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USGS Northern Prairie Wildlife Research Center US Geological Survey
1980
The Comparison of Usage and Availability Measurements for The Comparison of Usage and Availability Measurements for
Evaluating Resource Preference Evaluating Resource Preference
Douglas H. Johnson
USGS Northern Prairie Wildlife Research Center
, Douglas_H_Johnson@usgs.gov
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Johnson, Douglas H., "The Comparison of Usage and Availability Measurements for Evaluating Resource
Preference" (1980).
USGS Northern Prairie Wildlife Research Center
. 198.
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Ecology, 61(1),
1980, pp.
65-71
?
1980
by
the
Ecological
Society
of
America
THE
COMPARISON OF
USAGE
AND
AVAILABILITY
MEASUREMENTS
FOR
EVALUATING
RESOURCE
PREFERENCE'
DOUGLAS
H.
JOHNSON
United
States Fish
and
Wildlife
Sert'ice,
Northern
Prairie
Wildlife
Research
Center,
Jamestown,
North
Dakota
58401
USA
Abstract.
Modern
ecological
research
often
involves
the
comparison
of
the
usage
of habitat
types
or
food items to
the
availability of those
resources to the
animal.
Widely
used methods of
determining
preference from
measurements of
usage
and
availability
depend
critically
on the
array
of
components
that
the
researcher, often with a
degree
of
arbitrariness,
deems available
to
the
animal. This
paper
proposes a new
method,
based on
ranks of
components
by usage
and by
availability.
A virtue
of the
rank
procedure
is that it
provides
comparable results
whether a
questionable
component
is
included
or
excluded from
consideration.
Statistical
tests of
significance
are given
for the
method.
The
paper
also offers a
hierarchical
ordering of
selection
processes.
This
hierarchy
resolves certain
inconsistencies
among studies of
selection and is
compatible with
the
analytic
technique
offered
in
the
paper.
Key words:
availability;food
habits;
habitat
selection;
preference;
resource
utilization;
selection;
usage.
INTRODUCTION
Central
to
the
study
of animal
ecology
is
the
usage
an
animal
makes
of its
environment:
specifically,
the
kinds of
foods it
consumes
and
the varieties
of habitats
it
occupies.
Many
analytic
procedures
have
been
de-
vised
to
treat
data on
the
usage
of
such
resources,
particularly
in
relation
to
information on
their avail-
ability
to the
animal,
for the
purpose of
determining
"preference."
The
objectives
of this
report
are to
de-
scribe
the
problem
of
determining
preference
by com-
paring
usage
and
availability
data,
to
illustrate
a
seri-
ous
shortcoming
in
the
routine
application of
most
procedures
for
comparing
these
data,
and
to
suggest
a
new
method that
resolves this
difficulty.
The
pro-
posed
technique
results in a
ranking
of the
components
on the basis
of
preference, and
permits
significance
tests of
the
ranking.
Many
investigators
who use
analytic
procedures to
handle
usage
and
availability
data fail to
recognize
the
conditional
nature
of
inferences drawn
by
comparing
usage
to
availability. Conclusions
about
whether
an
individual
component is
used
above,
in
proportion
to,
or
below its
availability are
critically
dependent
upon
the
array
of
components
the
investigator
deems avail-
able to
the animal. This
decision is
often
made
some-
what
arbitrarily
by
the
investigator.
The
following
contrived
example
will
illustrate
the
point.
Suppose
an
investigator collects a
fish,
and
finds
that its
stomach
contains
food
items
A,
B
and
C in
the
percentages
shown in
Table
1(A)
under
"Usage."
A
sample
of the
animal's
feeding site
at the
time the
fish
was
collected
reveals that
the items
were
present
in
the
proportions
shown
under
"Availability."
Many
investigators
would
conclude
that Item
A is
avoided,
because
usage
was less
than
availability,
while
Items
B
and C
are
preferred,
because
usage
exceeded
avail-
ability.
But
suppose
another
investigator,
equally fa-
miliar
with the
biology
of the
fish, does
not
believe
that
Item
A is a
valid
food item
(perhaps he
thinks it
is
ingested only
accidentally
while the
animal is
con-
suming
other
foods). He
would
then
consider the
data
in
Table
1(B),
obtained
by
deleting Item
A
from the
analysis.
Now,
although
Item C
is still
deemed
pre-
ferred,
the
assessment
of Item B
has
changed
from
preferred
to
avoided.
Conclusions are
not apt to be drawn from
one
fish,
but
whatever
conclusions
are
reached
about the
pref-
erence or
avoidance of
any
particular
component
of
the
environment
depend
markedly upon the
array
of
components
deemed by
the
investigator
to be
available
to
the
animal. To
the
extent that
the
decision
is arbi-
trary, so
will be
the
conclusions
drawn from the anal-
ysis. This
inconsistency
can
result from the
use of
any
of
the
standard
methods,
e.g.,
the
forage
ratio
(Wil-
liams and
Marshall 1938,
Hess
and Rainwater
1939),
its
modifications
(Jacobs
1974,
Chesson
1978),
the in-
dex of
electivity
(Ivlev
1961), the
difference (Swanson
et
al.
1974, Gilmer
et
al.
1975),
or
contingency
tables
(Hanson
and
Labisky
1964, Buchler
1976). Some
au-
thors
have
recognized
the
difficulty.
Bartonek
and
Hickey
(1969)
noted
that their
decision
to
measure
only
items
they
considered
as potential foods was
sub-
jective.
Sugden
(1973:28-29)
mentioned
that
"the
presence
of other
items
will
influence
the rating for
a
given
item.
When
the available
food
includes
mostly
unimportant
items
measured in
the
habitat, other
items
will
be
given a
higher
rating."
Certain
other authors
1
Manuscript
received
23
May
1978; revised
1
May
1979;
accepted 8
May
1979.
This article is a U.S. government work, and is not subject to copyright in the United States.
66
DOUGLAS H. JOHNSON Ecology,
Vol.
61,
No.
1
TABLE 1. Example
illustrating results
of comparing
usage and availability
data when a common
but seldom-used
item
is
included 1(A)
and when excluded
1(B) from consideration.
Rank
Usage
Availability
Item
(%) (%)
Conclusion
Usage
Availability
Difference
(A)
A 2
60
Avoided
3 1
+2
B 43
30
Preferred
2
2
0
C 55
10
Preferred
1
3
-2
(B)
B
44
75
Avoided
2
1 +
1
C
56
25
Preferred
1
2
-1
(e.g., Ivlev
1961,
Chamrad and Box 1968)
have
been
circumspect
about
interpreting
usage-availability
data,
but many
others (e.g. Hess
and Swartz
1940, Bellrose
and Anderson
1943, Jones
1952, Van Dyne
and Heady
1965)
have termed a component
"preferred"
if
its
usage
exceeded its availability,
and "avoided"
if
the
reverse was
true.
For the
sequel, we define
the following
terms:
The
abundance
of
a
component
is
the quantity
of that com-
ponent
in
the environment,
as
defined
independently
of
the
consumer. The
availability
of that component
is
its accessibility
to
the consumer.
The usage of
a
component
by
the consumer
is
the
quantity
of
that
component
utilized
by
the consumer
in
a
fixed
period
of time. The selection
of
a
component
is a
process
in
which
an
animal actually
chooses
that component.
Usage
is
said to be
selective
if
components
are
used
disproportionately
to
their
availability.
The
preference
of
a
consumer
for
a
particular
component
is a reflec-
tion
of
the likelihood of
that
component
being
chosen
if offered
on
an
equal
basis with others.
In
theory,
components
can be
ranked from "most
preferred"
to
"least preferred."
Preference
is
ordinarily
claimed
to
be independent
of availability,
but is
generally
defined
by reference
to
the choice
made
at
equal
availabilities
(e.g.,
Pirnie
1935,
Ellis et al.
1976).
A
PROPOSED METHOD
The
method
that
I
suggest
for analyzing
usage-avail-
ability data
yields
rankings of items by
preference
with
the following
properties:
(1) significance
tests
can
be
made
for
differences
in
preference
among items;
and
more
important,
(2)
the
method gives
largely compa-
rable
results whether the
analysis
includes or excludes
doubtful items.
As
a
measure
of
preference,
I
propose
using
the
difference between
the
rank
of
usage
and the rank of
availability. Call
this difference
tij,
where i
indexes
the
component
and
j
indexes
the individual
animal.
The
differences can be
averaged
across animals,
to
obtain
a
mean
for the
ith
component.
Averages
for
different components
can
then
be
compared
to
deter-
mine
which
are more
preferred.
If
components
are
ordered
by these
average
differences,
the ranking
will
be from
least
preferred
to
most preferred.
Returning
to the
one-animal
example
previously
considered,
with Item
A included,
Table 1(A), the
dif-
ferences
in
the
ranks of usage
and
availability
are +2,
0,
and
-2 for
Items
A,
B,
and
C, respectively.
Should
Item
A be excluded
from the
analysis,
Table
1(B),
B
and
C have
values
+
1
and
-1, respectively.
Although
the
values themselves
change,
the
difference
between
B and C remains
2,
suggesting
that
C is
preferred
to
B,
regardless
of whether
A is included
or
excluded.
We thus
avoid absolute
statements
about
preference.
Standard
methods
(e.g.,
forage
ratio,
Ivlev's
index
of
electivity)
can
also be
used to
develop
rankings
in
order of preference.
Indeed,
Ivlev (1961)
recognized
that preference
values indicate
only
the relative
value
of
a
component
in
comparison
to
others,
and Chesson
(1978)
did
likewise.
But
many authors
go
much
further
and
make absolute
statements
about
preference
and
avoidance.
The proposed
method
discourages
this
by
using ranks,
which
by
their nature
represent
relative
values.
Furthermore,
the loss
of information
resulting
from
the
use
of ranks of
usage
and
availability,
instead
of
the
measured
values,
is
of
less
consequence
than
might
be
supposed
(Lehmann
1975).
First of
all,
sta-
tistical methods
based on
ranks are nearly
as
efficient
as methods
based
on the
original
data even
when
all
the
assumptions
necessary
to
treat
the
original
data
hold (e.g.,
measurements
are
exact, their
distribution
is
normal).
Moreover,
if
the
assumptions
are
not
met,
the
rank
methods
have considerable
advantages
of
ef-
ficiency
and
validity.
And we
have
good
reason
to
doubt the
strict
propriety
of
availability
measure-
ments. Sampling procedures
used
to determine
avail-
ability
values for
the various components
may
not
faithfully
reflect
the true
availabilities
to the
animal
under study (Savage
1931,
Landenberger
1968,
Bar-
tonek
and
Hickey
1969,
Sugden
1973,
and Mitchell
1975). Thus,
availability
values are
measured
inexactly
and
methods
based on ranks are
to be
preferred.
February 1980
COMPARISON OF
USAGE AND
AVAILABILITY
67
General formulation
Let
Xij
be some measure of usage of component
i
by individual
j,
and
Yij
be
a
measure of the availability
of component i to individual
j,
where i
=
1,
2,.
I (I= number of components) and j
=
1,
2,.
J (J
=
number of
individuals).
The
values
need not
be scaled to be percentages. Take
rij
to be the rank of
Xij
within
j
(animal) and
sij
the rank of
Yij
within
j.
The difference in these ranks,
tij
=
rij
-
sij,
is a mea-
sure of preference for component i by individual
j.
It is a simple step to average the
tij
across indi-
J
viduals, obtaining
ti
=
J-1
tij.
A ranking of com-
j=1
ponents
in
order
of
increasing
ti
will
then indicate
the relative preference
of the
components by
the
entire
sample
of animals.
To draw statistical conclusions
about the differ-
ences among components,
we invoke the
following
model:
tij
=
bL
+
ati
+
bj
+
Eij,
(1)
where
ju
is the overall mean,
ai
is the effect due to component
i
(i
=
1,.
I),
f3i
is
the effect due to
animal]
(j
=
1,
J),
Eij
is the random error
term,
and
l
=
a
f3
=
0.
I
.,
Because the
tijs
are differences
in
ranks within
in-
dividuals, they
sum to zero
across
i:
tij
=
0
for all
j,
(2)
which
implies
ju
=
0, hi
3
0,
and
y
=
0,
all].
(3)
i =1
Thus
the model (1) reduces to
tij
=
ai
+
Eij.
Interest lies
in
the
null
hypothesis
that
al
=
. ..
a,
(=0), (4)
that
is,
all
components
are
equally preferred.
Should
that
hypothesis
be
rejected
in favor of the alternative
that some
components
are
more
preferred
than
others,
we would then
wish to know which
of the
components
are
preferred
to which
others
(the problem
of
multiple
comparisons).
The distributional
properties
of our
statistic are
needed to test the
null
hypothesis.
The
average
tb
equals
the difference
in
the
averages
of the
ranks:
i
=
ri
-
Si.
It can be shown
(e.g., by
the method of
Haigh 1971)
that
under general conditions
Fr
and
si
are
normally
distributed in large samples. Thus, their
difference is
also asymptotically normal, which allows us to
employ
the
heavy statistical artillery developed for
normal
variables.
We
assume
the error terms
[Eij]
are
distributed
with
zero
mean,
and
independently between
animals. With-
in
an animal, however, error terms are
(slightly) cor-
related (they sum to zero by Eq. 3), so
standard anal-
ysis of variance techniques are
inappropriate.
A
procedure that allows for correlations of error
terms
within animals is Hotelling's T2 (e.g., Anderson
1958),
which is used to test the hypothesis that a multivariate
normal vector of means is equal to a specified
vector
(in the present case, a vector of zeroes).
Let
1jik
=
V 1) E
-)(tk-
be the covariance between components i
and k. (A
computational note: Because of Eq. 2, the
variance-
covariance matrix for all
components
is
singular.
The
following calculations are made by deleting
one com-
ponent
from the
analysis.
The same answer
ensues
regardless of which component is deleted.)
Let V be
the
(I
-
1)
x
(I- 1) covariance matrix,
V
=
[v&].
Then the statistic
F
=JJ-I+ 1)'-
'
(J
-
)(I
-
1)
i k=1
where
Uik
is
the designated element
of the inverse
matrix of V
and U
[Uik]
=
V-1,
is
distributed
under
the null
hypothesis (Eq. 4)
as
Snedecor's
F with I
-
1
and
J
-
I
+
1
degrees of freedom.
Should the calculated statistic be
larger
than the ta-
bled
F
value
at
some
assigned significance
level,
the
investigator will likely be interested
in
finding
the
source
of
the heterogeneity among the
a's. This is the
multiple comparisons problem,
which
has
been
at-
tacked
by
a
number
of
procedures. (See
review
by
O'Neill
and
Wetherill
1971.)
In
the
example
that
fol-
lows,
I
chose to use the
Bayesian decision procedure
developed by
Waller and Duncan
(1969).
It is
rather
simple to apply, solves the dilemma of whether to use
experimentwise
or
comparisonwise
error
rates,
and
has
performed nicely
in
comparative studies (Carmer
and Swanson
1973).
Waller and
Duncan
suggested declaring significant
a
difference between two
means
if
the
difference ex-
ceeds
WSd,
where S4
is
the
standard
error of
the dif-
ference and W is a
function of the number of means
under
comparison (in
our case
I
-
1),
the
degrees
of
freedom
(J
-
I
+
1),
and
the
F
statistic obtained ear-
lier.
The
dependence
of W on
F is
the characteristic
feature of the
Waller-Duncan
method;
its
use reduces
the
chance of
a
Type
I
error
by demanding
a
large
68
DOUGLAS H. JOHNSON
Ecology, Vol. 61, No.
1
TABLE
2.
An example of wetland usage* and
availability
data for 2 birds and 12
wetland classes.
Measured values
Rank
Bird 5198 Bird
5205
Bird 5198 Bird 5205
Avail- Avail- Avail-
Avail-
Wetland class Usage ability Usage ability Usage
ability Usage ability
1/2 0.0 0.1 0.0 0.4 10.5 11 9.5
12
3/8 10.7 1.2 0.0 1.4 4
7 9.5
6
9 4.7
2.9 21.0 3.5 6
5
2
4
10
20.1 0.8 0.0 0.4 3
9 9.5
11
11/14 22.1 20.1 5.3 1.2 2 2 6 7.5
15
0.0 1.4 10.5 4.9 10.5
6
4.5
3
17/20
2.7
12.6 0.0 1.0 7.5 3 9.5
9
31/34 29.5 4.7 15.8 5.1 1 4
3 2
35
0.0
0.0
10.5 0.7 10.5 12 4.5 10
36/38 2.7 0.2 36.8 1.8 7.5
10
1
5
39 7.4 1.1
0.0
1.2
5
8
9.5 7.5
Open
0.0
54.9 0.0 78.3
10.5
1
9.5
1
Total
99.9 100.0
99.9 99.9
8 Usage percentage
of
recorded locations
in
each wetland class.
t
Availability
=
percentage
of wetland area in
a bird's home
range
in each wetland class.
difference
if F is
small, and reduces the
chance
of
a
Type
II
error by
requiring
a
less
marked difference
if
F is
large.
Application to real
data
The
procedure described
above
is
illustrated
by
some habitat usage
and
availability data collected
by
Gilmer et al. (1975). Data
for
2
of
their
24
radio-marked
adult Mallards
(Anas
platyrhynchos) are displayed in
Table
2.
For each
bird,
a
measure
of usage
is
the
per-
centage of locations
recorded
in
each
of
12
wetland
classes, including
"open
water."
(For
this
example,
certain of
the wetland classes used
by Gilmer
et
al.
have been
combined.)
Availability is taken to be the
percentage
of
a
wetland area
in an
individual bird's
home range
constituted by each
wetland class.
Interest
lies
in determining
which classes
of wetlands
are fa-
vored,
in
the sense
of receiving
more intensive
use by
the
Mallards.
It
is
apparent
(Table 2) that the
availability of
open
water
far
surpasses
its usage. For this
reason,
usage
of
the other
classes tends to
exceed
availability, which
would
suggest,
if
caveats
about
absolute statements
were
disregarded,
that most of
the
other wetland
classes were
'"preferred,"
whereas
open
water
was
avoided.
In
fact,
in
their original
analysis,
Gilmer et
al.
(1975) excluded
most
of the available
open
water
from
consideration.
It
is
readily
seen that the question
of
inclusion/exclusion
is
germane
in
this
application.
To apply the new
procedure, we first
take the
ranks
of
usage
and
availability
values within
each
bird.
Ranks for
the two birds
are
shown in
Table 2, where
open
water is
included.
(Results
for
"open
water ex-
cluded"
are
not
shown.) Next,
for
each
bird,
we
take
the
difference between the rank of
usage
and the
rank
of
availability.
Averaging
across all 24 birds
in
the
complete sample
yields the average
differences shown
in Table 3.
The hypothesis
test outlined earlier
yields the F-sta-
tistics F
=
20.28
(df
= 11
and 13)
when open water
is
included and F
=
8.68 (df
=
10 and
14) when exclud-
ed. Both values
are highly significant
(P
<
.001), lead-
ing us to reject
the null hypothesis
that all wetland
classes
are
used
with equal intensity.
We
now seek
to
determine the
significant differences
in
preference
among the wetland
classes.
To declare
a difference significant,
it must exceed
in absolute value
WS,,,
where W
is obtained from
ta-
bles in Waller and Duncan (1969)
and
S(1
is
the stan-
dard error of
a difference between
two means.
For
example,
if
d
=
/i
-
tk.,
then
S(,2
= var
(f)
+ var
(bk)
-
2
cov
(ti,
fg).
To determine W the
investigator
must
select a value
for K, the Type I to
Type
II
error seri-
ousness ratio.
We use K
=
100, which Waller
and
TABLE 3. Average
differences between
ranks of wetland
class
usage
and the
availability
of
that class.
Average
difference in ranks
Open
water
Open
water
Wetland class
included
excluded
1/2
-2.44
-1.94
3/8
-3.29
-2.42
9 1.50
2.02
10
-1.33 -0.98
11/14
.52
1.31
15 3.60
3.96
17/20
2.94 3.35
31/34
-1.19 -0.19
35
-2.88
-2.38
36/38 -2.58
-1.81
39 -1.54
-0.94
Open
6.69
