Populations Of Single Species Research Articles

Boundedness, asymptotic behavior and oscillatory properties for the models of single-species population growth with impulsive effect

In this paper, we obtain the boundedness, asymptotic behavior and oscillatory properties for the single logistic models with impulse effect. Some examples are given to indicate the application of our results.

The consequences of seasonal reproductive strategies for the interpretation of settlement trials

Many temperate marine organisms, including the boreo‐arctic barnacle Semibalanus balanoides, have well‐delineated reproductive seasons. The aim of this study was to examine the consequences of small changes in deployment time of settlement experiments within such a settlement season upon long term demographic parameters. Repeat deployments of settlement tiles were made at 1‐week intervals for six weeks during the April 1996 S. balanoides settlement season in the Clyde Sea, UK. The colonies were harvested in November 1996 and density, mortality, fecundity, morphology, and dry weight of eggs, somatic tissue and shell determined. There were non‐linear relationships between density (D) and deployment time (W) (D = 1.11+1.38W‐0.24W 2), and between morphology (M) and deployment time (M = 21.2 + 0.54W‐0.13W 2). There were linear relationships between mortality (L) and deployment time (L = 61.49 ‐ 7.99 W), body weight (B) and deployment time (B = 0.0050 + 0.0012W), shell (S) dry weight and deployment time (S = 0.17 + 0.02W). Egg dry weight did not vary significantly with deployment time. This study demonstrates how small changes in deployment time of settlement can have substantial consequences on the long‐term demographic processes within single species populations. The relationships between deployment, density and other demographic parameters are discussed, as are strategies for dealing with the confounding effects of reproduction.

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POPULATIONS ON FRAGMENTED LANDSCAPES WITH SPATIALLY STRUCTURED HETEROGENEITIES: LANDSCAPE GENERATION AND LOCAL DISPERSAL

The goal of this investigation was to study the effects of spatially structured habitat heterogeneities on locally dispersing single-species populations. In this investigation, the environmental heterogeneities were not randomly distributed, but rather were clustered by specifying probabilities of small local configurations of the landscape, as in local structure or pair approximations. This allows the study of landscapes with the same amount of habitat loss but different levels of fragmentation or clustering. I describe a simple algorithm for generating such structured landscapes. Spatially explicit simulations of population models on these landscapes were performed using stochastic cellular automata and compared to predictions from mean-field and pair approximations, for which detailed derivations are presented. For populations with local dispersal, I show that the spatial correlations of habitat types completely determine equilibrium population density on suitable sites and that the amount of suitable habitat has no effect, precisely the opposite of what the mean-field approximation predicts. When habitat types are randomly distributed on the landscape, the two approximations do almost equally well, and thus the additional complexity of the pair approximation is not justified. However, when habitat types are not randomly distributed, the mean-field approximation gives qualitatively incorrect predictions for population response to varying habitat heterogeneity. Thus, pair approximations combine some of the best features of spatially explicit and implicit models and serve as a useful supplement to those methods for understanding spatially structured ecological systems, especially where environmental heterogeneities are spatially correlated.

Environmental colour affects aspects of single-species population dynamics.

Single-species populations of ciliates (Colpidium and Paramecium) experienced constant temperature or white or reddened temperature fluctuations in aquatic microcosms in order to test three hypotheses about how environmental colour influences population dynamics. (i) Models predict that the colour of population dynamics is tinged by the colour of the environmental variability. However, environmental colour had no effect on the colour of population dynamics. All population dynamics in this experiment were reddened, regardless of environmental colour. (ii) Models predict that populations will track reddened environmental variability more closely than white environmental variability and that populations with a higher intrinsic growth rate (r) will track environmental variability more closely than populations with a low r. The experimental populations behaved as predicted. (iii) Models predict that population variability is determined by interaction between r and the environmental variability. The experimental populations behaved as predicted. These results show that (i) reddened population dynamics may need no special explanation, such as reddened environments, spatial subdivision or interspecific interactions, and (ii) and (iii) that population dynamics are sensitive to environmental colour, in agreement with population models. Correct specification of the colour of the environmental variability in models is required for accurate predictions. Further work is needed to study the effects of environmental colour on communities and ecosystems.

Numerical simulations using a population model of three cladoceran species, Daphnia magna, D. galeata and Bosmina longirostris, in a single-species and a competition environment

Models were simulated for single species and two species together, to study population levels, food assimilation and usage for reproduction, average brood sizes, and effect of two levels of food on the time of first reproduction. In the simulation of a single-species population, both species had higher numbers in abundant environmental food conditions, whereas the smaller species had relatively better numbers than the larger species when food was less abundant. In the simulated two-species competition, the larger species dominated when food was abundant, whereas the smaller B. longirostris outnumbered the larger Daphnia species when food availability was low. The biomass conversion based on the length–weight relationship gave different results: even under low-food conditions the larger species, although few in number, had a clear dominance over their smallerBosmina counterparts in terms of biomass. At both food levels, the proportion of young adults (adolescents) and adults to juveniles was considerably higher in B. longirostris than in the Daphnia species. Extra keyword: assimilation

Stretched exponential survival statistics for microorganisms in radiation field

The so-called concave or tailed survival curves are reported both for multi and single species bacterial populations. Taking as an example Bacillus pumilus , frequently encountered in decontamination studies, it is shown that the tailed survival curves are adequately described by stretched (0< α <1) exponential SF =exp[−( D / D 0 ) α ], where SF denotes the fraction of species surviving the irradiation dose D , D 0 is the effective dose, and α is the dispersion parameter interpreted phenomenologically in terms of radiation sensivity distribution for single species population under the given experimental conditions.

Book Reviews

W.S.C. Gurney & R.M.Nisbet (1998) Ecological Dynamics. Pp. 335. Oxford University Press, New York. £29.95 (cloth), ISBN: 0-19-510443-9 This is a book in three parts: all excellent. The heart of the book is in the middle: four chapters take the reader from models of individuals to models of whole ecosystems via single species populations and interacting populations. This section presents a coherent body of theory for ecological dynamics. It is preceded by three chapters introducing the basic mathematical concepts required to formulate, analyse and understand dynamic models. The last section of the book covers two more difficult topics: physiological and spatial structure. Discrete and continuous approaches are discussed throughout, although by and large the book deals with those situations in which stochasticity is one of the details that can be ignored. The emphasis is on modelling real systems with the aim of understanding how they work. Silly claims about the generality of results from models of nothing in particular are absent. Instead, you get a rigorous and clear approach which stresses the generality of the modelling methods and of many of the dynamic principles presented. I think that this is a very good book at several levels (an irritating admission to have to make, as it deprives me of the chance to be revenged for all those hours spent struggling with the authors’ previous volume). For a start, it presents ecological dynamics as a subject with a coherent body of basic theory, rather than the random selection of rather arbitrary models that it sometimes appears. After reading the book I really felt that I had a better understanding of the subject than I had before. The second outstanding feature is the set of case studies. All but the first three chapters contain several case studies that use the ideas and models presented in the chapter. I found all of these excellent: real biological problems are addressed and answers obtained using simple and carefully constructed models. The breadth of coverage of the case studies is equally impressive, from the growth of a sea urchin to the dynamics of a fjord (the latter being perhaps the best of a good bunch). Furthermore, the reader can try out all the models presented (and more) using software freely available from the book's web site. The text was extensively field tested on undergraduate and postgraduate classes in biology and maths departments in the US, Canada and the UK. It shows. Most of the material is extremely clear and admirably concise: the footnotes used early on to ‘remind’ students of various mathematical facts provide examples of the care taken. Similarly, the high production standards have lead to a text almost free of mathematical typesetting errors: an important feature of a book some of whose audience will lack mathematical self-confidence. At the same time, clarity has not been achieved by omission of challenging material: a fair proportion of the subject matter is of contemporary research interest. The well thought out structure of the whole book is mirrored at the chapter-by-chapter level: key concepts are distinguished from details and chapters build up material in a well thought out manner. As important is the lively and interesting style (only in the first couple of sections of chapter 7 does the approach get somewhat tedious – but my will to live was rapidly restored by the superb case study that follows). Who will find this book useful? It looks like a superb book on which to build a course on ecological dynamic modelling (I wish I’d had it 3 years ago), but it would also be my recommendation for people wanting to teach themselves: not only is the book clear and well thought out, but the freely available modelling software enables the reader to start producing models from chapter 1. Researchers wanting an overview of established theory, jargon de-mystified and an introduction to structure, will also find it invaluable. In short: this is one to buy.

Characterization and diversity of microcystins in natural blooms and strains of the genera Microcystis and Planktothrix from German freshwaters

Fifteen microcystins (MC) were isolated from field samples dominated by Microcystis spp., Planktothrix agardhii or Planktothrix rubescens using reversed phase high-performance liquid chromatography (HPLC). Characterization of microcystins was performed with amino acid analysis followed by fast atom bombardment mass spectrometry (FABMS), and/or matrix assisted laser desorption ionization mass spectrometry (MALDI-TOF MS). In blooms of Microcystis spp. major microcystins were usually MC-RR, MC-YR and MC-LR, while in one strain [D-Asp 3 ] MC-LR and [D-Asp 3 ] MC-RR were also quantitatively abundant. The main microcystins found in field samples of Planktothrix agardhii were [D-Asp 3 ] MC-RR followed by [D-Asp 3 ] MC-LR and a [D-Asp 3 ] variant of MC-HtyR. Planktothrix agardhii strain HUB 076 produced [D-Asp 3 ] MC-RR as a single component. In all Planktothrix rubescens populations [D-Asp 3 , Dhb 7 ] MC-RR was the most abundant microcystin. Furthermore we found that microcystin composition in field populations of single species scarcely changed over time as long as dominance of this species persisted.

On Diffusive Population Models with Toxicants and Time Delays

In this article we study the global stability in reaction-diffusion models for single-species population growth under environmental toxicants with or without time delays. The existence and uniqueness of a positive steady-state solution are established in those models. It is shown that as long as the magnitude of the instantaneous self-limitation and toxicant effects is larger than that of the time-delay effects in the model with delays, the solution of both reaction-diffusion systems has the same asymptotic behavior (extinction or converging to the positive steady-state solution, depending on the growth rate of the species). Numerical simulations for both cases (with or without time delays) are demonstrated for the purpose of comparison.

Distinguishing direct from indirect effects of grazers in intertidal estuarine assemblages

Previous work demonstrated that gastropod grazers ( Bembicium auratum and Austrocochlea porcata) are important in structuring ecological succession in an intertidal estuarine assemblage in New South Wales, Australia. This paper describes work designed to test the hypothesis that the effects of grazers on the intertidal assemblages are primarily indirect, due to their removal of algae. The experiment done to distinguish direct from indirect effects included independent and replicated removals of grazers or algae in a crossed design, along with controls for potential artifacts associated with removals. In addition to specific tests on individual species, a new non-parametric multivariate randomization test (distance-based redundancy analysis, db-RDA) was used to test the hypothesis that simultaneous effects of grazers on the whole assemblage of species were indirect. Results showed that the grazers had indirect positive effects on oysters ( Saccostrea commercialis) and indirect negative effects on some species of barnacles ( Balanus variegatus and B. amphitrite). Other species of barnacles ( Hexaminius sp. and Elminius covertus) were not affected, either by algae or grazers. Multivariate analyses showed that the effects of grazers on the entire assemblage of species were indeed indirect, through their removal of algae. This study highlights the importance of considering the implications of indirect effects of herbivores on the ecology of whole communities, in addition to their impacts on single-species populations.

The Impact of a Copper Gradient on a Microarthropod Field Community

In order to evaluate the power of laboratory toxicity tests to predict the situation in the field, soil microarthropods were studied at the population and community levels in a copper contaminated field, and data were compared to the outcome of single species laboratory tests in the same soil type from a companion study. In addition to copper, the influence of several soil characteristics and plant cover data on soil microarthropod abundance and distribution was tested. Total microarthropod abundance was highest at intermediate copper concentrations, and linearly related to grass biomass. For single species populations no clear picture of abundance in relation to soil copper was seen. Two collembolan species, Folsomia quadrioculata and Folsomia fimetaria, were among the most sensitive. The Shannon-Wiener index of biodiversity decreased linearly with increasing soil copper concentrations. The application of multivariate statistics showed copper to be the parameter best fitting the distribution of microarthropod species in the field. A distinction could be made between sampling points with 50–199 mg Cu/kg soil and those with higher copper concentrations. The species composition of the microarthropod community was not correlated with plant species diversity or total grass biomass, but was affected by a nearby row of tall trees. Community analysis of field data proved as sensitive as laboratory testing, and seemed superior to single species field population data concerning detection of copper effects on soil microarthropods.

Towards a mechanistic model of plankton population dynamics

A plankton population model is developed from literature studies with mechanistic descriptions of interactions of individual plankton cells. Interactions considered include diffusion and convection of nutrients to phytoplankton cell surfaces, light capture by phytoplankton pigment assemblages, sinking rates of phytoplankton cells, and encounter rates of predators and prey. Mechanistic formulations are based on individual species characteristics, obtained from measurements in laboratory experiments, and are functions of local fluid properties such as small-scale turbulence and viscosity. Phytoplankton growth is modelled by analogy to chemical kinetics, and is a function of intracellular nutrient and energy reserves. Results from laboratory experiments on single-species populations found in the literature are used to test the applicability of the functional forms for quantifying interactions of populations of common marine plankton species. These functional forms are then used to construct a system of equations describing plankton population dynamics. Simulations of plankton population dynamics at environmental conditions similar to the oceanic mixed layer at Bermuda (32oN, 65oW) and Ocean Weather Station (OWS) ‘India’ (59oN, 19oW) are performed, and compared to existing models and field data sets.

The stability of nonlinear age-dependent population equation

A kind of size-dependent age-structured single species population equation with a random gestation period is discussed. A generalized population size E, called “the newborn equivalent quantity” is defined. The stability of a positive equilibrium is studied when the control function is chosen to be E. It is proved that if E is unfavorable to both survival and reproduction, the unique positive equilibrium is globally asymptotically stable.

Global attractivity in a discrete model with quadratic nonlinearity

A sufficient condition for the global attractivity of the positive equilibrium point of the delay difference equation, which appears as a model of a single-species population exhibiting the Allee effect in which the per-capita growth rate is a quadratic function of the density and is subject to time delays, is obtained by applying the method of diminishing intervals.

Corridors maintain species richness in the fragmented landscapes of a microecosystem

Theory predicts that species richness or single-species populations can be maintained, or at least extinctions minimized, by boosting rates of immigration. One possible way of achieving this is by establishing corridors of suitable habitat between reserves. Using moss patches as model microecosystems, we provide here probably the first field experimental test of the idea that corridors can reduce the rate of loss of species, and therefore help to maintain species richness. Connecting patches of habitat with corridors did indeed slow the rate of extinction of species, preserving species richness for longer periods of time than in disconnected habitat patches. The pattern of γ-diversity, the cumulative species richness of entire connected systems, is similarly higher than that of fragmented systems, despite the homogenizing effects of movement. Predators are predicted to be more susceptible to fragmentation because of their greater mobility and smaller population sizes. Our data are consistent with this prediction: the proportion of predator species declined significantly in disconnected as compared with connected treatments.

Global attractivity of a single species population model

The asymptotic attractivity of each positive solution to all others is proved for equations having the form dx (t) / dt = a (t) x (t)[1 - L (t,xt)] where a≥ 0 and the linear functional L (t,·) is positive. When the equation is (almost) periodic, sufficient conditions are given for the existence of a positive (almost) periodic solution that is globally attractive. Moreover, similar results are obtained for asymptotically (almost) periodic equations.

Controlling one-dimensional unimodal population maps by harvesting at a constant rate

Controlling chaos and periodic oscillations in dynamical systems is a well known problem. It has been studied by several types of algorithms, some of which were only demonstrated numerically with specific examples. We study here a class of one-dimensional discrete maps of the form ${x}_{n+1}{=f(x}_{n}),$ where $f(x)$ is a unimodal function satisfying a few natural conditions as a model for the dynamics of a single species population. For managing the population we seek to suppress any possible chaotic or periodic behavior that may emerge. The paper proposes a simple, rigorously proved algorithm for controlling unimodal maps, implemented by harvesting the population at a constant rate. This forces the orbits of the map to converge to a limit that we can compute a priori. The result holds for any initial conditions within an interval that we specify. Our control algorithm is easy to implement, requires no updated information on the population and no changes in the parameters of the system, which, in general, are fixed by the properties of the population. It can therefore be useful for exploiting a population while maintaining it at a fixed density.

A novel experimental apparatus to study the impact of white noise and 1/f noise on animal populations.

This paper reports on the design and construction of a novel apparatus that allows a set of aquatic microcosms to experience complex temporal environmental fluctuations. Replicate microcosms were maintained in 18 water baths with independent environmental controls. We give results from a preliminary experiment designed to look at the effects of varying temperatures with different variance spectra (i.e. white noise or 1/f noise) on single species population dynamics. Matching time series (with identical elements, differently ordered) of environmental temperatures with different Fourier spectra were created for use as input to the apparatus using a novel spectral mimicry method. The apparatus functioned well during the course of the experiment making this an extremely useful research tool. This apparatus now provides ecologists with a means of studying how environmental variability and directional trends in this variability, are filtered and translated by real populations and micro-ecosystems.

Allergen contents in Alstroemeria can be reduced by breeding

The allergen content in Alstroemeria was determined by high-performance liquid chromatography (HPLC) in order to investigate breeding possibilities for reducing the risk of contact dermatitis caused by Alstroemeria. The potentials of both cross breeding and mutagenesis were studied. The allergens (6-tuliposide A, tuliposide D and tulipalin A) were determined in leaves, stems, and flowers. 6-Tuliposide A was found in the highest amounts in all plant parts and tulipalin A was mainly present in the flowers. Environmental effects (season and growth conditions) on the allergen content were significant. For the concentration of allergens coefficients of variation generally were above 40% within populations of single species. Positive correlations for 6-tuliposide A between plant parts and between 6-tuliposide A and tulipalin A within leaves and stems were found. Tuliposide D was not correlated with the other allergens. Significant narrow sense heritabilities were found for total allergen content as well as for 6-tuliposide A and tuliposide D, but not for tulipalin A. The heritability was higher for total allergen content and tuliposide D as compared to 6-tuliposide A. Mutagenesis was able to reduce the content of 6-tuliposide A. Allergen production in Alstroemeria seems multigenically controlled.