Oscillatory reaction-diffusion equations on rings

We study the behavior of traveling waves in - systems on both homogeneous and inhomogeneous rings. The stability regions in parameter space of - waves were previously known [15, 19]; the results are extended here. We show the existence of Hopf bifurcations of traveling waves and the stability of the limit cycles born at the Hopf bifurcation for some parameter ranges. Using a Lindstedt-type perturbation scheme, we formally construct periodic solutions of the - system near a Hopf bifurcation and show that the periodic solutions superimposed on the original traveling wave have the effect of altering its overall frequency and amplitude. We also study the - system on an annulus ofvariable width, which does not possess reflection symmetry about any axis. We formally construct traveling waves on this variable-width annulus by a perturbation scheme, and find that perturbing the width of the annulus alters the amplitude and frequency of traveling waves on the domain by a small (order ²) amount. For typical parameter values, we find that the speed, frequency, and stability are unaffected by the direction of travel of the wave on the annulus, despite the rotationally asymmetric inhomogeneity. This indicates that the - system on a variable-width domain cannot account for directional preferences of traveling waves in biological systems.     

Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations

In this paper we use a dynamical systems approach to prove the existence of a unique critical value c ^* of the speed c for which the degenerate density-dependent diffusion equation u _ct = [D(u)u _x ] _x + g(u) has: 1. no travelling wave solutions for 0 < c < c ^*, 2. a travelling wave solution u(x, t) = (x - c ^* t) of sharp type satisfying (– ) = 1, () = 0 ^*; '(^*–) = – c ^*/D'(0), '(^*+) = 0 and 3. a continuum of travelling wave solutions of monotone decreasing front type for each c > c ^*. These fronts satisfy the boundary conditions (– ) = 1, '(– ) = (+ ) = '(+ ) = 0. We illustrate our analytical results with some numerical solutions.     

Exothermic responses of dormant Salix stems during exposure to subzero temperatures

Differential thermal analysis (DTA) was used to determine the exothermic responses in dormant stems and excised lengths of stem of Salix dasyclados Wimmer subjected to artificial freezing treatments.
The presence of ice on the surfaces of intact stems restricted the mechanism of freezing avoidance to temperatures above –4°C. In contrast, excised lengths of stem started to freeze as soon as the ambient temperature fell below –2°C, demonstrating that extracellular ice formation takes place earlier if cut surfaces are present. Exposure of dormant excised lengths of stem to subfreezing temperatures for more than 8 weeks did not alter their nucleation temperature not their exothermic differential responses. Early extracellular crystallisation of freezable cellular water provides conditions that allow dormant Salix dasyclados stems or excised lengths of stem to survive extreme freezing stress.
Crystallisation of extracellular and cellular water took place in the cortex, and did not result in visual damage or reduced survival. This nucleation of extracellular water took place over the same temperature range whether the excised dormant lengths of stem were partly (bark only) or completely thawed. Exposure of dormant tissue to 20°C for up to 24 h did not alter the level of freezing tolerance, nor did it increase the susceptibility of excised lengths of stem to damage by extreme temperature fluctuations.     

FEMALE REPRODUCTIVE EFFORT DEPENDS ON THE DEGREE OF ORNAMENTATION OF THEIR MATES

Sexual selection theory assumes that secondary sexual characters do not influence female reproductive effort. Female animals may invest relatively more in reproduction if they acquire mates of high phenotypic quality, because offspring sired by preferred males may be relatively more viable than offspring sired by less preferred males. Here we report for the first time in a field study that females of the monogamous barn swallow Hirundo rustica adjust their reproductive effort to the attractiveness of their mates. Experimental manipulation of male tail length, which is a trait currently subject to a directional female mating preference, affected the reproductive effort by females in single broods as well as their decision on the seasonal number of clutches. These results, and those of previous experiments, demonstrate that female barn swallows assess the quality of their mates throughout the reproductive season and adjust their reproductive decisions accordingly. This result has important implications for the theory of sexual selection and for the possibility of testing current models of female mate preferences, because the viability of offspring will be confounded by differential reproductive effort.     

Rapid changes in amplification and methylation pattern of genomic DNA in cultured carrot root explants (Daucus carota L.)

Summary Rapid genomic DNA variation due to methylation and copy number alteration was observed in carrot root explants 6 h after inoculation and during a 36-h period of exponential callus growth. De novo methylation and amplification of restricted BspNI fragments of low molecular weight occurred before cell cycle activation and should, therefore, be independent of progression through the S-phase of the cell cycle. Growth regulators seemed to influence the amplification pattern indirectly by regulating cell division activity. In exponentially growing callus tissue the copy number of most of the repetitive fragments was dramatically reduced. It is presumed that this reduction in the copy number of repetitive fragments is characteristic of rejuvenilization. 3-Indole-acetic-acid (IAA) and inositol in the medium increased the degree of unspecific genomic DNA methylation in growing rhizogenic carrot callus tissue in the absence of kinetin, which inhibits root induction at that stage. A possible relation to the induction of rhizogenesis is considered. The observed reduction in number of repetitive restriction fragments and the increase in DNA methylation are gross changes covering the total genome. The results are discussed in relation to the controversy concerning the general biological significance of the methylation and amplification of DNA sequences.     

A deterministic analysis of self-incompatibility alleles

A number of plant species have a self-incompatibility locus that prevents self-fertilization. We 'analyse a deterministic model with an arbitrary number of alleles. We prove that the only polymorphic equilibrium is the one for which all (heterozygous) genotypes are equally frequent, and we prove that all (initially) polymorphic populations converge to this equilibrium.     

Evaluating treatment effects in group sequential multivariate longitudinal studies with covariate adjustment

Jeffries et al. (2018) investigated testing for a treatment difference in the setting of a randomized clinical trial with a single outcome measured longitudinally over a series of common follow-up times while adjusting for covariates. That paper examined the null hypothesis of no difference at any follow-up time versus the alternative of a difference for at least one follow-up time. We extend those results here by considering multivariate outcome measurements, where each individual outcome is examined at common follow-up times. We consider the case where there is interest in first testing for a treatment difference in a global function of the outcomes (e.g., weighted average or sum) with subsequent interest in examining the individual outcomes, should the global function show a treatment difference. Testing is conducted for each follow-up time and may be performed in the setting of a group sequential trial. Testing procedures are developed to determine follow-up times for which a global treatment difference exists and which individual combinations of outcome and follow-up time show evidence of a difference while controlling for multiplicity in outcomes, follow-up, and interim analyses. These approaches are examined in a study evaluating the effects of tissue plasminogen activator on longitudinally obtained stroke severity measurements.     

QUALITATIVE ANALYSIS OF BIOECOLOGY DIFFERENTIAL SYSTEM

In this paper, the author studies the quartic bioecology differential system:Here n and q are positive constants, l、m and p are constants. The author also proves some theorems of existence and uniqueness of limit cycles of this differential system.