Languages cool as they expand: Allometric scaling and the decreasing need for new words

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This ‘‘cooling pattern’’ forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature

Network model of deviation from power-law distribution in complex network

Deviation from simple power law is widely observed in complex networks. We introduce a model including possible mechanisms leading to the deviation. In this model, probabilistic addition of nodes and links, as well as rewiring of links are considered. Using master equation, through theoretical calculation and numerical simulation, double power laws with one variable and one constant exponent are obtained. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Water level and fish-mediated cascading effects on the microbial community in eutrophic warm shallow lakes: a mesocosm experiment

Information on the effects of water level changes on microbial planktonic communities in lakes is limited but vital for understanding ecosystem dynamics in Mediterranean lakes subjected to major intra- and inter-annual variations in water level. We performed an in situ mesocosm experiment in an eutrophic Turkish lake at two different depths crossed with presence/absence of fish in order to explore the effects of water level variations and the role of top-down regulation at contrasting depths. Strong effects of fish were found on zooplankton, weakening through the food chain to ciliates, HNF and bacterioplankton, whereas the effect of water level variations was overall modest. Presence of fish resulted in lower biomass of zooplankton and higher biomasses of phytoplankton, ciliates and total plankton. The cascading effects of fish were strongest in the shallow mesocosms as evidenced by a lower zooplankton contribution to total plankton biomass and lower zooplankton:ciliate and HNF:bacteria biomass ratios. Our results suggest that a lowering of the water level in warm shallow lakes will enhance the contribution of bacteria, HNF and ciliates to the plankton biomass, likely due to increased density of submerged macrophytes (less phytoplankton); this effect will, however, be less pronounced in the presence of fish