The marine diversity spectrum

Abstract

Distributions of species body sizes within a taxonomic group, for example, mammals, are widely studied and important because they help illuminate the evolutionary processes that produced these distributions. Distributions of the sizes of species within an assemblage delineated by geography instead of taxonomy (all the species in a region regardless of clade) are much less studied but are equally important and will illuminate a different set of ecological and evolutionary processes. We develop and test a mechanistic model of how diversity varies with body mass in marine ecosystems. The model predicts the form of the 'diversity spectrum', which quantifies the distribution of species' asymptotic body masses, is a species analogue of the classic size spectrum of individuals, and which we have found to be a new and widely applicable description of diversity patterns. The marine diversity spectrum is predicted to be approximately linear across an asymptotic mass range spanning seven orders of magnitude. Slope -0.5 is predicted for the global marine diversity spectrum for all combined pelagic zones of continental shelf seas, and slopes for large regions are predicted to lie between -0.5 and -0.1. Slopes of -0.5 and -0.1 represent markedly different communities: a slope of -0.5 depicts a 10-fold reduction in diversity for every 100-fold increase in asymptotic mass; a slope of -0.1 depicts a 1.6-fold reduction. Steeper slopes are predicted for larger or colder regions, meaning fewer large species per small species for such regions. Predictions were largely validated by a global empirical analysis. Results explain for the first time a new and widespread phenomenon of biodiversity. Results have implications for estimating numbers of species of small asymptotic mass, where taxonomic inventories are far from complete. Results show that the relationship between diversity and body mass can be explained from the dependence of predation behaviour, dispersal, and life history on body mass, and a neutral assumption about speciation and extinction.

Keywords: biodiversity; body mass; community; neutral theory; power law; size spectrum.

Fig 1

Schematic illustration of basic definitions of spectra and distributions. Each species occurring in a region has an asymptotic mass (large dots), and the individuals of that species have masses less than or equal to the asymptotic mass (small dots, linear scale, (a); separate data on the log scale, (b)). Individuals of a species are all growing towards the species asymptotic mass, indicated by the thin coloured lines in (a) and (b). The individual size distribution (ISD; c) describes how the body sizes of all individuals in the region, regardless of species, are distributed. The size spectrum (d) provides equivalent information in different form – it is the log of the distribution of log individual body sizes. The species asymptotic-size distribution (SASD; e) is a species analogue of the ISD, and the diversity spectrum (f) is a species analogue of the size spectrum – these tools indicate how species asymptotic sizes are distributed.

Fig 2

(a) The joint distribution of individual mass, m, and asymptotic mass, m_∞, expressed as log₁₀(N(m, m_∞)) +  constant (see eqn 1) for m between m_egg (upper bound fish egg size) and 1000 kg and m_∞ between 1 and 1000 kg. The marginal distributions, which are the individual size distribution (ISD) and the individual asymptotic-size distribution (IASD), are labelled. The dashed line in the individual size distribution indicates the part of the plot to which organisms with m_∞ < 1 kg contribute. (b) The log₁₀ individual asymptotic-size distribution plotted and linearly approximated for m_∞ between m_egg and 1000 kg, illustrating the theoretical prediction that the individual asymptotic-size distribution is approximately a power law in m_∞ with exponent about −1·49.

Fig 3

Predicted regional diversity spectra and their slopes for different values of K₁ (the relative radius of the region), K₂ (the size of the community relative to speciation) and (the dispersal distance scaling exponent). Examples of predicted regional diversity spectra (a–c) were close to linear. These panels show the log₁₀ number of species in the region R (i.e. S_C(m_∞,l, αm_∞,l)) plotted for lower-bound asymptotic mass m_∞,l between m_egg and 1000 kg. S_C is computed using eqn 4. K₁ = 10^2·5 and K₂ = 10⁴ were used for a–c; , 0·3 and 0·4 were used for a, d; b, e; and c, f, respectively, spanning the range selected in the section Model parameters. The relationship between log₁₀(S_C) and log₁₀(m_∞,l) was always close to linear, not just in the examples shown (see text). Panels d–f are contour plots showing slopes of log₁₀(S_C) versus log₁₀(m_∞,l) for a range of values of , K₁, and K₂. Dashed lines in d–f delineate the bounds for K₁ and K₂ given in the section Bounds for k₁ and K₂. The minimum slope and maximum slope occurring in the bounds are given, and indicate that regional diversity spectrum slopes should be between −0·5 and about −0·1 for real regions.

Fig 4

Predicted variation in regional diversity spectrum slopes along environmental gradients. Contour lines show diversity spectrum slopes, enlarging part of Fig. 3e. Starting from reference values of K₁ and K₂ (solid dot), arrows show the predicted variation in K₁, K₂ and diversity spectrum slope along gradients of increasing temperature, T (solid arrows, several possible outcomes shown) and increasing region area, A_r (dashed arrow). Diversity spectrum slopes are predicted to become shallower with increasing T and steeper with increasing A_r. Arrows show directions of predicted effects but not magnitudes. Results are similar for other values of (Fig. 3).

Fig 5

Example results for testing the hypothesis that diversity spectra are linear. Empirical diversity spectra (see the section Methods for testing model predictions) and diversity spectra corresponding to fitted tP distributions for selected regions (a, e, i). Log-scale probability plots for truncated Pareto (tP; b, f, j) and quadratic truncated Pareto (qtP; c, g, k) fits. Comparison of diversity spectra corresponding to tP and qtP fits (d, h, l). Panels are as follows: a–d, the global region (all 63 LMEs combined); e–h, the Brazil Shelf; i–l the West Greenland Shelf. Numeric codes in the upper corners also identify regions – Tables S3 and S4 list the system names that correspond to the codes. See Fig. S11 for other regions.

Fig 6

Diversity spectrum slopes for regions with linear diversity spectra as a function of spatial scale. From left to right, dots represent LME, province, basin, latitudinal band and global region means for log₁₀ area (horizontal axis) and diversity spectrum slope (vertical axis). Error bars indicate standard deviations. There are no error bars for the global region point (the right point) because there was only one global region. Nonlinear regions were excluded.

Fig 7

Diversity spectrum slope estimates for LMEs, excluding LMEs for which insufficient species were present to estimate the diversity spectrum or for which the diversity spectrum was nonlinear.