Evolutionary entropy: a predictor of body size, metabolic rate and maximal life span

Abstract

Body size of organisms spans 24 orders of magnitude, and metabolic rate and life span present comparable differences across species. This article shows that this variation can be explained in terms of evolutionary entropy, a statistical parameter which characterizes the robustness of a population, and describes the uncertainty in the age of the mother of a randomly chosen newborn. We show that entropy also has a macroscopic description: It is linearly related to the logarithm of the variables body size, metabolic rate, and life span. Furthermore, entropy characterizes Darwinian fitness, the efficiency with which a population acquires and converts resources into viable offspring. Accordingly, entropy predicts the outcome of natural selection in populations subject to different classes of ecological constraints. This predictive property, when integrated with the macroscopic representation of entropy, is the basis for enormous differences in morphometric and life-history parameters across species.

Fig. 1

The relation of logarithm of generation time (T) to demographic entropy (S) for a random extended 2 × 2 Leslie matrix (1,000 realizations). Average values of demographic parameters: survival rates s ₀ = 0.2, s ₁ = 0.35, s ₂ = 0.5; fecundities f ₁ = f ₂ = 7.

Fig. 2

The relation of logarithm of generation time (T) to demographic entropy (S) with linear fit. (a) Birds data set. (b) Mammals data set (the large dot stands for Homo sapiens). (c) Insects data set.

Fig. 3

The relation of logarithm of body mass (W) to demographic entropy (S) with linear fit. (a) Birds data set (W in g). (b) Mammals data set (the large dot stands for Homo sapiens) (W in kg).

Fig. 4

The relation of logarithm of metabolic rate (P in W) to demographic entropy (S) with linear fit. (a) Birds data set. (b) Mammals data set (the large dot stands for Homo sapiens).

Fig. 5

The relation of logarithm of maximal life span (L) to demographic entropy (S) with linear fit. (a) Birds data set (L in years). (b) Mammals data set (the large dot stands for Homo sapiens) (L in years). (c) Insects data set (L in days).