Topography of chance

Examining the patterns and dynamics of species abundance distributions in succession of forest communities by model selection

There are a few common species and many rare species in a biological community or a multi-species collection in given space and time. This hollow distribution curve is called species abundance distribution (SAD). Few studies have examined the patterns and dynamics of SADs during the succession of forest communities by model selection. This study explored whether the communities in different successional stages followed different SAD models and whether there existed a best SAD model to reveal their intrinsic quantitative features of structure and dynamics in succession. The abundance (the number of individuals) of each vascular plant was surveyed by quadrat sampling method from the tree, shrub and herb layers in two typical communities (i.e., the evergreen needle- and broad-leaved mixed forest and the monsoon evergreen broad-leaved forest) in southern subtropical Dinghushan Biosphere Reserve, South China. The sites of two forest communities in different successional stages are both 1 ha in area. We collected seven widely representative SAD models with obviously different function forms and transformed them into the same octave (log2) scale. These models are simultaneously confronted with eight datasets from four layers of two communities, and their goodness-of-fits to the data were evaluated by the chi-squared test, the adjusted coefficient of determination and the information criteria. The results indicated that: (1) the logCauchy model followed all the datasets and was the best among seven models; (2) the fitness of each model to the data was not directly related to the successional stage of forest community; (3) according to the SAD curves predicted by the best model (i.e., the logCauchy), the proportion of rare species decreased but that of common ones increased in the upper layers with succession, while the reverse was true in the lower layers; and (4) the difference of the SADs increased between the upper and the lower layers with succession. We concluded that the logCauchy model had the widest applicability in describing the SADs, and could best mirror the SAD patterns and dynamics of communities and their different layers in the succession of forests. The logCauchy-modeled SADs can quantitatively guide the construction of ecological forests and the restoration of degraded vegetation.

From mild to wild fluctuations in crystal plasticity

Macroscopic crystal plasticity is classically viewed as an outcome of uncorrelated dislocation motions producing Gaussian fluctuations. An apparently conflicting picture emerged in recent years emphasizing highly correlated dislocation dynamics characterized by power-law distributed fluctuations. We use acoustic emission measurements in crystals with different symmetries to show that intermittent and continuous visions of plastic flow are not incompatible. We demonstrate the existence of crossover regimes where strongly intermittent events coexist with a Gaussian quasiequilibrium background and propose a simple theoretical framework compatible with these observations.

Rank distributions: a panoramic macroscopic outlook

This paper presents a panoramic macroscopic outlook of rank distributions. We establish a general framework for the analysis of rank distributions, which classifies them into five macroscopic "socioeconomic" states: monarchy, oligarchy-feudalism, criticality, socialism-capitalism, and communism. Oligarchy-feudalism is shown to be characterized by discrete macroscopic rank distributions, and socialism-capitalism is shown to be characterized by continuous macroscopic size distributions. Criticality is a transition state between oligarchy-feudalism and socialism-capitalism, which can manifest allometric scaling with multifractal spectra. Monarchy and communism are extreme forms of oligarchy-feudalism and socialism-capitalism, respectively, in which the intrinsic randomness vanishes. The general framework is applied to three different models of rank distributions-top-down, bottom-up, and global-and unveils each model's macroscopic universality and versatility. The global model yields a macroscopic classification of the generalized Zipf law, an omnipresent form of rank distributions observed across the sciences. An amalgamation of the three models establishes a universal rank-distribution explanation for the macroscopic emergence of a prevalent class of continuous size distributions, ones governed by unimodal densities with both Pareto and inverse-Pareto power-law tails.