Ecological equivalence of species within phytoplankton functional groups

1.There are tens of thousands of species of phytoplankton found throughout the tree of life. Despite this diversity, phytoplankton are often aggregated into a few functional groups according to metabolic traits or biogeochemical role. We investigate the extent to which phytoplankton species dynamics are neutral within functional groups. 2.Seasonal dynamics in many regions of the ocean are known to affect phytoplankton at the functional group level leading to largely predictable patterns of seasonal succession. It is much more difficult to make general statements about the dynamics of individual species. 3.We use a 7 year time-series at station L4 in the Western English Channel with 57 diatom and 17 dinoflagellate species enumerated weekly to test if the abundance of diatom and dinoflagellate species vary randomly within their functional group envelope or if each species is driven uniquely by external factors. 4.We show that the total biomass of the diatom and dinoflagellate functional groups is well predicted by irradiance and temperature and quantify trait values governing the growth rate of both functional groups. The biomass dynamics of the functional groups are not neutral and each has their own distinct responses to environmental forcing. Compared to dinoflagellates, diatoms have faster growth rates, and grow faster under lower irradiance, cooler temperatures, and higher nutrient conditions. 5.The biomass of most species vary randomly within their functional group biomass envelope, most of the time. As a consequence, modelers will find it difficult to predict the biomass of most individual species. Our analysis supports the approach of using a single set of traits for a functional group and suggests that it should be possible to determine these traits from natural communities.

K1 of Chevalley groups are nilpotent

Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.