Coevolutionary interactions between a haploid species and a diploid species

We investigate a general model describing coevolutionary interaction between a haploid population and a diploid population, each with two alleles at a single locus. Both species are allowed to evolve, with the fitness of the genotypes of each species assumed to depend linearly on the frequencies of the genotypes of the other species. We explore the resulting outcomes of these interactions, in particular determining the location of equilibria under various conditions. The coevolution here is much more complex than that between two haploid populations and allows for the possibility of two polymorphic equilibria. To allow for further analysis, we construct a semi-symmetric model. The variety of outcomes possible even in this second model provides support for the geographic mosaic theory of coevolution by suggesting the possibility of small local populations coevolving to very different outcomes, leading to a shifting geographic mosaic as neighboring populations interact with each other through migration.     

Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation and refuge design are discussed. Received: 10 June 1999 / Revised version: 7 July 2000 / Published online: 20 December 2000     

Stability analysis of the partial selfing selection model

We undertake a detailed study of the one-locus two-allele partial selfing selection model. We show that a polymorphic equilibrium can exist only in the cases of overdominance and underdominance and only for a certain range of selfing rates. Furthermore, when it exists, we show that the polymorphic equilibrium is unique. The local stability of the polymorphic equilibrium is investigated and exact analytical conditions are presented. We also carry out an analysis of local stability of the fixation states and then conclude that only overdominance can maintain polymorphism in the population. When the linear local analysis is inconclusive, a quadratic analysis is performed. For some sets of selective values, we demonstrate global convergence. Finally, we compare and discuss results under the partial selfing model and the random mating model.     

Chaos and population disappearances in simple ecological models

A class of truncated unimodal discrete-time single species models for which low or high densities result in extinction in the following generation are considered. A classification of the dynamics of these maps into five types is proven: (i) extinction in finite time for all initial densities, (ii) semistability in which all orbits tend toward the origin or a semi-stable fixed point, (iii) bistability for which the origin and an interval bounded away from the origin are attracting, (iv) chaotic semistability in which there is an interval of chaotic dynamics whose compliment lies in the origin’s basin of attraction and (v) essential extinction in which almost every (but not every) initial population density leads to extinction in finite time. Applying these results to the Logistic, Ricker and generalized Beverton-Holt maps with constant harvesting rates, two birfurcations are shown to lead to sudden population disappearances: a saddle node bifurcation corresponding to a transition from bistability to extinction and a chaotic blue sky catastrophe corresponding to a transition from bistability to essential extinction. Received: 14 February 2000 / Revised version: 15 August 2000 / Published online: 16 February 2001     

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     

Stochastic epidemics in dynamic populations: quasi-stationarity and extinction

Empirical evidence shows that childhood diseases persist in large communities whereas in smaller communities the epidemic goes extinct (and is later reintroduced by immigration). The present paper treats a stochastic model describing the spread of an infectious disease giving life-long immunity, in a community where individuals die and new individuals are born. The time to extinction of the disease starting in quasi-stationarity (conditional on non-extinction) is exponentially distributed. As the population size grows the epidemic process converges to a diffusion process. Properties of the limiting diffusion are used to obtain an approximate expression for τ, the mean-parameter in the exponential distribution of the time to extinction for the finite population. The expression is used to study how τ depends on the community size but also on certain properties of the disease/community: the basic reproduction number and the means and variances of the latency period, infectious period and life-length. Effects of introducing a vaccination program are also discussed as is the notion of the critical community size, defined as the size which distinguishes between the two qualitatively different behaviours. Received: 14 February 2000 / Revised version: 5 June 2000 / Published online: 24 November 2000     

Uniform persistence for sigmoidal diet selection with keystone prey species

In this paper we discuss uniform persistence (UP) criteria of two prey- one predator systems, where we consider that the predator's diet selection is a sigmoidal function of the most profitable prey type in place of a step function of conventional diet choice theory. We also derive UP results of the system with direct interspecific competition between the prey. The role of the most profitable prey item as a keystone species, the magnitude of its carrying capacity, the ability to withstand predation of both prey species, and the ratios of their profitability values (to predators) are important to whether or not adaptive foraging may promote UP. In general, foraging decision rules play no role in UP if the alternative prey item is the keystone species. The result is also not affected by the effect of direct competitive coexistence or dominance relationship of the prey. In some cases, dominance of one of the prey species provides the most advantageous situation for ensuring UP. Received: 1 February 1999 / Revised version: 20 September 1999 / Published online: 4 July 2000     

Coevolution of dispersal in a parasitoid–host system

Interspecific interactions and the evolution of dispersal are both of interest when considering the potential impact of habitat fragmentation on community ecology, but the interaction between these processes is not well studied. We address this by considering the coevolution of dispersal strategies in a host–parasitoid system. An individual-based host–parasitoid metapopulation model was constructed for a patchy environment, allowing for evolution in dispersal rates of both species. Highly rarefied environments with few suitable patches selected against dispersal in both species, as did relatively static environments. Provided that parasitoids persist, all the variables studied led to stable equilibria in dispersal rates for both species. There was a tendency toward higher dispersal rates in parasitoids because of the asymmetric relationships of the two species to the patches: vacant patches are most valuable for hosts, but unsuitable for parasitoids, which require an established host population to reproduce. High host dispersal rate was favoured by high host population growth rate, and in the parasitoid by high growth rates in both species. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

An explicit representation of the Luria–Delbrück distribution

The probability distribution of the number of mutant cells in a growing single-cell population is presented in explicit form. We use a discrete model for mutation and population growth which in the limit of large cell numbers and small mutation rates reduces to certain classical models of the Luria-Delbrück distribution. Our results hold for arbitrarily large values of the mutation rate and for cell populations of arbitrary size. We discuss the influence of cell death on fluctuation experiments and investigate a version of our model that accounts for the possibility that both daughter cells of a non-mutant cell might be mutants. An algorithm is presented for the quick calculation of the distribution. Then, we focus on the derivation of two essentially different limit laws, the first of which applies if the population size tends to infinity while the mutation rate tends to zero such that the product of mutation rate times population size converges. The second limit law emerges after a suitable rescaling of the distribution of non-mutant cells in the population and applies if the product of mutation rate times population size tends to infinity. We discuss the distribution of mutation events for arbitrary values of the mutation rate and cell populations of arbitrary size, and, finally, consider limit laws for this distribution with respect to the behavior of the product of mutation rate times population size. Thus, the present paper substantially extends results due to Lea and Coulson (1949), Bartlett (1955), Stewart et al. (1990), and others.     

A Phylogenetic Perspective on Sequence Evolution in Microsatellite Loci

We examined the evolution of the repeat regions of three noncoding microsatellite loci in 58 species of the Polistinae, a subfamily of wasps that diverged over 140 million years ago. A phylogenetic approach allows two new kinds of approaches to studying microsatellite evolution: character mapping and comparative analysis. The basic repeat structure of the loci was highly conserved, but was often punctuated with imperfections that appear to be phylogenetically informative. Repeat numbers evolved more rapidly than other changes in the repeat region. Changes in number of repeats among species seem consistent with the stepwise mutation model, which is based on slippage during replication as the main source of mutations. Changes in repeat numbers can occur even when there are very few tandem repeats but longer repeats, especially perfect repeats led to greater rates of evolutionary change. Species phylogenetically closer to the one from which we identified the loci had longer stretches of uninterrupted repeats and more different motifs, but not longer total repeat regions. The number of perfect repeats increased more often than it decreased. However, there was no evidence that some species have consistently greater numbers of repeats across loci than other species have, once ascertainment bias is eliminated. We also found no evidence for a population size effect posited by one form of the directionality hypothesis. Overall, phylogenetic variation in repeat regions can be explained by adding neutral evolution to what is already known about the mutation process. The life cycle of microsatellites appears to reflect a balance between growth by slippage and degradation by an essentially irreversible accumulation of imperfections. Received: 13 April 1999 / Accepted: 8 September 1999     

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     

A deterministic size-structured population model for the worm Naidis elinguis

In this paper we model the population dynamics of the worm Nais elinguis, which reproduces by division into two unequal parts. By using renewal theory we derive the asymptotic behaviour of a Naidis elinguis population. In particular we prove a certain relation between the fraction of the population that was born small (respectively the fraction that was born large) and the inter-division times. Received 20 January 1999 / Revised version: 1 August 1999?Published online: 10 April 2001     

Mathematical models and simulations of bacterial growth and chemotaxis in a diffusion gradient chamber

The diffusion gradient chamber (DGC) is a novel device developed to study the response of chemotactic bacteria to combinations of nutrients and attractants [7]. Its purpose is to characterize genetic variants that occur in many biological experiments. In this paper, a mathematical model which describes the spatial distribution of a bacterial population within the DGC is developed. Mathematical analysis of the model concerning positivity and boundedness of the solutions are given. An ADI (Alternating Direction Implicit) method is constructed for finding numerical solutions of the model and carrying out computer simulations. The numerical results of the model successfully reproduced the patterns that were observed in the experiments using the DGC. Received: 3 June 1997 / Revised version: 15 August 2000 / Published online: 20 December 2000     

Neutral and Nonneutral Mitochondrial Genetic Variation in Deep-Sea Clams from the Family Vesicomyidae

Nucleotide sequences at two mitochondrial genes from 57 individuals representing eight species of deep-sea clams (Vesicomyidae) were examined for variation consistent with the neutral model of molecular evolution. One gene, cytochrome oxidase subunit I (COI), deviated from the expectations of neutrality by containing an excess of intraspecific nonsynonymous polymorphism. Additionally, one species, Calyptogena kilmeri, showed a significant excess of rare polymorphism specifically at the COI locus. In contrast, a second mitochondrial gene, the large-subunit 16S ribosomal RNA gene (16S), showed little deviation from neutrality either between or within species. Together, COI and 16S show no deviation from neutral expectations by the HKA test, produce congruent phylogenetic relationships between species, and show correlated numbers of fixed differences between species and polymorphism within species. These patterns of both neutral and nonneutral evolution within the mitochondrial genome are most consistent with a model where intraspecific nonsynonymous polymorphism at COI is near neutrality. In addition to examining the forces of molecular evolution, we extend hypotheses about interspecific relationships within this family for geographical locations previously unexamined by molecular methods including habitats near the Middle Atlantic, the Aleutian Trench, and Costa Rica. Received: 10 March 1999 / Accepted: 13 September 1999     

The necessity of functional proteomics: protein species and molecular function elucidation exemplified by in vivo alpha A crystallin N-terminal truncation

Summary. Ten years after the establishment of the term proteome, the science surrounding it has yet to fulfill its potential. While a host of technologies have generated lists of protein names, there are only a few reported studies that have examined the individual proteins at the covalent chemical level defined as protein species in 1997 and their function. In the current study, we demonstrate that this is possible with two-dimensional gel electrophoresis (2-DE) and mass spectrometry by presenting clear evidence of in vivo N-terminal alpha A crystallin truncation and relating this newly detected protein species to alpha crystallin activity regulation by protease cleavage in the healthy young murine lens. We assess the present state of technology and suggest a shift in resources and paradigm for the routine attainment of the protein species level in proteomics.     

The effect of dispersal on single-species nonautonomous dispersal models with delays

In this paper, single-species nonautonomous dispersal models with delays are considered. An interesting result on the effect of dispersal for persistence and extinction is obtained. That is, if the species is persistent in a patch then it is also persistent in all other patches; if the species is permanent in a patch then it is also permanent in all other patches; if the species is extinct in a patch then it is also extinct in all other patches. Furthermore, some new sufficient conditions for the permanence and extinction of the species in a patch are established. The existence of positive periodic solutions is obtained in the periodic case by employing Teng and Chen's results on the existence of positive periodic solutions for functional differential equations. Received: 26 June 2000 / Revised version: 6 October 2000 / Published online: 10 April 2001     

Posttranslational synthesis of hypusine: evolutionary progression and specificity of the hypusine modification

Summary. A naturally occurring unusual amino acid, hypusine [N ^ɛ-(4-amino-2-hydroxybutyl)-lysine] is a component of a single cellular protein, eukaryotic translation initiation factor 5A (eIF5A). It is a modified lysine with structural contribution from the polyamine spermidine. Hypusine is formed in a novel posttranslational modification that involves two enzymes, deoxyhypusine synthase (DHS) and deoxyhypusine hydroxylase (DOHH). eIF5A and deoxyhypusine/hypusine modification are essential for growth of eukaryotic cells. The hypusine synthetic pathway has evolved in eukaryotes and eIF5A, DHS and DOHH are highly conserved, suggesting maintenance of a fundamental cellular function of eIF5A through evolution. The unique feature of the hypusine modification is the strict specificity of the enzymes toward its substrate protein, eIF5A. Moreover, DHS exhibits a narrow specificity toward spermidine. In view of the extraordinary specificity and the requirement for hypusine-containing eIF5A for mammalian cell proliferation, eIF5A and the hypusine biosynthetic enzymes present new potential targets for intervention in aberrant cell proliferation.     

High population density promotes the evolution of ownership

Previous studies have discussed the evolution of ownership using the Hawk–Dove–Bourgeois game. Decisive parameters are resource values (V) and contest costs (C). However, ownership may also evolve as a result of the effects of population density. To compare the effects of population density with those of resource values, I created a learning-based model of a revised Hawk–Dove–Bourgeois game. The game simulates the dynamics of agents that struggle for regions (“territories”) along a line. With appropriate sets of r (resource value) and l (reciprocal of the population density), the model showed that ownership is more likely to evolve when the resource value is small and population density is high. An area containing high-value resources is likely to accompany high population density. However, simulations showed that population density has stronger effects than resource value on the evolution of ownership.     

The effect of density-dependent treatment and behavior change on the dynamics of HIV transmission

In this work, we propose a model for heterosexual transmission of HIV/AIDS in a population of varying size with an intervention program in which treatment and/or behavior change of the infecteds occur as an increasing function of the density of the infected class in the population. This assumption has socio-economic implications which is important for public health considerations since density-dependent treatment/behavior change may be more cost-saving than a program where treatment/behavior change occurs linearly with respect to the number of infecteds. We will make use of the conservation law of total sexual contacts which enables us to reduce the two-sex model to a simpler one-sex formulation. Analytical results will be given. Unlike a similar model with linear treatment/behavior change in Hsieh (1996) where conditions were obtained for the eradication of disease, we will show that density-dependent treatment/behavior change cannot eradicate the disease if the disease is able to persist without any treatment/behavior change. This work demonstrates the need to further understand how treatment/behavior change occurs in a society with varying population.     

Asymmetrical (ADMA) and symmetrical dimethylarginine (SDMA) as potential risk factors for cardiovascular and renal outcome in chronic kidney disease – possible candidates for paradoxical epidemiology?

Summary. Background: Asymmetrical dimethylarginine (ADMA) is an inhibitor of nitric-oxide synthase. It has been linked to atherosclerotic risk in the general population as well as in end-stage renal disease patients (ESRD), whereas symmetrical dimethylarginine (SDMA) is thought to be biological inactive. Prospective data concerning the role of both dimethylarginines are rare in patients with chronic kidney disease. Methods: 200 patients with chronic kidney disease (mean age 57.6 ± 13.0 years, 69 female, 131 male); 82 with chronic renal failure (CRF), 81 on maintenance haemodialysis (HD) and 37 renal transplant recipients (RTR) were prospectively followed for 24 months. ADMA and SDMA were measured by HPLC. The relation of plasma levels of ADMA and SDMA together with conventional risk factors for the cardiovascular and renal outcome was investigated with Cox proportional hazards model. Results: Mean serum levels of SDMA were significantly increased in all groups compared to the control group (P ≤ 0.0005), ADMA was increased only in HD and RTR (P ≤ 0.004). Forty-seven cardiovascular events (CVE) occurred during follow-up, 35 patients died, and 39 patients reached ESRD. Multivariate analysis showed diabetes (RR 3.072, P = 0.01), ESRD (RR 11.915, P < 0.0005), elevated CRP levels (RR 3.916, P < 0.0005) and surprisingly a lower ADMA level (RR 0.271, P = 0.008) as independent risk factors for CVE. Serum creatinine (RR 11.378, P = 0.001), haemoglobin (RR 0.710, P = 0.038 for an increment of 1 mmol/l), and SDMA levels (RR 1.633, P = 0.006, per 1 μmol/l increment) were predictors for the progression to ESRD. Conclusions: Data from a heterogeneous group of patients with chronic kidney disease provide evidence that conventional risk factors seem to play a more important role than elevated serum levels of ADMA or SDMA for cardiovascular events. Increasing serum SDMA concentration seems to play an additive role for the renal outcome besides serum creatinine and haemoglobin levels. Whether ADMA might possibly be a candidate for the phenomenon of “paradoxical epidemiology” in chronic kidney disease needs further investigation.