The dry body weight of adult male Lepidoptera was estimated from thirteen linear measurements of the wings and body using multivariate regression techniques. A dataset comprising information from 2,645 species was used, significantly increasing sample size with respect to a similar former approach. Based on the logarithmically transformed values of dry body weight and several linear measurements the best single predictors for body weight are body length, thorax length and head width, none of which is among the most popular descriptors of size in this insect order (namely, forewing length and wingspan). The results show that combinations of several linear measurements lead to the most precise estimates of dry body weight. More simple models, e.g. based on wing length or wingspan and body length, may provide reasonable but suboptimal approaches. Variance partitioning of the regression residuals indicated that most of the non-explained variance is attributable to morphology rather than to phylogeny, so overall the results suggest that the best models may be stable and liable for prediction except for unusual morphologies. Alternative approaches such as a taxon-by-taxon approach or ANCOVA-based methods were tested, and the results -and problems involved- are discussed. The potential relevance of co-linearity is addressed to. Based on a limited number of species, the author attempted to estimate the female to male weight relation (which happened to be nearly isometric), as well as the percent water content (38% overall).

The dataset is made available so it can be accessed for any related research on this or related subjects.

Body size (or body size at reproduction) is among the key life history traits because of its many -often intricate- interrelations with other life history traits and with the environment (e.g. Schmidt-Nielsen 1984; Reiss 1989; Smith and Lyons 2013; for insects, see Chown and Gaston 2010). While the meaning of size is apparently obvious in most standard languages, it represents a comparative criterion between objects of similar proportions. This ambiguity is directly translated to the ecological or evolutionary context: body size has no single scientific standard definition. There are several potential meanings depending on the biological implications investigated (e.g. the volume or surface area of an individual organism, its height or weight, speed, caloric content, or the energy required to reach reproductive maturity). Such values are represented by surrogate one-, two- or three-dimensional variables (length, area, volume or weight) of which, in the Animal Kingdom, body length (or the combinations of body length and width) or body weight are the most frequent options (e.g. Rogers et al. 1976; Blackburn and Gaston 1994; Ganihar 1997; Wardhaugh 2013; Sohlström et al. 2018). Due to the practical problems for estimating the live (fresh) body weight (but see e.g., Sohlström et al. 2018), dry body weight is generally accepted as a practical estimate of body size in arthropods (Lister and Garcia 2018; Kinsella et al. 2020). Lepidoptera, one of the hyper-diverse insect orders (with more than 160,000 described species: Kristensen et al. 2007; van Nieukerken et al. 2011) provides an interesting basis for ecological and evolutionary studies on insect body size for many reasons, including those arising from the typical (though not universal) phytophagous condition of the larvae and the flying requirements of the adults (recent examples include Davies et al. 2012; Beck et al. 2016; Chazot et al. 2016; Kivela et al. 2020; Owens et al. 2020; Hamilton et al. 2022; Foerster et al. 2024a). Moreover, recent evidence of impacts of global change on terrestrial ecosystems suggests that changes in biomass may be occurring (e.g., Hallmann et al. 2017; Lister and Garcia 2018; Harris et al. 2019; Seibold et al. 2019; Bell et al. 2020; Roth et al. 2021; Wagner et al. 2021; Dalton et al. 2023; Müller et al. 2024). This makes clear that practical, standardized means to estimate moth and butterfly body masses are needed (e.g., Kinsella et al. 2020).

The body dimensions (such as body length or width) are seldom reported for the adult Lepidoptera in monographs and field guides, where the length of the forewing or the distance between the apex of the two forewings wings in extended position (wingspan) are most often presented (e.g. Miller 1991; van Hook et al. 2012; Kinsella et al. 2020 and references therein). The length of the forewing is, in fact, known to be well correlated with body weight in these insects (Miller 1997) even if it does not stand for the best linear predictor (García-Barros 2015). The diversity of body plans in the adults of this insect order occurs not only at high taxonomic levels but also at, or below the family rank (also long acknowledged, e.g. Janzen 1984; Owens et al. 2020) making evident that bi- or multivariate approaches may be by far more precise (Foerster et al. 2024b), which imposes a balance between accuracy and practicality depending on the objectives intended.

Some years ago, the author essayed a multivariate approach to the prediction of male dry body weight in the Order Lepidoptera (García-Barros, 2015). Although based on a relatively small number of species the results suggested high reliability overall, though probably some sensitivity in the case that morphological diversity within clades was underestimated. This could only be solved by increasing morphological diversity within the taxa already present in the database. Therefore, the present study represents an extension of that former work after substantially increasing taxonomic sampling and, within reasonable limits, the intra-taxon variation in morphology. The new dataset should provide evidence to (1) validate the former results, (2) propose one or several alternative indexes to estimate dry body weight using only linear measurements and (3) estimate the relative robustness of the results in terms of the body proportions and phylogenetic position, as this might illuminate the ways for any further improvement of the results. (4) For practical reasons, research on lepidopteran allometry and related issues often concentrates on one taxon (typically, a family). For this reason, I intend to provide -and discuss the merit of- dry body size estimates based on pre-selected subtaxa (family, superfamily or informal groupings such as ‘micromoths’ or ‘macromoths’), both on a taxon-by-taxon basis or from multivariate regression approaches such as those implemented by other authors (e.g., Kinsella et al. 2020; Weiss and Linde 2022, on carabid beetles). Next, (5) possible short-term solutions to two limitations of the results for ecological studies, i.e., the restriction of the data to the male sex and the relationship between dry body weight and fresh (live) body weight. Finally (6), making accessible the set of data used in this study, which may provide a basis for related research on body size related matters in the moths and butterflies.

The lowest range of body weights did not differ from that presented previously (García-Barros 2015) with some Nepticulidae and Heliozelidae as the smallest and lightest species (0.04–0.05 mg). From the results below, the weight of the reputedly smallest known Nepticulidae or Gracillariidae with forewing lengths of 1.2–1.3 mm (see Stonis et al. 2021) would be expected to be in the range 0.017–0.020 mg. The upper limits of body weight are of course occupied by large bombycoids and the hawk moths (Bombycoidea and Sphingidae), but in this sample these were exceeded by the dry weight of some tropical Cossidae like Xyleutes persona (Le Guillou, 1841) with DBw above three grams (3000 mg). On this basis the male dry body weight of known Lepidoptera covers five orders of magnitude, three in the case of the forewing length. Almost certainly, this range is underestimated since the male dry weight of the large Asuatralian Cossidae Endoxyla cinereus (Tepper, 1890) should at least duplicate that weight (the female fresh weight of this species reaches 30 grams: Beccaloni 2010; also see Thurman 2022).

On the logarithmically transformed values all the linear measurements were highly correlated with dry body weight (R > 0.97) and showed a clear phylogenetic structure, with lambda values close to 1.0 (Table 1). The slopes of the lines (the exponents in the traditional allometric equation) varied between 1.92 and 2.96, as expected from length / volume relations from the allometric equation. Bivariate correlations with DBw exceeded 0.9 except for FWw, HWl, HWw (R > 0.8) and, remarkably, the head length (Hl, R = 0.77). The covariation between the variables (correlation matrix in Suppl. material 4: table S1) suggests three groups of them (Fig. 1): (1) the best single linear predictors of body size (Tl followed by Bl and Hw, all R > 0.98), (2) the wing metrics and (3) the body width measures. The comparatively low correlations of Hl with the remaining variables probably reflect the low accuracy of this measurement (see methods).

Figure 1. 

Patterns of covariation between all the variables in the study included dry body weight (DBW) as illustrated by a cluster based in the square correlation (r) matrix of their log-transformed values (UPGMA method).

Among the formerly published models, the closest one to those presented in Table 2 (i.e., based on linear measurements and not wing areas) was García-Barros 2015: supplementary material 6 (Model 4, R²_adj = 0.979 from 375 species). This model worked remarkably well with the present data set (R = 0.989, adjusted R² = 0.979).

Eight alternative multivariate models were fitted, reflecting choices that would be expected to be preferred most often depending e.g., on the type of information available to predict DBw. Redundant combinations of composed measures with their components were avoided (e.g., Bl and Hl, Tl and Al or Wingspan with FWl and Tw). The statistics and coefficients are summarized in Table 2. Model 1 was obtained by stepwise selection of all the variables. Hl was ignored in the remaining models (e.g., Model 2: Fig. 2). In Model 3 Bl replaced (Hl, Tl and Al). Models 6 and 7 were restricted to FWl and the thorax measures. The combinations of wingspan and body length were represented in models 4 and 5. Model 8 was fitted using FWl as the primary explanatory variable, and the residuals of the remaining variables on FWl as additional predictors; the coefficients and fitting statistics were recalculated by reference to the original variables. This presented the advantage of a high linear independence of the variables in the regression.

Figure 2. 

Relationship between the Log₁₀-transformed species mean dry body weights (DBW) and one of the most widely used descriptors of body size in the Lepidoptera, forewing length (FWl), and with the predicted values from multivariate model 2 (details in Tables 1, 2). Notice Log-scale in both axes.

All the alternatives proved high fit (adjusted R² above 0.93) with models 1, 2 and 8 rendering the best predictive performance (lowest cross validation errors).

Regarding the ‘taxon-by-taxon approach’ the explanation of DBw in terms of FWl, WS1 and WS2 were acceptable (R² > 0.73, P < 0.001), on average respectively 0.83, 0.84 and 0.85 (Suppl. material 4: table S2). Detailed comparisons between closely related families proved useful sometimes (as for the Papilionoidea, Fig. 3). Most often than not, significantly different slopes or intercepts between sister groups precluded phylogeny-oriented clustering, while it was clear that moderately distant families might have been combined. The ANCOVA approach initially had high fitting, but with most of the interactions being non-significant. Only four to nine taxa remained after dropping the non-significant contributions, with the performance of the model not exceeding that of the former alternatives. Depending on whether FWl (model R² = 0.87) or Wsp1 (model R² = 0.91) were the variables retained, the taxa with significant coefficients included the Gelechioidea, Pyraloidea (or the family Pyralidae), Tineoidea (or just the Tineidae) and the Yponomeutoidea (Suppl. material 4: table S3).

Figure 3. 

The butterflies (Papilionoidea) as an example of the potential problems involved in pre-selected taxon-specific approaches the prediction of body weight (Log₁₀-transformed, DBw) from forewing length (Log₁₀-transformed, FWl). Although three families (Lycaenidae, Riodinidae and Nymphalidae) were found to be homogeneous for the slope and intercept of the linear relationship, these and the three remaining families differed significantly from each other in the intercept, the slope, or both. Notice the logarithmic scale in both axes.

As shown in Table 2 (and Suppl. material 4: table S3 for the ANCOVA-type approaches) the variance inflation factor (VIF) was high whenever more than one variable was included in the models, except in Model 8. With no exception, the regression residuals primarily reflected differences in the body plan (morphology) and to a lesser extent (by a 10-fold proportion) a shared effect of morphology and phylogeny, while the ‘pure’ effect of phylogeny was virtually negligible. Cross-validation testing (CVE) on the 534 species represented by at least three individuals largely parallelled the R² values.

The models based in the linearly independent factors representing morphology and phylogeny were slightly superior to any of the alternatives in Table 2: adjusted R² = 0.982, F_{[27, 2099]} = 4218 (P > 0.001), CVE = 0.012 and VIF values in the range 1.01–1.13. Using only the components derived from morphology would still render reliable results (R² = 0.981). The details of this model are not presented in length as it cannot be applied for predicting body weights for species not represented in the data set (see discussion).

Regarding fresh (live) body weight, on average and on the non-logarithmically transformed values the water content was slightly below 40% (38.64%, s.d.= 7.11, Fig. 4). Through regression on the log-transformed values, the slope for the female sex (n = 53) differed slightly but significantly from that of the males (F = 7.25, P = 0.008). Accordingly, fresh body weight was estimated as a function of BDw only from the male data, as: Log₁₀(fresh body weight) = 0.4829 + 0.9841·Log₁₀(dry body weight), R² = 0.987, P < 0.001 (n = 183 species). From this equation, the dry body weight accounts for 38.02% of the live weight for the male sex.

Figure 4. 

Fresh body weight as predicted by the Log10-transformed dry body weight values (DBW) of males and females from 237 species. The overall relationship was significant (adjusted R² = 0.985, p < 0.001) with a slope close to isometry: Log₁₀(Fresh body weight) = 0.428 + 0.992(Log₁₀DBW). The difference between the slope of the two sexes was small, but significant (details in the text). Notice the logarithmic scale in both axes.

For the 362 species with weight data from the two sexes (Fig. 5), sexual dimorphism was described by the equation DBw _female = 0.1574 + 0.9770(DBw _male), R² _adj = 0.953, P < 0.001. This suggests a nearly isometric relationship between the body mass of the two sexes, which was not expected.

Figure 5. 

Male dry body weight as a predictor of the female dry body weight, from a sample of 362 species. Overall, on the log-transformed values the female dry body weight can be approached as female DBW = 0.1574 + 0.9770(male BDW) (adjusted R² = 0.953, P < 0.0001). Notice the logarithmic scale in both axes.

The interpretation of the results allows for two opposed perspectives — both realistic — a pessimistic and an optimistic one.

As far as body weight prediction is concerned, the pessimistic point of view derives from the putatively low taxonomic and geographic representativity of the species used (hardly more than 2% of the described species of Lepidoptera: Kristensen et al. 2007; van Nieukerken et al. 2011), the small sample size (most often 1–3 individuals per species), the scarcity of data from the female sex and the frequently rough taxonomic identification. The amount of statistical error imposed by these shortfalls may exceed that caused by the technical details of the analytical methods adopted (Hansen and Bartoszek 2012). Moreover (as stated by Foerster et al. 2024b) the weights recorded here probably differ from the weight on emergence and this may partly obscure the life historical interpretation of the data.

Missing information from one part of the species is a recurrent problem in interspecific comparative studies (Nakagawa and Freckleton 2008; Penone et al. 2014). However, unlike for e.g., plants and the vertebrate animal taxa, the problem with hyper-diverse taxa such as the Lepidoptera is not one on interpolating the missing values for one part of the species but on the need to extrapolate them from a minority of species. Phylogenetic imputation (Young et al. 2014; Molina-Venegas et al. 2018) is an alternative to be explored, especially because such methods might render acceptable results if additional correlated variables (e.g. the body dimensions) can be coded for (Penone et al. 2014; Debastiani et al. 2021). However, while the broad lines of Lepidopteran phylogeny are progressively being fixed (e.g., Mayer et al. 2012; Heikkilä et al. 2015; Kawahara et al. 2019; other references and discussion in Rota et al. 2022), a comprehensive reference phylogenetic scheme may take years to come. Of course, some taxa in specific geographic regions are exceptions, such as the European Papilionoidea (Wiemers et al. 2020).

However, an optimistic interpretation is straightforward from the results. First, a seven-fold increase of sample size in comparison to García-Barros (2015) (375 to 2645 species) raised the fit of the best regression model by merely 1%. This, together with the low pure contribution of phylogeny in the non-explained variances, suggests that the variation of the broad lepidopteran morphology across taxa is redundant enough for dry body weight to be predicted with reasonable accuracy on a multivariate basis. Yet one or two variables cannot cover the morphological heterogeneity of the Lepidoptera so a multivariate model will generally perform better. This may impose costs in terms of collinearity, which in fact holds for any model with more than one predictor. A VIF value above 4–10 is generally identified as excessive (depending on authors: Neter et al. 1983; Legendre and Legendre 2012 and references therein). From this point of view only model 8 (Table 2) would be safe. The main risk of collinearity in the predictor variables is ‘overprediction’, meaning that unusual morphologies (body plans not covered by the dataset) would lead to inaccurately predicted body weights. This would represent a lesser concern under the assumption that the main morphological gradients were covered by the dataset. However, caution is required whenever any such unusual shaped species is involved. Alternatively, co-linearity may be avoided by a model constructed with the PCA factors derived from all the potential independent variables. Unfortunately, predictions from this model are possible only if the measurements of the candidate species are added to the data table before the PCA factors are extracted. After fitting the regression model (on the species with known DBw) the values can be interpolated for the problem species. The same holds for phylogenetic relations, the species to be predicted must be given a position and a branch length in the reference phylogeny before the PCoA factors describing phylogeny are extracted from the tree. All this makes these methods far less convenient for prediction than a ready to use equation (however, the PCoA alternative is feasible using the dataset provided in this study).

A taxon-specific approach (e.g., predictions for one single family or superfamily using only FWl or Wingspan) may eventually be justified for practical reasons despite the generally suboptimal results. Such approach implicitly assumes a high degree of phylogenetic conservatism within the taxon studied, which may or may not be the case. As found in the Papilionoidea, there is a risk that the weights of part of the species are systematically overestimated or underestimated. The low weight of phylogenetic structure in the regression residuals suggests that species clustering on morphological grounds rather than on taxonomic ones might by far be preferable. This applies equally to the ANCOVA-like approaches where the initial results are of high fit overall, but with many non-significant terms which ultimately lead to comparatively poor results.

In summary, the most complex regression models (based in five to seven body measurements) predicted dry body weight most accurately. The author would suggest that models 2 and 8 (in Table 2) are given preference. Estimates from a smaller number of variables (FWl, Wsp1, Wsp2 or combinations of these with Bl) should generally represent suboptimal solutions but may still be acceptable (as suggested by Foerster et al. 2024b) while it is acknowledged that high R² scores from this and similar datasets are not surprising given the wide range in body sizes and the possible underlying functional constraints on the body proportions. In any case, given the small sample size for each species in the dataset used, the species means should be interpreted as rough approaches of the true values. For similar reasons, ideally, reliable predictions for a species should not be done on the data from a single specimen but on the average from a) the measures from several individuals or b) the average of the individual predictions for those specimens.

It is not the author’s intention to negate the utility of traditional size standards used for the Lepidoptera such as wingspan and forewing length. As shown by the results these measures retain a good correlation with body weight and may represent the only metric available for most species, besides their interest as descriptive standards or as the basis for the study of e.g. intra-specific variation of moth and butterfly body size.

The fact that only male insects were analysed imposes severe limitations for implementation of the present results in field studies. In addition to the differences between live insects and preserved ones due to tissue contraction after desiccation (Van Hook et al. 2012), the female body weights or the fresh body weight may eventually be interesting. These shortfalls can tentatively be overcome by correcting the predicted body masses for female weight (to average the male and female values), and by estimating fresh body weights from the results described above. However, while the female to male body size relationship was clear-cut in the results, there is ample evidence that such relationship is not uniform across all the moth and butterfly families (Stillwell et al. 2009; Allen et al. 2011; Teder 2014). The available sample points out an approximate 38% water content, which falls within the typical range for adult insects (e.g., Hutchinson et al. 1997; Barker et al. 1998). Again, there is no reason to believe that this proportion is constant across all taxa. It is worth noting that the range of sizes used for those comparisons is markedly shorter than that of the general sample.

Incidentally, significant between-taxa differences (such as those within the Papilionoidea already mentioned, and probably other groups) may reflect differences in the broad body plans with ecological, life-historical or biomechanical implications which deserve further attention. On similar grounds, the bivariate slopes (form the regressions of dry body weight on the individual variables) revealed allometric slopes within the range 2.0–3.0, where 3.0 represents isometry. Interestingly, the steepest slopes (2.8–3.0) are among those involving body measurements explicitly (thorax width, total body length) or implicitly (such as wingspan 1) together with head width (as already documented by García-Barros 2015). Wing length values scale to dry body weight with slopes of ca. 2.7 while wing widths do so with lower values (1.9–2.2), so overall one might envisage a pattern of progressive wing narrowing along the positive gradient of body size, probably encompassed by comparatively higher wing loadings. While suggestive, these observations require corroboration from further research done under comparative methods to incorporate the effect of phylogenetic relatedness.

To conclude, the dry body weight of male Lepidoptera can be predicted with reasonable reliability from a combination of linear measures not difficult to obtain. Rough estimates of the live weight or of the average male-female dry weight may be possible at the cost of accuracy. For decades, work devoted to the estimation of body weight in insects has relied in the objective of finding reference equations whose results could be used for extrapolation to other species (to quote some examples: Rogers et al. 1976; Sage 1982; Ganihar 1997; Benke et al. 1999; Sohlström et al. 2018). While a single reference model (e.g. at the family or order levels) would of course represent a useful tool for standardizing results, the present facilities for statistical computing combined with the widespread tendency to make the research data available lead to new alternatives such as the ad-hoc assemblage of data sets for specific uses. Facing the urgency of detecting and understanding the possible effects of Global Change there is a renewed interest in collecting and compiling life history data under reasonable quality standards (Keller et al. 2022). Needless to say—and as argued in the introduction—the body size of moths and butterflies deserves a role in this research program, therefore the explicit publication of more data on this subject (e.g., Kinsella et al. 2020) should be encouraged.

Over the last few years, the author received help from several colleagues who either provided specimens, facilitated access to them or to documentation, assisted with identification or solved methodological issues. While discharging them from for any accuracies in the results, I am indebted to (in alphabetical order) N. Agustí, J. Baixeras, U. Benardo, J.W. Brown, J.P. Cancela, M. Corley, M. Costa, E. Drouet, J. de Freina, O. Karsholt, M. Laguerre, W. Mey, M.L. Munguira, J.E. Murria Beltrán, A. Orellana, L. Przybylowicz, F. Pühringer, J. Razowski, L. Ronkay, H. Romo, P. Sihvonen, H. Staude, J. Sumpich, G. Tarmann, E. Toro Delgado, A. Vives Moreno, T.J. Witt ^(†) and J.L. Yela.