The geometry of billiards in ellipses and their poncelet grids

The goal of this paper is an analysis of the geometry of billiards in ellipses, based on properties of confocal central conics. The extended sides of the billiards meet at points which are located on confocal ellipses and hyperbolas. They define the associated Poncelet grid. If a billiard is periodic then it closes for any choice of the initial vertex on the ellipse. This gives rise to a continuous variation of billiards which is called billiard motion though it is neither a Euclidean nor a projective motion. The extension of this motion to the associated Poncelet grid leads to new insights and invariants.

How to approach the study of syndromes in macroevolution

Syndromes, wherein multiple traits evolve convergently in response to a shared selective driver, form a central concept in ecology and evolution. Recent work has questioned the utility and indeed the existence of some of the classic syndromes, such as pollination and seed dispersal syndromes. Here, we discuss some of the major issues that have plagued research into syndromes in macroevolution. First, observation of co-evolving traits (sometimes called “trait syndromes'') is often used as evidence of adaptation to a particular driver, even when the link between traits and adaptation is not well-tested. Second, the study of syndromes often uses a biased sampling approach, focusing on the most extreme examples, which may obscure significant continuous variation between traits. Finally, researchers often focus on the traits that are easiest to measure even though these may not be the most directly relevant to adaptive hypotheses. We argue that these issues can be avoided by combining macroevolutionary studies of trait variation across entire clades with explicit tests of adaptive hypotheses, and that taking this approach will lead to a better understanding of syndrome-like evolution and its drivers.

Population-level survey of loss-of-function mutations revealed that background dependent fitness genes are rare and functionally related in yeast

In natural populations, the same mutation can lead to different phenotypic outcomes due to the genetic variation that exists among individuals. Such genetic background effects are commonly observed, including in the context of many human diseases. However, systematic characterization of these effects at the species level is still lacking to date. Here, we sought to comprehensively survey background-dependent traits associated with gene loss-of-function (LoF) mutations in 39 natural isolates of Saccharomyces cerevisiae using a transposon saturation strategy. By analyzing the modeled fitness variability of a total of 4,469 genes, we found that 15% of them, when impacted by a LoF mutation, exhibited a significant gain- or loss-of-fitness phenotype in certain natural isolates compared to the reference strain S288C. Out of these 632 genetic background-dependent fitness genes identified, a total of 2/3 show a continuous variation across the population while 1/3 are specific to a single genetic background. Genes related to mitochondrial function are significantly overrepresented in the set of genes showing a continuous variation and display a potential functional rewiring with other genes involved in transcription and chromatin remodeling as well as in nuclear-cytoplasmic transport. Such rewiring effects are likely modulated by both the genetic background and the environment. While background-specific cases are rare and span diverse cellular processes, they can be functionally related at the individual level. All background-dependent fitness genes tend to have an intermediate connectivity in the global genetic interaction network and have shown relaxed selection pressure at the population level, highlighting their potential evolutionary characteristics.

Female preferences for discrete and continuous male colour expression may help reinforce colour polymorphism in a desert lizard

Despite recognition that colour can vary continuously, colour expression in colour polymorphic species is usually treated as discrete. We conducted three experiments to evaluate the extent that discrete and continuous male coloration influenced female mating preferences in long-tailed brush lizards (Urosaurus graciosus). Each experiment provided females with a different social context: a dimorphic choice between a yellow and an orange male (coloration treated as discrete), and a choice between either two orange males or two yellow males (coloration treated as continuous variation). Females preferred orange males over yellow males in the first experiment, and the findings of our second experiment suggested that males with moderate orange coloration were most preferred. In contrast, females behaved randomly with respect to two yellow males. Our findings show that females in colour polymorphic species can evaluate both discrete and continuous aspects of morph coloration during mate assessment, which may help maintain their polymorphism.

The limits of egg recognition: testing acceptance thresholds of American robins in response to decreasingly egg-shaped objects in the nest

Some hosts of avian brood parasites reduce or eliminate the costs of parasitism by removing foreign eggs from the nest (rejecter hosts). In turn, even acceptor hosts typically remove most non-egg-shaped objects from the nest, including broken shells, fallen leaves and other detritus. In search for the evolutionary origins and sensory mechanisms of egg rejection, we assessed where the potential threshold between egg recognition and nest hygiene may lie when it comes to stimulus shape. Most previous studies applied comparisons of egg-sized objects with non-continuous variation in shape. Here, instead, we used two series of three-dimensional-printed objects, designed a priori to increasingly diverge from natural eggs along two axes (width or angularity) of shape variation. As predicted, we detected transitions from mostly acceptance to mostly rejection in the nests of American robins Turdus migratorius along each of the two axes. Our methods parallel previous innovations in egg-rejection studies through the use of continuous variation in egg coloration and maculation contrast, to better understand the sensory limits and thresholds of variation in egg recognition and rejection in diverse hosts of avian brood parasites.

Evaluation of Stoichiometry, Stability Constants and Gibbs Free Energies of Acetaminophen-Zn (II) complex at Different Temperatures

Acetaminophen also known as paracetamol, is a drug used in the treatment of pain and fever. It is essentially used for the relief of mild to moderate pain. The presence of phenol and carbonyl oxygen atom enables acetaminophen to behave as a bidentate ligand. The stoichiometry, stability constants and Gibbs free energies of acetaminophen-Zn (II) were determined colorimetrically at 25 and 40 oC using continuous variation and mole ratio methods. The formation of Zn (II) complex with acetaminophen was studied colorimetrically at an absorption maximum of 630 nm at different temperatures. The data showed that Zn (II) and acetaminophen combine in the molar ratio of 1:1 at pH 7.4 with ionic strength maintained using 0.1M KNO3. Calculated stability constants values were 2.70 x 103 and 2.20 x 103 using continuous variation method and 7.21 x 103 and 7.21 x 103 using mole ratio methods at 25 and 40 oC respectively. Calculated ΔGƟ for the complex were - 1.96 x 104 and -1.98 x 104 J using continuous variation method and -2.2 x 104 J and - 2.31 x 104 J using mole ratio method at 25 and 40 oC respectively. The stability constant and Gibbs free energy results suggested that acetaminophen used in the study is a good chelating agent and can be an efficient antidote in the therapy of Zn (II) overload or poisoning. Keywords: Acetaminophen, Zinc, complex, stability constant, Gibbs free energy.