Multiplicity of periodic solutions for systems of weakly coupled parametrized second order differential equations

We prove a multiplicity result of periodic solutions for a system of second order differential equations having asymmetric nonlinearities. The proof is based on a recent generalization of the Poincar\ue9\u2013Birkhoff fixed point theorem provided by Fonda and Ure\uf1a

Phenotypic variation and fitness in a metapopulation of tubeworms (Ridgeia piscesae Jones) at hydrothermal vents

We examine the nature of variation in a hot vent tubeworm, Ridgeia piscesae, to determine how phenotypes are maintained and how reproductive potential is dictated by habitat. This foundation species at northeast Pacific hydrothermal sites occupies a wide habitat range in a highly heterogeneous environment. Where fluids supply high levels of dissolved sulphide for symbionts, the worm grows rapidly in a ‘‘short-fat’’ phenotype characterized by lush gill plumes; when plumes are healthy, sperm package capture is higher. This form can mature within months and has a high fecundity with continuous gamete output and a lifespan of about three years in unstable conditions. Other phenotypes occupy low fluid flux habitats that are more stable and individuals grow very slowly; however, they have low reproductive readiness that is hampered further by small, predator cropped branchiae, thus reducing fertilization and metabolite uptake. Although only the largest worms were measured, only 17% of low flux worms were reproductively competent compared to 91% of high flux worms. A model of reproductive readiness illustrates that tube diameter is a good predictor of reproductive output and that few low flux worms reached critical reproductive size. We postulate that most of the propagules for the vent fields originate from the larger tubeworms that live in small, unstable habitat patches. The large expanses of worms in more stable low flux habitat sustain a small, but long-term, reproductive output. Phenotypic variation is an adaptation that fosters both morphological and physiological responses to differences in chemical milieu and predator pressure. This foundation species forms a metapopulation with variable growth characteristics in a heterogeneous environment where a strategy of phenotypic variation bestows an advantage over specialization

Optimising experimental design for high-throughput phenotyping in mice: a case study

To further the functional annotation of the mammalian genome, the Sanger Mouse Genetics Programme aims to generate and characterise knockout mice in a high-throughput manner. Annually, approximately 200 lines of knockout mice will be characterised using a standardised battery of phenotyping tests covering key disease indications ranging from obesity to sensory acuity. From these findings secondary centres will select putative mutants of interest for more in-depth, confirmatory experiments. Optimising experimental design and data analysis is essential to maximise output using the resources with greatest efficiency, thereby attaining our biological objective of understanding the role of genes in normal development and disease. This study uses the example of the noninvasive blood pressure test to demonstrate how statistical investigation is important for generating meaningful, reliable results and assessing the design for the defined research objectives. The analysis adjusts for the multiple-testing problem by applying the false discovery rate, which controls the number of false calls within those highlighted as significant. A variance analysis finds that the variation between mice dominates this assay. These variance measures were used to examine the interplay between days, readings, and number of mice on power, the ability to detect change. If an experiment is underpowered, we cannot conclude whether failure to detect a biological difference arises from low power or lack of a distinct phenotype, hence the mice are subjected to testing without gain. Consequently, in confirmatory studies, a power analysis along with the 3Rs can provide justification to increase the number of mice used