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155
Ecology,
86(1), 2005, pp. 155–163
q
2005 by the Ecological Society of America
RESTITUTION OF MASS–SIZE RESIDUALS: VALIDATING BODY
CONDITION INDICES
A
LBRECHT
I. S
CHULTE
-H
OSTEDDE
,
1,5
B
ERTRAM
Z
INNER
,
2
J
OHN
S. M
ILLAR
,
3
AND
G
RAHAM
J. H
ICKLING
4
1
Department of Biology, Laurentian University, Sudbury, Ontario P3E 2C6 Canada
2
Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849 USA
3
Department of Biology, University of Western Ontario, London, Ontario N6A 5B7 Canada
4
Department of Fisheries and Wildlife, Michigan State University, Lansing, Michigan 48824 USA
Abstract.
Body condition can have important fitness consequences, but measuring body
condition of live animals from wild populations has been the subject of much recent debate.
Using the residuals from a regression of body mass on a linear measure of body size is
one of the most common methods of measuring condition and has been used in many
vertebrate taxa. Recently, the use of this method has been criticized because assumptions
are likely violated. We tested several assumptions regarding the use of this method with
body composition and morphometric data from five species of small mammals and with
statistical simulations. We tested the assumptions that the relationship between body mass
and body size is linear, and that the proportion of mass associated with energy reserves is
independent of body size. In addition, we tested whether the residuals from reduced major
axis (RMA) regression or major axis (MA) regression performed better than the residuals
from ordinary least squares (OLS) regression as indices of body condition. We found no
evidence of nonlinear relationships between body mass and body size. Relative energy
reserves (fat and lean dry mass) were generally independent or weakly dependent on body
size. Residuals from MA and RMA regression consistently explained less variation in body
composition than OLS regression. Using statistical simulations, we compared the effects
of violations of the assumption that true condition and residual indices are independent of
body size on the OLS, MA, and RMA procedures and found that OLS performed better
than the RMA and MA procedures. Despite recent criticisms of residuals from mass–size
OLS regressions, these indices of body condition appear to satisfy critical assumptions.
Although some caution is warranted when using residuals, especially when both inter-
individual variation in body size and measurement error are high, we found no reason to
reject OLS residuals as legitimate indices of body condition.
Key words: body condition; body mass; body size;
Clethrionomys gapperi;
fat;
Microtus penn-
sylvanicus; Neotoma cinerea; Peromyscus maniculatus;
reduced major axis; regression analysis; re-
siduals;
Tamias amoenus
.
I
NTRODUCTION
The body condition of an animal refers to its ener-
getic state. An animal in good condition is assumed to
have more energy reserves than an animal in poor con-
dition. For instance, individuals with larger energy re-
serves may have better fasting endurance and higher
survival than individuals with smaller reserves (Millar
and Hickling 1990). Other fitness parameters related to
reproduction and survival have been found to correlate
with body condition among many taxa (e.g., Dobson
1992, Dobson and Michener 1995, Wauters and Dhondt
1995, Bachman and Widemo 1999, Shine et al. 2001).
Measuring the body condition of live animals has
been the subject of much recent debate (Jakob et al.
1996, Kotiaho 1999, Green 2001, Hayes and Shonk-
wiler 2001, Schulte-Hostedde et al. 2001, Speakman
2001). However, the common objective has been to
Manuscript received 29 January 2004; revised 4 June 2004;
accepted 22 June 2004. Corresponding Editor: F. S. Dobson.
5
E-mail: aschultehostedde@laurentian.ca
determine the mass of an individual relative to its body
size. An animal can be heavy because it is structurally
large or because it is carrying metabolizable tissue such
as fat and protein (Dobson 1992). Indices of body con-
dition attempt to determine the mass of the individual
associated with energy reserves after correcting for
structural body size. One of the most common methods
used to measure condition involves regressing body
mass on some linear index of body size, and using the
residuals from this regression (typically ordinary least
squares [OLS] regression) as an index of body con-
dition. An individual with a positive residual is con-
sidered to be in better condition than an individual with
a negative residual (Jakob et al. 1996, Schulte-Hosted-
de et al. 2001).
Recently, Green (2001) reviewed the use of residual
indices of condition in ecological studies and identified
six key assumptions underlying this methodology that
are likely to be violated in some or all studies. These
assumptions fall into three categories. The first two are
related to the initial regression between body mass and
156
ALBRECHT I. SCHULTE-HOSTEDDE ET AL.
Ecology, Vol. 86, No. 1
P
LATE
1. Yellow-pine chipmunk (
Tamais amoenus
). Pho-
to credit: J. S. Millar.
body size. These assumptions are (1) that mass in-
creases linearly with body size (or the body size in-
dicator [BSI]), and (2) that the residual index of con-
dition and true condition (the proportion of mass as-
sociated with energy reserves) of an animal are inde-
pendent of body size (or BSI). Assumptions 3 and 4
are related to the index of body size: (3) that the index
of body size (BSI) is an accurate measure of overall
structural size, and (4) that there is no correlation be-
tween the BSI relative to other structural components
and the parameter against which the residual index of
condition is analyzed. The final assumptions are related
to the use of OLS regression in determining residual
indices of condition. Ordinary least squares (OLS) re-
gression assumes (5) that Xis strictly independent of
Y(i.e., that Xand Yare not mutually interdependent),
and (6) that there is no ‘‘error’’ in X(i.e., the scatter
in points around a slope is due to variation in Y, not
X). Green (2001) concluded that many of these as-
sumptions are likely violated in some or all studies,
and suggested that alternative regression models such
as model II regression or nonparametric methods
should be used to calculate residual indices of condi-
tion.
Because of the extensive use of residuals as indices
of condition (e.g., mammals: Dobson et al. 1999, Fisher
1999; birds: Schluter and Gustafsson 1993, Weather-
head et al. 1999, Merila¨ et al. 2001; amphibians: Judge
and Brooks 2001; reptiles: Weatherhead et al. 1995,
Shine et al. 2001), it is critical that assumptions and
criticisms of this statistical technique be empirically
tested with appropriate data. Recently, we attempted
to determine whether the residual index of condition
(as calculated from OLS regression between body mass
and body size) was correlated with actual measure-
ments of body fat in five species of small mammals
(Schulte-Hostedde et al. 2001). Residual indices were
weakly correlated with fat, and more closely correlated
with lean dry mass (composed mostly of muscle pro-
tein) and water. Here, we reexamine these data to de-
termine whether Green’s (2001) concerns regarding the
use of residuals from ordinary least squares regression
are valid, and whether the assumptions which Green
(2001) outlined are likely to be violated in field studies.
For each of five species of small mammals, we first
assessed linearity between body mass and body size.
We then determined whether the portion of body mass
composed of energy reserves (body fat and lean dry
mass, which is predominantly composed of protein)
was independent of body size. Our major goal was to
determine which regression model produced residuals
that best predicted energy reserves. We used residuals
from OLS regression between a multivariate index of
body size (derived from a principal-components anal-
ysis) and body mass. It has been suggested that using
multiple regression to determine the direct relationship
between condition and an independent variable is a
preferred alternative to the use of residuals (Hayes and
Shonkwiler 2001). Thus we conducted a multiple re-
gression between body size and body mass, and com-
ponents of body mass (fat, lean dry mass, and water).
We interpreted the partial correlation coefficients be-
tween body mass and body components as measures
of the relationship between ‘‘condition’’ and body com-
position. Green (2001) suggested that alternative (Mod-
el II) regression models such as reduced major axis
(RMA) regression and major axis (MA) regression
should be preferred over OLS regression, because they
assume that error occurs in Xas well as Y(where X
corresponds to the measure of body size). Ordinary
least squares (OLS) regression assumes that there is no
error in X, because Xis set by the researcher (McArdle
1988). We assessed the relationship between residuals
obtained from both MA and RMA regression and body
composition, and compared this relationship to that
found between residuals from OLS regression and body
composition. Finally, we used numerical simulations
to compare the effects of a violation of the assumption
that the residual index of condition and true condition
(the proportion of mass associated with energy re-
serves) of an animal are independent of body size (or
BSI; Green 2001) on the different regression proce-
dures (OLS, MA, RMA).
M
ETHODS
We used data from five species of small mammal
collected in the Kananaskis Valley, Alberta, Canada,
in the Front Ranges of the Rocky Mountains (51
8
N,
115
8
W): yellow-pine chipmunks (
Tamias amoenus
Al-
len; see Plate 1), bushy-tailed woodrats (
Neotoma ci-
nerea
Ord; see Appendix), deer mice (
Peromyscus
maniculatus
Wagner), red-backed voles (
Clethriono-
mys gapperi
Vigors), and meadow voles (
Microtus
pennsylvanicus
Ord). All animals used in the analyses
were either adult males or adult females, which were
not pregnant or lactating.
Chipmunks (
n
5
22) were live trapped from early
May to late August 1998 using Longworth live traps
(baited with whole oats and sunflower seeds) and eu-
January 2005 157
BODY CONDITION INDICES
thanized with an overdose of isoflourine. Body mass
(
6
0.01 g), total body length including tail (
6
1 mm),
tail length (
6
1 mm), skull length (
6
0.1 mm), and skull
width (
6
0.1 mm) were measured and each body was
frozen. Woodrats (
n
5
62) were collected in summer
and winter of 1984–1985 using Conibear kill-traps
(Hickling et al. 1991). Body mass (
6
0.1 g), total body
length including tail (
6
1 mm), tail length (
6
1 mm),
skull length (
6
0.5 mm), and hind foot length (
6
0.5
mm) were measured and each body frozen. Deer mice
(
n
5
100), red-backed voles (
n
5
86), and meadow
voles (
n
5
34) were collected from early May to late
August 1987 using snap traps baited with a small string
that had been soaked in aromatic oils and then tied to
the treadle (Millar et al. 1990). Body mass (
6
0.1 g),
total body length including tail, tail length, hind foot
length, and ear length (all
6
1 mm) were measured, and
each body was frozen (Millar 1987, Millar et al. 1990).
Fat extractions were performed following Kerr et al.
(1982) and Dobush et al. (1985). For chipmunks, deer
mice, and voles, whole bodies (excluding stomach con-
tents) were dried, ground in a Wiley mill or aMoulinex
coffee grinder, and fat content was determined using
petroleum ether in a Soxhlet fat extractor. Mass of
stomach contents was measured (
6
0.01 g). Woodrat
carcasses (excluding stomach contents [weighed sep-
arately
6
0.1 g], skull, and pelt) were ground in a meat
grinder and dried. The carcass was then ground again
in a Moulinex coffee grinder. Fat extraction was per-
formed on two 4-g subsamples. Fat content of the pelt
was determined by soaking the intact pelt in ether for
24 h. Total fat content was calculated as the mean of
the two replicate estimates of carcass fat, plus pelt fat
(Hickling et al. 1991). Fat extractions for all species
were performed in the Department of Biology, Uni-
versity of Western Ontario. For all species, we calcu-
lated water content as the difference between fresh
mass (without stomach contents) and the mass of the
carcass after drying. Lean dry mass was determined by
the mass of the carcass following both water and fat
removal.
To measure overall structural size, we conducted a
principal-components analysis of log-transformed
body size variables for each of the five species (Iskjaer
et al. 1989, Dobson 1992). The first principal com-
ponent (PC1) was only used as an index of structural
size if all body size variables were positively correlated
with PC1 (Pimentel 1979). All variables were entered
into the analysis as measured except for total body
length and tail length. Body length was calculated by
subtracting tail length from total body length. We log-
transformed and standardized (mean of 0, standard de-
viation of 1) body mass and body size (PC1 scores) in
all analyses to remove the heteroscedastic nature of the
data and standardize all variables measured with dif-
ferent units (i.e., mass, PC scores). Residuals obtained
using untransformed body mass tended to increase with
body size (PC1).
Assessing linearity
We assessed whether the relationship between body
mass and body size (PC1 and body length) was linear
by inspecting plots of the residuals and the independent
variable (body size). If the residuals were evenly dis-
tributed across the range of body sizes, we assumed
that the relationship was linear. In addition, we con-
ducted quadratic regressions to determine whether the
addition of a second order term would improve the
proportion of variation in body mass explained by body
size. Colinearity between Xand X
2
may occur in poly-
nomial regressions, and it is appropriate to standardize
Xto a mean of 0 under these circumstances (Legendre
and Legendre 1998). In four of five species, we used
a principal-component score which had a mean of 0 as
X. For meadow voles, we standardized body length
(mean of 0, standard deviation of 1) for all individuals
for the polynomial regressions.
Testing for independence of energy reserves
from body size
To test for the independence of energy reserves from
body size, we conducted a multiple regression between
the mass of energy reserves (body fat and lean dry
mass) and both body size (PC1 or log body length) and
body mass. The partial correlation coefficient for body
size was used to determine whether energy reserves
were related to body size.
Comparing residuals
Slope and intercepts for OLS regression between
body mass and body size (PC1 or body length in the
case of meadow voles), and MA and RMA regressions
between body mass and body size (PC1 and body
length) were calculated for all five species. To calculate
RMA and MA slopes and intercepts, we used the pro-
gram ‘‘Model II regression’’ (Legendre 2001). Several
methods have been suggested for calculating residuals
as indices of condition. We used residuals (
y
-axis de-
viations) from OLS, RMA, and MA regressions as in-
dices of condition, and regressed them independently
on absolute fat (g), lean dry mass (g), and water (g).
We also used the partial correlation coefficient of mass
from a multiple regression of body components (fat,
lean dry mass, and water) on body size (PC1 or body
length) and body mass to describe the relationship be-
tween condition and body composition (Hayes and
Shonkwiler 2001). Finally, unlike OLS regression,
RMA and MA regression do not minimize the sum of
squared
y
-axis deviations, and therefore we used the
‘‘true’’ residual from these alternative regression mod-
els as indices of condition. Reduced major axis (RMA)
regression minimizes the sum of the areas of the tri-
angles defined by each data point, the point on the
regression line corresponding to the Xvalue, and the
point corresponding to the Yvalue (McArdle 1988).
Major axis (MA) regression minimizes the sum of
158
ALBRECHT I. SCHULTE-HOSTEDDE ET AL.
Ecology, Vol. 86, No. 1
squared distances perpendicular to the regression line.
Thus, the true residuals for these regression models are
the signed area of the triangle defined by each data
point and the points on the regression line correspond-
ing to the Xand Yvariables (RMA, where a triangle
above the slope is positive and a triangle below the
slope is negative), and the perpendicular distance be-
tween the data point and the regression line (MA).
Statistical simulations
We assumed an allometric relationship between the
body mass and the body size of an animal from a given
population. This relationship is an allometric equation:
b
median{body mass
z
body size}
5
a
(body size)
for some constants
a
and
b.
This equation can be trans-
formed into a linear equation by log transforming both
sides. After adding a random term to account for de-
viations from the allometric relationship, one obtains
log(body mass)
5b 1b
log(body size)
1d
01
where
b
0
and
b
1
are constants and
d
is a random variable
with median 0. The index of body condition (predicted
energy reserves) is
d
. To examine the effect of a vio-
lation of Assumption 2 (that the residual index of con-
dition and true condition [the proportion of mass as-
sociated with energy reserves] of an animal are inde-
pendent of body size [or BSI; Green 2001]), we pro-
duced data where there was no relationship between
energy reserves (
Z
) and body size (X). More specifi-
cally, we created random samples of X,Y(body mass),
and
Z
, where the random vector (X,Y) was independent
from the random variable
Z
. Then the residuals of the
regression of Yon X, calculated by OLS, MA, and
RMA regression are independent of
Z
. We randomly
introduced errors into the measurements of X,Y,
Z
,
and thereby obtained the measurements X
9
,Y
9
, and
Z
9
.
We then calculated the residuals of Y
9
with respect to
X
9
using OLS, MA, and RMA regression, and report
the number of times that the residuals and
Z
9
are found
to be significantly correlated. Because any detected
correlation is due to an error caused by a violation of
the assumption that body condition and size are in-
dependent, the method in which the detection rate is
significantly lower than the others is judged to be the
better method.
For four of the five data sets (yellow-pine chipmunk,
bushy-tailed woodrat, deer mouse, and red-backed
vole; because the index of size for the meadow vole
was univariate, this species was excluded), we ran-
domly created 10 000 new data sets, each with variables
standardized with a mean of 0 and a standard deviation
of 1. These new data sets ‘‘look like’’ the collected
data set except that there is no relationship between
the body size and true condition (mass associated with
energy reserves). To do this, we added a random
amount to each observed value of X. This random
amount is normally distributed with mean 0 and stan-
dard deviation 0.05 which corresponds roughly to 5%
error in the measurements. Instead of the measured
response
Z,
we used a random selection from all the
measured responses of
Z.
The random selection is de-
noted
Z
R
. Then (X
9
,Y) is independent of
Z
R
and in
particular there is no correlation between the residuals
of Yregressed on X
9
and the defined body condition
Z
R
.
To create a violation of the assumption that energy
reserves are independent of body size, we estimated
the parameters
b
0
and
b
1
in the linear model
Z
5b
0
1
b
1
X
1«
using the OLS procedure and calculated 90%
confidence intervals for the intercept and slope (I and
S, respectively). These intervals were fixed for all sim-
ulated data sets. We randomly chose
b
0
∈
I and
b
1
∈
S using the uniform distribution and let
Z
95
Z
R
1b
0
1b
1
X.
The simulation study was performed using the sta-
tistical software R, Version 1.7.1, for Microsoft Win-
dows (
available online
).
6
The programs used are avail-
able from the authors upon request.
R
ESULTS
The descriptive statistics for body size components,
body mass, and body composition are provided in
Schulte-Hostedde et al. (2001). The first principal com-
ponent (PC1) of morphological measurements for
woodrats, chipmunks, red-backed voles, and deer mice
was used to estimate body size. PC1 explained at least
50% of the overall variation in size measurements for
these species (Table 1). All morphological measure-
ments loaded positively and higher than 0.5 on PC1
except for hind foot length of red-backed voles (0.460).
Factor loadings for meadow voles were not in a con-
sistent direction (Table 1). Therefore, to describe body
size in meadow voles we only used log-transformed
body length (as in other studies of voles; e.g., Heske
and Ostfeld 1990). We used PC1 scores appropriately
standardized for all other species.
Assessing linearity
Visual inspection of residuals suggested that log-
transformation adequately linearized the data for all
species. The addition of a quadratic term to the re-
gression equations increased
r
2
negligibly (
,
0.02), and
the quadratic term was nonsignificant (
P
.
0.26) in all
cases.
Testing for independence of energy reserves
from body size
We found several cases in which energy reserves
were not independent of body size. In both deer mice
and red-backed voles, large individuals had less fat than
small individuals after controlling for body mass. In
bushy-tailed woodrats, deer mice, and red-backed
voles, large individuals had more lean dry mass than
6
^
http://www.r-project.org/
&
January 2005 159
BODY CONDITION INDICES
T
ABLE
1. Factor loadings of morphological traits on PC1 from principal-components analysis
for five species of small mammals sampled from the Kananaskis Valley, Alberta, Canada.
Trait Woodrat Chipmunk Meadow vole Red-backed
vole Deer mouse
Variance (%)
Body length
Skull length
Skull width
Hind foot
Ear length
75.1
0.883
0.916
NA
0.803
NA
50.0
0.799
0.535
0.757
NA
NA
49.3
2
0.718
NA
NA
0.620
2
0.761
55.0
0.840
NA
NA
0.460
0.856
51.0
0.756
NA
NA
0.679
0.726
Notes.
Variance refers to the percentage of the variation in the data explained by PC1 (see
Schulte-Hostedde et al. 2001). ‘‘
NA
’’ denotes not applicable.
T
ABLE
2. Partial correlation coefficients from multiple regression of body size (PC1 for all species except meadow voles)
and body mass on body components (fat, lean dry mass, water) for five species of small mammals.
Component Woodrat Chipmunk Meadow vole Red-backed
vole Deer mouse
PC1
Fat
Lean dry mass
2
0.221
0.337*
2
0.023
0.175
2
0.090
0.137
2
0.234*
0.256*
2
0.293*
0.266*
Mass
Fat
Lean dry mass
Water
0.426*
0.831*
0.969*
0.362
0.796*
0.820*
0.300
0.840*
0.980*
0.326*
0.777*
0.971*
0.360*
0.394*
0.887*
Note:
Body length was used as an index of body size for meadow voles because body size components did not load in
consistent directions in a principal-components analysis.
*
P
,
0.05.
small individuals after controlling for body mass (Table
2).
Comparing residuals from alternative regression
models to body composition
As expected, standardization of the body mass and
size (PC1 scores or body length) resulted in OLS slope
estimates equal to the correlation coefficient (
r
), and
intercepts equal to 0 for all five species (Table 3). In
addition, slope and intercept estimates for both RMA
and MA regression were 1 and 0, respectively, for all
five species. All regression models (OLS, RMA, MA)
pass through the mean of the Xand Yvariable, and
with standardized data the means of both Xand Yare
0. It follows from the equations for the slope for MA
and RMA regression (see formulae 10.11, 10.12 in Le-
gendre and Legendre [1998]), that the slope is 1 when
the variance in both Xand Yare equal, as occurs when
both variables are standardized.
Generally, residuals obtained by OLS regression
were more closely correlated with body components
(fat, lean dry mass, water) than residuals (both
y
-axis
residuals and ‘‘true’’ residuals) obtained from MA and
RMA regression (Tables 4 and 5).
Y
-axis residuals and
‘‘true’’ residuals from MA and RMA were similarly
correlated with body components (Tables 4 and 5).
When the relationship between body mass (corrected
for body size) and fat, lean dry mass, and water was
assessed directly via multiple regression (Table 2), the
partial correlation coefficients between mass and body
components were generally higher than those derived
from OLS residuals and body components, especially
with respect to lean dry mass and water.
Statistical simulations
The results of the statistical simulations revealed that
the proportion of simulations in which the null hy-
pothesis (that actual energy reserves are independent
of body size) was falsely rejected was substantially
higher with RMA and MA regression when compared
with OLS regression (Table 6). Residuals from OLS
regression tended to be falsely related to energy re-
serves 4–5% of the time, whereas residuals from RMA
and MA regression tended to be falsely related to en-
ergy reserves 10–30% of the time.
D
ISCUSSION
‘‘Condition’’ is a nebulous term and authors often
do not explicitly define its use. A major, though often
unstated, assumption is that condition refers to the en-
ergetic state of an animal. An animal in ‘‘good’’ con-
dition is thought to be in positive energy balance,
whereas an animal in ‘‘poor’’ condition is in negative
energy balance (Jakob et al. 1996, Speakman 2001).
While many authors assume that animals that are heavi-
er than predicted by their body size have more metab-
olizable tissue than individuals that are lighter than
predicted by body size (e.g., Dobson 1992), it is un-
likely that this extra mass is composed strictly of fat.
Unless animals are depositing energy (fat) for a specific
160
ALBRECHT I. SCHULTE-HOSTEDDE ET AL.
Ecology, Vol. 86, No. 1
T
ABLE
3. Intercepts and slopes obtained from ordinary least squares (OLS) regression between
standardized body mass (log-transformed) and body size (PC1 and log-transformed, or stan-
dardized body length for meadow voles) for five species of small mammals.
Species Intercept Slope (
5
r
) 95%
CI
P
Woodrat
Chipmunk
Meadow vole
Red-backed vole
Deer mouse
0
0
0
0
0
0.847
0.563
0.773
0.700
0.495
6
0.137
6
0.385
6
0.228
6
0.155
6
0.174
,
0.001
0.006
,
0.001
,
0.001
,
0.001
Notes:
Body length was used as an index of body size for meadow voles because body size
components did not load in consistent directions in a principal-components analysis. The 95%
confidence intervals for the slope, which must be equal to the correlation coefficient (
r
), and
corresponding
P
values are also included.
T
ABLE
4. Correlation coefficients (
r
) between
y
-axis residuals and absolute fat, lean dry mass, and water for five species
of small mammals.
Regression and
component Woodrat Chipmunk Meadow vole Red-backed
vole Deer mouse
OLS
Fat (g)
Lean dry mass (g)
Water (g)
0.409***
0.421***
0.518***
0.353†
0.660***
0.690***
0.287†
0.554***
0.631***
0.326*
0.547***
0.701***
0.357***
0.352***
0.832***
RMA/MA
Fat (g)
Lean dry mass (g)
Water (g)
0.315*
0.166
0.264*
0.207
0.323
0.357†
0.184
0.268
0.336†
0.303*
0.229*
0.378***
0.371***
0.078
0.545***
Notes:
Residuals were obtained from the regression between body mass and body size (PC1 or body length for meadow
voles) using ordinary least squares (OLS) regression, reduced major axis (RMA) regression, and majoraxis (MA) regression.
Body length was used as an index of body size for meadow voles because body size components did not load in consistent
directions in a principal-components analysis.
†
P
,
0.10; *
P
,
0.05; ***
P
,
0.001.
purpose (e.g., migration or hibernation), it seems likely
that variation in condition reflects variation in all con-
stituents of body composition including fat, protein,
water, and skeletal tissue. For example, residual indices
of condition reflect variation in all of these constituents
in small mammals (Schulte-Hostedde et al. 2001).
Therefore, our definition of condition does not restrict
variation in size-corrected mass to variation in fat
alone, but to all components of body composition. The
fact that condition reflects variation in all of fat, lean
dry mass, and water may explain why, in many cases,
residuals explain a moderate amount of variation in
body composition of small mammals.
Data from the five species of small mammals ex-
amined here generally fit the most critical assumptions
regarding the measurement of condition using residuals
from mass–size regressions (Green 2001). First, the
relationship between body mass and body size appeared
to be reasonably linear for all species. Nonlinear re-
lationships may be more likely when intraspecific var-
iation in body size (X) is larger than that found in small
mammals. For instance, allometric (nonlinear) rela-
tionships between body mass and body size may be
more likely in taxa with indeterminate growth, such as
reptiles and amphibians, than in taxa with determinate
growth, such as mammals and birds. Hayes and Shonk-
wiler (2001) examined bivariate plots of mass and body
size in six species: chuckwalla (
Sauromalus obesus
),
desert tortoise (
Gopherus agassizii
), trout (
Oncorhyn-
chus clarki
), mason bee (
Osmia
sp.), orange-crowned
warbler (
Vermivora celata
), and white-ankled mouse
(
Peromyscus pectoralis
). Relationships appeared to be
nonlinear when the range of body sizes was large
(
.
100%), and linear when the range of body sizes was
small (
,
25%).
Second, there was evidence of size dependence of
energy reserves among three of the five examined spe-
cies. The general pattern appears to be that larger in-
dividuals carry less fat and/or more lean dry mass than
smaller individuals. Nonetheless, the amount of vari-
ation in energy reserves explained by body size was
low (5.5–11.3%). The assumption that energy reserves
are independent of body size may occasionally be vi-
olated in natural populations, if larger individuals have
greater access to food resources.
The statistical simulations provide evidence that or-
dinary least squares (OLS) regression is preferred over
major axis (MA) and reduced major axis (RMA) re-
gressions. Residuals derived from both MA and RMA
regression of body mass (log-transformed) on body size
were far more likely to be falsely related to energy
reserves than residuals derived from OLS regression.
This result, coupled with the fact that RMA and MA
residuals consistently predicted less variation in body
January 2005 161
BODY CONDITION INDICES
T
ABLE
5. Correlation coefficients (
r
) between ‘‘true’’ residuals and absolute fat, lean dry
mass, and water for five species of small mammals.
Regression and
component Woodrat Chipmunk Meadow vole Red-backed
vole Deer mouse
RMA
Fat (g)
Lean dry mass (g)
Water (g)
0.340*
0.192
0.269*
0.221
0.332
0.355†
0.229
0.297†
0.387*
0.332*
0.170†
0.318*
0.405***
0.019
0.529***
MA
Fat (g)
Lean dry mass (g)
Water (g)
0.315*
0.167
0.264*
0.207
0.323
0.357†
0.184
0.268
0.336†
0.303*
0.228*
0.378***
0.371***
0.078
0.545***
Notes:
Residuals were obtained from the regression between body mass and body size (PC1
or body length) using reduced major axis (RMA) regression, and major axis (MA) regression.
Body length was used as an index of body size for meadow voles because body size components
did not load in consistent directions in a principal-components analysis.
†
P
,
0.10; *
P
,
0.05; ***
P
,
0.001.
T
ABLE
6. Proportion of false rejections of the null hypoth-
esis that energy reserves are independent of body size, in
simulations for four species of small mammals.
Species OLS MA RMA
Chipmunk
Deer mouse
Red-backed vole
Woodrat
0.0404
0.0476
0.0465
0.0408
0.1251
0.1746
0.0934
0.2902
0.1275
0.1815
0.0949
0.2966
Notes:
Proportions are based on 10 000 simulations for
each regression model. Key to abbreviations: OLS, ordinary
least squares regression; MA, major axis regression; RMA,
reduced major axis regression.
composition, suggests that RMA and MA regressions
do not offer many benefits when compared to OLS
regression.
Although recently called into question (Kotiaho
1999, Green 2001, Hayes and Shonkwiler 2001), re-
siduals from the body mass–body size OLS regressions
consistently explained significant amounts of variation
in fat, water, and lean dry mass. Residuals from RMA/
MA regression were often significantly correlated with
body components; however, the coefficient of deter-
mination was consistently lower in the RMA/MA anal-
ysis than in the OLS analysis. Therefore, qualitatively,
OLS residuals appeared to be somewhat superior to
RMA/MA residuals with respect to predicting body
composition.
RMA (or Model II) regression has been advocated
as a more appropriate approach for describing the func-
tional relationship between two variables measured
with error (LaBarbera 1989, Ebert and Russell 1994,
Herrera 1992, Fairbairn 1997). Most uses of regression
in ecology and evolution involve variables that are both
measured; thus there is error in both dependent and
independent variables. The use of OLS regression
(which assumes that Xvalues are measured without
error and set by the researcher) therefore seems inap-
propriate. There is abundant evidence that RMA slope
estimates accurately depict functional relationships be-
tween variables measured with error (McArdle 1988,
LaBarbera 1989, Legendre and Legendre 1998). How-
ever, if the purpose of regression is prediction, as is
done with residual indices of condition, OLS regression
is most appropriate (Legendre and Legendre 1998).
Calculating residuals as an index of condition requires
the comparison of observed mass to predicted mass. In
other words, residuals are used to determine why an
animal is heaver/lighter than predicted based on body
size. Because OLS regression minimizes error in Y
(mass), residuals from OLS regression should predict
body mass more precisely than RMA regression. Typ-
ically, measurement error is a major source of variation
in measures of body size (Yezerinac et al. 1992); there-
fore using the average of repeated measurements may
be one method of minimizing error in X(e.g., Schulte-
Hostedde and Millar 2000). Despite this approach, cor-
recting for measurement error, particularly in the con-
text of RMA and MA regression, requires the modeling
of error in both Xand Yvariables, something that is
rarely done (Carroll and Ruppert 1996). The arguments
contrasting OLS and RMA/MA residuals, however, be-
come trivial when
r
approaches 1 because the RMA
slope is equal to the OLS slope divided by the corre-
lation coefficient (Legendre and Legendre 1998).
An important issue in the evaluation of body con-
dition indices derived from mass–size regressions is
the high correlation between residuals and mass (Y).
In OLS regression, residuals and X(size) are indepen-
dent of each other, whereas residuals and Y(mass) are
positively related. In RMA regression, the correlations
between residuals and mass (Y) and size (X) are of
equal magnitude (Green 2001). This has the potential
to be a serious weakness of the use of OLS residuals
because, when validating residual indices of condition
against components of body mass (i.e., fat, lean dry
mass, water), these relationships may become biased
(i.e., relationships between residuals and fat, for ex-
ample, may tend to be significant because fat is a com-
ponent of mass). One reason for this bias is the cor-
related error structure which occurs between the mea-
162
ALBRECHT I. SCHULTE-HOSTEDDE ET AL.
Ecology, Vol. 86, No. 1
surement of total mass and its components (A. J. Green,
personal communication
). Any error in measuring mass
automatically affects the value of absolute fat, lean dry
mass, or water. Because modeling measurement error
was not done, it is impossible to assess the affects of
measurement error of mass on the error structure of the
data. Nonetheless, an alternative approach to validating
condition indices might be to examine these indices
against a mass-independent physiological measure of
condition such as levels of liver glycogen or blood
glucose.
Regardless of which condition index is used, it is
important that it correlate with constituents of body
composition. If condition is assumed to reflect variation
in fat, it is important to validate this assumption. As
seen here, condition does not necessarily reflect fat.
Body condition indices were more closely correlated
with lean dry mass and water in five species of small
mammals, perhaps because the proportion of body mass
composed of fat is often small (Schulte-Hostedde et al.
2001). Low protein reserves during periods of low food
resources indicate that small mammals may catabolize
protein to meet some energy requirements (Virgl and
Messier 1992, Zuercher et al. 1999). Determining the
degree to which condition indices correlate with energy
reserves requires the independent evaluation of body
composition.
A
CKNOWLEDGMENTS
We thank all the assistants who measured body size and
conducted body composition analysis on all the samples. C.
D. Ankney, J. P. Hayes, and P. J. Weatherhead participated
in stimulating discussions on issues related to body condition.
We also thank T. A. F. Long and R. D. Montgomerie for
discussion and review of the manuscript. The manuscriptwas
also greatly improved by reviews from F. S. Dobson, A. El-
lison, A. J. Green, P. Legendre, and three anonymous re-
viewers. We particularly thank F. S. Dobson for his willing-
ness to improve the manuscript. This study was supported by
an NSERC operating grant to JSM.
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APPENDIX
Images of bushy-tailed woodrats are available in ESA’s Electronic Data Archive:
Ecological Archives
E086-010-A1.
