Domains containing the field of values of a matrix

AbstractTwo groups of estimates are given for the field of values of a general complex matrix. The first group gives a domain containing both the field of values and the convex hull of the diagonal elements, while the second group gives a domain containing both the field of values and the convex hull of the eigenvalues. The domain given by the second group reduces to the smallest domain possible if the matrix is normal. The results have useful applications in control theory and in stability theory for differential equations

Comparing production-biomass ratios of benthos and suprabenthos in macrofaunal marine crustaceans

Using available data from the literature, we compared the productionbiomass ratios (P/B) between the suprabenthic (= hyperbenthic) and the benthic (infaunaepifauna) species within the group of the macrofaunal marine crustaceans. This data set consists of 91 P/B estimates (26 for suprabenthos and 65 for infaunaepifauna) for 49 different species. Suprabenthic crustacean P/B was significantly higher than P/B of benthic crustacean (post-hoc Scheffé test; one-way analysis of covariance, ANCOVA; p < 103) and also of other (noncrustacean) benthic invertebrate (p < 104). Predictive multilinear regression (MLR) analysis for macrofaunal marine crustaceans showed P/B to depend significantly on mean annual temperature (T) and mean individual weight (W) (R2 = 0.367). Adding the variable swimming capacity increased goodness-of-fit to R2 = 0.528. The higher P/B of suprabenthic (= swimming) macrofauna in comparison with that of the benthic compartment seems to be related to the most apparent feature of the suprabenthos, its swimming capacity. The high P/Bs reported for suprabenthic species indicate how a nontrivial part of benthic production can be ignored if suprabenthos is not well sampled, therefore biasing the models of energy flow generated for trophic webs