Data preparation

Allometry is the disproportionate change of body shape and other phenotypic traits with growing body size (Lleonart et al. 2000). As body size is in ants strongly dependent on particular environmental conditions during ontogenesis, in particular from larval nutrition (Tschinkel et al. 2003; Molet et al. 2017), removal of allometric variance (RAV) can be considered as approximation of the data to the genetically determined character space. As result, RAV can expose in comparative tables “true” genetically determined interspecific differences and unmask pseudo-differences (Seifert 2008). Furthermore, RAV may increase the performance of some exploratory data analyses – in particular of principle component analyses (PCA; Seifert 2021). If absolute measurements (raw data) are used in a PCA, the first principal component often indicates the size component which is not of interest in separation of cryptic species, and it may blur the analysis. RAV was performed here with two different methods.

To remove effects of the disproportionate size dependent trait size changes, SC calculated within-nest sample regression analyses of absolute measurements with cephalic length CL1 (Cephalic Length, see Table ​Table1)1) as the independent variable. Head size is one of the most popularly used size indicator in ants (see e.g., Tschinkel et al. 2003; Seifert 2008; Molet et al. 2017). Coefficients applied to calculate residuals are given in Table ​Table2.2. The resulting slope and intercept of the correction functions were then calculated as arithmetic means from the 52 samples’ slope and intercept values. RAV was then performed using residuals and with these data an alternative prior species hypothesis was generated via PCA. This procedure does not need a previous formation of species hypotheses but accepts unequal contribution of species to the RAV function finally calculated.

Removal of allometry via regression model (SC). Residuals for nest samples are calculated via regression analyses for every trait on Cephalic Length (CL1) as the independent variable, coefficients x, and intercept to calculate residuals are provided.

BS performed RAV by following the basic procedure described in Seifert (2008), which uses regression of index values against cephalic size CS as independent variable. The procedure requires a pre-established hypothesis on species identities and results in equal contribution of the considered species to the final RAV function. Slope and intercept were here calculated as the arithmetic mean of the species-specific functions, in this paper of 92 S.fugax and 66 S.juliae workers. RAV was then performed by calculating the quotient between the real value and the RAV-function value. In order to have a translucent presentation in comparative tables and descriptions, the quotients were then transformed to index values that would be achieved if all worker individuals had the same cephalic size of CS = 480 µm (Table ​(Table1).1). The procedure resulted in a reduction of within-species variance to 29% in CL2/CW, 73% in SL/CS, 76% in CLSPD/CS, and 65% in PEH/CS, but did not show notable effects in the remaining characters. Parameters for RAV in gynes were calculated alone on the basis of data in S.fugax as it was the only species with sufficient sample size.

The RAV functions for workers and gynes (sensu BS) are as follows:

CL2/CW₄₈₀=CL2/CW /(-0.5634*CS+1.4390)*1.1685)

SL/CS₄₈₀=SL/(-0.1460*CS+0.7688)*0.6987

FL/CS₄₈₀=FL/(0.0036*CS+0.2223)*0.2241

FR/CS₄₈₀=FR/(0.0131*CS+0.2083)*0.2146

EL/CS₄₈₀=EL/(0.0772*CS+0.0575)*0.0945

PrOc/CS₄₈₀=PROC/(-0.0135*CS+0.1939)*0.1874

CLSPLM/CS₄₈₀=CLSPLM/(-0.0388*CS+0.0750)*0.0564

CLSPLL/CS₄₈₀=CLSPLL/(-0.0239*CS+0.0314)*0.0199

CLSPD/CS₄₈₀=CLSPD/(0.1082*CS+0.0833)*0.1353

ML/CS₄₈₀=ML/(-0.0094*CS+1.1853)*1.1808

MW/CS₄₈₀=MW/(-0.0881*CS+0.6335)*0.5912

MpGr/CS₄₈₀=MPGR/(0.0051*CS+0.0244)*0.0269

PEW/CS₄₈₀=Pew/(0.0259*CS+0.2943)*0.3068

PPW/CS₄₈₀=PPw/(-0.0592*CS+0.3556)*0.3271

PEH/CS₄₈₀=PEH/(-0.1487*CS+0.4487)*0.3773

PPH/CS₄₈₀=PPH/(-0.0011*CS+0.3058)*0.3006

The RAV functions in gynes are:

CL2/CW₈₅₀=CL2/CW/(-0.2881*CS+1.1973)*0.9524

SL/CS₈₅₀=SL/(-0.2677*CS+0.8775)*0.6500

FL/CS₈₅₀=FL/(-0.1515*CS+0.3890)*0.2602

FR/CS₈₅₀=FR/(-0.1466*CS+0.3834)*0.2588

EL/CS₈₅₀=EL/(-0.1448*CS+0.4169)*0.2938

PrOc/CS₈₅₀=PROC/(0.0899*CS+0.0388)*0.1152

CLSPLM/CS₈₅₀=CLSPLM/(0.0108*CS+0.0403)*0.0494

CLSPLL/CS₈₅₀=CLSPLL/(0.0504*CS-0.0304)*0.0125

CLSPD/CS₈₅₀=CLSPD/(0.0011*CS+0.1395)*0.1405

ML/CS₈₅₀=ML/(0.5567*CS+1.5727)*2.0459

MW/CS₈₅₀=MW/(0.7122*CS+0.4779)*1.0833

MH/CS₈₅₀=MH/(0.6220*CS+0.7668)*1.2854

PEW/CS₈₅₀=Pew/(-0.1511*CS+0.5986)*0.4701

PPW/CS₈₅₀=PPw/(-0.2844*CS+0.7683)*0.5265

PEH/CS₈₅₀=PEH/(0.1010*CS+0.4025)*0.4883

PPH/CS₈₅₀=PPH/(-0.1000*CS+0.5682)*0.4832