Population Structure Dynamics Research Articles

Stability and instability of equilibria of an equation of size structured population dynamics

In this paper we consider a quasilinear equation with a nonlinear boundary condition modelling the dynamics of a biological population structured by size. We suppose vital rates depending on the total population. This hypothesis introduces some nonlinearities on the equation and on the boundary condition. We study the existence and uniqueness of solution of the initial value problem and the existence of stationary solutions. After we calculate the spectrum of the linearization at an equilibrium and we study its (local) stability.

Temporal variation in feeding morphology and size-structured population dynamics in fishes.

Considerable variation in morphology associated with resource use is a classic example of local adaptation to the environment. We demonstrate that a temporal change in feeding morphology might occur within a population. In a 5-year natural field experiment, we estimated gill raker morphology, resource density and population dynamics of the roach and its competitor, the perch. Despite a variation in density of zooplankton resources and perch across years, no change in roach density was observed. However, gill raker morphology in roach covaried with size structure of the zooplankton resource across years. A laboratory experiment confirmed that gill raker morphology has a great effect on roach foraging efficiency on zooplankton and that there is a functional trade-off with regard to zooplankton foraging. We suggest that the response in gill raker structure is an adaptation to deal with the rapid population dynamics of zooplankton, which are in turn mediated by changes in the size structure of the competing perch.

Wavefronts and global stability in a time-delayed population model with stage structure

We formulate and study a one–dimensional single–species diffusive–delay population model. The time delay is the time taken from birth to maturity. Without diffusion, the delay differential model extends the well–known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes. This delayed model is known to have simple global dynamics similar to that of the logistic equation. Through the use of a sub/supersolution pair method, we show that the diffusive delay model continues to generate simple global dynamics. This has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics. We also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population, connecting the zero solution of that equation with the positive steady state. Our main finding here is that our fronts appear to be all monotone, regardless of the size of the delay. This is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity, with the front developing a prominent hump in some other delay models.

Physiologically Structured Population Dynamics: A Modeling Perspective

Physiologically Structured Population Dynamics: A Modeling Perspective

Exact and approximate controllability of the age and space population dynamics structured model

We prove exact and approximate controllability for a linear age-dependent and spatially structured population dynamics problem. The birth process is nonlocal, and the demographic functions depends on age, time, and space. Our method relies on the derivation of a Carleman inequality for the backward nonlocal adjoint system.

Pilot study of the genetic diversity of the pneumococcal nasopharyngeal flora among children attending day care centers.

A pilot study was conducted to determine the genetic diversity of multiple colonies of pneumococci recovered from 37 nasopharyngeal (NP) samples of children. A total of 239 pneumococcal isolates (typically, six to eight colonies per sample) were typed by pulsed-field gel electrophoresis (PFGE). In most NP samples (89%) the multiple colonies shared common PFGE types and serotypes. However, four samples were heterogeneous (samples A through D): each contained two strains with different PFGE types, antibiotypes, and serotypes. Samples A and B each contained one strain of a vaccine capsular type and another expressing a non-vaccine type (according to the currently licensed seven-valent conjugate vaccine). In samples B and C the penicillin MIC for one strain was elevated and the other strain was susceptible. In each of the heterogeneous samples, one of the strains was a representative of an internationally disseminated clone. Samples A, C, and D contained strains which carried prophages that were inducible by mitomycin C and that could be visualized by electron microscopy. The comC gene allele (which encodes the competence-stimulating peptide) was the same in both strains found in each of samples A, B, and D. Carriage of multiple pneumococci with distinct properties should favor genetic exchange and provide a dynamic population structure for pneumococci in their ecological reservoir. Quantitative resolution of majority and minority components of the pneumococcal NP flora will be of importance for evaluation of the impact of intervention strategies such as vaccination or introduction of new antimicrobial agents.

Continuous dependence results for a general model of size-dependent population dynamics

We are concerned with a general model of size structured population dynamics with the growth rate depending on the individual's size and time. In this paper, we shall study the continuous dependence of the solution on all given data such as aging and birth functions, growth rate functions and initial data.

Effects of natural disturbance and selective logging onNothofagusforests in south‐central Chile

AimChanges in stand structure, floristic composition and tree population dynamics during the last four centuries were described in southern temperate rain forests. The impacts of natural and anthropogenic disturbance since the late 1560s were examined for old‐growth and logged forests.LocationThe study was conducted in montaneNothofagus alpinaforests in the Andean Range of south‐central Chile. Study sites were located at a range of altitudes between 1000 and 1250 m a.s.l.MethodsTemporal variation in species recruitment and annual dendroecological data were used to determine the historical development and disturbance history of three old‐growth forests, and three stands after selective logging in the late 1880s to early 1900s. Considering the spatial structure of evergreen vs. deciduous elements, the forests are a mixture of deciduous and evergreen tree species.ResultsStem density, maximum stem diameter and basal area differed between the old‐growth and logged stands, but species composition did not. At lower altitudes,N. alpinawas the dominant canopy species in both old‐growth and logged stands, but regeneration ofN. alpinawas significantly different in these stands. At higher altitudes,N. alpinaandN. dombeyiwere the dominant canopy species in both old‐growth and logged stands, and here regeneration patterns of theseNothofagusspecies were similar. After selective logging, in mixed forests of shade‐intolerantNothofagusand more shade‐tolerant trees (such asLaurelia philippiana) there has been a shift in regeneration from more shade‐tolerant resprouting species towardsNothofagus. Major and moderate releases in radial growth, indicative of disturbance, occurred in most of the older trees during the last four centuries, and especially during the last 100 years. Growth rates ofN. alpinaare higher than those of associated shade‐tolerant trees, and apparently increase after disturbances.Main conclusionsResults suggest that under disturbance regimes dominated by treefall gaps, and additionally canopy openings by selective logging, maintenance ofNothofagusspecies appears to be associated with complementary differences in growth rate, sprouting capacity, canopy residence time, and longevity. Such small‐scale canopy openings may help explain the relative abundance ofN. alpinain montane mixed rain forests in the Andean Range, where the maintenance ofNothofagusspecies in many stands has been attributed to a high frequency of coarse‐scale disturbance. My results serve to emphasize that understanding the species coexistence and forest dynamics inNothofagusforests may require attention to interspecific differences in life‐history characteristics.

Carabids in a Spring Wheat Agrocenosis to the South of Sverdlovsk Oblast and the Effect of Insecticide Treatment on Their Populations

Species composition, community structure, and seasonal population dynamics of carabids in spring wheat fields were studied in the vicinity of Yekaterinburg. In addition, the effects of crop treatment with the pyrethroid insecticide Decis on carabid populations was analyzed. The results showed that the numbers, species diversity, and the prevalence of certain trophic groups of carabids changed during the season. After the treatment of small areas with Decis, the number of carabids in catches decreased for a short period of time. During the second and third weeks after the treatment, the numbers of carabids increased above the control level. The structural rearrangement of the carabid community was observed in the areas treated with the insecticide.

Temporal self‐similarity created by spatial individual‐based population dynamics

We report an individual‐based single‐species model producing temporal scale‐free, self‐similar dynamics in time. Individuals in the population renew in an explicit space with a large number of loci. We show that reproduction, subsequent dispersal of the offspring, and mortality will organise population fluctuations such that the emerging dynamics represent power law and scale‐free structures. Further, we show that spatially structured population dynamics may show red frequency spectra, a property that the simple nonlinear population models are generally lacking.

Non‐linear structured population dynamics with co‐variates

Co‐variates are incorporated into a general model of non‐linear structured population dynamics. The proof of the existence and uniqueness of the solutions results from those of a special set, the invariance envelope. It is also valid in presence of state constraints, and solutions need only to have a closed graph (instead of being weakly differentiable as requested in semi‐group theory). Moreover, this invariance envelope provides a simple way to build the solutions, either explicitly in the linear exogenous case, or algo‐rithmically in the non‐linear case, both with co‐variates. The case of age‐structured systems and a model of demographic transition are discussed for illustration.

A Nonlinear Age and Maturity Structured Model of Population Dynamics: I. Basic Theory

A nonlinear model of age and maturity structured population dynamics is analyzed. The population is structured by age and maturity of the individuals and the nonlinearity in the equations corresponds to density dependent limitation of population growth. The existence and asymptotic behavior of solutions are studied.

A Nonlinear Age and Maturity Structured Model of Population Dynamics: II. Chaos

Instability, hypercyclicity and chaos are investigated in a nonlinear model of age and maturity structured population dynamics. It is demonstrated that the behavior of solutions depends on the viewpoint of the observer. Viewed in the direction of age structure the population stabilizes to a regular distribution. Viewed in the direction of maturity structure there is the possibility of chaotic behavior.

INSIGHT INTO SPECIATION FROM HISTORICAL DEMOGRAPHY IN THE PHYTOPHAGOUS BEETLE GENUS OPHRAELLA.

Speciation in phytophagous insects is commonly associated with shifts in host use. Using a phylogenetic framework to identify recently diverged taxa that have undergone a radical host shift, this study focuses on how reconstruction of the historical demography of a species, in conjunction with branching patterns between species, provides insight into mode of speciation. Analyses of mitochondrial cytochrome oxidase I sequences indicate that the leaf beetle Ophraella communa exhibits significant population structure, as shown by patterns of genealogical relationships among mitochondrial haplotypes and high FST -values. However, the absence of regional localization of old clades of haplotypes, negative Tajima's D, and unimodal rather than bimodal frequency distribution of the number of pairwise differences between sequences suggests an absence of long-term barriers to gene flow. Furthermore, we found no evidence of isolation by distance. This pattern of genetic variation is consistent with episodes of gene flow on a large geographic scale, perhaps owing to Pleistocene changes in climate. Ophraella communa and its sister species O. bilineata diverged during the early Pleistocene. The evidence of dynamic population structure in O. communa, potentially including episodic but massive gene flow, suggests that reproductive isolation evolved quite rapidly on a localized geographic scale, because speciation would probably have been reversed by gene flow if the evolution of reproductive isolation had been prolonged. That is, gene flow occasioned by range shifts during the Pleistocene would likely have interrupted speciation unless it occurred very rapidly. Sequence diversity implies a large effective population size (> 106 ) in both O. communa and O. bilineata. However, a model based on a drastic bottleneck did not have a lower likelihood than a model with no bottleneck, simply because the time since speciation has been great enough for coalescence to a single ancestor that existed after the speciation event. Sequence diversity in itself, without reference to the time since speciation, cannot provide evidence on the demography of speciation.

Discrete Event versus Continuous Approach to Reproduction in Structured Population Dynamics

The governing equations are derived for the dynamics of a population consisting of organisms which reproduce by laying one egg at the time, on the basis of a simple physiological model for the uptake and use of energy. Two life stages are assumed, the egg and the adult stage where the adults do not grow. These assumptions hold true, for instance, for rotifers. From the model for the life history of the individuals, a physiologically structured population model for a rotifer population is derived. On the basis of this discrete event reproduction population model a continuous reproduction population model is proposed. The population model together with the equation for the food result in chemostat equations which are solved numerically. We show that for the calculation of the transient population dynamic behaviour after a step-wise change of the dilution rate, an age structure suffices, despite the size and energy structure used to describe the dynamics of the individuals. Aggregation of the continuous reproduction population model yields an approximate lumped parameter model in terms of delay differential equations. In order to assess the performance of the models, experimental data from the literature are fitted. The main purpose of this paper is to discuss the consequences of discrete event versus continuous reproduction. In both population models death by starvation is taken into account. Unlike the continuous reproduction model, the discrete model captures the experimentally observed lack of egg production shortly after the step change in the dilution rate of the chemostat.

Microbial population changes during bioremediation of an experimental oil spill.

Three crude oil bioremediation techniques were applied in a randomized block field experiment simulating a coastal oil spill. Four treatments (no oil control, oil alone, oil plus nutrients, and oil plus nutrients plus an indigenous inoculum) were applied. In situ microbial community structures were monitored by phospholipid fatty acid (PLFA) analysis and 16S rDNA PCR-denaturing gradient gel electrophoresis (DGGE) to (i) identify the bacterial community members responsible for the decontamination of the site and (ii) define an end point for the removal of the hydrocarbon substrate. The results of PLFA analysis demonstrated a community shift in all plots from primarily eukaryotic biomass to gram-negative bacterial biomass with time. PLFA profiles from the oiled plots suggested increased gram-negative biomass and adaptation to metabolic stress compared to unoiled controls. DGGE analysis of untreated control plots revealed a simple, dynamic dominant population structure throughout the experiment. This banding pattern disappeared in all oiled plots, indicating that the structure and diversity of the dominant bacterial community changed substantially. No consistent differences were detected between nutrient-amended and indigenous inoculum-treated plots, but both differed from the oil-only plots. Prominent bands were excised for sequence analysis and indicated that oil treatment encouraged the growth of gram-negative microorganisms within the alpha-proteobacteria and Flexibacter-Cytophaga-Bacteroides phylum. alpha-Proteobacteria were never detected in unoiled controls. PLFA analysis indicated that by week 14 the microbial community structures of the oiled plots were becoming similar to those of the unoiled controls from the same time point, but DGGE analysis suggested that major differences in the bacterial communities remained.

Asymptotic behaviour of a model of hierarchically structured population dynamics

A hierarchically structured population model with a dependence of the vital rates on a function of the population density (environment) is considered. The existence, uniqueness and the asymptotic behaviour of the solutions is obtained transforming the original non-local PDE of the model into a local one. Under natural conditions, the global asymptotical stability of a nontrivial equilibrium is proved. Finally, if the environment is a function of the biomass distribution, the existence of a positive total biomass equilibrium without a nontrivial population equilibrium is shown.

Comments On the Population Structure of the Benthic Marine Isopod Politolana Concharum Collected By the Atlantic Sturgeon, Acipenser Oxyrhynchus

Examination of the stomach contents of 17 Atlantic sturgeons, Acipenser oxyrhynchus, collected over a period extending from November 1992 through June 1994, yielded sufficient numbers (703) of the marine benthic isopod Politolana concharum for an evaluation of its population structure and first order population dynamics. Of the 703 isopods examined, 262 were clearly identified as male and 441 were female; yielding a sex ratio of 1:1.68. A second order polynomial regression, Y = 0.049X2+0.015X-0.066, was found to best describe the length-weight relationship of these isopods. Logarithmic transformation of these data allowed for the determination of the growth coefficient of this population sample, and a statistical test indicated that growth was isometric. The utility of using fish stomach content analysis to gain insights into the population structure and first order population dynamics of invertebrate prey items is discussed.

Local existence for a general model of size‐dependent population dynamics

We shall investigate a size structured population dynamics with aging and birth functions having general forms. The growth rate we deal with depends not only on the size but also on time. We show the existence of a local solution and continuous dependence on the initial data, which shows the uniqueness of the solution as well.

Abstract Perron-Stieltjes integral

Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. \cite4). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. In \cite3 Ch. S. Honig presented a Stieltjes integral for Banach space valued functions. For Honig's integral the Dushnik interior integral presents the background. \endgraf It should be mentioned that abstract Stieltjes integration was recently used by O. Diekmann, M. Gyllenberg and H. R. Thieme in \cite1 and \cite2 for describing the behaviour of some evolutionary systems originating in problems concerning structured population dynamics.