p o r a r i l y

and

growth

stop,

optimum

t o ' b e near

sites

can

the

storms,

food.

breeding

of

from w a t e r , p r o t e c t i o n from

temporarily

In summary, breeding

distance

the are

predation,

their

s i z e by

17

altering

fecundity

individual of

physiologies

each r e g u l a t o r y

history 1981,

and b e h a v i o u r .

of

changing

depend

of the p o p u l a t i o n

importance

upon

(Watt,

the

life

1973; F o w l e r ,

1983b).

(1981) p r e d i c t s t h a t

regulated

until

capacity.

levels.

population

He s u g g e s t s t h a t

significantly

increase

Instead,

population

There

l a r g e mammals a r e n o t density

density

at

is

growth

factors are

high

close

strongly

to

carrying

d e p e n d e n t mechanisms do

population

regulating

increases

capacity.

at

low

believed

densities

not

population

to

relative

i s a wide range of p o p u l a t i o n

restrict

to carrying

l e v e l s over

which

r e g u l a t i n g changes a r e expected.

P r e d i c t i o n s made by F o w l e r large

mammal

northern of

population

fur seal

Pribilof

rates

at

compared the

herd

low adult

period

find

1972.

parameter 1983).

age

that The

levels.

1974

and

York

be

supported

during

and

between

the

first

rates

true

over

reproduction

of by

years

in vital

Hartley

(1981)

1958 and 1965 w i t h

find

S m i t h and P o l a c h e c k

i n pregnancy

is

to

studies

could

does n o t c o r r e l a t e w i t h same

the r e g u l a t i o n

i n d i c a t e no p o s i t i v e c h a n g e s

survival rates

to

of

appear

Population

decline

Similarly,

any change The

studies.

female

(1981 ) , about

sizes,

population

1966

difference. to

by means

The r e l a t i v e

mechanism a p p e a r s t o

characteristics

Fowler

no

and d i s p e r s a l p a t t e r n s

no

significant

(1980) were

the

period

i s another

fur seal

unable

1958

to

population

density

(York,

f o r e s t i m a t e s of j u v e n i l e s u r v i v a l

18

(Fowler,

1982b).

evidence

that

ever

been

In g e n e r a l ,

significant

operational

population

has

There are occurring

there

density during

a few

examples

of

f u r s e a l herd

10%

t h r o u g h the

weight

than those

been

low

spending

d e c r e a s e d as

The growth

Eberhardt

respect time,

less

time

effects

i n body are

(1977)

has

Pribilof

fur

feeding

size,

incidence

that

seal

(2)

male

an

changes

Three

from

examples

1958-74 were and

(3)

tooth

in

density

land

female

adult

increase

lactating and

and

trips, the

consistent for

the

body

dependent

mothers

pup

have

mortality

has

changes

in

positive

l a c k of c h a n g e s

with

m a r i n e mammal p o p u l a t i o n s Eberhardt

suggests

o b s e r v e d as

Behavioural

followed

of

r a t e s , age

by

diseases of

first

in

predictions

behaviour) i s speculated

in density,

population

similar

foraging

c h a n g e s t h a t might be

(birth

i s or

dropped.

female

aggressive

(growth,

regulation

d e c l i n e , and

of

numbers a r e

to c a r r y i n g c a p a c i t y .

to changes

of

birth

1950s,

a f t e r pup

carrying capacity.

population

lack

the

be

1982a).

weights at

examples

abundance

rates,

a

positive

1948-79 r e f l e c t i n g

herd

shorter and

vital

their

from

Additional

responses to

pup

increased

increased

size.

years

(Fowler,

(1)

rates

dependent the

of growth c h a n g e s a r e

growth

to

been d e c l i n i n g .

i n the

higher

seems

a

population

drawn that

are

from below

progression

d e n s i t i e s change

modification t o be

very

of in

(feeding sensitive

individual characteristics and

parasites),

reproduction),

and

reproductive population

19

aspects

(survival

changes i n the categories,

I may

behavioural

be

capacity.

The

adult

that

population

age

of

s e a l s are

fur

the

the

juvenile

reproductive observed

rates

f o r the

Juvenile

(Eberhardt,

1981).

life in

age

of

survival the

fur

that

of

has

age

1983).

The

Pribilof

R e s t r i c t i n g the effectively

age

This

most

reproduce. of

first

and

carrying

and

the

rates

the

large

harsh A

account

for

stability

of

that

the

mammal first

It also

have

been

the

few

years

suggests a

substantiated shown t o

factor"

populations

reproduction by

exist

population

the

delay

negative

between

juvenile

fur to

(ages 6.2

reproducing size.

of

(Eberhardt,

s u r v i v a l (0.15

numbers of

regulate

that

classes.

"proximate

females reproduced and

probably

assumes

age

e s t i m a t e s of

higher

rates

population.

t o be

r e c e n t l y been

(York,

s e a l s can

two

more r e s i s t a n t t o

survival

view a p p e a r s

reproduction

the

first

l e v e l s near

youngest

s u r v i v a l over

first

younger

years).

This

and

rates

fur seal

fewer w i l l

1981).

to the

parameter changes c o u l d

.adult

Poor

the

the

reproductive

increases.

the

survival

and

growth r a t e s and

correlation

of

abundance

means t h a t

1977b,

animal

s u r v i v a l i s thought

the

that

i n d i v i d u a l changes.

seal population

than

Pribilof

regulating

and

less vulnerable

expression

variable

conform only

seems

v a r i a t i o n in i n d i v i d u a l rates

environmental conditions progressive'

It

c h a n g e s i n s u r v i v a l and

amount of

the

distribution).

modification

observed at

d e c r e a s e s as the

Pribilof

suspect

only

rates,

the seal 0.45)

to

5.2

female

20

The

large variation in P r i b i l o f

suggests that

there

near

may

have

level

was

factor

i s the a v a i l a b i l i t y

(1978) b e l i e v e s limited very

by

young.

This

could

seal

of

have

impact

of most

be t r u e that

by

limitation,

factor that

the

availabilities a variable

I have

speculated

Northern same s i t e

pup

elephant

fidelity

changes t h a t

Reiter

of

both

greatest

fur seals. space

In

is

a

from g r o w i n g . might

occur

can be g a i n e d

from

( M i r o u n g a a n q u s t i r o s t r i s ) show t h e

rookery

e t a l (1981) r e p o r t

mortality

of

fur

species.

seals

to t h e i r

to

availability the

that

prevents c e r t a i n rookeries

pinniped

seal

t h e s i z e of n o r t h e r n

r o o k e r y d e n s i t i e s became i n c r e a s i n g l y h i g h of o t h e r

fur

has been a v a i l a b l e

i s l a n d s would have

i n t o the f u r s e a l p o p u l a t i o n

knowledge

is

Sea.

I t seems t h a t

the b r e e d i n g

White

have been t i m e s when an

of f o o d

suggested that

is restricted

limiting

foods f o r t h e

northern

t h e growth and s u r v i v a l of a l l young

t o food

likely

animal populations

of t h e

there

population

juveniles.

upon

Insights

and

the

near

secondary

seals.

the

food

contrast

as

when

The most

for

i n the Bering

space.

fur seal survival

s h o r t a g e of n i t r o g e n o u s

well

previously

and b r e e d i n g

seal

of food

q u a l i t y and q u a n t i t y

populations

food

capacity.

i s possible

weaned pups

times

t h e abundance

relative

It

insufficient

I

that

the

population.

recently

carrying

been

juvenile

elephant

of that seals

birth

as

northern

the r e p r o d u c t i v e appears

t o be

fur

success density

21

dependent. less able larger fail

As to

and

rookery

densities increase,

s u c c e s s f u l l y compete w i t h more e x p e r i e n c e d

at

to s u c c e s s f u l l y reproduce

different

site

faithful

to

formation

of

The depend

the

following

their new

new

formation

and

upon r o o k e r y

Antarctic

(Butterworth

g r o w t h of

higher

rookeries density

regulatory

rookeries

Island

decimated

by

stimulated

to

go

stopped

began

emigrate

to

slowed survival

and

rates

There invoked

are

females

that

The

the

to the

due

at

subsequently the

remain

emigration

when a r o o k e r y

a

and

is

full.

case

for

for

fur

and

the

Older

the

Cape that

fur

higher At

The

lower d e n s i t y

in part

of

The

a f t e r they

s e a l s were rookeries

point

growth now

until

the

of were

pup

females

(Vladimorov,

appears to

t o a s e r i e s of

low

initially

young

rookeries

of

same

recolonization

density this

seals

f e m a l e s r e m a i n on

the

for

emigration

expansion

seal rookeries

Population

(Vladimorov,

poor

have

juvenile

1984).

i s e v i d e n c e of a d d i t i o n a l r e g u l a t o r y

in pinniped

birth

T h i s a p p e a r s t o be

1977).

increasing.

stablized

that

seems t o

s e a l i n g i n 1910.

communication).

females

give

It i s speculated

accounts

to

are

where t h e y p r e v i o u s l y pupped.

northern

pelagic

production

personal

(Payne,

mechanism

Commander

Thus

( D o i d g e e t a l , 1984b)

et a l , 1984).

females

fur seal colonies also

young A n t a r c t i c f u r s e a l s a c c o u n t s density

to and

seems t o o c c u r

densities.

fur seals

season

young

pups.

apt

location.

colonies

older

raising are

the

populations

that

are

limited

mechanisms by

space

being during

22

the

breeding season.

younger

female

For

example, S t i r l i n g

Weddell

seals

(1971)

(Leptonychutes

e x c l u d e d f r o m b r e e d i n g when c r o w d i n g t a k e s p l a c e social

stresses

comparing four grypus),

seal

breeding

Coulson

s u r v i v a l are to

present

and

of

grey

increasing

breeding

densities

m o r t a l i t y i s d e n s i t y dependent 1982a).

d e n s i t i e s and

conclusions

s u r v i v a l estimates

might

be

could

on

to form.

In

(Halichoerus growth

These

In

northern

( L a n d e r and are

but

Paul

explained

and

responses fur

by

was

b u l l s and

summary,

could

probably 1950

of

be

applied

(Kenyon

been o b s e r v e d f o r A n t a r c t i c (1984a).

incidences

et

of

fur

More pups failed

pups

being

cows.

f u r s e a l s are

l e v e l s c l o s e to the

food

pup

rookery breeding d e n s i t i e s .

seems l i k e l y t h a t

most s t r o n g l y a t p o p u l a t i o n availabilities

1982;

variation in

Island rookeries

higher

b i t t e n by

land

Kajimura,

b e a c h e s b e c a u s e m o t h e r - p u p bonds

also

it

fur seal

b a s e d upon a v e r a g e i s l a n d

g a z e l l a ) by D o i d g e e t a l

high density There

t r a m p l e d by

the

maturity.

w e l l occur i n the

example t h e

d e p e n d e n t m o r t a l i t y has

(Arctocephalus

starved

For

(3-39%) among S a i n t

1954)

Density seal

The

individual rookeries.

mortality al,

the

that

population.

Fowler,

to

and

H i c k l i n g (1964) n o t e t h a t pup

A l l a v a i l a b l e evidence suggests that pup

are

seals

r e d u c e d under c r o w d e d c o n d i t i o n s .

that

weddelli)

at high d e n s i t i e s delay islands

found

and

breeding

g r o w t h a p p e a r s t o be p r i m a r i l y r e g u l a t e d

by

limits

space.

regulated set

by

Population

changes i n the

rates

23

of

survival,

r e p r o d u c t i o n , and d i s p e r s a l

4.3_

Based

upon

the

dynamics

of

conceptual

model

Islands

maximum is

other

carrying two

but

i s p r e s e n t l y empty.

Their

to

seals

site

number

of

population

I

of

propose

the

a

Pribilof

each

animals

density food,

i s referred

supply.

that

rookery

breeding

space,

a

f o r each

summer

to their

rookery

Density

r a t e s and land on

the

local

rookery.

It

rookery, i s not

of m o r t a l i t y .

rookery

i s reinforced

of

birth.

each

year

mechanisms

begin

pup s u r v i v a l the

of

its

population

dependent

'local'

t o a s t h e 'home'

i s below

sources

The

f o r each

c a p a c i t y a s t h e home

to natural

congregating

identical

determine

hypothetical

t o t h e home

pregnancy

food

i s the 'neighboring'

The

reproduce.

physically

a single

population

carrying

subject

return

fidelity

successfully affect

the

and i s s p e c i f i c

rookery

The second

potential

two

conditions

can vary

The f i r s t

and i s only

only

These

capacity.

Fur

dynamics

of a v a i l a b l e

a small

same

the

on

pinnipeds,

or e q u i l i b r i u m

by t h e a m o u n t s

resources.

the

other

t o be n e a r

and c o n t a i n s

harvested

they

size

capacity that

carrying has

and

describes

a r e assumed

rookeries.

rookery

Model

information

discussion,

population

restricted

and

seals

animals.

fur seal.

simplify sites

available

that

northern

To rookery

fur

Conceptual

f o r young

as the annual

breeding

grounds

24

approaches excluded

the l o c a l from

females

fail

properly

care

from

their

reproducing, to

form

a

for their

capacity. while

mother-pup

pups.

by b u l l s ,

bitten

as

population

young

bond

females a r e

inexperienced

and

a r e unable t o

Many o f t h e pups become starve t o death.

by mature

density

Some young

other

mothers and s u b s e q u e n t l y

trampled the

carrying

females,

approaches

separated Others a r e

o r d i e from

the

rookery

disease carrying

capacity.

The less

young

faithful

therefore

from

defend

a

both

on

season.

the

territory

rookery. ensures

to emigrate

breeding

breeding

Successful

and

capacities.

The

population and

population availability that

to successfully

high and

to

size

are

below t h e l i m i t s

the

neighboring

density maintain

rookery a and

rookeries

survival

approach

one h a l f

in

Figure

densities

the i s l a n d

s e t by b r e e d i n g

the

space.

successfully

of

the

pups

rookery

until

their

local

a r e shown f o r t h e home 4-1.

rookeries i s ultimately

Rookery

rookery

can

of t h e n e i g h b o r i n g

rookery

and a r e

harem on t h e n e i g h b o r i n g

growth t r a j e c t o r i e s

f o r both

of food.

the o l d e r females

t h a t were p r e v i o u s l y e x c l u d e d

reproduction

neighboring

reproduce a r e

than

Bulls

neighboring

carrying

levels

fail

continued c o l o n i z a t i o n

home

rookery

that

t o t h e home r o o k e r y

likely

following

females

limited

eventually

carrying

The

total by t h e

approach

c a p a c i t y and a r e

25

Figure

4-1. T r a j e c t o r i e s showing p o p u l a t i o n growth of the h y p o t h e t i c a l home r o o k e r y and n e i g h b o r i n g r o o k e r y o v e r time. T o t a l p o p u l a t i o n s i z e i s shown as a f r a c t i o n of t h e c a r r y i n g c a p a c i t y K which is d e t e r m i n e d by t h e a v a i l a b i l i t y of f u r s e a l f o o d ( f o o d l i m i t ) . There i s a l i m i t e d amount o f a v a i l a b l e b r e e d i n g space on each r o o k e r y (space l i m i t ) . The number o f s e a l s on e a c h r o o k e r y a p p r o a c h e s 1/2 K o v e r t i m e .

26

The

total

fur

seal

never

at

rookeries)

is

continually

fluctuating.

size

population

of

rates

the over

the

r e d u c e the

reproduce

and

sexually

rookeries

and

milk

transition Bering

fur

the

time

c o n d i t i o n s can

that

Growth abundance of

fur are

seal

Poor

seals

needed

the

mortality

environmental

that to

is

survive

grow and

conditions

to

become enhance

be

this

lactating of

starvation, unless

breeding

breeding the

seal

Changes

i s the

the

i n the

in v i t a l are

of

the

:

wintry

are

f u r s e a l s are

not

not

as

predation,

extreme.

thus l i m i t e d

the

Bering

of

by

food

the near

numbers becomes

Sea

r a t e s occur

and at

more a p p a r e n t

condition

produce

i n the

species

availability

Regulation

ultimate

foods

conditions,

is

near

Similarly

conditions are

near c a r r y i n g c a p a c i t y and Food

Adult

are

mothers to

prey

weather

seals congregate

grounds.

if

populations

s p a c e and

locations.

solid

period.

that

pups.

to

unsuccessful

critical

fur

species

needed by

j u v e n i l e s t o poor

of

i n f l u e n c e annual p r o d u c t i v i t y prey

weaning

will

and

a p p a r e n t as

of

recent

as

classes.

juvenile

life.

environmental

from

vulnerable

levels

of

survival

at

breeding

number

ensure

available

these

of

but

fluctuations in

variable

to

Sea

disease,

years

neighboring

equilibrium

major c a u s e o f

two

and

growth.

distribution

enough

(home

numeric

and

Good

Oceanographic and

true

The

increase

mature.

population

a

i s high

first

conditions

population

limiting

upon

the

population

i n young

age

population

27

size.

However, the l o c a l

could

well

food

becomes

rookery

c a r r y i n g c a p a c i t i e s of some

be d e t e r m i n e d by a s h o r t a g e of b r e e d i n g space limiting.

specific

accessibility

Total

and w i l l

dynamics limit

of b o t h f o o d

assumptions the

breeding

regulated

by

theory

limited

islands

and

of the c o n c e p t u a l

assumptions

s u c h as

mathematical fur

assumptions herd at

model

dynamics, low

conceptual capacity capacities

that

about

regulate

and

population

resources

major

amounts of f o o d

are a v a i l a b l e

near

that

growth

population that

growth.

that

Two

survive

to

is primarily reproduce.

model depends upon t h e v a l i d i t y

incorporates The

and a d u l t

of

hypothesis

juvenile rates

densities.

model a s s u m p t i o n s . cannot

rookeries

t h e major

using

features

survival remain

to

F o r example,

has

tested never

test the

because been

such

regulate

relatively

Unfortunately,

a t ' present

be

rates

a

of the.

m a t h e m a t i c a l model can t e s t

vital

information

of

fur seal

p r e d i c t i o n s can be t e s t e d

variable

population

insufficient

and

model.

as t h a t

be

these.

assumptions

seal conceptual

describing

assumptions

t h e numbers of young

Acceptance

Certain

p r i m a r i l y upon t h e q u a l i t y

mechanisms t h a t

are that

fur seals w i l l

Discussion

i s b a s e d upon s e v e r a l and

of

before

and b r e e d i n g s p a c e .

proposed general

density

numbers

depend

4.4

The

rookeries

constant

there all

of

is the

local

carrying

the

physical

quantified.

28

Nevertheless, certain

the

m a t h e m a t i c a l model can t e s t

hypothesised

provide

regulatory

further insight

A

mathematical

model

observations

decline,

1950 t o 1980, by

include

t h e impact

females.

greatest that

can

recorded

females and

produce

reproductive

rates.

Fur

nonbreeding adversely

males affecting

substantiated 1958 of

are

the

seal

of P r i b i l o f

in

would

and

Polacheck,

males h a r v e s t e d

1978).

rates

harvested

This

seems

r a t e over

and harem b u l l s

counted

since

cessation

of . the

1983).

be

( S m i t h and

s t u d i e s c o n d u c t e d on t h e P r i b i l o f

(Anonymous,

without

i n t h e number

behavioral

George

many

the p e r i o d

T h i s view a l s o a p p e a r s t o be s u p p o r t e d

Saint

herd

to

comparative the

suggests

that

be

i n pregnancy

are

response . i n

suggests

may

to

males

reduce

compensentary biology

herd

model

vital

t o 1972 when l a r g e f l u c t u a t i o n s were r e c o r d e d subadult

reproduce

dynamics o f h a r v e s t i n g

population.

by t h e c o n s t a n c y

to

conceptual

densities

no

excess

perhaps

near c a r r y i n g c a p a c i t y ,

low

productivity

the

t h a t changes

levels at

the years

may

dynamics.

constructed

during

upon p o p u l a t i o n

population

culling

be

extending

The h y p o t h e s i s

at

and

into fur seal population

historic

and

mechanisms

the soundness of

harvest

by t h e Islands in

1972

29

CHAPTER 5

An

A FUR

SEAL MATHEMATICAL MODEL

approach to understanding

Pribilof

Island population

has

f u r s e a l d y n a m i c s and

been

1950s i s t o r e c o n s t r u c t h i s t o r i c a l of

herd

decline.

Along

with

declining

since

observations

during

offering

t h e d e c l i n e , s i m u l a t i o n r e s u l t s may for

future

therefore spanning

management developed

the

period

and

that 1950

to

research.

(Table

s e t s of 5-1).

production period

to

the

differential female estimates

The

numbers survival

population,

been w i d e l y the

July comprise

set two

From of

of and

pups

1950

to

1960

estimates the

for

implications

reproduce

can

be

data

of

reconstructed with estimates

was sets

1950 born

to

1960,

using

to

over

Chapman

females,

rates.

Since

size

the

about of

1961,

program w i t h i n

Johnson,

The

there

exists

estimates

(Smith

and

field

estimates

some

Polacheck,

The

the have

controversy 1978).

S a i n t Paul

observations.

the pup

a mark r e c a p t u r e 1968).

pup

(1964)

assumptions

although

s e t of

a model

pertains

estimation procedures

of a d u l t male abundance on

second

years

A s i m u l a t i o n model to

pregnancy

(Chapman and

accepted,

suggest

j u v e n i l e males and

have been b a s e d on

summer of b i r t h

over

first

1980.

the

mid

Methods

data

c a l c u l a t e d using

1950

estimated

fur seal

the

1980.

5.1

Two

the

possible explanations

also

attempted

why

male

Island seals

30

Table

5-1.

Year

Pup e s t i m a t e s and c o u n t s o f harem and i d l e Saint Paul Island.

Pups Born

1 950 1951 1952 1953 1 954 1955 1956 1 957 1958 1959 1960 1961 1 962 1963 1964 1965 1 966 1 967 1968 1 969 1 970 1971 1 972 1 973 1 974 1 975 1976 1977 1978 1979 1 980

451 000 447 000 438 ,000 445 000 450 000 461 ,000 453 ,000 420 000 387 000 335 000 320 000 342 336 277 078 262 ,498 283 922 253 ,768 298 931 291 000 235 000~ 232 670 230 485 305 000~ 269 000 236 420# 266 000 278 261 298, 000 235, 210# 247, 1 32# 245, 932 199, 046#

Bulls Harem 9 292 9 434 9 318 9 848 9 906 9 034 9 384 9 582 9 970 10 003 10 247 1 1 163 10 332 9 212 9 085 8 553 7 925 7, 230* 6 1 76* 5, 467 4, 945 4 200* 3 738* 4 906* 4, 563* 5, 018 5, 324 6, 457 6, 496 6 242 5, 490#

Counted Idle 3 102 3 581 4 717 5 912 6 847 8 650 9 016 10 060 9 510 1 1 485 10 407 1 1 791 9 109 7 650 7 095 5 616 5 931 4 439* 3 100* 2 208 1 ,666 1 900* 2 384* 2 550* 1 782* 3 535 4 041 3 845 3, 908 4 457 4 248#

Sources: L a n d e r , 1980 * Lander and K a j i m u r a , 1975 S m i t h and P o l a c h e c k , 1978 # York, p e r s o n a l c o m m u n i c a t i o n

b u l l s on

31

of a d u l t either

size harem

territory half

( a t t a i n e d a t about masters

w i t h one

years.

Both

prior

8

t o the

years

and

old,

Polacheck,

structure over

about

of

time.

1978). the

to

be

idle

bull

A second

harem b u l l

maintain a

In

and

contrast

(Chapman,

a r e a of u n c e r t a i n t y p o p u l a t i o n and

and

the

reliable

how

a

of b r e e d i n g

males aged

a t sea

shortcomings,

adequate

being

of one

this period count.

as

to

counts, there i s a great deal

remain

6,

7,

1964; is

it

bull

of and

Smith

the

age

has,changed counts

are

indicators

of t h e f u r

model was

developed

population trend.

5.2

A simple s i n g l e for

after

number of i d l e

f o r some may

Despite these

considered seal

the t o t a l

Harem m a s t e r s

f o r an a v e r a g e

t o and

a c c u r a c y of the harem b u l l

uncertainty

7) a r e c l a s s i f i e d

i d l e males.

or more f e m a l e s

a d u l t males c o n t r i b u t e the

or

age

the Saint

Pribilof

group

population

was

stratified

by

Model

s p e c i e s age

structured

Paul p o p u l a t i o n that of n o r t h e r n f u r s e a l s considered sex

and

c o n s t i t u t e s about (Appendix

as , s p a t i a l l y 25

age

The

number of f u r s e a l s a t age

males and

N

determined to the

next

x

p

for females.

the number o f (age

interval

The

individuals x t o x+1)

density

the

modelled and

was

dependent

d e s i g n a t e d as N ^ x

cycle

that and

No

of

operational.

x was

annual

The

homogeneous

classes.

r e g u l a t o r y mechanisms were assumed t o be

A).

80%

of the model

survived

later

from one

removed t h e

for first year males

32

and

females k i l l e d

N

= N x+1,m

during

* S x,m

the h a r v e s t

according

-H

t o the

relation:

(5-1)

x,m

x+1 ,m

and N

= N x+1,f

The for

* S x,f

parameters

- H x,f

S

.

and S ^ f

X r n

were age s p e c i f i c

males and f e m a l e s r e s p e c t i v e l y and H

number of f u r s e a l s

After

using

N

the

population,

the

and

x > m

survival H

rates

were

x

the

harvested.

removing

simulated

(5-2)'

x+1,f

harvested

t h e number of

males and f e m a l e s pups

born

was

from t h e

determined

equations

24 = £ N * b 0, f x= 1 x , f x,f

(5-3)

and 24

N

Where

=

0,m b

abundance

X

ET

x, f

and

m

of

*

b

x=1

reproductive

The

N

b p

were

x

males

(5-4)

>

x,m

was

age

assumed

specific to

have

natality no

rates.

effect

The upon

rates.

total

number

of

bulls

counted

(B) was

expressed

in

33

terms of and

on

the

land

during

24 B = £ x=0 The

proportion

bull

for part

times

(Chapman,

of

the

of an

that

the

Computer that

counted.

initial

present

percent

the

age

of

6 were not

simulation

age

of

was

specific

from L a n d e r of

idle

Paul

population size

reported

kill

harvest bull

6,

be

and harem

bulls

at

other

fur

seals

began

stable

age

during

older

of

considered

harvests

(1980a)

York and

were

were p r e s e n t

8 year

and

Hartley

calculated

olds

on

that

by land

were

of

c o u n t were assumed t o be

10,

each year c l a s s r e s p e c t i v e l y . t o be

Males

mature b u l l s .

under

The

last

1980.

rates

of p r e g n a n c y and

(1981) and

simulation.

the

Historical

totals

and

a

from L a n d e r

counts

7,

of

having

454,000 pups.

numbers of

75

period

the

female

and

taken

mature m a l e s may

s e a s o n and

herd

produced

50,

age

Saint

generated

The and

All

some

a l l males 9 y e a r s and

size

y e a r of

breeding

the

were r e p r o d u c e d u s i n g extrapolating

because

d i s t i n g u i s h between harem

1961).

with

distribution

adult

count.

(5-5)

c o u n t s d i d not

categories

Simulation

and

size

x,m

bulls

assuming

the

.

x

male

(1981).

t i m e of

* N

simulated

1950

the

of m a l e s aged x y e a r s of a d u l t

P

idle

in

(P*)

The

s u r v i v a l were

assumed t o remain c o n s t a n t

s u r v i v a l r a t e s of

2 years) v a r i e d annually

adult

and

are

juveniles

contained

over (birth

in Table

5-2

the to and

34

Figure

5-1.

T h e s e v a l u e s were

numbers of pups born (Appendix

annual

juvenile

and

juvenile

been a common

ranging

females from

Hartley,

1.05

estimates

of

according to

age

f o r males o n l y .

It

of s e a l s k i l l e d

1981; that

conditions

during

has

no

been the

to

exceeds

that

model

of

that

1961,

run

juvenile

better

an

both

survival

York on

the

environmental However

assumption. equal

of

factor

1973;

been b a s e d

than m a l e s .

such

with

survival

1964,

T h i s has

experience

to support

the

males by a c o n s t a n t

pelagic l i f e

was

(1.1)

assume

1981).

females their

r a t e s are

(see Chapman

Eberhardt,

evidence

differentiated

survival

practice

t o 1.10

hypothesis

reason

counts

using

B).

The has

and

calculated

(1.0)

there

For

this

and

sex

r a t e s f o r ages 0 t o 2

years.

5.3_

Computer g e n e r a t e d field

estimates

results

of t h r e e

Curves

1

and

pup

Results

production

of S a i n t P a u l

reproduced

are

the

summarized

female

female male 3.

harvest and

with a

female

Overlayed

population

juvenile on

the

survival simulation

that

The

in Figure

5-2.

survival

values

of

production

Pup

1980.

and

1.00

respectively.

the

harvest

juvenile

1.10

to

with

commercial

assumed m a l e - f e m a l e d i f f e r e n t i a l and

compared

f o r t h e p e r i o d 1950

s i m u l a t i o n runs 2

is

i n t h e a b s e n c e of a

experienced

equivalent

rates i s represented results,

are

the

by

curve actual

Table

5-2. E s t i m a t e s of male j u v e n i l e f u r s e a l s u r v i v a l f o r S a i n t P a u l I s l a n d used t o s i m u l a t e pups born and b u l l counts.

Year Class

0-24 Months

1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1 970 1 971 1972 1973 1974 1 975 1 976 1977 1978

0.431 0.424 0.572 0.347 0.256 0.291 0. 120 0.359 0.521 0.454 0.297 0.349 0.414 0.487 0.502 0.424 0.380 0.434 0.507 0.436 0.558 0.322 0.329 0.347 0.323 0.275 0.271 0.295 0.298

Source: Appendix B.

36

1.0 0.3 CE

>

0.8

' ' 0.7

0.0

1

1950

J355

19G0

TERR

Figure

13G5

1970

1375

1380

CLASS

5-1. Male j u v e n i l e s u r v i v a l from b i r t h Data a r e t a k e n from Appendix B.

t o age

2 years.

37

estimates

The the

of pups b o r n

results

best

confirmed generated (X^)

at

sum

The

relative

deviations

between the

the

estimates

1980

TZ

t=l950 1980

IT

t=l950

(X^)

of

to f i e l d

and

5-7),

pup

production

of

the

and

the

three 5-6),

sum

5-8)

of

is

computer

(equation

(equation

production

1 is

This

the

each

deviations

G-test pup

estimates.

observed

for

(equation or

that curve

between

the

squared

simulated

(Table

suggest

difference

changes

minimized field

sum

Island.

5-2

t=1950,1951,...,1980

runs.

logarithmic

the

production

times

of

in Figure

simulation results

comparing

pup

simulation the

contained

f i t of by

upon S a i n t P a u l

of

are

a l l

1

and

curve

5-3).

2 REM * PURPOSE: TO SIMULATE ST. PAUL * * REM * HERD DYNAMICS FROM 1950 REM * (TI=0) UNTIL 1980 ( T I = 3 0 ) . * * REM * PROGRAM: 1. READS DATA REM * 2. SIMULATES SY YRS. * * REM * 3. SAVES RESULTS IN REM * SPECIFIED NUMERIC * * REM * DATA F I L E * REM * SIMULATION MODEL: * REM * ALL INPUT PARAMETRS * REM * (ADULT SRVL & FEC) ARE REM * KEPT CONSTANT THROUGHOUT * REM * SIMULATION. ONLY JUVENILE * * * REM SRVL AND SEX RATIO AT * REM * BIRTH ARE CHANGING. * REM * RESULTS: CAN BE VIEWED BY * REM * RUNNING 1) POKE & * REM * 2) GRAPH. * REM * DATA INPUT: REQUIRES THE USE REM * OF THREE NUMERIC DATA F I L E S * * REM * 1. LAND FEMALE KILL.NUM REM * 2. PELAGIC FEMALE KILL.NUM * * 3. MALE KILL.NUM REM * * REM * ANDREW TRITES * REM * SEPT. 1 , 1984. IARE. REM ********************************* REM REM REM INPUT "ENTER NUMBER OF YEARS TO BE SIMULATED: ";SY FOR TI = 0 TO SY IF TI > 0 THEN GO TO 1540 DIM N ( 2 7 , 2 ) , S ( 2 7 , 2 ) , B ( 2 7 ) , J S ( 3 0 ) , L F K ( 3 0 , 2 7 ) , P F K ( 3 0 , 2 7 ) , RMK(27),Z(9,SY),BULLS(30) REM

75

370 380 390 400 410 420 4 30 440 450 460 470 480 4 90 500 510 520 530 540 550 560 57 0 580 590 610 620 630 640 650 660 67 0 680 690 700 710 720 730 7 40 750 760 770 780 790 800 81 0 830 840 850 860 870 880 890 900 910 920

REM REM REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM R E A D I N D A T A REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM REM REM I N I T I A L NUMBERS REM REM FOR J = 1 TO 2 : REM 1=FEMALES 2=MALES FOR I = 0 TO 26 : REM AGES READ N ( I , J ) : REM I N I T I A L NUMBERS NEXT:NEXT REM REM LAND FEMALE K I L L (NUMBERS) REM REM D$=CHR$(4) FS$="LAND FEMALE KILL.NUM" PRINT D$ ; "OPEN" ; FS$ PRINT D$ ; "READ" ; FS$ INPUT NR INPUT VEC: REM COLUMN INPUT TUP: REM ROW INPUT LU: REM LABELS USED IF LU= 1 THEN DIM L$(VEC) FOR I = 1 TO VEC INPUT L $ ( I ) : NEXT REM DIM LFK(VEC+5,TUP) FOR J = 1 TO TUP FOR I = 1 TO VEC INPUT L F K ( I + 5 , J ) : REM (YEAR,AGE) NEXT:NEXT PRINT D$; "CLOSE"; FS$ REM REM PELAGIC FEMALE K I L L (NUMBERS) REM REM D$=CHR$(4) FS$="PELAGIC FEMALE KILL.NUM" PRINT D$; "OPEN"; FS$ PRINT D$; "READ"; FS$ INPUT NR INPUT VEC: REM COLUMN INPUT TUP: REM ROW INPUT LU: REM LABELS USED IF LU = 1 THEN DIM M$(VEC) FOR I = 1 TO VEC

76

930 INPUT M $ ( I ) : NEXT 940 FOR J = 1 TO TUP 950" FOR I = 1 TO VEC 960 INPUT P F K ( I + 7 , J ) : REM(YEAR,AGE) 970 NEXT:NEXT 980 PRINT D$; "CLOSE"; FS$ 1010 REM 1013 REM 1081 REM LAND MALE K I L L (NUMBERS) 1082 REM 1085 D$=CHR$(4) 1086 FS$ = "MALE KILL.NUM" 1087 PRINT D$; "OPEN"; FS$ 1088 PRINT D$; "READ"; FS$ 1089 INPUT NR 1090 INPUT VEC: REM COLUMNS 1091 INPUT TUP: REM ROW 1092 INPUT LU:. REM LABELS USED 1093 IF LU = 1 THEN DIM V$(VEC) 1094 FOR 1= 1 TO VEC 1095 INPUT L $ ( I ) : NEXT 1096 DIM LMK(TUP,VEC+18) 1097 FOR J = 0 TO TUP-1 1098 FOR I = 1 TO VEC 1099 INPUT L M K ( J , I ) : REM (YEAR,AGE) 1 100 NEXT 1101 LMK(J,1)=0: LMK(J,8)=0: REM REMOVES YEAR AND YEAR K I L L TOTALS 1102 NEXT 1103 PRINT D$; "CLOSE"; FS$ 1105 REM 1106 REM SURVIVAL RATES 1107 REM 1110 REM 1120 FOR J = 1 TO 2 1130 FOR I = 0 TO 26 1140 READ S ( I , J ) : REM AGE S P E C I F I C SURVIVAL RATES 1150 NEXT:NEXT 1155 FOR I = 1 TO 26: S ( I , 2 ) = S ( I , 2 ) * 1.035: NEXT 1160 REM 1170 REM BIRTH RATES 1180 REM 1190 REM 1200 FOR I = -0 TO 26 1210 READ B ( I ) : REM AGE S P E C I F I C BIRTH RATES (FEMALES) 1220 NEXT 1230.REM 1240 REM JUVENILE SURVIVAL 1250 REM 1260 REM 1270 FOR I = 0 TO 28 1280 READ J S ( I ) 1285 J S ( I ) = J S ( I ) / . 8 1290 NEXT 1300 FOR I = 29 TO 30

77

1310 1320 1330 1340 1350 1360 1370

1380

1400

1410 1420 1430

1 440 1 450 1460 1 470 1 480 1 490 1500 1510 1 520 1530 1540 1 550 1560 1570 1 580 1590 1600 1603 1604 1606 1610 1620 1630 1640 1650 1660

JS(I)=.495 NEXT REM REM DATA REM REM DATA 225.50,112.73,90.18,75.75,69.69,65.51,61.58,58.19, 55.28,52.52,49.26,45.51,41.24,36.46,31.28,27.40,21.62, 16.06,11.16,7.00,3.95,1.94,0.80,0.26,0.07,0.01,0: REM I N I T I A L NO. FEMALES (1950) -THOUSANDS DATA 225.50,112.73,88.67,68.98,32.98,11.28,7.69,2.85,2.28 1.82,1.39,1.01,0.71,0.46,0.28,0.15,0.06,0,0,0,0,0,0, 0,0,0,0 : REM I N I T I A L NO. MALES (1950) -THOUSANDS DATA .5, .8,.84,.92,.94,.94,.945,.95,.95,.938,.924,.906,.884, .858,.876,.789,.743,.692,.630,.564,.490,.411,.330,.252, .181,.120,.05 : REM AGE SPECIFIC SURVIVAL RATES FEMALES DATA .5,.80,.80 ,.80 ,.80 ,.80 ,.80,.80,.80,.76,.73,.70,.65, .59,.54,.43,.0,0,0,0,0,0,0,0,0,0,0: REM AGE SPECIFIC SURVIVAL RATES MALES (STPAUL). DATA 0,0,0,0,.04,.37,.70,.80,.85,.87,.88,.88,.88,.87,.84,.81, .77,.71,.63,.56,.47,.37,.26,.11,0,0,0 : REM AGE SPECIFIC BIRTH RATES FEMALES DATA .431,.424,.572,.347,.291,.280,.12,.359,.521,.454,.297, .349,.414,.487,.502,.424,.380,.434,.507,.436,.558,.322, .329,.347,.323,.275,.271,.295,.298 REM JUV. SURVIVAL RATES CALCULATED IN APPENDIX B NL=0: REM I N I T I A L TOTAL POPULATION SIZE LAST YEAR TN=0: REM TOTAL POPULATION S I Z E NB=0: REM NEW BORN PUPS REM REM REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM S I M U L A T I O N REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM SURVIVING SEALS BECOME REM ONE YEAR OLDER REM REM IF TI = 10 GO TO 1606 GO TO 1610 FOR I 1 TO 25: S ( I , 2 ) = S ( I , 2 ) / l . 0 3 5 : NEXT REM FOR J = 1 TO 2 FOR I = 25 TO 1 STEP-1 N(I + 1 , J ) = S ( I , J ) * N ( I , J ) NEXT:NEXT N(1,1)=JS(TI)*N(0,1)

78

1670 1680 1690 1700 1710 1720 1730 1740

N(1,2)=JS(TI)*N(0,2) REM REM MALE/FEMALE HARVEST REM '• REM TMK=0: TFK=0: REM TOTAL (MALE/FEMALE) K I L L FOR I = 0 TO 26 FK=(LFK(TI,I)+PFK(TI,I)*.8)/1000: REM LAND/PELAGIC FEMALE K I L L . 80% OF PELAGIC IS ST.PAUL SEALS (ACTUAL NUMBERS) 1750 MK=LMK(TI,I)/1000: REM LAND MALE K I L L 1760 TFK=TFK+FK: REM TOTAL FEMALE K I L L 1770 TMK=TMK+MK: REM TOTAL MALE K I L L 1780 N ( I , 1 ) = N ( I , 1 ) - F K : REM NO. EACH AGE GROUP SURVIVING HARVEST (FEMALES) 1785 PRINT"AGE "; I ; " "; N ( I , 2 ) ; " "; MK 1790 N(I,2)=N(I,2)-MK 1795 I F N ( I , 2 ) < 0 THEN N ( l , 2 ) = 0 1800 NEXT 1810 REM 1820 REM FEMALES GIVE BIRTH 1830 REM 1840 REM 1850 NB=0: REM NO. BORN 1860 FOR I = 1 TO 26 1870 NB=NB+B(I)*N(I,1) 1880 NEXT 1890 N(0,1)=NB*.50: REM FEMALE PUPS 1900 N(0,2)=NB*.50: REM MALE PUPS 1910 REM 1920 REM TOTAL POPULATION SIZE 1930 REM 1940 REM 1950 TN=0: REM TOTAL NO. 1960 FOR I = 0 TO 26 1970 TN=TN+N(I,1)+N(1,2) 1980 NEXT 1 990 BULLS (TI )=0~ 1991 BULLS(TI)=BULLS(TI)+N(6,2 ) * . 2 1992 B U L L S ( T I ) = B U L L S ( T I ) + N ( 7 , 2 ) * . 5 0 1993 B U L L S ( T I ) = B U L L S ( T I ) + N ( 8 , 2 ) * . 7 5 2000 FOR I = 9 TO 16 2010 B U L L S ( T I ) = B U L L S ( T I ) + N ( I , 2 ) 2020 NEXT 2030 NT(1)=0: NT(2)=0 2040 FOR J = 1 TO 2 2050 FOR I = 0 TO 25 2060 N T ( J ) = N T ( J ) + N ( I , J ) 2070 NEXT I : NEXT J 2080 REM 2090 REM RATE OF POP CHANGE 2100 REM 2110 REM 2120 R= (TN-ND/NL+1

2130 2140 2150 2160 2170 2180 .2190 2200 221 0 2220 2230 2240 2250 2260 2270 2280 2290 2300 2310 2320 2330 2340 2350 2360 2370 2380 2390 2400 241 0 .2420 2430 2440 2450 2460 2470 2480 2490 2500 2510 2520 2530 2540 2550 2560 2570 2580 2590 2600 261 0 2620

NL=TN: REM NL = NO. LAST YEAR REM REM SAVE OUTPUT VARIABLES REM REM Z ( 1 , T I )=TN Z(2,TI )=NB Z(3,TI )=R Z(4,TI )=TFK Z(5,TI )=TMK Z(6,TI )=JS(TI) Z(7,TI )=NT(1) Z(8,TI )=NT(2) Z(9,TI )=BULLS(TI) PRINTTI,R,TN,TFK,TMK,JS(TI),NB,BULLS(TI) PRINT" " NEXT REM REM REM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM S T O R E O U T P U T REM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * REM REM INPUT "NUMERIC MODEL DATA" F I L E NAME= ";FT$ PRINT D$; "OPEN"; FT$ PRINT D$; "WRITE"; FT$ PRINT 10003+8*(TI+1+1) PRINT »g» PRINT TI PRINT n ^ n PRINT "TN" PRINT "NB" PRINT "R" PRINT "TFK" PRINT "TMK" PRINT " J S " PRINT "# FEMALES" PRINT "# MALES" PRINT "BULLS 7+" FOR J = 0 TO TI FOR I = 1 TO 9 PRINT Z (I , J ) NEXT:NEXT PRINT D$; "CLOSE' FT$ END

80

T a b l e A-1.

Age

1956

1 0 2 1 32 2018 •3 4 5470 5 3497 6 2149 7 1599 8 1 248 9 738 10 482 1 1 661 1 2 601 1 3 530 14 455 1 5 398 1 6 313 1 7 231 18 160 '19 1 03 20 57 21 25 22 1 1 23 10 24 0 25 0 26 0 1-26 20888

The number of f e m a l e s h a r v e s t e d on S a i n t P a u l I s l a n d from 1956 t o 1968. The d a t a a r e e x t r a p l o a t e d from York and H a r t l e y ( 1 9 8 1 ) . The T a b l e c o r r e s p o n d s t o t h e computer program d a t a f i l e " l a n d f e m a l e k i l l . n u m " .

1957 0 0 953 4551 9373 4747 3201 2880 2599 1389 1 454 1321 1 1 65 1000 875 688 508 . 352 227 1 25 55 23 23 0 0 0 37509

1958 0 477 9762 6736 2719 2387 649 293 292 430 40 36 32 27 24 19 14 10 6 3 1 1 0 0 0 0 23958

1959 0 215 1769 6379 3098 2414 2847 1 495 913 849 787 715 630 541 474 372 275 1 90 1 23 68 30 1 3 1 2 0 0 0 24209

1960 0 19

258 466 763 478 296 271 222 1 35 73 67 59 50 44 35 " 26 18 1 1 6 3 1 1

0 0 0 3302

1961

1962

0 360 3624 5447 3547 3868 231 5 2183 2408 1 605 1810 1 644 1 450 1245 1090 856 632 438 282 1 56 68 29 29 0 0 0 35086

0 320 3438 6434 4951 2689 231 6 2267 1849 1 328 1751 1 591 1410 1215 1 054 828 612 422 273 1 50 66 28 1 1 0 0 0 35003

81

T a b l e A-1

Age 1 2 3 4 5 6 7 8 9 10 1 1 1 2 1 3 1 4 15 16 17 18 1 9 20 21 22 23 24 25 26 0-26

continued

1 963

1964

1965

0 502 2090 5947 6994 3170 1415 2060 1955 1835 1686 1538 1358 1 1 64 1015 806 597 403 254 1 49 60 30 15 0 0 0 35043

0 298 2506 2672 2756 1619 484 235 223 209 192 175 1 54 1 32 1 15 92 68 46 29 17 7 3 2 0 0 0 12034

0 284 1870 3327 1 167 387 286 29 27 25 23 21 1 9 1 6 1 4 1 2 9 6 4 2 1 1 0 0 0 0 7530

1966 0 3 29 103 50 39 45 24 1 5 1 4 1 3 1 1 1 0 9 8 7 6 3 1 1 0 0 0 0 0 0 391

1967 ' 0 18 571 1 109 1204 955 459 437 416 390 361 328 288 248 219 171 128 87 55 29 15 1 4 0 0 0 0 7502

1968 0 38 744 2572 1749 1 453 993 828 658 478 1 92 174 1 54 1 32 1 16 91 68 46 29 1 6 7 6 0 0 0 0 1 0544 .

1956-68 0 2666 29632 51213 41868 26355 16905 14250 1231 5 9169 9043 8222 7259 6234 5446 4290 3174 2181 1 397 779 338 160 103 0 0 0 252999

T a b l e A-2.

The number of f e m a l e s k i l l e d p e l a g i c a l l y from 1958 t o 1974. The d a t a a r e e x t r a p o l a t e d from York and H a r t l e y (1981). Note t h a t 80% o f t h e k i l l i s assumed t o be from S a i n t P a u l I s l a n d . The T a b l e c o r r e s p o n d s t o t h e computer program d a t a f i l e " p e l a g i c female k i l l . n u m " .

Age

1958

1 959

1960

1961

1962

1 963

1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1-26

150 29 75 73 95 121 1 28 118 97 105 130 147 121 101 78 62 39 25 16 4 2 1 0 0 0 0 1717

89 64 56 120 141 160 193 208 143 1 19 112 88 66 78 94 74 40 30 18 6 8 5 1 1 0 0 1914

27 56 68 52 85 79 1 12 1 49 179 159 1 49 1 16 1 28 11 4 73 55 49 25 20 8 7 0 1 1 0 0 1712

121 52 1 18 1 38 81 79 11 2 1 33 136 131 95 83 86 75 74 60 28 27 12 8 3 0 1 1 0 0 1654

38 38 11 3 183 1 65 90 1 18 1 33 120 1 30 11 1 111 75 77 64 55 49 29 17 1 2 4 3 0 1 0~ 0 1736

7 25 61 131 181 1 1 1 87 98 69 88 107 11 9 90 74 90 59 32 17 7 1 3 5 1 3 0 0 0 1475

T a b l e A-2

Age 1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 1-26

1964 27 44 79 84 83 93 74 42 34 51 43 53 34 39 41 23 21 20 7 10 0 0 1 0 0 0 903

continued

1 965 12 10 56 78 26 44 26 33 18 1 3 20 1 6 8 10 14 12 10 8 2 2 1 •0 1 0 0 0 420

1966 58 13 45 92 86 46 56 58 23 21 28 17 16 19 1 6 7 6 1 3 3 1 0 0 0 0 0 615

1967 10 12 28 18 19 27 17 12 19 13 6 6 4 1 3 7 2 0 0 1 0 1 0 0 0 0 206

1968 80 27 81 168 71 87 88 58 62 65 51 49 27 32 32 34 23 1 5 12 8 5 4 1 0 0 0 1 080

1969 55 23 55 66 56 38 38 31 1 1 31 34 34 1 4 1 0 5 8 8 4 6 4 1 0 0 1 0 0 533

T a b l e A-2

Age 1 2 .3 4 5 6 7 8 9 10 1 1 1 2 13 1 4 1 5 1 6 1 7 18 19 20 21 22 23 24 25 26 1-26

1970 15 21 69 71 44 56 28 29 30 22 18 18 22 4 7 3 1 8 3 1 1 0 0 0 0 0 471

continued.

1971 30 16 52 81 44 47 47 29 21 27 17 29 1 5 6 7 4 5 6 2 2 1 1 0 0 0 0 489

1972

1973

16 12 23 24 47 32 29 25 16 20 20 14 8 8 7 6 5 2 2 1 0 2 0 0 0 0 319

2 10 36 42 47 68 71 57 63 49 45 43 33 22 22 18 7 7 2 2 0 0 0 0 0 0 646

1974 1 6 1 6 34 34 32 45 44 39 34 21 1 4 1 2 1 5 9 1 1 5 1 3 1 0 0 2 0 0 0 379

1963-74 738 458 1031 1455 1305 1210 1269 1257 1080 1078 1007 957 759 685 636 498 330 225 1 32 86 39 18 1 1 5 0 0 1 6269

T a b l e A-3

Year 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1 964 1965 1966 1967 1968 1969 1970 1971 1 972 1973 1974 1975 1976 1977 1978 1979

The numbers of males h a r v e s t e d on S a i n t I s l a n d :from 1950 t o 1979. The d a t a a r e from L a n d e r (1980a). The c o r r e s p o n d i n g f i l e i n t h e computer model i s "male k i l l

Age 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Age 2 957 1012 885 1 384 1735 839 2859 1015 885 2590 1 977 2820 1619 1098 2539 1264 3143 2200 1673 2640 1725 323 916 577 1025 1642 893 1783 1479 2051

Age 3

Age 4

30743 31860 32610 40656 32350 30773 38290 23473 27863 10671 24283 48458 26456 14310 22468 19009 25535 26991 18706 17826 221 76 12888 15204 16337 14652 15186 13397 16476 1 3752 15245

16103 16689 17082 12216 15365 18083 31 448 8855 5599 1 0555 2762 1 5344 1 4149 14184 1 0533 12046 12156 1 1785 1 3279 1 0565 1 1 548 12503 14932 10800 1 5533 10768 8050 9421 8955 7918

Age 5 956 1011 1035 740 790 332 3057 675 54 554 11 5 532 773 1 587 1764 1240 1270 1287 1542 1 469 731 1338 2185 721 1631 1402 722 707 598 470

Paul taken data .num".

Age 6 0 0 0 0 , 0 0 0 0 0 9 0 0 0 68 1 22 73 0 96 92 121 17 1 90 53 22 1 35 95 19 9 45 18

Total 48799 50572 51612 54996 50240 5061 7 75654 34018 34401 24379 291 37 67154 42997 31247 37426 33632 421 04 42359 35292 32621 361 97 27242 33290 28457 32976 29093 23081 28396 24829 25702

86

APPENDIX B

Fur

seal

calculated

ESTIMATING THE

juvenile

for

the

survival male

SURVIVAL OF

rates (birth

The

1950

of a n n u a l

idle

1980

and

pups. July

on

bulls

Saint in

defend

Paul

in

The

of 80%

3 and

males

data

is

y e a r s of

The

cover

specific

Saint

be

population the

kills,

e s t i m a t e s of

period

counts

live

and

of

dead

harvested i n

George

harvest

or more f e m a l e s

with from

of t h e P r i b i l o f

no

herd

and

females.

Saint

Paul

breeds

of t h e d a t a has

was

as

idle

The Island

( T a b l e B-1

most where

and

B-

been p r e v i o u s l y r e v i e w e d

5.

born

t h r e e s e t s of p u b l i s h e d

on

Saint

three estimation procedures reconstruct

and

The

territory

There are c u r r e n t l y juvenile

age

c o n t a i n i n g one

reliability

Chapters

counts

data

can

Mature males a r e d e f i n e d as harem b u l l s i f

territory

approximately

and

available

Island.

1972.

set

2)

m a l e s aged 2 t o 5 a r e c o m m e r c i a l l y

i f they h o l d a

complete

2).

consist

harem b u l l s ,

Subadult

stopped they

and

t o age

component of t h e P r i b i l o f

(Callorhinus ursinus)• to

JUVENILES

t h e number of

are

Paul

Island

similar

estimates

(Table B-3).

in that

each

j u v e n i l e s which s u r v i v e d the

for The

tries

to

first

few

life.

first

set

of

estimates

(1961,1964,1973) u s i n g t h e t o t a l t h e number of pups b o r n

kill

is

derived

by

Chapman

of m a l e s p l u s e s t i m a t e s

w i t h i n the p a r t i c u l a r

year

class.

of

87

Table

B-1..

E s t i m a t e s of l i v e pups (number b o r n ) , dead pups ( s u b s e q u e n t l y c o u n t e d on l a n d ) , and age s p e c i f i c male k i l l by y e a r c l a s s on S a i n t P a u l I s l a n d .

Year c l ass

Pups Born

1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 198 1 1982 1983

451.000 447.000 4 38,000 44 5.000 450.000 461.000 453,000 4 20.000 387.000 335,000 320,000 342 , 336 277.078 262.498 283.922 253,768 298.931 291.000 235.000' 232.670 230,485 305.000" 269,000 236,420* 266.OOO 278.261 298.000 235,210* 247,132* 245.932 199.046* 179.444* 210.886* 165.902*

Dead Pups 53.420 70,663 40,800? 78,212 96,178 75.544 98,707 61,662 31.187 39,964 62.828 57,867 45.268 32.598 21.572 39,124 21,414 14,076 25,298 13,279 20,581 46,439 22,649 2 1 ,493? 13,053? 20.625 23,676 14,083 8,073 6,444 . 7,859* 6,798* 7,301* 5,997*

2 855* 1 ,384* 1 ,735* 839* 2,859 1 ,015 885 2,590 1 ,977 2,820 1,619 1 ,098 2,539 1 ,264 3. 143 2.200 1 .673 2,640 1 .725 323 916 577 1 ,025 1 ,642 893 1 ,783 1 ,479 2,051 2,180* 2,284* 1,930* 3,399*

Sources: Lander. 1980 Lander. 1979 Smith and P o l a c h e c k , 1978 '* Y o r k , p e r s o n a l c o m m u n i c a t i o n •

3

Age when k i 1 1 e d 4 5

40.656* 32,350* 30,773* 38.290 23,473 27.863 10,671 24.283 48.458 26,456 14,310 22.468 19.009 25.535 26.991 18,706 17,826 22. 176 12,888 15,024 16.337 14.652 15,186 13,397 16,476 13.752 15,245 13,157* 14.224* 15,123* 15,607*

15.365* 18.C83* 31 ,448 8.855 5, 599 10.555 2.762 15.344 14,149 14.184 10,533 12,046 12,156 1 1.785 13.279 10,565 11,548 12.503 14.932 10.800 15,533 10,768 8,050 9,421 8.955 7,918 8,183* 6,7 14* 7.016.* 6,679*

332* 3.057 675 54 554 1 15 532 733 1 ,587 1 ,764 1 .240 1 ,270 1 .287 1 ,542 1 ,469 731 1 .338 2, 185 721 1 ,631 1 ,402 722 707 598 470 725* 651* 517* 4 15*

6 0 0 0 9 10 0 0 68 122 73 0 96 92 12 1 17 190 53 22 135 95 19 • 9 45 18

88

T a b l e B-2.

Counts

Year 1950 1951 1 952 1 953 1 954 1955 #956 1957 1958 1 959 1960 1 961 1 962 1 963 1964 1 965 1966 1 967 1968 1 969 1970 1 971 1972 1973 1974 1 975 1976 1 977 1 978 1979 1980

o f harem and i d l e

Harem 9 292 9 434 9 318 9 848 9 906 9 034 9 384 9 582 9 970 1 0 003 10 247 1 1 1 63 10 332 9 212 9 085 8 553 7 925 7, 230* 6 176* 5 467 4 945 4 ,200* 3, 738* 4 ,906* 4 563* 5 018 5, 324 6, 457 6, 496 6, 242 5, 490#

Idle 3 102 3 581 4 717 5 912 6 847 8 650 9 016 10 060 9 510 1 1 485 1 0 407 1 1 791 9 109 7 650 7 095 5 616 5 931 4, 439* 3 100* 2 208 1 666 1 900* 2, 384* 2, 550* 1 782* 3 535 4, 041 3, 845 3, 908 4, 457 4, 248#

Sources: L a n d e r , 1980 * L a n d e r and K a j i m u r a , 1975 # York, p e r s o n a l communication

bulls

on S a i n t

Paul

Island.

89

T a b l e B-3.

Year class 1 950 1 951 1 952 1 953 1 954 1955 1 956 1957 1958 1 959 1 960 1961 1962 1 963 1964 1965 1 966 1967 1 968 1969 1 970 1971 1 972 1973 1 974 1 975 1976 1977

C a l c u l a t e d male j u v e n i l e f u r s e a l s u r v i v a l on S a i n t Paul I s l a n d . The Chapman and t h e S m i t h and P o l a c h e c k e s t i m a t e s a r e c a l c u l a t e d from b i r t h t o age 3. Their v a l u e s a r e r e d u c e d t o b i r t h t o age 2, f o r t h e p u r p o s e of c o m p a r i s o n w i t h t h e L a n d e r e s t i m a t e s , by a s s u m i n g a c o n s t a n t s u r v i v a l a t age 3 o f 0.80.

Chapman b i r t h - age 2

Smith & Polacheck b i r t h - age 2

0.444 0.430 0.515 0.398 0.243 0.288 0.110 0.346 0.525 0.450 0.334 0.385 0.377 0.445 0.454 0.374

0.274 0.315 0.380 0.394 0.301 0.274 0.348 0.323 0.296 0.371 0.214

Lander b i r t h - age 2 0.364 0.360 0.414 0.320 ' 0.237 0.274 0.139 0.314 0.451 0.383 0.281 0.327 0.366 0.329 0.385 0.375 0.355 0.416 0.284 0.293 0.323 0.293 0.323 0.311 0.278 0.276 0.296

Sources:. Chapman, 1973 S m i t h and P o l a c h e c k , L a n d e r , 1979

1978

90

The

s e c o n d s e t by S m i t h and P o l a c h e c k (1978)

Chapman

procedure

by

a s s u m p t i o n s about a d u l t harem

and

idle

incorporating survival,

bulls.

and

Polacheck,

Polacheck birth 2.

1981).

total

Both

kill

the

to

age 3 even

third

parameter

by L a n d e r With

1981). wide

survival

potential Fur

pup

use,

such

(Eberhardt, reproduction heavy

as

in

1981),

survival

pinniped

herd

size

from

b e g i n s a t age

original

Chapman

for

t o age

and

and j u v e n i l e

of p o p u l a t i o n

lower

how

status

increases

fur seals

(Eberhardt,

ages

possible

( F o w l e r , 1982).

for

dynamics

given

sustainable

changing

the s u r v i v a l

kill

males.

e s t i m a t e s have been

identifying

mortality

account

can

young

upper

maximum

interpreting

shown

life

using

population

predicting

have

y e a r s of

harvest

of subadult

( Y o r k , 1983), and

(1977)

of

e s t i m a t e s and age s p e c i f i c

of

juvenile

net entanglement

Siniff

(Smith

estimates (birth

i s a key component

indicator

seal

born

bound

and the S m i t h and

the

survival

(1975,1979)

d a t a he e s t i m a t e d the s u r v i v a l

and a

pups

of

was n o t known.

bounds.

Juvenile

of

counts

lower

survival

though a s u b s t a n t i a l

s e t of j u v e n i l e

i s calculated

by

the

the

kills,

only

Chapman

T h i s may be b e c a u s e a t t h e t i m e

The

specific

using

published

s e t s of e s t i m a t e s c a l c u l a t e d

work, t h e age of k i l l

2)

and by

They

e s t i m a t e s o b t a i n e d by d i v i d i n g

age

improved

of

yield first

years

E b e r h a r d t and

o v e r the f i r s t and

(Callorhinus

of

decreases ursinus),

two in harp

91

seals and

(Paqophilus Weddel

seals

r a t e s must be estimates survival

qroenlandicus),

high

of

to ensure

juvenile

s u r v i v a l has

wide

use

dynamics. is

to

all

derived

olds

by

that

the

three

of

the

the

is

the

to

killed

of

and

estimates

Estimating

of

by

the

by

age

5.

the

juvenile

two

fur

be.

Survival

juvenile survival

The

age

population

weaknesses of

Juvenile

(No). by

despite

Its

i f need

number of

or

number of

rates

three

i=2,3,4,5)

subadult The

animals

basic

escapement and

and

the

the some

from the

difference

whether

year

juveniles

back c a l c u l a t i o n , u s i n g

i (Ki;

of

review.

male

the

s u r v i v a l of until

following

estimators,

pups b o r n

treatment

juvenile

examined

in interpreting

estimate

reconstructed

j u v e n i l e stage

of

fur seal estimates

strengths

division

concerning

methods i s the

prompted

s e t s of

number of

present

confirmed

critically

importance

Methods of

number of male s e a l s assumption

been

improve the

the

from the

survive

published

have been used

D e t a i l s of

For

their

to

is

survival

given

importance

demography

hispida),

Juvenile

growth

The

the

never

discuss

(Phoca

5.

of

has

s u r v i v a l and

B.J_

are

and

This

procedures that seal

survival.

in Chapter

reliability

purpose

population

to ensuing p o p u l a t i o n

The

their

seals

(Leptonychotes w e d d e l l i ) .

adult

model d e v e l o p e d

ringed

in

end the

estimated

92

number s u r v i v i n g

i s an u p p e r , l o w e r ,

The s i m p l e s t e s t i m a t e (1961,1964,1973), olds

kill

first

S

and a d d i n g three years

=

the

percent

a t age 2 by summing t h e t o t a l

year

of l i f e

escapement

including

harem S

age

(E)

(H) and i d l e

survival into

5

(I) b u l l

.

5

slightly

Chapman

rates

calculation

( S i ; i=2,3,4,5) and reserve

using

/ ( S S ) + E / ( S S S )} / NO 34 5 3 4 5

(B-2)

counts.

+K

(B-1)

season.

the

the

over

from

i s s e t a t 40% b u t v a r i e s

(1978) m o d i f y

(E )

={SK +K +K/S 2 2 3 4 3

0,3

Survival

i s thus e s t i m a t e d

specific

escapement

Chapman year

a measure of escapement.

Smith and P o l a c h e c k

determining

by

minimum number of t h r e e

d e p e n d i n g upon the l e n g t h of t h e h a r v e s t

by

survival,

{ K + K + K + K + E ( K + K + K + K ) } / N o 2 3 4 5 2 3 4 5

0,3 The

juvenile

determines

i n the absence of a k i l l

class the

of

or mean v a l u e .

breeding Thus

where E

= {(H 5

The to

+ I ) - S (H +1 )} t a t-1 t-1

t

difference year

class

determines

between t h e t o t a l

t and t h e number

escapement.

(B-3)

number of b u l l s

surviving

Adult

.

from

survival

corresponding

previous

cohorts

(Sa) i s assumed

t o be

constant.

Lander

(1975,1979) c o m b i n e s

male

kill

records

with

pup

93

estimates and

to

determine

subadults (S).

approach

the s u r v i v a l

Given

i s to i d e n t i f y

parameter

Lander

p r o c e d u r e s and method,

survival

f o r the

estimator

lower e x t r e m e s

observed

is

such

to

place

'0,2

l o w e r and

c

the

of

basic

survival

kill.

Best

limits.

intuitive The

upper

(S* ^ )

of t h e t h r e e

first

step

bounds upon

in

juvenile

that -

u

i s the l e a s t

male these

r e q u i r e s more e x p l a n a t i o n .

* S

and

e s t i m a t e s a r e t a k e n t o be w i t h i n

The

his

t h e known numbers a t b i r t h ,

t h e upper

r a t e s which c o u l d a c c o u n t

r a t e s of j u v e n i l e s

= { K + K S 2 3

1 +KS 4

2 - 3 + K S } / N o 5

+ K S 4

+

(B~4)

and * Sj.

-1 =

{K

0,2 Lander

considers

estimate error S*

+ K S 2 3

t h e mean o f t h e s e

of j u v e n i l e

survival.

in using a point depends

upon t h e

four year o l d s exceeds

The

used

to

fix

limit

is arbitrarily

bound

i s written

annual

survival

This

limits

to

The

that

. be

i s presumably

important assumption

(B-5)

a

good

because upper

the

limit

exploitation

of

50%.

upper

and

lower p a r a m e t e r

subadult s u r v i v a l . set at u n i t y

as a f u n c t i o n

rates

two

estimate i s minimized.

p r o c e s s of s e t t i n g

also

2 3 (K + K )S } / No 4 5

i n terms

of of

(Su =

In t h i s 1.0)

limits

c a s e the

while

juvenile

survival.

average

monthly

the

is

upper lower

Defining mortalities

94

clarifies

the

Fur

c a l c u l a t i o n of

seal

mortality

from

juvenile

(birth

Average

monthly m o r t a l i t y

is

- age

e x p r e s s e d as

a

S^.

2)

and

1

birth

subadult

o v e r the

function

of

*

t o age

5 i s broken

(ages

first

juvenile

3-5)

24

into

a

component.

months o f

s u r v i v a l S*

life

(M*)

where

*

M =

(-In

S

) / 24

(B-6)

0,2 Subadult monthly m o r t a l i t y ages 3,

4,

and

insignificant

5

and

natural

(M) is

i s assumed t o calculated

mortality

remain c o n s t a n t

for

during

the

11

months

period

for

given

of

land

harvest. M = Combining value

(-In

j u v e n i l e and

from b i r t h

S)

/

11

produces

an

average

5,

T

* =

(B-7)

subadult m o r t a l i t y

t o age

M

.

(-In

3

S

S

) / 57

(B-8)

0,2 which

i s r e l a t e d to the

previous

* M

s t a g e s by

the

assumption

that

T >=

M

>=

M

(B-9)

0,2 It

i s from t h i s r e l a t i o n s h i p t h a t The

subadult

left

hand

side

s u r v i v a l w h i c h can

male k i l l .

If

of

S

L

may

equation

account

be B-9

f o r the

determined. sets

a

lower

observed

limit

pattern

on of

95

*

T

M

= M

(B-10)

0,2 then

* (-In

Substituting

S

in

U

)/24

equations

be

equations

for juvenile

will

S*

have t h e

juvenile

ultimate effect

than

limits,

kill

produce

a ratio

of

year year

olds after olds

sufficient must and

figures

four year

the

kill

account

for

calculate

subadult

of

.+

K

4

)S 5

in substituting

the

use

In t h i s

regard,

S^_ w i l l

L

appropriately Lander

is

one)

to

low

and

estimate

of

(previously set to

u

be

a final

and

the upper and

survival

limits

o l d seals before

too

year. kill

tight

limits

on

i s t o say

t h r e e and

four year

(S) s u c h

may

kill

and

the

subadult

be

Three

of the

This

lower

the

90%

-1 {[(K

S ,

high.

about

survival

unknown,

must

of p r o d u c i n g

numbers t o p r o v i d e

estimates

l e a v e s one

the p r e v i o u s

have been p r e s e n t . lower

B-5

estimated

i s too

(B-11 )

L

one

t a k i n g the mean of

survival

)/57

0,2

rates.

Lander

which

3 S

Note t h a t

i n s t e a d of S

u

The

survival

Rather

and

survival,

survival

in using S

determine

B-4

solved numerically.

subadult

incorrect

* S,

(-In

0,2

which can

bounded

=

are

used

to

to

three

and

four

taken

in

numbers

that

t h a t t h e mean of

upper

o l d s may

be

used

to

that -1

] + [(K U

+ K 4

)S 5

+ K L

]} / 2 4 (B-12)

S -1 {[(K

+ K 4

)S 5 U

-2 ] + [(K

+ K 4

)S 5 L

-1 + K S ]} / 2 4L

96

or S s

- 1 - 1 -1 + S + K (K + K ) U L 4 4 5

=

(B-1.3)

t

-1 -2 -1 -1 S + S + K ( K + K ) S U L 4 4 5 L The

upper

and lower

using

this

estimate

these

limits

*

U

s

L

survival

of subadult

bounds c a n be

survival.

Taking

g i v e s t h e b e s t e s t i m a t e of s u b a d u l t

* ^

juvenile

determined

the

mean

survival:

* S U 0,2

+ 0,2

U

(B-14)

=

0,2 Thus

2 the

survival for

Lander

the

observed

j u v e n i l e and s u b a d u l t

bounds on t h e s e p a r a m e t e r s

to

account

o f male pups and t h e s u b s e q u e n t

k i l l of

E v a l u a t i o n o f t h e Methods o f E s t i m a t i n g J u v e n i l e S u r v i v a l

considered

survival as

acceptability

lower

that

estimates parameter

depends l a r g e l y

of r e c r u i t m e n t .

suggests time.

birth

has e s t i m a t e d

cohort.

Juvenile

rate

procedure

r a t e s by p l a c i n g

the p a r t i c u l a r

B.2

of

Recent

upon

of

Chapman

can

bounds. the

escapement has p r o b a b l y

I t i s t h e r e f o r e more r e a s o n a b l e

Their

assumption

work by Smith

of

be

overall a

and P o l a c h e c k

varied to

only

fixed (1978)

c o n s i d e r a b l y over

estimate

escapement

97

based

on

constant of

a c t u a l counts

f u n c t i o n of t o t a l

S m i t h and

The arises and

Polacheck

major

weakness

survival

have been p u b l i s h e d restricted

survival

(Smith

The

a was

numerical

T h i s may

by

to

Polacheck,

analysis

parameterizing

subadult

be

why

exploitation

s u b s e q u e n t male k i l l subadult

survival

All 100,000

Instead

total

and

(S*=0.1,0.2,...1.0) rates. rates

The (Ui;

runs

runs

of

the

used

with

simulated to

juvenile

class

kill

by

simulated

used

a

different

and

subadult

The

technique

known

survival

numbers a t

predict

the

birth

and

juvenile

and

population.

constant

pup

combinations

production of

(S=0.1,0.2,...1.0)

v a r i o u s age

specific

i=2,3,..,5) some of w h i c h a r e

3

lower

s i m u l a t i o n models.

Here f o r example U =0.70 means a h a r v e s t males.

authors

conducted

The

by

year

these

evaluation; therefore, I

100

differed

a

estimates

procedure

r a t e s of t h e

simulation males

were

firm

Lander

using

rates.

no

1981).

manipulations analytic

analysis

Chapman.

producing

dividing

the

a

procedure

to c o n s t r u c t h y p o t h e t i c a l p o p u l a t i o n s

and

old

regard

i t t o be

Polacheck

estimator.

themselves

a simple

assuming

S m i t h and

in accurately

for this

and

In t h i s

the

rates.

algebraic

complicate

kill.

of

bound d e t e r m i n e d

pups born

r a t h e r than

i s s u p e r i o r t o t h a t of

from d i f f i c u l t i e s

adult

have

of b u l l s

of

juvenile survival

exploitation

shown i n T a b l e 70

of

percent

of

B-4. 3

year

T a b l e B-4.

Age Exploited 2 3 4 5

Some h y p o t h e t i c a l e x p l o i t a t i o n r a t e s u s e d i n t h e t h e s i m u l a t i o n model d e v e l o p e d t o t e s t t h e L a n d e r e s t i m a t o r of j u v e n i l e s u r v i v a l .

A 0.05 0.70 0.40 0.20

Simulation B

Run # C

0.05 0.70 0.50 0.20

0.05 0.70 0.90 0.20

D 0.05 0.50 0.70 0.20

99

A typical estimator 0.20

incorporated

(run

Lander S.

simulation

#D, T a b l e

e x h i b i t i n g the behaviour

e x p l o i t a t i o n r a t e s o f 0.05, B-4).

(1975) t o i l l u s t r a t e Error

in

difference

model

between

the small

prediction

estimate

The and

error isoclines

zero

error

given

set

of

by

vectors

p a r a m e t e r s and t h e i r There set

is

a unique

as

percent

and g r a p h i c a l l y

rates

represented

by

a given

set

of

of S

exploitation

c o n t a i n i n g no e r r o r .

F o r any

rates

the

selects

fixed

B-2)

Lander

line.

indicating

corresponding line

recorded

S* and

i n d i c a t e s unique combinations

from t h i s

(Figure

in calculating

of-S*

survival

parameter estimates

was

u s e d by

(Figure B-1).

isocline

p r o d u c e an e s t i m a t e

bias

0.70,

and a c t u a l j u v e n i l e s u r v i v a l

S* w h i c h when a s s o c i a t e d w i t h

rates,

0.50,

These were t h e same v a l u e s

([actual-estimate]/actual*100%) 10 p e r c e n t

of t h e L a n d e r

estimate

This the

estimates

of e s t i m a t e s

is

illustrated

true

population

(arrow

corresponding

head).

t o any g i v e n

o f t e s t e d e x p l o i t a t i o n r a t e s , U -U . 2 5 The

Lander

combinations Whether t h e Pribilof

estimator,

of

exploitation

method

Island

r e l a t i o n s h i p between experiencing a t p r e c i s e age

performs

given

will fur

and

produce seal

survival

well

only

population accurate

vital

rates

for

vital

estimates depends

and e x p l o i t a t i o n .

A

some

rates. of

the

upon

the

population

r a t e s o f S* and S would have t o be e x p l o i t e d

specific

rates

in

order

for

the

estimation

100

R e l a t i v e e r r o r i n p r e d i c t i n g the j u v e n i l e s u r v i v a l r a t e of h y p o t h e t i c a l p o p u l a t i o n s e x p l o i t e d a t t h e age s p e c i f i c r a t e s of 0.02, 0.50, 0.70, 0.20 f o r ages 2 t o 5 u s i n g the Lander e s t i m a t o r . E r r o r was c a l c u l a t e d as [true-estimate]/[true]*!00%.

101

Figure

B-2.

P r e d i c t i o n s f o r the j u v e n i l e and s u b a d u l t s u r v i v a l r a t e s of h y p o t h e t i c a l p o p u l a t i o n s e x p l o i t e d a t the age s p e c i f i c r a t e s of 0.05, 0.50, 0.70, 0.20 f o r ages 2 t o 5 u s i n g the L a n d e r e s t i m a t o r . . Vector o r i g i n s i n d i c a t e t r u e p a r a m e t e r v a l u e s ( t a i l ) and p o i n t t o e s t i m a t e d s u r v i v a l r a t e s (arrow h e a d ) .

102

technique

to

isoclines

examined

dependence validity

produce

these

doubt

limit

excess

of 0.60

algebraic

upon

for

incorrect

two

is

populations

from t h i s juvenile

from a l i n e

rates.

It

reasonable restrictive. predicts

i s important

upper

high

and

Within

this

schedule

to produce

in

calculating

survival

sets

of

does

parameter

exploitation

that the area

survival

estimates

with

I t i s thus estimates

t o be " i n t h e r i g h t subadult

same

procedure

rather selects

unique

associated

f o r small harvests.

appear

The

shape o f t h e lower

the Lander

but

by

bounds as

bounded by is

quite

region the Lander e s t i m a t o r g e n e r a l l y

survival

which

that

from

estimates.

to recognize

lower

survival

of b e s t

survival

determined

-a>-b.

the q u a d r a t i c

study

rates in

arises

survival

the

The e r r o r i s a n a l a g o u s t o

permitting

for

bound and u l t i m a t e l y t h e l i n e

estimate

B—11.

exceed

juvenile

inconsistency

casts

procedure.

bound

of upper and lower

erroneously

bounds

the Lander

experiencing

i n equation

the

question.

survival

This

obvious

putting

estimate

of

a l l zero

no

thereby

into

subadult

responsible

' I conclude

suggest

factors,

validity

manipulation

symbols

equation

the

(Figure B-3).

a s s u m i n g a>b, then

values

analysis

of t h e upper and lower

o f t h e lower

upper

not

Unfortunately

of the e s t i m a t i o n procedure

Predictions

the

error.

in' this

between

Examination further

zero

survival

ball

a large k i l l

and low

p o s s i b l e f o r the

from t h e L a n d e r park",

kill

procedure

d e s p i t e the e r r o r

r a t e s and t h e i n c o r r e c t

use

of

103

O

1

i

0.0

Figure

0.1

n

0.2

i

1

0.3

0.4

n

0.5

r

0.6

1——I—:—i

0.7

JUVENILE SURVIVAL

0.8

0.9

S*

1

1.0

B-3. Upper and lower e s t i m a t e s f o r the j u v e n i l e and s u b a d u l t s u r v i v a l r a t e s of h y p o t h e t i c a l p o p u l a t i o n s e x p l o i t e d a t the age s p e c i f i c r a t e s of 0.05, 0.50, 0.70, 0.20 f o r ages 2 t o 5 u s i n g the L a n d e r e s t i m a t o r . Vector o r i g i n s i n d i c a t e t r u e parameter v a l u e s (tail) and p o i n t t o e s t i m a t e d s u r v i v a l r a t e s (arrow h e a d ) . A l l upper e s t i m a t e s f a l l on the l i n e [ s * , 1 . 0 ] .

104

parameter

In

bounds.

summary,

contained

the

in Table

represent

the

estimates

B-3

are

Saint

The

Paul

values

contains

some l o g i c a l

which

various

estimators.

The

establishing

sound

assumptions

two

years

are Using

of

do

not

by

Eberhardt

survival

adequately

population.

Smith

juvenile

components

process

with

The

Chapman

(1981) must

and

Polacheck

refined.

The

be

represent

Lander

method

survival

of

the

of b u i l d i n g

upper and

lower

be

r e g a r d t o the

kill

can

be

obtained

previously

a new

estimator

juvenile

refined

Survival

by

discussed begins

survival

and

by

bounds.

introducing

process

by

various

dynamics of

the

population.

survival of

from

the method of

of

life.

determined

numbers

juvenile

errors.

range of e s t i m a t e s may

The

and

seal

be

of

R e v i s e d Methods of E s t i m a t i n g J u v e n i l e

modifying

seal

of

should

Improved e s t i m a t e s

fur

fur

estimates

minimal

The

inaccurate

which have s i n c e been u s e d

discarded.

B.3_

published estimates

of

seals

juveniles

(S*)

i s determined

Upper and

lower

juvenile

the

numbers

Lander at

age

of

2

are

the

survival

subadult

(1975,1979)

over

males

maximal

estimated

first bounds

killed.

and through

minimal back

105

calculations.

The

lower

limit

assumes

harvest

t h e upper

limit

i s constrained

that

while

at least

present

50% of t h e 4

year

management p o l i c i e s -1

S* ={K +KS 0,2 2 3

males

( L a n d e r , 1975). -2

+KS 4

L

old

no

seals by

escaped the

are

the

assumption

killed

under

Thus

-3 +KS 5

}/N0

(B-15)

and -1 S* = {K + K S 0,2 2 3

-2 + 2K

the

e x a c t range

assumptions

The

safest

subadult

} / NO

of j u v e n i l e

survival

limit

is

occurred

to

age

indicate

B-15

and

than

high

B-16

f o r the s u b a d u l t r a t e s ( S ) .

(S=1.0).

be b a s e d upon t h e a s s u m p t i o n 2 i s less

(B-16)

that

f o r subsequent

juvenile

e s t i m a t e s depends upon

o b t a i n e d by a s s u m i n g

may

would

survival

invoked to account

lower

.

4

v

The

S

survival

are rewritten

A reasonable

that upper

annual s u r v i v a l ages. if

to r e f l e c t

maximal bound

from

birth

Thus t h e k i l l

S= ^ S*

.

data

Equations

these assumptions

such

that

S*

= {K 0,2

+ K 2

+ K 3

4

+ K.} 5

/ NO

(B-17)

and S* U

= {K 0,2

The

+ K S* 2 3

juvenile

-0.5 -1 + 2K S* } / NO 4

survival

.

bounds can be t i g h t e n e d

(B-18)

considerably

106

if

more

seal

precise

life

subadult

tables indicate

to

6 is relatively

can

be

substituted

A second

way

survival

harem and

idle

olds. at

The

about age

proportion

next

i s 0.74.

of

life

and

total

bulls

lower

class

the

1980).

Fur

ages

This value

bounded

estimate

f o r numbers of

male w e i g h t p e r surviving of

of

the abundance of two

year

t h a t m a l e s become

estimate

2

B-16.

lower

tables indicate

from

age)

one

juvenile

bulls

and

year

that

to

the

survival

may

t as

-2 + K S 4

L

the

upon a v e r a g e

-1 S* = {K + K S 0,2 2 3

B-15

i n the c a l c u l a t i o n s

Thus t h e

w r i t t e n f o r year

(Lander

over

i s t o i n c l u d e i n f o r m a t i o n on

(based

the

be

improving

bulls

7

a t 0.80

into equations

Lander

e s t i m a t e s were u s e d .

annual*male s u r v i v a l

constant

of

juvenile

survival

-3 + K S 5

-5 + Bulls

S

} / NO

(B-19)

where Bulls =

(Harem

+ Idle t

B.4

Revised

T h r e e s e t s of progressively survival using of

and

) - 0.74

the

the o r i g i n a l

Estimates

juvenile

inclusion

the

estimates

assumptions

of b u l l kill

(equations

)

.

(B-20)

t-1

of J u v e n i l e S u r v i v a l

survival

e s t i m a t e s and limits

+ Idle t-1

refining

the pup

(Harem

t

counts. data B-15

are

concerning Each

of T a b l e and

produced

B-1.

B-16)

is

by

subadult obtained The

range

plotted

in

107

Figure

B-4

is

reduced

( F i g u r e B-5). if

Even t i g h t e r

the c o u n t s of

estimate

mean

reserve that

has

of

the

that

the

limits

can

harem b u l l s breeding

bull

have

difference

bounds f o r t h e s e

two

i s set at

80%

(Figure

B-6)

obtained

are

used

to

reserve.

recruitment

patterns

be

caused

the

1954

and

for

by

survival

( T a b l e B-2)

counts

been m i s r e p r e s e n t e d

However t h e

survival

subadult

upper e s t i m a t e

exploitation

1950s.

and

i n the

inclusion

bound t o e x c e e d might

idle

recruitment

The

when

of

males

the

above

changed

between

years

lower

survival

1955.

into

This

the

breeding

calculations

slightly

the

upper

i s s m a l l and

since and

not

or the

lower

considered

significant.

In g e n e r a l

the

a r e much n a r r o w e r sets

of

than

revised

assumptions rates.

For

last

two

the

f o r the

1960s and This

may

exploitation

each year

that

may

rates

were

higher

The different

estimates

for this

revised

juvenile

from t h o s e

1953

to

1970s f o r a l l indicate or

50%

only

during

the

three

survival

or more of

be

1958

incorrect

the

true

I t i s e q u a l l y p o s s i b l e t h a t the

c h a n g e s i n a s s u m p t i o n s would widen t h e survival

period

pattern

the a s s u m p t i o n

killed

decades.

survival

during

the

example

o l d males a r e

limits

estimates.

regarding

year

adult

parameter

the

for

the

subadult

1950s.

upper and

lower

estimates

are

B-7).

The

4

and

These juvenile

period.

survival

of L a n d e r

(Figure

not

very

estimates

108

Figure

B-4. .-Upper -(A) and lower (V) j u v e n i l e survival . e s t i m a t e s ( b i r t h t o age 2 y e a r s ) a s s u m i n g pup s u r v i v a l o v e r the f i r s t y e a r of l i f e r e m a i n s c o n s t a n t over time.

109

Figure

B-5. Upper ( A ) and lower ( V ) j u v e n i l e survival e s t i m a t e s ( b i r t h t o age 2 y e a r s ) a s s u m i n g the s u r v i v a l of s u b a d u l t males i s 80%.

annual

1 10

Figure

B-6. Upper (A) and lower {V) j u v e n i l e s u r v i v a l e s t i m a t e s ( b i r t h t o age 2 y e a r s ) assuming t h a t t h e a n n u a l s u r v i v a l of s u b a d u l t males i s 80% and t h a t c h a n g i n g b u l l c o u n t s a r e r e p r e s e n t a t i v e of y e a r c l a s s strength. M a l e s were assumed t o become b u l l s a t age 7 and e x p e r i e n c e an a n n u a l s u r v i v a l r a t e of 0.74.

111

derived factor of

from

the

bull

o f 1.1 and v a r y

the

Lander

counts exceed

f o r only

estimates

s h o r t c o m i n g s o f t h e method. explained ratio

by

is

proportional large

kill

correct

The s i m i l a r i t y

despite

validate

that

to the r a t i o

compared

that

considering

in results

to

survival

of k i l l natural

the l o g i c a l

be

t o pups b o r n

can

be The

as t h e

errors

inherent

estimates appear

close

if kill

mortality.

r e v i s e d methods of e s t i m a t i o n

past.

i s a c t u a l l y higher

This are

by

This

has

a

constant

1961,1964,1973; Y o r k

mortality

proportionally

i n t h e method.

The

t o be r e a s o n a b l e does n o t

bearing

upon

the s u r v i v a l of

Hartley,

to

exceed

1.05 t o 1.10

1981;

Eberhardt,

m a l e s and f e m a l e s

relatively

by assuming

similar rates

unreasonable

that

the f u r s e a l

of j u v e n i l e s u r v i v a l .

to expect

that

that

from

can

balanced

of

(Chapman 1981).

life

table

experience

It i s c e r t a i n l y

j u v e n i l e m a l e s and

t o s i m i l a r s o r t s of m o r t a l i t y .

in

the s u r v i v a l of j u v e n i l e

assumed

factor ranging and

show t h a t

that

subject

or

enables the

H i g h e r male s u r v i v a l e s t i m a t e s mean be

to

t h a n has been a c k n o w l e d g e d

f e m a l e s which h a s been p r e v i o u s l y males

will

t o produce e s t i m a t e s which

the Lander

j u v e n i l e males

not

the

the p r o c e d u r e .

The

the

intriguing,

consistency

t o pups b o r n e x h i b i t s t h e same t r e n d s

inevitable

Lander procedure

fact

is

The

estimates.

It

is

a few y e a r s .

t h e v a r i a t i o n i n t h e magnitude of the k i l l .

of t o t a l

Lander

t h e L a n d e r e s t i m a t e s by a

females

are

1 12

1950

1355

19G0

TERR

Figure

1365

1970

1375

1980

CLRSS

B-7. The mean (A) of t h e upper and lower j u v e n i l e s u r v i v a l bounds d e s c r i b e d i n f i g u r e B-6 a r e c o n t r a s t e d w i t h the L a n d e r e s t i m a t e s ( X ) . The L a n d e r e s t i m a t e s have been m u l t i p l i e d by a f a c t o r of 1.10. Both s e t s of e s t i m a t e s mimic the r a t i o of t o t a l k i l l t o pups born (+).

113

Table months)

B-5

and

survival

contains total

was

production born.

and

juvenile

as

sets

of

total

the

major

survival the

into

lies

the

mean of

the

B-5

B-6.

i n the

historical

alternative

juvenile

survival.

debris,

other

and

that

fur

the

share

component

data

seal

rates. the

population

of

pup pups

presented.

lower

survival

the

refined herd

estimating

required

immediate

the

are

of

estimates are

Future e f f o r t s

more

between

number

and

methods f o r

Monitoring

considering

the

Pup

is

procedure.

many y e a r s of

annual s u r v i v a l

investigated ensuing

estimation

(0-4

months).

survival

The

male

survival

difference

upper

to

be

of

the

same e c o s y s t e m

directed

estimating

juvenile

examining

juvenile

-reconstruct

should

means

s o u r c e s of

weather c o n d i t i o n s ) and

species

indicate

the

population.

t o w a r d an

(net

and

weakness of

the

juvenile

land

(0-24

dead pups, by

number of

more i n f o r m a t i o n a b o u t

The

survival

the

F i g u r e s B-4,

incorporated

pup

dividing

Each c o r r e s p o n d s to of

of

d e t e r m i n e d by

Three

bounds

estimates

mortalitiy

dynamics

of

(sea

birds)

may

These p o s s i b i l i t i e s

should

be

survival

to

i m p o r t a n c e of

demographies.

juvenile

114

T a b l e B-5.

R e v i s e d e s t i m a t e s of j u v e n i l e f u r s e a l s u r v i v a l f o r Saint Paul Island. Land s u r v i v a l (0-4 months) i s d e t e r m i n e d by d i v i d i n g t h e d i f f e r e n c e between pups born and dead pups c o u n t e d by t h e t o t a l number o f pups b o r n . T o t a l s u r v i v a l (0-24 months) a r e mean v a l u e s f o r t h e l i m i t s p r o d u c e d by r e f i n i n g a s s u m p t i o n s c o n c e r n i n g s u b a d u l t s u r v i v a l and t h e i n c l u s i o n of b u l l c o u n t s ( s e e t e x t f o r d e t a i l s ) .

Year Class

0-4 Months

1950 1 951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979

0.882 0.842 0.907 0.824 0.786 0.836 0.782 0.853 0.919 0.881 0.804 0.831 0.837 0.876 0.924 0.846 0.928 0.952 0.892 0.943 0.911 0.848 0.916 0.909 0.951 0.926 0.921 0.940 0.967 0.974

#1

v

0-24 Months #2 '•'

0.386 0.382 0.465 0.329 0.242 0.293 0.141 0.343 0.464 0.407 0.308 0.350 0.393 0.441 0.452 0.393 0.355 0.407 0.423 0.385 0.459 0.316 0.316 0.354 0.337 0.301 0.298 0.317 0.319

0.390 0.390 0.523 0.313 0.204 0.263 0.094 0.332 0.503 0.423 0.284 0.343 0.405 0.475 0.489 0.402 0.350 0.425 0.456 0.395 0.513 0.294 0.294 0.347 0.323 0.275 0.271 0.295 0.298

#1 S= >IT*" ( e q u a t i o n s B-15 and #2 S=0.80 #3 S=0.80; i n c l u d e b u l l c o u n t s of m a t u r i t y 7 y e a r s * lower

bound e x c e e d e d upper

#3 0.431 0.424 0.572 0.347* 0.256 0.291* 0.120* 0.359 0.521 0.454 0.297 0.349 0.414 0.487 0.502 0.424 0.380 0.434 0.507 0.436 0.558 0.322 0.329

B-16) w i t h Sa=0.74 and age limit.

115

APPENDIX C

MODEL VALIDATION BY

The

of t h i s s e c t i o n

analysis et

purpose

procedures developed

al.

(1976),

sensitivities 6. the

In

the

used

parameters

i s useful

Relative

analysis

(Majkowski

technique

(i=1..m) which

1981;

produces

altered

in

Chapter

to

The wish

improve detailed

to apply

the

Sensitivities

in

Miller

change U i such

that

+

Miller

m

parameters

and

et a l .

input 1976).

e s t i m a t e s P* o u t p u t x£

to

i s a l t e r e d by

Ui) .

parameters over

1974;

conditions

t o t h e s e t of p a r a m e t e r

the

X^

the r e s p o n s i v e n e s s of model

initial

of

input

output

deviance

Miller

methods of r e l a t i v e

t h e b e s t f i t of s i m u l a t i o n

Each

P-i = Pt (1

model

The

t o t h o s e who

determines

is applied

data. -

proportional

The

(1978).

(1974),

to a c c e p t or r e j e c t a model.

t o changes or e r r o r s

observed

by M i l l e r

sensitivity

of s e n s i t v i t y a n a l y s i s .

Sensitivity

This

used

the

c a s e of model v a l i d a t i o n , I have t r i e d

C.J_

output

and

Mohn

of m e t h o d o l o g y

technique

i s to e l u c i d a t e

and model v a l i d a t i o n have been a p p l i e d

criterion

outline

and

SENSITIVITY ANALYSIS

a

(C-1 )

P;

time

t.

between p e r t u r b e d X^

and

(i=1..m) A

determine

function

D^

perturbed

measures

u n p e r t u r b e d X^ v a l u e s .

the

116

Dt

This

has

the

or

property

D-measure

of

to vary

its the

f o r any

parameter

f o r each p a r a m e t e r

value against

the

The

relative

importance conditions This

of

of

given

independently

i n terms o f

Even

the

combined

methodology

is

required

which

and

or v a l i d i t y

predictions.

C.2

Uncertainties estimated uncertainty

input the

plotting

upon

model

i s not

picture

in

relative

and

initial

predictions.

actual

errors

introducing

such

predictable.

of

the

are

error

Thus

combines known p a r a m e t e r

a l l o w s an. e v a l u a t i o n

of

input.

the

"errors"

be

Allowing

then

reveals

e f f e c t of

w i t h model s t r u c t u r e of model

and

zero

may

t

time t .

l i m i t e d value unless

i n t o a l l parameters s i m u l t a n e o u s l y

D j

to changes

parameter

their effect of

equal

provides a useful

analysis

input

is

then

t

model o u t p u t

information

known.

i at

any

Majkowski

when a l l deviances

sensitivity

varying

from

Partial

resulting D

relative sensitivity

selected

disappearing

simplifies calculations.

calculated Ui

(C-2)

particular function

(1982) and

=

a

error

reliability

Numerical Model V a l i d a t i o n

in

model

errors. simulation

output

can

be

D e p e n d i n g upon the model may

be

determined amount of

either valid

or

from output

invalid.

117

A numerical

approach

c h o o s i n g model to

known

to

input parameters

distribution

simultaneously unperturbed

making

runs produces

other

model

input

input uncertainties

problems

are

calculated

a distribution

numerous

of d e v i a n c e s

C._3.J_

than a In

by t h e

errors.

i s costly

i n terms o f computer

information concerning the c o n t r i b u t i o n

to errors

overcome

if

in

the

model

prediction.

distribution

of

These

deviance

is

analytically.

C._3

Analytical

Model

Validation

D e t e r m i n i n g Dt

Analytic (1974)

and

model v a l i d a t i o n Miller

approach

deviances considering the

Conducting

i s t o be c o n s i d e r e d v a l i d .

validation

t i m e and p r o v i d e s l i t t l e

values

i s compared t o

v a r i a n c e which must be l e s s

i f t h e model

of r e a l i s t i c

Numerical

Their

output which

by

corresponding

words, model o u t p u t must n o t be c r i t i c a l l y a f f e c t e d

inclusion

of

begins

Running these

D-measure.

w i t h mean z e r o and a s s o c i a t e d level

decision

of i n p u t e r r o r s .

using the

Monte C a r l o s i m u l a t i o n

a

from d i s t r i b u t i o n s

i n t h e model p r o d u c e s

output

predetermined

such

has

e t a l (1976);

i s to a n a l y t i c a l l y

f o r estimated

been,

formulated

and a p p l i e d determine

input parameter

by Mohn

sensitivity

coefficient

errors.

R

Miller

(1979).

the d i s t r i b u t i o n

B

.

of

They b e g i n by

t h e measure o f d e v i a n c e D^ a s a l i n e a r

relative

by

function

and

of

individual

118

parameter p e r c e n t

D

+

R

N

c h a n g e s U\,

= D £o

m

+5T

i=1

R

where

u

D

(C-3)

L

t , i

and

=

(C-4)

am

t,i

.

EquationC-4 i s r e p l a c e d w i t h a n u m e r i c a l derivative

(first

simulation

model

expression.

term contain

From t h i s

R

of

the no

approximation

Taylor

easily

expansion)

differentiated

should

(C-5)

t,i

U\

or

R

t,i s i n c e Dx_ was i n t o C-3

(C-6)

=

D

U

C

chosen t o equal

zero.

Substituting

equation

C-6

yields

m

Dx = D j +

£

D

-t

;

—--

i = 1 Ui

U;

(C-7)

or m

= E Dt.i i= 1

the the

analytic

i t follows that

=

D

for

(C-8)

119

Summing

the

model o u t p u t

effect

of

individual

as shown i n e q u a t i o n

determining

the

deviance.

C-8 In

parameter e r r o r s

is

a. s i m p l e

order

to

p a r a m e t e r s must a c t upon t h e o u t p u t

variable

manner.

varified

Independence

calculated

values

perturbations in

can

be

obtained

and i n c l u d i n g

by

means

of

sum

input

an

independent

in by

comparing

summing

a l l parameter e r r o r s

two

individual simultaneously

t h e s i m u l a t i o n model.

A drawback t o e q u a t i o n still

C-8

r e q u i r e d to determine

i s t h e amount o f c o m p u t i n g

the d i s t r i b u t i o n

known p a r a m e t e r e r r o r s .

An

depends

relationship

upon

predicted

upon

a

a

linear

hence D.^ may

linear

any

given

determined

U\

calculation

between

of

D^-^ .

i n p u t e r r o r and

t

between p a r a m e t e r p e r c e n t

deviance. by

a t U^=1%.

D

Model o u t p u t

simply

multiplying

Rewriting equation

m = £ {U- * R i =1

a l s o means t h e r e l a t i v e

The

according to

be p r e d i c t e d f o r any g i v e n

relationship

the measure o f o u t p u t

overall

alternative

of

time

output.

and

for

upon

v

based

e r r o r and predicted with

C-7 as

(C-9)

-

t,(

importance

of l i n e a r i t y

t h i s value

. (Ui = .01 )}

D

model e r r o r c a n be e a s i l y

extent

c a n be

U;

of p a r a m e t e r c o n t r i b u t i o n s t o identified.

within individual

model

parameters

120

is

determined

incremented two

by

input

examining errors.

calculations

predicted,

using

calculated

by

within

of

the

one

set

p r o d u c t s of each parameter

The

two

test

deviance

of

Ui

equal

calculation

required

variance

the variance

i s simplified

independence

in

contrasts

variance

m

Var(D ) = t

The

second

between

E D i=1 R

a l l input

at

and is

parameters

by summing

the

1%.

to c o n s t r u c t

the

by

While

the

model.

presence

In

the r e l a t i v e

the d i s t r i b u t i o n

t h e mean i s

is analytically

assumed

determined. of

Its

linearity

and

a d d i t i o n the c a l c u l a t i o n of

importance

model u n c e r t a i n t y and d e t e r m i n e s

The

observed

Observed

i s determined

change by

contrasting

of Dt

statistics

zero,

measure,

values.

of d e v i a n c e s a r e mean and v a r i a n c e . to

o f model o u t p u t t o

requires

changing

The p r e d i c t e d

Distribution

response

A second

simultaneously

the run.

C.3.2

the

of i n p u t

the v a l i d i t y

errors

upon

of p r e d i c t i o n s .

o f D^ i s c a l c u l a t e d from

2

Var(U- ) + t , i L

term w i l l

2E

m m

i=1

I

R k=i

R Cov(Ui,Uk). t , i t,k

D

D

drop o f f p r o v i d e d

the parameters.

Var (D ) t

no c o r r e l a t i o n

(C-10)

exists

T h i s means t h a t m = l R

i=1

2 D

t , i

V a r (U- ) V

(C-11)

121

The v a r i a n c e

o f u\ c a n be d e t e r m i n e d

by f i r s t

reconsidering the

definition

p. U

- pf (C-12)

=

p?

From t h i s

i t follows

that Var (p. )

Var(U^) =

Assuming

that

(PD

(C-13) 4

P\ has an e r r o r

w i t h a mean z e r o

the r e a l

e^ w h i c h i s n o r m a l l y . d i s t r i b u t e d

P° must

be i n t h e i n t e r v a l

Z * e

P? ±

(C-14)

K

where Z i s t h e s t a n d a r d

normal d e v i a t e .



This

means

that

1

;

Var(U ) =

(C-15)

v

(Pi°)

All

that

distribution i'S

possible

given

is

required

of deviances

to



calculate

errors.

variance

i s an e s t i m a t e o f e^.

to determine the v a l i d i t y

known i n p u t

the

From

of t h e model

of

the

this

i t

predictions

122

C._3..3

Validation

The by

uncertainties

i n s i m u l a t i o n model o u t p u t

t h e mean and v a r i a n c e o f D^.

errors

is

contrasted

acceptability Different

within

with

which

approaches

a the

can

be

This

are quantified

distribution

previously model

to

output

d e f i n e d i n t e r v a l of

is

taken

of

considered define

valid.

the

critical

interval.

The

common method

observers

familiar

judgement

(Miller,

observers

are

perturbed asked

if

intuitively required

1974; M i l l e r

shown p l o t s

they

could

the

procedure

deciding

to validate

A

second

observation acceptable output

D

In

unacceptable the model.

the

Mohn

this

case

superimposed

the

two;

(1979)

variance

excessive

judgements

upon

They a r e thereby

circumvents

of

D^,

limits

I n b o t h c a s e s model

intuitive

t o ask intuitive

D^ v a l u e s .

between

value.

t

is

for their

1976).

using d i f f e r e n t

calculating

upon

critical,

system

et a l ,

distinguish

by f i r s t

the r e a l

D^

of t h e base o u t p u t

critical

d e c i s i o n s a r e based reflect

defining

with the modelled

output, produced

identifying this

of

then

would be validation

which

may

not

system.

approach

errors limits

rather

to than

on model

deviances

deem t h e s i m u l a t i o n

intuitive

output

exceeding model

model v a l i d a t i o n

field

invalid.

relies

upon

field

judgements t o c o n s t r u c t

errors.

Distributions

observation confidence Confidence

limits

of

limits can

be

123

placed expected used

upon

t h e model p r e d i c t i o n s

output.

to v i s u a l i z e

and c o n t r a s t e d

In a d d i t i o n ,

coefficients

t h e range o v e r

time where

c o n s i d e r e d v a l i d or i n v a l i d .

with those of

of v a r i a t i o n the

model

may may

be be