Cantor and band spectra for periodic quantum graphs with magnetic fields

We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant (Lyapunov function) of a suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spectrum is a Cantor set for an irrational flux, and is absolutely continuous and has a band structure for a rational flux. The Dirichlet eigenvalues can be isolated or embedded, subject to the choice of parameters. Conditions for both possibilities are given. We show that generically there are infinitely many gaps in the spectrum, and the Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte

Collaborative Cohort of Cohorts for COVID-19 Research (C4R) Study: Study Design

The Collaborative Cohort of Cohorts for COVID-19 Research (C4R) is a national prospective study of adults comprising 14 established US prospective cohort studies. Starting as early as 1971, investigators in the C4R cohort studies have collected data on clinical and subclinical diseases and their risk factors, including behavior, cognition, biomarkers, and social determinants of health. C4R links this pre-coronavirus disease 2019 (COVID-19) phenotyping to information on severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and acute and postacute COVID-related illness. C4R is largely population-based, has an age range of 18-108 years, and reflects the racial, ethnic, socioeconomic, and geographic diversity of the United States. C4R ascertains SARS-CoV-2 infection and COVID-19 illness using standardized questionnaires, ascertainment of COVID-related hospitalizations and deaths, and a SARS-CoV-2 serosurvey conducted via dried blood spots. Master protocols leverage existing robust retention rates for telephone and in-person examinations and high-quality event surveillance. Extensive prepandemic data minimize referral, survival, and recall bias. Data are harmonized with research-quality phenotyping unmatched by clinical and survey-based studies; these data will be pooled and shared widely to expedite collaboration and scientific findings. This resource will allow evaluation of risk and resilience factors for COVID-19 severity and outcomes, including postacute sequelae, and assessment of the social and behavioral impact of the pandemic on long-term health trajectories

Females increase current reproductive effort when future access to males is uncertain

Trade-offs between current and future reproduction shape life histories of organisms, e.g. increased mortality selects for earlier reproductive effort, and mate limitation has been shown to shape male life histories. Here, we show that female life histories respond adaptively to mate limitation. Female common gobies (Pomatoschistus microps) respond to a female-biased operational sex ratio by strongly increasing the size of their first clutch. The plastic response is predicted by a model that assumes that females use the current competitive situation to predict future difficulties of securing a mating. Because female clutch size decisions are much more closely linked to population dynamics than male life-history traits, plastic responses to mate-finding limitations may be an underappreciated force in population dynamics

Spawning, copulation and inbreeding coefficients in marine invertebrates

Patterns of population genetic variation have frequently been understood as consequences of life history covariates such as dispersal ability and breeding systems (e.g. selfing). For example, marine invertebrates show enormous variation in life history traits that are correlated with the extent of gene flow between populations and the magnitude of differentiation among populations at neutral genetic markers (F(ST)). Here we document an unexpected correlation between marine invertebrate life histories and deviation from Hardy–Weinberg equilibrium (non-zero values of F(IS), the inbreeding coefficient). F(IS) values were significantly higher in studies of species with free-spawned planktonic sperm than in studies of species that copulate or have some form of direct sperm transfer to females or benthic egg masses. This result was robust to several different analytical approaches. We note several mechanisms that might contribute to this pattern, and appeal for more studies and ideas that might help to explain our observations

In vitro fertilization experiments using sockeye salmon reveal that bigger eggs are more fertilizable under sperm limitation

Although theory and widespread evidence show that the evolution of egg size is driven primarily by offspring and maternal fitness demands, an additional explanation invokes sperm limitation as a selective force that could also influence egg size optima. Levitan proposed that constraints from gamete encounter in external fertilization environments could select for enlargement of ova to increase the physical size of the fertilization target. We test this theory using in vitro fertilization experiments in an externally fertilizing fish. Sockeye salmon (Onchorhyncus nerka) females show considerable between-individual variation in ovum size, and we explored the consequences of this natural variation for the fertilization success of individual eggs under conditions of sperm limitation. By engineering consistent conditions where in vitro fertilization rate was always intermediate, we were able to compare the sizes of fertilized and unfertilized eggs across 20 fertilization replicates. After controlling for any changes in volume through incubation, results showed that successfully fertilized eggs were significantly larger than the eggs that failed to achieve fertilization. Under conditions without sperm limitation, fertility was unaffected by egg size. Our findings therefore support Levitan's theory, demonstrating empirically that some element of egg size variation could be selected by fertilization demands under sperm limitation. However, further research on sperm limitation in natural spawnings is required to assess the selective importance of these results

Lonely hearts or sex in the city? Density-dependent effects in mating systems

Two very basic ideas in sexual selection are heavily influenced by numbers of potential mates: the evolution of anisogamy, leading to sex role differentiation, and the frequency dependence of reproductive success that tends to equalize primary sex ratios. However, being explicit about the numbers of potential mates is not typical to most evolutionary theory of sexual selection. Here, we argue that this may prevent us from finding the appropriate ecological equilibria that determine the evolutionary endpoints of selection. We review both theoretical and empirical advances on how population density may influence aspects of mating systems such as intrasexual competition, female choice or resistance, and parental care. Density can have strong effects on selective pressures, whether or not there is phenotypic plasticity in individual strategies with respect to density. Mating skew may either increase or decrease with density, which may be aided or counteracted by changes in female behaviour. Switchpoints between alternative mating strategies can be density dependent, and mate encounter rates may influence mate choice (including mutual mate choice), multiple mating, female resistance to male mating attempts, mate searching, mate guarding, parental care, and the probability of divorce. Considering density-dependent selection may be essential for understanding how populations can persist at all despite sexual conflict, but simple models seem to fail to predict the diversity of observed responses in nature. This highlights the importance of considering the interaction between mating systems and population dynamics, and we strongly encourage further work in this area