A user's guide to optimal transport

This text is an expanded version of the lectures given by the first author in the 2009 CIME summer school of Cetraro. It provides a quick and reasonably account of the classical theory of optimal mass transportation and of its more recent developments, including the metric theory of gradient flows, geometric and functional inequalities related to optimal transportation, the first and second order differential calculus in the Wasserstein space and the synthetic theory of metric measure spaces with Ricci curvature bounded from below

The role of isospin symmetry in collective nuclear structure

The nucleus is a unique laboratory in physics — a quantum many-body system comprising two types of fermion, the neutron and proton, differing in charge but otherwise essentially identical in their behaviour. The fact that the strong interaction between these fermions is largely independent of charge results in striking symmetries in nuclei. This neutron–proton exchange invariance is encompassed in the elegant concept and formalism of Wigner's isotopic spin — or isospin. The impact of isospin symmetry is maximal near the N=Z line where nuclei have equal numbers of neutrons and protons, and studies involving isospin effects have undergone a resurgence in recent years as such nuclei become more readily accessible. In this review we discuss three isospin-related phenomena: the elegant isospin symmetry of excited analogue states in nuclei, the origin of the extra binding for nuclei with equal numbers of neutrons and protons and the exotic phenomenon of neutron–proton pairing. These three topics, all of considerable current interest, demonstrate the power, simplicity and modern relevance of the isospin concept

Apparent annual survival of staging ruffs during a period of population decline: Insights from sex and site-use related differences

The ruff Philomachus pugnax, a lekking shorebird wintering in Africa and breeding across northern Eurasia, declined severely in its western range. Based on a capture-mark-resighting programme (2004–2011) in the westernmost staging area in Friesland (the Netherlands), we investigated changes in apparent annual survival in relation to age and sex to explore potential causes of decline. We also related temporal variation in apparent survival to environmental factors. We used the Capture- Mark-Recapture multievent statistical framework to overcome biases in survival estimates after testing for hidden heterogeneity of detection. This enabled the estimation of the probability to belong to high or low detectability classes. Apparent survival varied between years but was not related to weather patterns along the flyway, or to flood levels in the Sahel. Over time, a decline in apparent survival is suggested. Due to a short data series and flag loss in the last period this cannot be verified. Nevertheless, the patterns in sex-specific detectability and survival lead to new biological insights. Among highly detectable birds, supposedly most reliant on Friesland, males survived better than females (ΦHDmales = 0.74, range 0.51–0.93; ΦHDfemales = 0.51, range 0.24–0.81). Among low detectable birds, the pattern is reversed (ΦLDmales = 0.64, range 0.37–0.89; ΦLDfemales = 0.73, range 0.48–0.93). Probably the staging population contains a mixture of sexspecific migration strategies. A loss of staging females could greatly affect the dynamics of the western ruff population. Further unravelling of these population processes requires geographically extended demographic monitoring and the use of tracking devices

Is floral divergence sufficient to maintain species boundaries upon secondary contact in Mediterranean food-deceptive orchids?

Analyzing the processes that determine whether species boundaries are maintained on secondary contact may shed light on the early phase of speciation. In Anacamptis morio and Anacamptis longicornu, two Mediterranean orchid sister-species, we used molecular and morphological analyses, together with estimates of pollination success and experimental crosses, to assess whether floral isolation can shelter the species' genomes from genetic admixture on secondary contact. We found substantial genetic and morphological homogenization in sympatric populations in combination with an apparent lack of postmating isolation. We further detected asymmetric introgression in the sympatric populations and an imbalance in cytotype representation, which may be due either to a difference in flowering phenology or else be a consequence of cytonuclear incompatibilities. Estimates of genetic clines for markers across sympatric zones revealed markers that significantly deviated from neutral expectations. We observed a significant correlation between spur length and reproductive success in sympatric populations, which may suggest that directional selection is the main cause of morphological differentiation in this species pair. Our results suggest that allopatric divergence has not led to the evolution of sufficient reproductive isolation to prevent genomic admixture on secondary contact in this orchid species pair