The measurements were performed on dry set (pinned or spread), complete male specimens. When fresh adults were available, these were first dried in the position traditionally used for these insects in entomological collections. The measures described below were taken in one of four ways: (a) under a stereomicroscope with an ocular micrometer, (b) on a digitized scale drawing made with an optical camera lucida adapted to a stereomicroscope (× 10 to × 40), (c) on a digital photograph of the specimen taken together with a standard scale bar, taken either with a macro lens (up to 1:1) or on a photo microscope at low magnification, or (d) with a Vernier caliper (exceptionally in the case of some of the largest moths). The program ImageJ (Rasband 2012) was used to measure the digitized images.

Six linear measurements (in mm) were taken (Figure 1): thorax length (TL), thorax width (TW, taking the point of insertion of the fore wings as a reference), abdomen length (AL) excluding terminal hair pencils or protruding genital appendages, abdomen width (AW, taken at the midpoint of the line represented by AL), forewing length (FWL, from the insertion of the wing on its costal margin to its apex including the fimbriae) and forewing width (FWW, the distance between edges following a line perpendicular to FWL at its midpoint). In addition, the area of the fore- and hindwings (including the fringes) were recorded (FWA, HWA, as mm²). The mean species values are available as Supplementary material (Suppl. material 1: nexus format text).

Figure 1. 

Slightly idealized representations of three typical adult Lepidoptera (left to right: Lasiocampidae, Hepialidae, Gelechiidae) to illustrate the variables measured. The right side of the thoraces is represented as devoid of the scale cover to make more evident the limits of this tagma. The three drawings are scaled to the same forewing length. Linear measurements are indicated by bars and areas by a striped pattern. FWL = fore wing length, FWW = forewing width, FWA = forewing area, HWA = hind wing area, TL = thorax length, TW = thorax width, AL = abdomen length, AW = abdomen width.

To estimate the magnitude of error measurement, the mean within sample and mean within species coefficients of variation were calculated after replicated measurements taken on each individual and between individuals within species.

1. Every measurement was taken twice for each specimen using two different methods among those detailed above (most frequently a, b and c), on two different dates.

2. Whenever possible two male specimens of approximately the same size (judged from wingspan by naked eye) of the species were processed. However, replications were not always possible as data from single representatives of a number of species were included if this contributed to an increase in the taxonomic or geographic coverage of the species selection.

The insects were dried to a constant weight at 60° for 48 hours (72 h for the largest specimens). The pins, if present, were removed carefully (but see below). The weight of the whole specimen was determined to the nearest 0.01 mg in a Mettler AT261 balance (species of wingspan of ca. 15 mm or above) or in a Mettler Toledo XP6 microbalance with precision of 0.001 mg (individuals smaller than that size).

Although medium or larger sized collection specimens can generally be de-pinned and remounted without much difficulty, there is always some risk of damage. For a small number of loaned specimens (ca. 20 individuals) the weight of the pins was estimated, then subtracted from that of the dry mounted specimen. Samples of 10 individual pins from four different brands and numbers (gauges): 000, 00, 0 and 1 to 6 (all with nylon heads and 37 mm long) were measured and weighed. The weights were taken to the nearest 0.01 mg, and the widths measured with a precision of 0.0179 mm under a binocular microscope with an ocular scale line. The relationship between the log-transformed weights and widths was highly consistent: log_10∙(pin weight in mg) = 2.339 + 1.908 log_10∙(pin diameter in mm), R = 0.997, P < 0.0001, n = 350.

The smallest moths (broadly corresponding to the heterogeneous assemblage of the “microlepidoptera”) posed some special difficulties, which handicapped the use of reference collections as sources of size data. These moths are fragile and very likely to be damaged if treated in the way described above, and even though they are frequently mounted on smaller pins (‘minutiae’, weighting 0.69–3.15 mg for widths of 0.10 and 0.20 mm respectively) the small variation in the length of these tiny metal pieces represents an excessive error in terms of the specimen dry weight. Moreover, as the genital pieces are of interest for identification, collection specimens frequently lack the abdomen or a large part of it as it was removed for identification. Finally, most of them cannot be easily identified to species level without expertise. For these reasons the data from several families in this category were obtained from a small reference collection at the author’s department. This hosts expert-identified specimens collected two decades ago at a single site, so new samples were taken at the same location during 2011–2012 to reasonably cover the lower part of the size range, although at the cost of low geographic variation.

All the variables were transformed to their decimal logarithms. This facilitated comparisons with results from earlier research (as most size-weight relations have been modelled using the equation weight = a × size^b: Reiss 1989; Ganihar 1997), linear-regression approaches as well as some demands of the comparative method adopted (described below). After log-transformation, all the variables fitted reasonably to the normal distribution with Kolmogorov-Smirnov test values of d < 0.049, P > 0.05 in all instances (Suppl. material 2: frequency distribution graph).

The multivariate models were fitted using the General Regression Models module of Statistica (Statsoft 2004). For model selection, a manual iterative forward-backwards procedure was adopted to exclude redundant variables.

The method of phylogenetically independent contrasts (Felsenstein 1985; Harvey and Pagel 1991) was used to control for phylogenetic effects. The contrasts were calculated using the software PDAP:PDTREE (Midford et al. 2009) integrated in the package Mesquite (Maddison and Maddison 2011). Branch lengths were set to equal length (1.00), and the polytomies were estimated as single contrasts, which were calculated after the original output.

The working hypothesis on phylogenetic relationships was built according to the classification proposed by van Nieukerken et al. (2011), with the relationships above the family level adapted after the tree topologies from Kawahara and Breinholt (2014) complemented by Regier et al. (2009, 2013), Mutanen et al. (2010), Bazinet et al. (2013) and Martijn et al. (2014). Further information was gathered from other recent literature (details available in Suppl. material 3: documentation on phylogeny).

In the absence of any other references, the formal classifications of Fauna Europaea (Karsholt et al. 2013) for the European species and of the Lepindex database (Beccaloni et al. 2013) for other geographic regions was adopted. The tree was assembled manually; preference was given to the most recent results, or to those with the highest statistical support, but keeping any former hypotheses if these have not been contradicted. Thus, except in face of conflicting evidence the formal taxa at the levels of superfamily, family, subfamily and genus were adopted even when their monophyletic status had not been corroborated in all instances. The tree topology and data are available from the Suppl. material 4 and 1 (4: tree topology, 1: tree nexus format). The resulting dendrogram showed high resolution (ca. 77%), which of course is overoptimistic in terms of strictly phylogenetic criteria.

Regressions were done through the origin to estimate the correlations and slopes. After a multivariate regression model was obtained, Least Squares Regression was used to estimate the intercept for the working data set keeping the evolutionary slopes already obtained.

The number of species and of supraspecific taxa available for this study was obviously small if compared to the estimated number of existing species in the order Lepidoptera (more than 150,000 species: van Nieukerken et al. 2011). Thus, one further question can be posed – to what extent are the results presented sensitive to the addition of new taxa? The relationship between the errors in the predicted weight data and the diversity in body size, morphology (excluding body weight) and taxonomy were determined. The underlying idea is that any sources of diversity that are positively correlated to large errors in the predictions should denote species’ features liable to modify significantly the models obtained.

The error in the predicted dry body weight (DBW) values were measured as the mean of the absolute values of the residuals from the two best fit models (described below) calculated for randomly selected subsets of n species, where n = 5, 10, 25, 50, 100, 150, 200, 250, 300 and 350. Forty replicates were taken at each n plus one more sample consisting of the whole data set. The taxonomic and structural diversities of each of such 401 species samples were estimated using the following attributes:

1. Species diversity: the number of species in each sample.

2. Variation in dry body weight: the standard deviation of the log-transformed dry body weights.

3. Structural variation. This variable was intended to account for structural/anatomical variation as reflected by the measurements taken, irrespective of body weight. To do this, each of the eight variables were regressed on body weight, one at a time. The residuals of such bivariate regressions were used as the new variables, now linearly independent of body weight. Applying Principal Component Analysis to this set of residuals (Bartlett’s Sphericity test X² = 344.24, P < 0.001; KMO index = 0.72) resulted in three components accounting for 66.96% of the variance (respectively 41.51%, 14.59% and 10.86%). The standard deviation in these three components (weighted by the respective contribution of each component) was used as an index of structural (body shape) diversity, linearly independent from dry weight.

4. Taxonomic/phylogenetic diversity. This was tentatively estimated in four alternative ways: (1) Number of clades (absolute number of supra-specific nodes). (2) Phylogenetic diversity (PH): the number of clades or nodes represented in the sample minus one, plus the number of species as defined by Faith (1992), with all branches set to 1.00. (3) Relative Phylogenetic Diversity (RPD, the number of clades above the species level divided by the number of species). And (4) Taxonomic Distinctness (Clarke and Warwick 1998; Allen et al. 2009); this was calculated using the software PAST (Hammer et al. 2001) after simplifying the number of taxonomic categories to 10 which included the suborders, superfamilies, families, subfamilies and genera plus five intermediate levels.

As the relationships between the mean residuals and these variables tended to be asymptotic rather than linear, the bivariate and multivariate regressions were performed using Generalized Regression Models and the logarithmic link function.

The dry body mass of the selected species covered a range of variation of nearly five orders of magnitude, from 0.03 mg to more than 2 g, corresponding to forewing lengths of between 1.8 mm and 110 mm (see Suppl. material 2 and 5; 2: frequency distribution; 5: mean by superfamily). The lightest and smallest species belonged to the genus Stigmella (Nepticulidae, with one male weighting 0.034 mg), while two males of the reputedly longest-winged moth, the ErebiidaeThysannia agrippina (Cramer, 1776) (see e.g. Kons 1998) had dry weights of 916–1,300 mg and one male of the SaturniidaeAttacus atlas (L., 1758) weighed 1,126 mg. However the heaviest specimen weighed belonged to the hawk-moth family (Cocytius sp., Sphingidae, which exceeded 2.1 grams).

The replicated measurements (Table 1) suggested that the forewing and thoracic linear dimensions may reflect lower proportions of error than the abdomen length or width measurements when taken of the same specimen. Although the estimates between pairs of individuals from the same species differed to some extent, it was clear that the highest amount of variation was accounted for by the abdomen data. Forewing length appeared to be even more constant than the thorax measurements within individuals. This might reflect a bias in the observer’s abilities, although it is also likely that the reference landmarks to measure wing length (the tegulae and the tip of the wing) are more obvious than the other reference structures, especially when the body is coated by a dense cover of hair-like scales.

The results from bivariate regressions of DBW on the other variables as well as the full multivariate results (with all the variables in the model) are presented in Table 2 (species means, all R > 0.92) and Table 3 (independent contrasts, all R > 0.82). The effects of the linear estimates of wing size (FWL and FWW), although significant in the bivariate comparisons performed on the species data, were outweighed by those of the forewing area (FWA) in the multivariate approach. Across the contrasts, FWL had a significant but negative effect in the regression models suggesting a complex relationship between body weight and wing size and shape.

Several alternative models fit by stepwise regression were calculated with multiple R values above 0.979 in all instances. Models 1 and 2 (Table 4; Figure 2) are those with the highest multivariate R based in the species raw data and in the independent contrasts respectively. These two models included the effects of wing area, which may be more difficult to measure in spread specimens. However, because of their highest fits they were used as the basis for the last/next step. Several alternatives (Suppl. material 6: alternative models) should allow estimations of DBW in circumstances that are frequent in entomological collections such as specimens without abdomen or with its distal end missing due to identifications based in the external genitalia.

Figure 2. 

Dispersion plots illustrating the fit (predicted on observed weights) of the two multivariate models of highest R² scores based on the raw species data (above) and the independent contrasts (below) (respectively, models 1 and 2 in Table 4).

The regressions of the estimated error of the predictions (measured as the mean of the absolute value of the residuals) on the indicators of taxonomic, size and structural diversity led to the same results in the bivariate and multiple tests, irrespective of the data analyzed (species values or independent contrasts); thus, for simplicity, only the multivariate results are presented in Table 5. Only two of the variables had significant effects with opposite signs: morphological diversity (with a positive coefficient) and the relative phylogenetic diversity (with a negative effect).