The rapid increase in “big data” of the post-genomic era makes it crucial to appropriately measure the level of social complexity in comparative studies. We argue that commonly-used qualitative classifications lump together species showing a broad range of social complexity, and falsely imply that social evolution always progresses along a single linear stepwise trajectory that can be deduced from comparing extant species. To illustrate this point, we compared widely-used social complexity measures in "primitively eusocial" bumble bees with “advanced eusocial” stingless bees, honey bees, and attine ants. We find that a single species can have both higher and lower levels of complexity compared to other taxa, depending on the social trait measured. We propose that measuring the complexity of individual social traits switches focus from semantic discussions and offers several directions for progress. Firstly, quantitative social traits can be correlated with molecular, developmental, and physiological processes within and across lineages of social animals. This approach is particularly promising for identifying processes that influence or have been affected by social evolution. Secondly, key social complexity traits can be combined into multidimensional lineage-specific quantitative indices enabling fine scale comparison across species that are currently bundled within the same level of social complexity.

(Copied from Methods in ms)

To quantify bumble bee queen-worker size differentiation, we used data from Cumber (1949) and new data. In Cumber’s publication, wing lengths of females (n = 944) present in nine nests of six species were provided without distinguishing between workers and queens. However, all colonies were stated to contain queens and the size distribution was clearly bimodal in each colony, which we assumed to represent worker and queen modes. In the pollen-storing species (B. lapidarius, B. lucorum, B. terrestris, B. pratorum), there was clear separation of worker and queen distributions. For the pocket-making species (B. agrorum, B. hortorum), where queen-worker size distinction is less obvious, the size measurement with the minimum amount of records between the worker and queen modes (a clear trough in all three colonies) was assumed to consist of workers and queens equally, with all values smaller and larger than this assumed to be workers and queens, respectively. Additional size data using thorax width, was taken from all emerging workers (n = 434) and gynes (n = 26) in five B. terrestris colonies kept enclosed in standard laboratory conditions, from incipient colonies to queen death (de Medici & Bloch, unpublished data). A B. terrestris value was calculated from both studies using a mean weighted by sample size.  Queen worker size ratio, queen mean size / worker mean size, was calculated for comparison with stingless bee data from Toth et al. (Toth et al., 2004), and attine ant data from Fergusson-Gow et al (Ferguson-Gow et al., 2014). Additionally, a value for Apis mellifera was calculated using thorax size, and taking a mean from European and African strains (DeGrandi-Hoffman et al., 2004). To statistically compare bumble bees to stingless bees and (separately) to attine ants, we used species-level Wilcoxon Rank Sum tests (given the non-normality of the data). For comparing bumble bees and Apis mellifera (single value only), a Wilcoxon Rank Sum test does not provide sufficient power to allow such comparisons, thus we assumed a normal distribution and equal variances in a t test.

To quantify bumble bee among-worker size differentiation, we used the following: B. terrestris data obtained from i) wing marginal cell length of all workers (n = 1832) produced by nine freely-foraging colonies over the majority of colony growth (Holland et al., 2020 preprint); ii) thorax width of all workers (n = 4492) found in 28 freely-foraging colonies around the peak of colony growth (Goulson et al., 2002), iii) wing length of workers (n = 139) found in wild colonies (Cumber, 1949). B. impatiens data obtained from thorax width of all workers (n = 1133) produced by 12 enclosed colonies over the later stages of colony growth (Couvillon et al., 2010; J. Jandt, personal communication). Other Bombus spp. data obtained from wing lengths of workers (n = 570) found in seven wild colonies of five species (Cumber, 1949). For the data from Cumber’s (1949) study, workers were determined as described above. The coefficient of variation, 100 x (worker head width standard deviation / worker head width mean), was calculated for comparison with attine ant data from Fergusson Gow et al. (2014) meta-study. In addition, stingless bee data from Waddington et al. (1986) and Gruter et al. (2017) were also used to calculate coefficients of variation (there was no overlap in the species covered by each study). A value for Apis mellifera was obtained from Roulston & Cane (2000). Although size in bumble bees was measured as thorax width or wing marginal cell length, we assume this to be comparable to head width (which was used for ants and stingless bees), because both of these measures are strongly correlated with head width across the full size range of Bombus terrestris workers (Pearson correlation, thorax width-head width, rho = 0.92, R² = 0.85;  wing cell length-head width, rho = 0.95, R² = 0.90; n = 69, Holland unpublished data). To statistically compare bumble bee species to stingless bees and (separately) to attine ants, we used species-level Wilcoxon Rank Sum tests (given the non-normality of the data). As with the Queen-Worker comparison, for comparing bumble bees and Apis mellifera (single value only), a Wilcoxon Rank Sum test does not provide sufficient power to allow such comparisons, thus we assumed a normal distribution and equal variances in a t test.

We produced a genus-level phylogenetic tree for graphical comparison using relationships from the following studies: within Attini, Fergusson-Gow et al. 2014; within Meliponini, Rasmussen & Cameron 2009; between Meliponini, Bombini and Apini, Cardinal & Danforth 2011; between Apidae and Formicidae, numerous studies, e.g. Johnson et al. 2013. The trees were produced, without differences in branch length, using TreeGraph2.

As an example of comparing social complexity between species, we chose six species (Apis mellifera, Atta sexdens, Bombus terrestris, Euglossa viridissima, Melipona fasciata, and Trachymyrmex septentrionalis) for which quantitative data were available in five social traits. The traits were quantified as follows: 1) Worker size variation = log10 coefficient of variation in worker head-width (A. mellifera = Roulston & Cane 2000; A. sexdens, T. septentrionalis = Fergusson-Gow et al. 2014; B. terrestris = see above; M. fasciata = Waddington et al. 1986; E. viridissima = variation among females, Eltz et al 2011); 2) Queen-worker body size dimorphism = mean queen size / mean worker size (A. mellifera = deGrandi-Hoffman et al 2004, see above; A. sexdens, T. septentrionalis = Fergusson-Gow et al. 2014; B. terrestris = see above; E. viridissima = equal size assumed since all females can mate and disperse; M. fasciata = Toth et al. 2004); 3) Reproductive skew = the proportion of adult males which are queen-produced rather than worker-produced in queenright colonies (A. mellifera, B. terrestris, Trachymyrmex spp. = Wenseleers & Ratneiks 2006; A. sexdens = 1 implied given no viable worker-laid eggs in Dijkstra et al. 2005; E. viridissima = the mean proportion of eggs laid by dominant mother, Cocom Pech 2008; M. fasciata = Toth et al. 2004); 4) Colony size = log10 number of workers at peak colony size (A. mellifera = approximated at 10,000 workers; A. sexdens, T. septentrionalis = Fergusson-Gow et al. 2014; B. terrestris = approximated at 200 workers; E. viridissima = Cocom Pech 2008; M. fasciata = Toth et al. 2004); 5) Colony longevity = best estimate of lifespan in colonies surviving foundation (A. mellifera = mean of feral colonies, Seeley 1978; A. sexdens = Keller 1998; B. terrestris = approximated at 0.5 years;  E. viridissima = longevity of adults, Skov & Wiley 2005; M. fasciata = Roubik 1983; T. septentrionalis = approximated at 2 years, based on comments in Beshers & Traniello 1996 and Weber 1966). For plotting, traits were rescaled across species, so that the minimum was set to 0 and the maximum was set to 1. This rescaling was performed both for all species together (presented in Figure 4A) and for ants and bees separately (Figure 4B, C). To produce the combined indices (Figure 4B, C), unweighted means of the 6 scaled trait values were then calculated. This is not an exclusive list of traits that could be quantified as components of social complexity, and several of these traits could be quantified by alternative or complementary methods. These comparisons are obviously limited by the amount of comparable data available.

(Copied from readme file):

Data for Holland & Bloch 2020; The complexity of social complexity: a quantitative multidimensional approach for studies on social organisation (American Naturalist)

Readme file

WWdata

Worker size variation data. Further details in ms.

HeadWidth.mean, ThoraxWidth.mean, Mcell.mean, WingLength.mean = Mean sizes (mm) of workers taken for either head width, thorax width, wing marginal cell length, or wing length. NAs indicate unmeasured indicies, or values not given.

CV = coefficient of variation for the size index measured (100 x (sd/mean)).

Source = source of data. Gruter2017 = doi: 10.1038/s41467-016-0012-y; Waddington1986 = Waddington KD, Herbst LH, Roubik DW, 1986. Relationship between Recruitment Systems of Stingless Bees and Within-Nest Worker Size Variation. Journal of the Kansas Entomological Society 59:95-102; FergusonGow2014 = doi: 10.1098/rspb.2014.1411; Couvillon1949 = data from Jenny Jandt, relating to study in doi: 10.1111/j.1365-2311.2010.01198.x; Cumber1949 = doi: 10.1111/j.1365-2311.1949.tb01420.x.; Goulson2002 = doi: 10.1006/anbe.2002.3041; Holland2020 = doi: 10.1101/2020.05.06.079525; combination = taking a mean value from the three Bombus terrestris studies, weighted by sample size (Cumber, n = 139, Goulson, n = 4494, Holland, n = 1832); Roulston2000 = Roulston TaH, Cane JH, 2000. The Effect of Diet Breadth and Nesting Ecology on Body Size Variation in Bees (Apiformes). Journal of the Kansas Entomological Society 73:129-142.

QWdata

Worker-worker size difference data. Further details in ms.

QWratio = queen mean size / worker mean size.

Source = FergusonGow2014 = doi: 10.1098/rspb.2014.1411; Cumber1949 = doi: 10.1111/j.1365-2311.1949.tb01420.x.; MediciBloch = Igor Medici De Mattos & Guy Bloch, unpublished data; combination = taking a mean value from the two Bombus terrestris studies, weighted by sample size (MediciBloch = 460, Cumber, n = 178); Toth2004 = doi: 10.1007/s00040-003-0707-z; DeGrandiHoffman2004 = 10.1603/0013-8746(2004)097[1299:doaiba]2.0.co;2.

quantData

Data from five social traits in six species. Further details, and data sources, in ms.

value = value of metric specified in metric column

metric = Qwsize, queen mean size / worker mean size (i.e. QWratio); PcntMales, the proportion of adult males which are queen-produced rather than worker-produced in queenright colonies (i.e. reproductive skew); wCoV, coefficient of variation in worker size; ColSize, number of workers at peak colony size; Longevity, best estimate of lifespan in colonies surviving foundation.

scaledValue = value of the metric when rescaled across values for that metric from all six species, such that lowest value is 0 and highest value is 1.

AntScaledValue = value of the metric when rescaled across values for that metric from both ant species, such that lowest value is 0 and highest value is 1. Used to calculate combined index for ants.

BeeScaledValue = value of the metric when rescaled across values for that metric from all four bee species, such that lowest value is 0 and highest value is 1. Used to calculate combined index for bees.

Cumber female sizes

Data entered from Cumber 1949 (doi: 10.1111/j.1365-2311.1949.tb01420.x.;). Added here for convenience, since data in the original publication was presented in printed tables only. Further details in ms.