Linking scaling laws across eukaryotes

Abstract

Scaling laws relating body mass to species characteristics are among the most universal quantitative patterns in biology. Within major taxonomic groups, the 4 key ecological variables of metabolism, abundance, growth, and mortality are often well described by power laws with exponents near 3/4 or related to that value, a commonality often attributed to biophysical constraints on metabolism. However, metabolic scaling theories remain widely debated, and the links among the 4 variables have never been formally tested across the full domain of eukaryote life, to which prevailing theory applies. Here we present datasets of unprecedented scope to examine these 4 scaling laws across all eukaryotes and link them to test whether their combinations support theoretical expectations. We find that metabolism and abundance scale with body size in a remarkably reciprocal fashion, with exponents near ±3/4 within groups, as expected from metabolic theory, but with exponents near ±1 across all groups. This reciprocal scaling supports "energetic equivalence" across eukaryotes, which hypothesizes that the partitioning of energy in space across species does not vary significantly with body size. In contrast, growth and mortality rates scale similarly both within and across groups, with exponents of ±1/4. These findings are inconsistent with a metabolic basis for growth and mortality scaling across eukaryotes. We propose that rather than limiting growth, metabolism adjusts to the needs of growth within major groups, and that growth dynamics may offer a viable theoretical basis to biological scaling.

Keywords: biological scaling; macroecology; metabolic theory.

Fig. 1.

Scaling of basic variables with body mass. (A) Basal metabolism, (B) population abundance, (C) maximum growth, and (D) mortality rate. Points (n) in all plots (A–D) are separate species values, except for plants represented by multiple points for the same species. Ectotherms and protists were also not aggregated into species values in D, due to limited mortality data among smaller sized species. For illustration, we have split eukaryotes into mammals, protists, plants, and ectotherm vertebrates and invertebrates. More resolved groups down to taxonomic orders are detailed in SI Appendix, Figs. S1–S3 and Tables S1–S4. Birds (gray points) often have similar rates to mammals and thus are difficult to see in the plots (SI Appendix). We show bacteria (also gray points) for reference, where available, but limit our discussion to eukaryotes. Scaling exponents k and 95% CIs are shown in the insets for major groups (these exclude birds and bacteria). Black empty circles are humans, with ranges shown in B for cities and hunter-gatherer communities (not included in the analysis).

Fig. 2.

Scaling of transformed and combined variables with body mass. Data are the same as in Fig. 1 but transformed (A–D) and combined (E–H) as per Table 1, using taxonomic information down to the species level, where available. The dashed lines show within-group relationships, while the solid line shows the cross-group relationship. Colors of the exponent k correspond to colors of boxes in Table 1. The x- and y-axes have equal order of magnitude spacing. Boxplots are shown for each variable.

Fig. 3.

Growth and metabolism size class scaling. In A and B, original data from Fig. 1 A and C are binned into logarithmic body size classes to highlight the principal relationships and give equal representation to different size classes. Exponents and 95% CIs are shown to the right of each plot for the nonbinned data, with filled circles for metabolism (above) and empty circles for growth (below). (A) Scaling relationships for basal metabolism (W) and maximum growth (g/s) from Fig. 1 A and C (with additional taxonomic groups) reveal scaling similarities for most groups but a systematic divergence at larger body mass across groups. (B) Mammal scaling relationships for metabolism across activity levels and maximum growth across life stages shows the boundaries in which these characteristics vary. (C) The prevailing view is that metabolism determines growth scaling (orange arrows of causality) on the basis that within a given major group, both variables scale as k ∼ 3/4 (parallel thick lines). The metabolic view, however, cannot explain why growth follows the same universal k ∼ 3/4 scaling both within and across groups, given that metabolism often shows shifts in elevation between groups. A more parsimonious view is that across groups, metabolism adheres to isometric bounds (k ∼ 1), but that within major groups, metabolism adjusts to growth scaling of k ∼ 3/4 (blue arrows of causality).