Spatial variation in antler investment of Apennine red deer

Abstract

Heterogeneity in resource availability and quality can trigger spatial patterns in the expression of sexually selected traits such as body mass and weaponry. While relationships between habitat features and phenotypic quality are well established at broad geographical scales, information is poor on spatial patterns at finer, intrapopulation scales. We analyzed biometric data collected on 1965 red deer Cervus elaphus males over 20 years from a nonmigratory population living on two sides of a mountainous ridge, with substantial differences in land cover and habitat quality but similar climate and population density. We investigate spatial patterns in (i) body mass, (ii) antler mass, and (iii) antler investment. We also tested for site- and age-specific patterns in allometric relationship between body mass and antler mass. Statistically significant fine-scale spatial variations in body mass, antler mass, and, to a lesser extent, antler allocation matched spatial differences in land cover. All three traits were greater in the northern slope, characterized by higher habitat heterogeneity and greater availability of open habitats, than in the southern slope. Moreover, the allometric relationship between body mass and antler mass differed among age-classes, in a pattern that was consistent between the two mountain slopes. Our results support the occurrence of spatial patterns in the expression of individual attributes also at a fine, intrapopulation scale. Our findings emphasize the role of environmental heterogeneity in shaping spatial variations of key life-history traits, with potential consequences for reproductive success.

Full text

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1 | INTRODUCTION
Spatial variation of environmental factors has a major influence on
several ecological processes affecting individuals and populations
(e.g., Cromsigt et al., 2009; Karanth et al., 200 4; Post et al., 2009).
Sexually selected trait s, in par ticular, are sensitive to environmental
heterogeneity (Cornwallis & Uller, 2010; Maan & Seehausen, 2011);
hence, spatial variation is expected to occur in mating- related
morphological attributes (e.g., insects: Miller & Emlen, 2010;
fish: Mollet et al., 2013; amphibians: Lüpold et al., 2017; reptiles:
Kwiatkowski & Sullivan, 20 02; birds: Møller et al., 2006; mammals:
Post et al., 1999). Environmental heterogeneity can occur at multi-
ple geographical scales, resulting in interindividual variation in the
expression of morphological traits. In turn, environment- mediated
variation in the expression of sexually selected traits would be ex-
pected not only bet ween individuals belonging to different pop-
ulations (e.g., Kavčić et al., 2020; Lüpold et al., 2017), but also at
Received: 3 September 2020
|
Revised: 14 March 2021
|
Accepted: 12 April 2021
DOI: 10.100 2/ece3.7617
ORIGINAL RESEARCH
Spatial variation in antler investment of Apennine red deer
Stefano Mattioli1 | Francesco Ferretti1 | Sandro Nicoloso2 | Luca Corlatti3
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium,
provide d the orig inal work is proper ly cited .
© 2021 The Authors. Ecology and Evolution p ublished by John Wiley & Sons Ltd.
1Depar tment of L ife Science, Unive rsity of
Siena, Siena, It aly
2Research, Ecology and Environment
Dimensions (D.R.E.Am. Italia), Pistoia, Italy
3Chair of Wi ldlife Ecology an d Management,
University of Freiburg, Freiburg, Germany
Correspondence
Luca Corlatti, Chair of W ildlife Ecology
and Management, University of Freiburg,
Tennenbacher Str. 4, Freibu rg 76109,
Germa ny.
Email: luca.corlatti@wildlife.uni-freiburg.de
Funding information
The article pro cessing charge was funded by
the German Research Foundation (DFG) in
the funding program DEAL.
Abstract
Heterogeneity in resource availability and quality can trigger spatial patterns in the
expression of sexually selected traits such as body mass and weaponry. While rela-
tionships between habitat features and phenotypic quality are well established at
broad geographical scales, information is poor on spatial patterns at finer, intrapopu-
lation scales. We analyzed biometric data collected on 1965 red deer Cervus elaphus
males over 20 years from a nonmigratory population living on two sides of a moun-
tainous ridge, with substantial differences in land cover and habitat quality but simi-
lar climate and population density. We investigate spatial patterns in (i) body mass,
(ii) antler mass, and (iii) antler investment. We also tested for site- and age- specific
patterns in allometric relationship between body mass and antler mass. Statistically
significant fine- scale spatial variations in body mass, antler mass, and, to a lesser ex-
tent, antler allocation matched spatial differences in land cover. All three traits were
greater in the northern slope, characterized by higher habitat heterogeneity and
greater availability of open habitats, than in the southern slope. Moreover, the allo-
metric relationship between body mass and antler mass differed among age- classes,
in a pattern that was consistent between the two mountain slopes. Our results sup-
port the occurrence of spatial patterns in the expression of individual attributes also
at a fine, intrapopulation scale. Our findings emphasize the role of environmental
heterogeneity in shaping spatial variations of key life- history traits, with potential
consequences for reproductive success.
KEYWORDS
allometry, antler investment, deer, life- history traits, phenotypic quality, spatial pat terns,
ungulates

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MATTIOLI e T AL.
the intrapopulation scale (e.g., Clut ton- Brock et al., 1982; Miller &
Emlen, 2010).
In large herbivores, for example, heterogeneity in key resources
can trigger spatial patterns in expression of individual traits at
large geographical (e.g., Andersen et al., 1998; Kavčić et al., 2020)
as well as at intrapopulation scales (e.g., Clutton- Brock et al., 1986;
Pettorelli et al., 20 02). In polygynous ungulates, access to abundant
resources is expected to emphasize male investment on sexually
selected traits such as body mass and weapon size (e.g., Ashley
et al., 1998; Clutton- Brock et al., 1982; Leblanc et al., 20 01; Schmidt
et al., 2001). Thus, spatial variation of abundance of key resources
would be predicted to elicit spatial patterns of investment on traits
such as male horns or antlers.
Given their wide distribution range encompassing a variety of
landscapes, and large inter- and intraspecific variation in body mass,
male cervids are particularly suit able to investigate spatial cor-
relates of individual allocation to sexually selec ted secondary traits
(Geist, 1998). Since their origin in the early Miocene, cervids have
been characterized by the pre sence of deciduous cranial appendages
(antlers). Initially, deer lived in tropical and subtropical dense woods,
were small- sized and with relatively small antlers of simple structure,
possibly serving as offensive weapons (Geist, 1998). Since the early
Pliocene, larger deer species adapted to more open habitats began to
appear, with males bearing longer, heavier, and more complex antlers
(Croitor, 2018; Geist, 1998; Heckeberg, 2020). Open environments
presumably favoured more gregarious behavior and stronger male–
male competition for access to mates: Accordingly, size dimorphism
and antler size grew in response to more intense sexual selection
(Geist & Bayer, 1988; Kitchener, 1991; Pérez- Barbería et al., 2002).
Still today, antlers are relatively larger in cervids forming larger
breeding groups and with complex social behavior (Clutton- Brock
et al., 1982; Lincoln, 1992; Plard et al., 2011). Antlers are effective
weapons but also honest signals of fighting ability and genetic qual-
ity, a conspicuous ornament to threaten other males and attract
females (Clutton- Brock et al., 1980; Geist, 1966; Malo et al., 20 05;
Morina et al., 2019; Vanpé et al., 2007). With antler investment be-
coming more demanding and costly, antler development became
increasingly dependent on environmental productivity and climate
(Brown, 1990; Goss, 1983). At the end of the Early Pleistocene, the
first red deer Cervus elaphus appeared (Franzen et al., 2000; van der
Maden, 1999), characterized by large size and with relatively heavy
and well- branched antlers. Red deer size fluctuated for all Middle
and Late Pleistocene and for Holocene in relation to environmental
changes (cf. Saarinen et al., 2016).
Red deer is among the cervid species with the largest rela-
tive antler size (Geist, 1998; Geist & Bayer, 1988). Compared with
its more closely related species (sika deer Cervus nippon and wa-
piti Cervus canadensis), it has a higher plasticity and can produce a
greater relative antler mass under favorable environmental condi-
tions. In low- productivity habitats, such as Scottish moorlands and
Sardinian maquis scrub, red deer are represented by “maintenance
phenotypes” (sensu Geist, 1978) with relatively small antlers of sim-
plified structure. Conversely, in rich environments they give rise
to “luxur y phenot ypes,” that is, large- sized animals with large ant-
lers. For example, Scottish red deer translocated to New Zealand
in habitats with superabundant resources have grown heavy and
multipointed antlers (Huxley, 1931; Mitchell et al., 1977). Feeding
experiments demonstrated that red deer stags weighing 180 kg
(prerut live body mass) with 6 kg trophies can produce in three gen-
erations 300– 350 kg stags with 11– 14 kg trophies, if provided with
high nutrition planes (Geist , 1986; Vogt, 1947). In central and east-
ern Europe, some adult red deer stags have attained 320– 340 kg
of postrut body mass and 17– 19 kg of net antler mass (Botev, 1990;
Geist, 1986, 1998; Mager, 1941; Szunyoghy, 1959).
Like all highly dimorphic, large, and long- lived ungulates, the red
deer has a prolonged somatic grow th, especially in males. Given
the high energetic costs to produce skeleton and muscles, males
begin to allocate more resources to antlers only when they reach
prime age (Gómez et al., 2012). Generally, antlers reach the peak of
their development between 8 and 12 years (Drechsler, 1980, 1988;
Langvatn, 1986; Mysterud et al., 2005), which approximately coin-
cides with the highest potential reproductive success (Clut ton- Brock
et al., 1988; Kruuk et al., 2002; Nussey et al., 20 09). To maximize
antler mass, adult stags are more efficient than younger st ags in mo-
bilizing minerals from the skeleton to support antler growth (Gómez
et al., 2012). Antler investment is thus age- dependent and sensitive
to food availability and climate, making antlers reliable indicators of
individual qualit y (Brown, 1990; Peláez et al., 2018).
A strong allometric relationship has been reported between ant-
ler mass and eviscerated body mass in adult red deer of different
populations (Huxley, 1931). This “positive allometry ” is often associ-
ated with the growth of conspicuous secondary sexual traits (Kodric-
Brown et al., 2006; O’ Brien et al., 2018). Differences in allometric
relationship have been observed between subadults (2– 4 years old)
and adult s (aged 5+) (Schröder, 1983). The relationship bet ween ant-
ler mass an d body mass was also i nvestigated in fa rmed red deer s tags
(Ball et al., 1994; Hyvärinen et al., 1977; Moore et al., 1988; Muir &
Sykes, 1988) and in other cervid species including white- tailed deer
Odocoileus virginianus (McCullough 1982; Jones et al., 2018) and
mule deer O. hemionus (And erson & Med in 1965). However, informa-
tion on how local environmental conditions affec t positive allometry
is rare for cervids (but see Jones et al., 2018 for white- tailed deer).
Here, we investigate age- and site- dependent antler invest-
ment, body mass, and allometric relationships in a nonmigratory
red deer population. We considered two different slopes of an
Apennine ridge in Italy with different habitat composition, leading
to different productivit y. Red deer density and hunting pressure
are comparable bet ween the two slopes; there is no supplemental
feeding and proximit y between sites suggests no major dif ferences
in weather, thus allowing to exclude these potentially confounding
effects. We hypothesize the local occurrence of a relationship be-
tween different morphological features (antler mass, body mass, and
antler investment) and age, conditional on sites with different lev-
els of environmental heterogeneity. Namely, we predict that antler
mass, body mass, and antler investment will increase up to prime
age and then decline in old age (e.g., Drechsler, 1980, 1988), being

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greater for males in the mountain slope with abundant food- rich
patches (Brown, 1990). Second, we hypothesize age- specific and
spatial heterogeneity in the allometric relationships between body
mass and antler mass. Accordingly, we predicted that allometric re-
lationship will vary among age- classes, possibly increasing with age
(Schröder, 1983) and will be weaker in the less productive site (Jones
et al., 2018).
2 | MATERIALS AND METHODS
2.1 | Study sites
The study area (1,40 0 km2) stretches across the two sides of the
Apennine chain, at the border between northern and central Italy
(Figure 1). The climate is subcontinental cool temperate. Mean an-
nual temperatures range bet ween 9° and 12°C, and mean annual
precipitation ranges between 900 and 1,50 0 mm, mainly owing to
altitudinal variations. Winters are relatively mild, with scarce snow
fall. The tree vegetation of the hills and low mountains (200– 900 m
asl) is mainly composed of European hop- hornbeam Ostrya carpini-
folia, Turkey oak Quercus cerris, pubescent oak Q. pubescens, and ma-
ples Acer spp. and that of the medium- high mountain (900– 1600 m)
is primarily composed of beech Fagus sylvatica. Plantations of coni-
fers (especially of silver fir Abies alba and Douglas fir Pseudotsuga
menziezii) are uncommon. The landscape and land use of the two
slopes are very dif ferent (Corine Land Cover 2006: http://www.eea.
europa.eu/publi catio ns/COR0- landc over; Table 1). The nor thern
side (province of Bologna) is characterized by higher environmental
heterogeneity, with relatively vast forest tracts, small woods, shrubs,
meadows, and cultivations: Woods and open habitats cover 52.8%
and 39.5% of the red deer distribution, respectively (Table 1). The
southern side (province of Pistoia) is mainly made up of large rather
compact forests with a few restricted and clumped open habitats
(abandoned cultivations, small pastures): woods and open areas
cover 80% and 11.5% of the range, respectively (Table 1). Thus,
availability of meadows and fields is more than 3 times greater in
the northern slope (Bologna) than in the southern one (Pistoia).
Moreover, the ratio of the area covered with meadows and fields
over the area covered with woodland was 0.65 in Bologna and 0.14
in Pistoia, thereby suggesting higher productivity in the former than
in the latter site.
Red deer were reintroduced to the area in 1958– 1965 with
animals of Alpine stock (Mattioli et al., 2001). Counts were per-
formed since 1994, and the population has been hunted since 2000.
Population density in spring is maintained at about 2 ind./km2, and
no supplemental feeding is provided. The area is also inhabited by
wild boar Sus scrofa, roe deer Capreolus capreolus, fallow deer Dama
dama, and wolves Canis lupus.
2.2 | Data collection
Antler investment has been largely studied through the ratio of
antler size over body size. Geist (1987, 1998) and Geist and Bayer
(1988) analyzed the relative antler size (in terms of g of gross antler
mass per kg of “metabolic body mass,” that is the postrut live body
weight raised to the power of 0.75 and 1.35) of adult red deer and
FIGURE 1 Location of the study
area. The panel on the left shows the
location of the study area, in the Northern
Apennines (Italy). The panel on the right
shows the distribution range of the red
deer population (gray shaded areas) and
the location of the two provinces (Bologna
on top and Pistoia on bottom)

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MATTIOLI e T AL.
many other deer species to compare the antler investment within
the Cervidae. For antler mass data, Geist (1998:183) only used
data from exceptionally large- antlered males (so- called trophy-
sized males), which he considered more biologically meaningful
for taxonomic purposes. Gómez et al. (2012) studied the ratio of
antler mass to the skelet al mass in three age- groups of farmed red
deer (yearlings, subadults, and adults 5 years old). Antler mass
relative to body mass has been used also in white- tailed deer
(McCullough 1982; Jones et al., 2018), mule deer (Anderson &
Medin, 1969), and pampas deer Ozotoceros bezoarticus (Ungerfeld
et al., 2011). Antler size- to- body size ratio has been investigated
also using antler length (length of the main antler beam) instead
of antler mass (moose Alces alces: Stewart et al., 2000; reindeer
Rangifer tarandus: Melnycky et al., 2013; see Gould, 1973; Clutton-
Brock et al., 1980; Plard et al., 2011; Lemâitre et al., 2014 for re-
views on cer vid family). Bubenik (1985) proposed as a measure of
antler size the total length of the main beam and of all tines. To
analyze antler size in their surveys on cervid species, Lemâitre,
Vanpé, et al. (2014) and Ceacero (2015) used data on both mass
and length.
Here, consistent with most literature on red deer, we adopted
the ratio of antler mass over body mass, which quantifies better than
other measurement s antler investment in terms of efforts to build
conspicuous secondary sexual traits. Data on body mass and gross
antler mass (mass of upper skull plus antler mass) were collected
for 1965 red deer stags legally shot in the study areas (n = 1,451
in Bologna; n = 514 in Pistoia) between August and March, 2000 to
2019. For each animal, day of harvest and harvest location (hunting
district) were recorded. Whole mass and eviscerated body mass of
all freshly hunted animals were measured in check stations by tech-
nicians and specially trained hunters (Mattioli, 2019), with an elec-
tronic scale to the nearest 0.1 kg. Although whole body mass can be
affected by rumen content, it was used in this study instead of evis-
cerated mass because of the difficult y to guarantee uniform dressing
of the carcasses and because whole mass is biologic ally more mean-
ingful than the eviscerated mass to evaluate antler investment (cf.
Geist, 1998). Whole and eviscerated mass values, however, strongly
and positively correlated (Pearson's r = 0.98). Gross antler mass (ant-
lers with the whole cleaned upper skull) was weighed to the nearest
g after 3 months from culling (dry gross antler mass). The exact age
of a subsample of 207 red deer was assessed by counting cemen-
tum layers on the inner incisive and, from this sample, a visual guide
(De Marinis, 2015) was developed to calibrate estimates from tooth
eruption and wear. For the remaining individuals, age estimation was
conducted by following carefully the visual guide. Condylo- basal
length of the skull (hereafter “skull length”) was measured with a dig-
ital caliper following von den Driesch (1976), to the nearest 0.1 mm.
Given the absence of selective criteria in harvest guidelines and
the scarce opportunity to encounter and shoot red deer because
of the low density, we assumed that hunters did not select animals,
and thus, the sample was considered representative of the whole
population.
2.3 | Statistical analysis
To investigate age- specific variation in antler mass, body mass, and
antler investment and its potential difference between study sites,
three distinct generalized additive mixed models (GAMMs) were fit-
ted assuming a Tweedie conditional distribution, which generalizes
many exponential dispersion models and can handle a wide range
of data types, continuous or discrete (Dunn & Smyth, 2018). The re-
sponse variables “antler mass,” “body mass,” and “antler investment”
were thus assumed to be a nonlinear function of age in different
study sites (Bologna versus Pistoia). Year of hunting and hunting dis-
trict were fitted as random intercepts to account for potential differ-
ences among hunting seasons and districts. All models were of the
general form:
E(response
ijk
)
=𝜇ijk
and Var(response
ijk
)
=𝜙𝜇
p
ijk
𝜇ijk
=
f(Ageijk): Siteijk
+
Siteijk
+
Yearj
+
Districtk
TABLE 1 Percentage of major land cover types in the red
deer range in the opposing slopes of the Appenine mountains
(BO = Bologna and PT = Pistoia)
Land cover types BO PT
Cultivated crops and meadows 39. 5 11. 5
Orchards – 5.5
Deciduous woods 50.8 73.3
Coniferous woods 2.0 6.4
Shrubs 5.2 0.3
Water (lakes, rivers) 0.3 -
Urban areas and roads 2.2 3.0
FIGURE 2 Relationship between skull length and “reduced”
skull mass (i.e., antlerless skull mass) estimated from n = 18
individuals red deer stags collected in the study sites

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where
𝜇ijk
was the expected value of the response variable (antler
mass/body mass/antler investment) for measure i in hunting year j
and hunting district k, f the smoothing term for age by site selected
via cross- validation ( Wood, 2017), and
𝜙
the dispersion parameter esti-
mated from the data. In Tweedie models, the conditional distribution is
defined by an additional parameter p (the Tweedie power parameter):
For example, for
𝜙
= 1, p = 0 defines a normal distribution, while p = 1
defines a Poisson distribution. The parameter p is not constrained to be
an integer, and to appropriately model the variance, in this study it was
set at 1.5 for the antler mass model and at 1.25 for the body mass and
antler investment models, af ter preliminary inspections of residuals.
The random intercepts
Yearj
and
Districtk
were assumed to be normally
distributed with mean 0 and variance
𝜎2
Year
and
𝜎2
District
. All models were
fitted assuming identity link functions. Therefore, the fitted models es-
sentially reduced to nonlinear mixed models that accommodated the
nonconstant variance detected in preliminary analyses and the nonin-
dependence that stemmed from the hierarchical nature of our data.
Yearj
∼N(0, 𝜎
2
Year)
Districtk
∼N(0, 𝜎
2
District)
FIGURE 3 Residual diagnostics
(homogeneity of variance on the left
and normality on the right) for GAMMs
fitted to explain age- dependent variation
in net antler mass, full body mass, and
antler investment and for models fitted
to explore allometric relationships in
red deer in different study sites in the
Apennines

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MATTIOLI e T AL.
The measure of gross antler mass includes skull mass and net
mass. With the growing size of antlers, the ratio of the former over
the latter tends to decrease. In yearling stags, skull mass may make
up more than 70% of gross antler mass; the propor tion decreases to
ca. 40% in 2– 4 years old and to ca. 25% in individuals aged 5+ years
(S. Mattioli and S. Nicoloso, unpublished data). Thus, a proper anal-
ysis of age- dependent antler investment should include net antler
mass only (i.e., gross antler mass minus skull mass), to avoid biases
related to age- specific ratio between antler and skull masses. Since
net antler mass was not directly available, in the first model an “ex-
pected” net antler mass was calculated as the difference bet ween
measured gross skull mass (i.e., mass of upper skull plus antlers) and
predicted “reduced” skull mass (i.e., mass of upper skull without ant-
lers). For all individuals, the reduced skull mass was predicted from
their measured skull length: A small sample (n = 18) of antlerless
stags independently collected in the same study sites was used to
find the function that maximized the R2 (0.91) of the relationship
between “reduced” skull mass and skull length (Figure 2).
TABLE 2 Estimates of the GAMMs fitted to investigate
the age- dependent variation in antler mass, body mass, and
antler investment in red deer in different study sites in the
Apennines. The table reports estimates of parametric coefficients
(intercept and study site) and estimates of age- smoothed terms
(edf = estimated degrees of freedom)
Parametric
coefficients Estimate
SE
t- value
p-
valueSmoothing terms edf F- value
Antler mass
Intercept 2.430 0.026 93.4 <.0 01
Site (Pistoia versus
Bologna)
−0 .517 0.040 −13.0 <.001
s(age) : Bologna 7.0 3 6 1,195. 5 <.001
s(age) : Pistoia 6.757 486.6 <.001
Body mass
Intercept 15 9.36 8 0.665 23 9. 8 <.001
Site (Pistoia versus
Bologna)
−22 .9 92 1.344 −17.1 <.001
s(age) : Bologna 5.943 810.6 <.0 01
s(age) : Pistoia 6.964 2 0 7. 4 <.001
Antler investment
Intercept 1.383 0.017 82.5 <.001
Site (Pistoia versus
Bologna)
−0.150 0.022 −6.9 <.001
s(age) : Bologna 7.1 6 4 1,091.0 <.001
s(age) : Pistoia 6.507 51 3. 0 <.001
FIGURE 4 Estimated smoothing curves obtained by GAMMs
fitted to investigate the age- dependent variation in net antler
mass (a), full body mass (b), and antler investment (c) in red deer
in different study sites in the Apennines. Shaded areas represent
95% confidence interval. Datapoints have been jittered to improve
visualization
0
1
2
3
4
5
6
7
8
9
10
11
1234567891011121314
Age (in years)
Antler mass (in kg)
Bologna
Pistoia
75
100
125
150
175
200
225
250
275
300
1234567891011121314
Age (in years)
Body mass (in kg)
Bologna
Pistoia
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1234567891011121314
Age (in years)
Antler / body mass ratio (in %)
Bologna
Pistoia
(a)
(c)
(b)

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Since animals were hunted between August and March within
each hunting season, in the second model whole body mass was ad-
justed to 20 October (i.e., the end of the rut, which peaks between
20th and 30th September). Mass was adjusted by fit ting quadratic
linear models between body mass and Julian date from the first
day of hunting (10 August) for different age- classes, because age-
specific trends of mass variation over time are to be expected (cf.
Radler & Hattemer, 1982; Post et al., 1997). Preliminary quadratic
linear models relating whole body mass with Julian date by age-
classes suggested that that age- classes 1, 2– 4, 5– 7, and 8+ years
(Akaike information criterion [AIC] = −2202) were a better fit than
alternate age- classes 1, 2– 7, and 8+ (AIC = −1405) or 1, 2– 4, and 5+
(AIC = −2200).
In the third model, antler investment was defined for each indi-
vidual as the ratio between expected net antler mass and adjusted
whole body mass after the rut. For all models, the between- site
differences of smoothed cur ves were estimated. Notably, we ac-
knowledge that the inspection of tooth eruption and wear might
overestimate age in young individuals, and underestimate age in
old ones (Gee et al., 20 02; Storm et al., 2014). When measurement
errors in the explanatory variable are small, compared to the full
range of values, this should introduce minor bias in the estimators.
However, to investigate more formally the potential consequences
of measurement errors, all models were refitted by adding neg-
ative random noise (between −2 and 0 years) to the age of young
(3- to 7- year- old) stags and positive random noise (between 0 and
+2 years) to the age of old (8+) stags. Model results were consistent
between age– data– types; therefore, we decided to keep the original
dataset for final inference.
The coef ficients of variat ion of antler investm ent were calculated
for site- specific age- classes. Furthermore, we assessed allometric
relationships between expected net antler mass and adjusted whole
body mass for each age- class (1, 2– 4, 5– 7, and 8+ years). Allometric
coefficients corresponded to the age- class- specific slopes estimated
with standardized major axis robust regression models, to account
for possible measurement error in both mass metrics, using log-
transformed data (Warton et al., 2006). Allometric relationships
were assessed separately for the two populations. Within each pop-
ulation, an age- class- specific slope of 1 would suggest isometric re-
lationship, whereas slopes above or below 1 would indicate positive
and negative allometry, respectively (Jones et al., 2018).
For all models, goodness of fit was assessed visually through re-
sidual diagnostics. All analyses were conducted with R 3.6.1 (R Core
Team, 2019) in RStudio 1.2.1335 (RStudio Team, 2019). GAMMs
FIGURE 5 Estimated difference between the values of the
smoothed curves for the two study sites (Bologna— BO versus.
Pistoia— PT) obtained by GAMMs fitted to investigate the age-
dependent variation in antler mass (a), body mass (b), and antler
investment (c) in red deer in the Apennine. The shaded area
corresponds to the 95% confidence interval of the difference
between smoothed values. When the area does not overlap
zero, the values of the fitted curves for the two populations are
considered significantly different from a statistical standpoint
Age (in years)
Diff. in antler mass (in kg): BO vs. PT
12345678910111213
−1
0
1
2
3
4(a)
Age (in years)
Diff. in body mass (in kg): BO vs. PT
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0
10
20
30
40
50
60
70
80
90
100 (b)
Age (in years)
Diff.
in antler / body mass ratio (in %): BO vs
. PT
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−0.5
0.0
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MATTIOLI e T AL.
were fitted with the package “mgcv” (Wood, 2017), and their re-
sidual diagnostics and marginal effects were investigated with the
package “mgcViz” (Fasiolo et al., 2018). For all models, the differ-
ences bet ween the values of the site- specific smoothed curves were
investigated with the package “itsadug” (van Rij et al., 2017). The
allometric relationships were investigated with the package “smatr”
using Huber's M robust estimation (War ton et al., 2012), and their
residual diagnostics was investigated with the “stats” package (R
Core Team, 2019).
3 | RESULTS
Residual diagnostics indicated no major violation of assumptions for all
models (Figure 3). Mild residual heterogeneity occurred in the estima-
tor for allometry in Bologna (Figure 3), but this should be inconsequen-
tial, as the Huber's method used to fit the model offers robustness in
inference (Taskinen & Warton, 2011). The GAMMs for antler mass,
body mass, and antler investment explained, respectively, about 86%,
77%, and 83% of the variance. The smoothers for different study sites
were statistically significant (Table 2), revealing a nonlinear relationship
of net antler mass, whole body mass, and antler investment with age.
Since GAMM estimates are difficult to interpret, smoothing curves are
shown in Figure 4 for all response variables. Notably, preliminar y anal-
yses showed that very similar results can be obtained by fitting quasi-
likelihood GAMMs assuming equality between mean and variance.
This supports the goodness of Tweedie models, which were preferred
over quasimodels because of lower values of AIC (for quasimodels, the
values of AIC were obtained using a wrapper function available in the
package “MuMIn” [Bartoń, 2020]).
Net antler mass increased up to 6 years of age in Pistoia and up
to 7 years in Bologna, remained stable until 10– 11 years of age, and
then appeared to decline (Figure 4a). The greater antler mass ob-
served in Bologna than in Pistoia in the first 3 years of life, and af ter
5 years of age, was statistically significant (Figure 5a). The mean fig-
ure for adult stags (5+ years old) from Bologna was 20.6% higher
than from Pistoia (4.65 kg versus 3.83 kg for Pistoia; Table 3). The
heaviest recorded antler masses were 10.78 kg for Bologna and
6.66 kg for Pistoia. The CV of antler mass decreased on both side
of the Apennine from 48%– 51% in yearlings to 29%– 31% in adults.
Similarly, whole body mass increased up to 6 years of age in
Pistoia and up to 7 years in Bologna, but showed a steady decline
in the former while remaining stable in the latter (Figure 4b). The
heavier body mass observed in Bologna than in Pistoia was statis-
tically significantly for all age- classes (Figure 5b). Adult stags from
Bologna were on average 14.7% heavier than those from Pistoia
(194.7 kg versus 169.7 kg; Table 3). The heaviest recorded body
masses were 292 kg for Bologna and 263 kg for Pistoia. The coeffi-
cient of variation of body mass was approximately constant across
age- classes and in both slopes, at about 10%– 15%.
Antler investment increased up to 6 years of age in Pistoia and
up to 7 years in Bologna, was stable until 10– 11 years of age, and
then appeared to decline (Figure 4c). The greater antler investment
observed in Bologna than in Pistoia in the first 3 years of life, and be-
tween about 6 and 10 years, was statistically significant (Figure 5c).
The coefficient of variation decreased with increasing age- classes
in both populations, but the decrease after the first year of age was
much sharper in Bologna than in Pistoia (Figure 6). In terms of mean
values, antler investment was 0.2%– 0.4% in yearlings and increased
to 2.5%– 2.7% in adults 8+ years old. Mean relative antler mass of
prime- aged stags was 7.1 times greater than that of yearlings in
Bologna a nd 10.5 times in Pistoi a. The highest reco rded antler invest-
ments in adults were 4.3% in Bologna and 3.9% in Pistoia. Yearlings
from Bologna had a much higher mean antler investment than those
from Pistoia (+59.6%). The CV of antler investment decreased with
increasing age- classes in both populations, from around 40%– 50% in
yearlings to 25% in adults.
For both study sites, the allometric relationship between body
mass and antler mass was statistically different among age- classes
(Bologna: likelihood- ratio test [LRT] = 1 29.3 , df = 3, p- value <.001;
Pistoia: LRT = 17. 26 , df = 3, p- value = .001), although the effect sizes
of different age- class- specific slopes in Pistoia were broadly more
Age- class
Postrut body
mass (kg)
Net antler mass
(kg)
Antler investment
(%) N
Yea rl ings BO 1 19. 4 ± 11.9 0. 451 ± 0.228 0.375 ± 0.187 403
Yea rl ings PT 102.4 ± 12.7 0.245 ± 0.118 0.235 ± 0.099 97
Subadults 2– 4
y. BO
148.5 ± 16 .7 1.609 ± 0.535 1. 074 ± 0.308 5 41
Subadults 2– 4
y. PT
128.6 ± 18.8 1.232 ± 0.607 0.93 0 ± 0.369 227
Adults 5– 7 y. BO 191. 8 ± 22.9 4. 283 ± 1. 242 2.230 ± 0. 570 331
Adults 5– 7 y. PT 173.4 ± 20.3 3 .782 ± 1.136 2.173 ± 0. 576 120
Adults 8+ BO 200.1 ± 22.5 5.332 ± 1.24 8 2.666 ± 0.561 176
Adults 8+ PT 163.3 ± 19.8 4.043 ± 1 .131 2.464 ± 0.565 70
Adults 5+ BO 194.7 ± 23.1 4. 647 ± 1.339 2.381 ± 0.603 5 07
Adults 5+ PT 169.7 ± 20.7 3.878 ± 1.138 2.281 ± 0.588 190
TABLE 3 Mean (±SD) body mass, antler
mass, and antler investment of red deer
stags in Bologna (BO) and Pistoia (PT). The
table reports body mass adjusted to after
the rut (in kg), net antler mass (i.e., whole
skull mass - “reduced” skull mass, see text
for details), investment (ratio bet ween
adjusted body mass and net antler mass),
and sample size (N)

7858
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MATTIOL I eT AL.
similar than in Bologna (Table 4; Figure 7). All slopes and associated
95% confidence intervals were >1, suggesting positive allometric re-
lationships (Table 4; Figure 7). Generally, allometric relationship was
stronger in young stags and weaker in adult s over 8 years of age
(Table 4; Figure 7). No major differences in age- class- specific allo-
metric relationships were observed between sites, with a partial ex-
ception for yearlings, which showed a stronger effect size in Bologna
than in Pistoia (Table 4; Figure 7).
4 | DISCUSSION
We observed remarkable fine- scale spatial variations in male body
mass, antler mass, and antler inve stment in red deer. These variations
matched differences in land cover between two sides of a mountain
chain, with heavier and larger- antlered males on the northern slope
characterized by higher habitat heterogeneity and greater avail-
ability of open habitats than the southern slope. Accordingly, antler
investment of males was also greater in the nor thern than in the
southern side. Moreover, the allometric relationship between body
mass and antler mass became weaker in older age- classes, and it was
seemingly stronger in yearling stags from the northern than from the
southern side. Our results emphasize the role of environmental het-
erogeneity in shaping small- scale variations of key life- history traits
of a highly polygynous species, possibly related to reproductive suc-
cess (see Pet torelli et al., 2002 for the weakly polyg ynous roe deer).
As expected for secondary sexual traits of low growth priority,
antler investment increased with age and peaked in 8+- year- old
stags, with a mean production of 26.7 g of antler tissue per kg of
body mass in the “rich” side and 24.6 g in the “poor” side. Differences
in antler investment between the slopes of the mountain chain were
consistently high in yearlings (59.6%), but in prime age they de-
creased on average to 2.6%– 8.2%. It is noteworthy that yearlings
from Bologna invested so consistently in their first antler set. They
bear mostly simple spike antlers (on average about 40 cm long, but
with records of 55– 63 cm), but 13% had two or three tines per ant-
ler. Yearlings of Pistoia were all spikers, with spikes of approximately
the same length but lighter. Possibly, the abundance of food in late
spring and early summer was suf ficient to suppor t somatic growth
and, at the same time, to divert extra- energies to antler formation.
Yearlings are particularly responsive to nutrient availability (Clutton-
Brock & Albon, 1989; Schmidt et al., 2001; Suttie & Kay, 1982), and
their body growth and antler size are also influenced by maternal
condition and lactation (Gómez et al., 2006). A precocious develop-
ment of yearlings could exert a strong influence on final adult size,
dominance status, and breeding success (Clutton- Brock et al., 1988).
In farmed red deer, body and antler size of yearlings are good predic-
tors of adult size (Moore et al., 1988).
Body mass variability of Apennine red deer stags, as indicated by
the coefficient of variation, was consistent across slopes and age-
classes, around 10%– 15%, approximately the same as recorded in
Mississippi white- tailed deer (Jones et al., 2018). In contrast, ant-
ler mass variability decreased with age, suggesting that as deer
approach prime age, they become less sensitive to environmental
variation and interindividual differences in antler investment tend to
decline. As observed in a study on antler asymmetries (Mateos et al.,
2008), red deer stags in prime age appear to converge toward a basic
common configuration of their weaponry to enhance fighting ability,
FIGURE 6 Coefficient of variation in red deer antler investment
for different age- classes in the two study sites. Sample sizes in
parentheses
Study site
Age- class (in
years) nslope Lower CL Upper CL R2
Bologna 1403 4.89 4.45 5. 37 0.18
2– 4 541 3.04 2.83 3.27 0.35
5– 7 331 2.54 2.31 2.80 0.21
8+176 2.10 1. 81 2.44 0.20
Pistoia 197 4.01 3.40 4.73 0.25
2– 4 227 3.19 2.90 3. 51 0.54
5– 7 120 2.84 2.41 3.35 0.22
8+70 2.42 2.00 2 .92 0.32
TABLE 4 Allometric relationships
between estimated antler mass and
adjusted body mass after the rut for
different age- classes (1, 2– 4, 5– 7, and
8+ years) in Bologna (A) and Pistoia (B).
The table reports the site- and age- class-
specific values of sample size (n), slope of
relationship (slope), lower and upper 95%
confidence levels, and R2

|
7859
MATTIOLI e T AL.
thus possibly restraining antler mass variability. While in Mississippi
white- tailed deer average variation in antler mass was lower in the
areas with higher nutritional conditions (Jones et al., 2018), in red
deer from Apennine differences in food quantity and quality did
not appear to play a major role. If adult stags gradually weaken their
susceptibility to environmental stressors and interindividual differ-
ences in antler mass tend to decrease, this could be connected to
the increasing role of skeletal minerals mobilized for antler forma-
tion (Gómez et al., 2012; Muir et al., 1987a). When most of the final
body size is at tained, it is essential for a st ag to alloc ate adequate
resources in building strong, symmetrical, and well- branched antlers
(Bartoš & Bahbouh, 2006; Mateos et al., 2008) to successfully com-
pete for access to mating. Antler development becomes a trade- off
between fully expressing their potential, optimizing their functional-
ity, and obtaining minerals from diet and body stores. From a strictly
energetic perspective, antler grow th of adult stags seems to require
relatively modest expenditures, accounting for only 1% of the yearly
budget (Bo bek et al., 1990), but ac tually it is a markedl y costly activi ty
(Bubenik, 1982, 1985; Dryden, 2016; Moen & Pastor, 1998a,1998b).
In a restricted time window, during the 140– 165 days of antler for-
mation, and especially between 90 and 110 days from the beginning,
adult stags must deposit large amount s of calcium and phosphorus,
only partially available from forage (Muir et al., 1987a,1987b); an ef-
fort which takes place contemporarily to an increase food intake in
preparation for the rut.
With increasing size, antlers face physiological, mechanical, and
struc tural constraints, as suggested by comparative surveys of antler
and body size relationships among cervids (Ceacero, 2015; Lemâitre,
Vanpé, et al., 2014), but which seems valid also within species (Jones
et al., 2018). When approaching the peak of antler development, the
largest individuals appear to partly trade antler size for heavy body
mass, which can be more determinant in overt contests than longest
and heaviest antlers.
We observed a tendenc y for a decline in antler investment for
oldest stags, although our sample included only 26 individuals aged
12– 14 years; never theless, these results are consistent with those
of other studies (Drechsler, 1980, 1988; Langvatn, 1986; Mysterud
et al., 2005; but see Nussey et al., 2009 and Lemaître et al., 2014b
for the red deer stags of Rum, whose senescence in antler trait s was
minimal). Tooth wear may impair food assimilation in senescent ani-
mals, affecting their body and antler mass.
Our study also shed some light into the complex multiphase pos-
itive allometry of body and antler mass, with decreasing exponents
from yearlings to older adults. Antler size of Apennine stags contin-
ued to increase at a faster rate than body size, but it tended to slow
down in prime age, possibly under the influence of physiological and
mechanical constraints (Ceacero, 2015; Jones et al., 2018; Lemâitre,
Vanpé, et al., 2014). The weaker positive allometry of adult stags
at their peak may reflect also the need to adjust the allocation in
body mass, which could make the dif ference in direct fights more
than large antlers. Although there are no consistent differences be-
tween mountain sides, the degree of overlap of confidence intervals
in Table 1 suggest s that yearling stags from the most productive site
may have a higher allometric exponent than those with a lower nu-
tritional plane. This would indicate a higher antler investment in the
former than in the lat ter, a pattern similar to that observed by Jones
et al. (2018) in white- tailed deer.
In a red dee r population fro m Lower Saxony, a two- phase relat ion-
ship between subadults and adults was observed (Schröder, 1983),
but with a higher scaling exponent for adults. Strict selective crite-
ria applied to the young harvested stags (with higher pressure on
low performance individuals) could have influenced the results. In
white- tailed deer, allometric exponents decreased with increasing
FIGURE 7 Allometric relationships between net antler mass and
adjusted body mass after the rut for different age- classes (1, 2– 4,
5– 7, and 8+ years) in Bologna (a) and Pistoia (b)
100150 200250 300
0.1
0.2
0.5
1.0
2.0
5.0
10.0
Body mass (in kg) [log scale]
Antler mass (in kg) [log scale]
1 year
24 years
57 years
8+ years
(a)
100150 200250 300
0.1
0.2
0.5
1.0
2.0
5.0
10.0
Body mass (in kg) [log scale]
Antler mass (in kg) [log scale]
1 year
24 years
57 years
8+ years
(b)

7860
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MATTIOL I eT AL.
age- class until 4 years (Jones et al., 2018); regions with higher en-
vironmental productivity were associated with smaller exponents in
adult bucks.
For a species typical of open woodland and the interface be-
tween forest and meadows (Geist, 1998; Mitchell et al., 1977), the
rural landscape of the northern side of the Apennine is relatively
more suitable than the southern one. Also in SW Poland, forest
districts with a lower wood cover have relatively larger stags with
slightly heavier antlers (Wajdzik et al., 2018). In Norway, the pro-
portion of meadows within each municipality had a positive ef fect
on red deer body mass (Mysterud et al., 2002). The gradual clo-
sure of the wood after the abandonment of mountain rural econ-
omy has negatively affected the productivity of the southern side.
Conversely, the greater habitat heterogeneity of the northern side,
with woods, shrubs and open areas evenly distributed, provides a
higher availability of various food resources. Nevertheless, on a
continent al scale, body and antler size of red deer living on either
side of the Apennine appear relatively high, suggesting locally favor-
able environmental conditions (especially mild winters) and suitable
nutritional conditions, emphasized by the low population densities
. During the 1980s, this red deer population had an overall density
<1 individual/km2; moreover, open grasslands and fields were rela-
tively more abundant. In turn, stags of this population were known
for their extremely branched antlers (up to 26– 32 tines per pair) and
for the high incidence of palmation (20%) (Mattioli, 2003). Overall,
this finding confirms the high plasticity in antler growth of this
species, whose mean net antler tissue production can range from
around 10 g/k g BM in low productive habitats to 40 g/kg BM and
more in the most productive ones (cf. Table 5). The highest mean
figures are attained in the Pannonian fertile plains of Hungary and
in the open woodlands of Carpathian and Balkan Mountains of
Romania and Bulgaria (Botev, 1990; Geist, 1998; Szunyoghy, 1959).
The highest values recorded in Apennine (39 g/kg BM for Pistoia
and 43 g/kg BM for Bologna) are close to the mean values for east-
ern European countries. The highest values documented for the
species in wild conditions are around 50– 55 g/kg BM (17– 19 kg of
net antler mass for a postrut maximum body mass of 340 kg) (cf.
Geist, 1998).
Species/population
Age
(years) g/kg Source
Red deer, Baranja (H) 8– 1 0 36.5 S. Csányi 2018 pers. com., A. Bokor
pers. com. 2020
Red deer, Baranya (HR) 8– 10 34.3 Degmečić (2009), modified
Red deer, Apennine (I) 8+24.6 – 26 . 7 This study
Red deer, Car pathians
(PL)
9+22.6 Brewczynski (2002), modified
Red deer, Opole (PL) 7+19.0 Wajdzik et al. (2018), modified
Red deer, Lower Saxony
(D)
8+17. 4 Drechsler (1980), modified
Red deer, Słowinski N.
P. (PL)
8+16.2 Dzięciołowski et al. (1996),
modified
Red deer, Mesola Wood
(I)
10+12.2 Mattioli & Ferretti (2014)
Red deer, Rum (UK ) 5– 10 11 .7 Mitchell et al. (1976)
Red deer, Sardinia (I) 5+11.4 Mattioli & Ferretti (2014), modified
Red deer, Glenfeshie
(UK)
5– 1 0 10. 2 Mitchell et al. (1986)
Wapiti, Washington
(USA)
7– 8 34.4 McCorquodale et al. (1989), S. M.
McCorquodale pers. com. 1989
Wapiti, New Mexico
(USA)
8– 1 0 33.5 Wolfe (1983), L. Bernal pers. com.
2020
Wapiti, Michigan (USA) 9– 1 0 22.1 L. Bender, pers. com . 2020
Common fallow deer,
Apennine (I)
5+28.3 S. Mattioli, unpublished
Common fallow deer (D) 5+26.0 Siefke & Stubbe (2008), modified
White- tailed deer,
Mississippi (USA)
5– 7 11.5 Jones et al. (2018), adapted
European roe deer,
Apennine (I)
3+6.6 S. Mattioli, unpublished
European roe deer (D) 3+4.4 Stubbe (1990), modified
TABLE 5 Mean antler allocation
expressed in g of antler per kg of whole
body mass, in prime- aged males from
different red deer populations and other
Cervid species

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7861
MATTIOLI e T AL.
Our results emphasize the importance of environmental het-
erogeneity in promoting interindividual variability in the investment
in sexually selected trait s (e.g., Cornwallis & Uller, 2010; Mann &
Seehausen, 2011). While we focused on age- specific and spatial
components, further work would be required to explore temporal
heterogeneity (Cornwallis & Uller, 2010), also in relation to changes
in climatic and landscape features. Moreover, our results may pro-
vide insights into the relationships between investment in sexually
selected trait s, mating system and sexual size dimorphism. In fac t,
a comparative evaluation of antler investment in the Cer vidae fam-
ily would help evaluating the role of sexual size dimorphism, mating
tactic, and sexual selection in shaping antler investment, which indi-
cates an increasing allocation with growing sexual size dimorphism
(Geist & Bayer, 1988; Plard et al., 2011). For example, the roe deer, a
weakly dimorphic, territorial species, has the lowest value of antler
tissue production (ca 4– 7 g/kg BM). White- tailed deer have a rela-
tively modest sexual size dimorphism, a tending mating tactic (Airst
& Lingle, 2019; Hirth, 1977), and show a greater value of antler in-
vestment than roe deer. Red deer, wapiti, and fallow deer are highly
dimorphic ungulates showing harem defense (or equivalent mating
tactics) and have among the highest values of antler tissue produc-
tion. In conclusion, for polygynous ungulates antler investment,
that is, the net production of antler tissue relative to postrut whole
weight, can be used as a measure of physical per formance of prime-
aged males, with the potential for assessing ecological correlates of a
key life- history trait related to individual reproductive success.
ACKNOWLEDGMENTS
Our paper benefited from discussions with V. Geist, the critical read-
ing by M. Festa- Bianchet, and the comments by A. Mysterud. We
are indebted with the trained hunters who helped us in the biom-
etric monitoring. A. Gaggioli and P. Semenzato contributed to data
collection at the check stations of Pistoia. L. Bender (New Mexico
State University, Las Cruces, NM, USA), L. Bernal (Vermejo Park
Ranch, NM, USA), A . Bokor (University of Kaposvár, Hungary),
S. Csányi (Szent Istvan University, Gödöllő, Hungary), and S.M.
McCorquodale (Dept. Fish and Wildlife, Yakima, WA, USA) kindly
made available unpublished data. We thank the Associate Editor
of Ecology and Evolution, an anonymous reviewer, and S. Lingle
(University of Winnipeg) for insightful comment s on earlier drafts
of the manuscript.
CONFLICT OF INTEREST
We have no competing interests.
AUTHOR CONTRIBUTION
Stefano Mattioli: Conceptualization (equal); Data curation (equal);
Investigation (lead); Methodology (equal); Resources (lead);
Supervision (lead); Writing- original draft (lead); Writing- review
& editing (equal). Francesco Ferretti: Conceptualization (equal);
Investigation (equal); Methodology (equal); Supervision (equal);
Writing- original draft (equal); Writing- review & editing (equal).
Sandro Nicoloso: Conceptualization (equal); Data curation (equal);
Investigation (equal); Methodology (equal); Resources (equal);
Supervision (equal); Writing- original draft (suppor ting); Writing-
review & editing (supporting). Luca Corlatti: Conceptualization
(equal); Data curation (equal); Formal analysis (lead); Investigation
(equal); Methodology (equal); Writing- original draf t (equal); Writing-
review & editing (equal).
DATA AVAIL ABI LIT Y S TATEM ENT
Data used in this analysis are available at Dryad Digital Repository:
https://doi.org/10.5061/dryad.37pvm cvk7
ORCID
Luca Corlatti https://orcid.org/0000-0002-2706-3875
REFERENCES
Airst, J., & Lingle, S. (2019). Cour tship strategies of white- tailed deer and
mule deer males when living in sympatry. Behaviour, 156, 307– 330.
https://doi.org/10.1163/15685 39X- 00003543
Andersen, R., Duncan, P., & Linnell, J. D. (Eds.) (1998). The European roe
deer: The biology of success, Vol. 3 76. Scandinavian University Press.
Anderson, A. E., & Medin, E. (1969). Antler morphometry in a Colorado
mule deer population. Journal of Wildlife Management, 33, 520 – 53 3.
Ashley, E. P., McCullough, G. B., & Robinson, J. T. (1998). Morphological
responses of white- tailed deer to a severe population reduction.
Canadian Journal of Zoology, 76, 1– 5. https://doi.org/10.1139/z97- 159
Ball, A. J., Thompson, J. M., & Fennessy, P. F. (1994). Relationship be-
tween velvet antler weight and liveweight in red deer (Cervus ela-
phus). New Zealand Journal of A gricultural Research, 37, 153– 157.
Bartoń, K. (2020). MuMIn: Multi- Model Inference. R package version 1.43.17.
Retrieved from https://CRAN.R- proje ct.org/packa ge=MuMIn
Bartoš, L., & Bahbouh, R. (2006). Antler size and fluctuating asymme-
try in red deer (Cervus elaphus) stags and probability of becoming a
harem holder in rut. Biological Journal of the Linnean Society, 87, 59–
68. https://doi.org/10.1111/j.1095- 8312.2006.00555.x
Bobek, B., Perzanowski, K., & Weiner, J. (1990). Energy expenditure for
reproduction in male red deer. Journal of Mammalogy, 71, 230– 232.
htt ps://doi.o rg /10. 2307/1382171
Botev, N. (1990). Devel opment of the antlers of red de er in north- eastern
Bulgaria. Transactions of the I.U.G.B. (Trondheim) 1, 309– 314.
Brewczynski, P. (2002). Ciężar ciała i jakość poroża jelenia Cervus elaphus
L. w ośrodkach hodowli zwierzyny na terenie Regionalnej Dyrekcji
Lasów Państwowych w Krośnie (Karpaty) [Body weight and antler
qualit y of the red deer Cervus elaphus L. in the game breeding centres
in the Regional Directorate of State Forests in Krosno (Carpathians)].
Sylwan, 14 6 , 63– 7 5 .
Brown, R. D. (1990). Nutrition and antler development. In G. A. Bubenik,
& A. B. Bubenik (Eds.), Horns, pronghorns, and antlers (pp. 426– 441).
Springer.
Bubenik, A. B. (1982). Physiology. In J. W. Thomas, & D. E. Toweill
(Eds.), Elk of Nor th America: Ecology and management (pp. 125– 180).
Stackpole Books.
Bubenik, A. B. (1985). Reproductive strategies in Cervids. Royal Societ y of
New Zealand Bulletin, 22, 367– 374.
Ceacero, F. (2015). Long or heav y? Physiological constraints in the evolu-
tion of antlers. Journal of Mammalian Evolution, 23, 20 9– 216 .
Clutton- Brock, T. H., & Albon, S. D. (1989). Red deer in the Highlands.
Blackwell.
Clutton- Brock, T. H., Albon, S. D., & Guinness, F. E. (1986). Great expec-
tations: Dominance, breeding success and offspring sex ratios in red
deer. Animal Behaviour, 34, 460– 471. ht tps://doi.org/10.1016/S000 3
- 3472(86)80115 - 4

7862
|
MATTIOL I eT AL.
Clutton- Brock, T. H., Albon, S. D., & Guinness, F. E. (1988). Reproductive
success in male and female red de er. In T. H. Clutton- Brock (Ed.),
Reproductive success (pp. 325– 343). Chicago University Press.
Clutton- Brock, T. H., Albon, S. D., & Harvey, P. H. (1980). Antlers, body
size and breeding group size in the Cervidae. Nature, 285, 565– 566.
htt ps://doi.org /10.1038/2855 65a0
Clutton- Brock, T. H., Guinness, F. E., & Albon, S. D. (1982). Red deer:
Behaviour and ecology of two sexes. Univ. of Chicago Press.
Cornwallis, C. K ., & Uller, T. (2010). Towards an evolutionary ecology of
sexual traits. Trends in Ecology and Evolution, 25, 145– 152.
Croitor, R. (2018). Plio- Pleistocene deer of Western Palearctic: Taxonomy,
systematics, phylogeny. Institute of Zoology of the Academy of
Sciences of Moldova.
Cromsig t, J. P., Prins, H. H., & Olff, H. (2009). Habitat heterogeneity as
a driver of ungulate diversity and distribution patterns: Interaction
of body mass and digestive str ategy. Diversity and Distributions, 15,
513– 522. https://doi.o rg /10.1111 /j.1472- 4 642.2008.0 055 4.x
De Marinis, A . M. (2015). Valutazione dell’età nei Cervidi tramite esame
della dentatura. Guida pratica all’identificazione delle classi d’età del
cervo. Manuali E Linee Guida ISPRA, 90( 2), 1– 13 6 .
Degmečić, D. (2009). Model sustava za potporu pri uzgoju jelena obinog
(Cervus elaphus, L.) u slobodnoj prirodi [A support model for manag-
ing red deer in the open hunting grounds of Baranja]. (Ph. D. Thesis)
University of Osijek, Osijek, Croatia.
Drechsler, H. (1980). Ueber die Geweihbildung bei Rothirscen im
“Rotwildring Harz” in den Jahren 1959– 1978. Zeit schrift Für
Jagdwissenschaft, 26, 2 07– 2 19.
Drechsler, H. (1988). Altersentwicklung und Altersansprache beim Rotwild.
Parey.
Dryden, DMcL . (2016). Nutrition of antler growth in deer. Animal
Production Science, 56, 9 62– 970.
Dunn, P. K., & Smy th, G. K. (2018). Ge neralized linear m odels with example s
in R. Springer.
Dzięciołowski, R., Babińska- Werka, J., Wasilewski, M., & Gozsczynski, J.
(1996). Physical condition of red deer in a high density population.
Acta Theriologica, 41, 93– 105. https://doi.org/10.4098/AT.arch.96- 8
Fasiolo, M., Nedellec, R., Goude, Y., & Wood, S. N. (2018). Scalable visual-
isation methods for modern Generalized Additive Models. ArXiv preprint
ar Xi v :18 0 9.10 6 32.
Franzen, J., Gliozzi, E., Jellinek, T. M. et al (2000). Die spätaltpleis-
tozäne Fossilagerstatte D orn- Dürkheim 3 und ihre Bedeutung für
die Reconstruktion der Entwicklung des rheinischen Fluss- systems.
Senckenbergiana Lethea, 80, 305– 353.
Gee, K. L., Holman, J. H., Causey, M. K., Rossi, A. N., & Armstrong, J.
B. (2002). Aging white- tailed deer by tooth replacement and wear:
A critical evaluation of a time- honored technique. Wildlife Society
Bulletin, 30, 3 87– 3 93 .
Geist, V. (1966). The evolution of horn- like organs. Behaviour, 27, 175–
214. https://doi.org/10.1163/15685 3966X 00155
Geist, V. (1978). Life strategies, human evolution, environmental design:
Toward a biological theory of health. Springer.
Geist, V. (1986). Super antlers and pre- World War II European research.
Wildlife Society Bulletin, 14, 91– 9 4.
Geist, V. (1987). On the evolution of optical signal in deer: A prelimi-
nary analysis. In C. M. Wemmer (Ed.), Biology and management of the
Cervidae (pp. 235– 255). Smithsonian Ins titution Press.
Geist, V. (1998). Deer of the World: Their evolution, behavior, and ecology.
Stackpole Books.
Geist, V., & Bayer, M. (1988). Sexual dimorphism in the Cer vidae and
its relation to habitat. Journal of Zoology, 214, 45– 53. https://doi.
org /10.1111/j.1469- 7998.19 88.tb 049 85.x
Gómez, J. A., Ceacero, F., Landete- Castillejos, T., Gaspar- Lopez, E.,
García, A. J., & Gallego, L. (2012). Factors affecting antler investment
in Iberian red deer. Animal Production Science, 52, 867– 873. ht tps://
doi.org /10.1071/AN11316
Gómez, J. A ., Landete- Castillejos, T., García, A. J., & Gallego, L.
(2006). Importance of growth during lact ation on body size and
antler development in the Iberian red deer (Cervus elaphus his-
panicus). Livestock Science, 105, 27– 3 4. http s://doi.org/10.1016/j.
livsci.2006.04.028
Goss, R . J. (1983). Deer antlers. Regeneration, function and evolution.
Academic Press.
Gould, S. J. (1973). Positive allometr y of antler s in the “Irish elk”,
Megaloceros giganteus. Nature, 244, 375– 376. https://doi.
org /10.103 8/244 375a 0
Heckeberg, N. S. (2020). The systematics of the Cervidae: A total evi-
dence approach. PeerJ , 8, e8114. https://doi.org/10.7717/peerj.8114
Hirth , D. H. (1977). Social behavio r of white- tailed deer in relation to h ab-
itat. Wildlife Monographs, 53, 3– 55.
Huxley, J. S. (1931). The relative size of antlers in deer. Proceedings of the
Zoological Society of London, 101, 819– 864.
Hyvärinen, H., Kay, R. N. B., & Hamilton, W. J. (1977). Variation in the
weight, specific gravity and composition of the antlers of red deer
(Cervus elaphus L.). British Journal of Nutrition, 38, 30 1– 311 .
Jones, P. D., Strickland, B. K., Demarais, S. et al (2018). Nutrition and
ontogeny influence weapon development in a long- lived mammal.
Canadian Journal of Zoology, 96 , 955– 962. https://doi.org/10.1139/
cj z- 2 017- 0 3 45
Karanth, K. U., Nichols, J. D., Kumar, N. S. et al (2004). Tigers and
their prey: Predicting carnivore densities from prey abundance.
Proceedings of the National Academy of Sciences, 101, 4854– 4858.
htt ps://doi.org /10.1073/p nas .03 062 10101
Kavčić, K., Corlatti, L., Safner, T., Budak, N., & Šprem, N. (2020).
Contrasting patterns of s exually selec ted traits in Mediterra nean and
continental populations of European mouflon. Ecology and Evolution,
10, 2085– 2092. https://doi.org/10.1002/ece3.6041
Kitchener, A. C. (1991). The evolution and mechanical design of horn and
antlers. In: J. M. V. Rayner, & R. J. Wootton (Eds.), Biomechanics and
Evolution. Society for Experimental Biology Seminar Series 36 (pp. 229–
253), Cambridge Universit y Press.
Kodric- Brown, A., Sibly, R. M., & Brown, J. H. (2006). The allometry of or-
naments and weapons. Proceedings of the National Academy of S ciences,
103, 8733– 8738. htt ps://doi.org/10.1073/pnas .06029 94103
Kruuk, L. E. B., Slate, J., Pemberton, J. M. et al (2002). Antler size in red
deer: Heritability and selection but no evolution. Evolution, 56, 1683–
1695. https://doi.org/10.1111/j.0014- 3820.2002.tb014 80.x
Kwiatkowski, M. A ., & Sullivan, B. K. (2002). Geographic variation in sex-
ual selection among populations of an iguanid lizard, Sauromalus obe-
sus (=ater). Evolution, 56, 2039– 2051.
Langvatn, R. (1986). Size and age relationships in Norwegian red deer.
In: S. Linn ed. Das Rotwild. Proceedings of the CIC Symposium, Graz
(Austria), pp. 244– 266.
LeBlanc, M., Fes ta- Bianchet, M ., & Jorgenson, J. T. (2001). Sexual size
dimorphism in bighorn sheep (Ovis canadensis): Effects of population
density. Canadian Journal of Zoology, 79, 1661– 1670.
Lemâitre, J.- F., Gaillard, J.- M., Pemberton, J. M., Clutton- Brock, T. H., &
Nussey, D. H. (2014b). Early life expenditure in sexual competition
is associated with increased reproductive senescence in male red
deer. Proceedings of the Royal Society B, 281, 20140792. https://doi.
org /10.1098/rspb.2014.0792
Lemâitre, J.- F., Vanpé, C., Plard, F., & Gaillard, J.- M. (2014). The allometry
between secondary sexual traits and body size is nonlinear among
cervids. Biology Letters, 10 , 2013 0869. https://doi.org /10.1098/
rsbl.2013.0869
Lincoln, G. A. (1992). Biology of antlers. Journal of Zoology, 226, 517– 528.
https://doi. org/10.1111/j .1469- 7998.1992 .tb 074 95.x
Lüpold, S., Jin, L ., & Liao, W. B. (2017). Population density and s tructure
drive dif ferential investment in pre- and postmating sexual traits in
frogs. Evolution, 71, 1686– 1699. https://doi.org/10.1111/evo.13246
Mager, F. (1941). Wildbahn und Jagd Altpreussens. Neudamm.

|
7863
MATTIOLI e T AL.
Malo, A. F., Roldan, E. R. S., Garde, J. et al (2005). Antler honestly adver-
tise sperm production and qualit y. Proceedings of the Royal Society B,
272, 14 9 – 157.
Maan, M. E., & Seehausen, O. (2011). Ecology, sexual selec tion and spe-
ciation. Ecology Letters, 14, 591– 6 02.
Mattioli, S. (2003). Cervus elaphus. In L. Boitani, S. Lovari, & T. A. Vigna
(Eds.), Mammalia III, Carnivora- Artiodactyla (pp. 276– 294). Fauna
d’Italia.
Mattioli, S. (2019). The value of biometric monitoring in the management
of European Ungulates. Conservation Frontlines, 1– 2, 105– 109.
Mattioli, S., & Fer retti, F. (2014). Morphometric characterization of
Mesola red deer Cervus elaphus italicus (Mammalia: Cervidae). Italian
Journal of Zoology, 81, 1 4 4 – 1 5 4.
Mattioli, S., Meneguz, P. G., Brugnoli, A., & Nicoloso, S. (2001). Red deer
in Italy: Recent changes in distribution and numbers. Hystrix, Italian
Journal of Mammalogy, 12, 2 1– 3 5 .
McCorquodale, S. M., Eberhardt, L. E., & Sargeant, G. A. (1989). Antler
characteristics in a colonizing elk population. Journal of Wildlife
Management, 53, 618– 621. htt ps://doi.org /10.23 07/3809185
Melnycky, N. A., Weladji, R. B., Holand, O., & Nieminem, M. (2013).
Scaling of antler size in reindeer (Rangifer tarandus): Sexual dimor-
phism and variability in resource allocation. Journal of Mammalogy,
94, 1371– 1379.
Miller, C. W., & Emlen, D. J. (2010). Across- and within- population differ-
ences in the size and sc aling relationship of a sexually selected trait in
Leptoscelis tricolor (Hemiptera: Coreidae). Annals of the Entomological
Society of America, 103, 2 09– 21 5.
Mitchell, B., McCowan, D., & Nicholson, I. A. (1976). Annual cycles of body
weight and condition in Scottish red deer, Cervus elaphus. Journal of
Zoology, 180, 107– 127. ht tps://doi .or g/10.1111/j.1469- 7998 .1976.
tb046 67.x
Mitchell, B., McCowan, D., & Parish, T. (1986). Performance and popula-
tion dynamics in relation to management of red deer Cervus elaphus
at Glenfeshie, Inverness- shire, Scotland. Biological Conservation, 37,
237– 267. https://doi.org/10.1016/0006- 3207(86)90084 - 4
Mitchell, B., Staines, B. W., & Welch, D. (1977). Ecology of red deer: A
research review relevant to their management in Scotland. Institute of
Terrestrial Ecology.
Moen, R ., & Pastor, J. (1998a). Simulating antler grow th and energy, ni-
trogen, c alcium and phosphorus metabolism in caribou. Rangifer, 18,
85 – 9 7.
Moen, R., & Pastor, J. (1998b). A model to predict nutritional for antler
growth in moose. Alces, 34, 59– 74 .
Møller, A. P., Chabi, Y., Cuervo, J. J., Lope, F., Kilpimaa, J., Kose, M.,
Matyjasiak, P., Pap, P. L., Saino, N., Sakraoui, R ., Schifferli, L., &
Hirschheydt, J. (2006). An analysis of continent- wide patterns of
sexual selection in a passerine bird. Evolution, 60, 856– 868. https://
doi .or g/10.1111/ j.0014 - 3820.200 6.t b0 11 62. x
Mollet, F. M., Engelhard, G. H., Vainikka, A., Laugen, A. T., Rijnsdorp,
A. D., & Ernande, B. (2013). Spatial variation in growth, maturation
schedules and reproductive investment of female sole Solea solea in
the Northeast Atlantic. Journal of Sea Research, 84, 109– 121. https://
doi.org/10.1016/j.seares.2012.12.005
Moore, G . H., Lit tlejohn, R. P., & Cowie, G. M. (1988). Liveweights,
growth r ates, and antler measurements of farmed red deer stags and
their usefulness as predictors of performance. New Zealan d Journal of
Agricultural Research, 31, 285– 291. https://doi.org/10.1080/00288
233.1988.10 423 417
Morina, D. L., Demarais, S ., Strickland, B. K., & Larson, J. E . (2019). While
males fight, female choose: Male phenotypic qualit y informs female
mate choice in mammals. Animal Behaviour, 138, 69– 74 .
Muir, P. D., & Sykes, A. R. (1988). Effect of winter nutrition on antler de-
velopment in red deer (Cervus elaphus): A field study. New Zealand
Journal of Agricultural Research, 31, 145– 150.
Muir, P. D., Sykes, A. R., & Barrell, G. K. (1987a). Calcium metabolism in
red deer (Cer vus elaphus) offered herbages during antlerogenesis:
Kinetic and stable balance studies. Journal of Agricultural Science,
109, 357– 364.
Muir, P. D., Sykes, A. R., & Barrell, G. K. (1987b). Growth and mineraliza-
tion of antlers in red deer (Cervus elaphus): A field study. New Zealand
Journal of Agricultural Research, 30, 305– 315.
Mysterud, A., Langvatn, R., Yoccoz, N. G., & Stenseth, N. C. (2002).
Large- scale habit at variability, delayed densit y effects and red deer
population in Nor way. Journal of Animal Ecology, 71, 56 9– 58 0.
Mysterud, A., Meisingset, E., Langvatn, R. et al (2005). Climate- dependent
allocation of resources to secondar y sexual traits in red deer. Oikos,
111, 245– 252. https://doi.org/10.1111/j.0030- 1299.2005.14197.x
Mateos, C., Alarcos, S., Carranza, J., Sánchez- Prieto, C. B., & Valencia, J.
(2008). Fluctuating asymmetry of red deer antlers negatively relates
to individual condition and proximit y to prime age. Animal Behaviour,
75, 1629– 1640.
Nussey, D. H., Kruuk, L. E. B., Morris, A. et al (2009). Inter- and intrasex-
ual variation in aging patterns, across reproductive traits in a wild red
deer population. The American Naturalist, 174, 342– 357. https://doi.
org /10.108 6/603615
O’Brien, D. M., Allen, C. E., Van Kleeck, M. J., Hone, D., Knell, R ., Knapp,
A., Christiansen, S., & Emlen, D. J. (2018). On the evolution of ex-
treme structures: Static scaling and the function of sexually selected
signals. Animal Behaviour, 144, 95– 108. https://doi.org /10.1016/j.
anbeh av.2018.08.005
Peláez, M., Perea, R., Díaz, M., San Miguel, A., Rodríguez- Vigal, C., &
Côté, S. D. (2018). Use of cast antlers to assess antler size variation
in red deer populations: Effects of mast seeding, climate and popula-
tion features in Mediterranean environments. Journal of Zo ology, 306,
8– 15. https://doi.org/10.1111/jzo.12563
Pérez- Barbería, F. J., Gordon, I. J., & Pagel, M. (2002). The origins of sex-
ual dimorphism in body size in ungulates. Evolution, 56, 1276– 1285.
https://doi.org/10.1111/j.0014- 3820.2002.tb014 38.x
Pettorelli, N., G aillard, J.- M., Van Laere, G., Duncan, P., Kjellander, P.,
Liberg , O., Delor me, D., & Maillard, D. (20 02). Variations in adult
body mass in roe deer: The effects of population density at bir th and
of habitat quality. Proceedings of the Royal Society of London. Series B:
Biological Sciences, 269, 7 47– 75 3 .
Plard, F., Bonenfant, C ., & Gaillard, J.- M. (2011). Revisiting the al-
lometr y of antlers among deer species: Male- male sex-
ual competition as a driver. Oikos, 120, 601– 6 06. https://doi.
org /10.1111/j.160 0- 0706.20 10.18 934.x
Post, E., Brodie, J., Hebblewhite, M., Anders, A. D., Maier, J. A. K., &
Wilmers, C. C. (2009). Global population dynamics and hot spots
of response to climate change. BioScience, 59, 489– 497. https://doi.
org /10.1525/ bio.20 09.59.6.7
Post, E., Lang vatn, R ., Forchhammer, M. C., & Stenseth, N. C. (1999).
Environmental variation shapes sexual dimorphism in red deer.
Proceedings of the National Academy of Sciences, 96(8), 4467– 4471.
htt ps://doi.org /10.1073/p nas .96.8.4 467
Post, E., Stenseth, N. C., Langvatn, R., & Fromentin, J.- M. (1997). Global
climate change and phenotypic variation among red deer cohort s.
Proceedings of the Royal Society B, 264, 1317– 1324. https://doi.
org /10.1098/rsp b.1997.0182
R Core Team (2019). R: A language and environment for statistical comput-
ing. R Foundation for Statistical Computing. Retrieved from https://
www.R- proje ct.org/
Radler, K., & Hattemer, H. H. (1982). Unterschiede im Körpergewicht
des Rotwildes aus verschiedenen Gebieten der Bundesrepublik
Deutschland. Zeitschrift Für Jagdwissenschaft, 28, 79– 88.
RStudio Team (2019). RStudio: Integrated development for R. RStudio Inc.
Saarinen, J., Eronen, J., Fortelius, M., Seppä, H., & Lister, A. (2016).
Patter ns of diet and bo dy mass of large un gulates from t he Pleistoce ne

7864
|
MATTIOL I eT AL.
of Western Europe, and their relation to vegetation. Palaeontologia
Electronica, 19.3.32A, 1– 58. https://doi.org/10.26879/ 443
Schmidt, K. T., Stien, S. D., & Guinness, F. E. (2001). Antler le ng th of year-
ling red deer is deter mined by population densit y, weather and early
life- history. Oecologia, 127, 191– 197. https://doi.org/10.1007/s004 4
20000583
Schröder, J. (1983). Antler and body weight allom etry in red deer: A com-
parison of statis tical estimators. Biometrical Journal, 25, 669– 680.
https://doi.org/10.1002/bimj.19830 250706
Siefke, A., & Stubbe, C. (2008). Das Damwild. Neumann- Neudamm.
Stewart, K. M., Bowyer, R. T., & Gasaway, W. C. (2000). Antler size rela-
tive to body mass in moose: Tradeoff associated with reproduc tion.
Alces, 36, 7 7– 83.
Storm, D. J., Samuel, M. D., Rolley, R. E ., Beissel, T., Richards, B. J., &
Van Deelen, T. R. (2014). Estimating ages of white- tailed deer: Age
and sex pat terns of error using tooth wear and- replacement and con-
sistency of cementum annuli. Wildlife Society Bulletin, 38, 849– 856.
https://doi.org/10.1002/wsb.457
Stubbe, C . (1990). Rehwild. Deutscher Landwirtschaftsverlag.
Suttie, J. M., & Kay, R. N . B. (1982). The influence of nutrition and pho-
toperiod on the growth of antlers of young red deer. In R. D. Brown
(Ed.), Antler development in Cervidae (pp. 49– 59). Caesar K leberg
Wildlife.
Szunyoghy, J. (1959). Data to our knowledge concerning the body weight
of stags in the Carpathian Basin. Annales Historico- Naturales Musei
Nationalis Hungarici, 51, 483– 488.
Taskinen, S., & Warton, D. I. (2011). Robust estimation and inference for
bivariate line- fitting in allometry. Biometrical Journal, 53, 652– 672.
https://doi.org/10.1002/bimj.20100 0018
Ungerfeld, R., Villagran, M., & Gonzalez- Pensado, S. X. (2011). Antler
weight and body weight relationship in adult and young pampas deer
(Ozotoceros bezoarticus) males. North- Western Journal of Zoology, 7,
20 8– 21 2.
van der Made, J. (1999). Ungulates from Atapuerca TD6. Journal of H uman
Evolution, 37, 389– 413. https://doi.org/10.1006/jhev.1998.0264
van Rij, J., Wieling, M., Baayen, R., & van Rijn, H. (2017). “itsadug:
Interpreting Time Series and Autocorrelated Data Using GAMMs.”
R package version 2.3.
Vanpé, C., Gaillard, J.- M., Kjellander, P., Mysterud, A., Magnien, P.,
Delorme, D., Laere, G., Klein, F., Liberg, O., & Mark Hewison, A J
(2007). Antler size provides an honest signal of male phenotypic
qualit y in roe deer. American Naturalist, 169, 481– 493. https://doi.
org /10.108 6/512046
Vogt, F. (1947). Das Rotwild. Oesterreichische Jagd- und Fischereiverlag.
von den Driesch, A . (1976). A guide to the measurement of animal bones
from archeological sites. Peabody Museum Bulletin, 1, 1– 1 3 8 .
Wajdzik, M., Hink, K ., Szyinka, K., Nasiadka, P., & Skubis, J. (2018).
Wpływ lesistości na jacość osobncza samćow jelenia szlachetnego
(Cervus elaphus) na terenie opolszczyzny [the influence of forest
area on the individual quality of red deer males (Cervus elaphus) in
the Opole region]. Acta Scientiarum Polonorum Silvarum Colendarum
Ratio Et Industria Lignaria, 17, 69– 77. https://doi.org/10.17306/
J.AFW.2018.1.8
Warton, D. I., Duursma, R. A., Falster, D. S., & Taskinen, S. (2012). Smart
3 - an R package for estimation and inference about allometric lines.
Methods in Ecology and Evolution, 3, 2 57– 2 59.
Warton, D. I., Wright, I. J., Falster, D. S., & Westoby, M. (20 06). Bivariate
line- fitting methods for allometry. Biological Revi ews of the Cambridge
Philosophical Society, 81, 259– 291. http s://doi.org /10.1017/S1464
79310 60 07007
Wolfe, G. J. (1983). The relationship bet ween age and antler develop-
ment in wapiti. In R. D. Brown (Ed.), Antler development in Cervidae
(pp. 29– 36). Caesar Kleb erg Wildlife.
Wood, S. N. (2017). Generalized Additive Models: An Introduction with R ,
2nd ed. Chapman and Hall/CRC.
How to cite this article: Mattioli S, Ferretti F, Nicoloso S,
Corlatti L. Spatial variation in antler investment of Apennine
red deer. Ecol Evol. 2021;11:7850– 7864. h t t ps : //d o i .
org /10.1002/ece3.7617