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.

Theoretical and Experimental Studies of Dendritic Metacommunities

Francesco Carrara

The present thesis deals with the understanding of the origins and the mechanisms of maintenance of biodiversity in natural landscapes, in particular by identifying key processes that define large-scale patterns of abundance and diversity. Biological communities often occur in spatially structured habitats where connectivity directly affects dispersal and metacommunity processes. Recent theoretical work suggests that dispersal constrained by the connectivity of specific habitat structures affects diversity patterns and species interactions. This is particularly relevant in dendritic networks epitomized by fluvial ecological corridors. This thesis addresses whether connectivity alone can explain observed features of biodiversity and selectively promote different components of community composition in river-like landscapes, such as local species richness or the among-community similarity. The relevance of this thesis lies in the major ecological challenges posed by the topic, and its fundamental importance to conservation biology. The studies pursued herein are also deemed relevant because of the influence of the spatial connectivity and dispersal on population dynamics and of the relevance of biodiversity to ecosystem functioning. Mechanisms of species coexistence were investigated with a blend of theoretical tools (broadly related to statistical mechanics and the theory of stochastic processes) and experimental work using laboratory microbial communities. The research tools ranged from aspects of modern coexistence theory in a local perspective to the recent concept of the metacommunity in spatial ecology, within a unified framework. The study of biodiversity in riverine ecosystems guided by observational data has been addressed by combining theoretical metacommunity models with laboratory experiments. The results are diverse. First, they show experimentally that connectivity per se shapes key components of biodiversity in metacommunities. Local dispersal in isotropic lattice landscapes homogenizes local species richness and leads to pronounced spatial persistence. By contrast, dispersal along dendritic landscapes leads to higher variability in local diversity and among-community composition. Although headwaters exhibit relatively lower species richness, they are crucial for the maintenance of regional biodiversity. By suitably arranging patch sizes within river-like networks the effect of local habitat capacity (i.e., the patch size) and dendritic connectivity on biodiversity can be experimentally disentangled in aquatic microcosm metacommunities. It is shown in this thesis that species coexistence and community assembly depend on intricate, non-trivial interactions of local community capacity and network positioning. Furthermore, an interaction of spatial arrangement of habitat capacity and dispersal along river-like networks also affects a key ecosystem descriptor, namely regional evenness. High regional evenness in community composition is found only in landscapes preserving geomorphological scaling properties of patch sizes. In riverine environments some of the rarer species sustained regionally more abundant populations and were better able to track their own niche requirements compared to landscapes with homogeneous patch size or landscapes with spatially uncorrelated patch size. All the experimental results were supported and extended by a theoretical analysis where the above mechanisms have been generalized. This thesis provides the first direct experimental evidence that spatially constrained dendritic connectivity is a key factor for community composition and population persistence in riverine landscapes. As such, this thesis assesses a longstanding issue in spatial community ecology. It offers unique insights into the ecological forces structuring natural communities in a key ecosytem, and demonstrates principles that can be further tested in theoretical metacommunity models possibly to be extended to real riverine ecosystems. Taken together, the analyses show how the structure of ecological networks interacts with the spatial environmental matrix in determining biodiversity patterns and the functioning of biological communities. The analyses also suggest that altering the natural linkage between dendritic connectivity and patch size strongly affects community properties at multiple scales. The first part of this thesis (chapters 2 and 3) addresses key aspects of biodiversity-ecosystem functioning research where the combination of theory-guided experiments and theoretical investigations shows how a stochastic implementation of population dynamics proves fundamental for key community properties such as species persistence and community stability. The diversity-productivity and diversity-stability relationships are explored. Both experimental findings and the results of a stochastic model fitted to the experimental interaction matrix, suggest the emergence of strong stabilizing forces when species from different functional groups interact in the same environment, increasing species coexistence and community biomass production. The last part (chapter 6) provides a synthesis of this thesis work, in that it aims at unifying aspects from niche-theory, usually adopted in spatially implicit models, with those characteristic of a spatially explicit context from a typical real-life mountainous regions. It is dedicated to the possible explanation for a macroecological pattern routinely observed from organisms in different domains of life, that is, the mid-elevational peak in local species richness. Guided by empirical observations on diversity of macroinvertebrates in Swiss river basins, a theoretical ansatz is provided which is deemed to capture the essential geomorphological drivers and controls relating species-fitness to altitude. A set of overarching conclusions and perspectives for future research are discussed in the concluding chapter.

EPFL2013

Ecohydrological Footprints

Samir Suweis

Ecohydrological footprints are defined as the response of ecosystem functions or services to changes in their hydrologic drivers. In this thesis, several diverse footprints are addressed: noise-driven effects on storage-discharge relations and catchment streamflow distributions, that are important drivers of biodiversity; soil salinization and its ecohydrological implications; topological effects of the ecological interaction networks on living communities (e.g. on their species persistence); and form and function of the global virtual water trade network. The coherence of the conceptual framework is provided by the study of drivers and controls of ecohydrological variability using methodological approaches based on statistical mechanics. In fact, this thesis work outlines a significant portion of environmental statistical mechanics, an overarching discipline that is emerging in recent years, which applies mathematical tools from statistical mechanics to model several ecohydrological processes. The proposed relevance of this thesis lies in the major effects of hydrologic drivers on ecological process. The view that emerges from current research in ecohydrology, that this thesis supports, is that there exists a definite need for an integrated understanding of ecological and hydrological processes. Because stochasticity is intrinsic to environmental and ecohydrological variability, noise plays an important and constructive role in ecohydrological processes. In this thesis, a stochastic approach is applied to analyze different ecohydrological processes, ranging from green and blue water flows in river basins (part I), ecosystem dynamics affected by the directional dispersal provided by river networks (part II) to water footprints of human society (part III).Methods range from novel exact solutions to stochastic differential equations to random graph theory applications, and imply the analysis of suitable field data. An analytical framework for quantitative analysis is laid out to tackle complex problems and to estimate the effects of environmental change on the interaction of the hydrologic processes with the biota. The main results of this thesis are: i) the achievement of exact solutions for the probability distribution of catchment streamflow, that takes in account stochastic fluctuations in the storage-discharge relation and for the condition of a noise induced phenomena to the streamflows regimes; ii) the stationary solutions of soil salinity under stochastic hydrologic forcing; iii) a novel solution of the Ito-Stratonovich problem in multiplicative Poisson processes; iv) the proper framework for species' persistence time distributions, as a function of topological constraints on the ecosystem, and its connection with other important macroecological laws. A related length-bias sampling problem is also solved. v) A statistical analysis of the global virtual trade network and a semi-analytical model that is able to describe most of the observed properties.