Boolean like algebras

Using Vaggione’s concept of central element in a double pointed algebra, we introduce the notion of Boolean like variety as a generalization of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double pointed variety is discriminator i↵ it is semi-Boolean like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterization of double pointed discriminator varieties. Moreover, we show that every idempotent semi-Boolean-like variety is term equivalent to a variety of noncommutative Boolean algebras with additional regular operations

The importance of habitat and life history to extinction risk in sharks, skates, rays and chimaeras

We compared life-history traits and extinction risk of chondrichthyans (sharks, rays and chimaeras), a group of high conservation concern, from the three major marine habitats (continental shelves, open ocean and deep sea), controlling for phylogenetic correlation. Deep-water chondrichthyans had a higher age at maturity and longevity, and a lower growth completion rate than shallow-water species. The average fishing mortality needed to drive a deep-water chondrichthyan species to extinction (Fextinct) was 38–58% of that estimated for oceanic and continental shelf species, respectively. Mean values of Fextinct were 0.149, 0.250 and 0.368 for deep-water, oceanic and continental shelf species, respectively. Reproductive mode was an important determinant of extinction risk, while body size had a weak effect on extinction risk. As extinction risk was highly correlated with phylogeny, the loss of species will be accompanied by a loss of phylogenetic diversity. Conservation priority should not be restricted to large species, as is usually suggested, since many small species, like those inhabiting the deep ocean, are also highly vulnerable to extinction. Fishing mortality of deep-water chondrichthyans already exploited should be minimized, and new deep-water fisheries affecting chondrichthyans should be prevented