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Our starting point is recognition of some mixture relationships involving the (continuous) Gauss hypergeometric distribution. Our main emphasis is then to generalize these relationships to ones involving (discrete) generalized hypergeometric distributions and their rarely considered continuous counterparts. Two such sets of relationships are derived one involving beta distributions and the other gamma distributions. A wide variety of interesting special cases arise along the way: Poisson, binomial, negative binomial, logarithmic, Conway–Maxwell–Poisson and Libby–Novick distributions all appear. There are also comments on the wider context within which the relationships of interest in this article arise. [ABSTRACT FROM AUTHOR]

The Great Dismal Swamp wetland, spanning >400 km2 along the Virginia and North Carolina border, was shaped by a complex combination of geomorphic, climatic, and anthropogenic forcings during the last 14,000 years. Pollen, macrofossils, charcoal, and physical properties from sediment cores at seven sites provide a detailed record of the spatial heterogeneity of the wetland and the roles played by natural hydrologic variability, wildfire, and human modification of drainage in shaping vegetation and habitats. Cold-temperate forests occupied regional uplands from at least 13.5–10.3 cal ka BP. Marshes dominated by grasses and other herbaceous taxa began developing along low-elevation streams as early as 10.3 cal ka BP, resulting in accumulation of organic silts. Long-hydroperiod, peat accumulating marshes, with abundant floating aquatic plants, developed as early as 9.6 cal ka BP, as rapid rates of sea-level rise elevated the water table and facilitated wetland development and peat accumulation along stream courses. By the mid-Holocene (c. 7–6.5 cal ka BP), when local sea-level rise began slowing and reached about 12–15 m below present, shorter hydroperiod, peat-accumulating marshes dominated the landscape, with increased wildfire activity. Great Dismal Swamp vegetation shifted from marshes to peat-accumulating forested wetlands by c. 3.7 cal ka BP; these were dominated by varying combinations of Nyssa (tupelo), Taxodium (cypress), and Chamaecyparis thyoides (Atlantic white cedar). Wildfires were infrequent during this time, and the forested wetlands persisted, with minor compositional changes related to climate-driven fluctuations in stream flow, until colonial ditching and logging began in the swamp during the late 18th century. These activities decreased cypress and cedar populations, and, by the mid-20th century, expanded ditching resulted in even drier conditions and expansion of maple-gum (dominated by Acer and Liquidambar) , and pine-pocosin (dominated by Pinus) forests. The distribution of these forests differs from that of the late Holocene and represents a fundamental shift in hydrology, peat structure, vegetation, and fire regime due to landscape alterations of the last few centuries. • Dismal Swamp wetland development is documented by pollen and macrofossil records. • Great Dismal Swamp marshes began forming along streams as early as 10 cal ka BP. • Fire activity peaked in Great Dismal Swamp marshes in the mid-Holocene (7-4 cal ka BP). • Forested wetlands dominated the Great Dismal Swamp landscape by ∼3.7 cal ka BP. • Modern forested wetland distribution resulted from post-Colonial drainage actions. [ABSTRACT FROM AUTHOR]

Elsewhere, I have promoted (univariate continuous) “transformation of scale” (ToS) distributions having densities of the form 2g(Π−1(x)) wheregis a symmetric distribution and Π is a transformation function with a special property. Here, I develop bivariate (readily multivariate) ToS distributions. Univariate ToS distributions have a transformation of random variable relationship with Azzalini-type skew-symmetric distributions; the bivariate ToS distribution here arises from marginal variable transformation of a particular form of bivariate skew-symmetric distribution. Examples are given, as are basic properties—unimodality, a covariance property, random variate generation—and connections with a bivariate inverse Gaussian distribution are pointed out. [ABSTRACT FROM AUTHOR]