Species–area relationship | EPFL Graph Search

The species–area relationship or species–area curve describes the relationship between the area of a habitat, or of part of a habitat, and the number of species found within that area. Larger areas tend to contain larger numbers of species, and empirically, the relative numbers seem to follow systematic mathematical relationships. The species–area relationship is usually constructed for a single type of organism, such as all vascular plants or all species of a specific trophic level within a particular site. It is rarely if ever, constructed for all types of organisms if simply because of the prodigious data requirements. It is related but not identical to the species discovery curve. Ecologists have proposed a wide range of factors determining the slope and elevation of the species–area relationship. These factors include the relative balance between immigration and extinction, rate and magnitude of disturbance on small vs. large areas, predator-prey dynamics, and clustering of individuals of the same species as a result of dispersal limitation or habitat heterogeneity. The species–area relationship has been reputed to follow from the 2nd law of thermodynamics. In contrast to these "mechanistic" explanations, others assert the need to test whether the pattern is simply the result of a random sampling process. Species–area relationships are often evaluated in conservation science in order to predict extinction rates in the case of habitat loss and habitat fragmentation. Authors have classified the species–area relationship according to the type of habitats being sampled and the census design used. Frank W. Preston, an early investigator of the theory of the species–area relationship, divided it into two types: samples (a census of a contiguous habitat that grows in the census area, also called "mainland" species–area relationships), and isolates (a census of discontiguous habitats, such as islands, also called "island" species–area relationships).

On the probabilistic nature of the species-area relation

Andrea Rinaldo, Andrea Giometto, Jonathan Giezendanner, Silvia Zaoli, Amos Maritan

The Species-Area Relation (SAR), which describes the increase in the number of species S with increasing area A, is under intense scrutiny in contemporary ecology, in particular to probe its reliability in predicting the number of species going extinct as a direct result of habitat loss. Here, we focus on the island SAR, which is measured across a set of disjoint habitat patches, and we argue that the SAR portrays an average trend around which fluctuations are to be expected due to the stochasticity of community dynamics within the patches, external perturbations, and habitat heterogeneity across different patches. This probabilistic interpretation of the SAR, though already implicit in the theory of island biogeography and manifest in the scatter of data points in plots of empirical SAR curves, has not been investigated systematically from the theoretical point of view. Here, we show that the two main contributions to SAR fluctuations, which are due to community dynamics within the patches and to habitat heterogeneity between different patches, can be decoupled and analyzed independently. To investigate the community dynamics contribution to SAR fluctuations, we explore a suite of theoretical models of community dynamics where the number of species S inhabiting a patch emerges from diverse ecological and evolutionary processes, and we compare stationary predictions for the coefficient of variation of S, i.e. the fluctuations of S with respect to the mean. We find that different community dynamics models diverge radically in their predictions. In island biogeography and in neutral frameworks, where fluctuations are only driven by the stochasticity of diversification and extinction events, relative fluctuations decay when the mean increases. Computational evidence suggests that this result is robust in the presence of competition for space or resources. When species compete for finite resources, and mass is introduced as a trait determining species' birth, death and resource consumption rates based on empirical allometric scalings, relative fluctuations do not decay with increasing mean S due to the occasional introduction of new species with large resource demands causing mass extinctions in the community. Given this observation, we also investigate the contribution of external disturbance events to fluctuations of S in neutral community dynamics models and compare this scenario with the community dynamics in undisturbed non-neutral models. Habitat heterogeneity within a single patch, in the context of metapopulation models, causes variability in the number of coexisting species which proves negligible with respect to that caused by the stochasticity of the community dynamics. The second contribution to SAR fluctuations, which is due to habitat heterogeneity among different patches, introduces corrections to the coefficient of variation of S. Most importantly, inter-patches heterogeneity introduces a constant, lower bound on the relative fluctuations of S equal to the coefficient of variation of a habitat variable describing the heterogeneity among patches. Because heterogeneity across patches is inevitably present in natural ecosystems, we expect that the relative fluctuations of S always tend to a constant in the limit of large mean S or large patch area A, with contributions from community dynamics, inter-patches heterogeneity or both. We provide a theoretical framework for modelling these two contributions and we show that both can affect significantly the fluctuations of the SAR. (C) 2018 The Authors. Published by Elsevier Ltd.

2019

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

Silvia Zaoli

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.

EPFL2018

The geomorphometry of endorheic drainage basins: implications for interpreting and modelling their evolution

Andrea Rinaldo, Jean-Marc Dorsaz

Endorheic basins are catchments with no hydrological connection with marine environments. They cover 20% of the Earth's surface, and are mostly located in arid regions. Their drainage networks converge to lakes, salt flats or alluvial plains, whose dynamics are strongly driven by precipitation, evapotranspiration and groundwater discharge, among other factors. Integrated surface drainage and the creation of whole drainage systems typical of open basins are commonly restricted in these regions. Interestingly, the fluvial basin morphology of endorheic basins has not been extensively studied, and a variety of quantitative morphological descriptors used in open basins have not been utilized in the geomorphic analysis of endorheic basins. The objective of this study is to better understand the basin morphology of endorheic river basins by using well-known geomorphological properties and their variations across scales. For three basins in northern Chile we computed the following descriptors and the corresponding relevant scales: the cumulative distribution of contributing area, the horizontal shape of the basins (i.e. Hack's law, normalized Euclidean length, and sinuosity of the streams), slope-area relationship, Horton's ratios and drainage density. We detected several properties typically found in open basins, but certain features which seem to be unique to closed basins were also identified. In particular, we found that horizontal and vertical geomorphic features seem to be linked, which suggests that an independent treatment of these features may not be appropriate for closed basins. Similar results were found regardless of the basin area, which illustrates the relevant effects of features that are specific to these particular regions. It is expected that our findings will improve both the geomorphic assessment of these basins and hydrological modelling of surface water and groundwater. Copyright (c) 2013 John Wiley & Sons, Ltd.

Wiley-Blackwell2013