Reply to Nespolo's paper entitled "New invariants and dimensionless numbers: Futile renaissance of old fallacies?"

An identification of invariants in life history traits of amphibians and reptiles

“…Because criterion (5) is so frequently used in the study of type II invariance (Charnov, ) and it was used in Price et al (), we also analyzed relationships between pairs of life history traits (not body mass) in order to test whether they scale isometrically. An isometric relationship between two traits ultimately leads to products or ratios of life history traits, which can be dimensionless numbers (Charnov, ; Günther & Morgado, ; Savage et al, ). Some authors warn that “caution is needed when allometric equations are multiplied or divided to make new ones” (Nespolo, ).…”

“…An isometric relationship between two traits ultimately leads to products or ratios of life history traits, which can be dimensionless numbers (Charnov, 1993;Günther & Morgado, 2005;Savage et al, 2006). Some authors warn that "caution is needed when allometric equations are multiplied or divided to make new ones" (Nespolo, 2005).…”

“…The latter is in particular problematic because we need a threshold (such as the significance level of a test) which a trait should pass before being considered invariant (Charnov, 1993). This all led to the questioning of the whole concept of invariance by several authors (for a discussion on this topic see Günther & Morgado, 2005;Nee et al, 2005;Nespolo, 2005;Savage et al, 2006), but also to an improvement of methods available for the identification of invariant traits (Price et al, 2014). Price et al (2014) elaborated an objective statistical framework on type I, type II, and type I + II invariance (Savage et al, 2006).…”