Figures and data
Cubic isometric relationship between volume (∼weight) and length growth, and likelihood to detect an existing growth spurt (GS) in linear length (schematic).
(A-E): Top/bottom: Absolute size and growth rate (= 1st derivation of size). From left to right: Increasingly fast acceleration of volume (∼weight) growth and the aligned length growth, from (A) no acceleration (constant volume growth rate and linear increase in volume) through (B) constant acceleration (linear increase in volume growth rate and quadratic increase in volume) to (C) quadratic acceleration of volume growth rate (cubic increase in volume), and (D,E) even faster volume growth acceleration. Due to the cubic relationship, these volume growth rates would align with decreasing (A,B) or constant length growth rates (C), whereas a detectable acceleration in length growth rate may only be found in cases of very fast acceleration in volume growth rate (D,E). Therefore, the current dichotomy between absent and detectable length GSs would only differentiate between (A-C) and (D-E). Another consequence is that, in non-aquatic animals, a cubic relationship is more likely in smaller animals, whereas in larger animals like humans or bonobos, the relationship tends to follow a lower power of 2.5 or even 2 only, as a result from limitation on the bearable weight of a skeletal construction which relates to the sectional area of bones (for more details see e.g., Juul et al., 1995). This means that in case of an equal volume growth acceleration, an aligned acceleration in linear length growth may become more likely detectable in larger animals simply because of the different underlying scaling laws. (F) The above scaling rules lead to further dynamics depending on the temporal overlap of the curves, making length GSs more pronounced and detectable with increasing size (from left to right). A GS in linear length is detectable if the acceleration resulting from the volume-GS exceeds the deceleration in length growth rate that results from the cubic relationship, with the last one becoming weaker with increasing size, respective age. The figure shows how a change from a constant to a linearly accelerating volume growth rate (like in Fig. 1A and B; equal levels of acceleration) results in different levels of acceleration in linear length growth rate depending on the age/size at which this change occurs, from left (change right after birth, only deceleration in length growth rate (equal to Fig. 1B) to right (change at late age, strong acceleration in length growth rate). Additionally, this figure highlights that even if both volume and linear length show a GS and are perfectly aligned, the linear length growth rate reaches its peak and starts declining again at a time when volume growth rate still increases. See also supplemental Fig. S1 for non-linear acceleration in volume growth rate.
Statistical results of GAMM models on growth and physiology.
Green: Interaction term results from a separate model (see methods section). Red: Special model structure for IGFBP-3 models (random intercept per individual, random smooth per zoo not sex-specific; for details see methods). §: including maternal primiparity, rearing conditions (hand- vs mother-reared) and zoo- vs wild-born (see methods section). *: 
Growth trajectories in body weight and forearm length, and the importance of comparing them at the relevant dimension.
Fitted values and 95% CIs from GAMM models are shown, implementing variability in trajectories across individuals and zoos. (A,B) Investigating both weight and length growth at the dimension of weight growth reveals pronounced growth spurts (GS) in both which are strongly aligned with each other in timing and amplitude (see also Fig. 4A for easier comparison). (C,D) If instead examined at the scale of one-dimensional length growth, weight and length growth curves still align with each other but the GSs are not so easily detectable anymore. However, the GS is still evident in female growth, but appears at a younger age than if scale-corrected (A,B). The potential fast decrease in growth rate after birth was not covered by linear length data (first half year of age: 2 arm and 854 (729 male) weight measures).
Physiological changes during ontogeny: Markers of muscle growth (creatinine), adrenarche (DHEA) and adolescence (testosterone and IGFBP-3).
Fitted values and 95% CIs from GAMM models are shown, which implement variability in trajectories across individuals and zoos. (A) Males showed a pronounced growth spurt (GS) in lean body respective muscle mass, resulting in larger lean body mass in males compared to females where such a GS was not detectable. Be aware though that corrected creatinine values before the age of 3-4 years may be less reliable (47). (B) DHEA levels increased fastest during the first five years of life and reached maximal levels at ∼15 years. (C) Testosterone levels increased during development in both sexes, but in males, testosterone levels increased longer and reached higher adult levels. They increased fastest at 3.5-4years in females and seven years in males. Testosterone levels decreased again after the age of ∼ 30 years of age. (D) IGFBP-3 levels showed a peak of similar height in males and females, occurring at a younger age in females than males.
Direct comparison of age trajectories in growth patterns and physiological parameters until the age of 20 years.
All curves are the same as in Fig. 2,3, and for the respective variability and uncertainty in the trajectories including the occurrence, level and timing of peaks see the 95% CIs in Fig. 2,3. Blue and red dotted line: Age at peak growth velocity in cm2.5/year (blue) and in cm/year (red; females only). (A) Change of growth rate over age in weight, forearm length, and lean body respective muscle mass (measured as urinary creatinine). (B) Levels (top) and rate of change (bottom) in urinary testosterone, IGFBP-3 and DHEA-levels.
Evidence of length growth spurts (GS) from published literature using linear length growth.
Measures of linear length growth are taken of: Body length or height = B, Crown-rump/Shoulder-rump/Anterior trunk length = CR/SR/AT, Lower/Upper/Full arm length = LA/UA/A, Thigh/Tibia/Leg length = TH/TI/L. Methods: in zoos = direct measurements, in wild populations = photogrammetry, except on Macaca ochreata (direct on trapped animals). Growth rate acceleration can be seen as proof of a GS, but considering scale-correction, a GS is also very likely in case of a period with constant linear length growth rate, and would be possible in cases of just a slowdown in deceleration. For markers of adolescence see Table S1. m = male, f = female, w = wild, z = zoo.
