considered reliable if simulation parameters (particularly adult survival) contain ..... Pacific and Bering Sea is the ultimate factor limiting the size of the total ...
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