Population Dynamics Approach Research Articles

When is lethal deceptive pollination maintained? A population dynamics approach.

Not all plant-pollinator interactions are mutualistic, and in fact, deceptive pollination systems are widespread in nature. The genus Arisaema has a pollination system known as lethal deceptive pollination, in which plants not only attract pollinating insects without providing any rewards, but also trap them until they die. Many Arisaema species are endangered from various disturbances including reduction in forest habitat, modification of the forest understory owing to increasing deer abundance, and plant theft for horticultural cultivation. We aimed to theoretically investigate how lethal deceptive pollination can be maintained from a demographic perspective and how plant and pollinator populations respond to different types of disturbance. We developed and analysed a mathematical model to describe the population dynamics of a deceptive plant species and its victim pollinator. Calibrating the model based on empirical data, we assessed the conditions under which plants and pollinators could coexist, while manipulating relevant key parameters. The model exhibited qualitatively distinct behaviours depending on certain parameters. The plant becomes extinct when it has a low capability for vegetative reproduction and slow transition from male to female, and plant-insect co-extinction occurs especially when the plant is highly attractive to male insects. Increasing deer abundance has both positive and negative effects because of removal of other competitive plants and diminishing pollinators, respectively. Theft for horticultural cultivation can readily threaten plants whether male or female plants are frequently collected. The impact of forest habitat reduction may be limited compared to that of other disturbance types. Our results have emphasised that the demographic vulnerability of lethal deceptive pollination systems would differ qualitatively from that of general mutualistic pollination systems. It is therefore important to consider the demographics of both victim pollinators and deceptive plants to estimate how endangered Arisaema populations respond to various disturbances.

Using early detection data to estimate the date of emergence of an epidemic outbreak.

While the first infection of an emerging disease is often unknown, information on early cases can be used to date it. In the context of the COVID-19 pandemic, previous studies have estimated dates of emergence (e.g., first human SARS-CoV-2 infection, emergence of the Alpha SARS-CoV-2 variant) using mainly genomic data. Another dating attempt used a stochastic population dynamics approach and the date of the first reported case. Here, we extend this approach to use a larger set of early reported cases to estimate the delay from first infection to the Nth case. We first validate our framework by running our model on simulated data. We then apply our model using data on Alpha variant infections in the UK, dating the first Alpha infection at (median) August 21, 2020 (95% interpercentile range across retained simulations (IPR): July 23-September 5, 2020). Next, we apply our model to data on COVID-19 cases with symptom onset before mid-January 2020. We date the first SARS-CoV-2 infection in Wuhan at (median) November 28, 2019 (95% IPR: November 2-December 9, 2019). Our results fall within ranges previously estimated by studies relying on genomic data. Our population dynamics-based modelling framework is generic and flexible, and thus can be applied to estimate the starting time of outbreaks in contexts other than COVID-19.

Is the invasive Rhododendron ponticum L. an emergent threat to mainland Atlantic forests? A population dynamics approach

Understanding the population dynamics of invasive species is essential for identifying the key parameters of their success and guiding management actions. European temperate forests of the Atlantic domain are prone to be invaded by the Pontic Rhododendron (Rhododendron ponticum L. subsp. baeticum (Boiss. & Reut.) Hand.-Mazz.), a shade-tolerate evergreen shrub native to the Iberian peninsula. While the invasion has a long history in Ireland and the British Isles, it is an emerging threat in mainland Europe. It is therefore a timely challenge to better understanding the invasive dynamics of this species in this context. We studied the population dynamics of R. ponticum in 27 invaded forests of north-western France, examining population structure, and individuals’ growth, fertility and fecundity among contrasted light conditions. All invasive populations were found on acidic soils. Irrespective of light conditions, R. ponticum exhibited a regular radial growth, with a clear increase since the 1990s. The majority of stems were younger than 38 years on average, indicating a recent increase in population density. Light availability strongly impacted R. ponticum’s canopy structure, with higher canopy cover and stem numbers under sun conditions. Despite the production of a huge number of viable seeds, the observed number of seedlings was always very low irrespective of light conditions, indicating recruitment limitation and thus a limited ability to establish new, distant populations. In contrast, vegetative propagation via intense layering at the invasion front wave ensured local population spread from initially planted individuals, especially on moist soils. We conclude that where it has been planted, R. ponticum is able to actively layer, thereby forming dense bushes in the forest understories as long as the soil is acidic and relatively moist. The establishment of new, distant populations appears a rare event since recruitment is limited to particular microhabitats related to forest management-associated disturbances. Such disturbance should thus be avoided in sites where the species has already established, unless a post-disturbance eradication of R. ponticum’s seedling can be implemented the following years. The plantation of R. ponticum in forest must be avoided when the soil is acidic and moist. Because R. ponticum’s growth performances are increasing since the 1990s, as a likely consequence of climate change, monitoring established populations is recommended to detect a possible increasing invasiveness.

Exploring the Impact of Nonlinearities in Police Recruitment and Criminal Capture Rates: A Population Dynamics Approach

The interplay between criminal activity and crime control/prevention measures is inherently dynamic. This paper presents a simple nonlinear dynamical system in which criminal activity levels are coupled to policing effort. Through the process of non-dimensionalisation and sensitivity analysis, policing efficiency and the responsiveness of policing effort are identified as key parameter groupings. An analysis of the system shows that bi-stability is a feature of the dynamics. When there is no feedback between criminal activity and police recruitment, a saddle-node bifurcation occurs and threshold levels of criminal activity are required for the activity to be maintained. When feedback is permitted, we also find a backward bifurcation and criminal activity can be contained for policing efficiency below its threshold level. We demonstrate proof of concept for how the model might be used as a predictive tool with real data.

A Population Dynamics Approach to the Distribution of Space Debris in Low Earth Orbit

The presence of the debris in the Earth’s orbit poses a significant risk to human activity in outer space. This debris population continues to grow due to ground launches, the loss of external parts from space ships, and uncontrollable collisions between objects. A computationally feasible continuum model for the growth of the debris population and its spatial distribution is therefore critical. Here we propose a diffusion-collision model for the evolution of the debris density in the low-Earth orbit and its dependence on the ground-launch policy. We parametrize this model and test it against data from publicly available object catalogs to examine timescales for the uncontrolled growth. Finally, we consider sensible launch policies and cleanup strategies and how they reduce the future risk of collisions with active satellites or space ships.

Population Dynamics of the Hungarian Villages 1995–2016

Abstract In our pioneer study, we explore the number of population change in Hungarian villages based on the latest available statistical data (1995–2016), looking for the answer to whether the rapid and profound economic and social structural changes of post-socialism and the historically unique periods of accession to the European Union have rearranged the numerical dominance of the earlier largest rural population in Hungarian society. According to the concept of the post-socialist demographic turn, the population of the villages began to grow during the transformation crisis of the 1990s, and a significant part of the villages became marginalized. In contrast, agglomeration and suburbanization processes also intensified, which also contributed to changes in the number of villagers. We used the data of the Central Statistical Office (CSO) and the Regional Information System (RIS), which were organised into a new database for the purposes of the research. The theory and methods of the population dynamics approach emphasize the need for more complex demographic studies. We argue that the absolute population of the villages has greatly decreased, but this is only an apparent shift because it is a consequence of the administrative designation of a large number of villages as cities. The paper concludes that from 1995 to 2016 population number of villages with the same administrative classification (village) remained relatively stable, and this is radically different from previous research findings.

Mathematical Models of the Generation of Radiation-induced DNA Double-strand Breaks and Misrepair Cells by Direct and Indirect Action

Free radical carries an unpaired electron in the outer shell which is very reactive and becomes toxic to DNA. The direct action hits cell directly, while indirect action is the interaction between ionizing radiation and water molecule which later produces free radical. Hydrated electron (e), hydroxyl radical (OH), hydrogen radical (OH), ionized water, hydroperoxyl radical and hydrogen peroxide are examples of free radical products. Among of these three free radicals, DNA damage dominantly caused by hydroxyl radical (OH) because it is found to be highly reactive compared to others. This paper aimed to develop a model by using structured population dynamics approach to study the effects of ionizing radiation by direct and indirect actions. The effects of ionizing radiation are mathematically described in a model using Ordinary Differential Equations (ODEs). The simulation results are fitted to the Linear Quadratic (LQ) formulation to give the ratio for alpha/beta . Next, the parameter estimation of the model is carried out using experimental data of human colon carcinoma cell by the aid of the MATLAB programming. The estimated parameter values can explain the biological meaning, which can support the result of the experimental design. The result showed that the sum-squared error (SSE) between simulation data and experimental data obtained is 0.0019 which indicates an excellent t to the experimental data. Thus, the model developed is in line with the experimental result. The model is able to explain the dynamics process of the direct and indirect effect of ionizing radiation on the cell population.

A common gene drive language eases regulatory process and eco-evolutionary extensions

BackgroundSynthetic gene drive technologies aim to spread transgenic constructs into wild populations even when they impose organismal fitness disadvantages. The extraordinary diversity of plausible drive mechanisms and the range of selective parameters they may encounter makes it very difficult to convey their relative predicted properties, particularly where multiple approaches are combined. The sheer number of published manuscripts in this field, experimental and theoretical, the numerous techniques resulting in an explosion in the gene drive vocabulary hinder the regulators’ point of view. We address this concern by defining a simplified parameter based language of synthetic drives.ResultsEmploying the classical population dynamics approach, we show that different drive construct (replacement) mechanisms can be condensed and evaluated on an equal footing even where they incorporate multiple replacement drives approaches. Using a common language, it is then possible to compare various model properties, a task desired by regulators and policymakers. The generalization allows us to extend the study of the invasion dynamics of replacement drives analytically and, in a spatial setting, the resilience of the released drive constructs. The derived framework is available as a standalone tool.ConclusionBesides comparing available drive constructs, our tool is also useful for educational purpose. Users can also explore the evolutionary dynamics of future hypothetical combination drive scenarios. Thus, our results appraise the properties and robustness of drives and provide an intuitive and objective way for risk assessment, informing policies, and enhancing public engagement with proposed and future gene drive approaches.

Integrated model for describing the microstructure evolution of the inoculated Al-Zn-Mg-Cu alloys in continuous solidification

An integrated model based on the population dynamics approach and the cellular automaton method has been developed to simulate the solidification process of the Al-Zn-Mg-Cu alloys. The nucleation, spherical growth/dissolving and dendritic growth of the α-Al nuclei/grains are taken into account. The model is validated by comparing with the experimental results firstly, and then is applied to calculate the details of the microstructure formation in Al-Zn-Mg-Cu alloys inoculated with Al-5Ti-1B master alloys. The effects of the size distribution of TiB2 and the solidification conditions on the grain size are investigated. At last, an empirical formula for predicting grain size has been put forward based on the numerical calculations. The formula gives the dependent relationship between the grain size, the cooling rate of melt, the additive amount of refiner, the composition of the solutes and the size distribution of TiB2 particles.

Prey and predator density-dependent interactions under different water volumes.

Predation is a critical ecological process that directly and indirectly mediates population stabilities, as well as ecosystem structure and function. The strength of interactions between predators and prey may be mediated by multiple density dependences concerning numbers of predators and prey. In temporary wetland ecosystems in particular, fluctuating water volumes may alter predation rates through differing search space and prey encounter rates. Using a functional response approach, we examined the influence of predator and prey densities on interaction strengths of the temporary pond specialist copepod Lovenula raynerae preying on cladoceran prey, Daphnia pulex, under contrasting water volumes. Further, using a population dynamic modeling approach, we quantified multiple predator effects across differences in prey density and water volume. Predators exhibited type II functional responses under both water volumes, with significant antagonistic multiple predator effects (i.e., antagonisms) exhibited overall. The strengths of antagonistic interactions were, however, enhanced under reduced water volumes and at intermediate prey densities. These findings indicate important biotic and abiotic contexts that mediate predator–prey dynamics, whereby multiple predator effects are contingent on both prey density and search area characteristics. In particular, reduced search areas (i.e., water volumes) under intermediate prey densities could enhance antagonisms by heightening predator–predator interference effects.

Constrained proteome allocation affects coexistence in models of competitive microbial communities

Microbial communities are ubiquitous and play crucial roles in many natural processes. Despite their importance for the environment, industry and human health, there are still many aspects of microbial community dynamics that we do not understand quantitatively. Recent experiments have shown that the structure and composition of microbial communities are intertwined with the metabolism of the species that inhabit them, suggesting that properties at the intracellular level such as the allocation of cellular proteomic resources must be taken into account when describing microbial communities with a population dynamics approach. In this work, we reconsider one of the theoretical frameworks most commonly used to model population dynamics in competitive ecosystems, MacArthur’s consumer-resource model, in light of experimental evidence showing how proteome allocation affects microbial growth. This new framework allows us to describe community dynamics at an intermediate level of complexity between classical consumer-resource models and biochemical models of microbial metabolism, accounting for temporally-varying proteome allocation subject to constraints on growth and protein synthesis in the presence of multiple resources, while preserving analytical insight into the dynamics of the system. We first show with a simple experiment that proteome allocation needs to be accounted for to properly understand the dynamics of even the simplest microbial community, i.e. two bacterial strains competing for one common resource. Then, we study our consumer-proteome-resource model analytically and numerically to determine the conditions that allow multiple species to coexist in systems with arbitrary numbers of species and resources.

Mechanisms of Grazing Management in Heterogeneous Swards

We explored the effects of heterogeneity of sward height on the functioning of grazing systems through a spatially implicit mechanistic model of grazing and sward growth. The model uses a population dynamic approach where a sward is spatially structured by height, which changes as a function of defoliation, trampling, and growth. The grazing component incorporates mechanisms of bite formation, intake, and digestion rates, but excludes sward quality effects. Sward height selection is determined by maximization of the instantaneous intake rate of forage dry mass. For any given average sward height, intake rate increased with increasing spatial heterogeneity. Spatio-temporal distribution of animal density over paddocks did not markedly affect animal performance but it modified the balance of vegetation heterogeneity within and between paddocks. Herbage allowance was a weak predictor of animal performance because the same value can result from multiples combinations of herbage mass per unit area, number of animals, animal liveweight, and paddock area, which are the proximate determinants of intake rate. Our results differ from models that assume homogeneity and provide strong evidence of how heterogeneity influences the dynamic of grazing systems. Thus, we argue that grazing management and research need to incorporate the concept of heterogeneity into the design of future grazing systems.

A framework for predicting the effects of climate change on the annual distribution of Lyme borreliosis incidences

Global climate change is predicted to affect both the spatial and annual distributions of vector-borne diseases. Tick-borne diseases are particularly sensitive to the changing climatic conditions. Modelling them is, however, challenging due to the input-intensity of these models. A framework with low number of inputs (easily accessible weekly temperature data and week numbers) on modelling the seasonality of Lyme borreliosis incidences is presented. The modelling framework enables predicting the annual distribution of Ixodes ricinus tick's biting activity and Lyme borreliosis in two cascading phases, incorporating a population dynamics approach. The model is calibrated for Hungary as a case study, for the period of 1998-2008, using tick-borne encephalitis series as a proxy for biting activity. Prediction to the future period of 2081-2100 is also provided. Climate change may significantly alter both the annual distribution of I. ricinus activity and that of the Lyme borreliosis incidences. The currently unimodal annual distribution of Lyme borreliosis is predicted to become bimodal with a long summer pause and a spring maximum shifted 8 weeks earlier.

A framework for predicting the effects of climate change on the annual distribution of Lyme borreliosis incidences

Global climate change is predicted to affect both the spatial and annual distributions of vector-borne diseases. Tick-borne diseases are particularly sensitive to the changing climatic conditions. Modelling them is, however, challenging due to the input-intensity of these models. A framework with low number of inputs (easily accessible weekly temperature data and week numbers) on modelling the seasonality of Lyme borreliosis incidences is presented. The modelling framework enables predicting the annual distribution of Ixodes ricinus tick's biting activity and Lyme borreliosis in two cascading phases, incorporating a population dynamics approach. The model is calibrated for Hungary as a case study, for the period of 1998-2008, using tick-borne encephalitis series as a proxy for biting activity. Prediction to the future period of 2081-2100 is also provided. Climate change may significantly alter both the annual distribution of I. ricinus activity and that of the Lyme borreliosis incidences. The currently unimodal annual distribution of Lyme borreliosis is predicted to become bimodal with a long summer pause and a spring maximum shifted 8 weeks earlier.

Do salt marshes survive sea level rise? Modelling wave action, morphodynamics and vegetation dynamics

This paper aims to fundamentally assess the resilience of salt marsh-mudflat systems under sea level rise. We applied an open-source schematized 2D area model (Delft3D) that couples intertidal flow, wave-action, sediment transport, geomorphological development with a population dynamics approach including temporal and spatial growth of vegetation and bio-accumulation. Wave-action maintains a high sediment concentration on the mudflat while the tidal motion transports the sediments within the vegetated marsh areas during flood. The marsh-mudflat system attained dynamic equilibrium within 120 years. Sediment deposition and bio-accumulation within the marsh make the system initially resilient to sea level rise scenarios. However, after 50–60 years the marsh system starts to drown with vegetated-levees being the last surviving features. Biomass accumulation and sediment supply are critical determinants for the marsh drowning rate and survival. Our model methodology can be applied to assess the resilience of vegetated coast lines and combined engineering solutions for long-term sustainability.

On the use of functional responses to quantify emergent multiple predator effects

Non-independent interactions among predators can have important consequences for the structure and dynamics of ecological communities by enhancing or reducing prey mortality rate through, e.g., predator facilitation or interference. The multiplicative risk model, traditionally used to detect these emergent multiple predator effects (MPEs), is biased because it assumes linear functional response (FR) and no prey depletion. To rectify these biases, two approaches based on FR modelling have recently been proposed: the direct FR approach and the population-dynamic approach. Here we compare the strengths, limitations and predictions of the three approaches using simulated data sets. We found that the predictions of the direct FR and the multiplicative risk models are very similar and underestimate predation rates when prey density is high or prey depletion is substantial. As a consequence, these two approaches often fail in detecting risk reduction. Finally, parameters estimated with the direct FR approach lack mechanistic interpretation, which limits the understanding of the mechanisms driving multiple predator interactions and potential extension of this approach to more complex food webs. We thus strongly recommend using the population-dynamic approach because it is robust, precise, and provides a scalable mechanistic framework to detect and quantify MPEs.

Heterogeneous micro-structure of percolation in sparse networks

We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the probability of a particular node to remain part of the giant component, and in the expected size of small clusters containing that node. In the vicinity of the percolation threshold, weakly non-linear analysis reveals that node-to-node heterogeneity is captured by the recently introduced notion of non-backtracking centrality. We supplement these results for fixed finite networks by a population dynamics approach to analyse random graph models in the infinite system size limit, also providing closed-form approximations for the large mean degree limit of Erdős-Rényi random graphs. Interpreted in terms of the application of percolation to real-world processes, our results shed light on the heterogeneous exposure of different nodes to cascading failures, epidemic spread, and information flow.

Stem Cell Fate Decision Making: Modeling Approaches.

Mathematical (computational) modeling approaches can be effective tools in providing insight into cell-fate decisions. In this article, several major approaches to the modeling of embryonic, hematopoietic, adipose-derived, cancer, and neural stem cell differentiation are discussed. First, the population dynamics approach is considered. The models described as bifurcating dynamical systems that result in bistability or periodic oscillations are then discussed. Also, spatiotemporal models of cell differentiation, including continuum and discrete (agent- and rule-based) approaches, are reviewed. Further, the effects of the mechanical factors are discussed, including the convergence of the differentiation and mechanotransducton pathways and computational analysis of the extracellular matrix (surrounding tissue). Finally, the stochastic models that take into account the molecular noise of internal and external origins are reviewed. The effectiveness of the modeling in the creation of the improved differentiation platforms, elucidation of various pathological conditions, and analysis of treatment regiments has been demonstrated.

Resistance to genetic insect control: Modelling the effects of space

Genetic insect control, such as self-limiting RIDL22RIDL® is a registered trademark of Oxitec Limited, UK. (Release of Insects Carrying a Dominant Lethal) technology, is a development of the sterile insect technique which is proposed to suppress wild populations of a number of major agricultural and public health insect pests. This is achieved by mass rearing and releasing male insects that are homozygous for a repressible dominant lethal genetic construct, which causes death in progeny when inherited. The released genetically engineered (‘GE’) insects compete for mates with wild individuals, resulting in population suppression. A previous study modelled the evolution of a hypothetical resistance to the lethal construct using a frequency-dependent population genetic and population dynamic approach. This found that proliferation of resistance is possible but can be diluted by the introgression of susceptible alleles from the released homozygous-susceptible GE males. We develop this approach within a spatial context by modelling the spread of a lethal construct and resistance trait, and the effect on population control, in a two deme metapopulation, with GE release in one deme. Results show that spatial effects can drive an increased or decreased evolution of resistance in both the target and non-target demes, depending on the effectiveness and associated costs of the resistant trait, and on the rate of dispersal. A recurrent theme is the potential for the non-target deme to act as a source of resistant or susceptible alleles for the target deme through dispersal. This can in turn have a major impact on the effectiveness of insect population control.

Effects of the obesity on optimal control schedules of chemotherapy on a cancerous tumor

Obesity as a risk factor has been found in different types of cancers such as breast cancer and colorectal cancer among others. This challenges us to study the cancer–obesity relationship and the tumor response to chemotherapy. In this work, we study and analyze optimal control protocols for chemotherapy treatments for a mathematical model of cancerous growing tumor that is interacting with the healthy cells, the immune system cells and the stored fat in the organism. This model considers different cell populations using a population dynamics approach. Our main interest is to provide insights about the qualitative and quantitative possible affects of a low/high caloric diet on the chemotherapy protocols when different immune system responses are considered. According to our model the immune system response and the diet are important factors and their inclusion could lead to improved chemotherapy protocols.