Allometry and the removal of body size effects in the morphometric analysis of tardigrades

Quantitative traits are an important part of tardigrade taxonomy for both heterotardigrades and eutardigrades. Because most quantitative traits vary as a function of body size, variation in body size complicates comparisons between individuals or populations. Thus, body size effects must be eliminated in morphometric analysis. Although ratios (size of character/body size) are often used to attempt this, they only work for the specific case of isometry (i.e. when a structure grows proportionally to body size). Ratios do not eliminate body size effects for allometric (disproportionate) growth. In eutardigrades, body size is highly correlated with the length of the rigid buccal tube, whereas body length (BL) is highly variable because of the flexibility of the cuticle and the orientation and coverslip pressure on the specimen. In heterotardigrades, BL is typically used to indicate body size because the thickened dorsal plates provide more rigidity and reliability in measurements. We measured 27 traits in 97 specimens of Paramacrobiotus tonollii (Eutardigrada) and 14 traits in 100 specimens of Echiniscus virginicus (Heterotardigrada) and found that many traits are allometric rather than isometric. Thorpe (1975, Biol J Linn Soc 7:27) provided a normalization technique to eliminate body size effects for any trait regardless of its relationship to body size. Using the data from P. tonollii, we show that Thorpe's size normalization does successfully remove buccal tube length effects (body size effects), while pt indices generally do not. We also demonstrate the effectiveness of Thorpe's normalization in species delineations of Macrobiotus recens and Macrobiotus hufelandi, two species that differ primarily in a few quantitative traits and overall body size in addition to the eggs. Based on these examples, we propose that the allometric exponent (b) and the Y-intercept (a*) of the regression of Thorpe normalized traits versus body size are valuable metrics in tardigrade systematics.