The document reanalyzes a previous study on patch selection by red deer in relation to energy and protein intake. The reanalysis uses an energy intake model that incorporates the effect of gut filling on daily intake rates. The results show that: 1) Patch use by red deer was just as strongly correlated with estimated daily intake of digestible energy as digestible protein in four of the seven trials studied. 2) In all cases, daily intake of digestible energy was a better predictor of patch preference than dry matter intake alone. 3) Estimated daily energy intake was highly correlated with short-term estimates of protein intake, suggesting patch use could maximize both energy and protein gain simultaneously.

1. Oecologia(1995) 104:297-300 9 Springer-Verlag 1995
John F. Wilmshurst 9John M. Fryxell
Patch selection by red deer in relation to energy and protein intake:
a re-evaluation of Langvatn and Hanley's (1993) results
Received: 10October 1994/ Accepted:27 May 1995
Abstract Langvatn and Hanley (1993) recently reported
that patch use by red deer (Cervus elaphus) was more
strongly correlated with short term rates of intake of di-
gestible protein than dry matter. Such short term mea-
sures overlook effects of gut filling, which may constrain
intake by ruminants over longer time scales (i.e., daily
rates of gain). We reanalyzed Langvatn and Hanley's da-
ta using an energy intake model incorporating such a
processing constraint, to determine whether their conclu-
sions are robust. We found that the use of patches by red
deer was just as strongly correlated with an estimate of
the daily rate of intake of digestible energy as one of di-
gestible protein during four out of seven trials, but slight-
ly lower in three out of seven trials. In all cases, daily in-
take of digestible energy was a much better predictor of
patch preference by red deer than was the intake of dry
matter. Our reanalysis suggests that the daily intake of
energy was highly correlated with that of protein in these
trials, as may often be the case for herbivores feeding on
graminoids. Hence the observed pattern of patch use by
red deer could simultaneously enhance rates of both pro-
tein and energy intake.
Key words Energy 9Cervus elaphus 9Foraging 9Patch
selection 9Protein
Introduction
Langvatn and Hanley (1993) recently reported on an ele-
gant experimental study of the evolutionary basis for
patch selection by red deer (Cervus elaphus). In their ex-
periment, captive red deer were permitted to select
among 16 large patches of timothy (Phleum pretense)
maintained at four different levels of biomass. They
J.E Wilmshurst 9J.M. Fryxell(~)
Department ofZoology,Universityof Guelph,
Guelph,Ontario, N1G 2W1,Canada
Ph: 519-824-4120ext. 3630
Fax: 519-767-1656
e-mail:jfryxell@uoguelph.ca
compared the time spent in each patch with estimated
rates of intake of digestible protein (DP) and digestible
dry matter (DDM) within those patches. Their results
clearly showed that patch use by red deer was more
strongly correlated with short term rates of intake of pro-
tein than of dry matter.
Langvatn and Hanley (1993) stated that their experi-
mental results do not conclusively demonstrate the basis
for patch selection by red deer. Indeed, they argued that
protein was a better indicator than digestible dry matter
largely because protein was a more sensitive index of
plant phenological stage and therefore plant quality.
Nonetheless, some naive readers might be tempted to
conclude from Langvatn and Hanley's results that dry
matter or energy gain are unimportant currencies in red
deer foraging strategies.
A substantial body of research suggests that daily
rates of intake by herbivores are ultimately constrained
by rates of processing and clearance of ingesta through
the gut (Amann et al. 1973; Belovsky 1978; Mould and
Robbins 1982; Doucet and Fryxell 1993; Fryxell et al.
1994). If rates of digestive processing change with matu-
ration stage of the vegetation, due to changes in fiber or
lignin content, than short term rates may give a mislead-
ing impression about the benefits of feeding in a patch of
given biomass.
In this paper we reanalyze Langvatn and Hanley's
(1993) data using an energy intake model that predicts
daily rates of energy intake for grazing ruminants (Fryx-
ell 1991), using experimentally determined parameters
for Cervus elaphus (Wilmshurst et al. 1995). We show
that Langvatn and Hanley's (1993) results are consistent
with maximization of daily intake of both protein and
energy, after taking into account the effect of plant
phenological stage on digestive passage rates. The latter
possibility was briefly mentioned by Langvatn and Han-
ley, but they were not in a position to consider its poten-
tial implications. We also explain why short term mea-
sures of digestible dry matter intake may be poor predic-
tors of patch use.

2. 298 OECOLOGIA 104 (1995) 9 Springer-Verlag
Materials and methods
The model
In this reanalysis, we are concerned exclusively with predicting
daily energy gain from measures of herbivore dry matter intake
and forage quality. The general model we use was described in de-
tail by Fryxelt (1991), with subsequent elaboration and application
by Wilmshurst et al. (1995) to Cervus elaphus in North America.
The model is based on the premise that there is a fundamental
trade-off between the availability of grass and its rate of process-
ing by ruminants.
The availability constraint is modelled as the product of the
functional response and forage digestible energy (DE) content,
where the functional response is an increasing function of grass
biomass (Wickstrom et al. 1984; Gross et al. 1993; Wilmshurst et
al. 1995). Hence, this constraint should increase monotonically
over the range of grass biomasses considered in Langvatn and
Hanley's (1993) experiments.
The processing constraint is modelled as ad libitum intake
multiplied by forage DE content. Given that passage rate limits in-
take (Arnold 1985) and passage is slow for poor quality forage
(Van Soest 1982), the digestive constraint should decrease with in-
creasing grass biomass (Ammann et al. 1973; Mould and Robbins
1982). The minimum of these functions with slopes of opposite
signs dictates the daily rate of energy intake. The model generally
predicts that the daily rate of energy gain should often be maxi-
mized for ruminants at low to intermediate forage biomass (Fryx-
el1 1991; Wilmshurst et al. 1995).
Data analysis
We incorporated Langvatn and Hanley's (1993) data into our mod-
el to estimate the daily rate of energy gain for red deer feeding on
patches of timothy of various biomass levels. We assume an aver-
age body mass of 106 kg for red deer and an energy density for
timothy of 19.25 kJ/g (Mellin et al. 1962; Armstrong 1964).
To estimate forage DE content, we multiplied Langvatn and Han-
ley's (1993) DDM values by a regression formula relating forage
DDM to DE for wapiti (Cervuselaphus nelsoni;Mould and Robbins
1982). This value was multiplied by the functional response used by
Langvatn and Hanley (1993) in their estimate of dry matter intake
(Wickstrom et al. 1984) to estimate the availabilityconstraint. To es-
timate the processing constraint we multiplied the DE function by ad
libitum intake values for wapiti (Mould and Robbins 1982). Foraging
costs were taken from wapiti bioenergetic data (Gates and Hudson
1978; Wickstrom et al. 1984) scaled to red deer body size.
The daily rate of energy intake was calculated for various bio-
mass levels of timothy, over the range 0-6000 kg/ha. We followed
Langvatn and Hanley's (1993) methodology in using the magni-
tude of r2 values (Casella 1983; Myers 1986) to evaluate the alter-
nate hypotheses that patch use by red deer was proportional to (1)
daily energy intake, (2) short term protein intake or (3) short term
dry matter intake.
Table 1 R2 values relating the goodness-of-fit between observed
red deer patch use and predicted patch use taken from Langvatn
and Hanley (1993) (L & H) and calculated by us (W & F). Nota-
tion corresponds to that of Langvatn and Hanley (1993). Ho pre-
dicts patch use of a model forager moving among patches random-
Results
Langvatn and Hanley's (1993) data suggest that DE de-
clined linearly with increasing biomass (kg/ha)
(y = 67.6-0.003x, F1,24 = 81.5, P < 0.001, r2 = 0.77).
Multiplying this by the functional response gave an in-
creasing availability constraint, and multiplying by ad
libitum intake gave a decreasing processing constraint.
This resulted in a dome-shaped intake function (Fig. 1),
the shape of which suggests that red deer should maxi-
mize their daily rate of energy gain when feeding in
grass swards with a biomass of 930 kg/ha. We used this
function to estimate the daily rate of energy gain by red
deer for each experimental patch and trial reported by
Langvatn and Hanley (1993).
In all trials, patch use was more strongly correlated
with daily energy gain than DDM intake (Table 1). In
four of seven trials, there was just as strong a correlation
between patch use and the daily rate of energy gain as
protein gain (Table 1). In three of seven trials, however,
the correlation between patch use and protein gain was
slightly higher than that of energy gain. To evaluate the
degree of similarity between our estimates of daily rates
of energy intake and Langvatn and Hanley's (1993) esti-
mates of DDM and DP intake, we calculated Pearson
correlation coefficients (1"). Daily rates of energy intake
were more strongly correlated with short term protein in-
141
Zm
>.
re
DJ
Z
UJ
F-
UJ
Z
90
60
30
i i
~ 2 4 6
FORAGE BIOMASS
Fig. 1 Function predicting daily net energy intake (kJ day-1 kg
body mass ~) for red deer over a range of vegetation densities
(kg/ha x 103). Daily net energy intake is maximized at 930 kg/ha
ly, H2a predicts patch use of a forager matching time in patch with
digestible protein intake, H2b predicts patch use of a forager
matching time in patch with digestible dry matter intake and DE
predicts patch use of a forager matching time in patch with daily
net energy intake
Hypothesis Trial number
1 2 3 4 5 6 7
L & H, Ho 0.384 0.531 0.521 0.532 0.555 0.651 0.515
L & H, H2a 0.941 0.946 0.952 0.841 0.863 0.888 0.739
L & H, H2b 0.211 0.045 - 0.158 0.451 0.599 0.455
W & F, DE 0.671 0.591 0.758 0.876 0.933 0.877 0.736

3. take (r2 = 0.79) than short term rates of dry matter intake
(r2 = 0.49), presumably because protein content covaried
with digestible energy content. Hence, it is not surprising
that both measures had similar predictive power.
Discussion
Our reanalysis of Langvatn and Hanley's data, incorpo-
rating a model with a digestive constraint on daily food
intake, suggests that patch use by red deer may be just as
strongly correlated with daily rates of energy intake as
short term rates of protein intake. At the very least, our
results show that estimated DE intake is a much better
predictor of patch use than DDM intake.
Of course, it is always possible in science that none of
the alternate hypotheses under consideration explain the
pattern of interest. In this case, there are certainly viable
alternate hypotheses that have not been explicitly consid-
ered. For example, one could postulate (as did one of our
anonymous reviewers) that red deer simply choose the
youngest plants available, on the grounds that immature
plants often have the lowest level of fiber, as well as the
highest levels of soluble nitrogen and protein [e.g. Lang-
vatn and Hanley's (1993) Figs. 3, 4]. The plant quality
hypothesis is inconsistent, however, with Langvatn and
Hanley's (1993) observations.
Langvatn and Hanley's (1993) protocol involved four
grass treatments, comprising different planting dates. At
the beginning of the foraging experiment, grasses in
treatment I had grown undisturbed for 1 year, treatment
II for 5 weeks, treatment III for 3 weeks, and treatment
IV for less than 1 week. Accordingly, the plant quality
hypothesis predicts that treatment III should have been
preferred during the first two trials (because the newly
planted grasses in treatment IV had not yet germinated)
and treatment IV thereafter. In fact, treatment II was pre-
ferred by deer during the first three trials, treatment III
during the next three trials, and treatment IV during the
last trial. Hence, the plant quality hypothesis failed in 6/7
trials, a poorer record than one would expect even if deer
chose patches at random.
The same kind of reasoning supports both the protein
and energy maximization hypotheses. Swards of approx-
imately 500-1000 kg/ha dry mass, were predicted to
yield the highest rates of protein or energy gain per day
(Figs. 1, 2). During the first four trials, treatment II was
closest to the optimal biomass range. Both treatments II
and III were in the optimal range during the next two tri-
als. Treatments III and IV were in the optimal range dur-
ing the last trial. These predictions square well with the
observed patch preferences: treatment II was preferred
during the first three trials, treatment III was preferred
during the next three trials and treatment IV was pre-
ferred during the last trial. This pattern suggests that the
preferred treatment changed over time as some grass
patches (e.g. treatment II) grew out of the optimal bio-
mass range at the same time as other grass patches (first
treatment III and later IV) grew into the optimal range.
OECOLOGIA 104 (1995) 9 Springer-Verlag 299
800
600
LLI
_ 400
200
o o
AA
i i 9 9
2 4 6
FORAGE BIOMASS
Fig. 2 Langvatn and Hanley's (1993) estimates of digestible dry
matter intake (o; g min-1) and digestible protein intake (A; g
min-1) on each of four vegetation densities (kg/ha x 103)oversev-
en foraging trials with red deer
Without access to the original data, this assertion cannot
be tested more rigorously, nor can we reject the remote
possibility that feeding preferences were determined by
concentrations of soluble nitrogen, secondary metabo-
lites, or other plant nutrients that were uncorrelated with
plant biomass.
The critical difference between our analysis and that
of Langvatn and Hanley (1993) is our inclusion of a pro-
cessing constraint. Everything else being equal, the
availability constraint predicts a positive relationship be-
tween DDM intake and grass biomass. This is due to the
functional response increasing faster than digestibility
declines with increasing grass biomass. While the avail-
ability no doubt reflects the short term benefits of patch
selection, natural selection should favor behaviors that
maximize fitness over longer time scales.
Ultimately, foraging rates in ruminants are limited by
the rate of gut clearance, that is, animals could theoreti-
cally bite more food than they can process through their
digestive tracts. Langvatn and Hanley's (1993) implicit
short term model therefore predicts that DDM intake
should approach an asymptote at high forage biomass,
whereas our long term model predicts a decline in DDM
intake with increasing grass biomass (Fig. 2).
Langvatn and Hanley have clearly shown that patch
use by red deer is strongly correlated with rates of pro-
tein gain. We agree with this result, but also argue that
patch use may be as strongly correlated with daily rates
of energy gain in red deer, as indicated by our analagous
experiments with Cervus elaphus in North America
(Wilmshurst et al. 1995). Teasing apart these covarying
nutritional currencies may not be a simple matter.
Finally, we note with interest that in Langvatn and
Hanley's (1993) experiments and Wilmshurst et al.'s
(1995) analogous experiments, deer used patches in pro-
portion to fitness gains, rather than concentrating entirely
within the best patch. Such matching behavior (some-
times termed partial preference behavior) is common
even in tightly controlled foraging experiments and is of-
ten interpreted as reflecting the necessity of repeated

4. 300 OECOLOGIA 104 (I995) 9 Springer-VerIag
sampling by animals in order to assess patch quality or
simply discrimination errors (Krebs and McCleery
1984). Indeed, it would be rare in biology to see no vari-
ation around any threshold function, such as optimal diet
selection or optimal patch selection (Stephens 1985). It
certainly cannot be regarded as suitable grounds for re-
jection of optimality models.
Acknowledgements This work was funded by an Ontario Gradu-
ate Scholarship to J.EW. and a Natural Science and Engineering
Research Council of Canada operating grant to J.M.E We thank
Rolf Langvatn, Tom Hanley, and two anonymous reviewers for
their critical comments on the manuscript.
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