Progress in the Spanish National Barley Breeding Program

The Spanish Barley Breeding Program is carried out by four public research organizations, located at the most representative barley growing regions of Spain. The aim of this study is to evaluate the program retrospectively, attending to: i) the progress achieved in grain yield, and ii) the extent and impact of genotype-by-environment interaction of grain yield. Grain yields and flowering dates of 349 advanced lines in generations F8, F9 and F10, plus checks, tested at 163 trials over 11 years were analized. The locations are in the provinces of Albacete, Lleida, Valladolid and Zaragoza. The data are highly unbalanced because the lines stayed at the program for a maximum of three years. Progress was estimated using relative grain yield and mixed models (REML) to homogenize the results among years and locations. There was evident progress in the program over the period studied, with increasing relative yields in each generation, and with advanced lines surpassing the checks in the last two generations, although the rate of progress was uneven across locations. The genetic gain was greater from F8 to F9 than from F9 to F10. The largest non-purely environmental component of variance was genotype-by-location-by-year, meaning that the genotype-by-location pattern was highly unpredictable. The relationship between yield and flowering time overall was weak in the locations under study at this advanced stage of the program. The program can be continued with the same structure, although measures should be taken to explore the causes of slower progress at certain locations.

Some things couples always wanted to know about stable matchings (but were afraid to ask)

It is well-known that couples that look jointly for jobs in the same centralized labor market may cause instabilities. We demonstrate that for a natural preference domain for couples, namely the domain of responsive preferences, the existence of stable matchings can easily be established. However, a small deviation from responsiveness in one couple's preference relation that models the wish of a couple to be closer together may already cause instability. This demonstrates that the nonexistence of stable matchings in couples markets is not a singular theoretical irregularity. Our nonexistence result persists even when a weaker stability notion is used that excludes myopic blocking. Moreover, we show that even if preferences are responsive there are problems that do not arise for singles markets. Even though for couples markets with responsive preferences the set of stable matchings is nonempty, the lattice structure that this set has for singles markets does not carry over. Furthermore we demonstrate that the new algorithm adopted by the National Resident Matching Program to fill positions for physicians in the United States may cycle, while in fact a stable matchings does exist, and be prone to strategic manipulation if the members of a couple pretend to be single.