Data from: The complexity of social complexity: a quantitative multidimensional approach for studies on social organisation

(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colonies kept enclosed in standard laboratory conditions, from incipient colonies to queen death (de Medici & Bloch, unpublished data).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.（摘自论文方法学章节）为量化熊蜂蜂王与工蜂的体型分化，我们采用了Cumber（1949）的数据集与新增实验数据。在Cumber的发表成果中，记录了6个物种9个蜂群内944头雌性成虫的翅长，但未区分工蜂与蜂王。不过所有蜂群均被证实存在蜂王，且每个蜂群的体型分布均呈现显著的双峰模式，我们据此将两个峰分别对应工蜂与蜂王。对于储粉型熊蜂（B. lapidarius、B. lucorum、B. terrestris、B. pratorum），工蜂与蜂王的体型分布存在清晰分界；而对于筑巢储囊型熊蜂（B. agrorum、B. hortorum），二者体型差异相对模糊，我们以工蜂与蜂王峰之间记录量最少的数值（三个蜂群均存在明显的谷值）作为分界点，假设该点两侧的个体分别等量属于工蜂与蜂王，即小于该值的个体为工蜂、大于该值的个体为蜂王。我们还获取了另一组体型数据，测量指标为胸宽，样本来自5个人工封闭饲养的B. terrestris蜂群，从建群初期至蜂王死亡阶段的所有羽化工蜂（n=434）与处女蜂王（gynes），数据来源为de Medici & Bloch, unpublished data。我们以样本量加权的均值整合了两项研究中的B. terrestris相关数值。我们计算了蜂王-工蜂体型比（蜂王平均体型/工蜂平均体型），用于与Toth等人（2004）的无刺蜂数据以及Ferguson-Gow等人（2014）的切叶蚁数据进行对比。此外，我们还通过胸宽指标计算了西方蜜蜂（Apis mellifera）的体型比，整合了欧洲与非洲亚种的均值（DeGrandi-Hoffman et al., 2004）。为在物种层面将熊蜂与无刺蜂、切叶蚁分别进行统计学比较，我们采用了威尔科克森秩和检验（Wilcoxon Rank Sum test），因为数据不符合正态分布。而在比较熊蜂与西方蜜蜂（仅单组数值）时，威尔科克森秩和检验的统计效力不足，因此我们假设数据符合正态分布且方差齐一，采用t检验进行比较。为量化熊蜂种内工蜂间的体型分化，我们从以下途径获取数据：1. 地熊蜂（B. terrestris）数据：i) 9个自由觅食蜂群在整个蜂群生长周期大部分阶段所产的所有工蜂的翅缘细胞长度（n=1832, Holland et al., 2020 preprint）；ii) 28个自由觅食蜂群在蜂群生长峰值期采集的所有工蜂的胸宽（n=4492, Goulson et al., 2002）；iii) 野生蜂群中的工蜂翅长（n=139, Cumber, 1949）。2. 拟熊蜂（B. impatiens）数据：来自12个封闭饲养蜂群在蜂群生长后期的所有羽化工蜂的胸宽（n=1133, Couvillon et al., 2010; J. Jandt, personal communication）。3. 其他熊蜂属（Bombus spp.）数据：来自5个物种7个野生蜂群的工蜂翅长（n=570, Cumber, 1949）。对于Cumber（1949）研究中的数据，我们按照前述方法区分了工蜂个体。我们计算了变异系数（coefficient of variation, CV），计算公式为100 ×（工蜂头宽标准差/工蜂头宽均值），用于与Fergusson-Gow等人（2014）的元分析中切叶蚁的数据进行对比。此外，我们还采用Waddington等人（1986）与Gruter等人（2017）的无刺蜂数据计算了变异系数，两项研究覆盖的物种无重叠。西方蜜蜂的变异系数数据来自Roulston & Cane（2000）。尽管熊蜂的体型测量指标为胸宽或翅缘细胞长度，但我们假设这些指标与头宽（蚂蚁与无刺蜂采用的测量指标）具有可比性，因为在地熊蜂工蜂的全体型范围内，这两类指标均与头宽存在强相关性（Pearson相关分析：胸宽-头宽, rho=0.92, R²=0.85；翅缘细胞长度-头宽, rho=0.95, R²=0.90; n=69, Holland unpublished data）。为在物种层面比较熊蜂与无刺蜂、切叶蚁，我们仍采用威尔科克森秩和检验。与蜂王-工蜂体型比的比较一致，在比较熊蜂与西方蜜蜂时，由于仅单组数值，威尔科克森秩和检验效力不足，因此采用正态分布假设且方差齐一的t检验。我们基于以下研究的类群关系构建了属水平系统发育树用于可视化比较：切叶蚁族（Attini）内的类群关系来自Fergusson-Gow et al. 2014；无刺蜂族（Meliponini）内的类群关系来自Rasmussen & Cameron 2009；无刺蜂族、熊蜂族（Bombini）与蜜蜂族（Apini）之间的类群关系来自Cardinal & Danforth 2011；蜜蜂科（Apidae）与蚁科（Formicidae）之间的类群关系参考多项研究，例如Johnson et al. 2013。我们使用TreeGraph2构建了系统发育树，未设置分支长度差异。为举例比较不同物种的社会复杂性，我们选取了6个物种：西方蜜蜂（Apis mellifera）、Atta sexdens、地熊蜂（B. terrestris）、Euglossa viridissima、Melipona fasciata、Trachymyrmex septentrionalis，这些物种均有5项社会性状的量化数据。各项性状的量化方法如下：1. 工蜂体型变异度：工蜂头宽的以10为底的对数转换后的变异系数（西方蜜蜂：Roulston & Cane 2000；Atta sexdens、Trachymyrmex septentrionalis：Fergusson-Gow et al. 2014；地熊蜂：见前文；Melipona fasciata：Waddington et al. 1986；Euglossa viridissima：采用雌性个体间的变异度，Eltz et al 2011）；2. 蜂王-工蜂体型二型性：蜂王平均体型与工蜂平均体型的比值（西方蜜蜂：deGrandi-Hoffman et al 2004，见前文；Atta sexdens、Trachymyrmex septentrionalis：Fergusson-Gow et al. 2014；地熊蜂：见前文；Euglossa viridissima：假设体型无差异，因为所有雌性均可交配并扩散；Melipona fasciata：Toth et al. 2004）；3. 生殖偏倚：有王群中由蜂王产下的雄蜂占总雄蜂的比例（西方蜜蜂、地熊蜂、Trachymyrmex spp.：Wenseleers & Ratneiks 2006；Atta sexdens：假设为1，因为Dijkstra et al. 2005中未发现可育的工蜂产雄卵；Euglossa viridissima：采用优势雌蜂产卵的平均比例，Cocom Pech 2008；Melipona fasciata：Toth et al. 2004）；4. 蜂群规模：蜂群生长峰值时的工蜂数量的以10为底的对数转换值（西方蜜蜂：近似为10000头工蜂；Atta sexdens、Trachymyrmex septentrionalis：Fergusson-Gow et al. 2014；地熊蜂：近似为200头工蜂；Euglossa viridissima：Cocom Pech 2008；Melipona fasciata：Toth et al. 2004）；5. 蜂群寿命：蜂群成功奠基后的最佳寿命估计值（西方蜜蜂：野生蜂群的平均寿命，Seeley 1978；Atta sexdens：Keller 1998；地熊蜂：近似为0.5年；Euglossa viridissima：成虫寿命，Skov & Wiley 2005；Melipona fasciata：Roubik 1983；Trachymyrmex septentrionalis：基于Beshers & Traniello 1996与Weber 1966的论述，近似为2年）。为绘制图表，我们对所有物种的性状进行了标准化，将最小值设为0、最大值设为1。该标准化同时针对全部物种（对应图4A）以及蚂蚁与蜜蜂分别进行（对应图4B、4C）。为构建综合指数（图4B、4C），我们计算了6项标准化后性状的未加权均值。本研究并未穷尽所有可用于量化社会复杂性的性状，部分性状可通过其他或互补的方法进行量化。此类比较显然受限于可获取的可比数据量。