A Finite-size Scaling Framework Uncovers the Covariations of Ecological Scaling Laws
Starts 16 Feb 2018 11:00
Ends 16 Feb 2018 12:00
Central European Time
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Scaling laws in ecology are recurrent and pervasive patterns observed in ecosystems, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence. Well-known examples include the Species-Area relationship (SAR), quantifying the increase of biodiversity with ecosystem area, and Kleiber’s law, the allometric relation between organismic size and metabolic rate. The interest in these laws lies in their intrinsic predictive power: how many species would go extinct if the ecosystem shrinks to half its size? What is the mass of the largest organisms inhabiting ecosystems of different extent? Are there more large-sized or small-sized organisms and species? Scaling laws observed empirically often conform to power-laws, A=Ba, where a is the scaling exponent. Although their functional form appears to be ubiquitous, empirical scaling exponents may vary with ecosystem type and resource supply rate.
While ecological laws have been often studied independently, simple heuristic reasonings show that they are linked. Such reasonings, however, do not allow accounting for finite-size effects, restricting the range for power-law behavior in finite ecosystem due to ecological or biological constraints on organismic size, or for other deviations from pure power-laws. These limits demand for a different approach. The ubiquity of power-laws and the presence of finite-size constraints suggest finite-size scaling theory as a useful tool in this context. A scaling hypothesis for the joint probability distribution of abundance and body mass of species inhabiting an ecosystem of finite size is proposed and used to derive macroecological patterns. The hypothesis is supported by a broad class of resource-limited community dynamics stochastic models. Precise linkages among ecological laws were derived from the proposed scaling hypothesis, in the form of algebraic relationships among scaling exponents. Such relationships rationalize the observed variability of ecological exponents across ecosystems, clarifying how changes in one ecological pattern affect the remaining ones. Predicted covariations were verified on empirical data. This model-free approach allows investigating the effects of different ecological or biological assumptions on the covariation of scaling exponents.
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