Single-species Population Dynamics Research Articles

Intervention Time in Target-Oriented Chaos Control

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

Synchronized Tick Population Oscillations Driven by Host Mobility and Spatially Heterogeneous Developmental Delays Combined

We consider a coupled system of delay differential equations for a single-species tick population dynamics, assuming feeding adult ticks are distributed by their hosts in a spatially heterogeneous environment consisting of two patches where egg ticks produced will complete their life cycles with different, normal and diapause, developmental delays. We show that the mobility of adult tick host and the diapause developmental delay combined drive a synchronized oscillation in the total tick populations around a uniquely defined positive equilibrium, and this synchronization makes the oscillatory patterns much simpler in comparison with multi-peak oscillations exhibited in the absence of host mobility.

Population and Inequality Dynamics in Simple Economies

While the use of spatial agent-based and individual-based models has flourished across many scientific disciplines, the complexities these models generate are often difficult to manage and quantify. This research reduces population-driven, spatial modeling of individuals to the simplest configurations and parameters: an equal resource opportunity landscape with equally capable individuals; and asks the question, Will valid complex population and inequality dynamics emerge from this simple economic model? Two foraging economies are modeled: subsistence and surplus. The resulting, emergent population dynamics are characterized by their sensitivities to agent and landscape parameters. The various steady and oscillating regimes of single-species population dynamics are generated by appropriate selection of model growth parameters. These emergent dynamics are shown to be consistent with the equation-based, continuum modeling of single-species populations in biology and ecology. The intrinsic growth rates, carry capacities, and delay parameters of these models are implied for these simple economies. Aggregate measures of individual distributions are used to understand the sensitivities to model parameters. New local measures are defined to describe complex behaviors driven by spatial effects, especially extinctions. This simple economic model is shown to generate significantly complex population and inequality dynamics. Model parameters generating the intrinsic growth rate have strong effects on these dynamics, including large variations in inequality. Significant inequality effects are shown to be caused by birth costs above and beyond their contribution to the intrinsic growth rate. The highest levels of inequality are found during the initial non-equilibrium period and are driven by factors different than those driving steady state inequality.

Single species population dynamics in seasonal environment with short reproduction period

We present a periodic nonlinear scalar delay differential equation model for a population with short reproduction period. By transforming the equation to a discrete dynamical system, we reduce the infinite dimensional problem to one dimension. We determine the basic reproduction number not merely as the spectral radius of an operator, but as an explicit formula and show that is serves as a threshold parameter for the stability of the trivial equilibrium and for permanence.

On first-order hyperbolic partial differential equations with two internal variables modeling population dynamics of two physiological structures

In this paper we develop fundamental theories for a scalar first-order hyperbolic partial differential equation with two internal variables which models single-species population dynamics with two physiological structures such as age–age, age–maturation, age–size, and age–stage. Classical techniques of treating structured models with a single internal variable are generalized to study the double physiologically structured model. First, the semigroup is defined based on the solutions and its infinitesimal generator is determined. Then, the compactness of solution trajectories is established. Finally, spectrum theory is employed to investigate stability of the zero steady state and asynchronous exponential growth of solutions is studied when the zero steady state is unstable.

Stochastic control of single-species population dynamics model subject to jump ambiguity

A logistic type stochastic control model for cost-effective single-species population management subject to an ambiguous jump intensity is presented based on the modern multiplier-robust formulation. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation for finding the optimal control is then derived. Mathematical analysis of the HJBI equation from the viewpoint of viscosity solutions is carried out with an emphasis on the non-linear and non-local term, which is a key term arising due to the jump ambiguity. We show that this term can be efficiently handled in the framework of viscosity solutions by utilizing its monotonicity property. A numerical scheme to discretize the HJBI equation is presented as well. Our model is finally applied to management of algae population in river environment. Optimal management policies ranging from the short-term to long-term viewpoints are numerically investigated.

Delay-induced instabilities of stationary solutions in a single species nonlocal hyperbolic-parabolic population model

The present work investigates the effects of maturation and dispersal delays on dynamics of single species populations. Both delays have been incorporated in a single species nonlocal hyperbolic-parabolic population model, which admits traveling and stationary wave solutions. We reduce the model into various forms and obtain the corresponding analytical solutions. Analysis of the reduced models indicates that the dispersal delay can result in loss of monotonicity, where the solutions oscillate as they converge to a positive equilibrium. The stability analysis of the general model reveals that the maturation time delay admits a Hopf bifurcation threshold, which is expressed as a function of the dispersal delay. The numerical simulations of the general model suggest that the global stability of the stationary wave solutions is lost when the dispersal delay is increased from zero. In conclusion, population models with maturation and dispersal delays can give new insights into the complex dynamics of single species.

A Lyapunov Function For Logistic Equation On Time Scales

In this study we focus on the stability of dynamic logistic equation which is used in single species population dynamics. Here we have introduced a quadratic Lyapunov function for generalized dynamic logistic equation on time scales. By using proposed Lyapunov function, asymptotic stability conditions for the equilibrium solution of dynamic logistic equation have been investigated.

Impact of environmental colored noise in single-species population dynamics.

Variability on external conditions has important consequences for the dynamics and the organization of biological systems. In many cases, the characteristic timescale of environmental changes as well as their correlations play a fundamental role in the way living systems adapt and respond to it. A proper mathematical approach to understand population dynamics, thus, requires approaches more refined than, e.g., simple white-noise approximations. To shed further light onto this problem, in this paper we propose a unifying framework based on different analytical and numerical tools available to deal with “colored” environmental noise. In particular, we employ a “unified colored noise approximation” to map the original problem into an effective one with white noise, and then we apply a standard path integral approach to gain analytical understanding. For the sake of specificity, we present our approach using as a guideline a variation of the contact process—which can also be seen as a birth-death process of the Malthus-Verhulst class—where the propagation or birth rate varies stochastically in time. Our approach allows us to tackle in a systematic manner some of the relevant questions concerning population dynamics under environmental variability, such as determining the stationary population density, establishing the conditions under which a population may become extinct, and estimating extinction times. We focus on the emerging phase diagram and its possible phase transitions, underlying how these are affected by the presence of environmental noise time-correlations.

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects.

We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

Effects of an increased temperature regime on the population dynamics and species interactions of marine nematodes

Although changes in average environmental conditions can have serious consequences, the main impacts of global climate change on populations and communities may well result from changes in short-term climate variability. Both an increased frequency and intensity of extremes and changing amplitudes of diurnal temperature fluctuations may affect the fitness of species and the interactions between them. Such changing temperature regimes may affect reproductive success, population dynamics, species interactions and community structure. The present study compares the effects of an increased temperature regime with diurnal fluctuations with those of a constant temperature regime on the fitness and population dynamics of free-living marine nematodes and on their interspecific interactions. Microcosm experiments were performed on two congeneric monhysterid nematode species, which co-occur in their natural habitat, under a constant vs. an increased fluctuating temperature regime. The latter affected population dynamics of single species and altered the outcome of the interspecific interaction from a symmetrical to an asymmetrical inhibitory effect of D. meyli over D. oschei. Changes in the amplitude of diurnal temperature fluctuations as well as in the frequency of extreme temperatures may be very important determinants of the effects of temperature change on species interactions, potentially affecting assemblage structure and ecosystem functioning.

A heterogeneous diffusive logistic model of a single species population dynamics with predation and harvesting terms

We study existence and multiplicity of positive solutions of a heterogeneous diffusive logistic equation with predation and harvesting terms, −Δu=au−b(x)u2−cu1+mu−dh(x)inΩ,∂u∂ν=0on∂Ω, where a,c,m and d are positive constants, Ω a bounded smooth domain in RN, and b(x) is a nonnegative function on Ω¯, with Ω0 a region such that Ω¯0⊂Ω and Ω¯0={x∈Ω:b(x)=0}. Under the strong growth rate assumption, that is, when a is greater than the first eigenvalue of −Δ in Ω0 with Dirichlet boundary condition, we show that the equation has at least one positive solution for 0≤d<da, for some da>0. In addition, in case c<a we prove some multiplicity results when m<m0, with m0=∫Ωb(x)dx/(a|Ω|).

Neutral or non‐neutral communities: temporal dynamics provide the answer

Neutral models for community dynamics are based on the assumption that temporal variation is only influenced by demographic stochasticity, ignoring the influence of fluctuations in the environment. Demographic and environmental stochasticity are known to have very different effects on the population dynamics of single species. Communities, however, are usually analyzed with emphasis on the shape of the species abundance distribution rather than on their dynamical characteristics. Accordingly, examination of the validity of the neutral model has typically been based on statistical analyses of the shape of the species abundance distribution or form of the species–area relationships. Here we illustrate that both demographic and environmental noise must be included to obtain realistic description of community dynamics. We do this by a simple approach comparing two different dynamic models both leading to Fisher's log series species abundance distribution: the neutral model with only demographic noise, and a limiting form of an approximate gamma model most strongly affected by environmental noise. While keeping Fisher's diversity parameter α constant, the turnover rates for observable species become much greater and average life‐times of species much smaller in the gamma model than in the neutral model. In practice, the neutral model tends to produce unrealistically small turnover rates for large populations. This illustrates that realistic assumptions about the stochastic components of the underlying population dynamics of single species are important for correctly characterizing dynamical changes in species composition of communities. This approach can provide a powerful tool for identifying the principal factors affecting the structure of communities.

A multispecies biomass dynamics model for investigating predator–prey interactions in the Bering Sea groundfish community

Concerns over long-term cumulative impacts of fishing on marine ecosystems and the status of many marine species have led to calls for ecosystem-based approaches to fishery management. Single-species population dynamics models traditionally used in fisheries stock assessments lack separate accounting of predation mortality and often underestimate natural mortality. Age-structured models used for stock assessments in the Alaska region are biologically realistic, but their applicability is limited to a relatively small number of commercially exploited species because they require accurate survey and fishery age composition data. The objective of this study was to develop relatively simple age-aggregated multispecies models that describe biomass dynamics of some commercially and ecologically important groundfish species in the eastern Bering Sea by accounting for their trophic interactions. We developed and contrasted two alternative model formulations: a multispecies biomass dynamics (MBD) model and a multispecies delay difference (MDD) model. Both MBD and MDD models were able to capture observed trends in survey biomass data over 1982–2009. Although the MDD model fit the survey biomass estimates better than the MBD model, the MDD model and its maximum likelihood parameters produced biologically unrealistic biomass projections at values of instantaneous fishing mortality (F)>0.14. Strong positive correlations among many of the predation parameters resulted in highly uncertain parameter estimates. Consistent with previous studies, both multispecies models predicted the multispecies B0, MSY, and FMSY to be lower than the sum of the estimates from single-species assessment models. Although the results of the current study should be taken with caution because of high estimation uncertainty, our multispecies models can be a useful addition to the current management process by providing estimates of natural mortality and tactical advice on the implications of single-species harvest strategies for the broader groundfish community in the eastern Bering Sea.

Are time delays always destabilizing? Revisiting the role of time delays and the Allee effect

One of the main challenges in ecology is to determine the cause of population fluctuations. Both theoretical and empirical studies suggest that delayed density dependence instigates cyclic behavior in many populations; however, underlying mechanisms through which this occurs are often difficult to determine and may vary within species. In this paper, we consider single species population dynamics affected by the Allee effect coupled with discrete time delay. We use two different mathematical formulations of the Allee effect and analyze (both analytically and numerically) the role of time delay in different feedback mechanisms such as competition and cooperation. The bifurcation value of the delay (that results in the Hopf bifurcation) as a function of the strength of the Allee effect is obtained analytically. Interestingly, depending on the chosen delayed mechanism, even a large time delay may not necessarily lead to instability. We also show that, in case the time delay affects positive feedback (such as cooperation), the population dynamics can lead to self-organized formation of intermediate quasi-stationary states. Finally, we discuss ecological implications of our findings.

Open questions: are the dynamics of ecological communities predictable?

Open questions: are the dynamics of ecological communities predictable?

Predation effects on mean time to extinction under demographic stochasticity

Methods for predicting the probability and timing of a species’ extinction are typically based on single species population dynamics. Assessments of extinction risk often lack effects of interspecific interactions. We study a birth and death process in which the death rate includes an effect of predation. Predation is included via a general nonlinear expression for the functional response of predation to prey density. We investigate the effects of the foraging parameters (e.g. attack rate and handling time) on the mean time to extinction. Mean time to extinction varies by orders of magnitude when we alter the foraging parameters, even when we exclude the effects of these parameters on the equilibrium population size. Conclusions are robust to assumptions about initial conditions and variable predator abundance. These findings clearly show that accounting for the nature of interspecific interactions is likely to be critically important when estimating extinction risk.

Stability conditions for a class of delay differential equations in single species population dynamics

We consider a class of nonlinear delay differential equations,which describes single species population growth with stage structure. By constructing appropriate Lyapunov functionals, the global asymptotic stability criteria, which are independent of delay, are established. Much sharper stability conditions than known results are provided. Applications of the results to some population models show the effectiveness of the methods described in the paper.

Deterministic individual-based cellular automata modelling of single species population dynamics

AbstractThis presentation was created to characterise foundations of cellular automata modelling of single species population dynamics. We show models of single species population growth based on deterministic birth-death-regeneration process and demonstrate a relationship between fecundity rate and population growth rate. Our models provide mechanistic simulation of logistic-like and double logistic-like curves of population growth that is not possible in the classical Verhulst model (logistic growth model). This method is deterministic individual-based and is based on logical “if-then” statements only. As this method is bottom-up mechanistic and provides a direct visual insight into dynamics of complex systems, we used it to study mechanisms of interspecific competition in further experiments.

Deterministic individual-based cellular automata modelling of single species population dynamics

Deterministic individual-based cellular automata modelling of single species population dynamics