Synergy,redundancy, and multivariate information measures: an experimentalist’s perspective

Information theory has long been used to quantify interactions between two variables. With the rise of complex systems research, multivariate information measures have been increasingly used to investigate interactions between groups of three or more variables, often with an emphasis on so called synergistic and redundant interactions. While bivariate information measures are commonly agreed upon, the multivariate information measures in use today have been developed by many different groups, and differ in subtle, yet significant ways. Here, we will review these multivariate information measures with special emphasis paid to their relationship to synergy and redundancy, as well as examine the differences between these measures by applying them to several simple model systems. In addition to these systems, we will illustrate the usefulness of the information measures by analyzing neural spiking data from a dissociated culture through early stages of its development. Our aim is that this work will aid other researchers as they seek the best multivariate information measure for their specific research goals and system. Finally, we have made software available online which allows the user to calculate all of the information measures discussedwithin this paper.     

Chemical biology: Paper alert

A selection of interesting papers that were published in the two months before our press date in major journals most likely to report significant results in chemical biology.     

Species trait diversity sustains multiple dietary nutrients supplied by freshwater fisheries

Species, through their traits, influence how ecosystems simultaneously sustain multiple functions. However, it is unclear how trait diversity sustains the multiple contributions biodiversity makes to people. Freshwater fisheries nourish hundreds of millions of people globally, but overharvesting and river fragmentation are increasingly affecting catches. We analyse how loss of nutritional trait diversity in consumed fish portfolios affects the simultaneous provisioning of six essential dietary nutrients using household data from the Amazon and Tonlé Sap, two of Earth's most productive and diverse freshwater fisheries. We find that fish portfolios with high trait diversity meet higher thresholds of required daily intakes for a greater variety of nutrients with less fish biomass. This beneficial biodiversity effect is driven by low redundancy in species nutrient content profiles. Our findings imply that sustaining the dietary contributions fish make to people given declining biodiversity could require more biomass and ultimately exacerbate fishing pressure in already-stressed ecosystems.     

Invasive aquarium fish transform ecosystem nutrient dynamics

Trade of ornamental aquatic species is a multi-billion dollar industry responsible for the introduction of myriad fishes into novel ecosystems. Although aquarium invaders have the potential to alter ecosystem function, regulation of the trade is minimal and little is known about the ecosystem-level consequences of invasion for all but a small number of aquarium species. Here, we demonstrate how ecological stoichiometry can be used as a framework to identify aquarium invaders with the potential to modify ecosystem processes. We show that explosive growth of an introduced population of stoichiometrically unique, phosphorus (P)-rich catfish in a river in southern Mexico significantly transformed stream nutrient dynamics by altering nutrient storage and remineralization rates. Notably, changes varied between elements; the P-rich fish acted as net sinks of P and net remineralizers of nitrogen. Results from this study suggest species-specific stoichiometry may be insightful for understanding how invasive species modify nutrient dynamics when their population densities and elemental composition differ substantially from native organisms. Risk analysis for potential aquarium imports should consider species traits such as body stoichiometry, which may increase the likelihood that an invasion will alter the structure and function of ecosystems.     

Acclimation or stress symptom? An integrated study of intraspecific variation in the clonal plant Aechmea bromeliifolia,a widespread CAM tank‐bromeliad

The clonal tank-bromeliad Aechmea bromeliifolia (Rudge) Baker was found in four different habitats in a restinga (vegetation mosaic on sandy coastal plains), of south-eastern Brazil. These habitats (swamp forest, dry forest, dry shrubland and herbaceous marsh) lie within a few hundred metres of each other along a gradient extending inland from the coast, and differ markedly in terms of light and flood regime. We compared ramet morphology, leaf anatomy and physiology, and population parameters to examine the amplitude of trait variation of this widespread species in the studied restinga. This integrated approach allowed us to examine which variation conferred acclimation and which was merely a stress symptom. A . bromeliifolia showed site-specific differences in abundance, distribution, rosette size and shape, leaf anatomical arrangement and photochemical efficiency (potential quantum yield; F _v/ F _m) during the day. Most of the variation found seemed to be related to the interaction of light and flooding. The lowest number and size of ramets at the exposed, dry shrubland was matched by a marked leaf photoinhibition, which suggested poor acclimation to local levels of light intensity and limited water supply. In the other habitats, the morpho-physiological parameters measured suggested adequate foraging behaviour and site acclimation.  © 2002 The Linnean Society of London, Botanical Journal of the Linnean Society, 2002, 140 , 391-401.