Single-species Population Dynamics Research Articles

Linking optimization and ecological models in a decision support tool for oyster restoration and management

Restoration of ecologically important marine species and habitats is restricted by funding constraints and hindered by lack of information about trade-offs among restoration goals and the effectiveness of alternative restoration strategies. Because ecosystems provide diverse human and ecological benefits, achieving one restoration benefit may take place at the expense of other benefits. This poses challenges when attempting to allocate limited resources to optimally achieve multiple benefits, and when defining measures of restoration success. We present a restoration decision-support tool that links ecosystem prediction and human use in a flexible "optimization" framework that clarifies important restoration trade-offs, makes location-specific recommendations, predicts benefits, and quantifies the associated costs (in the form of lost opportunities). The tool is illustrated by examining restoration options related to the eastern oyster, Crassostrea virginica, which supported an historically important fishery in Chesapeake Bay and provides a range of ecosystem services such as removing seston, enhancing water clarity, and creating benthic habitat. We use an optimization approach to identify the locations where oyster restoration efforts are most likely to maximize one or more benefits such as reduction in seston, increase in light penetration, spawning stock enhancement, and harvest, subject to funding constraints and other limitations. This proof-of-concept Oyster Restoration Optimization model (ORO) incorporates predictions from three-dimensional water quality (nutrients-phytoplankton zooplankton-detritus [NPZD] with oyster filtration) and larval transport models; calculates size- and salinity-dependent growth, mortality, and fecundity of oysters; and includes economic costs of restoration efforts. Model results indicate that restoration of oysters in different regions of the Chesapeake Bay would maximize different suites of benefits due to interactions between the physical characteristics of a system and nonlinear biological processes. For example, restoration locations that maximize harvest are not the same as those that would maximize spawning stock enhancement. Although preliminary, the ORO model demonstrates that our understanding of circulation patterns, single-species population dynamics and their interactions with the ecosystem can be integrated into one quantitative framework that optimizes spending allocations and provides explicit advice along with testable predictions. The ORO model has strengths and constraints as a tool to support restoration efforts and ecosystem approaches to fisheries management.

Age-dependent single-species population dynamics with delayed argument

The model of age-dependent population dynamics was for the first time described by McKendrick (1926). This model was based on the first-order partial differential equation with the standard initial condition and the non-local boundary condition in integral form. Gurtin and MacCamy in their paper (1974) analyzed a more general model, where the progress of the population depends on its number. They proved the existence of the unique solution to their model for all time. In our paper the results of Gurtin and MacCamy will be generalized on the case, when the dependence on a number of a population is delayed. Copyright © 2009 John Wiley & Sons, Ltd.

A paradox in discrete single species population dynamics with harvesting/thinning

We analyze a general time-discrete mathematical model of single species population dynamics with the intraspecific density effect and the harvesting/thinning effect. We harvest a portion of the population at a moment in each year. We investigate the condition under which the harvesting/thinning causes an eventual increase of its population at the equilibrium, and show that such a paradoxical increase could occur for the discrete single species population dynamics with a large family of density effect functions. Some typical models are analyzed in detail according to the possibility of the paradox emergence. Our result implies that the contest competition would never cause the paradox, while the scramble competition would be likely to cause it.

Development and Application of Crop Growth Simulation Modelling in Pest Management

Crop growth simulation models based on crop ecological and physiological processes, and coupled with pest damage mechanisms, are useful tools for analysing the interaction of pests with other biophysical components of agroecosystems. The use of simulation models in pest management started with the development of single-species population dynamics models in the late 1960s. Later, population dynamics models for bitrophic interactions between pests and natural enemies were devised. Crop growth simulation models were coupled with pest damage mechanisms in the mid-80s, but the approach was described as a one-way analysis of crop–pest interactions because these models accounted for pest effects on crop growth without the reverse being considered. A two-way approach for crop–pest interactions came into being with the interlinking of pest population dynamics models with crop growth simulation models in the 1990s. Pest management research is required to produce practical tools for developing tactics and strategies for pest management. Simulation models help to produce such tools and decision models. They are used for various applications, such as rationalizing pesticide use, pest risk analysis, pest zonation, analysis of climate change impact on pests, and assessing the effect of transgenic crops on the environment. These models have the potential to play even greater roles in the future.

A New BEAST: Bayesian Software Tools for Ecological Trend Analysis

Many software tools available to biologists are either case-specific or require the ability to write computer programs. The learning curve for newer Bayesian approaches is much steeper than traditional approaches, often requiring an investment of several years. This article introduces a new free software package, BEAST (Bayesian Ecological Analysis of Statistical Trends), for Bayesian estimation of population trends, which requires the user to do no programming. A wide range of single-species population dynamics models are supported, including single-stage population models, stage-structured population models, and age-structured population models. In addition to Bayesian parameter estimation, this software allows users to do population projections, and may be used as a teaching tool by agencies and universities. I provide an example of a theta-logistic population model of stock pigeon (Columba oenas) breeding pairs. The degree of density dependence for this population was found to be stronger when compared to maximum likelihood parameter estimates available from the literature. Short-term population projections indicate that the number of breeding pairs is relatively stable, indicating that the population is at (or near) carrying capacity. This result is in agreement with the most recent data available, which indicate the breeding counts have remained relatively constant.

Two‐species asymmetric competition: effects of age structure on intra‐ and interspecific interactions

1. The patterns of density-dependent resource competition and the mechanisms leading to competitive exclusion in an experimental two-species insect age-structured interaction were investigated. 2. The modes of competition (scramble or contest) and strength of competition (under- to overcompensatory) operating within and between the stages of the two species was found to be influenced by total competitor density, the age structure of the competitor community and whether competition is between stages of single or two species. 3. The effect of imposed resource limitation on survival was found to be asymmetric between stages and species. Environments supporting both dominant and subordinate competitors were found to increase survival of subordinate competitors at lower total competitor densities. Competitive environments during development within individual stage cohorts (i.e. small or large larvae), differed from the competitive environment in lumped age classes (i.e. development from egg-->pupae). 4. Competition within mixed-age, stage or species cohorts, when compared with uniform-aged or species cohorts, altered the position of a competitive environment on the scramble-contest spectrum. In some cases the competitive environment switched from undercompensatory contest to overcompensatory scramble competition. 5. Such switching modes of competition suggest that the relative importance of the mechanisms regulating single-species population dynamics (i.e. resource competition) may change when organisms are embedded within a wider community.

Analysis on the critical speed of traveling waves

The note is concerned with a time-delayed reaction–diffusion equation with nonlocality for the population dynamics of single species. For the critical speed of traveling waves, we give a detailed analysis on its location and asymptotic behavior with respect to the parameters of the diffusion rate and mature age, respectively.

Effect of dispersal at range edges on the structure of species ranges

Range edges are of particular interest to ecology because they hold key insights into the limits of the realized niche and associated population dynamics. A recent feature of Oikos summarized the state of the art on range edge ecology. While the typical question is what causes range edges, another important question is how range edges influence the distribution of abundances across a species geographic range when dispersal is present. We used a single species population dynamics model on a coupled‐lattice to determine the effects of dispersal on peripheral populations as compared to populations at the core of the range. In the absence of resource gradients, the reduced neighborhood and thus lower connectivity or higher isolation among populations at the range edge alone led to significantly lower population sizes in the periphery of the range than in the core. Lower population sizes mean higher extinction risks and lower adaptability at the range edge, which could inhibit or slow range expansions, and thus effectively stabilize range edges. The strength of this effect depended on the potential population growth rate and the maximum dispersal distance. Lower potential population growth rates led to a stronger effect of dispersal resulting in a higher difference in population sizes between the two areas. The differential effect of dispersal on population sizes at the core and periphery of the range in the absence of resource gradients implies that traditional, habitat‐based distribution models could result in misleading conclusions about the habitat quality in the periphery. Lower population sizes at the periphery are also relevant to conservation, because habitat removal not only eliminates populations but also creates new edges. Populations bordering these new edges may experience declines, due to their increased isolation.

From the discrete to the continuous: Relationships and results for single-species population models

To be useful, and therefore successful, a model of single-species population dynamics should be: a satisfactory description of the experimental and natural settings; useful for opening new doors of understanding of population dynamics; and capable of incorporation into more complex models of intra- and inter-specific interaction. In this paper, we compare the qualitative and quantitative features of several simple one-species ‘density-functional’ population models. Furthermore, we derive novel analytic results pertaining to various regimes of population behaviour and investigate in detail the relationships between different types of mathematical functionality. We propose and critique novel models, generated in both ad hoc and systematic fashion from existing population functionals.

Climatic effects on the phenology of lake processes

AbstractPopulations living in seasonal environments are exposed to systematic changes in physical conditions that restrict the growth and reproduction of many species to only a short time window of the annual cycle. Several studies have shown that climate changes over the latter part of the 20th century affected the phenology and population dynamics of single species. However, the key limitation to forecasting the effects of changing climate on ecosystems lies in understanding how it will affect interactions among species. We investigated the effects of climatic and biotic drivers on physical and biological lake processes, using a historical dataset of 40 years from Lake Washington, USA, and dynamic time‐series models to explain changes in the phenological patterns among physical and biological components of pelagic ecosystems. Long‐term climate warming and variability because of large‐scale climatic patterns like Pacific decadal oscillation (PDO) and El Niño–southern oscillation (ENSO) extended the duration of the stratification period by 25 days over the last 40 years. This change was due mainly to earlier spring stratification (16 days) and less to later stratification termination in fall (9 days). The phytoplankton spring bloom advanced roughly in parallel to stratification onset and in 2002 it occurred about 19 days earlier than it did in 1962, indicating the tight connection of spring phytoplankton growth to turbulent conditions. In contrast, the timing of the clear‐water phase showed high variability and was mainly driven by biotic factors. Among the zooplankton species, the timing of spring peaks in the rotifer Keratella advanced strongly, whereas Leptodiaptomus and Daphnia showed slight or no changes. These changes have generated a growing time lag between the spring phytoplankton peak and zooplankton peak, which can be especially critical for the cladoceran Daphnia. Water temperature, PDO, and food availability affected the timing of the spring peak in zooplankton. Overall, the impact of PDO on the phenological processes were stronger compared with ENSO. Our results highlight that climate affects physical and biological processes differently, which can interrupt energy flow among trophic levels, making ecosystem responses to climate change difficult to forecast.

Two general models for the simulation of insect population dynamics

Detailed studies of single species population dynamics are important for understanding population behaviour and the analysis of large complex ecosystems. Here we present two general models for simulating insect population dynamics: The distributed delay processes and Poisson Process models. In the distributed delay processes model, the simulated population has the characteristic property that the time required for maturation from one stage of growth (instar) to another is directly related to ambient temperature. In this model the parameters DEL and K are significant to the simulated process. The discrete Poisson model deals with the individual development of a group of free entities with random forward movement. These two general component models can be used to simulate the population growth of many insects currently the subject of research interest. The application of distributed delay processes to dynamics of cotton bollworm <em>helicoverpa armigera</em> is presented. The results show the simulation data quite "fit" the observed data.

Species interactions can explain Taylor's power law for ecological time series.

One of the few generalities in ecology, Taylor's power law, describes the species-specific relationship between the temporal or spatial variance of populations and their mean abundances. For populations experiencing constant per capita environmental variability, the regression of log variance versus log mean abundance gives a line with a slope of 2. Despite this expectation, most species have slopes of less than 2 (refs 2, 3-4), indicating that more abundant populations of a species are relatively less variable than expected on the basis of simple statistical grounds. What causes abundant populations to be less variable has received considerable attention, but an explanation for the generality of this pattern is still lacking. Here we suggest a novel explanation for the scaling of temporal variability in population abundances. Using stochastic simulation and analytical models, we demonstrate how negative interactions among species in a community can produce slopes of Taylor's power law of less than 2, like those observed in real data sets. This result provides an example in which the population dynamics of single species can be understood only in the context of interactions within an ecological community.

Single-species Models of the Allee Effect: Extinction Boundaries, Sex Ratios and Mate Encounters

We critically review and classify models of single-species population dynamics subject to the demographic Allee effect with emphasis on non-spatial, deterministic approach. Inclusion of spatial movement and stochastic phenomena does not substantially change the behaviour; stochasticity only “blurs” step-like character of the Allee effect into a sigmoidal form. The outcome of all non-spatial, deterministic models is either unconditional extinction, extinction-survival scenario (ES), or unconditional survival. Three major model classes are recognized: (1) one-dimensional heuristic models, (2) one-dimensional models with mating probability and fixed sex ratio, and (3) two-sex models with variable adult sex ratio. Each class is characterized by the shape of extinction boundary which separates extinction from survival in the ES scenario. The latter two classes may give better predictions of extinction thresholds than heuristic models but require specific information and are data intensive. In one-dimensional models with fixed sex ratio, population cannot survive if density/number of males decreases below some threshold while there is no such restriction on females. Individual-based models seem to be most capable of explaining mechanisms leading to the Allee effect.

Internal Stabilizability of Some Diffusive Models

We consider a single species population dynamics model with age dependence, spatial structure, and a nonlocal birth process arising as a boundary condition. We prove that under a suitable internal feedback control, one can improve the stabilizability results given in Kubo and Langlais [J. Math. Biol.29 (1991), 363–378]. This result is optimal.Our proof relies on an identical stabilizability result of independent interest for the heat equation, that we state and prove in Section 3.

Inverse bifurcation problem, singular Wiener-Hopf equations, and mathematical models in ecology.

A single-species population dynamics with dispersal in a spatially heterogeneous environment is modeled by a nonlinear reaction-diffusion equation with a potential term. To each nonlinear kinetics there corresponds a bifurcation curve that describes the relation between the growth rate and the central density of a steady-state population distribution. Our main concern is an inverse problem for this correspondence. The existence of nonlinear kinetics realizing a prescribed bifurcation curve is established. It is shown that the freedom of such kinetics is of degree finite and even, depending only on the heterogeneity of the environment, and conversely that any nonnegative even integer occurs as the degree of freedom in some environments. A discussion is also made on under what kind of environment the degree is equal to zero or is positive. The mathematical analysis involves the development of a general theory for singular multiplicative Wiener-Hopf integral equations.

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.

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.

Population dynamics of the house dust mites Dermatophagoides farinae, D. pteronyssinus, and Euroglyphus maynei (Acari: Pyroglyphidae) at specific relative humidities.

Experiments were conducted to determine the effects of relative humidity on the population dynamics of single and mixed species of Dermatophagoides farinae Hughes, D. pteronyssinus (Trouessart), and Euroglyphus maynei (Cooreman) at specific relative humidities maintained at 20 degrees C, with unlimited food. The population density of single and mixed species (D. farinae and D. pteronyssinus) increased exponentially when cultured at 65, 70, and 75% RH. The mean population growth rates were 17.3 +/- 4.4 SD and 32.5% +/- 4.7/wk for D. farinae and D. pteronyssinus, respectively. Mean population doubling times were 2.2 +/- 0.3 and 4.2 +/- 1.3 wk for D. pteronyssinus and D. farinae, respectively. Mixed species cultures, started with equal numbers of D. farinae and D. pteronyssinus, resulted in higher percentages of D. farinae than D. pteronyssinus. In cultures started with 75% of one species and 25% of the other, the more numerous species remained dominant and in similar ratios throughout the experiment. Both D. farinae and D. pteronyssinus population densities maintained at 85% RH declined over a 12-wk culture period because of mold growth. E. maynei were unable to survive at 65, 70, 75, and 85% RH, which indicated that their climatic requirements were different from those of D. farinae and D. pteronyssinus. Population densities of D. farinae and D. pteronyssinus cultures declined when held at 21-22 degrees C and relative humidities of < or = 50%; however, at 50% RH, significant proportions of the populations survived for 10 wk. Half-life for desiccation of D. farinae and D. pteronyssinus at 45% RH was 11.5 and 1.2 wk, respectively, but at 50% RH was 86.3 and 4.0 wk, respectively. The data indicated that a < or = 50% RH would have to be maintained for long periods to reduce both D. farinae and D. pteronyssinus by desiccation procedures. The results of this study show that D. farinae and D. pteronyssinus have high reproductive potentials and population growth rates, which indicate that mite reduction procedures must be thorough or mite densities will return to high levels quickly following remediation if adequate food and suitable microclimatic conditions exist.

Population Dynamics with Sequential Density-Dependencies

We analyse the importance of sequential density-dependent processes to population dynamics of single species. We divide a year into several processes of density-dependent reproduction and/or mortality. A sequence of n processes can be arranged in n ! different sequences. However, only (n - 1) ! of these represent unique relative orderings that have different stability properties and dynamics. Models with several sequential density-dependent processes have a much wider repertoire of dynamics than, e.g., ordinary models based on the logistic equation. Stable equilibrium density and the maximum density of cycles and unstable dynamics do not necessarily increase with increasing b (maximum per capita birth rate). The maps of density at time t + 1 (x t+1 ) versus density at time t (x t ) can have more than one hump, i.e., be bi- or multimodal, with multiple equilibria. In this type of system, chaos is not the only inevitable outcome of increased b. Instead stable equilibrium and/or periodic solutions may occur beyond the chaotic region as b increases. It is suggested that this type of model may apply to many kinds of organisms in seasonal environments. The explicit consideration of sequential density-dependence may be of critical importance for resource and conservation managers, to avoid switches between multiple equilibria or extinction due to poorly timed harvest or pest control.

Spatially Induced Bifurcations in Single-Species Population Dynamics

The paper by Hassell, Lawton & May (1976) on the characterization of natural population dynamics by fitting field and laboratory data to a discrete model is reviewed. In particular, we study the effects of spatial degrees of freedom on the qualitative behaviour of such single population maps. Using the spatially extended counterpart of these discrete systems by means of the Coupled Map Lattice formalism, we show that space is able to induce dynamical bifurcations. As the spatial domain is increased, the stability boundaries in the parameter space are modified, driving the population through different kinds of dynamics. The same result is reached by increasing the diffusion rate for a given lattice size. Our results suggest that the dynamical behaviour shown by a population depends not only on intrinsic factors, but also on external or environmental ones