­­­­­
Original
Message­­­­­

From:
Roger
Nisbet
[
mailto:
nisbet@
lifesci.
ucsb.
edu]

Sent:
Thursday,
December
08,
2005
8:
24
PM
To:
Beaulieu,
Stephen
M.

Subject:
Ashley's
question
Hi
Steve,

Our
report
stated
that
".
.
.
increase
in
survival
of
the
youngest
fish
to
compensate
for
I&
E
may
force
a
long­
term,
substantial
decrease
in
adult
stock."
Ashley
responded,
"
It
would
seem
that
increased
survival
could
mitigate
the
decrease
in
stock,
rather
than
causing
a
decrease.
Can
the
panel
clarify
this
comment?
How
can
increased
survival
cause
a
decrease
in
stock?

To
see
how
increased
survival
may
lead
to
a
decrease
in
stock,
assume
compensation
occurs
only
at
the
youngest
(
pre­
entrainment)
life
stage.
Then
if
entrainment
reduces
survival
through
the
vulnerable
stage,
there
must,
at
equilibrium,
be
a
compensatory
increase
in
survival
of
these
youngest
individuals.
This
implies
that
the
equilibrium
population
of
these
youngest
individuals
must
decrease.
If
fecundity
is
density
independent,
this
in
turn
implies
that
the
equilibrium
adult
stock
must
decrease.

The
question
of
whether
increased
survival
can
"
mitigate"
a
decrease
in
stock
is
much
subtler,
and
here
I
have
to
appeal
to
the
algebra.
This
requires
defining
some
reference
level
of
decrease
to
which
the
actual
decrease
is
compared.
Nisbet
et
al.
(
1996)
did
this
by
defining
a
sensitivity
index
(
page
163
 
equations
9a
and
9b)
where
the
proportional
change
in
adult
stock
was
compared
to
the
proportional
change
in
survival
through
the
vulnerable
stages.
A
value
less
than
one
for
our
sensitivity
index
corresponds
intuitively
to
the
idea
of
"
mitigation"
in
the
question.
The
case
of
density­
dependent
survival
of
the
pre­
entrainment
stage
turns
out
to
be
mathematically
equivalent
to
the
case
of
density­
dependent
fecundity
(
see
page
268).
We
show
that
a
sensitivity
index
less
than
one
occurs
only
with
very
strong
density
dependence.
Since
we
typically
don't
have
a
measure
of
the
strength
of
density
dependence
in
any
particular
application,
the
quoted
phrase
in
our
report
(
cautiously)
used
the
word
"
may".

Hope
this
helps,

Roger
Reference:
Nisbet,
R.
M.,
Murdoch,
W.
W.,
Stewart­
Oaten,
A.
1996.
Consequences
for
adult
fish
stocks
of
human­
induced
mortality
on
immatures.
Pages
257­
277
in
C.
Osenberg
and
R.
J.
Schmitt,
editors.
Detecting
Ecological
Impacts.
San
Diego:
Academic
Press.
