Egg-eating age-structured predators in interaction with age-structured prey

In this paper, we consider a system of integrodifferential equations which models a predator-prey system with both species (predator and prey) age-structured and predators living only on the eggs of prey. The present model is a generalization of the model given in [20]. The existence, stability, and instability of nonnegative equilibria is studied assuming a general fecundity rate function for the prey. With a special choice of fecundity rate function for the predator it is shown here that a large maturation period m of the predator leads to stability. This seems to be contrary to the usual rule of thumb that increasing delays in growth rate responses cause instabilities.     

On Ebenman's model for the dynamics of a population with competing juveniles and adults

A general version of a model of Ebenman for the dynamics of a population consisting of competing juveniles and adults is analyzed using methods of bifurcation theory. A very general existence results is obtained for non-trivial equilibria and non-negative synchronous two-cycles that bifurcate simultaneously at the critical valuer=1 of the inherent net reproductive rater. Stability is studied in this general setting near the bifurcation point and conditions are derived that determine which of these two bifurcating branches is the stable branch. These general results are supplemented by numerical studies of the asymptotic dynamics over wider parameter ranges where various other bifurcations and stable attractors are found. The implications of these results are discussed with respect to the effects on stability that age class competition within a population can have and whether such competition is stabilizing or destabilizing. Supported by National Science Foundation Grant No. DMS-8714810.     

Competing predators for a prey in a chemostat model with periodic nutrient input

A system of ordinary differential equations is used to model the interactions of n competing predators on a single prey population in a chemostat environment with a periodic nutrient input. In the case of one or no predators, criteria for the existence of periodic solutions are given. In the general case, conditions for all populations to persist are derived.Research is in part based on a Ph.D. thesis submitted to the Faculty of Graduate Studies, University of AlbertaResearch is partly supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A4823     

A kinetic study of muscular contractions

Summary In the present work the kinetics of muscular contractions are studied, based on a three-state model which is introduced in Section I. The general properties of this class of models for muscular contractions are derived in Sections II–VI. The kinetic equations are solved for four particular examples in Sections VII–X. These analytical results should be useful for comparison with experimental data to determine the functional dependence of the rate constants and on muscle length.This work was partly supported by the National Research Council of Canada Grant NRC-A4345 and by the Medical Research Council of Canada Grant MRC-MA-3307 through the University of Alberta.     

Intra-specific competition and density dependent juvenile growth

A difference equation model for the dynamics of a semelparous size-structured species consisting of juvenile and adult individuals is derived and studied. The adult population consists of two size classes, a smaller class and a larger more fertile class. Negative feedback occurs through slowed juvenile growth due to increased total population levels during the developmental period and consequently a smaller adult size at maturation. Intra-specific competition coefficients are size dependent and measure the strength of intra-specific competition between juveniles and adults. It is shown that equilibrium states in which adults and juveniles occur together at all times are in general destabilized by significantly increased juvenilevs adults competition with the result that stable periodic cycles appear, in which the generations alternate in time and hence avoid competition. This result supports the tenet that intra-specific competition between juveniles and adults is destabilizing. Exceptions to this destabilization principle are found, however, in which populations exhibiting non-equilibrium, aperiodic dynamics can be equilibrated by increase competition between juveniles and adults. This occurs, for example, when adult fertility and competition coefficients are significantly size class dependent. The author gratefully acknowledges the support of the Applied Mathematics Division and the Population Biology/Ecology Division of the National Science Foundation under NSF grant No. DMS-8902508. Research supported by the Department of Energy under contracts W-7405-ENG-36 and KC-07-01-01.     

The generalized multiplicative model for viability selection at multiple loci

Selection due to differential viability is studied in an n-locus two-allele model using a set indexation that allows the simplicity of the one-locus two-allele model to be carried to multi-locus models. The existence condition is analyzed for polymorphic equilibria with linkage equilibrium: Robbins' equilibria. The local stability condition is given for the Robbins' equilibria on the boundaries in the generalized non-epistatic selection regimes of Karlin and Liberman (1979). These generalized non-epistatic regimes include the additive selection model, the multiplicative selection model and the multiplicative interaction model, and their symmetric versions cover all the symmetric viability models.Research supported by grant no. 11-7805 from the Danish Natural Science Research Council, by NIH grant GM 28016, by a fellowship from the Research Foundation of Aarhus University, and by a visiting fellowship from the University of New England, N.S.W.     

Field evidence that shrimp predation regulates meiofauna

Summary The grass shrimp Palaemonetes pugio, a suspected predator/disturber on meiofauna, and other large natant forms (>2 mm) were selectively excluded from microecosystem tanks for nine months during which time replicability between the tanks was established. Subsequently, shrimp were reintroduced into one of the four tanks via an aquarium and the meiofauna populations monitored in the shrimp and control tanks. In the presence of the predator/disturber, total meiofauna, nematode, oligochaete, and polychaete densities were significantly lower than in control tanks. In the presence of the predator/disturber, total meiofauna, nematode, oligochaete, and polychaete densities were significantly lower than in control tanks. Shrimp predation/disturbance significantly reduced meiofauna abundance in this salt marsh habitat but it did not alter the species diversity of the dominant taxon. The meiobenthos displayed characteristics common to other biologically regulated assemblages and our data provide the first field evidence of macrofaunal control of meiofauna community structure.Research supported by Oceanography Section, National Science Foundation, NSF Grant OCE 72-01573AO2. Contribution No. 217 from the Belle W. Baruch Institute for Marine Biology and Coastal Research     

An analysis of neutral-alleles and variable-environment diffusion models

Three diffusion models are formulated for the evolution of a diploid population with K alleles at one locus with completely symmetric mutation and random genetic drift, a variable-environment, and all the above mechanisms. For the diallelic case, the transient behavior is studied by solving the corresponding diffusion equations by an asymptotic method valid for short time intervals. The transient behavior of the three models is compared for the case when their stationary distributions are identical. The expected amount of heterozygosity is computed using the asymptotic solution and is compared to an exact result. The asymptotic results are extended to the general case with K alleles at the locus for the symmetric mutation and variable-environment models.Research supported by the National Science Foundation under Grant MCS 79-01718     

Characterization of the calcium sensitivity of differentiation in SCC-13 human squamous carcinoma cells

Summary The sensitivity to calcium of the human squamous carcinoma cell line, SCC-13, was demonstrated and characterized. Cultures grown to confluence in the presence of 0.2 to 2 mM calcium had approximately 10-fold higher levels of particulate transglutaminase activity and envelope competence than those grown in low calcium (0.025 to 0.05 mM) medium. Raising the calcium from 0.025 to 1.8 mM induced expression of this enzyme and of competence over the course of a week. Conversely, for cultures grown to confluence in 1.8 mM calcium, subsequent reduction of calcium to 0.025 mM resulted in a substantial decline in transglutaminase over a similar time period. Immunoprecipitable transglutaminase was clearly identifiable in cultures grown in 1.8 mM calcium-containing medium but not in those grown in low calcium medium or in the presence of retinoic acid, suggestive of regulation at the level of mRNA accumulation or translation rather than posttranslational modification. This research was supported by Public Health Service grant AR 27130 from the National Institute of Arthritis, Musculoskeletal and Skin Diseases, Bethesda, MD, and National Research Service postdoctoral fellowship ES 05336 from the National Institute of Environmental Health Sciences, Research Triangle Park, NC.     

6-Phosphogluconate dehydrogenase from Drosophila melanogaster. I. Purification and properties of the a isozyme

6-Phosphogluconate dehyrogenase is evident at all developmental stages of Drosophila melanogaster. The activity level is highest in early third instar larvae and declines to a lower, but relatively constant, level at all later stages of development. The enzyme is localized in the cytosolic portion of the cell. The A-isozymic form of 6-phosphogluconate dehydrogenase was purified to homogeneity and has a molecular weight of 105,000. The enzyme is a dimer consisting of subunits with molecular weights of 55,000 and 53,000. For the oxidative decarboxylation of 6-phosphogluconate the K_m for substrate is 81 µm while that for NADP⁺ is 22.3 µm. The optimum pH for activity is 7.8 while the optimum temperature is 37 C.This work was supported by National Research Council of Canada Grant A5860 and by the University of Calgary Research Policy and Grants Committee.     

Pharmacokinetics of anti-ganglioside GD2 mAb 14G2a in a phase I trial in pediatric cancer patients

A phase I trial of a murine anti-ganglioside (GD2) monoclonal antibody (mAb) 14G2a was conducted in 14 neuroblastoma patients and 1 osteosarcoma patient to assess its safety, toxicity and pharmacokinetics in pediatric patients. The pharmacokinetics of mAb 14G2a were biphasic with at ₁ ^2/ of 2.8±2.8 h and at ₁ ^2/ of 18.3±11.8 h. In general,t ₁ ^2/ was dose-dependent with a level of significance ofP=0.036, and it reached a plateau at doses of 250 mg/m² or more. Overall the peak serum levels were dose-dependent atP<0.001. However, they demonstrated an abrupt increase between doses of 100 mg/m² and 250 mg/m². The latter two suggest a saturable mechanism for mAb elimination. In addition, peak serum concentrations were observed earlier at higher mAb doses, which indicates the achievement of a steady state. Thet ₁ ^2/ of mAb 14G2a in children appears to be shorter than in adults. Furthermore, 2 patients demonstrated a considerable decrease int ₁ ^2/ following retreatment with 14G2a. This was paralleled by high human anti-(mouse Ig) antibody levels. This study represents the first comprehensive analysis of murine mAb pharmacokinetics in children and will be useful in the future design of mAb therapy.This work was supported by grants from FDA, FD-R-000377 and NIH U10 CA 28439 and in part by a grant from the general Clinical Research Center program, MOI RR00827, of the National Center for Research Resources, National Institutes of Health. M. M. U.-F. and C.-S. H. were supported in part by a grant from the Children's Cancer Research Foundation, and R. A. R. was supported in part by NIH grant CA 42508     

Interactions leading to persistence in predator-prey systems with group defence

In previous work (Freedman and Wolkowicz, 1986;Bull. math. Biol. 48, 493–508) it was shown that in a predator-prey system where the prey population exhibits group defence, it is possible that enrichment of the environment could lead to extinction of the predator population. In this paper a third population is introduced and criteria are derived under which persistence of all populations will occur. In particular, criteria for a superpredator and for a competitor to stabilize the system in the sense of persistence are analyzed. Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823. This research was carried out while the author was a visiting scholar at the University of Alberta.     

Juvenile versus adult competition

A general class of age-structured models based upon the McKendrick/von Foerster equations are used to study intraspecific competition between juveniles and adults. Criteria for the existence and stability of equilibria are obtained and the dependence of equilibrium stability (i.e. equilibrium resilience) on competition coefficients is analyzed for low inherent net reproductive numbers. The results are applied to the question of whether juvenile vs. adult intraspecific competition is stabilizing or destabilizing. Two types of competition are studied. The first, involving suppressed adult fertility due to competition from juveniles, was found to be destabilizing in that equilibrium levels are lowered and equilibrium resilience weakened by increased competition. The second, involving increased juvenile mortality due to competition from adults, was found to be considerably more complicated. While equilibrium levels were again reduced by increased competition, equilibrium resilience can either be weakened or strengthened. A criterion for determining the effects on resilience is derived and several examples are given to illustrate various possibilities in this case.The author gratefully acknowledges the support of the Applied Mathematics Division and the Population Biology/Ecology Division of the National Science Foundation under NSF grant No. DMS-8902508Research supported by the Department of Energy under contracts W-7405-ENG-36 and KC-07-01-01     

Global dynamics of a selection model for the growth of a population with genotypic fertility differences

A population growth model is considered for a one locus two allele problem with selection based entirely on fertility differences. A local stability analysis is carried out for the critical points — which include possible polymorphic states — of the resulting nonlinear differential equations. The methods of dynamical systems theory are applied to obtain limiting genotypic proportions for every initial state. Thus the results are global and there are no periodic solutions.Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-8130Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-4823Research supported by NSF Grant MCS 7901069. A portion of the work was carried out while the author was a Visiting Professor at the University of Utah, Salt Lake City, Utah     

Deoxyribonucleic acid synthesis in isolated polytene nuclei of Drosophila hydei

DNA synthesis has been studied in polytene nuclei isolated from larval salivary glands of Drosophila hydei. The incubation conditions employed promote maximum incorporation of TTP-H³ and retention of normal polytene chromosome morphology. The chromosome structure is sensitive to the Mg²⁺ concentration; a normal banding pattern is observed between 4 and 10 mM Mg²⁺. At the optimum pH of 7.8, incorporation continues for over an hour. All four deoxyribonucleoside triphosphates are required for maximum incorporation. The reaction is stimulated by 0.6 mmATP and strongly inhibited at higher ATP concentrations. Competition experiments demonstrate that either TDP or TTP is the effective labeled precursor. The labeled product is sensitive to DNase and has a density identical to that of nuclear DNA. Autoradiographs prepared from spread chromosomes demonstrate that discontinuous and continuous labeling patterns observed in vivo are also produced with isolated nuclei in the absence of cytoplasmic factors. Incubation of the isolated nuclei results in a low level of uniform incorporation that is superimposed on the normal autoradiographic pattern obtained after in vivo labeling. This background incorporation can be greatly increased by prior irradiation of the glands. The presence of exogenous DNA during nuclear incubation stimulates total incorporation. These observations demonstrate that the isolated nuclei possess a reserve synthetic capacity. About 20% of the isolated nuclei are inactive in DNA synthesis.This investigation was supported by PHS Research Grant No. 5 R01 GM 16298 from the National Institute of General Medical Sciences.     

Stability regions in predator-prey systems with constant-rate prey harvesting

Summary We analyze the global behavior of a predator-prey system, modelled by a pair of non-linear ordinary differential equations, under constant-rate prey harvesting. By methods analogous to those used to study predator harvesting, we characterize the theoretically possible structures and transitions. With the aid of a computer simulation we construct examples to show which of these transitions can be realized in a biologically plausible model.Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and the National Research Council of Canada, Grant No. 67-3138.     

Two species competition in a periodic environment

The classical Lotka-Volterra equations for two competing species have constant coefficients. In this paper these equations are studied under the assumption that the coefficients are periodic functions of a common period. As a generalization of the existence theory for equilibria in the constant coefficient case, it is shown that there exists a branch of positive periodic solutions which connects (i.e. bifurcates from) the two nontrivial periodic solutions lying on the coordinate axes. This branch exists for a finite interval or spectrum of bifurcation parameter values (the bifurcation parameter being the average of the net inherent growth rate of one species). The stability of these periodic solutions is studied and is related to the theory of competitive exclusion. A specific example of independent ecological interest is examined by means of which it is shown under what circumstances two species, which could not coexist in a constant environment, can coexist in a limit cycle fashion when subjected to suitable periodic harvesting or removal rates.Research supported by National Science Foundation Grant No. MCS-7901307     

Predator-prey populations with parasitic infection

A predator-prey model, where both species are subjected to parasitism, is developed and analyzed. For the case where there is coexistence of the predator with the uninfected prey, an epidemic threshold theorem is proved. It is shown that in the case where the uninfected predator cannot survive only on uninfected prey, the parasitization could lead to persistence of the predator provided a certain threshold of transmission is surpassed.Support by the Central Research Fund of the University of Alberta is gratefully acknowledgedResearch partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A4823     

Progression age enhanced backward bifurcation in an epidemic model with super-infection

 We consider a model for a disease with a progressing and a quiescent exposed class and variable susceptibility to super-infection. The model exhibits backward bifurcations under certain conditions, which allow for both stable and unstable endemic states when the basic reproduction number is smaller than one. Received: 11 October 2001 / Revised version: 17 September 2002 / Published online: 17 January 2003 Present address: Department of Biological Statistics and Computational Biology, 434 Warren Hall, Cornell University, Ithaca, NY 14853-7801 This author was visiting Arizona State University when most of the research was done. Research partially supported by NSF grant DMS-0137687. This author's research was partially supported by NSF grant DMS-9706787. Key words or phrases: Backward bifurcation – Multiple endemic equilibria – Alternating stability – Break-point density – Super-infection – Dose-dependent latent period – Progressive and quiescent latent stages – Progression age structure – Threshold type disease activation – Operator semigroups – Hille-Yosida operators – Dynamical systems – Persistence – Global compact attractor     

Dynamical synaptic plasticity: a model and connection to some experiments

 Using a modified version of a phenomenological model for the dynamics of synaptic plasticity, we examine some recent experiments of Wu et al. [(2001) J Physiol 533:745–755]. We show that the model is quantitatively consistent with their experimental protocols producing long-term potentiation (LTP) and long-term depression (LTD) in slice preparations of rat hippocampus. We also predict the outcome of similar experiments using different frequencies and depolarization levels than reported in their results. Received: 3 September 2002 / Accepted in revised form: 22 October 2002 / Published online: 24 February 2003 Correspondence to: H.D.I. Abarbanel (e-mail: hdia@jacobi.ucsd.edu) Acknowledgements. We are very grateful to A. Selverston and D. Feldman for conversations about this work. This work was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Engineering and Geosciences, under grants No. DE-FG03-90ER14138 and No. DE-FG03-96ER14592, by a grant from the National Science Foundation, NSF PHY0097134, by a grant from the Army Research Office, DAAD19-01-1-0026, by a grant from the Office of Naval Research, N00014-00-1-0181, and by a grant from the National Institutes of Health, NIH R01 NS40110-01A2. This work was also partially supported by M. Ciencia y Tecnologa BFI2000-0157 (R.H.).