Intron Distribution in Ancient Paralogs Supports Random Insertion and Not Random Loss

The intron positions of ten different protein families were examined to determine (the statistical likelihood of) whether spliceosomal introns are the result of random insertion events into previously intronless genes, on the one hand, or the result of random loss from common ancestral introns, on the other. The number of expected matches for the alternative scenarios was calculated for a binomial distribution by considering currently observed introns relative to all possible locations for insertion or loss. Introns occurring at approximately the same location (hereafter called a ``match') were tallied for each of the paired proteins. Matches were identified by their positions in the multiple alignment and were defined as any two introns occurring within a window of 11 possible nucleotide positions, thereby allowing for possible alignment errors and ``intron sliding.' Matches were tallied from the raw data and compared with the expected number of matches for the two different scenarios. The results suggest that the distribution of introns in genes encoding proteins is due to random insertion and not random loss. Received: 8 September 1996 / Accepted: 24 January 1997     

Random binding of dimers to chains

We develop a probabilistic model for the binding of a small linear polymer to a larger chain. We assume that we can approximate the energy of interaction of the two chains by summing the pairwise interactions between subunits. Because the energy of interaction between a pair of subunits can depend on neighboring subunits, which we assume vary along the chain, we assign the pairwise energies of interactions according to a specified probability distribution. Thus we develop a statistical model for the binding of two molecules. While such models may not be appropriate for studying the interaction of a particular pair of molecules, they can provide insight into questions that deal with populations of molecules, such as why do MHC molecules bind peptides of a certain size? Here we analyze in detail the special case of a heterodimer binding to a polymer.     

The effects of diet mixing on consumer fitness: macroalgae, epiphytes, and animal matter as food for marine amphipods

Herbivores are thought to achieve adequate nutrition by consuming numerous species of plants or by occasionally consuming animal tissue. Although active selection of diverse foods is common in nature, the relationship between diet mixing and consumer fitness is poorly understood, especially in marine environments. We studied the fitness-based consequences of dietary mixing in the sympatric amphipods Ampithoe marcuzzii, A. valida, Cymadusa compta, and Gammarus mucronatus by measuring survivorship, growth, and fecundity of these amphipods when they were offered single species of algae, a single animal food, a mixture of algal species, or a combination of algae and animal matter. For the more sedentary, tube-building amphipods A. marcuzzii, A. valida, and C. compta, fitness on mixed algal diets was matched by fitness on at least one of the monospecific algal diets, suggesting that they could benefit from preferential feeding on those algae in the field. The more mobile amphipod, G. mucronatus, survived and grew similarly on the mixed diets and on the filamentous brown alga Ectocarpus siliculosus. However, its fecundity was significantly higher when feeding on the algal and animal mixture than on Ectocarpus alone. Additionally, for G. mucronatus, fitness on mixed algae, mixed algae plus animal matter, and animal matter alone was equivalent, although female growth (but not gonad production) was slightly lower on animal matter alone than on the mixed algae combined with animal food. Thus the more mobile amphipod, G. mucronatus, was the only species able to perform well on animal food alone. In contrast, A. valida and C. compta experienced large negative effects when limited to consuming animal matter alone. For these two species, combining algae and animal matter did not enhance fitness over combining only algae. Fitness effects of specific algal diets showed some general similarities, but also considerable variance among the amphipods. For example, E. siliculosus was generally better food than other algae for all four amphipods, whereas Sargassum filipendula was generally poor. However, A. marcuzzii did not suffer negative effects of consuming only Sargassum. The red alga Polysiphonia sp. and the green alga Enteromorpha flexuosa decreased fitness in A. marcuzzii, C. compta, and G. mucronatus, but not A. valida, and the negative effects of Polysiphonia were considerably larger for A. marcuzzii than for the other amphipods. Our data show that nutritional requirements, even among related species (e.g., A. marcuzzii and A. valida), can be dramatically different. Diet mixing may benefit more mobile consumers like Gammarus that are better able to search for different foods, and may be less important for more sedentary herbivores like Ampithoe and Cymadusa that consume, and live in close association with, individual host plants. Received: 14 September 1998 / Accepted: 22 October 1999     

Genetic modification of lignin concentration affects fitness of perennial herbaceous plants

Populations of four perennial herbaceous species that were genetically modified for altered lignin content (or associated forage digestibility) by conventional plant breeding were evaluated for two agricultural fitness traits, plant survival and plant biomass, in three Northcentral USA environments for more than 4 years. Reduced lignin concentration or increased digestibility resulted in increased winter mortality in two of four species and reduced biomass in one species. Results from other experiment indicate that these apparent genetic correlations may be ephemeral, suggesting that selection for fitness can be successful within high-digestibility or low-lignin germplasm. Results indicate that perennial plants genetically engineered with altered lignin concentration or composition for use in livestock, pulp and paper, or bioenergy production should be evaluated for fitness in field environments prior to use in agriculture. Received: 12 December 2000 / Accepted: 27 February 2001     

Effect of power frequency harmonics on magnetic field measurements

This paper presents a study of the effect of harmonic frequencies on magnetic field measurements. We introduced magnetic field meters in a known magnetic field of different frequencies: power frequency (50 Hz) as well as 3rd (150 Hz) and 5th (250 Hz) harmonic frequencies. Two magnetic field levels (0.25 A and 2.5 A) were used. A Helmholtz coil was applied to generate an exact magnetic field. The difference between the measurement results at harmonic frequencies and at power frequency was analyzed using the t-test for matched pairs. The test results show significant differences (P≤0.01) for 13 out of 28 tests carried out, which is probably due to a curved frequency response near the power frequency. It is, therefore, essential to consider harmonic frequencies in magnetic field measurements in practice. Received: 12 January 1998 / Accepted in revised form: 1 October 1999     

Clutch size manipulations in the chestnut weevil, Curculio elephas: fitness of oviposition strategies

We test the adaptive value of clutch size observed in a natural population of the chestnut weevil Curculio elephas. Clutch size is defined as the number of immatures per infested chestnut. In natural conditions, clutch size averages 1.7 eggs. By manipulating clutch size in the field, we demonstrate that deviations from the theoretical ”Lack clutch size”, estimated as eight immatures, are mainly due to proximate and delayed effects of clutch size on offspring performance. We show the existence of a trade-off between clutch size and larval weight. The latter, a key life-history trait, is highly correlated with fitness because it is a strong determinant of larval survival and potential fecundity of offspring females. The fitness of different potential oviposition strategies characterized by their clutch sizes, ranging from one to nine immatures, was calculated from field- estimated parameters. Chestnut weevil females obtain an evolutionary advantage by laying their eggs singly, since, for instance, fitness of single-egg clutches exceeds fitness of two-egg clutches and four-egg clutches by 8.0% and 15.1% respectively. Received 4 August 1999 / Accepted: 7 October 1999     

Simple models for excitable and oscillatory neural networks

 Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey.. Received: 25 November 1996 / Revised version: 9 December 1997     

Optimization models for the force and energy in competitive running

 In [2] the author has developed an optimization model for the force and energy in competitive running. In this paper the energy processes in the muscle were described by a three-compartment hydraulic model. Here this is reviewed briefly and applied to the current world records in order to determine the key parameters, maximal force, energy reserves and oxygen uptake. These values agree well with those given in the literature and those obtained by other means. The velocity profiles for 100 m sprints are described equally well. The model is then applied to older world records to deduce a relation between the force and energy by linear regression. Finally the fully parameterized model is used to compute the effects of adverse wind and altitude. Inasmuch as there are data available, there is a good agreement. Received 19 July 1995; received in revised form 27 February 1996     

Convergence in almost periodic Fisher and Kolmogorov models

 We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an almost periodic global attractor is also discussed. Received: 11 November 1996 / Revised version: 8 January 1998     

Mapping of the Rf-3 nuclear fertility-restoring gene for WA cytoplasmic male sterility in rice using RAPD and RFLP markers

The cytoplasmic male sterility (CMS) of wild-abortive (WA) cytoplasm has been widely used for breeding hybrid rice. Two restorer genes for the CMS have been found by traditional genetic analysis. To tag the restorer genes we used a set of near-isogenic lines (NILs) of Zhenshan 97 carrying different genotypes for fertility restoration from IR24, to perform RAPD analysis. From the survey of 720 random primers, six RAPD markers were identified to be associated with Rf-3. Three of these OPK05-800, OPU10-1100 and OPW01-350, were mapped on chromosome 1. Two populations from the crosses between Zhenshan 97 A and a near-isogenic restorer line ZSR21 and between Zhenshan 97 A and IR24 were used for mapping Rf-3. The three RAPD markers and three RFLP markers, RG532, RG140 and RG458, were found to be closely linked to Rf-3 in the two populations. The same location of Rf-3 was also found in a population from the cross of IR58025 A//IR36/IR58025 B. At the RG532 locus, different alleles were found between two CMS lines, Zhenshan 97 A and IR58025 A, and between two restorer lines, IR24 and IR36. The use of these molecular markers closely linked to Rf-3 in facilitating the development of hybrid rice is discussed. Received: 3 January 1996 / Accepted: 17 May 1996     

Two SIS epidemiologic models with delays

 The SIS epidemiologic models have a delay corresponding to the infectious period, and disease-related deaths, so that the population size is variable. The population dynamics structures are either logistic or recruitment with natural deaths. Here the thresholds and equilibria are determined, and stabilities are examined. In a similar SIS model with exponential population dynamics, the delay destabilized the endemic equilibrium and led to periodic solutions. In the model with logistic dynamics, periodic solutions in the infectious fraction can occur as the population approaches extinction for a small set of parameter values. Received: 10 January 1997 / 18 November 1997     

Analysis of a mathematical model for the growth of tumors

 In this paper we study a recently proposed model for the growth of a nonnecrotic, vascularized tumor. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. The tumor is assumed to be spherically symmetric, and its boundary is an unknown function r=s(t). We concentrate on the case where at the boundary of the tumor the birth rate of cells exceeds their death rate, a necessary condition for the existence of a unique stationary solution with radius r=R ₀ (which depends on the various parameters of the problem). Denoting by c the quotient of the diffusion time scale to the tumor doubling time scale, so that c is small, we rigorously prove that (i) lim inf _t→∞ s(t)>0, i.e. once engendered, tumors persist in time. Indeed, we further show that (ii) If c is sufficiently small then s(t)→R ₀ exponentially fast as t→∞, i.e. the steady state solution is globally asymptotically stable. Further, (iii) If c is not “sufficiently small” but is smaller than some constant γ determined explicitly by the parameters of the problem, then lim sup _t→∞ s(t)<∞; if however c is “somewhat” larger than γ then generally s(t) does not remain bounded and, in fact, s(t)→∞ exponentially fast as t→∞. Received: 25 February 1998 / Revised version: 30 April 1998     

A generalized transport model for biased cell migration in an anisotropic environment

 A generalized transport model is derived for cell migration in an anisotropic environment and is applied to the specific cases of biased cell migration in a gradient of a stimulus (taxis; e.g., chemotaxis or haptotaxis) or along an axis of anisotropy (e.g., contact guidance). The model accounts for spatial or directional dependence of cell speed and cell turning behavior to predict a constitutive cell flux equation with drift velocity and diffusivity tensor (termed random motility tensor) that are explicit functions of the parameters of the underlying random walk model. This model provides the connection between cell locomotion and the resulting persistent random walk behavior to the observed cell migration on longer time scales, thus it provides a framework for interpreting cell migration data in terms of underlying motility mechanisms. Received: 8 April 1999     

Equivalence of two Fourier methods for biological sequences

 Two methods for defining Fourier power spectra for DNA sequences or other biological sequences are compared. The first method uses indicator sequences for each letter. The second method by Silverman and Linsker assigns to each letter a vertex of a regular tetrahedron in space, and this can be generalized to any dimension. While giving different Fourier transforms, it is shown that the power spectra of the two methods are essentially the same. This is also true if one replaces the Fourier transform in both methods with another linear transform, such as the Walsh transform. Received 4 December 1995     

Persistent solutions for age-dependent pair-formation models

Conditions on the vital rates and the mating function are derived which imply existence or nonexistence of exponentially growing persistent age-distributions for age-dependent pair-formation models.     

A Turing model with correlated random walk

 If in the classical Turing model the diffusion process (Brownian motion) is replaced by a more general correlated random walk, then the parameters describing spatial spread are the particle speeds and the rates of change in direction. As in the Turing model, a spatially constant equilibrium can become unstable if the different species have different turning rates and different speeds. Furthermore, a Hopf bifurcation can be found if the reproduction rate of the activator is greater than its rate of change of direction, and oscillating patterns are possible. Received 24 February 1995; received in revised form 6 September 1995     

Discrete chiasma formation models and their associated high order interference

. We introduce some special chiasma formation processes. First a family of discrete chiasma formation processes is introduced and we determine the nature of higher order interference associated with those processes. Secondly we consider a two-stage chiasma formation process, where the associated recombination frequency between two markers depends not only on their map distance but also on their location along the chromosomes. We characterise under this process, in some cases, the nature of interference between two segments. Received: 22 January 1996 / Revised version: 17 September 1997     

A unifying framework for chaos and stochastic stability in discrete population models

 In this paper we propose a general framework for discrete time one-dimensional Markov population models which is based on two fundamental premises in population dynamics. We show that this framework incorporates both earlier population models, like the Ricker and Hassell models, and experimental observations concerning the structure of density dependence. The two fundamental premises of population dynamics are sufficient to guarantee that the model will exhibit chaotic behaviour for high values of the natural growth and the density-dependent feedback, and this observation is independent of the particular structure of the model. We also study these models when the environment of the population varies stochastically and address the question under what conditions we can find an invariant probability distribution for the population under consideration. The sufficient conditions for this stochastic stability that we derive are of some interest, since studying certain statistical characteristics of these stochastic population processes may only be possible if the process converges to such an invariant distribution. Received 15 May 1995; received in revised form 17 April 1996     

Overcompensatory recruitment and generation delay in discrete age-structured population models

 The effect of overcompensatory recruitment and the combined effect of overcompensatory recruitment and generation delay in discrete nonlinear age-structured population models is studied. Considering overcompensatory recruitment alone, we present formal proofs of the supercritical nature of bifurcations (both flip and Hopf) as well as an extensive analysis of dynamics in unstable parameter regions. One important finding here is that in case of small and moderate year to year survival probabilities there are large regions in parameter space where the qualitative behaviour found in a general n+1 dimensional model is retained already in a one-dimensional model. Another result is that the dynamics at or near the boundary of parameter space may be very complicated. Generally, generation delay is found to act as a destabilizing effect but its effect on dynamics is by no means unique. The most profound effect occurs in the n-generation delay cases. In these cases there is no stable equilibrium X ^* at all, but whenever X ^* small, a stable cycle of period n+1 where the periodic points in the cycle are on a very special form. In other cases generation delay does not alter the dynamics in any substantial way. Received 25 April 1995; received in revised form 21 November 1995