Rapid Anthropocene realignment of allometric scaling rules

The negative relationship between body size and population density (SDR) in mammals is often interpreted as resulting from energetic constraints. In a global change scenario, however, this relationship might be expected to change, given the size-dependent nature of anthropogenic pressures and vulnerability to extinction. Here we test whether the SDR in mammals has changed over the last 50 years. We show that the relationship has shifted down and became shallower, corresponding to a decline in population density of 32-72%, for the largest and smallest mammals, respectively. However, the SDRs become steeper in some groups (e.g. carnivores) and shallower in others (e.g. herbivores). The Anthropocene reorganization of biotic systems is apparent in macroecological relationships that were previously believed to be immutable, reinforcing the notion that biodiversity pattens are contingent upon conditions at the time of investigation. We call for an increased attention on the role of global change on macroecological inferences.


Introduction
Macroecology seeks to establish relationships that are informative of nature's underlying mechanisms. The relationship between species body mass and population density, also known as the size-density relationship (SDR), has long been studied to shed light on how the abundance of animals scales with their size (Damuth 1981; Allen et al. 2002;Brown et al. 2004;White et al. 2007). Studies have shown that a clear negative relationship exists (Damuth 1981), which was initially explained in terms of the scaling between body mass and metabolic rate (Kleiber 1932). Damuth (1981Damuth ( , 1987 noted that the scaling coefficients between body mass and metabolic rate (~0.75) and body mass and population density were inverse (~-0.75), suggesting that the energy flux was invariant to body mass, i.e. energy equivalence rule (Brown et al. 2004). The energyequivalence rule implied an energetic tradeoff between physiological and ecological process, Competing explanations for the existence of the SDR in endotherms have focused on differential resource availability and accessibility across trophic levels, and energy conversion efficiency (Damuth 1987  The action of these anthropogenic pressures, simultaneously and/or heterogeneously, creates potential for both the intercept and slope of the SDR to shift over time. By contrast, theory emphasises fixed physiological and environmental constraints as the primary forces responsible for allometric scaling parameters, so the null expectation would be that these constraints somehow overcome or balance out the effects of anthropogenic forcing (Fig 1a). Anthropogenic pressures have the potential to exert directional pressure on both parameters of the SDR: a general reduction in wild biomass reduce the intercept (Fig 1b), whereas size-dependent declines could lead to a reduction in the slope (Fig. 1c), although these are not mutually exclusive (Fig. 1d). These changes might be further complicated by extinctions (resulting the removal of species from the SDR) and trophic interactions (e.g. reduction in predation pressure and competitive release).
Here we assess if and how the SDR has shifted in time across a 50-year period that coincided with unprecedented transformation of natural habitats. We focus on mammals on which SDR investigation has largely focused (Damuth 1981(Damuth , 1987

Data
We extracted all population density estimates for mammals from an updated unpublished version invertebrate-based diet as insectivores (n=300, sps=59). Species with <20% of animal-based diet were classified as frugivore if with >=40% fruit in diet (n=1571, sps=159) and as granivores if with >=30% seed-based diet (n=785, sps=63). Although EltonTraits does not differentiate between leaves and grass, we further distinguished herbivores from folivores by considering herbivores species with >=80% plant-based diet belonging to cetartiodactyla and perissodactyla (n=6119, sps=184), and as folivores species not belonging to these groups (with the exception of Giraffidae) with >=60% plant-based diet (n=545, sps=53). All species that did not fit the previous two categories were classified as omnivores (n=2950, sps=184).
To account for phylogenetic relatedness in the modelling, we used the phylogeny in Upham et al. (2019). We extracted 1000 random trees and generated a majority-rule consensus setting the frequency of in the sample with which each clade or bipartition is encountered at 0.8. We then computed a principal component analysis on the phylogenetic distance matrix of the consensus tree, and extracted the first 5 eigenvectors explaining >99% of the total variance.
All data used in this study are made available as part of the supporting information.

Modelling approach
We fitted a set of generalized mixed effect linear models (GLMM) using a gaussian distribution to test and compare our hypotheses (Table 1). All models included a random effect at the level of species to control for the effect of pseudo-replicas and possible species turnover through time. We also included a random effect to control for different sampling methodologies broadly classified into eight categories: censuses ('complete' counts, which assume full detection of individuals), distance sampling (including different algorithms and sampling design), home range extrapolation (derived from home range area estimation), mark-recapture (including different algorithms and capture approaches), N-Mixture models, Random Encounter models, incomplete counts (any incomplete count that is extrapolated to a larger area), trapping (removal methods, indicate the minimum number known to be alive).
The model representing our null hypothesis (Fig. 1a) only included body mass (Table 1). To assess whether the intercept has changed, we tested the additive effect of time by including sampling year as a fixed effect. To assess whether the slope has changed, we tested the effect of time along the body mass range by included an interaction term between sampling year and body mass (Table 1).
In order to test whether our hypotheses were only valid for a specific diet category, we repeated the model selection for each diet category separately.
Models were compared using the Akaike Information Criterion (AIC). We also present results using the Bayesian Information Criterion (BIC), which tends to be more conservative than AIC and is We also plot the residuals against time to assess a possible temporal autocorrelation effect in the residuals.

Results
The most supported model explaining the SDR across all species was the one accounting for a shift in both intercept and slope (IntSlope model; Table 2, S1). The same model was the most supported according to AIC in all diet groups except for insectivores and folivores ( Table 2, S1). While in both insectivores and folivores the IntSlope model was also competitive (within 2-AIC units from the best models), in these cases we selected the most parsimonious models, the Null and the Intercept-only model, respectively. ( BIC-based selection concurs for all groups except in frugivores, carnivores and omnivores.
In frugivores the null model is more supported by BIC, whereas in carnivores and omnivores the most supported models by AIC are also ranked as competitive by BIC, but the intercept-only model would be preferred as more parsimonious.
We did not detect an effect of phylogenetic, spatial or temporal autocorrelation in the residuals of the selected models (Table S2, Fig. S1-S2).

Discussion
Our results suggest that the relationship between body mass and population density, which has long been subject of macroecological investigation (Damuth 1981 The mismatch between AIC-based and BIC-based selection reflects the highly noisy nature of population density data. While our sample sizes were undoubtedly large, detecting a temporal trend within 50 years in a dataset including many species and their trends require a considerable sample size, so uncertainty remain regarding the change in SDR in frugivores, omnivores and carnivores.
The likelihood of their models including an interactive term was higher, but not sufficiently high to undeniably justify increased model complexity.
It is possible that our dataset of empirical density estimates suffers of temporal biases which may partly explain our results. For example, it was noted that global mass -density relationship there is no evidence emergent properties were more stable before humans.
Our understanding of natural world is biased to a compromised situation. The collection of large databases including data collected over long time spans may help us to capture these biases and possibly correct for them. It is crucial that the effect of humans is increasingly considered while assessing and interpreting natural patterns and their causes.