Scaling as a key conceptual tool for the interpretation of empirical and experimental patterns in ecology and biology

This thesis is concerned with regular patterns found in ecology and biology, their linkages and the statistical description of their fluctuations around average trends. Among such patterns, often conforming to power laws, well-known examples include the Species-Area relationship (SAR), quantifying the increase of the number of species S inhabiting an ecosystem with ecosystem area, and the scale-invariant body size spectrum, routinely observed, e.g., in aquatic ecosystems. In biology, Kleiber's law is an allometric relationship describing how metabolic rates scale with an organism's body size.

While ecological laws have often been studied independently, simple heuristic reasonings show that they are linked. The need for a unifying effort in ecology, coherently synthesizing the vast and diverse set of empirical observations across scales, has been often voiced. However, a theoretical framework answering this need was still lacking. Furthermore, ecological variables are the result of the interplay between several stochastic ecological processes, and are therefore stochastic variables fluctuating around average values. Ecological and biological scaling laws typically make predictions for such averages, but the issue of fluctuations received scarce attention in the literature. Similarly, biological fluctuations have been typically neglected in the study of the size-scaling of metabolic rates, even though body sizes and metabolic rates may have a significant variability within a species. Fluctuations may be relevant to interpret empirical observations, judge the reliability of predictions and understand ecosystem dynamics.

An hypothesis for the distribution of abundances and body sizes of species inhabiting an ecosystem of finite area is proposed here. The hypothesis is inspired by finite-size scaling and is used to derive macroecological patterns and their linkages within a coherent theoretical framework. Stochastic models of community dynamics are used to support the hypothesis, and the derived linkages are tested on empirical datasets. Several stochastic models of community dynamics are also used here to study the fluctuations of S and how they scale with the average S. The intra-specific variability of metabolic rates and body sizes is investigated experimentally using freshwater phytoplankton species by nanoscale secondary ion mass spectrometry (NanoSIMS).

The linkages among ecological scaling laws predicted by the theoretical framework are verified in several empirical datasets. Theoretical generalizations including deviations from pure power-law behavior and heavy-tailed intra-specific size distributions are also addressed. The theoretical study of the relative scaling of the fluctuations of S with the mean $\langle S \rangle$ in various community dynamics models shows that different ecological processes predict radically different fluctuations scalings, highlighting the need of empirical investigations to sort out which scenario applies to real ecosystems. Experiments on phytoplankton metabolic rate scaling with body size suggest that intra-specific metabolic rate distributions are described by a universal scaling form across different taxa and over three orders of magnitude in body size.

This thesis, along with previous works, suggests that scaling concepts derived for inanimate systems can provide new insights into the dynamics of ecosystems and help unraveling regularities across scales of biological complexity.