Table 1.
The species analyzed, their collectors/donors, collection locality and vial ID number.
Figure 1.
Disassembled ants were arranged on a gridded card covered with double stick tape in preparation for photography and measurement.
A 2 mm scale was photographed at the same magnification to serve as the scale for measuring lengths.
Figure 2.
The measures taken, and the aspect measured.
Abbreviations are explained in Table 2.
Table 2.
The measures, as shown in Fig. 2, and their abbreviations.
Figure 3.
The mean, minimum and maximum dry weights of workers in relation to the range of body length (max. – min.).
Body weight range increased more rapidly than body length range because the former is related to the cube of the latter, but changing allometry of body parts contributed to the irregularity of this trend. Maximum worker weight varied a great deal more than minimum. The hatches show 95% confidence intervals for the means.
Table 3.
Body dry weight (WT) and body length (BL) means and extremes of species of Solenopsis.
Table 4.
Regression parameters for the log ratio of gaster volume: body weight (GV/BW) vs. body weight (BW) for all species.
Figure 4.
Body length is strongly correlated with body weight (here transformed to the same dimensional order as the cube root of dry weight).
When all species were combined, weight−3 increased slightly faster than length (log log slope = 1.12). Thus, after adjusting for dimensions, larger workers were somewhat heavier than small ones, suggesting allometries or changes in density not apparent in BL. However, whereas the majority of the species were positively allometric, some were isometric (see text).
Figure 5.
Comparison within species of the allometry of the body parts making up the body length (BL).
Slopes for RBL of each body part regressed against BL is shown. The mean and 95% CI (green = +, red = −) of each colony sample is shown. Isometry is indicated by the horizontal line at zero on the ordinate. In most species, GL was positively allometric, PL negatively and HL and AL isometric. S. geminata was exceptional in these allometries.
Figure 6.
Comparison across species of slopes and 95% CI for the RBL of each measure regressed against BL.
Slopes significantly greater than zero are positively allometric (grey background; the measure become relatively larger) and less than zero are negatively allometric (pink background; the measure becomes relatively smaller). This figure allows comparison of the allometries among species.
Figure 7.
ab. All slopes arranged in species panels, allowing comparison of allometries within species.
The left panel includes slopes of RBL vs. BL, the central panel, RHL and RHW1 and RHW3 slopes and the RANT slopes. Figs. 7a and 7b together present all the species.
Figure 8.
a–f. The slopes of the ratio regressions arranged for comparison across species.
a. head-body length allometries; b. antennal allometries; c. mesosomal allometries; d. metasomal allometries; e. within-head allometries; f. within-antenna allometries. Positive allometries are shown on a grey background, negative on pink. Error bars are +95%CI (green) and −95%CI (red).
Figure 9.
Sillhouettes of the smallest worker body parts (grey) superimposed on those of the largest workers (black) scaled to the same HL, MsL or GL, illuminating the changes of shape occurring during growth.
Images of heads were resized until HL was equal for the smallest and largest worker heads. For images of the mesosoma, MsL was set to be equal (ignoring the petiole), and for images of the gaster, GL was set to be equal. The black zone in the bar under each species shows the size range (BL) of workers on a 5 mm scale. The percent values next to each silhouette are the changes in volume of the body part as a fraction of the whole body (i.e. if the head is 20% of the total body volume in small workers, and 25% in large, the change would be +5%).
Figure 10.
Percent of total body volume making up each body part for workers weighing 0.1
The differences represent the volume change for a 10-fold increase in weight, and were computed from the regressions of WT vs. BL solved for 0.1 and 1.0.
Figure 11.
The slopes of the regressions of RBL vs. BL in relationship to their intercepts, marked for the ratio’s identity.
The grey zone indicates isometric relationships, positive allometries have larger slopes and negative smaller ones. For all regressions, the greater the slope, the lower the intercept. See text for a discussion of these patterns.
Figure 12.
The same plots as in Fig. 11, but marked for whether the best fit was linear (upper panel, blue) or polynomial (upper panel, red).
In the lower panel, the points are coded for ratios to BL, ratios to ANT or ratios to head measures.
Figure 13.
An example using GL/BL illustrating the rotation of plots around a zone within the data cloud.
It is this rotation that leads to the negative relationship between the slopes and intercepts seen in Figs. 11 and 12. Each color and line represents one of the species.
Figure 14.
Examples of the range of regression fits plotted as Measure vs. BL (left column) and Measure/BL vs. BL (right column).
As the allometry becomes stronger, the plots become curved such that a polynomial improves the fit. The plots illustrate isometry, positive and negative linear allometry and positive and negative polynomial allometry.
Figure 15.
A comparison of the polynomial parameters for regressions best fit by linear or polynomial equations.
The “+” symbols show the relationships with a linear best fit, and the solid symbols those with a polynomial best fit. Red symbols code for the x-parameter and green the x2 parameter. Polynomial best fits are strongly associated with extreme values of the linear slopes, that is, with strong positive or negative allometry, but the effect was stronger for positive allometry. The larger the x2-parameter and the smaller the x-parameter, the more curved was the allometric relationship.
Figure 16.
The same data as Fig. 15, but with parameters plotted in separate panels.
The more extreme the linear slope, the more curved the allometric relationship is likely to be, and the more likely that it will be best fit by a polynomial relationship. This can be seen by comparing the top and bottom panels: as linear slope increases, the x2 parameter increases (positive allometry) or decreases (negative allometry) at the expense of the x-parameter. Their opposite trends define the curvature of the allometry. The center panels show the sums of the absolute values of the x2 and x parameters, illustrating that the compensation is not complete. In this figure, the symbols are coded by body part (left panels) or by S. geminata and other species (right panels). Curved, polynomial best fits are more common in S. geminata, and are more likely to affect the head, antennae and gaster.
Table 5.
Frequency of fit type for S. geminata and all other spp.
Table 6.
Frequency of fit type by body part and species.
Figure 17.
The mean allometry patterns for all Solenopsis species superimposed on the same axes.
Size-related changes in shape follow similar patterns in all species except S. geminata in which the head allometries are much stronger. Other species are not identified in this plot. Antennal allometries (excluding the club), mesosomal height, and gaster width are more variable than other allometries.