Morphometric traits of Dorcus parallelipipedus (Coleoptera: Lucanidae) larvae and adults: can differences between populations be ruled out?

Summary Stag beetles are saproxylic insects that live in deadwood colonised by fungi and other microorganisms. Due to the cryptic habits of these species, little is known on their biological aspects, especially for the immature stage. In this study, we investigated morphometric traits of lesser stag beetle, Dorcus parallelipipedus (Linnaeus, 1758) (Coleoptera: Lucanidae) larvae and adults, with comparisons between populations. Instar identification by measuring larval head capsule was performed, and the relationship between larval body mass and head capsule width was investigated for each surveyed population. To assess the differences among populations, the scaling relationships for adults between their body and mandibles length was also considered, especially for adult males. Morphometric relationships were described by exponential equations. Differences between populations were sometimes limited to one or the other feature, and particularly ascribed to the larval body mass. These differences could be imputed to several factors, among with those of environmental or genetic order. The scaling relationship of lesser stag beetle adult males showed a positive allometry but did not differ among populations, indicating that morphological traits within a species and sex may be biologically retained. Findings are discussed from the perspective of D. parallelipipedus life history.

In forest ecosystems, saproxylic insects directly or indirectly depend on decaying or deadwood for their life cycle (Speight 1989;Stokland et al. 2012;Ulyshen & Šobotník 2018). Biodiversity in deadwood can reach 30% of the total forest biodiversity (Vallauri et al. 2005), and it mainly consists of beetles (Coleoptera), with about 65% of families including at least a saproxylic species (Stokland et al. 2012;Carpaneto et al. 2015;Gimmel & Ferro 2018). Stag beetles (Coleoptera: Lucanidae) belong to one of the most specialised saproxylic families that live in both temperate and tropical regions, comprising about 20 species distributed in European countries (Bartolozzi et al. 2016).
Stag beetles of the genus Dorcus Macleay, 1819 belong to the polyphyletic tribe Dorcini, subfamily Lucaninae (Kim & Farrell 2015); it is a genus showing sexual dimorphism and size variation in the adult stage (e.g. Paulian 1935;Franciscolo 1997;Klausnitzer & Sprecher-Uebersax 2008;Hendriks 2019), and this is especially marked in the case of Asian Dorcus species (e.g. Kawano 1997;Iguchi 2001Iguchi , 2013. In Europe, three species of the genus Dorcus can be found, i.e. Dorcus alexisi Muret & Drumont, 1999 (Coleoptera: Lucanidae), D. musimon Gené, 1836 (Coleoptera: Lucanidae), and D. parallelipipedus (Linnaeus, 1758) (Coleoptera: Lucanidae) (Vit & Bartolozzi 2013; Bartolozzi et al. 2016). The latter, also known as the lesser stag beetle, is distributed in more than 40 countries, not only in Europe, but also in North Africa and Asia (Franciscolo 1997;Klausnitzer & Sprecher-Uebersax 2008; Bartolozzi et al. 2016). Adults of D. parallelipipedus are dull black and variable in size, from ∼15 to 35 mm long with slight sexual dimorphism (Jessop 1986;Franciscolo 1997;Hendriks 2013; Figure  S1A in Supplementary file), and the species is listed as "Least Concern" in the International Union for Conservation of Nature (IUCN) European Red List (Nieto & Alexander 2010;Carpaneto et al. 2015). It exhibits a quite long adult lifespan, with a possible lifespan of three years, and it is usually active from spring to fall (Franciscolo 1997;Fremlin & Hendriks 2011. Dorcus parallelipipedus larvae mostly develop above the ground in white-rotted wood, in sites that are often subject to higher temperatures than those of other European stag beetle species, usually at lower altitudes and with a large amount of deadwood (Bartolozzi & Maggini 2007;Lachat et al. 2012). Lesser stag beetle larvae develop during one to two years and through three instars (cf. van Emden 1941;Hendriks 2019) in about 15 genera of broadleaved trees (Franciscolo 1997;Klausnitzer & Sprecher-Uebersax 2008).
Due to the cryptic habits of this stag beetle, little is known on their biological and ecological aspects, especially for the immature stage that are often overlooked. The aim of this study is to investigate the morphometric parameters of larvae and adults, as well as the body mass of larvae, in a saproxylic insect from different populations, using the lesser stag beetle as a model species. Our study confirmed and revised earlier data on D. parallelipipedus instar identification by measuring a large number of larvae and assessing regression equations of instar identification for each site, even considering comparisons between populations. The relationship between larval body mass and head capsule width was also investigated for each surveyed population. Head capsule width-instar and body mass-head capsule width relationships were described by exponential equations. Furthermore, we explored the scaling relationships or static allometry (i.e. the relationship observed between traits in a two-dimensional scatter plots) for adults between their body length vs. the length of their mandibles, to prove if these traits differ across populations. A special attention was given to males, on whom these kinds of studies are usually carried out. Scaling relationships on body vs. mandible length were described by exponential equations. Our results shed light on morphometric features of D. parallelipipedus larvae and adults, also improving the knowledge on biological features, even considering different populations in the lesser stag beetle distribution range.

Study area and sampling design
In the present work, four populations of D. parallelipipedus were studied for their morphometry and body mass traits in larvae and adults. Insects were collected in natural and urban environments in three European countries, the Netherlands (hereafter NL), UK, and Italy (two sites, IT and IT2), from 2009 to 2022 ( Figure S2 in Supplementary file). For these sites, information on minimum, average and maximum monthly temperature and rainfall is provided in Figure S3 (in Supplementary file).
NL is a site located in the village of Oostwold, province Groningen, the Netherlands. This village is part of a polder system with high (ground) water levels, it covers an area of approximately 40 hectares and is surrounded by grassland. Its shaded areas are planted with broadleaved trees: Betula pendula Roth, Fraxinus excelsior L., Quercus robur L., Salix alba L. and Salix caprea L. All biometric measurements of adults and larvae were taken from D. parallelipipedus found in PH's garden, which covers an area of 1000 m 2 (53.20305°N, 6.44042°E, 0 m asl). This species appeared in this garden in 2010. Since then, it has colonised the available deadwood in the site, mostly decayed logs (Hendriks 2019). Therefore, NL comprises a population isolated from the current distribution of the species in the country, occurring about 100 km north of the nearest population in the Veluwe, province Gelderland, the Netherlands (Waarneming.nl 2023).
UK is a site in Colchester, north-east Essex (51.88262°N, 0.88312°E, 52 m asl). Private gardens in the south-west part of the town are a well-known hotspot for European stag beetle Lucanus cervus (Linnaeus, 1758) (Coleoptera: Lucanidae), first studied by Clark (1964Clark ( , 1965, followed by Bowdrey (1997) and afterwards by MF in her garden and elsewhere (e.g. Fremlin & Fremlin 2010). In recent years, lesser stag beetles have been quick to colonise (or benefited from) the deadwood habitats created for the European stag beetle in this area and it is where lesser stag beetle adults and larvae were often found; however, only larvae were considered in this study. Other sightings were also recorded in the decaying wood of broadleaved trees either standing or fallen.
IT is a site located in an agricultural landscape in Piacenza province, Lombardy region, north-western Italy (44. 92142°N, 9.57350°E, 246 m asl), and is a forest dominated by Castanea sativa Mill. and Quercus spp., alongside tree species including Fraxinus ornus L., Prunus sp. and Sorbus torminalis (L.) Crantz. In this site, both larva and adult traits were investigated.
IT2 is a site in the Euganean Hills in Padua province, Veneto region, north-eastern Italy (45.28265°N, 11.70933°E, 250 m asl), represented by a forest with Carpinus betulus L., C. sativa, F. ornus, Prunus sp., Quercus spp., Robinia pseudoacacia L., and other broadleaved trees, together with some conifers. In this site, morphometric data were collected only for adults.
In each site, insect collection was performed by searching for specimens in dying and rotting wood pieces on the groundup to a few centimetres under the groundopening the wood pieces by hand and with a knife or screwdriver (larvae and adults), and with direct search on the ground and on trees (adults). The identification to species level of each stag beetle found, was confirmed by using identification keys on external characters of larvae and adults, and adults were sexed (Jessop 1986;Franciscolo 1997;Klausnitzer & Sprecher-Uebersax 2008;Ballerio et al. 2014). Insects were measured and weighed to collect morphometric and body mass data (see below).

Morphometry and body mass
Measurements were taken from living insects. For larvae, we registered the maximum head capsule width (HCW) in mm, as previously done in studies on other stag beetles (e.g. van Emden 1941;Klausnitzer & Sprecher-Uebersax 2008;Fremlin & Hendriks 2014;Scaccini 2015), together with body mass (BM) in mg. Larval BM was quantified using a Mettler Toledo PM100 weighing scale, precision 1 mg (NL); either in the field with a Salter electronic diet scale, model 1250, or indoors with a Scalix CB-310 electronic scale, to 10 mg accuracy (UK); and using a RADWAG -PS 1200.X2 scale, precision 10 mg (IT). For adults, total body length and mandible length were taken as reported by Hendriks (2013), thus measuring the total length from the tip of the mandibles to the tip of the elytra, and mandibles length from the base of the mandible to its tip. All body measurements were taken with electronic callipers, precision 0.01 mm.

Data analysis
Dorcus parallelipipedus larvae. In the analyses, the input data used were the number of instars, HCW and BM of D. parallelipipedus larvae. To obtain the instar identification, two methodologies were followed as reported in studies on stag beetle larvae (e.g. Fremlin & Hendriks 2014), based on D. parallelipipedus HCW features (van Emden 1941; Hendriks 2019). In the first method, larval instars were identified through the analysis of HCW frequency distribution after plotting the data on the graph, where each series of non-overlapping peaks represent a larval instar (Daly 1985)three in stag beetles. The second method follows the Brooks-Dyar's rule, which is valid for holometabolous insects that have a constant larval HCW in pre-and post-moult (Brooks 1886;Dyar 1890). According to the Brooks-Dyar's rule, the geometric progression can be described in the equation.
that can be written as the inverse of the exponential equation (i.e. linearised) as: where x is the larval instar number, y is the HCW, a and b are constants that depend on the species, and e b is the constant growth rate (Dyar 1890;Floater 1996). Furthermore, two different regression analyses were run, the first to study the relationship between larval instar and HCW, the second between HCW (mm) and larval BM (mg). Based on the instar identification, in the first regression analysis the number of instars was plotted on the x axis and the ln(HCW) on the y axis, following Equation (2). Logarithmic transformations were performed to linearise the observations for the inference on the studied traits among populations. In the second regression, ln (HCW) (x axis) was plotted on ln(BM) (y axis). Since both axes are in logarithmic scale, the exponential equation becomes: considering that w = ae by (see Equation (1)), thus w = ae bln(y) = ae ln(y b ) = ay b . Its inverse, linear equation is: In these equations, w indicates BM values, y refers to HCW values, and z = ln(HCW). Note that a and b, constants in this equation, differ from those in Equations (1) and (2) as they refer to a different x-y relationship. Regression analyses of lines obtained from plotted data in Equations (2) and (4) were performed through an F test (α = 0.05). Regression lines for both instar-ln(HCW) and ln(HCW)-ln (BM) relationships were compared in pairs in their slope and intercept, testing all the possible combinations between populations (i.e. NL vs. UK, NL vs. IT, UK vs. IT). These comparisons were performed using the method described in Stack Exchange (2016) and Real Statistics (2021), with the formula where b 0 and b 2 are elements of the intercept, b 1 and b 3 are elements of the slope, and p (for "population") is the dummy variable. For each comparison, the dummy variable p changes its value according to the referred population, with p = 0 for one of the two populations and p = 1 for the other one. Thus, in the case of the first population in a comparison, the regression model results as . Consequently, the null hypothesis is the two slopes are equal if b 3 = 0, and the intercepts if b 2 = 0 (Stack Exchange 2016; Real Statistics 2021). In the analysis on instar and HCW, x is the larval instar, and y is the HCW in Equation (5). In the analysis on HCW and BM, w (instead of y, in Equation (5)) indicates body mass values, and y, which refers to HCW values, is placed instead of x as in Equations (3) and (4). Regression lines were run through an F test (α = 0.05). All regression analyses were performed in R version 4.2.1 (R Core Team 2012), using RStudio (RStudio Team 2016). Furthermore, larval HCW and BM were compared among the three populations in two independent analyses through Generalised Linear Mixed Models (GLMM) with the procedure GLIMMIX of SAS (ver. 9.4) (SAS Institute 2016), considering the site as independent variable. The analysis was run by larval instar. Their effect was tested with an F test (α = 0.05), and the Tukey-Kramer test (α = 0.05) was used as post hoc. Data were transformed in log(x + 1) to meet model assumptions. Data are presented as mean ± standard deviation.
Dorcus parallelipipedus adults. Data on D. parallelipipedus adults used in the scaling relationship analysis were the total length of the insect and its mandible length, in two different analyses run separately by sex. Mandible and total lengths were studied through the equation proposed by Huxley (1932) and adopted by Paulian (1935) for polymorphic beetle males (here adapted in its components), also known as "law of simple allometry": that can be linearised as: where x is the total length in mm, y is the mandible length in mm, z = ln(x), and β and α are two constant values that depend on the investigated system (cf. Paulian 1935). If the coefficient of allometry α > 1, positive allometry occurs; when α < 1, the relationship between traits represents a negative allometry; α = 1 consists in the isometry (Huxley & Teissier 1936).
In the regression analyses on static allometry, we used sites with at least 30 measured males or females. As has been described previously for D. parallelipipedus larvae, the obtained regression lines were compared in pairs in their slope and intercept, for all the possible combinations between populations (i.e. NL vs. IT2, NL vs. IT, IT2 vs. IT). Comparisons were performed using the method described in Stack Exchange (2016) and Real Statistics (2021), using Equation (5), where x is the total length and y the mandible length. Regression lines were run through an F test (α = 0.05), and performed in R version 4.2.1 (R Core Team 2012), using RStudio (RStudio Team 2016).
Finally, to test if different populations show differences in insect mandible and total lengths, these parameters were investigated in two independent analyses and by sex with GLMM though the procedure GLIMMIX of SAS (ver. 9.4) (SAS Institute 2016), considering the site as independent variable. Their effect was tested with an F test (α = 0.05), and the Tukey-Kramer test (α = 0.05) was used as post hoc. Data were transformed in log (x + 1) to meet model assumptions. Data are presented as mean ± standard deviation.

Dorcus parallelipipedus larvae
Field investigations resulted in the measurement of 507 larvae, 223 in NL, 169 in UK, and 115 in IT. In the first method for instar identification, the graph on HCW frequency distribution described three different main peaks, one for each larval instar, for all the investigated populations (Figure 1).
Concerning the second methodology, Brooks-Dyar's Equation (1) was obtained, per site, plotting the instar number and ln(HCW) (Equation (2)), with regression line details shown in Table 1 and Figure 2. The three instars described from regression analyses were built on Equation (2) for the surveyed sites, with linear regressions that were significant in all the cases (Table 1; Figure 2). In the analysis on HCW-BM, we used a subset of data for UK (153 larvae) and IT (74 larvae) populations due to missing data for larval mass; NL data refer to all the 223 larvae. Linear regression analyses performed for the relationship between the natural logarithm of larval HCW and of the BM are reported in Figure 3. Differences between insect populations for intercept and slope, following Equation (5), are detailed in Table 1 for both instar-HCW and HCW-BM, at times showing lower values for IT larvae and higher values for NL.
Furthermore, HCW and BM of the larvae differed among populations, for second and third instar larvae in particular. While HCW (Gaussian GLMM, F 2,48 = 2.66, p = 0.0804) and BM (Gaussian GLMM, F 2,43 = 0.47, p = 0.6288) of first instar larvae did not differ among the investigated populations, in the second and the third instars NL showed the highest values. IT second instar larvae had intermediate HCWs (Gaussian GLMM, F 2,145 = 7.50, p = 0.0008), while third instar ones had lower HCW values if compared to the other populations, with UK larvae placed in the middle (Gaussian GLMM, F 2,305 = 22.29, p < 0.0001). Despite no differences being recorded in the BM of the second instar (Gaussian GLMM, F 2,141 = 2.12, p = 0.1235), NL and UK third instar larvae were heavier than the IT counterparts (Gaussian GLMM, F 2,257 = 69.40, p < 0.0001; Figure 4).
Finally, while first and second instar larvae were less commonly found, third instar larvae were generally observed in any period of the yeareven in winterfor all the populations we investigated. Lesser stag beetle larvae undergo a winter diapause and larvae with their gut filled with a clear fluid ( Figure S1B in Supplementary file) were found until late March, observed in all populations. This was observed in a second instar larva and for some third instar ones.

Dorcus parallelipipedus adults
Field surveys yielded 130 males and 78 females. Adults found in this study were active from April to September. The exponential Huxley's Equation (6) was obtained for each site by plotting total body vs. mandible length in the regression lines, whose details are reported in Table 2, and in Figures 5 (males) and S4 (females, in Supplementary file). In the case of females, data plotted on linear regressions were quite scattered, with low R 2 values for both populations ( Figure S4 in Supplementary file). From the analysis on comparisons of linear regressions (Equation (5)) run on male data, no differences resulted among the three populations, for both intercept and slope (Table 2) Table 2). No differences were recorded in intercept and slope between the two populations of female ( Figure S4 in Supplementary file).  Table 1. Output and details of the regression analyses on Dorcus parallelipipedus larval instar, head capsule width (HCW), and body mass (BM) by site, showing the comparison between lines in intercept and slope, the obtained Brooks-Dyar's Equation (1) (first group of analyses), and the exponential Equation (3) (second group of analyses). Among sites, groups sharing the same letter are not different on intercept or slope as inferred from the intercept and slope analyses (Equation (5)). NL = the Netherlands, IT = Italy, w = larval mass in mg, x = instar (1-3), y = HCW in mm, and z = ln(HCW). Sites are listed by latitude, with the highest first. Mandible and total length of both males and females did not differ between the investigated populations (males, total length: Gaussian GLMM, F 2,127 = 0.22, p = 0.7998; males, mandible length: Gaussian GLMM, F 2,127 = 2.48, p = 0.0875; females, total length: Gaussian GLMM, F 1,76 = 0.01, p = 0.9386; females, mandible length: Gaussian GLMM, F 1,76 = 0.26, p = 0.6089). In the investigated sites, the difference within the same population was higher than that recorded for different populations ( Figure S5 in Supplementary file).

Discussion
The morphological traits of D. parallelipipedus larvae and adults were compared between sites, confirming that they  Table 1. had three larval instars and revealing that differences between populations were often limited. Larval stage data are frequently overlooked or lacking for stag beetles, and with this study we shed light on morphometry and body mass features for the three instars. Here we confirmed data on HCW of the D. parallelipipedus instars and described the exponential equations for each population.
In the three populations, each larval instar was identified through the two approaches we used, based on HCW measurements. Results were consistent with the previous published material on instars of the same species by van Emden (1941), Niklas (1974;as in Klausnitzer & Sprecher-Uebersax 2008), and Hendriks (2019), with HCW mean value ranges of 1.70-2.20, 3.05-3.20 and 5.35-5.70 mm, respectively, for first, second and third instar larvae. In the populations investigated in this study, HCW mean values for first, second, and third instar larvae were, respectively, 1.64-1.76, 3.01-3.16 and 5.18-5.54 mm.
Lesser stag beetle larvae were detected throughout the year, in particular the third instar. In the northern populations some larvae overwintered in the second instar,  Table 1. thus needing the subsequent year to complete their development, resulting in a two-year larval stage duration (Hendriks 2019). As previously reported (Hendriks 2019), during overwintering in the three populations some larvae entered a diapause by replacing their gut contents with a translucent fluid ( Figure S1B in Supplementary file). This diapause has been observed on other stag beetle species that develop above the ground such as Platycerus Geoffroy, 1762 (D. Scaccini, pers. obs.) and Ceruchus piceus (Weber, 1801) (Coleoptera: Lucanidae) (Neven et al. 1986;Xu et al. 1990), but not in L. cervus, which develops in the soil-wood interface mostly below the ground (M. Fremlin and P. Hendriks, pers. obs.). Indeed, the larvae of other saproxylic beetle species that develop above the ground may have identical freeze tolerance-avoidance tactics and even change their diet, and body colour (e.g. Togashi 1991;Leather et al. 1993;Přikryl et al. 2012). This raises the question about the heat tolerance and avoidance tactics to very high temperatures for D. parallelipipedus, for which nothing is known. It is only known that L. cervus larvae cannot tolerate temperatures above 26°C (Lai & Shin-ping 2008;P. Hendriks, pers. obs.); but the temperature inside logs above the ground, even though it is somewhat buffered, can reach above 30°C (Lawhorn & Yanoviak 2022). Both strategies need to be further studied for stag beetles.
Even though we found some similarities with previous published studies, differences between populations in larval HCW, body mass, and in the regression lines parameters were seldom observed. NL third instar larvae were often heavier and showed bigger head capsules than IT larvae, while no differences were detected between NL and UK, or for ones of IT and UK. These observations only reflect in a different slope for the IT HCW-BM Figure 4. Mean values ± standard error (error bars) of Dorcus parallelipipedus, by instar, for the three larval populations. A, Head capsule width (HCW, mm). B, Body mass (BM, mg). NL = the Netherlands, IT = Italy. Different letters indicate significant differences with the Tukey-Kramer test (α = 0.05). 'ns' refers to no significant differences. Table 2. Output and details of the regression analyses on Dorcus parallelipipedus adult males, total length, and mandible length by site, showing the comparison between lines in intercept and slope, and the exponential Huxley's Equation (6). Among sites, groups sharing the same letter are not different on intercept or slope as inferred from the intercept and slope analyses (Equation (5)). NL = the Netherlands, IT2 = Italy, second sitenorth-east, IT = Italy, first sitenorth-west, y = mandible length in mm, x = total length in mm, y = mandible length in mm, and z = ln(total length). Sites are listed by latitude, with the highest first.

Site
Linear Intercept Slope Exponential eq. regression line, which had a lower slope than those obtained for NL and UK. IT third instar larvae were significantly lighter (almost 50% less) than those of the other two populations. However, regression lines were much more conservative, with differences to be ascribed solely to the slope. It should be noted that in comparisons of traits with different units, like mm vs. mg, scale-dependent issues can arise, affecting inference accuracy despite the Figure 5. Scaling relationship between natural logarithm of total length and natural logarithm of mandible length for Dorcus parallelipipedus males in the three investigated populations. NL = the Netherlands, IT2 = Italy, second sitenorth-east, IT = Italy, first sitenorth-west, y = mandible length in mm, and z = ln(total length). Number of specimens, line equations and R 2 values are reported in the graphs and in Table 2. logarithmic transformation of data (Warton et al. 2006). Nevertheless, several factors may have shaped the difference we observed, such as related to environmental (temperature, photoperiod, food source, etc.) or to those of genetic order (e.g. Sebens 1987;Delbac et al. 2010;Dhillon & Hasan 2018;Hendriks 2019). Abiotic factors like temperature and photoperiod were found to significantly influence head capsule size in larvae of Lepidoptera (Morris 1991;Delbac et al. 2010). In the present study, sites were different in their climatic characteristics, for instance NL and UK have a lower mean temperature in summer than IT ( Figure S3 in Supplementary file), which may affect D. parallelipipedus larval features like HCW and BM. In longhorn beetles (Coleoptera: Cerambycidae), HCW and even instar number can vary for larvae reared at different temperatures, with a smaller head capsule at low temperature at least for the first instars (Go et al. 2019). Besides, in the European grapevine moth Lobesia botrana (Denis & Schiffermuller, 1775) (Lepidoptera: Tortricidae), instar numbers increased (six instead of five) in cooler environments for second-generation larvae that undergo overwintering diapause (Pavan et al. 2013). In this species, high temperatures triggered smaller HCW values if compared to lower and nonconstant temperatures (Saenz-de-Cabezón Irigaray et al. 2006). In D. parallelipipedus, body mass is lighter for third instar larvae that go through a one-year cycle than that for those that experienced a two-year cycle (Hendriks 2019). Temperature and photoperiod also affected larval BM, length, and HCW of Chilo partellus (Swinhoe, 1885) (Lepidoptera: Crambidae), which increase with the rise of these two abiotic factors (Dhillon & Hasan 2018). Temperature influences larval growth in L. cervus, with a gain of mass mainly during the warm season, and constant values or body mass losses in the cold season with temperature lower than about 10-15°C (Thomaes et al. 2022). In flea beetles (Coleoptera: Chrysomelidae: Galerucinae: Alticini), HCW distribution differs according to degreedays accumulation and latitude among different populations in the field, but head size also depends on larval density that is inversely proportional to insect growth rate and head capsule development, possibly due to intraspecific competition (Goguen & Moreau 2013). Larval traits and size are affected by intraspecific competition also in Dorcus species and may be linked to larval cannibalism, with cannibals that are heavier and larger in head size than their prey, showing an influence of the food quality ).
Food source may also affect morphometric parameters, as demonstrated in the larvae of the moth L. botrana where HCW increased as the generations progressed in the year, being related to the phenology of its host plant (Delbac et al. 2010). Stag beetles depend on fungi and mycangium symbionts to gather the nutritional elements from whiterotted wood required for their growth and development (e.g. Tanahashi & Kubota 2013). The growth efficiency of Dorcus depends on the chemical elements assimilated by the larva (Tanahashi et al. 2018), also with the influence of both the soluble and insoluble fractions of mycelium (Tanahashi & Kubota 2013). Stag beetle larvae growth performance and body mass are related to the amount of total food consumed, increasing when food is more abundant, thus affecting adult morphological traits and fitness (Songvorawit et al. 2022). In our study, lesser stag beetle larvae developed on different plant taxa. For those in NL, identified wood sources were mainly F. sylvatica; for UK trees of the genera Acer, Castanea, Fraxinus, Prunus, Quercus, and other broadleaved trees; for IT primarily Quercus, and with a lesser extent Castanea and Prunus. Based on the previous literature, the differences we observed could thus be linked to multiple factors possibly related to microclimatic features, larval density, and stage of decay of the whiterotted wood, but these attributes were not considered in this study and thus require further investigation.
Furthermore, lesser stag beetle third instar larvae, which generally live longer than the preceding two instars, may gain weight while ageing, which could partially explain the differences observed between IT and the other two larval groups (Hendriks 2019;P. Hendriks, pers. obs.). A longer period spent as larva, due to environmental conditions such as the microclimate and the quality of the food source, may indeed affect stag beetle growth, physiological processes and fitness, resulting in differences in body mass and even adult size (e.g. Kawano 2000;Klausnitzer & Sprecher-Uebersax 2008;Rink & Sinsch 2008;Hendriks & Méndez 2018;Songvorawit et al. 2018Songvorawit et al. , 2022Hendriks 2019;Thomaes et al. 2022).
In our study, Italian larvae were smaller and may have developed faster than the ones in the northern populations, leading to adults that were slightlybut not significantlysmaller than in the Netherlands. This fits with a recent study that found that in a saproxylic species developing in tree hollows, Osmoderma eremita (Scopoli, 1763) (Coleoptera: Scarabaeidae), adult body size decreased with a warmer microclimate (Lindman et al. 2023), as this could probably be ascribed to our populations. Indeed, in Lucanidae differences in adult size have been ascribed to complex factors related to climate and latitude (e.g. Rink & Sinsch 2008;Romiti et al. 2017;Hendriks 2019), quality of food sources and the duration of the immature stage (Kawano 2000;Songvorawit et al. 2018Songvorawit et al. , 2022, the above-mentioned larval competition, but also to their genetic aspect and nutrient-dependent hormones (Gotoh et al. 2011(Gotoh et al. , 2012(Gotoh et al. , 2014. In the scaling relationship between mandibles and body size of D. parallelipipedus males, the coefficient of allometry (α in Equation (7)) was about 1.80-1.92, thus reflecting a positive allometry in the growth of mandibles on the total body. These results are consistent with those of Paulian (1935), where the coefficient α on body-mandibles length was found as 2.00. On the other hand, for females these values were consistently lower, close to an isometric scaling relationship and even a negative allometry possibly due to their phylogeny and life histories, even if curves had low coefficient of determination.
For D. parallelipipedus adult males, differences in regression line parameters were not detected between populations. In the family Lucanidae, it was suggested that the ontogeny can act as a phylogenetic constraint on the abundance of shared morphological traits among species within the same genus (Kawano 2000) and, considering the scaling relationships as reported in the present study, this could be even more retained at species level and even sex. In Aegus chelifer chelifer MacLeay, 1819 (Coleoptera: Lucanidae), the allometric slope did not differ between the urban vs. forest populations they investigated, suggesting that growing under different environmental conditions may lead to high individual variation in the scaling relationship that could mask the difference between populations (Songvorawit et al. 2017). In addition, in studies on the European stag beetle L. cervus reported changes in allometric traits among countries and sites, indicating a possible influence of developmental conditions and also genetic differences among populations (Harvey et al. 2011;Romiti et al. 2017).
Moreover, in our populations adults did not differ in total body or mandible length, independently for females or males. Indeed, D. parallelipipedus exhibits strong differences in size within and among sexes, reflected for instance in body and mandible features (e.g . Franciscolo 1997;Klausnitzer & Sprecher-Uebersax 2008;Hendriks 2013Hendriks , 2019, shown here to be greater within the same population than among them. It should be noted that in the case of the lesser stag beetle, and differently from other stag beetles even belonging to the same genus, not much is known about their courtship behaviour because they spend their lives in deadwood. Their body shape and mandibles seem perfectly adapted to digging tunnels in the woody material (e.g. Franciscolo 1997;Fremlin & Hendriks 2013;Hendriks 2013). Thus, it is not sensible to consider the study of mandible size as a measure of weaponry for this particular species (e.g. Kawano 1997;Emlen 2008;Goyens et al. 2015;Somjee 2021).

Conclusions
In this study, HCW data of D. parallelipipedus instars were confirmed, and exponential equations for each population were described even considering data on larval mass. For adult males, exponential polynomial equations were also built following Huxley's equation. Differences between populations in insect traits were sometimes limited to one or the other feature, with mean values that differed in particular for body mass of larvae of the IT population. These differences could be ascribed to several factors, including environmental or genetic factors. Despite the difference found in larval body mass, morphometric traits of lesser stag beetle adult males did not differ in the investigated populations, showing instead a higher difference within the same population than differences among populations. Even though we could not determine for certain the factors affecting the model we studied, our results showed that morphological traits within a species, and within the same sex, may be biologically retained, especially for adult males. Further studies should investigate this issue in more populations and in other saproxylic beetle species with similar life histories, possibly considering sex-related traits also in larvae and pupae.