Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility Theories

This article compares classical expected utility (EU) with the more general rank-dependent utility (RDU) models. The difference between the independence condition for preferences of EU and its comonotonic generalization in RDU provides the exact demarcation between EU and rank-dependent models. Other axiomatic differences are not essential. An experimental design is described that tests this difference between independence and comonotonic independence in its most basic form and is robust against violations of other assumptions that may confound the results, in particular the reduction principle and transitivity. It is well known that in the classical counterexamples to EU, comonotonic independence performs better than full-force independence. For our more general choice pairs, however, we find that comonotonic independence does not perform better. This is contrary to our prior expectation and suggests that rank-dependent models, in full generality, do not provide a descriptive improvement over EU. For rank-dependent models to have a future, submodels and choice situations need to be identified for which rank-dependence does contribute descriptively

Genetic Diversity and Ecological Niche Modelling of Wild Barley:Refugia, Large-Scale Post-LGM Range Expansion and Limited Mid-Future Climate Threats?

Describing genetic diversity in wild barley (Hordeum vulgare ssp. spontaneum) in geographic and environmental space in the context of current, past and potential future climates is important for conservation and for breeding the domesticated crop (Hordeum vulgare ssp. vulgare). Spatial genetic diversity in wild barley was revealed by both nuclear- (2,505 SNP, 24 nSSR) and chloroplast-derived (5 cpSSR) markers in 256 widely-sampled geo-referenced accessions. Results were compared with MaxEnt-modelled geographic distributions under current, past (Last Glacial Maximum, LGM) and mid-term future (anthropogenic scenario A2, the 2080s) climates. Comparisons suggest large-scale post-LGM range expansion in Central Asia and relatively small, but statistically significant, reductions in range-wide genetic diversity under future climate. Our analyses support the utility of ecological niche modelling for locating genetic diversity hotspots and determine priority geographic areas for wild barley conservation under anthropogenic climate change. Similar research on other cereal crop progenitors could play an important role in tailoring conservation and crop improvement strategies to support future human food security