Population Dynamics Model Research Articles

Establishing new populations in water-secure locations may benefit species persistence more than interventions in water-stressed locations

The effects of climate and land-use change, coupled with limited management resources, mean that managers are increasingly faced with decisions to invest in some locations at the expense of others. Given their potentially controversial nature, such decisions require predictions of likely outcomes under different management strategies and potential future climates. We develop an approach to prioritise management interventions across multiple locations in highly variable and uncertain environments, using a stochastic model of population dynamics structured to include the (dynamic) effects of environmental conditions on key vital rates. We demonstrate this approach with a case study on the endangered Australian freshwater fish, the Macquarie perch (Macquaria australasica), assessing the effectiveness of seven management interventions under five scenarios of deterministic climate change. All management interventions were predicted to improve Macquarie perch population outcomes (increased abundances, reduced risk of quasi-extinction), with the risk of declines lowest when management included augmented gene flow and enforcement of fishing regulations. The lowest levels of risk occurred in locations with stable environmental conditions, which suggests that reintroducing Macquarie perch to large, regulated rivers with suitable access to spawning habitat may be more beneficial than investment in small, unregulated streams where populations were unlikely to persist under any scenario. Population reintroductions provide opportunities to shift populations from water-stressed to water-secure locations where required (e.g. to preserve unique genetic diversity). This finding likely applies to many aquatic species, and highlights a potential need to supplement threat mitigation in water-stressed locations with efforts to establish new populations in water-secure locations.

Neural Network Modelling of Phenolic Content, Antioxidant Capacity and Microbial Population Dynamics of a Household Scale Spontaneous Fermentation of Carica Papaya Leaf

Neural Network Modelling of Phenolic Content, Antioxidant Capacity and Microbial Population Dynamics of a Household Scale Spontaneous Fermentation of Carica Papaya Leaf

Numerical approximation of the optimal control of a population dynamics model

AbstractIn this paper, we present a numerical approach to an inverse problem of a population dynamics model. We propose a numerical approximation of the optimal control for obtaining the desired observation state using the augmented Lagrangian method. Moreover, the existence and uniqueness of the numerical solutions are mathematically investigated in this work. Finally, we present some numerical experiments to illustrate our theoretical results.

Modeling and migration-based control of depopulation

This study deals with the problem of the population shrinking in habitats affected by aging and excessive migration outflows. First, a control-oriented population dynamics model was proposed that catches the effect of depopulation. The model also includes the effect of spatial interaction-driven migration flows on population size. The resulting model is a non-homogeneous ordinary differential equation. It includes such phenomena that are important from the control point of view, such as the influence of migration costs on population dynamics, the impact of aging on population size, or the effect of the habitats’ carrying capacity on migration flows. Based on the model, controllability conditions are formulated and a control strategy was developed that is meant to avoid the depopulation of the habitat. The control method acts on the migration costs to achieve the control goal and requires only population size measurements. Simulation measurements are presented in the paper to show the effectiveness of the proposed modeling and control methods.

Trophic model closure influences ecosystem response to enrichment

There exists considerable uncertainty about the most appropriate functional form to describe mortality at the highest trophic level (the closure problem). Although linear and quadratic formulations predict strongly different dynamics, it is unclear which of these formulations is more realistic. We introduce an implicit predator population feeding on the highest trophic level, parameterized through a Holling Type II functional response and empirically observed predator–prey scaling relations. Thus, we arrive at a hyperbolic mortality formulation that is a hybrid between the linear and quadratic forms. Subsequently, we investigate the impact of this formulation on the modeled population dynamics. In particular, we compare the stability properties of simple food-chain models with a hyperbolic mortality and a linear mortality. Contrary to classical theory, the model with a hyperbolic mortality does not exhibit destabilization due to nutrient enrichment. For this model, we find that limit cycles are rather associated with a top-heavy ecosystem structure (high predator, low prey densities). The weak response to enrichment emerges because populations of both the predator and prey increase with nutrient supply, consistent with observations. We discuss the mechanism behind the relationship between top-heaviness and instability from an ecological and a mathematical perspective.

On the effect of forcing on fold bifurcations and early-warning signals in population dynamics

The classical fold bifurcation is a paradigmatic example of a critical transition. It has been used in a variety of contexts, including in particular ecology and climate science, to motivate the role of slow recovery rates and increased autocorrelations as early-warning signals of such transitions. We study the influence of external forcing on fold bifurcations and the respective early-warning signals. Thereby, our prime examples are single-species population dynamical models with Allee effect under the influence of either quasiperiodic forcing or bounded random noise. We show that the presence of these external factors may lead to so-called non-smooth fold bifurcations, and thereby has a significant impact on the behaviour of the Lyapunov exponents (and hence the recovery rates). In particular, it may lead to the absence of critical slowing down prior to population collapse. More precisely, unlike in the unforced case, the question whether slow recovery rates can be observed or detected prior to the transition crucially depends on the chosen time-scales and the size of the considered data set.

Assessment of Enterprise Life Cycle Based on Two-Stage Logistic Model: Exemplified by China’s Automobile Manufacturing Enterprises

Enterprises in socio-economic ecosystems, like organisms in natural ecosystems, have life cycles. Since the enterprise life cycle theory was proposed, how to measure the enterprise life cycle has been a hot research topic. In order to assess the life cycle of an enterprise, a two-stage logistic model was proposed in this research, based on ecological theory and a population dynamics model. The first-stage logistic model measures the internal inhibition coefficient, intrinsic growth rate, and theoretical upper limit of enterprise development scale. The second-stage logistic model deals with the theoretical upper limit of enterprise development scale in the declining period, and measures the intrinsic growth rate, internal inhibition coefficient, and the theoretical upper limit of enterprise development scale in the declining period. In this study, an empirical analysis is conducted with Chinese automobile enterprises, which shows that an enterprise should withdraw from the market by insolvency liquidation or restructuring when both the intrinsic growth rate and internal inhibition coefficient are less than zero. Finally, this paper proposes the evaluation matrix of intrinsic growth and market potential. This matrix can intuitively give the evaluation method of the enterprise life cycle.

Analyzing population dynamics models via Sumudu transform

This study demonstrates how to construct the solutions of a more general form of population dynamics models via a blend of variational iterative method with Sumudu transform. Evolution of population growth models are presented and new models which are more general, are proposed in form of delay differential equations of pantograph type. This study presents suitable reformulation and reconstruction for some existing population growth models in terms of delay differential equations of pantograph type. Also, presentation is given on innovative ways to obtain the solutions of population growth models where other analytic methods fail. Stimulating procedures for finding patterns and regularities in seemingly chaotic processes are elucidated in this paper. Some single and interacting species population models are illustrated graphically and analyzed. How, when and why the changes in population sizes occur can be deduced through this study.

A Deep View into the Nucleus of the Sagittarius Dwarf Spheroidal Galaxy with MUSE. III. Discrete Multicomponent Population-dynamical Models Based on the Jeans Equations

We present comprehensive multicomponent dynamical models of M54 (NGC 6715), the nuclear star cluster of the Sagittarius (Sgr) dwarf galaxy, which is undergoing a tidal disruption in the Milky Way halo. Previous papers in this series used a large MUSE mosaic data set to identify multiple stellar populations in the system and study their kinematic differences. Here, we use Jeans-based dynamical models that fit the population properties (mean age and metallicity), spatial distributions, and kinematics simultaneously. They provide a solid physical explanation for our previous findings. Population-dynamical models deliver a comprehensive view of the whole system, and allow us to disentangle the different stellar populations. We explore their dynamical interplay and confirm our previous findings about the build-up of Sgr’s nuclear cluster via contributions from globular cluster stars, Sgr inner field stars, and in situ star formation. We explore various parameterizations of the gravitational potential and show the importance of a radially varying mass-to-light ratio for the proper treatment of the mass profile. We find a total dynamical mass within M54's tidal radius (∼75 pc) of 1.60 ± 0.07 × 106 M ⊙ in excellent agreement with N-body simulations. Metal-poor globular cluster stars contribute about 65% of the total mass or 1.04 ± 0.05 × 106 M ⊙. Metal-rich stars can be further divided into young and intermediate-age populations, which contribute 0.32 ± 0.02 × 106 M ⊙ (20%) and 0.24 ± 0.02 × 106 M ⊙ (15%), respectively. Our population-dynamical models successfully distinguish the different stellar populations in Sgr’s nucleus because of their different spatial distributions, ages, metallicities, and kinematic features.

Ranking species based on sensitivity to perturbations under non-equilibrium community dynamics.

Managing ecological communities requires fast detection of species that are sensitive to perturbations. Yet, the focus on recovery to equilibrium has prevented us from assessing species responses to perturbations when abundances fluctuate over time. Here, we introduce two data-driven approaches (expected sensitivity and eigenvector rankings) based on the time-varying Jacobian matrix to rank species over time according to their sensitivity to perturbations on abundances. Using several population dynamics models, we demonstrate that we can infer these rankings from time-series data to predict the order of species sensitivities. We find that the most sensitive species are not always the ones with the most rapidly changing or lowest abundance, which are typical criteria used to monitor populations. Finally, using two empirical time series, we show that sensitive species tend to be harder to forecast. Our results suggest that incorporating information on species interactions can improve how we manage communities out of equilibrium.

Modelling can reduce contamination from mosquito population control

Environmental contamination due to pest control in general, and mosquito control in particular, is an important issue expected to increase with climate change. We use a validated model for population dynamics of mosquitoes and historical environmental data to explore performance of larvicidal, adulticidal, and combined treatments. Results show that depending on treatment timing, larvicidal treatments can induce very good results, or have negative outcomes that increase overall mosquito population. Combined larvicidal and adulticidal treatments, however, exhibit much lesser dependence on timing, and therefore give the greatest chance of positive outcomes if environmental conditions are not known. Based on the results, we argue for adaptive mosquito management, in which weather data and forecasts are used to drive a model that identifies best intervals for insecticide use. Such an approach can have considerably better results than static, calendar-driven management and, therefore, considerably reduce environmental contamination. Adaptive management could consider larvicidal treatment because it gives good results if the timing is correct. Static management should, however, combine larvicidal and adulticidal treatments for the greatest chance of success.

Prevalence of mutualism in a simple model of microbial coevolution

Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might shift through evolution, but within an ecological regime. Here we use adaptive dynamics combined with a generalized logistic model of population dynamics to show that transitions of ecological interactions might appear as a consequence of evolution. To this purpose, we introduce a two-microbial toy model in which population parameters are determined by a bookkeeping of resources taken from (and excreted to) the environment, as well as from the byproducts of the other species. Despite its simplicity, this model exhibits all kinds of potential ecological transitions, some of which resemble those found in nature. Overall, the model shows a clear trend toward the emergence of mutualism.

ОЦЕНКИ РЕШЕНИЙ ДЛЯ ОДНОЙ МОДЕЛИ ДИНАМИКИ ПОПУЛЯЦИЙ С ЗАПАЗДЫВАНИЕМ

We consider a model of the single population dynamics described by a delay differential equation. The asymptotic behavior of solutions for this model is studied in cases of asymptotic stability of equilibrium points corresponding to the complete extinction of the population and to the constant positive population size. In each case, Lyapunov–Krasovskii functionals are constructed, with the help of which estimates characterizing the rate of extinction of the population and the rate of stabilization of the population to a constant value are obtained.

Irregular population cycles driven by environmental stochasticity and saddle crawlbys

Despite considerable study of population cycles, the striking variability of cycle periods in many cyclic populations has received relatively little attention. Mathematical models of cyclic population dynamics have historically exhibited much greater regularity in cycle periods than many real populations, even when accounting for environmental stochasticity. We contend, however, that the recent focus on understanding the impact of long, transient but recurrent epochs within population oscillations points the way to a previously unrecognized means by which environmental stochasticity can create cycle period variation. Specifically, consumer–resource cycles that bring the populations near a saddle point (a combination of population sizes toward which the populations tend, before eventually transitioning to substantially different levels) may be subject to a slow passage effect that has been dubbed a ‘saddle crawlby'. In this study, we illustrate how stochasticity that generates variability in how close predator and prey populations come to saddles can result in substantial variability in the durations of crawlbys and, as a result, in the periods of population cycles. Our work suggests a new mechanistic hypothesis to explain an important factor in the irregular timing of population cycles and provides a basis for understanding when environmental stochasticity is, and is not, expected to generate cyclic dynamics with variability across periods.

Population Dynamics of American Bullfrog (Lithobates catesbeianus) and Implications for Control.

Simple SummaryLithobates catesbeianus (American bullfrog) was introduced to South Korea and caused various damage in the Korean natural environment for the past 25 years. Although several management strategies were implemented, the effectiveness of past control decisions is largely unknown. We built a population dynamics model for L. catesbeianus in the Onseok reservoir, South Korea, in order to assist managerial decisions. Control scenarios with varying intensities were simulated to evaluate their effectiveness. The population of the American bullfrog in the reservoir was reduced to a manageable level under intensive control of the tadpole stage, using three sets of double fyke nets and 80% direct removal of juvenile and adult stages. According to our results, integrated, intensive, and continuous control is essential for managing the invasive American bullfrog population.Lithobates catesbeianus (American bullfrog), known to be one of the notorious invasive species, was introduced to South Korea and has proliferated in the Korean natural environment for the past 25 years. The ecological impact caused by the species is well known, and several management decisions have been implemented to cull its population. However, the effectiveness of past control decisions is largely unknown. We built a population dynamics model for L. catesbeianus in the Onseok reservoir, South Korea, using STELLA architect software. The population model was based on the demographics and ecological process of the species developing through several life stages, with respective parameters for survivorship and carrying capacity. Control scenarios with varying intensities were simulated to evaluate their effectiveness. The limitations of isolated control methods and the importance of integrated management are shown in our results. The population of the American bullfrog in the reservoir was reduced to a manageable level under intensive control of the tadpole stage, using three sets of double fyke nets and 80% direct removal of juvenile and adult stages. According to our results, integrated, intensive, and continuous control is essential for managing the invasive American bullfrog population. Finally, our modeling approach can assist in determining the control intensity to improve the efficiency of measures against L. catesbeianus.

Optimal resource allocation for spatiotemporal control of invasive species

Controlling and planning the removal of invasive species are topics of outmost importance in management of natural resources because of the severe ecological damages and economic losses caused by non-native alien species. Optimal management strategies often rely on coupling population dynamics models with optimization procedures to achieve an effective allocation of limited resources for removing invasive species from hosting ecosystems. We analyse a parabolic optimal control model to simulate the best spatiotemporal strategy for the removal of the species when a budget constraint is applied. The model also predicts the species spread under the control action. We improve the capability of the model to reproduce realistic scenarios by introducing an advection term in the state equation. That allows to model the action of external forces, like currents or winds, which might bias dispersal in certain directions. The analytical properties of the model are discussed under suitable boundary conditions. As a further original contribution, we introduce a novel numerical procedure for approximating the solution reducing the computational costs in view of its implementation as a support decision tool. Then we test the approach by simulating the spread and the control of a hypothetical invasive plant in the territory of the Italian Sardinia island. To reproduce the anisotropy of the diffusion we include the effect of the altitude in the habitat suitability of the species.

Predicting the number of hunting animals in the State complex “Zavidovo” based on a mathematical model

It is necessary to predict the number of hunting animals under the conditions of the impact of endogenous and exogenous factors the habitat and economic use, for rational and inexhaustible their use. Understanding changes in the number of hunting animals is an important tool for managing hunting resources. Predicting of the number of hunting animals in the region as a rule, is based on trend models of population dynamics. In practice, the calculation and constructive method and the method of mathematical modeling have become the most widespread in predicting the population of hunting animals in dynamics. The computational and constructive method is based on the use of correlation and regression models, but it does not take into account the main indicators of population size formation: the fertility rate, which is formed on the basis of the specic weight of males, the percentage of yeldness and the number of calves (young animals) in the calving (litter), and the livability depending on the percentage of natural death and losses from poaching. The method of mathematical modeling involves the compilation of mathematical models and conducting model experiments to predict the number of species of hunting animals in dynamics. The relevance of this mathematical analysis lies in its multifactorial nature and rather high reliability. In the eld of predicting the number of hunting animals the modied P. H. Leslie model is of particular interest. The purpose of the work was to predict the number of wild ungulates (roe deer, elk, maral and spotted deer) in the Zavidovo State Complex in the Tver region until 2035. The use of the modied P. H. Leslie model makes it possible to predict the development of hunting animal populations both in the Zavidovo State Complex as a whole and in individual hunting areas with precise adjustment of models according to area parameters.

Litter, Plant Competition, and Ecosystem Dynamics: A Theoretical Perspective.

AbstractCommunity structure depends jointly on species' responses to, and effects on, environmental factors. Many such factors, including detritus, are studied in ecosystem ecology. Detritus in terrestrial ecosystems is dominated by plant litter (nonliving organic material), which, in addition to its role in material cycling, can act as a niche factor modulating interactions among plants. Litter thus links traditional community and ecosystem processes, which are often studied separately. We explore this connection using population dynamics models of two plant species and a litter pool. We first find conditions determining the outcome of interactions between these species, highlighting the role that litter plays and the role of broader ecosystem parameters, such as decomposition rate. Species trade-offs in tolerance to direct competition and litter-based interference competition allow for coexistence, provided the litter-tolerant species produces more litter at the population level; otherwise, priority effects may result. When species coexist, litter-mediated interactions between plants disrupt the traditional relationship between biomass accumulation and decomposition. Increasing decomposition rate may have no effect on standing litter density and, in some cases, may even increase litter load. These results illustrate how ecosystem variables can influence community outcomes that then feed back to influence the ecosystem.

Understanding the depth limit of the seagrass Cymodocea nodosa as a critical transition: Field and modeling evidence

Changes in light and sediment conditions can sometimes trigger abrupt regime shifts in seagrass meadows resulting in dramatic and unexpected die-offs of seagrass. Light attenuates rapidly with depth, and in seagrass systems with non-linear behaviours, can serve as a sharp boundary beyond which the meadow transitions to bare sand. Determining system behaviour is therefore essential to ensuring resilience is maintained and to prevent stubborn critical ecosystem transitions caused by declines in water quality. Here we combined field and modelling studies to explore the transition from meadow to bare sand in the seagrass Cymodocea nodosa at the limit of its depth distribution in a shallow, light-limited bay. We first describe the relationship between light availability and seagrass density along a depth gradient in an extensive unfragmented meadow (Alfacs bay, NE Spain). We then develop a simple mechanistic model to characterise system behaviour. In the field, we identified sharp decline in shoot density beyond a threshold of ∼1.9 m depth, shifting from a vegetated state to bare sand. The dynamic population model we developed assumes light-dependent growth and an inverse density-dependent mortality due to facilitation between shoots (mortality rate decreases as shoot density increases). The model closely tracked our empirical observations, and both the model and the field data showed signs of bistability. This strongly suggests that the depth limit of C. nodosa is a critical transition driven by photosynthetic light requirements. While the mechanisms still need to be confirmed with experimental evidence, recognizing the non-linear behaviour of C. nodosa meadows is vital not only in improving our understanding of light effects on seagrass dynamics, but also in managing shallow-water meadows. Given the shallow threshold (<2m), light-limited systems may experience significant and recalcitrant meadow retractions with even small changes in sediment and light conditions. Understanding the processes underlying meadow resilience can inform the maintenance and restoration of meadows worldwide.

Coexistence conditions in generalized discrete-time models of insect population dynamics

Motivated by the annual life histories of insects residing in the temperate-regions of the world, there is a rich tradition of modeling their population dynamics using a discrete-time formalism. Here, we consider an antagonistic interaction between two insect species – a parasitoid wasp that lays an egg within its host insect species. The egg hatches into juvenile parasitoid that develops within the body of the host by using it as resource and this ultimately results in host death. The parasitoid emerges from the host as a free-living insect that goes on to attack other hosts. Such interaction are ubiquitous with over 65,000 known species of parasitoid wasps and such wasps have potential in biologic control of pest insect species. We introduce a general class of discrete-time models for capturing the population dynamics of two competing parasitoid species that attack the same vulnerable stage of the host species. These models are characterized by two density-dependent functions: an escape response defined by the fraction of hosts escaping parasitism; and a competition response defined by the fraction of parasitized hosts that develop into adult parasitoids of either species. Model analysis reveals remarkably simple stability conditions for the coexistence of competing parasitoids. Coexistence occurs, if and only if, the adult host population increases with host reproduction rate, and the log sensitivity of the competition response is less than half. The latter condition implies that any increase in the adult parasitoid population will result in a sufficiently slow increase in the fraction of parasitized hosts that develop into parasitoids of that type. We also consider a semi-discrete formulation of a competing species model that incorporates host density-dependence in the attack rate. This model expands the class of models for which the analytical results apply, and we systematically compare the numerical results of this model to the established coexistence conditions