Size and shape of terrestrial animals

TL;DR

The paper addresses why terrestrial animals exhibit a size-dependent frontal body shape by proposing that stability on uneven natural terrain shapes macroevolution of frontal geometry. It develops a terrain-based stability framework using a fractional Brownian description of ground roughness, deriving how marginal stability constrains the relationship between mass $m$ and frontal aspect ratio $a$. Across 364 species spanning eight orders of magnitude in mass, the authors find a robust negative allometry ($\log a$ vs $\log m$ slope around $-0.13$) that aligns with the terrain-driven prediction and persists after phylogenetic correction ($p\approx 2\times10^{-8}$ for $\log a$ on $\log m$). The study demonstrates that terrain roughness, encapsulated by the Hurst exponent $H$, can explain cross-taxa variation in frontal shape with a single fitting parameter, highlighting a global environmental driver for the macroevolution of terrestrial locomotion morphology.

Abstract

Natural selection for terrestrial locomotion has yielded unifying patterns in the body shape of legged animals, often manifesting as scaling laws. One such pattern appears in the frontal aspect ratio. Smaller animals like insects typically adopt a landscape frontal aspect ratio, with a wider side-to-side base of support than center of mass height. Larger animals like elephants, however, are taller than wide with a portrait aspect ratio. Known explanations for postural scaling are restricted to animal groups with similar anatomical and behavioural motifs, but the trend in frontal aspect ratio transcends such commonalities. Here we show that vertebrates and invertebrates with diverse body plans, ranging in mass from 28 mg to 22000 kg, exhibit size-dependent scaling of the frontal aspect ratio driven by the need for lateral stability on uneven natural terrain. Because natural terrain exhibit scale-dependent unevenness, and the frontal aspect ratio is important for lateral stability during locomotion, smaller animals need a wider aspect ratio for stability. This prediction is based on the fractal property of natural terrain unevenness, requires no anatomical or behavioural parameters, and agrees with the measured scaling despite vast anatomical and behavioural differences. Furthermore, a statistical phylogenetic comparative analysis found that shared ancestry and random trait evolution cannot explain the measured scaling. Thus, our findings reveal that terrain roughness, acting through natural selection for stability, likely drove the macroevolution of frontal shape in terrestrial animals.

Figures (9)

• Figure 1: Aspect ratio and mass of terrestrial animals.a, Aspect ratio $a$ of the species is the ratio of the base of support $w$ to the height $h$ of the center of mass above ground. b, Phylogeny, aspect ratio $a$, and mass $m$ of 364 terrestrial species spanning vertebrates and invertebrates. c, Mass versus aspect ratio, on a log-log scale, showing that animals get narrower as they get heavier.
• Figure 2: Effect of width on stability.a, Definitions of base of support width $w$, center of mass height $h$ for an animal of mass $m$ that is laterally tilted by $\theta_{\rm ter}=\tan^{-1}(z/\ell)$ when the ground support points are horizontally separated by $\ell$ and experience a height difference $z$. The point of marginal stability is when $\theta_{\rm ter}=\theta_{\rm fall}$, i.e. the center of mass resides exactly above one of the support points. b, The distribution $z/\ell=\tan\theta_{\rm ter}$, for typical natural terrain with Hurst exponent $H=0.6$ shows that natural terrain appear rougher at smaller lengths (wider distribution). c, Mapping of $p_{Z}(z;\ell)$ univariate distributions for ten values of $\ell$ to the corresponding constant $\ell$ curves in the $(\log a, \log m)$ space. The calculation is performed with $H=0.6$ and $D=0.0135$.
• Figure 3: Probability density of aspect ratio $a$ and mass $m$ (heatmap) overlaid with data (grey circles). The grey curve is the loci of the mode of the density at each mass $m$, representing the most likely scaling law.
• Figure 4: Procedure of $\boldsymbol{\log}$-transform. The $\log$-transformation of the a, uniform distribution and b, half-normal distribution is equivalent to converting the x-axis to $\log$-scale followed by equalizing the bin-widths in the $\log$-space.
• Figure 5: Scaling law for the varying value of Hurst exponent $H$ and Monte Carlo simulation of the probability densities.a, Predicted allometry for varying values of the Hurst exponent $H$ conserves the trend in the scaling of aspect ratio with mass. b, Probability densities of aspect ratio and mass in the $\log$-space computed by propagating the distribution of the terrain height increments through the governing equations using Monte Carlo simulations.