The scaling of genetic diversity in a changing and fragmented world

Most species do not live in a constant environment over space or time. Their environment is often heterogeneous with a huge variability in resource availability and exposure to pathogens or predators, which may affect the local densities of the species. Moreover, the habitat might be fragmented, preventing free and isotropic migrations between local sub-populations (demes) of a species, making some demes more isolated than others. For example, during the last ice age populations of many species migrated towards refuge areas from which re-colonization originated when conditions improved. However, populations that could not move fast enough or could not adapt to the new environmental conditions faced extinctions. Populations living in these types of dynamic environments are often referred to as metapopulations and modeled as an array of subdivisions (or demes) that exchange migrants with their neighbors. Several studies have focused on the description of their demography, probability of extinction and expected patterns of diversity at different scales. Importantly, all these evolutionary processes may affect genetic diversity, which can affect the chance of populations to persist. In this chapter we provide an overview on the consequences of fragmentation, long-distance dispersal, range contractions and range shifts on genetic diversity. In addition, we describe new methods to detect and quantify underlying evolutionary processes from sampled genetic data.

Lateglacial and Holocene vegetation belts in the Pirin Mountains (southwestern Bulgaria)

Pollen stratigraphy of a core 270 cm long from Lake Dalgoto at 2310 m in the Northern Pirin Mountains, southern Bulgaria, was treated by optimal partitioning and compared to a broken-stick model to reveal statistically significant pollen zones. The vegetational reconstructions presented here are based on pollen percentages and pollen influx, on comparisons of modern and fossil pollen spectra, and on macrofossil dates from other sites in the mountains. During the Younger Dryas (11000–10200 14C yr BP), an open xerophytic herb vegetation with Artemisia and Chenopodiaceae was widely developed around the lake. Deciduous trees growing at lower elevations contributed to the pollen rain deposited at the higher-elevation sampling sites. Specifically, from 10200 to 8500 yr BP, Quercus, Ulmus, Tilia and Betula expanded rapidly at low and intermediate elevations, and between 8500 and 6500 yr BP they extended to higher elevations close to the upper forest limit, which was formed by Betula pendula at about 1900 m. Coniferous species were limited in the region at this time. After 6500 yr BP, the expansion of conifers (Pinus peuce, P. sylvestris, P. mugo, Abies alba) at high elevations forced the deciduous trees downward. Between 6500 and 3000 yr BP, the forest limit at 2200 m was formed by P. peuce, and A. alba had its maximum vertical range up to 1900 m. Later the abundance and vertical range of P. peuce and A. alba were reduced. After 3000 yr BP, Picea expanded.

Exact Unification and Admissibility

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.