The Lee-Yang and P\'olya-Schur Programs. I. Linear Operators Preserving Stability

In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis, probability theory, combinatorics, and matrix theory. We characterize all linear operators on finite or infinite-dimensional spaces of multivariate polynomials preserving the property of being non-vanishing whenever the variables are in prescribed open circular domains. In particular, this solves the higher dimensional counterpart of a long-standing classification problem originating from classical works of Hermite, Laguerre, Hurwitz and P\'olya-Schur on univariate polynomials with such properties.Comment: Final version, to appear in Inventiones Mathematicae; 27 pages, no figures, LaTeX2

Data from: Cascading effects of host plant inbreeding on the larval growth, muscle molecular composition, and flight capacity of an adult herbivorous insect.

A primary function of adult winged insects is dispersal. Limiting larval dietary intake (partial starvation) has been shown to affect the flight muscle metabolism of adult moths reared on artificial diet, but a more ecologically relevant question is whether natural variation in host plant quality can lead to differences in the flight capacity of adult insects. Recent studies have shown that inbreeding compromises plant anti-herbivore defenses. We created inbred and outbred progeny from locally collected horsenettle (Solanum carolinense L.) and examined how host plant inbreeding affects the growth, development, and flight muscle physiology of tobacco hornworm (Manduca sexta L.), a specialist herbivore on Solanaceae. We tested the hypothesis that within population genetic variation in host plant quality, resulting from inbreeding, can create significant changes to the larval development and flight physiology of an adult insect. We found that Manduca larvae reared on inbred horsenettle plants grew faster and developed into larger pupae compared to larvae reared on outbred plants. Adult flight metabolic rate was greater in adults reared on inbred plants compared to outbred plants, and this elevation was independent of body mass when we excluded one plant family that produced small, low metabolic rate moths regardless of breeding regime. Differences in mass-specific flight metabolism were associated with changes in alternative splicing of Troponin t, a flight muscle protein that regulates muscle contraction. These results show that host plant inbreeding can create effects that cascade through larval and pupal development to affect dispersal-related traits of the adult stage. Hence, plant inbreeding may also impact herbivore population dynamics, particularly their ability to spread away from, and possibly into, isolated patches of inbred plants creating increased herbivore pressure on these plant populations. More generally, our findings reveal that changes in population biology at one trophic level can affect the metabolic physiology and flight capacity of an animal at a higher trophic level

A candidate locus for variation in dispersal rate in a butterfly metapopulation

Frequent extinctions of local populations in metapopulations create opportunities for migrant females to establish new populations. In a metapopulation of the Glanville fritillary butterfly (Melitaea cinxia), more mobile individuals are more likely to establish new populations, especially in habitat patches that are poorly connected to existing populations. Here we show that flight metabolic rate and the frequency of a specific allele of the metabolic enzyme phosphoglucose isomerase (pgi) were both highest in newly established, isolated populations. Furthermore, genotypes with this pgi allele had elevated flight metabolic rates. These results suggest that genetic variation in pgi or a closely linked locus has a direct effect on flight metabolism, dispersal rate, and thereby on metapopulation dynamics in this species. These results also contribute to an emerging understanding of the mechanisms by which population turnover in heterogeneous landscapes may maintain genetic and phenotypic variation across populations